TSTP Solution File: ITP188^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP188^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n011.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 03:19:01 EDT 2023
% Result : Theorem 0.85s 1.03s
% Output : Proof 0.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.16 % Problem : ITP188^1 : TPTP v8.1.2. Released v7.5.0.
% 0.17/0.17 % Command : do_cvc5 %s %d
% 0.17/0.38 % Computer : n011.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Sun Aug 27 15:31:55 EDT 2023
% 0.17/0.38 % CPUTime :
% 0.25/0.58 %----Proving TH0
% 0.25/0.58 %------------------------------------------------------------------------------
% 0.25/0.58 % File : ITP188^1 : TPTP v8.1.2. Released v7.5.0.
% 0.25/0.58 % Domain : Interactive Theorem Proving
% 0.25/0.58 % Problem : Sledgehammer Strong_Late_Sim_SC problem prob_690__3415376_1
% 0.25/0.58 % Version : Especial.
% 0.25/0.58 % English :
% 0.25/0.58
% 0.25/0.58 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.25/0.58 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.25/0.58 % Source : [Des21]
% 0.25/0.58 % Names : Strong_Late_Sim_SC/prob_690__3415376_1 [Des21]
% 0.25/0.58
% 0.25/0.58 % Status : Theorem
% 0.25/0.58 % Rating : 0.31 v8.1.0, 0.27 v7.5.0
% 0.25/0.58 % Syntax : Number of formulae : 441 ( 202 unt; 102 typ; 0 def)
% 0.25/0.58 % Number of atoms : 901 ( 371 equ; 0 cnn)
% 0.25/0.58 % Maximal formula atoms : 16 ( 2 avg)
% 0.25/0.58 % Number of connectives : 4374 ( 181 ~; 11 |; 83 &;3518 @)
% 0.25/0.58 % ( 0 <=>; 581 =>; 0 <=; 0 <~>)
% 0.25/0.58 % Maximal formula depth : 27 ( 9 avg)
% 0.25/0.58 % Number of types : 26 ( 25 usr)
% 0.25/0.58 % Number of type conns : 294 ( 294 >; 0 *; 0 +; 0 <<)
% 0.25/0.58 % Number of symbols : 80 ( 77 usr; 13 con; 0-5 aty)
% 0.25/0.58 % Number of variables : 1730 ( 9 ^;1681 !; 40 ?;1730 :)
% 0.25/0.58 % SPC : TH0_THM_EQU_NAR
% 0.25/0.58
% 0.25/0.58 % Comments : This file was generated by Sledgehammer 2021-02-23 15:32:00.397
% 0.25/0.58 %------------------------------------------------------------------------------
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% 0.25/0.58 produc1505598906reeRes: ( name > noption_pi ) > late_freeRes > produc1834551554reeRes ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 0.25/0.58 produc1275980869_pi_pi: ( name > noption_pi ) > produc1141751126_pi_pi > produc53907987_pi_pi ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Agent__Oname,type,
% 0.25/0.58 produc1570949143e_name: name > name > produc367475239e_name ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Agent__Opi,type,
% 0.25/0.58 product_Pair_name_pi: name > pi > product_prod_name_pi ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
% 0.25/0.58 produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.25/0.58 produc235456326_pi_pi: name > product_prod_pi_pi > produc1141751126_pi_pi ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Agent__Oname,type,
% 0.25/0.58 product_Pair_pi_name: pi > name > product_prod_pi_name ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Agent__Opi,type,
% 0.25/0.58 product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Late____Semantics__OfreeRes,type,
% 0.25/0.58 produc1638681944reeRes: pi > late_freeRes > produc649380958reeRes ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Oname,type,
% 0.25/0.58 produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Opi,type,
% 0.25/0.58 produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__OfreeRes,type,
% 0.25/0.58 produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Rel_Oeqvt_001t__Agent__Opi,type,
% 0.25/0.58 eqvt_pi: set_Pr1834926343_pi_pi > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.25/0.58 collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 0.25/0.58 strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 0.25/0.58 strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.25/0.58 member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v_P,type,
% 0.25/0.58 p: pi ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v_P_H____,type,
% 0.25/0.58 p2: pi ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v_PxQ____,type,
% 0.25/0.58 pxQ: pi ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v_Q,type,
% 0.25/0.58 q: pi ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v_Rel,type,
% 0.25/0.58 rel: set_Pr1834926343_pi_pi ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v_aa____,type,
% 0.25/0.58 aa: late_subject ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v_u____,type,
% 0.25/0.58 u: name ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v_x,type,
% 0.25/0.58 x: name ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v_y____,type,
% 0.25/0.58 y: name ).
% 0.25/0.58
% 0.25/0.58 % Relevant facts (335)
% 0.25/0.58 thf(fact_0_False,axiom,
% 0.25/0.58 x != u ).
% 0.25/0.58
% 0.25/0.58 % False
% 0.25/0.58 thf(fact_1__092_060open_062_060_092_060nu_062x_062Q_091y_058_058_061u_093_A_061_A_060_092_060nu_062x_062Q_091y_058_058_061u_093_092_060close_062,axiom,
% 0.25/0.58 ( ( subs @ ( res @ x @ q ) @ y @ u )
% 0.25/0.58 = ( res @ x @ ( subs @ q @ y @ u ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % \<open><\<nu>x>Q[y::=u] = <\<nu>x>Q[y::=u]\<close>
% 0.25/0.58 thf(fact_2__092_060open_062y_A_092_060noteq_062_Ax_092_060close_062,axiom,
% 0.25/0.58 y != x ).
% 0.25/0.58
% 0.25/0.58 % \<open>y \<noteq> x\<close>
% 0.25/0.58 thf(fact_3__092_060open_062x_A_092_060sharp_062_AP_H_091y_058_058_061u_093_092_060close_062,axiom,
% 0.25/0.58 fresh_name_pi @ x @ ( subs @ p2 @ y @ u ) ).
% 0.25/0.58
% 0.25/0.58 % \<open>x \<sharp> P'[y::=u]\<close>
% 0.25/0.58 thf(fact_4_EqvtRel,axiom,
% 0.25/0.58 eqvt_pi @ rel ).
% 0.25/0.58
% 0.25/0.58 % EqvtRel
% 0.25/0.58 thf(fact_5__092_060open_062_060_092_060nu_062x_062_IP_H_A_092_060parallel_062_AQ_J_091y_058_058_061u_093_A_061_A_060_092_060nu_062x_062_IP_H_091y_058_058_061u_093_A_092_060parallel_062_AQ_091y_058_058_061u_093_J_092_060close_062,axiom,
% 0.25/0.58 ( ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u )
% 0.25/0.58 = ( res @ x @ ( par @ ( subs @ p2 @ y @ u ) @ ( subs @ q @ y @ u ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % \<open><\<nu>x>(P' \<parallel> Q)[y::=u] = <\<nu>x>(P'[y::=u] \<parallel> Q[y::=u])\<close>
% 0.25/0.58 thf(fact_6__092_060open_062y_A_092_060sharp_062_AQ_092_060close_062,axiom,
% 0.25/0.58 fresh_name_pi @ y @ q ).
% 0.25/0.58
% 0.25/0.58 % \<open>y \<sharp> Q\<close>
% 0.25/0.58 thf(fact_7__092_060open_062x_A_092_060sharp_062_AP_H_092_060close_062,axiom,
% 0.25/0.58 fresh_name_pi @ x @ p2 ).
% 0.25/0.58
% 0.25/0.58 % \<open>x \<sharp> P'\<close>
% 0.25/0.58 thf(fact_8_Res,axiom,
% 0.25/0.58 ! [Y: name,R: pi,S: pi] :
% 0.25/0.58 ( ( fresh_name_pi @ Y @ R )
% 0.25/0.58 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ Y @ ( par @ R @ S ) ) @ ( par @ R @ ( res @ Y @ S ) ) ) @ rel ) ) ).
% 0.25/0.58
% 0.25/0.58 % Res
% 0.25/0.58 thf(fact_9_ScopeExt,axiom,
% 0.25/0.58 ! [Y: name,R: pi,Z: name,S: pi] :
% 0.25/0.58 ( ( fresh_name_pi @ Y @ R )
% 0.25/0.58 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ Y @ ( res @ Z @ ( par @ R @ S ) ) ) @ ( res @ Z @ ( par @ R @ ( res @ Y @ S ) ) ) ) @ rel ) ) ).
% 0.25/0.58
% 0.25/0.58 % ScopeExt
% 0.25/0.58 thf(fact_10__092_060open_062y_A_092_060sharp_062_A_060_092_060nu_062x_062Q_092_060close_062,axiom,
% 0.25/0.58 fresh_name_pi @ y @ ( res @ x @ q ) ).
% 0.25/0.58
% 0.25/0.58 % \<open>y \<sharp> <\<nu>x>Q\<close>
% 0.25/0.58 thf(fact_11_assms_I1_J,axiom,
% 0.25/0.58 fresh_name_pi @ x @ p ).
% 0.25/0.58
% 0.25/0.58 % assms(1)
% 0.25/0.58 thf(fact_12_Bound_Ohyps_I3_J,axiom,
% 0.25/0.58 fresh_name_pi @ y @ ( par @ p @ ( res @ x @ q ) ) ).
% 0.25/0.58
% 0.25/0.58 % Bound.hyps(3)
% 0.25/0.58 thf(fact_13_Bound_Ohyps_I2_J,axiom,
% 0.25/0.58 fresh_name_pi @ y @ ( res @ x @ ( par @ p @ q ) ) ).
% 0.25/0.58
% 0.25/0.58 % Bound.hyps(2)
% 0.25/0.58 thf(fact_14_simps_I8_J,axiom,
% 0.25/0.58 ! [P: pi,Q: pi,C: name,D: name] :
% 0.25/0.58 ( ( subs @ ( par @ P @ Q ) @ C @ D )
% 0.25/0.58 = ( par @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % simps(8)
% 0.25/0.58 thf(fact_15_simps_I9_J,axiom,
% 0.25/0.58 ! [X: name,C: name,D: name,P: pi] :
% 0.25/0.58 ( ( X != C )
% 0.25/0.58 => ( ( X != D )
% 0.25/0.58 => ( ( subs @ ( res @ X @ P ) @ C @ D )
% 0.25/0.58 = ( res @ X @ ( subs @ P @ C @ D ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % simps(9)
% 0.25/0.58 thf(fact_16_subst__identity,axiom,
% 0.25/0.58 ! [P: pi,A: name] :
% 0.25/0.58 ( ( subs @ P @ A @ A )
% 0.25/0.58 = P ) ).
% 0.25/0.58
% 0.25/0.58 % subst_identity
% 0.25/0.58 thf(fact_17_prod_Oinject,axiom,
% 0.25/0.58 ! [X1: name > noption_pi,X2: late_freeRes,Y1: name > noption_pi,Y2: late_freeRes] :
% 0.25/0.58 ( ( ( produc1505598906reeRes @ X1 @ X2 )
% 0.25/0.58 = ( produc1505598906reeRes @ Y1 @ Y2 ) )
% 0.25/0.58 = ( ( X1 = Y1 )
% 0.25/0.58 & ( X2 = Y2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % prod.inject
% 0.25/0.58 thf(fact_18_prod_Oinject,axiom,
% 0.25/0.58 ! [X1: name > noption_pi,X2: produc1141751126_pi_pi,Y1: name > noption_pi,Y2: produc1141751126_pi_pi] :
% 0.25/0.58 ( ( ( produc1275980869_pi_pi @ X1 @ X2 )
% 0.25/0.58 = ( produc1275980869_pi_pi @ Y1 @ Y2 ) )
% 0.25/0.58 = ( ( X1 = Y1 )
% 0.25/0.58 & ( X2 = Y2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % prod.inject
% 0.25/0.58 thf(fact_19_prod_Oinject,axiom,
% 0.25/0.58 ! [X1: name > noption_pi,X2: name,Y1: name > noption_pi,Y2: name] :
% 0.25/0.58 ( ( ( produc540578151i_name @ X1 @ X2 )
% 0.25/0.58 = ( produc540578151i_name @ Y1 @ Y2 ) )
% 0.25/0.58 = ( ( X1 = Y1 )
% 0.25/0.58 & ( X2 = Y2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % prod.inject
% 0.25/0.58 thf(fact_20_prod_Oinject,axiom,
% 0.25/0.58 ! [X1: name > noption_pi,X2: pi,Y1: name > noption_pi,Y2: pi] :
% 0.25/0.58 ( ( ( produc1820286517_pi_pi @ X1 @ X2 )
% 0.25/0.58 = ( produc1820286517_pi_pi @ Y1 @ Y2 ) )
% 0.25/0.58 = ( ( X1 = Y1 )
% 0.25/0.58 & ( X2 = Y2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % prod.inject
% 0.25/0.58 thf(fact_21_prod_Oinject,axiom,
% 0.25/0.58 ! [X1: name > noption_pi,X2: name > noption_pi,Y1: name > noption_pi,Y2: name > noption_pi] :
% 0.25/0.58 ( ( ( produc1342893193ion_pi @ X1 @ X2 )
% 0.25/0.58 = ( produc1342893193ion_pi @ Y1 @ Y2 ) )
% 0.25/0.58 = ( ( X1 = Y1 )
% 0.25/0.58 & ( X2 = Y2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % prod.inject
% 0.25/0.58 thf(fact_22_prod_Oinject,axiom,
% 0.25/0.58 ! [X1: pi,X2: pi,Y1: pi,Y2: pi] :
% 0.25/0.58 ( ( ( product_Pair_pi_pi @ X1 @ X2 )
% 0.25/0.58 = ( product_Pair_pi_pi @ Y1 @ Y2 ) )
% 0.25/0.58 = ( ( X1 = Y1 )
% 0.25/0.58 & ( X2 = Y2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % prod.inject
% 0.25/0.58 thf(fact_23_prod_Oinject,axiom,
% 0.25/0.58 ! [X1: name,X2: product_prod_pi_pi,Y1: name,Y2: product_prod_pi_pi] :
% 0.25/0.58 ( ( ( produc235456326_pi_pi @ X1 @ X2 )
% 0.25/0.58 = ( produc235456326_pi_pi @ Y1 @ Y2 ) )
% 0.25/0.58 = ( ( X1 = Y1 )
% 0.25/0.58 & ( X2 = Y2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % prod.inject
% 0.25/0.58 thf(fact_24_old_Oprod_Oinject,axiom,
% 0.25/0.58 ! [A: name > noption_pi,B: late_freeRes,A2: name > noption_pi,B2: late_freeRes] :
% 0.25/0.58 ( ( ( produc1505598906reeRes @ A @ B )
% 0.25/0.58 = ( produc1505598906reeRes @ A2 @ B2 ) )
% 0.25/0.58 = ( ( A = A2 )
% 0.25/0.58 & ( B = B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % old.prod.inject
% 0.25/0.58 thf(fact_25_old_Oprod_Oinject,axiom,
% 0.25/0.58 ! [A: name > noption_pi,B: produc1141751126_pi_pi,A2: name > noption_pi,B2: produc1141751126_pi_pi] :
% 0.25/0.58 ( ( ( produc1275980869_pi_pi @ A @ B )
% 0.25/0.58 = ( produc1275980869_pi_pi @ A2 @ B2 ) )
% 0.25/0.58 = ( ( A = A2 )
% 0.25/0.58 & ( B = B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % old.prod.inject
% 0.25/0.58 thf(fact_26_old_Oprod_Oinject,axiom,
% 0.25/0.58 ! [A: name > noption_pi,B: name,A2: name > noption_pi,B2: name] :
% 0.25/0.58 ( ( ( produc540578151i_name @ A @ B )
% 0.25/0.58 = ( produc540578151i_name @ A2 @ B2 ) )
% 0.25/0.58 = ( ( A = A2 )
% 0.25/0.58 & ( B = B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % old.prod.inject
% 0.25/0.58 thf(fact_27_old_Oprod_Oinject,axiom,
% 0.25/0.58 ! [A: name > noption_pi,B: pi,A2: name > noption_pi,B2: pi] :
% 0.25/0.58 ( ( ( produc1820286517_pi_pi @ A @ B )
% 0.25/0.58 = ( produc1820286517_pi_pi @ A2 @ B2 ) )
% 0.25/0.58 = ( ( A = A2 )
% 0.25/0.58 & ( B = B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % old.prod.inject
% 0.25/0.58 thf(fact_28_old_Oprod_Oinject,axiom,
% 0.25/0.58 ! [A: name > noption_pi,B: name > noption_pi,A2: name > noption_pi,B2: name > noption_pi] :
% 0.25/0.58 ( ( ( produc1342893193ion_pi @ A @ B )
% 0.25/0.58 = ( produc1342893193ion_pi @ A2 @ B2 ) )
% 0.25/0.58 = ( ( A = A2 )
% 0.25/0.58 & ( B = B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % old.prod.inject
% 0.25/0.58 thf(fact_29_old_Oprod_Oinject,axiom,
% 0.25/0.58 ! [A: pi,B: pi,A2: pi,B2: pi] :
% 0.25/0.58 ( ( ( product_Pair_pi_pi @ A @ B )
% 0.25/0.58 = ( product_Pair_pi_pi @ A2 @ B2 ) )
% 0.25/0.58 = ( ( A = A2 )
% 0.25/0.58 & ( B = B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % old.prod.inject
% 0.25/0.58 thf(fact_30_old_Oprod_Oinject,axiom,
% 0.25/0.58 ! [A: name,B: product_prod_pi_pi,A2: name,B2: product_prod_pi_pi] :
% 0.25/0.58 ( ( ( produc235456326_pi_pi @ A @ B )
% 0.25/0.58 = ( produc235456326_pi_pi @ A2 @ B2 ) )
% 0.25/0.58 = ( ( A = A2 )
% 0.25/0.58 & ( B = B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % old.prod.inject
% 0.25/0.58 thf(fact_31_pi_Odistinct_I85_J,axiom,
% 0.25/0.58 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 0.25/0.58 ( ( par @ Pi1 @ Pi2 )
% 0.25/0.58 != ( res @ Name @ Pi ) ) ).
% 0.25/0.58
% 0.25/0.58 % pi.distinct(85)
% 0.25/0.58 thf(fact_32__092_060open_062y_A_092_060sharp_062_AP_092_060close_062,axiom,
% 0.25/0.58 fresh_name_pi @ y @ p ).
% 0.25/0.58
% 0.25/0.58 % \<open>y \<sharp> P\<close>
% 0.25/0.58 thf(fact_33_Bound_Ohyps_I5_J,axiom,
% 0.25/0.58 fresh_1376661020_pi_pi @ y @ ( produc235456326_pi_pi @ x @ ( product_Pair_pi_pi @ p @ q ) ) ).
% 0.25/0.58
% 0.25/0.58 % Bound.hyps(5)
% 0.25/0.58 thf(fact_34_parSym,axiom,
% 0.25/0.58 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi] :
% 0.25/0.58 ( ! [R2: pi,S2: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ R2 @ S2 ) @ ( par @ S2 @ R2 ) ) @ Rel )
% 0.25/0.58 => ( ! [R2: pi,S2: pi,X3: name] :
% 0.25/0.58 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ R2 @ S2 ) @ Rel )
% 0.25/0.58 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X3 @ R2 ) @ ( res @ X3 @ S2 ) ) @ Rel ) )
% 0.25/0.58 => ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % parSym
% 0.25/0.58 thf(fact_35_substRes2,axiom,
% 0.25/0.58 ! [B: name,P: pi,A: name] :
% 0.25/0.58 ( ( fresh_name_pi @ B @ P )
% 0.25/0.58 => ( ( res @ A @ P )
% 0.25/0.58 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % substRes2
% 0.25/0.58 thf(fact_36_Agent_OsubstRes3,axiom,
% 0.25/0.58 ! [B: name,P: pi,A: name] :
% 0.25/0.58 ( ( fresh_name_pi @ B @ P )
% 0.25/0.58 => ( ( subs @ ( res @ A @ P ) @ A @ B )
% 0.25/0.58 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Agent.substRes3
% 0.25/0.58 thf(fact_37_Bound_Ohyps_I4_J,axiom,
% 0.25/0.58 fresh_717452603ubject @ y @ aa ).
% 0.25/0.58
% 0.25/0.58 % Bound.hyps(4)
% 0.25/0.58 thf(fact_38__092_060open_062x_A_092_060sharp_062_Aa_092_060close_062,axiom,
% 0.25/0.58 fresh_717452603ubject @ x @ aa ).
% 0.25/0.58
% 0.25/0.58 % \<open>x \<sharp> a\<close>
% 0.25/0.58 thf(fact_39_pi_Ofresh_I8_J,axiom,
% 0.25/0.58 ! [A: name,X2: pi,X1: pi] :
% 0.25/0.58 ( ( fresh_name_pi @ A @ ( par @ X2 @ X1 ) )
% 0.25/0.58 = ( ( fresh_name_pi @ A @ X2 )
% 0.25/0.58 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % pi.fresh(8)
% 0.25/0.58 thf(fact_40_name__exists__fresh,axiom,
% 0.25/0.58 ! [X: late_freeRes] :
% 0.25/0.58 ~ ! [C2: name] :
% 0.25/0.58 ~ ( fresh_1641682979reeRes @ C2 @ X ) ).
% 0.25/0.58
% 0.25/0.58 % name_exists_fresh
% 0.25/0.58 thf(fact_41_name__exists__fresh,axiom,
% 0.25/0.58 ! [X: produc1141751126_pi_pi] :
% 0.25/0.58 ~ ! [C2: name] :
% 0.25/0.58 ~ ( fresh_1376661020_pi_pi @ C2 @ X ) ).
% 0.25/0.58
% 0.25/0.58 % name_exists_fresh
% 0.25/0.58 thf(fact_42_name__exists__fresh,axiom,
% 0.25/0.58 ! [X: name] :
% 0.25/0.58 ~ ! [C2: name] :
% 0.25/0.58 ~ ( fresh_name_name @ C2 @ X ) ).
% 0.25/0.58
% 0.25/0.58 % name_exists_fresh
% 0.25/0.58 thf(fact_43_name__exists__fresh,axiom,
% 0.25/0.58 ! [X: pi] :
% 0.25/0.58 ~ ! [C2: name] :
% 0.25/0.58 ~ ( fresh_name_pi @ C2 @ X ) ).
% 0.25/0.58
% 0.25/0.58 % name_exists_fresh
% 0.25/0.58 thf(fact_44_freshRes,axiom,
% 0.25/0.58 ! [A: name,P: pi] : ( fresh_name_pi @ A @ ( res @ A @ P ) ) ).
% 0.25/0.58
% 0.25/0.58 % freshRes
% 0.25/0.58 thf(fact_45_fresh__fact2,axiom,
% 0.25/0.58 ! [A: name,B: name,P: pi] :
% 0.25/0.58 ( ( A != B )
% 0.25/0.58 => ( fresh_name_pi @ A @ ( subs @ P @ A @ B ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % fresh_fact2
% 0.25/0.58 thf(fact_46_fresh__fact1,axiom,
% 0.25/0.58 ! [A: name,P: pi,C: name,B: name] :
% 0.25/0.58 ( ( fresh_name_pi @ A @ P )
% 0.25/0.58 => ( ( A != C )
% 0.25/0.58 => ( fresh_name_pi @ A @ ( subs @ P @ B @ C ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % fresh_fact1
% 0.25/0.58 thf(fact_47_forget,axiom,
% 0.25/0.58 ! [A: name,P: pi,B: name] :
% 0.25/0.58 ( ( fresh_name_pi @ A @ P )
% 0.25/0.58 => ( ( subs @ P @ A @ B )
% 0.25/0.58 = P ) ) ).
% 0.25/0.58
% 0.25/0.58 % forget
% 0.25/0.58 thf(fact_48_parAssocLeft,axiom,
% 0.25/0.58 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi,R: pi] :
% 0.25/0.58 ( ! [S2: pi,T: pi,U: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( par @ S2 @ T ) @ U ) @ ( par @ S2 @ ( par @ T @ U ) ) ) @ Rel )
% 0.25/0.58 => ( ! [S2: pi,T: pi,X3: name] :
% 0.25/0.58 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ S2 @ T ) @ Rel )
% 0.25/0.58 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X3 @ S2 ) @ ( res @ X3 @ T ) ) @ Rel ) )
% 0.25/0.58 => ( ! [S2: pi,T: pi,U: pi,X3: name] :
% 0.25/0.58 ( ( fresh_name_pi @ X3 @ S2 )
% 0.25/0.58 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X3 @ ( par @ ( par @ S2 @ T ) @ U ) ) @ ( par @ S2 @ ( res @ X3 @ ( par @ T @ U ) ) ) ) @ Rel ) )
% 0.25/0.58 => ( ! [S2: pi,T: pi,U: pi,X3: name] :
% 0.25/0.58 ( ( fresh_name_pi @ X3 @ U )
% 0.25/0.58 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ X3 @ ( par @ S2 @ T ) ) @ U ) @ ( res @ X3 @ ( par @ S2 @ ( par @ T @ U ) ) ) ) @ Rel ) )
% 0.25/0.58 => ( strong743114133lation @ ( par @ ( par @ P @ Q ) @ R ) @ Rel @ ( par @ P @ ( par @ Q @ R ) ) ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % parAssocLeft
% 0.25/0.58 thf(fact_49_old_Oprod_Oinducts,axiom,
% 0.25/0.58 ! [P: produc1834551554reeRes > $o,Prod: produc1834551554reeRes] :
% 0.25/0.58 ( ! [A3: name > noption_pi,B3: late_freeRes] : ( P @ ( produc1505598906reeRes @ A3 @ B3 ) )
% 0.25/0.58 => ( P @ Prod ) ) ).
% 0.25/0.58
% 0.25/0.58 % old.prod.inducts
% 0.25/0.58 thf(fact_50_old_Oprod_Oinducts,axiom,
% 0.25/0.58 ! [P: produc53907987_pi_pi > $o,Prod: produc53907987_pi_pi] :
% 0.25/0.58 ( ! [A3: name > noption_pi,B3: produc1141751126_pi_pi] : ( P @ ( produc1275980869_pi_pi @ A3 @ B3 ) )
% 0.25/0.58 => ( P @ Prod ) ) ).
% 0.25/0.58
% 0.25/0.58 % old.prod.inducts
% 0.25/0.58 thf(fact_51_old_Oprod_Oinducts,axiom,
% 0.25/0.58 ! [P: produc405342261i_name > $o,Prod: produc405342261i_name] :
% 0.25/0.58 ( ! [A3: name > noption_pi,B3: name] : ( P @ ( produc540578151i_name @ A3 @ B3 ) )
% 0.25/0.58 => ( P @ Prod ) ) ).
% 0.25/0.58
% 0.25/0.58 % old.prod.inducts
% 0.25/0.58 thf(fact_52_old_Oprod_Oinducts,axiom,
% 0.25/0.58 ! [P: produc629157763_pi_pi > $o,Prod: produc629157763_pi_pi] :
% 0.25/0.58 ( ! [A3: name > noption_pi,B3: pi] : ( P @ ( produc1820286517_pi_pi @ A3 @ B3 ) )
% 0.25/0.58 => ( P @ Prod ) ) ).
% 0.25/0.58
% 0.25/0.58 % old.prod.inducts
% 0.25/0.58 thf(fact_53_old_Oprod_Oinducts,axiom,
% 0.25/0.58 ! [P: produc1462499409ion_pi > $o,Prod: produc1462499409ion_pi] :
% 0.25/0.58 ( ! [A3: name > noption_pi,B3: name > noption_pi] : ( P @ ( produc1342893193ion_pi @ A3 @ B3 ) )
% 0.25/0.58 => ( P @ Prod ) ) ).
% 0.25/0.58
% 0.25/0.58 % old.prod.inducts
% 0.25/0.58 thf(fact_54_old_Oprod_Oinducts,axiom,
% 0.25/0.58 ! [P: product_prod_pi_pi > $o,Prod: product_prod_pi_pi] :
% 0.25/0.58 ( ! [A3: pi,B3: pi] : ( P @ ( product_Pair_pi_pi @ A3 @ B3 ) )
% 0.25/0.58 => ( P @ Prod ) ) ).
% 0.25/0.58
% 0.25/0.58 % old.prod.inducts
% 0.25/0.58 thf(fact_55_old_Oprod_Oinducts,axiom,
% 0.25/0.58 ! [P: produc1141751126_pi_pi > $o,Prod: produc1141751126_pi_pi] :
% 0.25/0.58 ( ! [A3: name,B3: product_prod_pi_pi] : ( P @ ( produc235456326_pi_pi @ A3 @ B3 ) )
% 0.25/0.58 => ( P @ Prod ) ) ).
% 0.25/0.58
% 0.25/0.58 % old.prod.inducts
% 0.25/0.58 thf(fact_56_old_Oprod_Oexhaust,axiom,
% 0.25/0.58 ! [Y: produc1834551554reeRes] :
% 0.25/0.58 ~ ! [A3: name > noption_pi,B3: late_freeRes] :
% 0.25/0.58 ( Y
% 0.25/0.58 != ( produc1505598906reeRes @ A3 @ B3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % old.prod.exhaust
% 0.25/0.58 thf(fact_57_old_Oprod_Oexhaust,axiom,
% 0.25/0.58 ! [Y: produc53907987_pi_pi] :
% 0.25/0.58 ~ ! [A3: name > noption_pi,B3: produc1141751126_pi_pi] :
% 0.25/0.58 ( Y
% 0.25/0.58 != ( produc1275980869_pi_pi @ A3 @ B3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % old.prod.exhaust
% 0.25/0.58 thf(fact_58_old_Oprod_Oexhaust,axiom,
% 0.25/0.58 ! [Y: produc405342261i_name] :
% 0.25/0.58 ~ ! [A3: name > noption_pi,B3: name] :
% 0.25/0.58 ( Y
% 0.25/0.58 != ( produc540578151i_name @ A3 @ B3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % old.prod.exhaust
% 0.25/0.58 thf(fact_59_old_Oprod_Oexhaust,axiom,
% 0.25/0.58 ! [Y: produc629157763_pi_pi] :
% 0.25/0.58 ~ ! [A3: name > noption_pi,B3: pi] :
% 0.25/0.58 ( Y
% 0.25/0.58 != ( produc1820286517_pi_pi @ A3 @ B3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % old.prod.exhaust
% 0.25/0.58 thf(fact_60_old_Oprod_Oexhaust,axiom,
% 0.25/0.58 ! [Y: produc1462499409ion_pi] :
% 0.25/0.58 ~ ! [A3: name > noption_pi,B3: name > noption_pi] :
% 0.25/0.58 ( Y
% 0.25/0.58 != ( produc1342893193ion_pi @ A3 @ B3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % old.prod.exhaust
% 0.25/0.58 thf(fact_61_old_Oprod_Oexhaust,axiom,
% 0.25/0.58 ! [Y: product_prod_pi_pi] :
% 0.25/0.58 ~ ! [A3: pi,B3: pi] :
% 0.25/0.58 ( Y
% 0.25/0.58 != ( product_Pair_pi_pi @ A3 @ B3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % old.prod.exhaust
% 0.25/0.58 thf(fact_62_old_Oprod_Oexhaust,axiom,
% 0.25/0.58 ! [Y: produc1141751126_pi_pi] :
% 0.25/0.58 ~ ! [A3: name,B3: product_prod_pi_pi] :
% 0.25/0.58 ( Y
% 0.25/0.58 != ( produc235456326_pi_pi @ A3 @ B3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % old.prod.exhaust
% 0.25/0.58 thf(fact_63_prod__induct4,axiom,
% 0.25/0.58 ! [P: produc53907987_pi_pi > $o,X: produc53907987_pi_pi] :
% 0.25/0.58 ( ! [A3: name > noption_pi,B3: name,C2: pi,D2: pi] : ( P @ ( produc1275980869_pi_pi @ A3 @ ( produc235456326_pi_pi @ B3 @ ( product_Pair_pi_pi @ C2 @ D2 ) ) ) )
% 0.25/0.58 => ( P @ X ) ) ).
% 0.25/0.58
% 0.25/0.58 % prod_induct4
% 0.25/0.58 thf(fact_64_prod__induct3,axiom,
% 0.25/0.58 ! [P: produc53907987_pi_pi > $o,X: produc53907987_pi_pi] :
% 0.25/0.58 ( ! [A3: name > noption_pi,B3: name,C2: product_prod_pi_pi] : ( P @ ( produc1275980869_pi_pi @ A3 @ ( produc235456326_pi_pi @ B3 @ C2 ) ) )
% 0.25/0.58 => ( P @ X ) ) ).
% 0.25/0.58
% 0.25/0.58 % prod_induct3
% 0.25/0.58 thf(fact_65_prod__induct3,axiom,
% 0.25/0.58 ! [P: produc1141751126_pi_pi > $o,X: produc1141751126_pi_pi] :
% 0.25/0.58 ( ! [A3: name,B3: pi,C2: pi] : ( P @ ( produc235456326_pi_pi @ A3 @ ( product_Pair_pi_pi @ B3 @ C2 ) ) )
% 0.25/0.58 => ( P @ X ) ) ).
% 0.25/0.58
% 0.25/0.58 % prod_induct3
% 0.25/0.58 thf(fact_66_prod__cases4,axiom,
% 0.25/0.58 ! [Y: produc53907987_pi_pi] :
% 0.25/0.58 ~ ! [A3: name > noption_pi,B3: name,C2: pi,D2: pi] :
% 0.25/0.58 ( Y
% 0.25/0.58 != ( produc1275980869_pi_pi @ A3 @ ( produc235456326_pi_pi @ B3 @ ( product_Pair_pi_pi @ C2 @ D2 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % prod_cases4
% 0.25/0.58 thf(fact_67_mem__Collect__eq,axiom,
% 0.25/0.58 ! [A: product_prod_pi_pi,P: product_prod_pi_pi > $o] :
% 0.25/0.58 ( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ P ) )
% 0.25/0.58 = ( P @ A ) ) ).
% 0.25/0.58
% 0.25/0.58 % mem_Collect_eq
% 0.25/0.58 thf(fact_68_Collect__mem__eq,axiom,
% 0.25/0.58 ! [A4: set_Pr1834926343_pi_pi] :
% 0.25/0.58 ( ( collec1051790738_pi_pi
% 0.25/0.58 @ ^ [X4: product_prod_pi_pi] : ( member558706512_pi_pi @ X4 @ A4 ) )
% 0.25/0.58 = A4 ) ).
% 0.25/0.58
% 0.25/0.58 % Collect_mem_eq
% 0.25/0.58 thf(fact_69_Collect__cong,axiom,
% 0.25/0.58 ! [P: product_prod_pi_pi > $o,Q: product_prod_pi_pi > $o] :
% 0.25/0.58 ( ! [X3: product_prod_pi_pi] :
% 0.25/0.58 ( ( P @ X3 )
% 0.25/0.58 = ( Q @ X3 ) )
% 0.25/0.58 => ( ( collec1051790738_pi_pi @ P )
% 0.25/0.58 = ( collec1051790738_pi_pi @ Q ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Collect_cong
% 0.25/0.58 thf(fact_70_prod__cases3,axiom,
% 0.25/0.58 ! [Y: produc53907987_pi_pi] :
% 0.25/0.58 ~ ! [A3: name > noption_pi,B3: name,C2: product_prod_pi_pi] :
% 0.25/0.58 ( Y
% 0.25/0.58 != ( produc1275980869_pi_pi @ A3 @ ( produc235456326_pi_pi @ B3 @ C2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % prod_cases3
% 0.25/0.58 thf(fact_71_prod__cases3,axiom,
% 0.25/0.58 ! [Y: produc1141751126_pi_pi] :
% 0.25/0.58 ~ ! [A3: name,B3: pi,C2: pi] :
% 0.25/0.58 ( Y
% 0.25/0.58 != ( produc235456326_pi_pi @ A3 @ ( product_Pair_pi_pi @ B3 @ C2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % prod_cases3
% 0.25/0.58 thf(fact_72_Pair__inject,axiom,
% 0.25/0.58 ! [A: name > noption_pi,B: late_freeRes,A2: name > noption_pi,B2: late_freeRes] :
% 0.25/0.58 ( ( ( produc1505598906reeRes @ A @ B )
% 0.25/0.58 = ( produc1505598906reeRes @ A2 @ B2 ) )
% 0.25/0.58 => ~ ( ( A = A2 )
% 0.25/0.58 => ( B != B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Pair_inject
% 0.25/0.58 thf(fact_73_Pair__inject,axiom,
% 0.25/0.58 ! [A: name > noption_pi,B: produc1141751126_pi_pi,A2: name > noption_pi,B2: produc1141751126_pi_pi] :
% 0.25/0.58 ( ( ( produc1275980869_pi_pi @ A @ B )
% 0.25/0.58 = ( produc1275980869_pi_pi @ A2 @ B2 ) )
% 0.25/0.58 => ~ ( ( A = A2 )
% 0.25/0.58 => ( B != B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Pair_inject
% 0.25/0.58 thf(fact_74_Pair__inject,axiom,
% 0.25/0.58 ! [A: name > noption_pi,B: name,A2: name > noption_pi,B2: name] :
% 0.25/0.58 ( ( ( produc540578151i_name @ A @ B )
% 0.25/0.58 = ( produc540578151i_name @ A2 @ B2 ) )
% 0.25/0.58 => ~ ( ( A = A2 )
% 0.25/0.58 => ( B != B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Pair_inject
% 0.25/0.58 thf(fact_75_Pair__inject,axiom,
% 0.25/0.58 ! [A: name > noption_pi,B: pi,A2: name > noption_pi,B2: pi] :
% 0.25/0.58 ( ( ( produc1820286517_pi_pi @ A @ B )
% 0.25/0.58 = ( produc1820286517_pi_pi @ A2 @ B2 ) )
% 0.25/0.58 => ~ ( ( A = A2 )
% 0.25/0.58 => ( B != B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Pair_inject
% 0.25/0.58 thf(fact_76_Pair__inject,axiom,
% 0.25/0.58 ! [A: name > noption_pi,B: name > noption_pi,A2: name > noption_pi,B2: name > noption_pi] :
% 0.25/0.58 ( ( ( produc1342893193ion_pi @ A @ B )
% 0.25/0.58 = ( produc1342893193ion_pi @ A2 @ B2 ) )
% 0.25/0.58 => ~ ( ( A = A2 )
% 0.25/0.58 => ( B != B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Pair_inject
% 0.25/0.58 thf(fact_77_Pair__inject,axiom,
% 0.25/0.58 ! [A: pi,B: pi,A2: pi,B2: pi] :
% 0.25/0.58 ( ( ( product_Pair_pi_pi @ A @ B )
% 0.25/0.58 = ( product_Pair_pi_pi @ A2 @ B2 ) )
% 0.25/0.58 => ~ ( ( A = A2 )
% 0.25/0.58 => ( B != B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Pair_inject
% 0.25/0.58 thf(fact_78_Pair__inject,axiom,
% 0.25/0.58 ! [A: name,B: product_prod_pi_pi,A2: name,B2: product_prod_pi_pi] :
% 0.25/0.58 ( ( ( produc235456326_pi_pi @ A @ B )
% 0.25/0.58 = ( produc235456326_pi_pi @ A2 @ B2 ) )
% 0.25/0.58 => ~ ( ( A = A2 )
% 0.25/0.58 => ( B != B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Pair_inject
% 0.25/0.58 thf(fact_79_prod__cases,axiom,
% 0.25/0.58 ! [P: produc1834551554reeRes > $o,P2: produc1834551554reeRes] :
% 0.25/0.58 ( ! [A3: name > noption_pi,B3: late_freeRes] : ( P @ ( produc1505598906reeRes @ A3 @ B3 ) )
% 0.25/0.58 => ( P @ P2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % prod_cases
% 0.25/0.58 thf(fact_80_prod__cases,axiom,
% 0.25/0.58 ! [P: produc53907987_pi_pi > $o,P2: produc53907987_pi_pi] :
% 0.25/0.58 ( ! [A3: name > noption_pi,B3: produc1141751126_pi_pi] : ( P @ ( produc1275980869_pi_pi @ A3 @ B3 ) )
% 0.25/0.58 => ( P @ P2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % prod_cases
% 0.25/0.58 thf(fact_81_prod__cases,axiom,
% 0.25/0.58 ! [P: produc405342261i_name > $o,P2: produc405342261i_name] :
% 0.25/0.58 ( ! [A3: name > noption_pi,B3: name] : ( P @ ( produc540578151i_name @ A3 @ B3 ) )
% 0.25/0.58 => ( P @ P2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % prod_cases
% 0.25/0.58 thf(fact_82_prod__cases,axiom,
% 0.25/0.58 ! [P: produc629157763_pi_pi > $o,P2: produc629157763_pi_pi] :
% 0.25/0.58 ( ! [A3: name > noption_pi,B3: pi] : ( P @ ( produc1820286517_pi_pi @ A3 @ B3 ) )
% 0.25/0.58 => ( P @ P2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % prod_cases
% 0.25/0.58 thf(fact_83_prod__cases,axiom,
% 0.25/0.58 ! [P: produc1462499409ion_pi > $o,P2: produc1462499409ion_pi] :
% 0.25/0.58 ( ! [A3: name > noption_pi,B3: name > noption_pi] : ( P @ ( produc1342893193ion_pi @ A3 @ B3 ) )
% 0.25/0.58 => ( P @ P2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % prod_cases
% 0.25/0.58 thf(fact_84_prod__cases,axiom,
% 0.25/0.58 ! [P: product_prod_pi_pi > $o,P2: product_prod_pi_pi] :
% 0.25/0.58 ( ! [A3: pi,B3: pi] : ( P @ ( product_Pair_pi_pi @ A3 @ B3 ) )
% 0.25/0.58 => ( P @ P2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % prod_cases
% 0.25/0.58 thf(fact_85_prod__cases,axiom,
% 0.25/0.58 ! [P: produc1141751126_pi_pi > $o,P2: produc1141751126_pi_pi] :
% 0.25/0.58 ( ! [A3: name,B3: product_prod_pi_pi] : ( P @ ( produc235456326_pi_pi @ A3 @ B3 ) )
% 0.25/0.58 => ( P @ P2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % prod_cases
% 0.25/0.58 thf(fact_86_surj__pair,axiom,
% 0.25/0.58 ! [P2: produc1834551554reeRes] :
% 0.25/0.58 ? [X3: name > noption_pi,Y3: late_freeRes] :
% 0.25/0.58 ( P2
% 0.25/0.58 = ( produc1505598906reeRes @ X3 @ Y3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % surj_pair
% 0.25/0.58 thf(fact_87_surj__pair,axiom,
% 0.25/0.58 ! [P2: produc53907987_pi_pi] :
% 0.25/0.58 ? [X3: name > noption_pi,Y3: produc1141751126_pi_pi] :
% 0.25/0.58 ( P2
% 0.25/0.58 = ( produc1275980869_pi_pi @ X3 @ Y3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % surj_pair
% 0.25/0.58 thf(fact_88_surj__pair,axiom,
% 0.25/0.58 ! [P2: produc405342261i_name] :
% 0.25/0.58 ? [X3: name > noption_pi,Y3: name] :
% 0.25/0.58 ( P2
% 0.25/0.58 = ( produc540578151i_name @ X3 @ Y3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % surj_pair
% 0.25/0.58 thf(fact_89_surj__pair,axiom,
% 0.25/0.58 ! [P2: produc629157763_pi_pi] :
% 0.25/0.58 ? [X3: name > noption_pi,Y3: pi] :
% 0.25/0.58 ( P2
% 0.25/0.58 = ( produc1820286517_pi_pi @ X3 @ Y3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % surj_pair
% 0.25/0.58 thf(fact_90_surj__pair,axiom,
% 0.25/0.58 ! [P2: produc1462499409ion_pi] :
% 0.25/0.58 ? [X3: name > noption_pi,Y3: name > noption_pi] :
% 0.25/0.58 ( P2
% 0.25/0.58 = ( produc1342893193ion_pi @ X3 @ Y3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % surj_pair
% 0.25/0.58 thf(fact_91_surj__pair,axiom,
% 0.25/0.58 ! [P2: product_prod_pi_pi] :
% 0.25/0.58 ? [X3: pi,Y3: pi] :
% 0.25/0.58 ( P2
% 0.25/0.58 = ( product_Pair_pi_pi @ X3 @ Y3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % surj_pair
% 0.25/0.58 thf(fact_92_surj__pair,axiom,
% 0.25/0.58 ! [P2: produc1141751126_pi_pi] :
% 0.25/0.58 ? [X3: name,Y3: product_prod_pi_pi] :
% 0.25/0.58 ( P2
% 0.25/0.58 = ( produc235456326_pi_pi @ X3 @ Y3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % surj_pair
% 0.25/0.58 thf(fact_93_pi_Oinject_I7_J,axiom,
% 0.25/0.58 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.25/0.58 ( ( ( par @ X2 @ X1 )
% 0.25/0.58 = ( par @ Y2 @ Y1 ) )
% 0.25/0.58 = ( ( X2 = Y2 )
% 0.25/0.58 & ( X1 = Y1 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % pi.inject(7)
% 0.25/0.58 thf(fact_94_fresh__prod,axiom,
% 0.25/0.58 ! [A: name,X: late_freeRes,Y: late_freeRes] :
% 0.25/0.58 ( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ X @ Y ) )
% 0.25/0.58 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.25/0.58 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % fresh_prod
% 0.25/0.58 thf(fact_95_fresh__prod,axiom,
% 0.25/0.58 ! [A: name,X: late_freeRes,Y: name] :
% 0.25/0.58 ( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ X @ Y ) )
% 0.25/0.58 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.25/0.58 & ( fresh_name_name @ A @ Y ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % fresh_prod
% 0.25/0.58 thf(fact_96_fresh__prod,axiom,
% 0.25/0.58 ! [A: name,X: late_freeRes,Y: pi] :
% 0.25/0.58 ( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ X @ Y ) )
% 0.25/0.58 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.25/0.58 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % fresh_prod
% 0.25/0.58 thf(fact_97_fresh__prod,axiom,
% 0.25/0.58 ! [A: name,X: name,Y: late_freeRes] :
% 0.25/0.58 ( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ X @ Y ) )
% 0.25/0.58 = ( ( fresh_name_name @ A @ X )
% 0.25/0.58 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % fresh_prod
% 0.25/0.58 thf(fact_98_fresh__prod,axiom,
% 0.25/0.58 ! [A: name,X: name,Y: name] :
% 0.25/0.58 ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y ) )
% 0.25/0.58 = ( ( fresh_name_name @ A @ X )
% 0.25/0.58 & ( fresh_name_name @ A @ Y ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % fresh_prod
% 0.25/0.58 thf(fact_99_fresh__prod,axiom,
% 0.25/0.58 ! [A: name,X: name,Y: pi] :
% 0.25/0.58 ( ( fresh_93646139ame_pi @ A @ ( product_Pair_name_pi @ X @ Y ) )
% 0.25/0.58 = ( ( fresh_name_name @ A @ X )
% 0.25/0.58 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % fresh_prod
% 0.25/0.58 thf(fact_100_fresh__prod,axiom,
% 0.25/0.58 ! [A: name,X: pi,Y: late_freeRes] :
% 0.25/0.58 ( ( fresh_1504024600reeRes @ A @ ( produc1638681944reeRes @ X @ Y ) )
% 0.25/0.58 = ( ( fresh_name_pi @ A @ X )
% 0.25/0.58 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % fresh_prod
% 0.25/0.58 thf(fact_101_fresh__prod,axiom,
% 0.25/0.58 ! [A: name,X: pi,Y: name] :
% 0.25/0.58 ( ( fresh_261416607i_name @ A @ ( product_Pair_pi_name @ X @ Y ) )
% 0.25/0.58 = ( ( fresh_name_pi @ A @ X )
% 0.25/0.58 & ( fresh_name_name @ A @ Y ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % fresh_prod
% 0.25/0.58 thf(fact_102_fresh__prod,axiom,
% 0.25/0.58 ! [A: name,X: pi,Y: pi] :
% 0.25/0.58 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 0.25/0.58 = ( ( fresh_name_pi @ A @ X )
% 0.25/0.58 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % fresh_prod
% 0.25/0.58 thf(fact_103_fresh__prod,axiom,
% 0.25/0.58 ! [A: name,X: name,Y: product_prod_pi_pi] :
% 0.25/0.58 ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
% 0.25/0.58 = ( ( fresh_name_name @ A @ X )
% 0.25/0.58 & ( fresh_1627595501_pi_pi @ A @ Y ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % fresh_prod
% 0.25/0.58 thf(fact_104_substTrans,axiom,
% 0.25/0.58 ! [B: name,P: pi,A: name,C: name] :
% 0.25/0.58 ( ( fresh_name_pi @ B @ P )
% 0.25/0.58 => ( ( subs @ ( subs @ P @ A @ B ) @ B @ C )
% 0.25/0.58 = ( subs @ P @ A @ C ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % substTrans
% 0.25/0.58 thf(fact_105_fresh__prodD_I1_J,axiom,
% 0.25/0.58 ! [A: name,X: name > noption_pi,Y: late_freeRes] :
% 0.25/0.58 ( ( fresh_1711070152reeRes @ A @ ( produc1505598906reeRes @ X @ Y ) )
% 0.25/0.58 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.25/0.58
% 0.25/0.58 % fresh_prodD(1)
% 0.25/0.58 thf(fact_106_fresh__prodD_I1_J,axiom,
% 0.25/0.58 ! [A: name,X: name > noption_pi,Y: produc1141751126_pi_pi] :
% 0.25/0.58 ( ( fresh_975559885_pi_pi @ A @ ( produc1275980869_pi_pi @ X @ Y ) )
% 0.25/0.58 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.25/0.58
% 0.25/0.58 % fresh_prodD(1)
% 0.25/0.58 thf(fact_107_fresh__prodD_I1_J,axiom,
% 0.25/0.58 ! [A: name,X: name > noption_pi,Y: name] :
% 0.25/0.58 ( ( fresh_453496559i_name @ A @ ( produc540578151i_name @ X @ Y ) )
% 0.25/0.58 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.25/0.58
% 0.25/0.58 % fresh_prodD(1)
% 0.25/0.58 thf(fact_108_fresh__prodD_I1_J,axiom,
% 0.25/0.58 ! [A: name,X: name > noption_pi,Y: pi] :
% 0.25/0.58 ( ( fresh_253309757_pi_pi @ A @ ( produc1820286517_pi_pi @ X @ Y ) )
% 0.25/0.58 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.25/0.58
% 0.25/0.58 % fresh_prodD(1)
% 0.25/0.58 thf(fact_109_fresh__prodD_I1_J,axiom,
% 0.25/0.58 ! [A: name,X: name > noption_pi,Y: name > noption_pi] :
% 0.25/0.58 ( ( fresh_225680151ion_pi @ A @ ( produc1342893193ion_pi @ X @ Y ) )
% 0.25/0.58 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.25/0.58
% 0.25/0.58 % fresh_prodD(1)
% 0.25/0.58 thf(fact_110_fresh__prodD_I1_J,axiom,
% 0.25/0.58 ! [A: name,X: pi,Y: pi] :
% 0.25/0.58 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 0.25/0.58 => ( fresh_name_pi @ A @ X ) ) ).
% 0.25/0.58
% 0.25/0.58 % fresh_prodD(1)
% 0.25/0.58 thf(fact_111_fresh__prodD_I1_J,axiom,
% 0.25/0.58 ! [A: name,X: name,Y: product_prod_pi_pi] :
% 0.25/0.58 ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
% 0.25/0.58 => ( fresh_name_name @ A @ X ) ) ).
% 0.25/0.58
% 0.25/0.58 % fresh_prodD(1)
% 0.25/0.58 thf(fact_112_fresh__prodD_I2_J,axiom,
% 0.25/0.58 ! [A: name,X: name > noption_pi,Y: late_freeRes] :
% 0.25/0.58 ( ( fresh_1711070152reeRes @ A @ ( produc1505598906reeRes @ X @ Y ) )
% 0.25/0.58 => ( fresh_1641682979reeRes @ A @ Y ) ) ).
% 0.25/0.58
% 0.25/0.58 % fresh_prodD(2)
% 0.25/0.58 thf(fact_113_fresh__prodD_I2_J,axiom,
% 0.25/0.58 ! [A: name,X: name > noption_pi,Y: produc1141751126_pi_pi] :
% 0.25/0.58 ( ( fresh_975559885_pi_pi @ A @ ( produc1275980869_pi_pi @ X @ Y ) )
% 0.25/0.58 => ( fresh_1376661020_pi_pi @ A @ Y ) ) ).
% 0.25/0.58
% 0.25/0.58 % fresh_prodD(2)
% 0.25/0.58 thf(fact_114_fresh__prodD_I2_J,axiom,
% 0.25/0.58 ! [A: name,X: name > noption_pi,Y: name] :
% 0.25/0.58 ( ( fresh_453496559i_name @ A @ ( produc540578151i_name @ X @ Y ) )
% 0.25/0.58 => ( fresh_name_name @ A @ Y ) ) ).
% 0.25/0.58
% 0.25/0.58 % fresh_prodD(2)
% 0.25/0.58 thf(fact_115_fresh__prodD_I2_J,axiom,
% 0.25/0.58 ! [A: name,X: name > noption_pi,Y: pi] :
% 0.25/0.58 ( ( fresh_253309757_pi_pi @ A @ ( produc1820286517_pi_pi @ X @ Y ) )
% 0.25/0.58 => ( fresh_name_pi @ A @ Y ) ) ).
% 0.25/0.58
% 0.25/0.58 % fresh_prodD(2)
% 0.25/0.58 thf(fact_116_fresh__prodD_I2_J,axiom,
% 0.25/0.58 ! [A: name,X: name > noption_pi,Y: name > noption_pi] :
% 0.25/0.58 ( ( fresh_225680151ion_pi @ A @ ( produc1342893193ion_pi @ X @ Y ) )
% 0.25/0.58 => ( fresh_543891186ion_pi @ A @ Y ) ) ).
% 0.25/0.58
% 0.25/0.58 % fresh_prodD(2)
% 0.25/0.58 thf(fact_117_fresh__prodD_I2_J,axiom,
% 0.25/0.58 ! [A: name,X: pi,Y: pi] :
% 0.25/0.58 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 0.25/0.58 => ( fresh_name_pi @ A @ Y ) ) ).
% 0.25/0.58
% 0.25/0.58 % fresh_prodD(2)
% 0.25/0.58 thf(fact_118_fresh__prodD_I2_J,axiom,
% 0.25/0.58 ! [A: name,X: name,Y: product_prod_pi_pi] :
% 0.25/0.58 ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
% 0.25/0.58 => ( fresh_1627595501_pi_pi @ A @ Y ) ) ).
% 0.25/0.58
% 0.25/0.58 % fresh_prodD(2)
% 0.25/0.58 thf(fact_119_Bound_Ohyps_I1_J,axiom,
% 0.25/0.58 late_transitions @ ( par @ p @ ( res @ x @ q ) ) @ ( late_BoundR @ aa @ y @ pxQ ) ).
% 0.25/0.58
% 0.25/0.58 % Bound.hyps(1)
% 0.25/0.58 thf(fact_120__092_060open_062_060_092_060nu_062x_062_IP_A_092_060parallel_062_AQ_J_A_092_060longmapsto_062_Aa_092_060guillemotleft_062y_092_060guillemotright_062_A_092_060prec_062_A_060_092_060nu_062x_062_IP_H_A_092_060parallel_062_AQ_J_092_060close_062,axiom,
% 0.25/0.58 late_transitions @ ( res @ x @ ( par @ p @ q ) ) @ ( late_BoundR @ aa @ y @ ( res @ x @ ( par @ p2 @ q ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % \<open><\<nu>x>(P \<parallel> Q) \<longmapsto> a\<guillemotleft>y\<guillemotright> \<prec> <\<nu>x>(P' \<parallel> Q)\<close>
% 0.25/0.58 thf(fact_121_cPar1_Ohyps,axiom,
% 0.25/0.58 late_transitions @ p @ ( late_BoundR @ aa @ y @ p2 ) ).
% 0.25/0.58
% 0.25/0.58 % cPar1.hyps
% 0.25/0.58 thf(fact_122__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_Aa_092_060guillemotleft_062y_092_060guillemotright_062_A_092_060prec_062_AP_H_A_092_060parallel_062_AQ_092_060close_062,axiom,
% 0.25/0.58 late_transitions @ ( par @ p @ q ) @ ( late_BoundR @ aa @ y @ ( par @ p2 @ q ) ) ).
% 0.25/0.58
% 0.25/0.58 % \<open>P \<parallel> Q \<longmapsto> a\<guillemotleft>y\<guillemotright> \<prec> P' \<parallel> Q\<close>
% 0.25/0.58 thf(fact_123_freshBoundDerivative_I2_J,axiom,
% 0.25/0.58 ! [P: pi,A: late_subject,X: name,P3: pi,Y: name] :
% 0.25/0.58 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.25/0.58 => ( ( fresh_name_pi @ Y @ P )
% 0.25/0.58 => ( ( Y != X )
% 0.25/0.58 => ( fresh_name_pi @ Y @ P3 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % freshBoundDerivative(2)
% 0.25/0.58 thf(fact_124_freshResidual,axiom,
% 0.25/0.58 ! [P: pi,Rs: late_residual,X: name] :
% 0.25/0.58 ( ( late_transitions @ P @ Rs )
% 0.25/0.58 => ( ( fresh_name_pi @ X @ P )
% 0.25/0.58 => ( fresh_81631222sidual @ X @ Rs ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % freshResidual
% 0.25/0.58 thf(fact_125_parCasesB,axiom,
% 0.25/0.58 ! [P: pi,Q: pi,A: late_subject,X: name,PQ: pi,Prop: pi > $o] :
% 0.25/0.58 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ PQ ) )
% 0.25/0.58 => ( ( fresh_name_pi @ X @ P )
% 0.25/0.58 => ( ( fresh_name_pi @ X @ Q )
% 0.25/0.58 => ( ! [P4: pi] :
% 0.25/0.58 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P4 ) )
% 0.25/0.58 => ( Prop @ ( par @ P4 @ Q ) ) )
% 0.25/0.58 => ( ! [Q2: pi] :
% 0.25/0.58 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 0.25/0.58 => ( Prop @ ( par @ P @ Q2 ) ) )
% 0.25/0.58 => ( Prop @ PQ ) ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % parCasesB
% 0.25/0.58 thf(fact_126_Late__Semantics_OPar2B,axiom,
% 0.25/0.58 ! [Q: pi,A: late_subject,X: name,Q3: pi,P: pi] :
% 0.25/0.58 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q3 ) )
% 0.25/0.58 => ( ( fresh_name_pi @ X @ P )
% 0.25/0.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q3 ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Late_Semantics.Par2B
% 0.25/0.58 thf(fact_127_Late__Semantics_OPar1B,axiom,
% 0.25/0.58 ! [P: pi,A: late_subject,X: name,P3: pi,Q: pi] :
% 0.25/0.58 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.25/0.58 => ( ( fresh_name_pi @ X @ Q )
% 0.25/0.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P3 @ Q ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Late_Semantics.Par1B
% 0.25/0.58 thf(fact_128_Late__Semantics_OResB,axiom,
% 0.25/0.58 ! [P: pi,A: late_subject,X: name,P3: pi,Y: name] :
% 0.25/0.58 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.25/0.58 => ( ( fresh_717452603ubject @ Y @ A )
% 0.25/0.58 => ( ( Y != X )
% 0.25/0.58 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P3 ) ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Late_Semantics.ResB
% 0.25/0.58 thf(fact_129_freshBoundDerivative_I1_J,axiom,
% 0.25/0.58 ! [P: pi,A: late_subject,X: name,P3: pi,Y: name] :
% 0.25/0.58 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.25/0.58 => ( ( fresh_name_pi @ Y @ P )
% 0.25/0.58 => ( fresh_717452603ubject @ Y @ A ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % freshBoundDerivative(1)
% 0.25/0.58 thf(fact_130_transitions_OResB,axiom,
% 0.25/0.58 ! [P: pi,A: late_subject,X: name,P3: pi,Y: name] :
% 0.25/0.58 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.25/0.58 => ( ( fresh_717452603ubject @ Y @ A )
% 0.25/0.58 => ( ( Y != X )
% 0.25/0.58 => ( ( fresh_name_pi @ X @ P )
% 0.25/0.58 => ( ( fresh_717452603ubject @ X @ A )
% 0.25/0.58 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P3 ) ) ) ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % transitions.ResB
% 0.25/0.58 thf(fact_131_transitions_OPar2B,axiom,
% 0.25/0.58 ! [Q: pi,A: late_subject,X: name,Q3: pi,P: pi] :
% 0.25/0.58 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q3 ) )
% 0.25/0.58 => ( ( fresh_name_pi @ X @ P )
% 0.25/0.58 => ( ( fresh_name_pi @ X @ Q )
% 0.25/0.58 => ( ( fresh_717452603ubject @ X @ A )
% 0.25/0.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q3 ) ) ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % transitions.Par2B
% 0.25/0.58 thf(fact_132_transitions_OPar1B,axiom,
% 0.25/0.58 ! [P: pi,A: late_subject,X: name,P3: pi,Q: pi] :
% 0.25/0.58 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.25/0.58 => ( ( fresh_name_pi @ X @ P )
% 0.25/0.59 => ( ( fresh_name_pi @ X @ Q )
% 0.25/0.59 => ( ( fresh_717452603ubject @ X @ A )
% 0.25/0.59 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P3 @ Q ) ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % transitions.Par1B
% 0.25/0.59 thf(fact_133_parCasesB_H,axiom,
% 0.25/0.59 ! [P: pi,Q: pi,B: late_subject,Y: name,P3: pi] :
% 0.25/0.59 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B @ Y @ P3 ) )
% 0.25/0.59 => ( ! [P5: pi,A3: late_subject,X3: name,P4: pi,Q4: pi] :
% 0.25/0.59 ( ( ( par @ P @ Q )
% 0.25/0.59 = ( par @ P5 @ Q4 ) )
% 0.25/0.59 => ( ( ( late_BoundR @ B @ Y @ P3 )
% 0.25/0.59 = ( late_BoundR @ A3 @ X3 @ ( par @ P4 @ Q4 ) ) )
% 0.25/0.59 => ( ( late_transitions @ P5 @ ( late_BoundR @ A3 @ X3 @ P4 ) )
% 0.25/0.59 => ( ( fresh_name_pi @ X3 @ P5 )
% 0.25/0.59 => ( ( fresh_name_pi @ X3 @ Q4 )
% 0.25/0.59 => ~ ( fresh_717452603ubject @ X3 @ A3 ) ) ) ) ) )
% 0.25/0.59 => ~ ! [Q4: pi,A3: late_subject,X3: name,Q2: pi,P5: pi] :
% 0.25/0.59 ( ( ( par @ P @ Q )
% 0.25/0.59 = ( par @ P5 @ Q4 ) )
% 0.25/0.59 => ( ( ( late_BoundR @ B @ Y @ P3 )
% 0.25/0.59 = ( late_BoundR @ A3 @ X3 @ ( par @ P5 @ Q2 ) ) )
% 0.25/0.59 => ( ( late_transitions @ Q4 @ ( late_BoundR @ A3 @ X3 @ Q2 ) )
% 0.25/0.59 => ( ( fresh_name_pi @ X3 @ P5 )
% 0.25/0.59 => ( ( fresh_name_pi @ X3 @ Q4 )
% 0.25/0.59 => ~ ( fresh_717452603ubject @ X3 @ A3 ) ) ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % parCasesB'
% 0.25/0.59 thf(fact_134_simE_I1_J,axiom,
% 0.25/0.59 ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,A: late_subject,X: name,Q3: pi] :
% 0.25/0.59 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.25/0.59 => ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q3 ) )
% 0.25/0.59 => ( ( fresh_name_pi @ X @ P )
% 0.25/0.59 => ? [P4: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P4 ) )
% 0.25/0.59 & ( strong2129052853vative @ P4 @ Q3 @ A @ X @ Rel ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % simE(1)
% 0.25/0.59 thf(fact_135_simCasesCont,axiom,
% 0.25/0.59 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: late_freeRes] :
% 0.25/0.59 ( ( eqvt_pi @ Rel )
% 0.25/0.59 => ( ! [A3: late_subject,X3: name,Q2: pi] :
% 0.25/0.59 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X3 @ Q2 ) )
% 0.25/0.59 => ( ( fresh_name_pi @ X3 @ P )
% 0.25/0.59 => ( ( fresh_name_pi @ X3 @ Q )
% 0.25/0.59 => ( ( fresh_717452603ubject @ X3 @ A3 )
% 0.25/0.59 => ( ( fresh_1641682979reeRes @ X3 @ C3 )
% 0.25/0.59 => ? [P6: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X3 @ P6 ) )
% 0.25/0.59 & ( strong2129052853vative @ P6 @ Q2 @ A3 @ X3 @ Rel ) ) ) ) ) ) )
% 0.25/0.59 => ( ! [Alpha: late_freeRes,Q2: pi] :
% 0.25/0.59 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.25/0.59 => ? [P6: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 0.25/0.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) )
% 0.25/0.59 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % simCasesCont
% 0.25/0.59 thf(fact_136_simCasesCont,axiom,
% 0.25/0.59 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: produc1141751126_pi_pi] :
% 0.25/0.59 ( ( eqvt_pi @ Rel )
% 0.25/0.59 => ( ! [A3: late_subject,X3: name,Q2: pi] :
% 0.25/0.59 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X3 @ Q2 ) )
% 0.25/0.59 => ( ( fresh_name_pi @ X3 @ P )
% 0.25/0.59 => ( ( fresh_name_pi @ X3 @ Q )
% 0.25/0.59 => ( ( fresh_717452603ubject @ X3 @ A3 )
% 0.25/0.59 => ( ( fresh_1376661020_pi_pi @ X3 @ C3 )
% 0.25/0.59 => ? [P6: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X3 @ P6 ) )
% 0.25/0.59 & ( strong2129052853vative @ P6 @ Q2 @ A3 @ X3 @ Rel ) ) ) ) ) ) )
% 0.25/0.59 => ( ! [Alpha: late_freeRes,Q2: pi] :
% 0.25/0.59 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.25/0.59 => ? [P6: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 0.25/0.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) )
% 0.25/0.59 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % simCasesCont
% 0.25/0.59 thf(fact_137_simCasesCont,axiom,
% 0.25/0.59 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: name] :
% 0.25/0.59 ( ( eqvt_pi @ Rel )
% 0.25/0.59 => ( ! [A3: late_subject,X3: name,Q2: pi] :
% 0.25/0.59 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X3 @ Q2 ) )
% 0.25/0.59 => ( ( fresh_name_pi @ X3 @ P )
% 0.25/0.59 => ( ( fresh_name_pi @ X3 @ Q )
% 0.25/0.59 => ( ( fresh_717452603ubject @ X3 @ A3 )
% 0.25/0.59 => ( ( fresh_name_name @ X3 @ C3 )
% 0.25/0.59 => ? [P6: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X3 @ P6 ) )
% 0.25/0.59 & ( strong2129052853vative @ P6 @ Q2 @ A3 @ X3 @ Rel ) ) ) ) ) ) )
% 0.25/0.59 => ( ! [Alpha: late_freeRes,Q2: pi] :
% 0.25/0.59 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.25/0.59 => ? [P6: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 0.25/0.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) )
% 0.25/0.59 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % simCasesCont
% 0.25/0.59 thf(fact_138_simCasesCont,axiom,
% 0.25/0.59 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: pi] :
% 0.25/0.59 ( ( eqvt_pi @ Rel )
% 0.25/0.59 => ( ! [A3: late_subject,X3: name,Q2: pi] :
% 0.25/0.59 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X3 @ Q2 ) )
% 0.25/0.59 => ( ( fresh_name_pi @ X3 @ P )
% 0.25/0.59 => ( ( fresh_name_pi @ X3 @ Q )
% 0.25/0.59 => ( ( fresh_717452603ubject @ X3 @ A3 )
% 0.25/0.59 => ( ( fresh_name_pi @ X3 @ C3 )
% 0.25/0.59 => ? [P6: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X3 @ P6 ) )
% 0.25/0.59 & ( strong2129052853vative @ P6 @ Q2 @ A3 @ X3 @ Rel ) ) ) ) ) ) )
% 0.25/0.59 => ( ! [Alpha: late_freeRes,Q2: pi] :
% 0.25/0.59 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.25/0.59 => ? [P6: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 0.25/0.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) )
% 0.25/0.59 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % simCasesCont
% 0.25/0.59 thf(fact_139_parZeroLeft,axiom,
% 0.25/0.59 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.25/0.59 ( ! [Q4: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ Q4 @ piNil ) @ Q4 ) @ Rel )
% 0.25/0.59 => ( strong743114133lation @ ( par @ P @ piNil ) @ Rel @ P ) ) ).
% 0.25/0.59
% 0.25/0.59 % parZeroLeft
% 0.25/0.59 thf(fact_140_parZeroRight,axiom,
% 0.25/0.59 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.25/0.59 ( ! [Q4: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ Q4 @ ( par @ Q4 @ piNil ) ) @ Rel )
% 0.25/0.59 => ( strong743114133lation @ P @ Rel @ ( par @ P @ piNil ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % parZeroRight
% 0.25/0.59 thf(fact_141_inputIneqTrans,axiom,
% 0.25/0.59 ! [A: name,X: name,P: pi,B: late_subject,Y: name,P3: pi] :
% 0.25/0.59 ( ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ B @ Y @ P3 ) )
% 0.25/0.59 => ~ ( fresh_717452603ubject @ A @ B ) ) ).
% 0.25/0.59
% 0.25/0.59 % inputIneqTrans
% 0.25/0.59 thf(fact_142_resTauBoundTrans,axiom,
% 0.25/0.59 ! [X: name,P: pi,A: late_subject,Y: name,P3: pi] :
% 0.25/0.59 ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_BoundR @ A @ Y @ P3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % resTauBoundTrans
% 0.25/0.59 thf(fact_143_pi_Ofresh_I1_J,axiom,
% 0.25/0.59 ! [A: name] : ( fresh_name_pi @ A @ piNil ) ).
% 0.25/0.59
% 0.25/0.59 % pi.fresh(1)
% 0.25/0.59 thf(fact_144_pi_Ofresh_I3_J,axiom,
% 0.25/0.59 ! [A: name,X1: pi] :
% 0.25/0.59 ( ( fresh_name_pi @ A @ ( tau @ X1 ) )
% 0.25/0.59 = ( fresh_name_pi @ A @ X1 ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.fresh(3)
% 0.25/0.59 thf(fact_145_simps_I1_J,axiom,
% 0.25/0.59 ! [C: name,D: name] :
% 0.25/0.59 ( ( subs @ piNil @ C @ D )
% 0.25/0.59 = piNil ) ).
% 0.25/0.59
% 0.25/0.59 % simps(1)
% 0.25/0.59 thf(fact_146_simps_I2_J,axiom,
% 0.25/0.59 ! [P: pi,C: name,D: name] :
% 0.25/0.59 ( ( subs @ ( tau @ P ) @ C @ D )
% 0.25/0.59 = ( tau @ ( subs @ P @ C @ D ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % simps(2)
% 0.25/0.59 thf(fact_147_residual_Ofresh_I2_J,axiom,
% 0.25/0.59 ! [A: name,X2: late_freeRes,X1: pi] :
% 0.25/0.59 ( ( fresh_81631222sidual @ A @ ( late_FreeR @ X2 @ X1 ) )
% 0.25/0.59 = ( ( fresh_1641682979reeRes @ A @ X2 )
% 0.25/0.59 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % residual.fresh(2)
% 0.25/0.59 thf(fact_148_inputFreeTrans,axiom,
% 0.25/0.59 ! [A: name,X: name,P: pi,Alpha2: late_freeRes,P3: pi] :
% 0.25/0.59 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_FreeR @ Alpha2 @ P3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % inputFreeTrans
% 0.25/0.59 thf(fact_149_residual_Oinject_I2_J,axiom,
% 0.25/0.59 ! [X2: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 0.25/0.59 ( ( ( late_FreeR @ X2 @ X1 )
% 0.25/0.59 = ( late_FreeR @ Y2 @ Y1 ) )
% 0.25/0.59 = ( ( X2 = Y2 )
% 0.25/0.59 & ( X1 = Y1 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % residual.inject(2)
% 0.25/0.59 thf(fact_150_nilSim_I2_J,axiom,
% 0.25/0.59 ! [Rel: set_Pr1834926343_pi_pi,A: name,X: name,P: pi] :
% 0.25/0.59 ~ ( strong743114133lation @ piNil @ Rel @ ( input @ A @ X @ P ) ) ).
% 0.25/0.59
% 0.25/0.59 % nilSim(2)
% 0.25/0.59 thf(fact_151_nilSim_I1_J,axiom,
% 0.25/0.59 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.25/0.59 ~ ( strong743114133lation @ piNil @ Rel @ ( tau @ P ) ) ).
% 0.25/0.59
% 0.25/0.59 % nilSim(1)
% 0.25/0.59 thf(fact_152_pi_Odistinct_I3_J,axiom,
% 0.25/0.59 ! [Pi: pi] :
% 0.25/0.59 ( piNil
% 0.25/0.59 != ( tau @ Pi ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(3)
% 0.25/0.59 thf(fact_153_pi_Odistinct_I5_J,axiom,
% 0.25/0.59 ! [Name1: name,Name2: name,Pi: pi] :
% 0.25/0.59 ( piNil
% 0.25/0.59 != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(5)
% 0.25/0.59 thf(fact_154_pi_Odistinct_I35_J,axiom,
% 0.25/0.59 ! [Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.25/0.59 ( ( tau @ Pi3 )
% 0.25/0.59 != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(35)
% 0.25/0.59 thf(fact_155_pi_Oinject_I2_J,axiom,
% 0.25/0.59 ! [X1: pi,Y1: pi] :
% 0.25/0.59 ( ( ( tau @ X1 )
% 0.25/0.59 = ( tau @ Y1 ) )
% 0.25/0.59 = ( X1 = Y1 ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.inject(2)
% 0.25/0.59 thf(fact_156_resInputFreeTrans,axiom,
% 0.25/0.59 ! [X: name,A: name,Y: name,P: pi,Alpha2: late_freeRes,P3: pi] :
% 0.25/0.59 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_FreeR @ Alpha2 @ P3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % resInputFreeTrans
% 0.25/0.59 thf(fact_157_residual_Odistinct_I1_J,axiom,
% 0.25/0.59 ! [Subject: late_subject,Name3: name,Pi3: pi,FreeRes: late_freeRes,Pi: pi] :
% 0.25/0.59 ( ( late_BoundR @ Subject @ Name3 @ Pi3 )
% 0.25/0.59 != ( late_FreeR @ FreeRes @ Pi ) ) ).
% 0.25/0.59
% 0.25/0.59 % residual.distinct(1)
% 0.25/0.59 thf(fact_158_residual_Oinducts,axiom,
% 0.25/0.59 ! [P: late_residual > $o,Residual: late_residual] :
% 0.25/0.59 ( ! [Subject2: late_subject,Name4: name,Pi4: pi] : ( P @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) )
% 0.25/0.59 => ( ! [FreeRes2: late_freeRes,Pi4: pi] : ( P @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.25/0.59 => ( P @ Residual ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % residual.inducts
% 0.25/0.59 thf(fact_159_pi_Odistinct_I57_J,axiom,
% 0.25/0.59 ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.25/0.59 ( ( input @ Name12 @ Name22 @ Pi3 )
% 0.25/0.59 != ( res @ Name @ Pi ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(57)
% 0.25/0.59 thf(fact_160_pi_Odistinct_I55_J,axiom,
% 0.25/0.59 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.25/0.59 ( ( input @ Name12 @ Name22 @ Pi3 )
% 0.25/0.59 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(55)
% 0.25/0.59 thf(fact_161_pi_Odistinct_I45_J,axiom,
% 0.25/0.59 ! [Pi3: pi,Name: name,Pi: pi] :
% 0.25/0.59 ( ( tau @ Pi3 )
% 0.25/0.59 != ( res @ Name @ Pi ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(45)
% 0.25/0.59 thf(fact_162_pi_Odistinct_I43_J,axiom,
% 0.25/0.59 ! [Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.25/0.59 ( ( tau @ Pi3 )
% 0.25/0.59 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(43)
% 0.25/0.59 thf(fact_163_nilCases_H,axiom,
% 0.25/0.59 ! [Rs: late_residual] :
% 0.25/0.59 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.25/0.59
% 0.25/0.59 % nilCases'
% 0.25/0.59 thf(fact_164_zeroTrans,axiom,
% 0.25/0.59 ! [Rs: late_residual] :
% 0.25/0.59 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.25/0.59
% 0.25/0.59 % zeroTrans
% 0.25/0.59 thf(fact_165_pi_Odistinct_I15_J,axiom,
% 0.25/0.59 ! [Name: name,Pi: pi] :
% 0.25/0.59 ( piNil
% 0.25/0.59 != ( res @ Name @ Pi ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(15)
% 0.25/0.59 thf(fact_166_pi_Odistinct_I13_J,axiom,
% 0.25/0.59 ! [Pi12: pi,Pi22: pi] :
% 0.25/0.59 ( piNil
% 0.25/0.59 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(13)
% 0.25/0.59 thf(fact_167_nilSimRight,axiom,
% 0.25/0.59 ! [P: pi,Rel: set_Pr1834926343_pi_pi] : ( strong743114133lation @ P @ Rel @ piNil ) ).
% 0.25/0.59
% 0.25/0.59 % nilSimRight
% 0.25/0.59 thf(fact_168_ResF,axiom,
% 0.25/0.59 ! [P: pi,Alpha2: late_freeRes,P3: pi,Y: name] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.25/0.59 => ( ( fresh_1641682979reeRes @ Y @ Alpha2 )
% 0.25/0.59 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha2 @ ( res @ Y @ P3 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % ResF
% 0.25/0.59 thf(fact_169_resCasesF_H,axiom,
% 0.25/0.59 ! [X: name,P: pi,Alpha2: late_freeRes,P3: pi] :
% 0.25/0.59 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.25/0.59 => ~ ! [P5: pi,Alpha: late_freeRes,P4: pi,Y3: name] :
% 0.25/0.59 ( ( ( res @ X @ P )
% 0.25/0.59 = ( res @ Y3 @ P5 ) )
% 0.25/0.59 => ( ( ( late_FreeR @ Alpha2 @ P3 )
% 0.25/0.59 = ( late_FreeR @ Alpha @ ( res @ Y3 @ P4 ) ) )
% 0.25/0.59 => ( ( late_transitions @ P5 @ ( late_FreeR @ Alpha @ P4 ) )
% 0.25/0.59 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % resCasesF'
% 0.25/0.59 thf(fact_170_resCasesF,axiom,
% 0.25/0.59 ! [X: name,P: pi,Alpha2: late_freeRes,XP: pi,F: pi > $o] :
% 0.25/0.59 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha2 @ XP ) )
% 0.25/0.59 => ( ! [P4: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P4 ) )
% 0.25/0.59 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 0.25/0.59 => ( F @ ( res @ X @ P4 ) ) ) )
% 0.25/0.59 => ( F @ XP ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % resCasesF
% 0.25/0.59 thf(fact_171_Par1F,axiom,
% 0.25/0.59 ! [P: pi,Alpha2: late_freeRes,P3: pi,Q: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.25/0.59 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha2 @ ( par @ P3 @ Q ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % Par1F
% 0.25/0.59 thf(fact_172_Par2F,axiom,
% 0.25/0.59 ! [Q: pi,Alpha2: late_freeRes,Q3: pi,P: pi] :
% 0.25/0.59 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.25/0.59 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha2 @ ( par @ P @ Q3 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % Par2F
% 0.25/0.59 thf(fact_173_freshFreeDerivative_I1_J,axiom,
% 0.25/0.59 ! [P: pi,Alpha2: late_freeRes,P3: pi,Y: name] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.25/0.59 => ( ( fresh_name_pi @ Y @ P )
% 0.25/0.59 => ( fresh_1641682979reeRes @ Y @ Alpha2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % freshFreeDerivative(1)
% 0.25/0.59 thf(fact_174_freshFreeDerivative_I2_J,axiom,
% 0.25/0.59 ! [P: pi,Alpha2: late_freeRes,P3: pi,Y: name] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.25/0.59 => ( ( fresh_name_pi @ Y @ P )
% 0.25/0.59 => ( fresh_name_pi @ Y @ P3 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % freshFreeDerivative(2)
% 0.25/0.59 thf(fact_175_simE_I2_J,axiom,
% 0.25/0.59 ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,Alpha2: late_freeRes,Q3: pi] :
% 0.25/0.59 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.25/0.59 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.25/0.59 => ? [P4: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P4 ) )
% 0.25/0.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P4 @ Q3 ) @ Rel ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % simE(2)
% 0.25/0.59 thf(fact_176_resTrans_I2_J,axiom,
% 0.25/0.59 ! [X: name,Y: name,P: pi,Rs: late_residual] :
% 0.25/0.59 ~ ( late_transitions @ ( res @ X @ ( input @ X @ Y @ P ) ) @ Rs ) ).
% 0.25/0.59
% 0.25/0.59 % resTrans(2)
% 0.25/0.59 thf(fact_177_simCases,axiom,
% 0.25/0.59 ! [Q: pi,P: pi,Rel: set_Pr1834926343_pi_pi] :
% 0.25/0.59 ( ! [A3: late_subject,Y3: name,Q2: pi] :
% 0.25/0.59 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q2 ) )
% 0.25/0.59 => ( ( fresh_name_pi @ Y3 @ P )
% 0.25/0.59 => ? [P6: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 0.25/0.59 & ( strong2129052853vative @ P6 @ Q2 @ A3 @ Y3 @ Rel ) ) ) )
% 0.25/0.59 => ( ! [Alpha: late_freeRes,Q2: pi] :
% 0.25/0.59 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.25/0.59 => ? [P6: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 0.25/0.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) )
% 0.25/0.59 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % simCases
% 0.25/0.59 thf(fact_178_simulation__def,axiom,
% 0.25/0.59 ( strong743114133lation
% 0.25/0.59 = ( ^ [P7: pi,Rel2: set_Pr1834926343_pi_pi,Q5: pi] :
% 0.25/0.59 ( ! [A5: late_subject,X4: name,Q6: pi] :
% 0.25/0.59 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A5 @ X4 @ Q6 ) )
% 0.25/0.59 & ( fresh_name_pi @ X4 @ P7 ) )
% 0.25/0.59 => ? [P8: pi] :
% 0.25/0.59 ( ( late_transitions @ P7 @ ( late_BoundR @ A5 @ X4 @ P8 ) )
% 0.25/0.59 & ( strong2129052853vative @ P8 @ Q6 @ A5 @ X4 @ Rel2 ) ) )
% 0.25/0.59 & ! [Alpha3: late_freeRes,Q6: pi] :
% 0.25/0.59 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 0.25/0.59 => ? [P8: pi] :
% 0.25/0.59 ( ( late_transitions @ P7 @ ( late_FreeR @ Alpha3 @ P8 ) )
% 0.25/0.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % simulation_def
% 0.25/0.59 thf(fact_179_tauBoundTrans,axiom,
% 0.25/0.59 ! [P: pi,A: late_subject,X: name,P3: pi] :
% 0.25/0.59 ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A @ X @ P3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % tauBoundTrans
% 0.25/0.59 thf(fact_180_resZeroTrans,axiom,
% 0.25/0.59 ! [X: name,Rs: late_residual] :
% 0.25/0.59 ~ ( late_transitions @ ( res @ X @ piNil ) @ Rs ) ).
% 0.25/0.59
% 0.25/0.59 % resZeroTrans
% 0.25/0.59 thf(fact_181_residual_Ostrong__induct,axiom,
% 0.25/0.59 ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 0.25/0.59 ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: late_freeRes] :
% 0.25/0.59 ( ( fresh_1641682979reeRes @ Name4 @ Z2 )
% 0.25/0.59 => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 0.25/0.59 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 0.25/0.59 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.25/0.59 => ( P @ Z @ Residual ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % residual.strong_induct
% 0.25/0.59 thf(fact_182_residual_Ostrong__induct,axiom,
% 0.25/0.59 ! [P: produc1141751126_pi_pi > late_residual > $o,Z: produc1141751126_pi_pi,Residual: late_residual] :
% 0.25/0.59 ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.25/0.59 ( ( fresh_1376661020_pi_pi @ Name4 @ Z2 )
% 0.25/0.59 => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 0.25/0.59 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 0.25/0.59 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: produc1141751126_pi_pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.25/0.59 => ( P @ Z @ Residual ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % residual.strong_induct
% 0.25/0.59 thf(fact_183_residual_Ostrong__induct,axiom,
% 0.25/0.59 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 0.25/0.59 ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: name] :
% 0.25/0.59 ( ( fresh_name_name @ Name4 @ Z2 )
% 0.25/0.59 => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 0.25/0.59 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 0.25/0.59 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.25/0.59 => ( P @ Z @ Residual ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % residual.strong_induct
% 0.25/0.59 thf(fact_184_residual_Ostrong__induct,axiom,
% 0.25/0.59 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 0.25/0.59 ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: pi] :
% 0.25/0.59 ( ( fresh_name_pi @ Name4 @ Z2 )
% 0.25/0.59 => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 0.25/0.59 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 0.25/0.59 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.25/0.59 => ( P @ Z @ Residual ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % residual.strong_induct
% 0.25/0.59 thf(fact_185_residual_Ostrong__inducts,axiom,
% 0.25/0.59 ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 0.25/0.59 ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: late_freeRes] :
% 0.25/0.59 ( ( fresh_1641682979reeRes @ Name4 @ Z2 )
% 0.25/0.59 => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 0.25/0.59 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 0.25/0.59 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.25/0.59 => ( P @ Z @ Residual ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % residual.strong_inducts
% 0.25/0.59 thf(fact_186_residual_Ostrong__inducts,axiom,
% 0.25/0.59 ! [P: produc1141751126_pi_pi > late_residual > $o,Z: produc1141751126_pi_pi,Residual: late_residual] :
% 0.25/0.59 ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.25/0.59 ( ( fresh_1376661020_pi_pi @ Name4 @ Z2 )
% 0.25/0.59 => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 0.25/0.59 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 0.25/0.59 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: produc1141751126_pi_pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.25/0.59 => ( P @ Z @ Residual ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % residual.strong_inducts
% 0.25/0.59 thf(fact_187_residual_Ostrong__inducts,axiom,
% 0.25/0.59 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 0.25/0.59 ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: name] :
% 0.25/0.59 ( ( fresh_name_name @ Name4 @ Z2 )
% 0.25/0.59 => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 0.25/0.59 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 0.25/0.59 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.25/0.59 => ( P @ Z @ Residual ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % residual.strong_inducts
% 0.25/0.59 thf(fact_188_residual_Ostrong__inducts,axiom,
% 0.25/0.59 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 0.25/0.59 ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: pi] :
% 0.25/0.59 ( ( fresh_name_pi @ Name4 @ Z2 )
% 0.25/0.59 => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 0.25/0.59 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 0.25/0.59 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.25/0.59 => ( P @ Z @ Residual ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % residual.strong_inducts
% 0.25/0.59 thf(fact_189_resSimCases,axiom,
% 0.25/0.59 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: late_freeRes] :
% 0.25/0.59 ( ( eqvt_pi @ Rel )
% 0.25/0.59 => ( ! [Q2: pi,A3: name] :
% 0.25/0.59 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q2 ) )
% 0.25/0.59 => ( ( A3 != X )
% 0.25/0.59 => ? [P6: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 0.25/0.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) ) )
% 0.25/0.59 => ( ! [Q2: pi,A3: late_subject,Y3: name] :
% 0.25/0.59 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q2 ) )
% 0.25/0.59 => ( ( fresh_717452603ubject @ X @ A3 )
% 0.25/0.59 => ( ( X != Y3 )
% 0.25/0.59 => ( ( fresh_1641682979reeRes @ Y3 @ C3 )
% 0.25/0.59 => ? [P6: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 0.25/0.59 & ( strong2129052853vative @ P6 @ ( res @ X @ Q2 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 0.25/0.59 => ( ! [Q2: pi,Alpha: late_freeRes] :
% 0.25/0.59 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.25/0.59 => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 0.25/0.59 => ? [P6: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 0.25/0.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q2 ) ) @ Rel ) ) ) )
% 0.25/0.59 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % resSimCases
% 0.25/0.59 thf(fact_190_resSimCases,axiom,
% 0.25/0.59 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: produc1141751126_pi_pi] :
% 0.25/0.59 ( ( eqvt_pi @ Rel )
% 0.25/0.59 => ( ! [Q2: pi,A3: name] :
% 0.25/0.59 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q2 ) )
% 0.25/0.59 => ( ( A3 != X )
% 0.25/0.59 => ? [P6: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 0.25/0.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) ) )
% 0.25/0.59 => ( ! [Q2: pi,A3: late_subject,Y3: name] :
% 0.25/0.59 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q2 ) )
% 0.25/0.59 => ( ( fresh_717452603ubject @ X @ A3 )
% 0.25/0.59 => ( ( X != Y3 )
% 0.25/0.59 => ( ( fresh_1376661020_pi_pi @ Y3 @ C3 )
% 0.25/0.59 => ? [P6: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 0.25/0.59 & ( strong2129052853vative @ P6 @ ( res @ X @ Q2 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 0.25/0.59 => ( ! [Q2: pi,Alpha: late_freeRes] :
% 0.25/0.59 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.25/0.59 => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 0.25/0.59 => ? [P6: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 0.25/0.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q2 ) ) @ Rel ) ) ) )
% 0.25/0.59 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % resSimCases
% 0.25/0.59 thf(fact_191_resSimCases,axiom,
% 0.25/0.59 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: name] :
% 0.25/0.59 ( ( eqvt_pi @ Rel )
% 0.25/0.59 => ( ! [Q2: pi,A3: name] :
% 0.25/0.59 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q2 ) )
% 0.25/0.59 => ( ( A3 != X )
% 0.25/0.59 => ? [P6: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 0.25/0.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) ) )
% 0.25/0.59 => ( ! [Q2: pi,A3: late_subject,Y3: name] :
% 0.25/0.59 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q2 ) )
% 0.25/0.59 => ( ( fresh_717452603ubject @ X @ A3 )
% 0.25/0.59 => ( ( X != Y3 )
% 0.25/0.59 => ( ( fresh_name_name @ Y3 @ C3 )
% 0.25/0.59 => ? [P6: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 0.25/0.59 & ( strong2129052853vative @ P6 @ ( res @ X @ Q2 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 0.25/0.59 => ( ! [Q2: pi,Alpha: late_freeRes] :
% 0.25/0.59 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.25/0.59 => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 0.25/0.59 => ? [P6: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 0.25/0.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q2 ) ) @ Rel ) ) ) )
% 0.25/0.59 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % resSimCases
% 0.25/0.59 thf(fact_192_resSimCases,axiom,
% 0.25/0.59 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: pi] :
% 0.25/0.59 ( ( eqvt_pi @ Rel )
% 0.25/0.59 => ( ! [Q2: pi,A3: name] :
% 0.25/0.59 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q2 ) )
% 0.25/0.59 => ( ( A3 != X )
% 0.25/0.59 => ? [P6: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 0.25/0.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) ) )
% 0.25/0.59 => ( ! [Q2: pi,A3: late_subject,Y3: name] :
% 0.25/0.59 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q2 ) )
% 0.25/0.59 => ( ( fresh_717452603ubject @ X @ A3 )
% 0.25/0.59 => ( ( X != Y3 )
% 0.25/0.59 => ( ( fresh_name_pi @ Y3 @ C3 )
% 0.25/0.59 => ? [P6: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 0.25/0.59 & ( strong2129052853vative @ P6 @ ( res @ X @ Q2 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 0.25/0.59 => ( ! [Q2: pi,Alpha: late_freeRes] :
% 0.25/0.59 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.25/0.59 => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 0.25/0.59 => ? [P6: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 0.25/0.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q2 ) ) @ Rel ) ) ) )
% 0.25/0.59 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % resSimCases
% 0.25/0.59 thf(fact_193_resInputBoundOutputTrans,axiom,
% 0.25/0.59 ! [X: name,A: name,Y: name,P: pi,B: name,Z: name,P3: pi] :
% 0.25/0.59 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z @ P3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % resInputBoundOutputTrans
% 0.25/0.59 thf(fact_194_resTauOutputTrans,axiom,
% 0.25/0.59 ! [X: name,P: pi,A: name,B: name,P3: pi] :
% 0.25/0.59 ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % resTauOutputTrans
% 0.25/0.59 thf(fact_195_residual_Ofresh_I1_J,axiom,
% 0.25/0.59 ! [A: name,X32: late_subject,X1: name,X2: pi] :
% 0.25/0.59 ( ( fresh_81631222sidual @ A @ ( late_BoundR @ X32 @ X1 @ X2 ) )
% 0.25/0.59 = ( ( fresh_717452603ubject @ A @ X32 )
% 0.25/0.59 & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % residual.fresh(1)
% 0.25/0.59 thf(fact_196_Tau,axiom,
% 0.25/0.59 ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 0.25/0.59
% 0.25/0.59 % Tau
% 0.25/0.59 thf(fact_197_tauCases_H,axiom,
% 0.25/0.59 ! [P: pi,Rs: late_residual] :
% 0.25/0.59 ( ( late_transitions @ ( tau @ P ) @ Rs )
% 0.25/0.59 => ~ ! [P5: pi] :
% 0.25/0.59 ( ( ( tau @ P )
% 0.25/0.59 = ( tau @ P5 ) )
% 0.25/0.59 => ( Rs
% 0.25/0.59 != ( late_FreeR @ late_TauR @ P5 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % tauCases'
% 0.25/0.59 thf(fact_198_Late__Semantics_OfreeRes_Oinject,axiom,
% 0.25/0.59 ! [X2: name,X1: name,Y2: name,Y1: name] :
% 0.25/0.59 ( ( ( late_OutputR @ X2 @ X1 )
% 0.25/0.59 = ( late_OutputR @ Y2 @ Y1 ) )
% 0.25/0.59 = ( ( X2 = Y2 )
% 0.25/0.59 & ( X1 = Y1 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % Late_Semantics.freeRes.inject
% 0.25/0.59 thf(fact_199_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 0.25/0.59 ! [X1: name,Y1: name] :
% 0.25/0.59 ( ( ( late_BoundOutputS @ X1 )
% 0.25/0.59 = ( late_BoundOutputS @ Y1 ) )
% 0.25/0.59 = ( X1 = Y1 ) ) ).
% 0.25/0.59
% 0.25/0.59 % Late_Semantics.subject.inject(2)
% 0.25/0.59 thf(fact_200_subject_Ofresh_I2_J,axiom,
% 0.25/0.59 ! [A: name,X1: name] :
% 0.25/0.59 ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ X1 ) )
% 0.25/0.59 = ( fresh_name_name @ A @ X1 ) ) ).
% 0.25/0.59
% 0.25/0.59 % subject.fresh(2)
% 0.25/0.59 thf(fact_201_freeRes_Ofresh_I1_J,axiom,
% 0.25/0.59 ! [A: name,X2: name,X1: name] :
% 0.25/0.59 ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ X2 @ X1 ) )
% 0.25/0.59 = ( ( fresh_name_name @ A @ X2 )
% 0.25/0.59 & ( fresh_name_name @ A @ X1 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % freeRes.fresh(1)
% 0.25/0.59 thf(fact_202_freeRes_Ofresh_I2_J,axiom,
% 0.25/0.59 ! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ) ).
% 0.25/0.59
% 0.25/0.59 % freeRes.fresh(2)
% 0.25/0.59 thf(fact_203_pi_Ofresh_I9_J,axiom,
% 0.25/0.59 ! [A: name,X1: name,X2: pi] :
% 0.25/0.59 ( ( fresh_name_pi @ A @ ( res @ X1 @ X2 ) )
% 0.25/0.59 = ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.fresh(9)
% 0.25/0.59 thf(fact_204_pi_Ofresh_I4_J,axiom,
% 0.25/0.59 ! [A: name,X32: name,X1: name,X2: pi] :
% 0.25/0.59 ( ( fresh_name_pi @ A @ ( input @ X32 @ X1 @ X2 ) )
% 0.25/0.59 = ( ( fresh_name_name @ A @ X32 )
% 0.25/0.59 & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.fresh(4)
% 0.25/0.59 thf(fact_205_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 0.25/0.59 ! [Name12: name,Name22: name] :
% 0.25/0.59 ( ( late_OutputR @ Name12 @ Name22 )
% 0.25/0.59 != late_TauR ) ).
% 0.25/0.59
% 0.25/0.59 % Late_Semantics.freeRes.distinct(1)
% 0.25/0.59 thf(fact_206_abs__fun__eq1,axiom,
% 0.25/0.59 ! [A: name,X: name,Y: name] :
% 0.25/0.59 ( ( ( abs_fun_name_name @ A @ X )
% 0.25/0.59 = ( abs_fun_name_name @ A @ Y ) )
% 0.25/0.59 = ( X = Y ) ) ).
% 0.25/0.59
% 0.25/0.59 % abs_fun_eq1
% 0.25/0.59 thf(fact_207_abs__fun__eq1,axiom,
% 0.25/0.59 ! [A: name,X: produc1141751126_pi_pi,Y: produc1141751126_pi_pi] :
% 0.25/0.59 ( ( ( abs_fu385186459_pi_pi @ A @ X )
% 0.25/0.59 = ( abs_fu385186459_pi_pi @ A @ Y ) )
% 0.25/0.59 = ( X = Y ) ) ).
% 0.25/0.59
% 0.25/0.59 % abs_fun_eq1
% 0.25/0.59 thf(fact_208_abs__fun__eq1,axiom,
% 0.25/0.59 ! [A: name,X: late_freeRes,Y: late_freeRes] :
% 0.25/0.59 ( ( ( abs_fu681348580reeRes @ A @ X )
% 0.25/0.59 = ( abs_fu681348580reeRes @ A @ Y ) )
% 0.25/0.59 = ( X = Y ) ) ).
% 0.25/0.59
% 0.25/0.59 % abs_fun_eq1
% 0.25/0.59 thf(fact_209_abs__fun__eq1,axiom,
% 0.25/0.59 ! [A: name,X: pi,Y: pi] :
% 0.25/0.59 ( ( ( abs_fun_name_pi @ A @ X )
% 0.25/0.59 = ( abs_fun_name_pi @ A @ Y ) )
% 0.25/0.59 = ( X = Y ) ) ).
% 0.25/0.59
% 0.25/0.59 % abs_fun_eq1
% 0.25/0.59 thf(fact_210_freeRes_Oinducts,axiom,
% 0.25/0.59 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 0.25/0.59 ( ! [Name13: name,Name23: name] : ( P @ ( late_OutputR @ Name13 @ Name23 ) )
% 0.25/0.59 => ( ( P @ late_TauR )
% 0.25/0.59 => ( P @ FreeRes3 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % freeRes.inducts
% 0.25/0.59 thf(fact_211_pi_Oinject_I8_J,axiom,
% 0.25/0.59 ! [X1: name,X2: pi,Y1: name,Y2: pi] :
% 0.25/0.59 ( ( ( res @ X1 @ X2 )
% 0.25/0.59 = ( res @ Y1 @ Y2 ) )
% 0.25/0.59 = ( ( abs_fun_name_pi @ X1 @ X2 )
% 0.25/0.59 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.inject(8)
% 0.25/0.59 thf(fact_212_residual_Oinject_I1_J,axiom,
% 0.25/0.59 ! [X32: late_subject,X1: name,X2: pi,Y32: late_subject,Y1: name,Y2: pi] :
% 0.25/0.59 ( ( ( late_BoundR @ X32 @ X1 @ X2 )
% 0.25/0.59 = ( late_BoundR @ Y32 @ Y1 @ Y2 ) )
% 0.25/0.59 = ( ( X32 = Y32 )
% 0.25/0.59 & ( ( abs_fun_name_pi @ X1 @ X2 )
% 0.25/0.59 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % residual.inject(1)
% 0.25/0.59 thf(fact_213_name__fresh__abs,axiom,
% 0.25/0.59 ! [B: name,A: name,X: late_freeRes] :
% 0.25/0.59 ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 0.25/0.59 = ( ( B = A )
% 0.25/0.59 | ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % name_fresh_abs
% 0.25/0.59 thf(fact_214_name__fresh__abs,axiom,
% 0.25/0.59 ! [B: name,A: name,X: produc1141751126_pi_pi] :
% 0.25/0.59 ( ( fresh_2065563522_pi_pi @ B @ ( abs_fu385186459_pi_pi @ A @ X ) )
% 0.25/0.59 = ( ( B = A )
% 0.25/0.59 | ( fresh_1376661020_pi_pi @ B @ X ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % name_fresh_abs
% 0.25/0.59 thf(fact_215_name__fresh__abs,axiom,
% 0.25/0.59 ! [B: name,A: name,X: name] :
% 0.25/0.59 ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 0.25/0.59 = ( ( B = A )
% 0.25/0.59 | ( fresh_name_name @ B @ X ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % name_fresh_abs
% 0.25/0.59 thf(fact_216_name__fresh__abs,axiom,
% 0.25/0.59 ! [B: name,A: name,X: pi] :
% 0.25/0.59 ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 0.25/0.59 = ( ( B = A )
% 0.25/0.59 | ( fresh_name_pi @ B @ X ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % name_fresh_abs
% 0.25/0.59 thf(fact_217_abs__fresh_I1_J,axiom,
% 0.25/0.59 ! [B: name,A: name,X: late_freeRes] :
% 0.25/0.59 ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 0.25/0.59 = ( ( B = A )
% 0.25/0.59 | ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % abs_fresh(1)
% 0.25/0.59 thf(fact_218_abs__fresh_I1_J,axiom,
% 0.25/0.59 ! [B: name,A: name,X: produc1141751126_pi_pi] :
% 0.25/0.59 ( ( fresh_2065563522_pi_pi @ B @ ( abs_fu385186459_pi_pi @ A @ X ) )
% 0.25/0.59 = ( ( B = A )
% 0.25/0.59 | ( fresh_1376661020_pi_pi @ B @ X ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % abs_fresh(1)
% 0.25/0.59 thf(fact_219_abs__fresh_I1_J,axiom,
% 0.25/0.59 ! [B: name,A: name,X: name] :
% 0.25/0.59 ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 0.25/0.59 = ( ( B = A )
% 0.25/0.59 | ( fresh_name_name @ B @ X ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % abs_fresh(1)
% 0.25/0.59 thf(fact_220_abs__fresh_I1_J,axiom,
% 0.25/0.59 ! [B: name,A: name,X: pi] :
% 0.25/0.59 ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 0.25/0.59 = ( ( B = A )
% 0.25/0.59 | ( fresh_name_pi @ B @ X ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % abs_fresh(1)
% 0.25/0.59 thf(fact_221_pi_Oinject_I3_J,axiom,
% 0.25/0.59 ! [X32: name,X1: name,X2: pi,Y32: name,Y1: name,Y2: pi] :
% 0.25/0.59 ( ( ( input @ X32 @ X1 @ X2 )
% 0.25/0.59 = ( input @ Y32 @ Y1 @ Y2 ) )
% 0.25/0.59 = ( ( X32 = Y32 )
% 0.25/0.59 & ( ( abs_fun_name_pi @ X1 @ X2 )
% 0.25/0.59 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.inject(3)
% 0.25/0.59 thf(fact_222_Open,axiom,
% 0.25/0.59 ! [P: pi,A: name,B: name,P3: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) )
% 0.25/0.59 => ( ( A != B )
% 0.25/0.59 => ( late_transitions @ ( res @ B @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ B @ P3 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % Open
% 0.25/0.59 thf(fact_223_resCases_H,axiom,
% 0.25/0.59 ! [X: name,P: pi,Rs: late_residual] :
% 0.25/0.59 ( ( late_transitions @ ( res @ X @ P ) @ Rs )
% 0.25/0.59 => ( ! [P5: pi,A3: name,B3: name] :
% 0.25/0.59 ( ( ( res @ X @ P )
% 0.25/0.59 = ( res @ B3 @ P5 ) )
% 0.25/0.59 => ! [P4: pi] :
% 0.25/0.59 ( ( Rs
% 0.25/0.59 = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B3 @ P4 ) )
% 0.25/0.59 => ( ( late_transitions @ P5 @ ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P4 ) )
% 0.25/0.59 => ( A3 = B3 ) ) ) )
% 0.25/0.59 => ( ! [P5: pi,A3: late_subject,X3: name,P4: pi,Y3: name] :
% 0.25/0.59 ( ( ( res @ X @ P )
% 0.25/0.59 = ( res @ Y3 @ P5 ) )
% 0.25/0.59 => ( ( Rs
% 0.25/0.59 = ( late_BoundR @ A3 @ X3 @ ( res @ Y3 @ P4 ) ) )
% 0.25/0.59 => ( ( late_transitions @ P5 @ ( late_BoundR @ A3 @ X3 @ P4 ) )
% 0.25/0.59 => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 0.25/0.59 => ( ( Y3 != X3 )
% 0.25/0.59 => ( ( fresh_name_pi @ X3 @ P5 )
% 0.25/0.59 => ~ ( fresh_717452603ubject @ X3 @ A3 ) ) ) ) ) ) )
% 0.25/0.59 => ~ ! [P5: pi,Alpha: late_freeRes,P4: pi,Y3: name] :
% 0.25/0.59 ( ( ( res @ X @ P )
% 0.25/0.59 = ( res @ Y3 @ P5 ) )
% 0.25/0.59 => ( ( Rs
% 0.25/0.59 = ( late_FreeR @ Alpha @ ( res @ Y3 @ P4 ) ) )
% 0.25/0.59 => ( ( late_transitions @ P5 @ ( late_FreeR @ Alpha @ P4 ) )
% 0.25/0.59 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha ) ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % resCases'
% 0.25/0.59 thf(fact_224_resCasesB_H,axiom,
% 0.25/0.59 ! [X5: name,P: pi,A: late_subject,Y4: name,P3: pi] :
% 0.25/0.59 ( ( late_transitions @ ( res @ X5 @ P ) @ ( late_BoundR @ A @ Y4 @ P3 ) )
% 0.25/0.59 => ( ! [P5: pi,A3: name,B3: name] :
% 0.25/0.59 ( ( ( res @ X5 @ P )
% 0.25/0.59 = ( res @ B3 @ P5 ) )
% 0.25/0.59 => ! [P4: pi] :
% 0.25/0.59 ( ( ( late_BoundR @ A @ Y4 @ P3 )
% 0.25/0.59 = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B3 @ P4 ) )
% 0.25/0.59 => ( ( late_transitions @ P5 @ ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P4 ) )
% 0.25/0.59 => ( A3 = B3 ) ) ) )
% 0.25/0.59 => ~ ! [P5: pi,A3: late_subject,X3: name,P4: pi,Y3: name] :
% 0.25/0.59 ( ( ( res @ X5 @ P )
% 0.25/0.59 = ( res @ Y3 @ P5 ) )
% 0.25/0.59 => ( ( ( late_BoundR @ A @ Y4 @ P3 )
% 0.25/0.59 = ( late_BoundR @ A3 @ X3 @ ( res @ Y3 @ P4 ) ) )
% 0.25/0.59 => ( ( late_transitions @ P5 @ ( late_BoundR @ A3 @ X3 @ P4 ) )
% 0.25/0.59 => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 0.25/0.59 => ( ( Y3 != X3 )
% 0.25/0.59 => ( ( fresh_name_pi @ X3 @ P5 )
% 0.25/0.59 => ~ ( fresh_717452603ubject @ X3 @ A3 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % resCasesB'
% 0.25/0.59 thf(fact_225_tauOutputTrans,axiom,
% 0.25/0.59 ! [P: pi,A: name,B: name,P3: pi] :
% 0.25/0.59 ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % tauOutputTrans
% 0.25/0.59 thf(fact_226_inputBoundOutputTrans,axiom,
% 0.25/0.59 ! [A: name,X: name,P: pi,B: name,Y: name,P3: pi] :
% 0.25/0.59 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y @ P3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % inputBoundOutputTrans
% 0.25/0.59 thf(fact_227_tauCases,axiom,
% 0.25/0.59 ! [P: pi,Alpha2: late_freeRes,P3: pi,Prop: late_freeRes > pi > $o] :
% 0.25/0.59 ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.25/0.59 => ( ( ( Alpha2 = late_TauR )
% 0.25/0.59 => ( ( P = P3 )
% 0.25/0.59 => ( Prop @ late_TauR @ P ) ) )
% 0.25/0.59 => ( Prop @ Alpha2 @ P3 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % tauCases
% 0.25/0.59 thf(fact_228_transitions_OClose2,axiom,
% 0.25/0.59 ! [P: pi,A: name,Y: name,P3: pi,Q: pi,X: name,Q3: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P3 ) )
% 0.25/0.59 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q3 ) )
% 0.25/0.59 => ( ( fresh_name_pi @ X @ P )
% 0.25/0.59 => ( ( fresh_name_pi @ X @ Q )
% 0.25/0.59 => ( ( fresh_name_pi @ Y @ P )
% 0.25/0.59 => ( ( fresh_name_pi @ Y @ Q )
% 0.25/0.59 => ( ( X != A )
% 0.25/0.59 => ( ( fresh_name_pi @ X @ P3 )
% 0.25/0.59 => ( ( Y != A )
% 0.25/0.59 => ( ( fresh_name_pi @ Y @ Q3 )
% 0.25/0.59 => ( ( X != Y )
% 0.25/0.59 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P3 @ ( subs @ Q3 @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % transitions.Close2
% 0.25/0.59 thf(fact_229_transitions_OClose1,axiom,
% 0.25/0.59 ! [P: pi,A: name,X: name,P3: pi,Q: pi,Y: name,Q3: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 0.25/0.59 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q3 ) )
% 0.25/0.59 => ( ( fresh_name_pi @ X @ P )
% 0.25/0.59 => ( ( fresh_name_pi @ X @ Q )
% 0.25/0.59 => ( ( fresh_name_pi @ Y @ P )
% 0.25/0.59 => ( ( fresh_name_pi @ Y @ Q )
% 0.25/0.59 => ( ( X != A )
% 0.25/0.59 => ( ( fresh_name_pi @ X @ Q3 )
% 0.25/0.59 => ( ( Y != A )
% 0.25/0.59 => ( ( fresh_name_pi @ Y @ P3 )
% 0.25/0.59 => ( ( X != Y )
% 0.25/0.59 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P3 @ X @ Y ) @ Q3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % transitions.Close1
% 0.25/0.59 thf(fact_230_Late__Semantics_OClose2,axiom,
% 0.25/0.59 ! [P: pi,A: name,Y: name,P3: pi,Q: pi,X: name,Q3: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P3 ) )
% 0.25/0.59 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q3 ) )
% 0.25/0.59 => ( ( fresh_name_pi @ Y @ Q )
% 0.25/0.59 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P3 @ ( subs @ Q3 @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % Late_Semantics.Close2
% 0.25/0.59 thf(fact_231_Late__Semantics_OClose1,axiom,
% 0.25/0.59 ! [P: pi,A: name,X: name,P3: pi,Q: pi,Y: name,Q3: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 0.25/0.59 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q3 ) )
% 0.25/0.59 => ( ( fresh_name_pi @ Y @ P )
% 0.25/0.59 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P3 @ X @ Y ) @ Q3 ) ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % Late_Semantics.Close1
% 0.25/0.59 thf(fact_232_name__fresh,axiom,
% 0.25/0.59 ( fresh_name_name
% 0.25/0.59 = ( ^ [A5: name,B4: name] : ( A5 != B4 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % name_fresh
% 0.25/0.59 thf(fact_233_subject_Ofresh_I1_J,axiom,
% 0.25/0.59 ! [A: name,X1: name] :
% 0.25/0.59 ( ( fresh_717452603ubject @ A @ ( late_InputS @ X1 ) )
% 0.25/0.59 = ( fresh_name_name @ A @ X1 ) ) ).
% 0.25/0.59
% 0.25/0.59 % subject.fresh(1)
% 0.25/0.59 thf(fact_234_subject_Oinducts,axiom,
% 0.25/0.59 ! [P: late_subject > $o,Subject: late_subject] :
% 0.25/0.59 ( ! [Name4: name] : ( P @ ( late_InputS @ Name4 ) )
% 0.25/0.59 => ( ! [Name4: name] : ( P @ ( late_BoundOutputS @ Name4 ) )
% 0.25/0.59 => ( P @ Subject ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % subject.inducts
% 0.25/0.59 thf(fact_235_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 0.25/0.59 ! [Name3: name,Name: name] :
% 0.25/0.59 ( ( late_InputS @ Name3 )
% 0.25/0.59 != ( late_BoundOutputS @ Name ) ) ).
% 0.25/0.59
% 0.25/0.59 % Late_Semantics.subject.distinct(1)
% 0.25/0.59 thf(fact_236_Late__Semantics_OInput,axiom,
% 0.25/0.59 ! [A: name,X: name,P: pi] : ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ).
% 0.25/0.59
% 0.25/0.59 % Late_Semantics.Input
% 0.25/0.59 thf(fact_237_transitions_OInput,axiom,
% 0.25/0.59 ! [X: name,A: name,P: pi] :
% 0.25/0.59 ( ( X != A )
% 0.25/0.59 => ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % transitions.Input
% 0.25/0.59 thf(fact_238_inputCases_H,axiom,
% 0.25/0.59 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.25/0.59 ( ( late_transitions @ ( input @ A @ B @ P ) @ Rs )
% 0.25/0.59 => ~ ! [X3: name,A3: name,P5: pi] :
% 0.25/0.59 ( ( ( A = A3 )
% 0.25/0.59 & ( ( abs_fun_name_pi @ B @ P )
% 0.25/0.59 = ( abs_fun_name_pi @ X3 @ P5 ) ) )
% 0.25/0.59 => ( ( Rs
% 0.25/0.59 = ( late_BoundR @ ( late_InputS @ A3 ) @ X3 @ P5 ) )
% 0.25/0.59 => ( X3 = A3 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % inputCases'
% 0.25/0.59 thf(fact_239_Late__Semantics_OComm1,axiom,
% 0.25/0.59 ! [P: pi,A: name,X: name,P3: pi,Q: pi,B: name,Q3: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 0.25/0.59 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q3 ) )
% 0.25/0.59 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P3 @ X @ B ) @ Q3 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % Late_Semantics.Comm1
% 0.25/0.59 thf(fact_240_Late__Semantics_OComm2,axiom,
% 0.25/0.59 ! [P: pi,A: name,B: name,P3: pi,Q: pi,X: name,Q3: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) )
% 0.25/0.59 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q3 ) )
% 0.25/0.59 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P3 @ ( subs @ Q3 @ X @ B ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % Late_Semantics.Comm2
% 0.25/0.59 thf(fact_241_transitions_OComm2,axiom,
% 0.25/0.59 ! [P: pi,A: name,B: name,P3: pi,Q: pi,X: name,Q3: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) )
% 0.25/0.59 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q3 ) )
% 0.25/0.59 => ( ( fresh_name_pi @ X @ P )
% 0.25/0.59 => ( ( fresh_name_pi @ X @ Q )
% 0.25/0.59 => ( ( X != A )
% 0.25/0.59 => ( ( X != B )
% 0.25/0.59 => ( ( fresh_name_pi @ X @ P3 )
% 0.25/0.59 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P3 @ ( subs @ Q3 @ X @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % transitions.Comm2
% 0.25/0.59 thf(fact_242_transitions_OComm1,axiom,
% 0.25/0.59 ! [P: pi,A: name,X: name,P3: pi,Q: pi,B: name,Q3: pi] :
% 0.25/0.59 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 0.25/0.59 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q3 ) )
% 0.25/0.59 => ( ( fresh_name_pi @ X @ P )
% 0.25/0.59 => ( ( fresh_name_pi @ X @ Q )
% 0.25/0.59 => ( ( X != A )
% 0.25/0.59 => ( ( X != B )
% 0.25/0.59 => ( ( fresh_name_pi @ X @ Q3 )
% 0.25/0.59 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P3 @ X @ B ) @ Q3 ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % transitions.Comm1
% 0.25/0.59 thf(fact_243_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 0.25/0.59 ! [X1: name,Y1: name] :
% 0.25/0.59 ( ( ( late_InputS @ X1 )
% 0.25/0.59 = ( late_InputS @ Y1 ) )
% 0.25/0.59 = ( X1 = Y1 ) ) ).
% 0.25/0.59
% 0.25/0.59 % Late_Semantics1.subject.inject(1)
% 0.25/0.59 thf(fact_244_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 0.25/0.59 ! [X2: name,Y2: name] :
% 0.25/0.59 ( ( ( late_BoundOutputS @ X2 )
% 0.25/0.59 = ( late_BoundOutputS @ Y2 ) )
% 0.25/0.59 = ( X2 = Y2 ) ) ).
% 0.25/0.59
% 0.25/0.59 % Late_Semantics1.subject.inject(2)
% 0.25/0.59 thf(fact_245_Late__Semantics1_OfreeRes_Oinject,axiom,
% 0.25/0.59 ! [X11: name,X12: name,Y11: name,Y12: name] :
% 0.25/0.59 ( ( ( late_OutputR @ X11 @ X12 )
% 0.25/0.59 = ( late_OutputR @ Y11 @ Y12 ) )
% 0.25/0.59 = ( ( X11 = Y11 )
% 0.25/0.59 & ( X12 = Y12 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % Late_Semantics1.freeRes.inject
% 0.25/0.59 thf(fact_246_freeRes_Oexhaust,axiom,
% 0.25/0.59 ! [Y: late_freeRes] :
% 0.25/0.59 ( ! [X112: name,X122: name] :
% 0.25/0.59 ( Y
% 0.25/0.59 != ( late_OutputR @ X112 @ X122 ) )
% 0.25/0.59 => ( Y = late_TauR ) ) ).
% 0.25/0.59
% 0.25/0.59 % freeRes.exhaust
% 0.25/0.59 thf(fact_247_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 0.25/0.59 ! [X11: name,X12: name] :
% 0.25/0.59 ( ( late_OutputR @ X11 @ X12 )
% 0.25/0.59 != late_TauR ) ).
% 0.25/0.59
% 0.25/0.59 % Late_Semantics1.freeRes.distinct(1)
% 0.25/0.59 thf(fact_248_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 0.25/0.59 ! [X1: name,X2: name] :
% 0.25/0.59 ( ( late_InputS @ X1 )
% 0.25/0.59 != ( late_BoundOutputS @ X2 ) ) ).
% 0.25/0.59
% 0.25/0.59 % Late_Semantics1.subject.distinct(1)
% 0.25/0.59 thf(fact_249_subject_Oexhaust,axiom,
% 0.25/0.59 ! [Y: late_subject] :
% 0.25/0.59 ( ! [X13: name] :
% 0.25/0.59 ( Y
% 0.25/0.59 != ( late_InputS @ X13 ) )
% 0.25/0.59 => ~ ! [X22: name] :
% 0.25/0.59 ( Y
% 0.25/0.59 != ( late_BoundOutputS @ X22 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % subject.exhaust
% 0.25/0.59 thf(fact_250_resOutputTauTrans,axiom,
% 0.25/0.59 ! [X: name,A: name,B: name,P: pi,P3: pi] :
% 0.25/0.59 ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_FreeR @ late_TauR @ P3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % resOutputTauTrans
% 0.25/0.59 thf(fact_251_resOutputInputTrans,axiom,
% 0.25/0.59 ! [X: name,A: name,B: name,P: pi,C: name,Y: name,P3: pi] :
% 0.25/0.59 ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_BoundR @ ( late_InputS @ C ) @ Y @ P3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % resOutputInputTrans
% 0.25/0.59 thf(fact_252_resOutputOutputTrans,axiom,
% 0.25/0.59 ! [X: name,A: name,P: pi,B: name,Y: name,P3: pi] :
% 0.25/0.59 ~ ( late_transitions @ ( res @ X @ ( output @ A @ X @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B @ Y ) @ P3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % resOutputOutputTrans
% 0.25/0.59 thf(fact_253_pi_Ofresh_I2_J,axiom,
% 0.25/0.59 ! [A: name,X32: name,X2: name,X1: pi] :
% 0.25/0.59 ( ( fresh_name_pi @ A @ ( output @ X32 @ X2 @ X1 ) )
% 0.25/0.59 = ( ( fresh_name_name @ A @ X32 )
% 0.25/0.59 & ( fresh_name_name @ A @ X2 )
% 0.25/0.59 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.fresh(2)
% 0.25/0.59 thf(fact_254_pi_Odistinct_I31_J,axiom,
% 0.25/0.59 ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.25/0.59 ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.25/0.59 != ( res @ Name @ Pi ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(31)
% 0.25/0.59 thf(fact_255_pi_Odistinct_I29_J,axiom,
% 0.25/0.59 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.25/0.59 ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.25/0.59 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(29)
% 0.25/0.59 thf(fact_256_pi_Odistinct_I21_J,axiom,
% 0.25/0.59 ! [Name12: name,Name22: name,Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.25/0.59 ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.25/0.59 != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(21)
% 0.25/0.59 thf(fact_257_pi_Odistinct_I1_J,axiom,
% 0.25/0.59 ! [Name1: name,Name2: name,Pi: pi] :
% 0.25/0.59 ( piNil
% 0.25/0.59 != ( output @ Name1 @ Name2 @ Pi ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(1)
% 0.25/0.59 thf(fact_258_pi_Odistinct_I19_J,axiom,
% 0.25/0.59 ! [Name12: name,Name22: name,Pi3: pi,Pi: pi] :
% 0.25/0.59 ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.25/0.59 != ( tau @ Pi ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(19)
% 0.25/0.59 thf(fact_259_pi_Oinject_I1_J,axiom,
% 0.25/0.59 ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 0.25/0.59 ( ( ( output @ X32 @ X2 @ X1 )
% 0.25/0.59 = ( output @ Y32 @ Y2 @ Y1 ) )
% 0.25/0.59 = ( ( X32 = Y32 )
% 0.25/0.59 & ( X2 = Y2 )
% 0.25/0.59 & ( X1 = Y1 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.inject(1)
% 0.25/0.59 thf(fact_260_resTrans_I1_J,axiom,
% 0.25/0.59 ! [X: name,B: name,P: pi,Rs: late_residual] :
% 0.25/0.59 ~ ( late_transitions @ ( res @ X @ ( output @ X @ B @ P ) ) @ Rs ) ).
% 0.25/0.59
% 0.25/0.59 % resTrans(1)
% 0.25/0.59 thf(fact_261_outputBoundTrans,axiom,
% 0.25/0.59 ! [A: name,B: name,P: pi,C: late_subject,X: name,P3: pi] :
% 0.25/0.59 ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_BoundR @ C @ X @ P3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % outputBoundTrans
% 0.25/0.59 thf(fact_262_nilSim_I3_J,axiom,
% 0.25/0.59 ! [Rel: set_Pr1834926343_pi_pi,A: name,B: name,P: pi] :
% 0.25/0.59 ~ ( strong743114133lation @ piNil @ Rel @ ( output @ A @ B @ P ) ) ).
% 0.25/0.59
% 0.25/0.59 % nilSim(3)
% 0.25/0.59 thf(fact_263_outputCases,axiom,
% 0.25/0.59 ! [A: name,B: name,P: pi,Alpha2: late_freeRes,P3: pi,Prop: late_freeRes > pi > $o] :
% 0.25/0.59 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.25/0.59 => ( ( ( Alpha2
% 0.25/0.59 = ( late_OutputR @ A @ B ) )
% 0.25/0.59 => ( ( P = P3 )
% 0.25/0.59 => ( Prop @ ( late_OutputR @ A @ B ) @ P ) ) )
% 0.25/0.59 => ( Prop @ Alpha2 @ P3 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % outputCases
% 0.25/0.59 thf(fact_264_outputCases_H,axiom,
% 0.25/0.59 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.25/0.59 ( ( late_transitions @ ( output @ A @ B @ P ) @ Rs )
% 0.25/0.59 => ~ ! [A3: name,B3: name,P5: pi] :
% 0.25/0.59 ( ( ( A = A3 )
% 0.25/0.59 & ( B = B3 )
% 0.25/0.59 & ( P = P5 ) )
% 0.25/0.59 => ( Rs
% 0.25/0.59 != ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P5 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % outputCases'
% 0.25/0.59 thf(fact_265_outputIneqTrans,axiom,
% 0.25/0.59 ! [A: name,B: name,P: pi,C: name,D: name,P3: pi] :
% 0.25/0.59 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ C @ D ) @ P3 ) )
% 0.25/0.59 => ~ ( ( A != C )
% 0.25/0.59 | ( B != D ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % outputIneqTrans
% 0.25/0.59 thf(fact_266_Output,axiom,
% 0.25/0.59 ! [A: name,B: name,P: pi] : ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P ) ) ).
% 0.25/0.59
% 0.25/0.59 % Output
% 0.25/0.59 thf(fact_267_outputTauTrans,axiom,
% 0.25/0.59 ! [A: name,B: name,P: pi,P3: pi] :
% 0.25/0.59 ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ late_TauR @ P3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % outputTauTrans
% 0.25/0.59 thf(fact_268_outputFreshTrans,axiom,
% 0.25/0.59 ! [A: name,B: name,P: pi,Alpha2: late_freeRes,P3: pi] :
% 0.25/0.59 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.25/0.59 => ~ ( ( fresh_1641682979reeRes @ A @ Alpha2 )
% 0.25/0.59 | ( fresh_1641682979reeRes @ B @ Alpha2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % outputFreshTrans
% 0.25/0.59 thf(fact_269_simps_I3_J,axiom,
% 0.25/0.59 ! [A: name,B: name,P: pi,C: name,D: name] :
% 0.25/0.59 ( ( subs @ ( output @ A @ B @ P ) @ C @ D )
% 0.25/0.59 = ( output @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % simps(3)
% 0.25/0.59 thf(fact_270_simps_I4_J,axiom,
% 0.25/0.59 ! [X: name,A: name,C: name,D: name,P: pi] :
% 0.25/0.59 ( ( X != A )
% 0.25/0.59 => ( ( X != C )
% 0.25/0.59 => ( ( X != D )
% 0.25/0.59 => ( ( subs @ ( input @ A @ X @ P ) @ C @ D )
% 0.25/0.59 = ( input @ ( subst_name @ A @ C @ D ) @ X @ ( subs @ P @ C @ D ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % simps(4)
% 0.25/0.59 thf(fact_271_substInput,axiom,
% 0.25/0.59 ! [X: name,B: name,C: name,A: name,P: pi] :
% 0.25/0.59 ( ( X != B )
% 0.25/0.59 => ( ( X != C )
% 0.25/0.59 => ( ( subs @ ( input @ A @ X @ P ) @ B @ C )
% 0.25/0.59 = ( input @ ( subst_name @ A @ B @ C ) @ X @ ( subs @ P @ B @ C ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % substInput
% 0.25/0.59 thf(fact_272_subst__name__def,axiom,
% 0.25/0.59 ( subst_name
% 0.25/0.59 = ( ^ [A5: name,B4: name,C4: name] : ( if_name @ ( A5 = B4 ) @ C4 @ A5 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % subst_name_def
% 0.25/0.59 thf(fact_273_simps_I6_J,axiom,
% 0.25/0.59 ! [A: name,B: name,P: pi,C: name,D: name] :
% 0.25/0.59 ( ( subs @ ( mismatch @ A @ B @ P ) @ C @ D )
% 0.25/0.59 = ( mismatch @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % simps(6)
% 0.25/0.59 thf(fact_274_simps_I5_J,axiom,
% 0.25/0.59 ! [A: name,B: name,P: pi,C: name,D: name] :
% 0.25/0.59 ( ( subs @ ( match @ A @ B @ P ) @ C @ D )
% 0.25/0.59 = ( match @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % simps(5)
% 0.25/0.59 thf(fact_275_pi_Ofresh_I5_J,axiom,
% 0.25/0.59 ! [A: name,X32: name,X2: name,X1: pi] :
% 0.25/0.59 ( ( fresh_name_pi @ A @ ( match @ X32 @ X2 @ X1 ) )
% 0.25/0.59 = ( ( fresh_name_name @ A @ X32 )
% 0.25/0.59 & ( fresh_name_name @ A @ X2 )
% 0.25/0.59 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.fresh(5)
% 0.25/0.59 thf(fact_276_pi_Ofresh_I6_J,axiom,
% 0.25/0.59 ! [A: name,X32: name,X2: name,X1: pi] :
% 0.25/0.59 ( ( fresh_name_pi @ A @ ( mismatch @ X32 @ X2 @ X1 ) )
% 0.25/0.59 = ( ( fresh_name_name @ A @ X32 )
% 0.25/0.59 & ( fresh_name_name @ A @ X2 )
% 0.25/0.59 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.fresh(6)
% 0.25/0.59 thf(fact_277_matchCases,axiom,
% 0.25/0.59 ! [A: name,B: name,P: pi,Rs: late_residual,F: name > name > $o] :
% 0.25/0.59 ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 0.25/0.59 => ( ( ( late_transitions @ P @ Rs )
% 0.25/0.59 => ( ( A = B )
% 0.25/0.59 => ( F @ A @ A ) ) )
% 0.25/0.59 => ( F @ A @ B ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % matchCases
% 0.25/0.59 thf(fact_278_matchTrans,axiom,
% 0.25/0.59 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.25/0.59 ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 0.25/0.59 => ( A = B ) ) ).
% 0.25/0.59
% 0.25/0.59 % matchTrans
% 0.25/0.59 thf(fact_279_matchCases_H,axiom,
% 0.25/0.59 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.25/0.59 ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 0.25/0.59 => ~ ! [P5: pi] :
% 0.25/0.59 ( ( ( B = A )
% 0.25/0.59 & ( P = P5 ) )
% 0.25/0.59 => ~ ( late_transitions @ P5 @ Rs ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % matchCases'
% 0.25/0.59 thf(fact_280_mismatchCases,axiom,
% 0.25/0.59 ! [A: name,B: name,P: pi,Rs: late_residual,F: name > name > $o] :
% 0.25/0.59 ( ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs )
% 0.25/0.59 => ( ( ( late_transitions @ P @ Rs )
% 0.25/0.59 => ( ( A != B )
% 0.25/0.59 => ( F @ A @ B ) ) )
% 0.25/0.59 => ( F @ A @ B ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % mismatchCases
% 0.25/0.59 thf(fact_281_mismatchTrans,axiom,
% 0.25/0.59 ! [A: name,P: pi,Rs: late_residual] :
% 0.25/0.59 ~ ( late_transitions @ ( mismatch @ A @ A @ P ) @ Rs ) ).
% 0.25/0.59
% 0.25/0.59 % mismatchTrans
% 0.25/0.59 thf(fact_282_mismatchCases_H,axiom,
% 0.25/0.59 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.25/0.59 ( ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs )
% 0.25/0.59 => ~ ! [P5: pi,A3: name,B3: name] :
% 0.25/0.59 ( ( ( A = A3 )
% 0.25/0.59 & ( B = B3 )
% 0.25/0.59 & ( P = P5 ) )
% 0.25/0.59 => ( ( late_transitions @ P5 @ Rs )
% 0.25/0.59 => ( A3 = B3 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % mismatchCases'
% 0.25/0.59 thf(fact_283_Match,axiom,
% 0.25/0.59 ! [P: pi,Rs: late_residual,B: name] :
% 0.25/0.59 ( ( late_transitions @ P @ Rs )
% 0.25/0.59 => ( late_transitions @ ( match @ B @ B @ P ) @ Rs ) ) ).
% 0.25/0.59
% 0.25/0.59 % Match
% 0.25/0.59 thf(fact_284_Mismatch,axiom,
% 0.25/0.59 ! [P: pi,Rs: late_residual,A: name,B: name] :
% 0.25/0.59 ( ( late_transitions @ P @ Rs )
% 0.25/0.59 => ( ( A != B )
% 0.25/0.59 => ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % Mismatch
% 0.25/0.59 thf(fact_285_pi_Odistinct_I67_J,axiom,
% 0.25/0.59 ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.25/0.59 ( ( match @ Name12 @ Name22 @ Pi3 )
% 0.25/0.59 != ( res @ Name @ Pi ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(67)
% 0.25/0.59 thf(fact_286_pi_Odistinct_I75_J,axiom,
% 0.25/0.59 ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.25/0.59 ( ( mismatch @ Name12 @ Name22 @ Pi3 )
% 0.25/0.59 != ( res @ Name @ Pi ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(75)
% 0.25/0.59 thf(fact_287_pi_Odistinct_I65_J,axiom,
% 0.25/0.59 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.25/0.59 ( ( match @ Name12 @ Name22 @ Pi3 )
% 0.25/0.59 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(65)
% 0.25/0.59 thf(fact_288_pi_Odistinct_I73_J,axiom,
% 0.25/0.59 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.25/0.59 ( ( mismatch @ Name12 @ Name22 @ Pi3 )
% 0.25/0.59 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(73)
% 0.25/0.59 thf(fact_289_pi_Odistinct_I49_J,axiom,
% 0.25/0.59 ! [Name12: name,Name22: name,Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.25/0.59 ( ( input @ Name12 @ Name22 @ Pi3 )
% 0.25/0.59 != ( match @ Name1 @ Name2 @ Pi ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(49)
% 0.25/0.59 thf(fact_290_pi_Odistinct_I51_J,axiom,
% 0.25/0.59 ! [Name12: name,Name22: name,Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.25/0.59 ( ( input @ Name12 @ Name22 @ Pi3 )
% 0.25/0.59 != ( mismatch @ Name1 @ Name2 @ Pi ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(51)
% 0.25/0.59 thf(fact_291_pi_Odistinct_I7_J,axiom,
% 0.25/0.59 ! [Name1: name,Name2: name,Pi: pi] :
% 0.25/0.59 ( piNil
% 0.25/0.59 != ( match @ Name1 @ Name2 @ Pi ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(7)
% 0.25/0.59 thf(fact_292_pi_Odistinct_I9_J,axiom,
% 0.25/0.59 ! [Name1: name,Name2: name,Pi: pi] :
% 0.25/0.59 ( piNil
% 0.25/0.59 != ( mismatch @ Name1 @ Name2 @ Pi ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(9)
% 0.25/0.59 thf(fact_293_pi_Odistinct_I37_J,axiom,
% 0.25/0.59 ! [Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.25/0.59 ( ( tau @ Pi3 )
% 0.25/0.59 != ( match @ Name1 @ Name2 @ Pi ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(37)
% 0.25/0.59 thf(fact_294_pi_Odistinct_I39_J,axiom,
% 0.25/0.59 ! [Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.25/0.59 ( ( tau @ Pi3 )
% 0.25/0.59 != ( mismatch @ Name1 @ Name2 @ Pi ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(39)
% 0.25/0.59 thf(fact_295_pi_Oinject_I5_J,axiom,
% 0.25/0.59 ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 0.25/0.59 ( ( ( mismatch @ X32 @ X2 @ X1 )
% 0.25/0.59 = ( mismatch @ Y32 @ Y2 @ Y1 ) )
% 0.25/0.59 = ( ( X32 = Y32 )
% 0.25/0.59 & ( X2 = Y2 )
% 0.25/0.59 & ( X1 = Y1 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.inject(5)
% 0.25/0.59 thf(fact_296_pi_Oinject_I4_J,axiom,
% 0.25/0.59 ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 0.25/0.59 ( ( ( match @ X32 @ X2 @ X1 )
% 0.25/0.59 = ( match @ Y32 @ Y2 @ Y1 ) )
% 0.25/0.59 = ( ( X32 = Y32 )
% 0.25/0.59 & ( X2 = Y2 )
% 0.25/0.59 & ( X1 = Y1 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.inject(4)
% 0.25/0.59 thf(fact_297_pi_Odistinct_I61_J,axiom,
% 0.25/0.59 ! [Name12: name,Name22: name,Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.25/0.59 ( ( match @ Name12 @ Name22 @ Pi3 )
% 0.25/0.59 != ( mismatch @ Name1 @ Name2 @ Pi ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(61)
% 0.25/0.59 thf(fact_298_pi_Odistinct_I23_J,axiom,
% 0.25/0.59 ! [Name12: name,Name22: name,Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.25/0.59 ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.25/0.59 != ( match @ Name1 @ Name2 @ Pi ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(23)
% 0.25/0.59 thf(fact_299_pi_Odistinct_I25_J,axiom,
% 0.25/0.59 ! [Name12: name,Name22: name,Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.25/0.59 ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.25/0.59 != ( mismatch @ Name1 @ Name2 @ Pi ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(25)
% 0.25/0.59 thf(fact_300_matchNilLeft,axiom,
% 0.25/0.59 ! [A: name,B: name,Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.25/0.59 ( ( A != B )
% 0.25/0.59 => ( strong743114133lation @ piNil @ Rel @ ( match @ A @ B @ P ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % matchNilLeft
% 0.25/0.59 thf(fact_301_mismatchNilLeft,axiom,
% 0.25/0.59 ! [Rel: set_Pr1834926343_pi_pi,A: name,P: pi] : ( strong743114133lation @ piNil @ Rel @ ( mismatch @ A @ A @ P ) ) ).
% 0.25/0.59
% 0.25/0.59 % mismatchNilLeft
% 0.25/0.59 thf(fact_302_pi_Ostrong__induct,axiom,
% 0.25/0.59 ! [P: late_freeRes > pi > $o,Z: late_freeRes,Pi3: pi] :
% 0.25/0.59 ( ! [Z2: late_freeRes] : ( P @ Z2 @ piNil )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 0.25/0.59 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Pi4: pi,Z2: late_freeRes] :
% 0.25/0.59 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 0.25/0.59 ( ( fresh_1641682979reeRes @ Name23 @ Z2 )
% 0.25/0.59 => ( ( fresh_name_name @ Name23 @ Name13 )
% 0.25/0.59 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi4 ) ) ) ) )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 0.25/0.59 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 0.25/0.59 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 0.25/0.59 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 0.25/0.59 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 0.25/0.59 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.25/0.59 => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 0.25/0.59 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 0.25/0.59 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 0.25/0.59 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.25/0.59 => ( ! [Name4: name,Pi4: pi,Z2: late_freeRes] :
% 0.25/0.59 ( ( fresh_1641682979reeRes @ Name4 @ Z2 )
% 0.25/0.59 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( res @ Name4 @ Pi4 ) ) ) )
% 0.25/0.59 => ( ! [Pi4: pi,Z2: late_freeRes] :
% 0.25/0.59 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 0.25/0.59 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.strong_induct
% 0.25/0.59 thf(fact_303_pi_Ostrong__induct,axiom,
% 0.25/0.59 ! [P: produc1141751126_pi_pi > pi > $o,Z: produc1141751126_pi_pi,Pi3: pi] :
% 0.25/0.59 ( ! [Z2: produc1141751126_pi_pi] : ( P @ Z2 @ piNil )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.25/0.59 ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.25/0.59 ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.25/0.59 ( ( fresh_1376661020_pi_pi @ Name23 @ Z2 )
% 0.25/0.59 => ( ( fresh_name_name @ Name23 @ Name13 )
% 0.25/0.59 => ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi4 ) ) ) ) )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.25/0.59 ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.25/0.59 ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Pi13: pi,Pi23: pi,Z2: produc1141751126_pi_pi] :
% 0.25/0.59 ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi13 )
% 0.25/0.59 => ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi23 )
% 0.25/0.59 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.25/0.59 => ( ! [Pi13: pi,Pi23: pi,Z2: produc1141751126_pi_pi] :
% 0.25/0.59 ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi13 )
% 0.25/0.59 => ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi23 )
% 0.25/0.59 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.25/0.59 => ( ! [Name4: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.25/0.59 ( ( fresh_1376661020_pi_pi @ Name4 @ Z2 )
% 0.25/0.59 => ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( res @ Name4 @ Pi4 ) ) ) )
% 0.25/0.59 => ( ! [Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.25/0.59 ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 0.25/0.59 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.strong_induct
% 0.25/0.59 thf(fact_304_pi_Ostrong__induct,axiom,
% 0.25/0.59 ! [P: name > pi > $o,Z: name,Pi3: pi] :
% 0.25/0.59 ( ! [Z2: name] : ( P @ Z2 @ piNil )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: name] :
% 0.25/0.59 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Pi4: pi,Z2: name] :
% 0.25/0.59 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: name] :
% 0.25/0.59 ( ( fresh_name_name @ Name23 @ Z2 )
% 0.25/0.59 => ( ( fresh_name_name @ Name23 @ Name13 )
% 0.25/0.59 => ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi4 ) ) ) ) )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: name] :
% 0.25/0.59 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: name] :
% 0.25/0.59 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 0.25/0.59 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 0.25/0.59 => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 0.25/0.59 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.25/0.59 => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 0.25/0.59 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 0.25/0.59 => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 0.25/0.59 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.25/0.59 => ( ! [Name4: name,Pi4: pi,Z2: name] :
% 0.25/0.59 ( ( fresh_name_name @ Name4 @ Z2 )
% 0.25/0.59 => ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( res @ Name4 @ Pi4 ) ) ) )
% 0.25/0.59 => ( ! [Pi4: pi,Z2: name] :
% 0.25/0.59 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 0.25/0.59 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.strong_induct
% 0.25/0.59 thf(fact_305_pi_Ostrong__induct,axiom,
% 0.25/0.59 ! [P: pi > pi > $o,Z: pi,Pi3: pi] :
% 0.25/0.59 ( ! [Z2: pi] : ( P @ Z2 @ piNil )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: pi] :
% 0.25/0.59 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Pi4: pi,Z2: pi] :
% 0.25/0.59 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: pi] :
% 0.25/0.59 ( ( fresh_name_pi @ Name23 @ Z2 )
% 0.25/0.59 => ( ( fresh_name_name @ Name23 @ Name13 )
% 0.25/0.59 => ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi4 ) ) ) ) )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: pi] :
% 0.25/0.59 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: pi] :
% 0.25/0.59 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 0.25/0.59 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 0.25/0.59 => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 0.25/0.59 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.25/0.59 => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 0.25/0.59 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 0.25/0.59 => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 0.25/0.59 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.25/0.59 => ( ! [Name4: name,Pi4: pi,Z2: pi] :
% 0.25/0.59 ( ( fresh_name_pi @ Name4 @ Z2 )
% 0.25/0.59 => ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( res @ Name4 @ Pi4 ) ) ) )
% 0.25/0.59 => ( ! [Pi4: pi,Z2: pi] :
% 0.25/0.59 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 0.25/0.59 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.strong_induct
% 0.25/0.59 thf(fact_306_pi_Ostrong__inducts,axiom,
% 0.25/0.59 ! [P: late_freeRes > pi > $o,Z: late_freeRes,Pi3: pi] :
% 0.25/0.59 ( ! [Z2: late_freeRes] : ( P @ Z2 @ piNil )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 0.25/0.59 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Pi4: pi,Z2: late_freeRes] :
% 0.25/0.59 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 0.25/0.59 ( ( fresh_1641682979reeRes @ Name23 @ Z2 )
% 0.25/0.59 => ( ( fresh_name_name @ Name23 @ Name13 )
% 0.25/0.59 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi4 ) ) ) ) )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 0.25/0.59 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 0.25/0.59 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 0.25/0.59 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 0.25/0.59 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 0.25/0.59 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.25/0.59 => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 0.25/0.59 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 0.25/0.59 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 0.25/0.59 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.25/0.59 => ( ! [Name4: name,Pi4: pi,Z2: late_freeRes] :
% 0.25/0.59 ( ( fresh_1641682979reeRes @ Name4 @ Z2 )
% 0.25/0.59 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( res @ Name4 @ Pi4 ) ) ) )
% 0.25/0.59 => ( ! [Pi4: pi,Z2: late_freeRes] :
% 0.25/0.59 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 0.25/0.59 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.strong_inducts
% 0.25/0.59 thf(fact_307_pi_Ostrong__inducts,axiom,
% 0.25/0.59 ! [P: produc1141751126_pi_pi > pi > $o,Z: produc1141751126_pi_pi,Pi3: pi] :
% 0.25/0.59 ( ! [Z2: produc1141751126_pi_pi] : ( P @ Z2 @ piNil )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.25/0.59 ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.25/0.59 ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.25/0.59 ( ( fresh_1376661020_pi_pi @ Name23 @ Z2 )
% 0.25/0.59 => ( ( fresh_name_name @ Name23 @ Name13 )
% 0.25/0.59 => ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi4 ) ) ) ) )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.25/0.59 ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.25/0.59 ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Pi13: pi,Pi23: pi,Z2: produc1141751126_pi_pi] :
% 0.25/0.59 ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi13 )
% 0.25/0.59 => ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi23 )
% 0.25/0.59 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.25/0.59 => ( ! [Pi13: pi,Pi23: pi,Z2: produc1141751126_pi_pi] :
% 0.25/0.59 ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi13 )
% 0.25/0.59 => ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi23 )
% 0.25/0.59 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.25/0.59 => ( ! [Name4: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.25/0.59 ( ( fresh_1376661020_pi_pi @ Name4 @ Z2 )
% 0.25/0.59 => ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( res @ Name4 @ Pi4 ) ) ) )
% 0.25/0.59 => ( ! [Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.25/0.59 ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 0.25/0.59 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.strong_inducts
% 0.25/0.59 thf(fact_308_pi_Ostrong__inducts,axiom,
% 0.25/0.59 ! [P: name > pi > $o,Z: name,Pi3: pi] :
% 0.25/0.59 ( ! [Z2: name] : ( P @ Z2 @ piNil )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: name] :
% 0.25/0.59 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Pi4: pi,Z2: name] :
% 0.25/0.59 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: name] :
% 0.25/0.59 ( ( fresh_name_name @ Name23 @ Z2 )
% 0.25/0.59 => ( ( fresh_name_name @ Name23 @ Name13 )
% 0.25/0.59 => ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi4 ) ) ) ) )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: name] :
% 0.25/0.59 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: name] :
% 0.25/0.59 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 0.25/0.59 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 0.25/0.59 => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 0.25/0.59 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.25/0.59 => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 0.25/0.59 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 0.25/0.59 => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 0.25/0.59 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.25/0.59 => ( ! [Name4: name,Pi4: pi,Z2: name] :
% 0.25/0.59 ( ( fresh_name_name @ Name4 @ Z2 )
% 0.25/0.59 => ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( res @ Name4 @ Pi4 ) ) ) )
% 0.25/0.59 => ( ! [Pi4: pi,Z2: name] :
% 0.25/0.59 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 0.25/0.59 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.strong_inducts
% 0.25/0.59 thf(fact_309_pi_Ostrong__inducts,axiom,
% 0.25/0.59 ! [P: pi > pi > $o,Z: pi,Pi3: pi] :
% 0.25/0.59 ( ! [Z2: pi] : ( P @ Z2 @ piNil )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: pi] :
% 0.25/0.59 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Pi4: pi,Z2: pi] :
% 0.25/0.59 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: pi] :
% 0.25/0.59 ( ( fresh_name_pi @ Name23 @ Z2 )
% 0.25/0.59 => ( ( fresh_name_name @ Name23 @ Name13 )
% 0.25/0.59 => ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi4 ) ) ) ) )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: pi] :
% 0.25/0.59 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: pi] :
% 0.25/0.59 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi4 ) ) )
% 0.25/0.59 => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 0.25/0.59 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 0.25/0.59 => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 0.25/0.59 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.25/0.59 => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 0.25/0.59 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 0.25/0.59 => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 0.25/0.59 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.25/0.59 => ( ! [Name4: name,Pi4: pi,Z2: pi] :
% 0.25/0.59 ( ( fresh_name_pi @ Name4 @ Z2 )
% 0.25/0.59 => ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( res @ Name4 @ Pi4 ) ) ) )
% 0.25/0.59 => ( ! [Pi4: pi,Z2: pi] :
% 0.25/0.59 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.25/0.59 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 0.25/0.59 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.strong_inducts
% 0.25/0.59 thf(fact_310_pi_Ofresh_I10_J,axiom,
% 0.25/0.59 ! [A: name,X1: pi] :
% 0.25/0.59 ( ( fresh_name_pi @ A @ ( bang @ X1 ) )
% 0.25/0.59 = ( fresh_name_pi @ A @ X1 ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.fresh(10)
% 0.25/0.59 thf(fact_311_pi_Ofresh_I7_J,axiom,
% 0.25/0.59 ! [A: name,X2: pi,X1: pi] :
% 0.25/0.59 ( ( fresh_name_pi @ A @ ( sum @ X2 @ X1 ) )
% 0.25/0.59 = ( ( fresh_name_pi @ A @ X2 )
% 0.25/0.59 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.fresh(7)
% 0.25/0.59 thf(fact_312_simps_I10_J,axiom,
% 0.25/0.59 ! [P: pi,C: name,D: name] :
% 0.25/0.59 ( ( subs @ ( bang @ P ) @ C @ D )
% 0.25/0.59 = ( bang @ ( subs @ P @ C @ D ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % simps(10)
% 0.25/0.59 thf(fact_313_simps_I7_J,axiom,
% 0.25/0.59 ! [P: pi,Q: pi,C: name,D: name] :
% 0.25/0.59 ( ( subs @ ( sum @ P @ Q ) @ C @ D )
% 0.25/0.59 = ( sum @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % simps(7)
% 0.25/0.59 thf(fact_314_pi_Odistinct_I77_J,axiom,
% 0.25/0.59 ! [Name12: name,Name22: name,Pi3: pi,Pi: pi] :
% 0.25/0.59 ( ( mismatch @ Name12 @ Name22 @ Pi3 )
% 0.25/0.59 != ( bang @ Pi ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(77)
% 0.25/0.59 thf(fact_315_pi_Odistinct_I71_J,axiom,
% 0.25/0.59 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.25/0.59 ( ( mismatch @ Name12 @ Name22 @ Pi3 )
% 0.25/0.59 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.25/0.59
% 0.25/0.59 % pi.distinct(71)
% 0.25/0.59 thf(fact_316_pi_Odistinct_I69_J,axiom,
% 0.25/0.59 ! [Name12: name,Name22: name,Pi3: pi,Pi: pi] :
% 0.25/0.59 ( ( match @ Name12 @ Name22 @ Pi3 )
% 0.25/0.69 != ( bang @ Pi ) ) ).
% 0.25/0.69
% 0.25/0.69 % pi.distinct(69)
% 0.25/0.69 thf(fact_317_pi_Odistinct_I63_J,axiom,
% 0.25/0.69 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.25/0.69 ( ( match @ Name12 @ Name22 @ Pi3 )
% 0.25/0.69 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.25/0.69
% 0.25/0.69 % pi.distinct(63)
% 0.25/0.69 thf(fact_318_pi_Odistinct_I33_J,axiom,
% 0.25/0.69 ! [Name12: name,Name22: name,Pi3: pi,Pi: pi] :
% 0.25/0.69 ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.25/0.69 != ( bang @ Pi ) ) ).
% 0.25/0.69
% 0.25/0.69 % pi.distinct(33)
% 0.25/0.69 thf(fact_319_pi_Odistinct_I27_J,axiom,
% 0.25/0.69 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.25/0.69 ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.25/0.69 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.25/0.69
% 0.25/0.69 % pi.distinct(27)
% 0.25/0.69 thf(fact_320_pi_Odistinct_I89_J,axiom,
% 0.25/0.69 ! [Name3: name,Pi3: pi,Pi: pi] :
% 0.25/0.69 ( ( res @ Name3 @ Pi3 )
% 0.25/0.69 != ( bang @ Pi ) ) ).
% 0.25/0.69
% 0.25/0.69 % pi.distinct(89)
% 0.25/0.69 thf(fact_321_pi_Odistinct_I87_J,axiom,
% 0.25/0.69 ! [Pi1: pi,Pi2: pi,Pi: pi] :
% 0.25/0.69 ( ( par @ Pi1 @ Pi2 )
% 0.25/0.69 != ( bang @ Pi ) ) ).
% 0.25/0.69
% 0.25/0.69 % pi.distinct(87)
% 0.25/0.69 thf(fact_322_pi_Odistinct_I59_J,axiom,
% 0.25/0.69 ! [Name12: name,Name22: name,Pi3: pi,Pi: pi] :
% 0.25/0.69 ( ( input @ Name12 @ Name22 @ Pi3 )
% 0.25/0.69 != ( bang @ Pi ) ) ).
% 0.25/0.69
% 0.25/0.69 % pi.distinct(59)
% 0.25/0.69 thf(fact_323_pi_Odistinct_I17_J,axiom,
% 0.25/0.69 ! [Pi: pi] :
% 0.25/0.69 ( piNil
% 0.25/0.69 != ( bang @ Pi ) ) ).
% 0.25/0.69
% 0.25/0.69 % pi.distinct(17)
% 0.25/0.69 thf(fact_324_Sum2,axiom,
% 0.25/0.69 ! [Q: pi,Rs: late_residual,P: pi] :
% 0.25/0.69 ( ( late_transitions @ Q @ Rs )
% 0.25/0.69 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.25/0.69
% 0.25/0.69 % Sum2
% 0.25/0.69 thf(fact_325_Sum1,axiom,
% 0.25/0.69 ! [P: pi,Rs: late_residual,Q: pi] :
% 0.25/0.69 ( ( late_transitions @ P @ Rs )
% 0.25/0.69 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.25/0.69
% 0.25/0.69 % Sum1
% 0.25/0.69 thf(fact_326_sumCases_H,axiom,
% 0.25/0.69 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.25/0.69 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.25/0.69 => ( ~ ( late_transitions @ P @ Rs )
% 0.25/0.69 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.25/0.69
% 0.25/0.69 % sumCases'
% 0.25/0.69 thf(fact_327_sumCases,axiom,
% 0.25/0.69 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.25/0.69 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.25/0.69 => ( ~ ( late_transitions @ P @ Rs )
% 0.25/0.69 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.25/0.69
% 0.25/0.69 % sumCases
% 0.25/0.69 thf(fact_328_pi_Odistinct_I47_J,axiom,
% 0.25/0.69 ! [Pi3: pi,Pi: pi] :
% 0.25/0.69 ( ( tau @ Pi3 )
% 0.25/0.69 != ( bang @ Pi ) ) ).
% 0.25/0.69
% 0.25/0.69 % pi.distinct(47)
% 0.25/0.69 thf(fact_329_pi_Odistinct_I81_J,axiom,
% 0.25/0.69 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 0.25/0.69 ( ( sum @ Pi1 @ Pi2 )
% 0.25/0.69 != ( res @ Name @ Pi ) ) ).
% 0.25/0.69
% 0.25/0.69 % pi.distinct(81)
% 0.25/0.69 thf(fact_330_pi_Odistinct_I79_J,axiom,
% 0.25/0.69 ! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
% 0.25/0.69 ( ( sum @ Pi1 @ Pi2 )
% 0.25/0.69 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.25/0.69
% 0.25/0.69 % pi.distinct(79)
% 0.25/0.69 thf(fact_331_pi_Odistinct_I83_J,axiom,
% 0.25/0.69 ! [Pi1: pi,Pi2: pi,Pi: pi] :
% 0.25/0.69 ( ( sum @ Pi1 @ Pi2 )
% 0.25/0.69 != ( bang @ Pi ) ) ).
% 0.25/0.69
% 0.25/0.69 % pi.distinct(83)
% 0.25/0.69 thf(fact_332_pi_Oinject_I6_J,axiom,
% 0.25/0.69 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.25/0.69 ( ( ( sum @ X2 @ X1 )
% 0.25/0.69 = ( sum @ Y2 @ Y1 ) )
% 0.25/0.69 = ( ( X2 = Y2 )
% 0.25/0.69 & ( X1 = Y1 ) ) ) ).
% 0.25/0.69
% 0.25/0.69 % pi.inject(6)
% 0.25/0.69 thf(fact_333_pi_Oinject_I9_J,axiom,
% 0.25/0.69 ! [X1: pi,Y1: pi] :
% 0.25/0.69 ( ( ( bang @ X1 )
% 0.25/0.69 = ( bang @ Y1 ) )
% 0.25/0.69 = ( X1 = Y1 ) ) ).
% 0.25/0.69
% 0.25/0.69 % pi.inject(9)
% 0.25/0.69 thf(fact_334_pi_Odistinct_I41_J,axiom,
% 0.25/0.69 ! [Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.25/0.69 ( ( tau @ Pi3 )
% 0.25/0.69 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.25/0.69
% 0.25/0.69 % pi.distinct(41)
% 0.25/0.69
% 0.25/0.69 % Helper facts (3)
% 0.25/0.69 thf(help_If_3_1_If_001t__Agent__Oname_T,axiom,
% 0.25/0.69 ! [P: $o] :
% 0.25/0.69 ( ( P = $true )
% 0.25/0.69 | ( P = $false ) ) ).
% 0.25/0.69
% 0.25/0.69 thf(help_If_2_1_If_001t__Agent__Oname_T,axiom,
% 0.25/0.69 ! [X: name,Y: name] :
% 0.25/0.69 ( ( if_name @ $false @ X @ Y )
% 0.25/0.69 = Y ) ).
% 0.25/0.69
% 0.25/0.69 thf(help_If_1_1_If_001t__Agent__Oname_T,axiom,
% 0.25/0.69 ! [X: name,Y: name] :
% 0.25/0.69 ( ( if_name @ $true @ X @ Y )
% 0.25/0.69 = X ) ).
% 0.25/0.69
% 0.25/0.69 % Conjectures (1)
% 0.25/0.69 thf(conj_0,conjecture,
% 0.25/0.69 member558706512_pi_pi @ ( product_Pair_pi_pi @ ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u ) @ ( par @ ( subs @ p2 @ y @ u ) @ ( subs @ ( res @ x @ q ) @ y @ u ) ) ) @ rel ).
% 0.25/0.69
% 0.25/0.69 %------------------------------------------------------------------------------
% 0.25/0.69 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.A0f9rKOzGS/cvc5---1.0.5_26572.p...
% 0.25/0.69 (declare-sort $$unsorted 0)
% 0.25/0.69 (declare-sort tptp.produc53907987_pi_pi 0)
% 0.25/0.69 (declare-sort tptp.produc1462499409ion_pi 0)
% 0.25/0.69 (declare-sort tptp.noptio1575811931_pi_pi 0)
% 0.25/0.69 (declare-sort tptp.produc1834551554reeRes 0)
% 0.25/0.69 (declare-sort tptp.produc405342261i_name 0)
% 0.25/0.69 (declare-sort tptp.produc629157763_pi_pi 0)
% 0.25/0.69 (declare-sort tptp.produc1141751126_pi_pi 0)
% 0.25/0.69 (declare-sort tptp.produc1357834675reeRes 0)
% 0.25/0.69 (declare-sort tptp.produc2052722628s_name 0)
% 0.25/0.69 (declare-sort tptp.produc2008547984reeRes 0)
% 0.25/0.69 (declare-sort tptp.produc992857746Res_pi 0)
% 0.25/0.69 (declare-sort tptp.produc649380958reeRes 0)
% 0.25/0.69 (declare-sort tptp.set_Pr1834926343_pi_pi 0)
% 0.25/0.69 (declare-sort tptp.produc367475239e_name 0)
% 0.25/0.69 (declare-sort tptp.product_prod_pi_name 0)
% 0.25/0.69 (declare-sort tptp.product_prod_name_pi 0)
% 0.25/0.69 (declare-sort tptp.product_prod_pi_pi 0)
% 0.25/0.69 (declare-sort tptp.noption_Late_freeRes 0)
% 0.25/0.69 (declare-sort tptp.noption_name 0)
% 0.25/0.69 (declare-sort tptp.noption_pi 0)
% 0.25/0.69 (declare-sort tptp.late_residual 0)
% 0.25/0.69 (declare-sort tptp.late_subject 0)
% 0.25/0.69 (declare-sort tptp.late_freeRes 0)
% 0.25/0.69 (declare-sort tptp.name 0)
% 0.25/0.69 (declare-sort tptp.pi 0)
% 0.25/0.69 (declare-fun tptp.bang (tptp.pi) tptp.pi)
% 0.25/0.69 (declare-fun tptp.input (tptp.name tptp.name tptp.pi) tptp.pi)
% 0.25/0.69 (declare-fun tptp.match (tptp.name tptp.name tptp.pi) tptp.pi)
% 0.25/0.69 (declare-fun tptp.mismatch (tptp.name tptp.name tptp.pi) tptp.pi)
% 0.25/0.69 (declare-fun tptp.output (tptp.name tptp.name tptp.pi) tptp.pi)
% 0.25/0.69 (declare-fun tptp.par (tptp.pi tptp.pi) tptp.pi)
% 0.25/0.69 (declare-fun tptp.piNil () tptp.pi)
% 0.25/0.69 (declare-fun tptp.res (tptp.name tptp.pi) tptp.pi)
% 0.25/0.69 (declare-fun tptp.sum (tptp.pi tptp.pi) tptp.pi)
% 0.25/0.69 (declare-fun tptp.tau (tptp.pi) tptp.pi)
% 0.25/0.69 (declare-fun tptp.subs (tptp.pi tptp.name tptp.name) tptp.pi)
% 0.25/0.69 (declare-fun tptp.subst_name (tptp.name tptp.name tptp.name) tptp.name)
% 0.25/0.69 (declare-fun tptp.if_name (Bool tptp.name tptp.name) tptp.name)
% 0.25/0.69 (declare-fun tptp.late_OutputR (tptp.name tptp.name) tptp.late_freeRes)
% 0.25/0.69 (declare-fun tptp.late_TauR () tptp.late_freeRes)
% 0.25/0.69 (declare-fun tptp.late_BoundR (tptp.late_subject tptp.name tptp.pi) tptp.late_residual)
% 0.25/0.69 (declare-fun tptp.late_FreeR (tptp.late_freeRes tptp.pi) tptp.late_residual)
% 0.25/0.69 (declare-fun tptp.late_BoundOutputS (tptp.name) tptp.late_subject)
% 0.25/0.69 (declare-fun tptp.late_InputS (tptp.name) tptp.late_subject)
% 0.25/0.69 (declare-fun tptp.late_transitions (tptp.pi tptp.late_residual) Bool)
% 0.25/0.69 (declare-fun tptp.abs_fun_name_name (tptp.name tptp.name tptp.name) tptp.noption_name)
% 0.25/0.69 (declare-fun tptp.abs_fun_name_pi (tptp.name tptp.pi tptp.name) tptp.noption_pi)
% 0.25/0.69 (declare-fun tptp.abs_fu681348580reeRes (tptp.name tptp.late_freeRes tptp.name) tptp.noption_Late_freeRes)
% 0.25/0.69 (declare-fun tptp.abs_fu385186459_pi_pi (tptp.name tptp.produc1141751126_pi_pi tptp.name) tptp.noptio1575811931_pi_pi)
% 0.25/0.69 (declare-fun tptp.fresh_1093033124n_name (tptp.name (-> tptp.name tptp.noption_name)) Bool)
% 0.25/0.69 (declare-fun tptp.fresh_543891186ion_pi (tptp.name (-> tptp.name tptp.noption_pi)) Bool)
% 0.25/0.69 (declare-fun tptp.fresh_785364841reeRes (tptp.name (-> tptp.name tptp.noption_Late_freeRes)) Bool)
% 0.25/0.69 (declare-fun tptp.fresh_2065563522_pi_pi (tptp.name (-> tptp.name tptp.noptio1575811931_pi_pi)) Bool)
% 0.25/0.69 (declare-fun tptp.fresh_name_name (tptp.name tptp.name) Bool)
% 0.25/0.69 (declare-fun tptp.fresh_name_pi (tptp.name tptp.pi) Bool)
% 0.25/0.69 (declare-fun tptp.fresh_1641682979reeRes (tptp.name tptp.late_freeRes) Bool)
% 0.25/0.69 (declare-fun tptp.fresh_81631222sidual (tptp.name tptp.late_residual) Bool)
% 0.25/0.69 (declare-fun tptp.fresh_717452603ubject (tptp.name tptp.late_subject) Bool)
% 0.25/0.69 (declare-fun tptp.fresh_225680151ion_pi (tptp.name tptp.produc1462499409ion_pi) Bool)
% 0.25/0.69 (declare-fun tptp.fresh_453496559i_name (tptp.name tptp.produc405342261i_name) Bool)
% 0.25/0.69 (declare-fun tptp.fresh_253309757_pi_pi (tptp.name tptp.produc629157763_pi_pi) Bool)
% 0.25/0.69 (declare-fun tptp.fresh_1711070152reeRes (tptp.name tptp.produc1834551554reeRes) Bool)
% 0.25/0.69 (declare-fun tptp.fresh_975559885_pi_pi (tptp.name tptp.produc53907987_pi_pi) Bool)
% 0.25/0.69 (declare-fun tptp.fresh_441084397e_name (tptp.name tptp.produc367475239e_name) Bool)
% 0.25/0.69 (declare-fun tptp.fresh_93646139ame_pi (tptp.name tptp.product_prod_name_pi) Bool)
% 0.25/0.69 (declare-fun tptp.fresh_1963366730reeRes (tptp.name tptp.produc2008547984reeRes) Bool)
% 0.25/0.69 (declare-fun tptp.fresh_1376661020_pi_pi (tptp.name tptp.produc1141751126_pi_pi) Bool)
% 0.25/0.69 (declare-fun tptp.fresh_261416607i_name (tptp.name tptp.product_prod_pi_name) Bool)
% 0.25/0.69 (declare-fun tptp.fresh_1627595501_pi_pi (tptp.name tptp.product_prod_pi_pi) Bool)
% 0.25/0.69 (declare-fun tptp.fresh_1504024600reeRes (tptp.name tptp.produc649380958reeRes) Bool)
% 0.25/0.69 (declare-fun tptp.fresh_2007541374s_name (tptp.name tptp.produc2052722628s_name) Bool)
% 0.25/0.69 (declare-fun tptp.fresh_1847501388Res_pi (tptp.name tptp.produc992857746Res_pi) Bool)
% 0.25/0.69 (declare-fun tptp.fresh_493808761reeRes (tptp.name tptp.produc1357834675reeRes) Bool)
% 0.25/0.69 (declare-fun tptp.produc1342893193ion_pi ((-> tptp.name tptp.noption_pi) (-> tptp.name tptp.noption_pi)) tptp.produc1462499409ion_pi)
% 0.25/0.69 (declare-fun tptp.produc540578151i_name ((-> tptp.name tptp.noption_pi) tptp.name) tptp.produc405342261i_name)
% 0.25/0.69 (declare-fun tptp.produc1820286517_pi_pi ((-> tptp.name tptp.noption_pi) tptp.pi) tptp.produc629157763_pi_pi)
% 0.25/0.69 (declare-fun tptp.produc1505598906reeRes ((-> tptp.name tptp.noption_pi) tptp.late_freeRes) tptp.produc1834551554reeRes)
% 0.25/0.69 (declare-fun tptp.produc1275980869_pi_pi ((-> tptp.name tptp.noption_pi) tptp.produc1141751126_pi_pi) tptp.produc53907987_pi_pi)
% 0.25/0.69 (declare-fun tptp.produc1570949143e_name (tptp.name tptp.name) tptp.produc367475239e_name)
% 0.25/0.69 (declare-fun tptp.product_Pair_name_pi (tptp.name tptp.pi) tptp.product_prod_name_pi)
% 0.25/0.69 (declare-fun tptp.produc1531804426reeRes (tptp.name tptp.late_freeRes) tptp.produc2008547984reeRes)
% 0.25/0.69 (declare-fun tptp.produc235456326_pi_pi (tptp.name tptp.product_prod_pi_pi) tptp.produc1141751126_pi_pi)
% 0.25/0.69 (declare-fun tptp.product_Pair_pi_name (tptp.pi tptp.name) tptp.product_prod_pi_name)
% 0.25/0.69 (declare-fun tptp.product_Pair_pi_pi (tptp.pi tptp.pi) tptp.product_prod_pi_pi)
% 0.25/0.69 (declare-fun tptp.produc1638681944reeRes (tptp.pi tptp.late_freeRes) tptp.produc649380958reeRes)
% 0.25/0.69 (declare-fun tptp.produc1701355766s_name (tptp.late_freeRes tptp.name) tptp.produc2052722628s_name)
% 0.25/0.69 (declare-fun tptp.produc1177552196Res_pi (tptp.late_freeRes tptp.pi) tptp.produc992857746Res_pi)
% 0.25/0.69 (declare-fun tptp.produc1244821099reeRes (tptp.late_freeRes tptp.late_freeRes) tptp.produc1357834675reeRes)
% 0.25/0.69 (declare-fun tptp.eqvt_pi (tptp.set_Pr1834926343_pi_pi) Bool)
% 0.25/0.69 (declare-fun tptp.collec1051790738_pi_pi ((-> tptp.product_prod_pi_pi Bool)) tptp.set_Pr1834926343_pi_pi)
% 0.25/0.69 (declare-fun tptp.strong2129052853vative (tptp.pi tptp.pi tptp.late_subject tptp.name tptp.set_Pr1834926343_pi_pi) Bool)
% 0.25/0.69 (declare-fun tptp.strong743114133lation (tptp.pi tptp.set_Pr1834926343_pi_pi tptp.pi) Bool)
% 0.25/0.69 (declare-fun tptp.member558706512_pi_pi (tptp.product_prod_pi_pi tptp.set_Pr1834926343_pi_pi) Bool)
% 0.25/0.69 (declare-fun tptp.p () tptp.pi)
% 0.25/0.69 (declare-fun tptp.p2 () tptp.pi)
% 0.25/0.69 (declare-fun tptp.pxQ () tptp.pi)
% 0.25/0.69 (declare-fun tptp.q () tptp.pi)
% 0.25/0.69 (declare-fun tptp.rel () tptp.set_Pr1834926343_pi_pi)
% 0.25/0.69 (declare-fun tptp.aa () tptp.late_subject)
% 0.25/0.69 (declare-fun tptp.u () tptp.name)
% 0.25/0.69 (declare-fun tptp.x () tptp.name)
% 0.25/0.69 (declare-fun tptp.y () tptp.name)
% 0.25/0.69 (assert (not (= tptp.x tptp.u)))
% 0.25/0.69 (assert (let ((_let_1 (@ tptp.res tptp.x))) (= (@ (@ (@ tptp.subs (@ _let_1 tptp.q)) tptp.y) tptp.u) (@ _let_1 (@ (@ (@ tptp.subs tptp.q) tptp.y) tptp.u)))))
% 0.25/0.69 (assert (not (= tptp.y tptp.x)))
% 0.25/0.69 (assert (@ (@ tptp.fresh_name_pi tptp.x) (@ (@ (@ tptp.subs tptp.p2) tptp.y) tptp.u)))
% 0.25/0.69 (assert (@ tptp.eqvt_pi tptp.rel))
% 0.25/0.69 (assert (let ((_let_1 (@ tptp.res tptp.x))) (= (@ (@ (@ tptp.subs (@ _let_1 (@ (@ tptp.par tptp.p2) tptp.q))) tptp.y) tptp.u) (@ _let_1 (@ (@ tptp.par (@ (@ (@ tptp.subs tptp.p2) tptp.y) tptp.u)) (@ (@ (@ tptp.subs tptp.q) tptp.y) tptp.u))))))
% 0.25/0.69 (assert (@ (@ tptp.fresh_name_pi tptp.y) tptp.q))
% 0.25/0.69 (assert (@ (@ tptp.fresh_name_pi tptp.x) tptp.p2))
% 0.25/0.69 (assert (forall ((Y tptp.name) (R tptp.pi) (S tptp.pi)) (let ((_let_1 (@ tptp.res Y))) (let ((_let_2 (@ tptp.par R))) (=> (@ (@ tptp.fresh_name_pi Y) R) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi (@ _let_1 (@ _let_2 S))) (@ _let_2 (@ _let_1 S)))) tptp.rel))))))
% 0.25/0.69 (assert (forall ((Y tptp.name) (R tptp.pi) (Z tptp.name) (S tptp.pi)) (let ((_let_1 (@ tptp.res Y))) (let ((_let_2 (@ tptp.par R))) (let ((_let_3 (@ tptp.res Z))) (=> (@ (@ tptp.fresh_name_pi Y) R) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi (@ _let_1 (@ _let_3 (@ _let_2 S)))) (@ _let_3 (@ _let_2 (@ _let_1 S))))) tptp.rel)))))))
% 0.25/0.69 (assert (@ (@ tptp.fresh_name_pi tptp.y) (@ (@ tptp.res tptp.x) tptp.q)))
% 0.25/0.69 (assert (@ (@ tptp.fresh_name_pi tptp.x) tptp.p))
% 0.25/0.69 (assert (@ (@ tptp.fresh_name_pi tptp.y) (@ (@ tptp.par tptp.p) (@ (@ tptp.res tptp.x) tptp.q))))
% 0.25/0.69 (assert (@ (@ tptp.fresh_name_pi tptp.y) (@ (@ tptp.res tptp.x) (@ (@ tptp.par tptp.p) tptp.q))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (Q tptp.pi) (C tptp.name) (D tptp.name)) (= (@ (@ (@ tptp.subs (@ (@ tptp.par P) Q)) C) D) (@ (@ tptp.par (@ (@ (@ tptp.subs P) C) D)) (@ (@ (@ tptp.subs Q) C) D)))))
% 0.25/0.69 (assert (forall ((X tptp.name) (C tptp.name) (D tptp.name) (P tptp.pi)) (let ((_let_1 (@ tptp.res X))) (=> (not (= X C)) (=> (not (= X D)) (= (@ (@ (@ tptp.subs (@ _let_1 P)) C) D) (@ _let_1 (@ (@ (@ tptp.subs P) C) D))))))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (A tptp.name)) (= (@ (@ (@ tptp.subs P) A) A) P)))
% 0.25/0.69 (assert (forall ((X1 (-> tptp.name tptp.noption_pi)) (X2 tptp.late_freeRes) (Y1 (-> tptp.name tptp.noption_pi)) (Y2 tptp.late_freeRes)) (= (= (@ (@ tptp.produc1505598906reeRes X1) X2) (@ (@ tptp.produc1505598906reeRes Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.25/0.69 (assert (forall ((X1 (-> tptp.name tptp.noption_pi)) (X2 tptp.produc1141751126_pi_pi) (Y1 (-> tptp.name tptp.noption_pi)) (Y2 tptp.produc1141751126_pi_pi)) (= (= (@ (@ tptp.produc1275980869_pi_pi X1) X2) (@ (@ tptp.produc1275980869_pi_pi Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.25/0.69 (assert (forall ((X1 (-> tptp.name tptp.noption_pi)) (X2 tptp.name) (Y1 (-> tptp.name tptp.noption_pi)) (Y2 tptp.name)) (= (= (@ (@ tptp.produc540578151i_name X1) X2) (@ (@ tptp.produc540578151i_name Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.25/0.69 (assert (forall ((X1 (-> tptp.name tptp.noption_pi)) (X2 tptp.pi) (Y1 (-> tptp.name tptp.noption_pi)) (Y2 tptp.pi)) (= (= (@ (@ tptp.produc1820286517_pi_pi X1) X2) (@ (@ tptp.produc1820286517_pi_pi Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.25/0.69 (assert (forall ((X1 (-> tptp.name tptp.noption_pi)) (X2 (-> tptp.name tptp.noption_pi)) (Y1 (-> tptp.name tptp.noption_pi)) (Y2 (-> tptp.name tptp.noption_pi))) (= (= (@ (@ tptp.produc1342893193ion_pi X1) X2) (@ (@ tptp.produc1342893193ion_pi Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.25/0.69 (assert (forall ((X1 tptp.pi) (X2 tptp.pi) (Y1 tptp.pi) (Y2 tptp.pi)) (= (= (@ (@ tptp.product_Pair_pi_pi X1) X2) (@ (@ tptp.product_Pair_pi_pi Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.25/0.69 (assert (forall ((X1 tptp.name) (X2 tptp.product_prod_pi_pi) (Y1 tptp.name) (Y2 tptp.product_prod_pi_pi)) (= (= (@ (@ tptp.produc235456326_pi_pi X1) X2) (@ (@ tptp.produc235456326_pi_pi Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 0.25/0.69 (assert (forall ((A (-> tptp.name tptp.noption_pi)) (B tptp.late_freeRes) (A2 (-> tptp.name tptp.noption_pi)) (B2 tptp.late_freeRes)) (= (= (@ (@ tptp.produc1505598906reeRes A) B) (@ (@ tptp.produc1505598906reeRes A2) B2)) (and (= A A2) (= B B2)))))
% 0.25/0.69 (assert (forall ((A (-> tptp.name tptp.noption_pi)) (B tptp.produc1141751126_pi_pi) (A2 (-> tptp.name tptp.noption_pi)) (B2 tptp.produc1141751126_pi_pi)) (= (= (@ (@ tptp.produc1275980869_pi_pi A) B) (@ (@ tptp.produc1275980869_pi_pi A2) B2)) (and (= A A2) (= B B2)))))
% 0.25/0.69 (assert (forall ((A (-> tptp.name tptp.noption_pi)) (B tptp.name) (A2 (-> tptp.name tptp.noption_pi)) (B2 tptp.name)) (= (= (@ (@ tptp.produc540578151i_name A) B) (@ (@ tptp.produc540578151i_name A2) B2)) (and (= A A2) (= B B2)))))
% 0.25/0.69 (assert (forall ((A (-> tptp.name tptp.noption_pi)) (B tptp.pi) (A2 (-> tptp.name tptp.noption_pi)) (B2 tptp.pi)) (= (= (@ (@ tptp.produc1820286517_pi_pi A) B) (@ (@ tptp.produc1820286517_pi_pi A2) B2)) (and (= A A2) (= B B2)))))
% 0.25/0.69 (assert (forall ((A (-> tptp.name tptp.noption_pi)) (B (-> tptp.name tptp.noption_pi)) (A2 (-> tptp.name tptp.noption_pi)) (B2 (-> tptp.name tptp.noption_pi))) (= (= (@ (@ tptp.produc1342893193ion_pi A) B) (@ (@ tptp.produc1342893193ion_pi A2) B2)) (and (= A A2) (= B B2)))))
% 0.25/0.69 (assert (forall ((A tptp.pi) (B tptp.pi) (A2 tptp.pi) (B2 tptp.pi)) (= (= (@ (@ tptp.product_Pair_pi_pi A) B) (@ (@ tptp.product_Pair_pi_pi A2) B2)) (and (= A A2) (= B B2)))))
% 0.25/0.69 (assert (forall ((A tptp.name) (B tptp.product_prod_pi_pi) (A2 tptp.name) (B2 tptp.product_prod_pi_pi)) (= (= (@ (@ tptp.produc235456326_pi_pi A) B) (@ (@ tptp.produc235456326_pi_pi A2) B2)) (and (= A A2) (= B B2)))))
% 0.25/0.69 (assert (forall ((Pi1 tptp.pi) (Pi2 tptp.pi) (Name tptp.name) (Pi tptp.pi)) (not (= (@ (@ tptp.par Pi1) Pi2) (@ (@ tptp.res Name) Pi)))))
% 0.25/0.69 (assert (@ (@ tptp.fresh_name_pi tptp.y) tptp.p))
% 0.25/0.69 (assert (@ (@ tptp.fresh_1376661020_pi_pi tptp.y) (@ (@ tptp.produc235456326_pi_pi tptp.x) (@ (@ tptp.product_Pair_pi_pi tptp.p) tptp.q))))
% 0.25/0.69 (assert (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P tptp.pi) (Q tptp.pi)) (=> (forall ((R2 tptp.pi) (S2 tptp.pi)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi (@ (@ tptp.par R2) S2)) (@ (@ tptp.par S2) R2))) Rel)) (=> (forall ((R2 tptp.pi) (S2 tptp.pi) (X3 tptp.name)) (let ((_let_1 (@ tptp.res X3))) (=> (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi R2) S2)) Rel) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi (@ _let_1 R2)) (@ _let_1 S2))) Rel)))) (@ (@ (@ tptp.strong743114133lation (@ (@ tptp.par P) Q)) Rel) (@ (@ tptp.par Q) P))))))
% 0.25/0.69 (assert (forall ((B tptp.name) (P tptp.pi) (A tptp.name)) (=> (@ (@ tptp.fresh_name_pi B) P) (= (@ (@ tptp.res A) P) (@ (@ tptp.res B) (@ (@ (@ tptp.subs P) A) B))))))
% 0.25/0.69 (assert (forall ((B tptp.name) (P tptp.pi) (A tptp.name)) (=> (@ (@ tptp.fresh_name_pi B) P) (= (@ (@ (@ tptp.subs (@ (@ tptp.res A) P)) A) B) (@ (@ tptp.res B) (@ (@ (@ tptp.subs P) A) B))))))
% 0.25/0.69 (assert (@ (@ tptp.fresh_717452603ubject tptp.y) tptp.aa))
% 0.25/0.69 (assert (@ (@ tptp.fresh_717452603ubject tptp.x) tptp.aa))
% 0.25/0.69 (assert (forall ((A tptp.name) (X2 tptp.pi) (X1 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi A))) (= (@ _let_1 (@ (@ tptp.par X2) X1)) (and (@ _let_1 X2) (@ _let_1 X1))))))
% 0.25/0.69 (assert (forall ((X tptp.late_freeRes)) (not (forall ((C2 tptp.name)) (not (@ (@ tptp.fresh_1641682979reeRes C2) X))))))
% 0.25/0.69 (assert (forall ((X tptp.produc1141751126_pi_pi)) (not (forall ((C2 tptp.name)) (not (@ (@ tptp.fresh_1376661020_pi_pi C2) X))))))
% 0.25/0.69 (assert (forall ((X tptp.name)) (not (forall ((C2 tptp.name)) (not (@ (@ tptp.fresh_name_name C2) X))))))
% 0.25/0.69 (assert (forall ((X tptp.pi)) (not (forall ((C2 tptp.name)) (not (@ (@ tptp.fresh_name_pi C2) X))))))
% 0.25/0.69 (assert (forall ((A tptp.name) (P tptp.pi)) (@ (@ tptp.fresh_name_pi A) (@ (@ tptp.res A) P))))
% 0.25/0.69 (assert (forall ((A tptp.name) (B tptp.name) (P tptp.pi)) (=> (not (= A B)) (@ (@ tptp.fresh_name_pi A) (@ (@ (@ tptp.subs P) A) B)))))
% 0.25/0.69 (assert (forall ((A tptp.name) (P tptp.pi) (C tptp.name) (B tptp.name)) (let ((_let_1 (@ tptp.fresh_name_pi A))) (=> (@ _let_1 P) (=> (not (= A C)) (@ _let_1 (@ (@ (@ tptp.subs P) B) C)))))))
% 0.25/0.69 (assert (forall ((A tptp.name) (P tptp.pi) (B tptp.name)) (=> (@ (@ tptp.fresh_name_pi A) P) (= (@ (@ (@ tptp.subs P) A) B) P))))
% 0.25/0.69 (assert (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P tptp.pi) (Q tptp.pi) (R tptp.pi)) (let ((_let_1 (@ tptp.par P))) (=> (forall ((S2 tptp.pi) (T tptp.pi) (U tptp.pi)) (let ((_let_1 (@ tptp.par S2))) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi (@ (@ tptp.par (@ _let_1 T)) U)) (@ _let_1 (@ (@ tptp.par T) U)))) Rel))) (=> (forall ((S2 tptp.pi) (T tptp.pi) (X3 tptp.name)) (let ((_let_1 (@ tptp.res X3))) (=> (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi S2) T)) Rel) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi (@ _let_1 S2)) (@ _let_1 T))) Rel)))) (=> (forall ((S2 tptp.pi) (T tptp.pi) (U tptp.pi) (X3 tptp.name)) (let ((_let_1 (@ tptp.res X3))) (let ((_let_2 (@ tptp.par S2))) (=> (@ (@ tptp.fresh_name_pi X3) S2) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi (@ _let_1 (@ (@ tptp.par (@ _let_2 T)) U))) (@ _let_2 (@ _let_1 (@ (@ tptp.par T) U))))) Rel))))) (=> (forall ((S2 tptp.pi) (T tptp.pi) (U tptp.pi) (X3 tptp.name)) (let ((_let_1 (@ tptp.par S2))) (let ((_let_2 (@ tptp.res X3))) (=> (@ (@ tptp.fresh_name_pi X3) U) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi (@ (@ tptp.par (@ _let_2 (@ _let_1 T))) U)) (@ _let_2 (@ _let_1 (@ (@ tptp.par T) U))))) Rel))))) (@ (@ (@ tptp.strong743114133lation (@ (@ tptp.par (@ _let_1 Q)) R)) Rel) (@ _let_1 (@ (@ tptp.par Q) R))))))))))
% 0.25/0.69 (assert (forall ((P (-> tptp.produc1834551554reeRes Bool)) (Prod tptp.produc1834551554reeRes)) (=> (forall ((A3 (-> tptp.name tptp.noption_pi)) (B3 tptp.late_freeRes)) (@ P (@ (@ tptp.produc1505598906reeRes A3) B3))) (@ P Prod))))
% 0.25/0.69 (assert (forall ((P (-> tptp.produc53907987_pi_pi Bool)) (Prod tptp.produc53907987_pi_pi)) (=> (forall ((A3 (-> tptp.name tptp.noption_pi)) (B3 tptp.produc1141751126_pi_pi)) (@ P (@ (@ tptp.produc1275980869_pi_pi A3) B3))) (@ P Prod))))
% 0.25/0.69 (assert (forall ((P (-> tptp.produc405342261i_name Bool)) (Prod tptp.produc405342261i_name)) (=> (forall ((A3 (-> tptp.name tptp.noption_pi)) (B3 tptp.name)) (@ P (@ (@ tptp.produc540578151i_name A3) B3))) (@ P Prod))))
% 0.25/0.69 (assert (forall ((P (-> tptp.produc629157763_pi_pi Bool)) (Prod tptp.produc629157763_pi_pi)) (=> (forall ((A3 (-> tptp.name tptp.noption_pi)) (B3 tptp.pi)) (@ P (@ (@ tptp.produc1820286517_pi_pi A3) B3))) (@ P Prod))))
% 0.25/0.69 (assert (forall ((P (-> tptp.produc1462499409ion_pi Bool)) (Prod tptp.produc1462499409ion_pi)) (=> (forall ((A3 (-> tptp.name tptp.noption_pi)) (B3 (-> tptp.name tptp.noption_pi))) (@ P (@ (@ tptp.produc1342893193ion_pi A3) B3))) (@ P Prod))))
% 0.25/0.69 (assert (forall ((P (-> tptp.product_prod_pi_pi Bool)) (Prod tptp.product_prod_pi_pi)) (=> (forall ((A3 tptp.pi) (B3 tptp.pi)) (@ P (@ (@ tptp.product_Pair_pi_pi A3) B3))) (@ P Prod))))
% 0.25/0.69 (assert (forall ((P (-> tptp.produc1141751126_pi_pi Bool)) (Prod tptp.produc1141751126_pi_pi)) (=> (forall ((A3 tptp.name) (B3 tptp.product_prod_pi_pi)) (@ P (@ (@ tptp.produc235456326_pi_pi A3) B3))) (@ P Prod))))
% 0.25/0.69 (assert (forall ((Y tptp.produc1834551554reeRes)) (not (forall ((A3 (-> tptp.name tptp.noption_pi)) (B3 tptp.late_freeRes)) (not (= Y (@ (@ tptp.produc1505598906reeRes A3) B3)))))))
% 0.25/0.69 (assert (forall ((Y tptp.produc53907987_pi_pi)) (not (forall ((A3 (-> tptp.name tptp.noption_pi)) (B3 tptp.produc1141751126_pi_pi)) (not (= Y (@ (@ tptp.produc1275980869_pi_pi A3) B3)))))))
% 0.25/0.69 (assert (forall ((Y tptp.produc405342261i_name)) (not (forall ((A3 (-> tptp.name tptp.noption_pi)) (B3 tptp.name)) (not (= Y (@ (@ tptp.produc540578151i_name A3) B3)))))))
% 0.25/0.69 (assert (forall ((Y tptp.produc629157763_pi_pi)) (not (forall ((A3 (-> tptp.name tptp.noption_pi)) (B3 tptp.pi)) (not (= Y (@ (@ tptp.produc1820286517_pi_pi A3) B3)))))))
% 0.25/0.69 (assert (forall ((Y tptp.produc1462499409ion_pi)) (not (forall ((A3 (-> tptp.name tptp.noption_pi)) (B3 (-> tptp.name tptp.noption_pi))) (not (= Y (@ (@ tptp.produc1342893193ion_pi A3) B3)))))))
% 0.25/0.69 (assert (forall ((Y tptp.product_prod_pi_pi)) (not (forall ((A3 tptp.pi) (B3 tptp.pi)) (not (= Y (@ (@ tptp.product_Pair_pi_pi A3) B3)))))))
% 0.25/0.69 (assert (forall ((Y tptp.produc1141751126_pi_pi)) (not (forall ((A3 tptp.name) (B3 tptp.product_prod_pi_pi)) (not (= Y (@ (@ tptp.produc235456326_pi_pi A3) B3)))))))
% 0.25/0.69 (assert (forall ((P (-> tptp.produc53907987_pi_pi Bool)) (X tptp.produc53907987_pi_pi)) (=> (forall ((A3 (-> tptp.name tptp.noption_pi)) (B3 tptp.name) (C2 tptp.pi) (D2 tptp.pi)) (@ P (@ (@ tptp.produc1275980869_pi_pi A3) (@ (@ tptp.produc235456326_pi_pi B3) (@ (@ tptp.product_Pair_pi_pi C2) D2))))) (@ P X))))
% 0.25/0.69 (assert (forall ((P (-> tptp.produc53907987_pi_pi Bool)) (X tptp.produc53907987_pi_pi)) (=> (forall ((A3 (-> tptp.name tptp.noption_pi)) (B3 tptp.name) (C2 tptp.product_prod_pi_pi)) (@ P (@ (@ tptp.produc1275980869_pi_pi A3) (@ (@ tptp.produc235456326_pi_pi B3) C2)))) (@ P X))))
% 0.25/0.69 (assert (forall ((P (-> tptp.produc1141751126_pi_pi Bool)) (X tptp.produc1141751126_pi_pi)) (=> (forall ((A3 tptp.name) (B3 tptp.pi) (C2 tptp.pi)) (@ P (@ (@ tptp.produc235456326_pi_pi A3) (@ (@ tptp.product_Pair_pi_pi B3) C2)))) (@ P X))))
% 0.25/0.69 (assert (forall ((Y tptp.produc53907987_pi_pi)) (not (forall ((A3 (-> tptp.name tptp.noption_pi)) (B3 tptp.name) (C2 tptp.pi) (D2 tptp.pi)) (not (= Y (@ (@ tptp.produc1275980869_pi_pi A3) (@ (@ tptp.produc235456326_pi_pi B3) (@ (@ tptp.product_Pair_pi_pi C2) D2)))))))))
% 0.25/0.69 (assert (forall ((A tptp.product_prod_pi_pi) (P (-> tptp.product_prod_pi_pi Bool))) (= (@ (@ tptp.member558706512_pi_pi A) (@ tptp.collec1051790738_pi_pi P)) (@ P A))))
% 0.25/0.69 (assert (forall ((A4 tptp.set_Pr1834926343_pi_pi)) (= (@ tptp.collec1051790738_pi_pi (lambda ((X4 tptp.product_prod_pi_pi)) (@ (@ tptp.member558706512_pi_pi X4) A4))) A4)))
% 0.25/0.69 (assert (forall ((P (-> tptp.product_prod_pi_pi Bool)) (Q (-> tptp.product_prod_pi_pi Bool))) (=> (forall ((X3 tptp.product_prod_pi_pi)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collec1051790738_pi_pi P) (@ tptp.collec1051790738_pi_pi Q)))))
% 0.25/0.69 (assert (forall ((Y tptp.produc53907987_pi_pi)) (not (forall ((A3 (-> tptp.name tptp.noption_pi)) (B3 tptp.name) (C2 tptp.product_prod_pi_pi)) (not (= Y (@ (@ tptp.produc1275980869_pi_pi A3) (@ (@ tptp.produc235456326_pi_pi B3) C2))))))))
% 0.25/0.69 (assert (forall ((Y tptp.produc1141751126_pi_pi)) (not (forall ((A3 tptp.name) (B3 tptp.pi) (C2 tptp.pi)) (not (= Y (@ (@ tptp.produc235456326_pi_pi A3) (@ (@ tptp.product_Pair_pi_pi B3) C2))))))))
% 0.25/0.69 (assert (forall ((A (-> tptp.name tptp.noption_pi)) (B tptp.late_freeRes) (A2 (-> tptp.name tptp.noption_pi)) (B2 tptp.late_freeRes)) (=> (= (@ (@ tptp.produc1505598906reeRes A) B) (@ (@ tptp.produc1505598906reeRes A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 0.25/0.69 (assert (forall ((A (-> tptp.name tptp.noption_pi)) (B tptp.produc1141751126_pi_pi) (A2 (-> tptp.name tptp.noption_pi)) (B2 tptp.produc1141751126_pi_pi)) (=> (= (@ (@ tptp.produc1275980869_pi_pi A) B) (@ (@ tptp.produc1275980869_pi_pi A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 0.25/0.69 (assert (forall ((A (-> tptp.name tptp.noption_pi)) (B tptp.name) (A2 (-> tptp.name tptp.noption_pi)) (B2 tptp.name)) (=> (= (@ (@ tptp.produc540578151i_name A) B) (@ (@ tptp.produc540578151i_name A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 0.25/0.69 (assert (forall ((A (-> tptp.name tptp.noption_pi)) (B tptp.pi) (A2 (-> tptp.name tptp.noption_pi)) (B2 tptp.pi)) (=> (= (@ (@ tptp.produc1820286517_pi_pi A) B) (@ (@ tptp.produc1820286517_pi_pi A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 0.25/0.69 (assert (forall ((A (-> tptp.name tptp.noption_pi)) (B (-> tptp.name tptp.noption_pi)) (A2 (-> tptp.name tptp.noption_pi)) (B2 (-> tptp.name tptp.noption_pi))) (=> (= (@ (@ tptp.produc1342893193ion_pi A) B) (@ (@ tptp.produc1342893193ion_pi A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 0.25/0.69 (assert (forall ((A tptp.pi) (B tptp.pi) (A2 tptp.pi) (B2 tptp.pi)) (=> (= (@ (@ tptp.product_Pair_pi_pi A) B) (@ (@ tptp.product_Pair_pi_pi A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 0.25/0.69 (assert (forall ((A tptp.name) (B tptp.product_prod_pi_pi) (A2 tptp.name) (B2 tptp.product_prod_pi_pi)) (=> (= (@ (@ tptp.produc235456326_pi_pi A) B) (@ (@ tptp.produc235456326_pi_pi A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 0.25/0.69 (assert (forall ((P (-> tptp.produc1834551554reeRes Bool)) (P2 tptp.produc1834551554reeRes)) (=> (forall ((A3 (-> tptp.name tptp.noption_pi)) (B3 tptp.late_freeRes)) (@ P (@ (@ tptp.produc1505598906reeRes A3) B3))) (@ P P2))))
% 0.25/0.69 (assert (forall ((P (-> tptp.produc53907987_pi_pi Bool)) (P2 tptp.produc53907987_pi_pi)) (=> (forall ((A3 (-> tptp.name tptp.noption_pi)) (B3 tptp.produc1141751126_pi_pi)) (@ P (@ (@ tptp.produc1275980869_pi_pi A3) B3))) (@ P P2))))
% 0.25/0.69 (assert (forall ((P (-> tptp.produc405342261i_name Bool)) (P2 tptp.produc405342261i_name)) (=> (forall ((A3 (-> tptp.name tptp.noption_pi)) (B3 tptp.name)) (@ P (@ (@ tptp.produc540578151i_name A3) B3))) (@ P P2))))
% 0.25/0.69 (assert (forall ((P (-> tptp.produc629157763_pi_pi Bool)) (P2 tptp.produc629157763_pi_pi)) (=> (forall ((A3 (-> tptp.name tptp.noption_pi)) (B3 tptp.pi)) (@ P (@ (@ tptp.produc1820286517_pi_pi A3) B3))) (@ P P2))))
% 0.25/0.69 (assert (forall ((P (-> tptp.produc1462499409ion_pi Bool)) (P2 tptp.produc1462499409ion_pi)) (=> (forall ((A3 (-> tptp.name tptp.noption_pi)) (B3 (-> tptp.name tptp.noption_pi))) (@ P (@ (@ tptp.produc1342893193ion_pi A3) B3))) (@ P P2))))
% 0.25/0.69 (assert (forall ((P (-> tptp.product_prod_pi_pi Bool)) (P2 tptp.product_prod_pi_pi)) (=> (forall ((A3 tptp.pi) (B3 tptp.pi)) (@ P (@ (@ tptp.product_Pair_pi_pi A3) B3))) (@ P P2))))
% 0.25/0.69 (assert (forall ((P (-> tptp.produc1141751126_pi_pi Bool)) (P2 tptp.produc1141751126_pi_pi)) (=> (forall ((A3 tptp.name) (B3 tptp.product_prod_pi_pi)) (@ P (@ (@ tptp.produc235456326_pi_pi A3) B3))) (@ P P2))))
% 0.25/0.69 (assert (forall ((P2 tptp.produc1834551554reeRes)) (exists ((X3 (-> tptp.name tptp.noption_pi)) (Y3 tptp.late_freeRes)) (= P2 (@ (@ tptp.produc1505598906reeRes X3) Y3)))))
% 0.25/0.69 (assert (forall ((P2 tptp.produc53907987_pi_pi)) (exists ((X3 (-> tptp.name tptp.noption_pi)) (Y3 tptp.produc1141751126_pi_pi)) (= P2 (@ (@ tptp.produc1275980869_pi_pi X3) Y3)))))
% 0.25/0.69 (assert (forall ((P2 tptp.produc405342261i_name)) (exists ((X3 (-> tptp.name tptp.noption_pi)) (Y3 tptp.name)) (= P2 (@ (@ tptp.produc540578151i_name X3) Y3)))))
% 0.25/0.69 (assert (forall ((P2 tptp.produc629157763_pi_pi)) (exists ((X3 (-> tptp.name tptp.noption_pi)) (Y3 tptp.pi)) (= P2 (@ (@ tptp.produc1820286517_pi_pi X3) Y3)))))
% 0.25/0.69 (assert (forall ((P2 tptp.produc1462499409ion_pi)) (exists ((X3 (-> tptp.name tptp.noption_pi)) (Y3 (-> tptp.name tptp.noption_pi))) (= P2 (@ (@ tptp.produc1342893193ion_pi X3) Y3)))))
% 0.25/0.69 (assert (forall ((P2 tptp.product_prod_pi_pi)) (exists ((X3 tptp.pi) (Y3 tptp.pi)) (= P2 (@ (@ tptp.product_Pair_pi_pi X3) Y3)))))
% 0.25/0.69 (assert (forall ((P2 tptp.produc1141751126_pi_pi)) (exists ((X3 tptp.name) (Y3 tptp.product_prod_pi_pi)) (= P2 (@ (@ tptp.produc235456326_pi_pi X3) Y3)))))
% 0.25/0.69 (assert (forall ((X2 tptp.pi) (X1 tptp.pi) (Y2 tptp.pi) (Y1 tptp.pi)) (= (= (@ (@ tptp.par X2) X1) (@ (@ tptp.par Y2) Y1)) (and (= X2 Y2) (= X1 Y1)))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X tptp.late_freeRes) (Y tptp.late_freeRes)) (let ((_let_1 (@ tptp.fresh_1641682979reeRes A))) (= (@ (@ tptp.fresh_493808761reeRes A) (@ (@ tptp.produc1244821099reeRes X) Y)) (and (@ _let_1 X) (@ _let_1 Y))))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X tptp.late_freeRes) (Y tptp.name)) (= (@ (@ tptp.fresh_2007541374s_name A) (@ (@ tptp.produc1701355766s_name X) Y)) (and (@ (@ tptp.fresh_1641682979reeRes A) X) (@ (@ tptp.fresh_name_name A) Y)))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X tptp.late_freeRes) (Y tptp.pi)) (= (@ (@ tptp.fresh_1847501388Res_pi A) (@ (@ tptp.produc1177552196Res_pi X) Y)) (and (@ (@ tptp.fresh_1641682979reeRes A) X) (@ (@ tptp.fresh_name_pi A) Y)))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X tptp.name) (Y tptp.late_freeRes)) (= (@ (@ tptp.fresh_1963366730reeRes A) (@ (@ tptp.produc1531804426reeRes X) Y)) (and (@ (@ tptp.fresh_name_name A) X) (@ (@ tptp.fresh_1641682979reeRes A) Y)))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X tptp.name) (Y tptp.name)) (let ((_let_1 (@ tptp.fresh_name_name A))) (= (@ (@ tptp.fresh_441084397e_name A) (@ (@ tptp.produc1570949143e_name X) Y)) (and (@ _let_1 X) (@ _let_1 Y))))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X tptp.name) (Y tptp.pi)) (= (@ (@ tptp.fresh_93646139ame_pi A) (@ (@ tptp.product_Pair_name_pi X) Y)) (and (@ (@ tptp.fresh_name_name A) X) (@ (@ tptp.fresh_name_pi A) Y)))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X tptp.pi) (Y tptp.late_freeRes)) (= (@ (@ tptp.fresh_1504024600reeRes A) (@ (@ tptp.produc1638681944reeRes X) Y)) (and (@ (@ tptp.fresh_name_pi A) X) (@ (@ tptp.fresh_1641682979reeRes A) Y)))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X tptp.pi) (Y tptp.name)) (= (@ (@ tptp.fresh_261416607i_name A) (@ (@ tptp.product_Pair_pi_name X) Y)) (and (@ (@ tptp.fresh_name_pi A) X) (@ (@ tptp.fresh_name_name A) Y)))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X tptp.pi) (Y tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi A))) (= (@ (@ tptp.fresh_1627595501_pi_pi A) (@ (@ tptp.product_Pair_pi_pi X) Y)) (and (@ _let_1 X) (@ _let_1 Y))))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X tptp.name) (Y tptp.product_prod_pi_pi)) (= (@ (@ tptp.fresh_1376661020_pi_pi A) (@ (@ tptp.produc235456326_pi_pi X) Y)) (and (@ (@ tptp.fresh_name_name A) X) (@ (@ tptp.fresh_1627595501_pi_pi A) Y)))))
% 0.25/0.69 (assert (forall ((B tptp.name) (P tptp.pi) (A tptp.name) (C tptp.name)) (let ((_let_1 (@ (@ tptp.subs P) A))) (=> (@ (@ tptp.fresh_name_pi B) P) (= (@ (@ (@ tptp.subs (@ _let_1 B)) B) C) (@ _let_1 C))))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X (-> tptp.name tptp.noption_pi)) (Y tptp.late_freeRes)) (=> (@ (@ tptp.fresh_1711070152reeRes A) (@ (@ tptp.produc1505598906reeRes X) Y)) (@ (@ tptp.fresh_543891186ion_pi A) X))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X (-> tptp.name tptp.noption_pi)) (Y tptp.produc1141751126_pi_pi)) (=> (@ (@ tptp.fresh_975559885_pi_pi A) (@ (@ tptp.produc1275980869_pi_pi X) Y)) (@ (@ tptp.fresh_543891186ion_pi A) X))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X (-> tptp.name tptp.noption_pi)) (Y tptp.name)) (=> (@ (@ tptp.fresh_453496559i_name A) (@ (@ tptp.produc540578151i_name X) Y)) (@ (@ tptp.fresh_543891186ion_pi A) X))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X (-> tptp.name tptp.noption_pi)) (Y tptp.pi)) (=> (@ (@ tptp.fresh_253309757_pi_pi A) (@ (@ tptp.produc1820286517_pi_pi X) Y)) (@ (@ tptp.fresh_543891186ion_pi A) X))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X (-> tptp.name tptp.noption_pi)) (Y (-> tptp.name tptp.noption_pi))) (=> (@ (@ tptp.fresh_225680151ion_pi A) (@ (@ tptp.produc1342893193ion_pi X) Y)) (@ (@ tptp.fresh_543891186ion_pi A) X))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X tptp.pi) (Y tptp.pi)) (=> (@ (@ tptp.fresh_1627595501_pi_pi A) (@ (@ tptp.product_Pair_pi_pi X) Y)) (@ (@ tptp.fresh_name_pi A) X))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X tptp.name) (Y tptp.product_prod_pi_pi)) (=> (@ (@ tptp.fresh_1376661020_pi_pi A) (@ (@ tptp.produc235456326_pi_pi X) Y)) (@ (@ tptp.fresh_name_name A) X))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X (-> tptp.name tptp.noption_pi)) (Y tptp.late_freeRes)) (=> (@ (@ tptp.fresh_1711070152reeRes A) (@ (@ tptp.produc1505598906reeRes X) Y)) (@ (@ tptp.fresh_1641682979reeRes A) Y))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X (-> tptp.name tptp.noption_pi)) (Y tptp.produc1141751126_pi_pi)) (=> (@ (@ tptp.fresh_975559885_pi_pi A) (@ (@ tptp.produc1275980869_pi_pi X) Y)) (@ (@ tptp.fresh_1376661020_pi_pi A) Y))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X (-> tptp.name tptp.noption_pi)) (Y tptp.name)) (=> (@ (@ tptp.fresh_453496559i_name A) (@ (@ tptp.produc540578151i_name X) Y)) (@ (@ tptp.fresh_name_name A) Y))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X (-> tptp.name tptp.noption_pi)) (Y tptp.pi)) (=> (@ (@ tptp.fresh_253309757_pi_pi A) (@ (@ tptp.produc1820286517_pi_pi X) Y)) (@ (@ tptp.fresh_name_pi A) Y))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X (-> tptp.name tptp.noption_pi)) (Y (-> tptp.name tptp.noption_pi))) (=> (@ (@ tptp.fresh_225680151ion_pi A) (@ (@ tptp.produc1342893193ion_pi X) Y)) (@ (@ tptp.fresh_543891186ion_pi A) Y))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X tptp.pi) (Y tptp.pi)) (=> (@ (@ tptp.fresh_1627595501_pi_pi A) (@ (@ tptp.product_Pair_pi_pi X) Y)) (@ (@ tptp.fresh_name_pi A) Y))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X tptp.name) (Y tptp.product_prod_pi_pi)) (=> (@ (@ tptp.fresh_1376661020_pi_pi A) (@ (@ tptp.produc235456326_pi_pi X) Y)) (@ (@ tptp.fresh_1627595501_pi_pi A) Y))))
% 0.25/0.69 (assert (@ (@ tptp.late_transitions (@ (@ tptp.par tptp.p) (@ (@ tptp.res tptp.x) tptp.q))) (@ (@ (@ tptp.late_BoundR tptp.aa) tptp.y) tptp.pxQ)))
% 0.25/0.69 (assert (let ((_let_1 (@ tptp.res tptp.x))) (@ (@ tptp.late_transitions (@ _let_1 (@ (@ tptp.par tptp.p) tptp.q))) (@ (@ (@ tptp.late_BoundR tptp.aa) tptp.y) (@ _let_1 (@ (@ tptp.par tptp.p2) tptp.q))))))
% 0.25/0.69 (assert (@ (@ tptp.late_transitions tptp.p) (@ (@ (@ tptp.late_BoundR tptp.aa) tptp.y) tptp.p2)))
% 0.25/0.69 (assert (@ (@ tptp.late_transitions (@ (@ tptp.par tptp.p) tptp.q)) (@ (@ (@ tptp.late_BoundR tptp.aa) tptp.y) (@ (@ tptp.par tptp.p2) tptp.q))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (A tptp.late_subject) (X tptp.name) (P3 tptp.pi) (Y tptp.name)) (let ((_let_1 (@ tptp.fresh_name_pi Y))) (=> (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR A) X) P3)) (=> (@ _let_1 P) (=> (not (= Y X)) (@ _let_1 P3)))))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (Rs tptp.late_residual) (X tptp.name)) (=> (@ (@ tptp.late_transitions P) Rs) (=> (@ (@ tptp.fresh_name_pi X) P) (@ (@ tptp.fresh_81631222sidual X) Rs)))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (Q tptp.pi) (A tptp.late_subject) (X tptp.name) (PQ tptp.pi) (Prop (-> tptp.pi Bool))) (let ((_let_1 (@ tptp.fresh_name_pi X))) (=> (@ (@ tptp.late_transitions (@ (@ tptp.par P) Q)) (@ (@ (@ tptp.late_BoundR A) X) PQ)) (=> (@ _let_1 P) (=> (@ _let_1 Q) (=> (forall ((P4 tptp.pi)) (=> (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR A) X) P4)) (@ Prop (@ (@ tptp.par P4) Q)))) (=> (forall ((Q2 tptp.pi)) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR A) X) Q2)) (@ Prop (@ (@ tptp.par P) Q2)))) (@ Prop PQ)))))))))
% 0.25/0.69 (assert (forall ((Q tptp.pi) (A tptp.late_subject) (X tptp.name) (Q3 tptp.pi) (P tptp.pi)) (let ((_let_1 (@ tptp.par P))) (let ((_let_2 (@ (@ tptp.late_BoundR A) X))) (=> (@ (@ tptp.late_transitions Q) (@ _let_2 Q3)) (=> (@ (@ tptp.fresh_name_pi X) P) (@ (@ tptp.late_transitions (@ _let_1 Q)) (@ _let_2 (@ _let_1 Q3)))))))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (A tptp.late_subject) (X tptp.name) (P3 tptp.pi) (Q tptp.pi)) (let ((_let_1 (@ (@ tptp.late_BoundR A) X))) (=> (@ (@ tptp.late_transitions P) (@ _let_1 P3)) (=> (@ (@ tptp.fresh_name_pi X) Q) (@ (@ tptp.late_transitions (@ (@ tptp.par P) Q)) (@ _let_1 (@ (@ tptp.par P3) Q))))))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (A tptp.late_subject) (X tptp.name) (P3 tptp.pi) (Y tptp.name)) (let ((_let_1 (@ tptp.res Y))) (let ((_let_2 (@ (@ tptp.late_BoundR A) X))) (=> (@ (@ tptp.late_transitions P) (@ _let_2 P3)) (=> (@ (@ tptp.fresh_717452603ubject Y) A) (=> (not (= Y X)) (@ (@ tptp.late_transitions (@ _let_1 P)) (@ _let_2 (@ _let_1 P3))))))))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (A tptp.late_subject) (X tptp.name) (P3 tptp.pi) (Y tptp.name)) (=> (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR A) X) P3)) (=> (@ (@ tptp.fresh_name_pi Y) P) (@ (@ tptp.fresh_717452603ubject Y) A)))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (A tptp.late_subject) (X tptp.name) (P3 tptp.pi) (Y tptp.name)) (let ((_let_1 (@ tptp.res Y))) (let ((_let_2 (@ (@ tptp.late_BoundR A) X))) (=> (@ (@ tptp.late_transitions P) (@ _let_2 P3)) (=> (@ (@ tptp.fresh_717452603ubject Y) A) (=> (not (= Y X)) (=> (@ (@ tptp.fresh_name_pi X) P) (=> (@ (@ tptp.fresh_717452603ubject X) A) (@ (@ tptp.late_transitions (@ _let_1 P)) (@ _let_2 (@ _let_1 P3))))))))))))
% 0.25/0.69 (assert (forall ((Q tptp.pi) (A tptp.late_subject) (X tptp.name) (Q3 tptp.pi) (P tptp.pi)) (let ((_let_1 (@ tptp.par P))) (let ((_let_2 (@ (@ tptp.late_BoundR A) X))) (let ((_let_3 (@ tptp.fresh_name_pi X))) (=> (@ (@ tptp.late_transitions Q) (@ _let_2 Q3)) (=> (@ _let_3 P) (=> (@ _let_3 Q) (=> (@ (@ tptp.fresh_717452603ubject X) A) (@ (@ tptp.late_transitions (@ _let_1 Q)) (@ _let_2 (@ _let_1 Q3))))))))))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (A tptp.late_subject) (X tptp.name) (P3 tptp.pi) (Q tptp.pi)) (let ((_let_1 (@ (@ tptp.late_BoundR A) X))) (let ((_let_2 (@ tptp.fresh_name_pi X))) (=> (@ (@ tptp.late_transitions P) (@ _let_1 P3)) (=> (@ _let_2 P) (=> (@ _let_2 Q) (=> (@ (@ tptp.fresh_717452603ubject X) A) (@ (@ tptp.late_transitions (@ (@ tptp.par P) Q)) (@ _let_1 (@ (@ tptp.par P3) Q)))))))))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (Q tptp.pi) (B tptp.late_subject) (Y tptp.name) (P3 tptp.pi)) (=> (@ (@ tptp.late_transitions (@ (@ tptp.par P) Q)) (@ (@ (@ tptp.late_BoundR B) Y) P3)) (=> (forall ((P5 tptp.pi) (A3 tptp.late_subject) (X3 tptp.name) (P4 tptp.pi) (Q4 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi X3))) (let ((_let_2 (@ (@ tptp.late_BoundR A3) X3))) (=> (= (@ (@ tptp.par P) Q) (@ (@ tptp.par P5) Q4)) (=> (= (@ (@ (@ tptp.late_BoundR B) Y) P3) (@ _let_2 (@ (@ tptp.par P4) Q4))) (=> (@ (@ tptp.late_transitions P5) (@ _let_2 P4)) (=> (@ _let_1 P5) (=> (@ _let_1 Q4) (not (@ (@ tptp.fresh_717452603ubject X3) A3)))))))))) (not (forall ((Q4 tptp.pi) (A3 tptp.late_subject) (X3 tptp.name) (Q2 tptp.pi) (P5 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi X3))) (let ((_let_2 (@ (@ tptp.late_BoundR A3) X3))) (let ((_let_3 (@ tptp.par P5))) (=> (= (@ (@ tptp.par P) Q) (@ _let_3 Q4)) (=> (= (@ (@ (@ tptp.late_BoundR B) Y) P3) (@ _let_2 (@ _let_3 Q2))) (=> (@ (@ tptp.late_transitions Q4) (@ _let_2 Q2)) (=> (@ _let_1 P5) (=> (@ _let_1 Q4) (not (@ (@ tptp.fresh_717452603ubject X3) A3))))))))))))))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (Rel tptp.set_Pr1834926343_pi_pi) (Q tptp.pi) (A tptp.late_subject) (X tptp.name) (Q3 tptp.pi)) (=> (@ (@ (@ tptp.strong743114133lation P) Rel) Q) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR A) X) Q3)) (=> (@ (@ tptp.fresh_name_pi X) P) (exists ((P4 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR A) X) P4)) (@ (@ (@ (@ (@ tptp.strong2129052853vative P4) Q3) A) X) Rel))))))))
% 0.25/0.69 (assert (forall ((Rel tptp.set_Pr1834926343_pi_pi) (Q tptp.pi) (P tptp.pi) (C3 tptp.late_freeRes)) (=> (@ tptp.eqvt_pi Rel) (=> (forall ((A3 tptp.late_subject) (X3 tptp.name) (Q2 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi X3))) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR A3) X3) Q2)) (=> (@ _let_1 P) (=> (@ _let_1 Q) (=> (@ (@ tptp.fresh_717452603ubject X3) A3) (=> (@ (@ tptp.fresh_1641682979reeRes X3) C3) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR A3) X3) P6)) (@ (@ (@ (@ (@ tptp.strong2129052853vative P6) Q2) A3) X3) Rel)))))))))) (=> (forall ((Alpha tptp.late_freeRes) (Q2 tptp.pi)) (=> (@ (@ tptp.late_transitions Q) (@ (@ tptp.late_FreeR Alpha) Q2)) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR Alpha) P6)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P6) Q2)) Rel))))) (@ (@ (@ tptp.strong743114133lation P) Rel) Q))))))
% 0.25/0.69 (assert (forall ((Rel tptp.set_Pr1834926343_pi_pi) (Q tptp.pi) (P tptp.pi) (C3 tptp.produc1141751126_pi_pi)) (=> (@ tptp.eqvt_pi Rel) (=> (forall ((A3 tptp.late_subject) (X3 tptp.name) (Q2 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi X3))) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR A3) X3) Q2)) (=> (@ _let_1 P) (=> (@ _let_1 Q) (=> (@ (@ tptp.fresh_717452603ubject X3) A3) (=> (@ (@ tptp.fresh_1376661020_pi_pi X3) C3) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR A3) X3) P6)) (@ (@ (@ (@ (@ tptp.strong2129052853vative P6) Q2) A3) X3) Rel)))))))))) (=> (forall ((Alpha tptp.late_freeRes) (Q2 tptp.pi)) (=> (@ (@ tptp.late_transitions Q) (@ (@ tptp.late_FreeR Alpha) Q2)) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR Alpha) P6)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P6) Q2)) Rel))))) (@ (@ (@ tptp.strong743114133lation P) Rel) Q))))))
% 0.25/0.69 (assert (forall ((Rel tptp.set_Pr1834926343_pi_pi) (Q tptp.pi) (P tptp.pi) (C3 tptp.name)) (=> (@ tptp.eqvt_pi Rel) (=> (forall ((A3 tptp.late_subject) (X3 tptp.name) (Q2 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi X3))) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR A3) X3) Q2)) (=> (@ _let_1 P) (=> (@ _let_1 Q) (=> (@ (@ tptp.fresh_717452603ubject X3) A3) (=> (@ (@ tptp.fresh_name_name X3) C3) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR A3) X3) P6)) (@ (@ (@ (@ (@ tptp.strong2129052853vative P6) Q2) A3) X3) Rel)))))))))) (=> (forall ((Alpha tptp.late_freeRes) (Q2 tptp.pi)) (=> (@ (@ tptp.late_transitions Q) (@ (@ tptp.late_FreeR Alpha) Q2)) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR Alpha) P6)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P6) Q2)) Rel))))) (@ (@ (@ tptp.strong743114133lation P) Rel) Q))))))
% 0.25/0.69 (assert (forall ((Rel tptp.set_Pr1834926343_pi_pi) (Q tptp.pi) (P tptp.pi) (C3 tptp.pi)) (=> (@ tptp.eqvt_pi Rel) (=> (forall ((A3 tptp.late_subject) (X3 tptp.name) (Q2 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi X3))) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR A3) X3) Q2)) (=> (@ _let_1 P) (=> (@ _let_1 Q) (=> (@ (@ tptp.fresh_717452603ubject X3) A3) (=> (@ _let_1 C3) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR A3) X3) P6)) (@ (@ (@ (@ (@ tptp.strong2129052853vative P6) Q2) A3) X3) Rel)))))))))) (=> (forall ((Alpha tptp.late_freeRes) (Q2 tptp.pi)) (=> (@ (@ tptp.late_transitions Q) (@ (@ tptp.late_FreeR Alpha) Q2)) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR Alpha) P6)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P6) Q2)) Rel))))) (@ (@ (@ tptp.strong743114133lation P) Rel) Q))))))
% 0.25/0.69 (assert (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P tptp.pi)) (=> (forall ((Q4 tptp.pi)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi (@ (@ tptp.par Q4) tptp.piNil)) Q4)) Rel)) (@ (@ (@ tptp.strong743114133lation (@ (@ tptp.par P) tptp.piNil)) Rel) P))))
% 0.25/0.69 (assert (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P tptp.pi)) (=> (forall ((Q4 tptp.pi)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi Q4) (@ (@ tptp.par Q4) tptp.piNil))) Rel)) (@ (@ (@ tptp.strong743114133lation P) Rel) (@ (@ tptp.par P) tptp.piNil)))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X tptp.name) (P tptp.pi) (B tptp.late_subject) (Y tptp.name) (P3 tptp.pi)) (=> (@ (@ tptp.late_transitions (@ (@ (@ tptp.input A) X) P)) (@ (@ (@ tptp.late_BoundR B) Y) P3)) (not (@ (@ tptp.fresh_717452603ubject A) B)))))
% 0.25/0.69 (assert (forall ((X tptp.name) (P tptp.pi) (A tptp.late_subject) (Y tptp.name) (P3 tptp.pi)) (not (@ (@ tptp.late_transitions (@ (@ tptp.res X) (@ tptp.tau P))) (@ (@ (@ tptp.late_BoundR A) Y) P3)))))
% 0.25/0.69 (assert (forall ((A tptp.name)) (@ (@ tptp.fresh_name_pi A) tptp.piNil)))
% 0.25/0.69 (assert (forall ((A tptp.name) (X1 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi A))) (= (@ _let_1 (@ tptp.tau X1)) (@ _let_1 X1)))))
% 0.25/0.69 (assert (forall ((C tptp.name) (D tptp.name)) (= (@ (@ (@ tptp.subs tptp.piNil) C) D) tptp.piNil)))
% 0.25/0.69 (assert (forall ((P tptp.pi) (C tptp.name) (D tptp.name)) (= (@ (@ (@ tptp.subs (@ tptp.tau P)) C) D) (@ tptp.tau (@ (@ (@ tptp.subs P) C) D)))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X2 tptp.late_freeRes) (X1 tptp.pi)) (= (@ (@ tptp.fresh_81631222sidual A) (@ (@ tptp.late_FreeR X2) X1)) (and (@ (@ tptp.fresh_1641682979reeRes A) X2) (@ (@ tptp.fresh_name_pi A) X1)))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X tptp.name) (P tptp.pi) (Alpha2 tptp.late_freeRes) (P3 tptp.pi)) (not (@ (@ tptp.late_transitions (@ (@ (@ tptp.input A) X) P)) (@ (@ tptp.late_FreeR Alpha2) P3)))))
% 0.25/0.69 (assert (forall ((X2 tptp.late_freeRes) (X1 tptp.pi) (Y2 tptp.late_freeRes) (Y1 tptp.pi)) (= (= (@ (@ tptp.late_FreeR X2) X1) (@ (@ tptp.late_FreeR Y2) Y1)) (and (= X2 Y2) (= X1 Y1)))))
% 0.25/0.69 (assert (forall ((Rel tptp.set_Pr1834926343_pi_pi) (A tptp.name) (X tptp.name) (P tptp.pi)) (not (@ (@ (@ tptp.strong743114133lation tptp.piNil) Rel) (@ (@ (@ tptp.input A) X) P)))))
% 0.25/0.69 (assert (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P tptp.pi)) (not (@ (@ (@ tptp.strong743114133lation tptp.piNil) Rel) (@ tptp.tau P)))))
% 0.25/0.69 (assert (forall ((Pi tptp.pi)) (not (= tptp.piNil (@ tptp.tau Pi)))))
% 0.25/0.69 (assert (forall ((Name1 tptp.name) (Name2 tptp.name) (Pi tptp.pi)) (not (= tptp.piNil (@ (@ (@ tptp.input Name1) Name2) Pi)))))
% 0.25/0.69 (assert (forall ((Pi3 tptp.pi) (Name1 tptp.name) (Name2 tptp.name) (Pi tptp.pi)) (not (= (@ tptp.tau Pi3) (@ (@ (@ tptp.input Name1) Name2) Pi)))))
% 0.25/0.69 (assert (forall ((X1 tptp.pi) (Y1 tptp.pi)) (= (= (@ tptp.tau X1) (@ tptp.tau Y1)) (= X1 Y1))))
% 0.25/0.69 (assert (forall ((X tptp.name) (A tptp.name) (Y tptp.name) (P tptp.pi) (Alpha2 tptp.late_freeRes) (P3 tptp.pi)) (not (@ (@ tptp.late_transitions (@ (@ tptp.res X) (@ (@ (@ tptp.input A) Y) P))) (@ (@ tptp.late_FreeR Alpha2) P3)))))
% 0.25/0.69 (assert (forall ((Subject tptp.late_subject) (Name3 tptp.name) (Pi3 tptp.pi) (FreeRes tptp.late_freeRes) (Pi tptp.pi)) (not (= (@ (@ (@ tptp.late_BoundR Subject) Name3) Pi3) (@ (@ tptp.late_FreeR FreeRes) Pi)))))
% 0.25/0.69 (assert (forall ((P (-> tptp.late_residual Bool)) (Residual tptp.late_residual)) (=> (forall ((Subject2 tptp.late_subject) (Name4 tptp.name) (Pi4 tptp.pi)) (@ P (@ (@ (@ tptp.late_BoundR Subject2) Name4) Pi4))) (=> (forall ((FreeRes2 tptp.late_freeRes) (Pi4 tptp.pi)) (@ P (@ (@ tptp.late_FreeR FreeRes2) Pi4))) (@ P Residual)))))
% 0.25/0.69 (assert (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Name tptp.name) (Pi tptp.pi)) (not (= (@ (@ (@ tptp.input Name12) Name22) Pi3) (@ (@ tptp.res Name) Pi)))))
% 0.25/0.69 (assert (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Pi12 tptp.pi) (Pi22 tptp.pi)) (not (= (@ (@ (@ tptp.input Name12) Name22) Pi3) (@ (@ tptp.par Pi12) Pi22)))))
% 0.25/0.69 (assert (forall ((Pi3 tptp.pi) (Name tptp.name) (Pi tptp.pi)) (not (= (@ tptp.tau Pi3) (@ (@ tptp.res Name) Pi)))))
% 0.25/0.69 (assert (forall ((Pi3 tptp.pi) (Pi12 tptp.pi) (Pi22 tptp.pi)) (not (= (@ tptp.tau Pi3) (@ (@ tptp.par Pi12) Pi22)))))
% 0.25/0.69 (assert (forall ((Rs tptp.late_residual)) (not (@ (@ tptp.late_transitions tptp.piNil) Rs))))
% 0.25/0.69 (assert (forall ((Rs tptp.late_residual)) (not (@ (@ tptp.late_transitions tptp.piNil) Rs))))
% 0.25/0.69 (assert (forall ((Name tptp.name) (Pi tptp.pi)) (not (= tptp.piNil (@ (@ tptp.res Name) Pi)))))
% 0.25/0.69 (assert (forall ((Pi12 tptp.pi) (Pi22 tptp.pi)) (not (= tptp.piNil (@ (@ tptp.par Pi12) Pi22)))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (Rel tptp.set_Pr1834926343_pi_pi)) (@ (@ (@ tptp.strong743114133lation P) Rel) tptp.piNil)))
% 0.25/0.69 (assert (forall ((P tptp.pi) (Alpha2 tptp.late_freeRes) (P3 tptp.pi) (Y tptp.name)) (let ((_let_1 (@ tptp.res Y))) (let ((_let_2 (@ tptp.late_FreeR Alpha2))) (=> (@ (@ tptp.late_transitions P) (@ _let_2 P3)) (=> (@ (@ tptp.fresh_1641682979reeRes Y) Alpha2) (@ (@ tptp.late_transitions (@ _let_1 P)) (@ _let_2 (@ _let_1 P3)))))))))
% 0.25/0.69 (assert (forall ((X tptp.name) (P tptp.pi) (Alpha2 tptp.late_freeRes) (P3 tptp.pi)) (=> (@ (@ tptp.late_transitions (@ (@ tptp.res X) P)) (@ (@ tptp.late_FreeR Alpha2) P3)) (not (forall ((P5 tptp.pi) (Alpha tptp.late_freeRes) (P4 tptp.pi) (Y3 tptp.name)) (let ((_let_1 (@ tptp.late_FreeR Alpha))) (let ((_let_2 (@ tptp.res Y3))) (=> (= (@ (@ tptp.res X) P) (@ _let_2 P5)) (=> (= (@ (@ tptp.late_FreeR Alpha2) P3) (@ _let_1 (@ _let_2 P4))) (=> (@ (@ tptp.late_transitions P5) (@ _let_1 P4)) (not (@ (@ tptp.fresh_1641682979reeRes Y3) Alpha))))))))))))
% 0.25/0.69 (assert (forall ((X tptp.name) (P tptp.pi) (Alpha2 tptp.late_freeRes) (XP tptp.pi) (F (-> tptp.pi Bool))) (=> (@ (@ tptp.late_transitions (@ (@ tptp.res X) P)) (@ (@ tptp.late_FreeR Alpha2) XP)) (=> (forall ((P4 tptp.pi)) (=> (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR Alpha2) P4)) (=> (@ (@ tptp.fresh_1641682979reeRes X) Alpha2) (@ F (@ (@ tptp.res X) P4))))) (@ F XP)))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (Alpha2 tptp.late_freeRes) (P3 tptp.pi) (Q tptp.pi)) (let ((_let_1 (@ tptp.late_FreeR Alpha2))) (=> (@ (@ tptp.late_transitions P) (@ _let_1 P3)) (@ (@ tptp.late_transitions (@ (@ tptp.par P) Q)) (@ _let_1 (@ (@ tptp.par P3) Q)))))))
% 0.25/0.69 (assert (forall ((Q tptp.pi) (Alpha2 tptp.late_freeRes) (Q3 tptp.pi) (P tptp.pi)) (let ((_let_1 (@ tptp.par P))) (let ((_let_2 (@ tptp.late_FreeR Alpha2))) (=> (@ (@ tptp.late_transitions Q) (@ _let_2 Q3)) (@ (@ tptp.late_transitions (@ _let_1 Q)) (@ _let_2 (@ _let_1 Q3))))))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (Alpha2 tptp.late_freeRes) (P3 tptp.pi) (Y tptp.name)) (=> (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR Alpha2) P3)) (=> (@ (@ tptp.fresh_name_pi Y) P) (@ (@ tptp.fresh_1641682979reeRes Y) Alpha2)))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (Alpha2 tptp.late_freeRes) (P3 tptp.pi) (Y tptp.name)) (let ((_let_1 (@ tptp.fresh_name_pi Y))) (=> (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR Alpha2) P3)) (=> (@ _let_1 P) (@ _let_1 P3))))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (Rel tptp.set_Pr1834926343_pi_pi) (Q tptp.pi) (Alpha2 tptp.late_freeRes) (Q3 tptp.pi)) (=> (@ (@ (@ tptp.strong743114133lation P) Rel) Q) (=> (@ (@ tptp.late_transitions Q) (@ (@ tptp.late_FreeR Alpha2) Q3)) (exists ((P4 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR Alpha2) P4)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P4) Q3)) Rel)))))))
% 0.25/0.69 (assert (forall ((X tptp.name) (Y tptp.name) (P tptp.pi) (Rs tptp.late_residual)) (not (@ (@ tptp.late_transitions (@ (@ tptp.res X) (@ (@ (@ tptp.input X) Y) P))) Rs))))
% 0.25/0.69 (assert (forall ((Q tptp.pi) (P tptp.pi) (Rel tptp.set_Pr1834926343_pi_pi)) (=> (forall ((A3 tptp.late_subject) (Y3 tptp.name) (Q2 tptp.pi)) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR A3) Y3) Q2)) (=> (@ (@ tptp.fresh_name_pi Y3) P) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR A3) Y3) P6)) (@ (@ (@ (@ (@ tptp.strong2129052853vative P6) Q2) A3) Y3) Rel)))))) (=> (forall ((Alpha tptp.late_freeRes) (Q2 tptp.pi)) (=> (@ (@ tptp.late_transitions Q) (@ (@ tptp.late_FreeR Alpha) Q2)) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR Alpha) P6)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P6) Q2)) Rel))))) (@ (@ (@ tptp.strong743114133lation P) Rel) Q)))))
% 0.25/0.69 (assert (= tptp.strong743114133lation (lambda ((P7 tptp.pi) (Rel2 tptp.set_Pr1834926343_pi_pi) (Q5 tptp.pi)) (and (forall ((A5 tptp.late_subject) (X4 tptp.name) (Q6 tptp.pi)) (=> (and (@ (@ tptp.late_transitions Q5) (@ (@ (@ tptp.late_BoundR A5) X4) Q6)) (@ (@ tptp.fresh_name_pi X4) P7)) (exists ((P8 tptp.pi)) (and (@ (@ tptp.late_transitions P7) (@ (@ (@ tptp.late_BoundR A5) X4) P8)) (@ (@ (@ (@ (@ tptp.strong2129052853vative P8) Q6) A5) X4) Rel2))))) (forall ((Alpha3 tptp.late_freeRes) (Q6 tptp.pi)) (=> (@ (@ tptp.late_transitions Q5) (@ (@ tptp.late_FreeR Alpha3) Q6)) (exists ((P8 tptp.pi)) (and (@ (@ tptp.late_transitions P7) (@ (@ tptp.late_FreeR Alpha3) P8)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P8) Q6)) Rel2)))))))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (A tptp.late_subject) (X tptp.name) (P3 tptp.pi)) (not (@ (@ tptp.late_transitions (@ tptp.tau P)) (@ (@ (@ tptp.late_BoundR A) X) P3)))))
% 0.25/0.69 (assert (forall ((X tptp.name) (Rs tptp.late_residual)) (not (@ (@ tptp.late_transitions (@ (@ tptp.res X) tptp.piNil)) Rs))))
% 0.25/0.69 (assert (forall ((P (-> tptp.late_freeRes tptp.late_residual Bool)) (Z tptp.late_freeRes) (Residual tptp.late_residual)) (=> (forall ((Subject2 tptp.late_subject) (Name4 tptp.name) (Pi4 tptp.pi) (Z2 tptp.late_freeRes)) (=> (@ (@ tptp.fresh_1641682979reeRes Name4) Z2) (=> (@ (@ tptp.fresh_717452603ubject Name4) Subject2) (@ (@ P Z2) (@ (@ (@ tptp.late_BoundR Subject2) Name4) Pi4))))) (=> (forall ((FreeRes2 tptp.late_freeRes) (Pi4 tptp.pi) (Z2 tptp.late_freeRes)) (@ (@ P Z2) (@ (@ tptp.late_FreeR FreeRes2) Pi4))) (@ (@ P Z) Residual)))))
% 0.25/0.69 (assert (forall ((P (-> tptp.produc1141751126_pi_pi tptp.late_residual Bool)) (Z tptp.produc1141751126_pi_pi) (Residual tptp.late_residual)) (=> (forall ((Subject2 tptp.late_subject) (Name4 tptp.name) (Pi4 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (@ (@ tptp.fresh_1376661020_pi_pi Name4) Z2) (=> (@ (@ tptp.fresh_717452603ubject Name4) Subject2) (@ (@ P Z2) (@ (@ (@ tptp.late_BoundR Subject2) Name4) Pi4))))) (=> (forall ((FreeRes2 tptp.late_freeRes) (Pi4 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (@ (@ P Z2) (@ (@ tptp.late_FreeR FreeRes2) Pi4))) (@ (@ P Z) Residual)))))
% 0.25/0.69 (assert (forall ((P (-> tptp.name tptp.late_residual Bool)) (Z tptp.name) (Residual tptp.late_residual)) (=> (forall ((Subject2 tptp.late_subject) (Name4 tptp.name) (Pi4 tptp.pi) (Z2 tptp.name)) (=> (@ (@ tptp.fresh_name_name Name4) Z2) (=> (@ (@ tptp.fresh_717452603ubject Name4) Subject2) (@ (@ P Z2) (@ (@ (@ tptp.late_BoundR Subject2) Name4) Pi4))))) (=> (forall ((FreeRes2 tptp.late_freeRes) (Pi4 tptp.pi) (Z2 tptp.name)) (@ (@ P Z2) (@ (@ tptp.late_FreeR FreeRes2) Pi4))) (@ (@ P Z) Residual)))))
% 0.25/0.69 (assert (forall ((P (-> tptp.pi tptp.late_residual Bool)) (Z tptp.pi) (Residual tptp.late_residual)) (=> (forall ((Subject2 tptp.late_subject) (Name4 tptp.name) (Pi4 tptp.pi) (Z2 tptp.pi)) (=> (@ (@ tptp.fresh_name_pi Name4) Z2) (=> (@ (@ tptp.fresh_717452603ubject Name4) Subject2) (@ (@ P Z2) (@ (@ (@ tptp.late_BoundR Subject2) Name4) Pi4))))) (=> (forall ((FreeRes2 tptp.late_freeRes) (Pi4 tptp.pi) (Z2 tptp.pi)) (@ (@ P Z2) (@ (@ tptp.late_FreeR FreeRes2) Pi4))) (@ (@ P Z) Residual)))))
% 0.25/0.69 (assert (forall ((P (-> tptp.late_freeRes tptp.late_residual Bool)) (Z tptp.late_freeRes) (Residual tptp.late_residual)) (=> (forall ((Subject2 tptp.late_subject) (Name4 tptp.name) (Pi4 tptp.pi) (Z2 tptp.late_freeRes)) (=> (@ (@ tptp.fresh_1641682979reeRes Name4) Z2) (=> (@ (@ tptp.fresh_717452603ubject Name4) Subject2) (@ (@ P Z2) (@ (@ (@ tptp.late_BoundR Subject2) Name4) Pi4))))) (=> (forall ((FreeRes2 tptp.late_freeRes) (Pi4 tptp.pi) (Z2 tptp.late_freeRes)) (@ (@ P Z2) (@ (@ tptp.late_FreeR FreeRes2) Pi4))) (@ (@ P Z) Residual)))))
% 0.25/0.69 (assert (forall ((P (-> tptp.produc1141751126_pi_pi tptp.late_residual Bool)) (Z tptp.produc1141751126_pi_pi) (Residual tptp.late_residual)) (=> (forall ((Subject2 tptp.late_subject) (Name4 tptp.name) (Pi4 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (@ (@ tptp.fresh_1376661020_pi_pi Name4) Z2) (=> (@ (@ tptp.fresh_717452603ubject Name4) Subject2) (@ (@ P Z2) (@ (@ (@ tptp.late_BoundR Subject2) Name4) Pi4))))) (=> (forall ((FreeRes2 tptp.late_freeRes) (Pi4 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (@ (@ P Z2) (@ (@ tptp.late_FreeR FreeRes2) Pi4))) (@ (@ P Z) Residual)))))
% 0.25/0.69 (assert (forall ((P (-> tptp.name tptp.late_residual Bool)) (Z tptp.name) (Residual tptp.late_residual)) (=> (forall ((Subject2 tptp.late_subject) (Name4 tptp.name) (Pi4 tptp.pi) (Z2 tptp.name)) (=> (@ (@ tptp.fresh_name_name Name4) Z2) (=> (@ (@ tptp.fresh_717452603ubject Name4) Subject2) (@ (@ P Z2) (@ (@ (@ tptp.late_BoundR Subject2) Name4) Pi4))))) (=> (forall ((FreeRes2 tptp.late_freeRes) (Pi4 tptp.pi) (Z2 tptp.name)) (@ (@ P Z2) (@ (@ tptp.late_FreeR FreeRes2) Pi4))) (@ (@ P Z) Residual)))))
% 0.25/0.69 (assert (forall ((P (-> tptp.pi tptp.late_residual Bool)) (Z tptp.pi) (Residual tptp.late_residual)) (=> (forall ((Subject2 tptp.late_subject) (Name4 tptp.name) (Pi4 tptp.pi) (Z2 tptp.pi)) (=> (@ (@ tptp.fresh_name_pi Name4) Z2) (=> (@ (@ tptp.fresh_717452603ubject Name4) Subject2) (@ (@ P Z2) (@ (@ (@ tptp.late_BoundR Subject2) Name4) Pi4))))) (=> (forall ((FreeRes2 tptp.late_freeRes) (Pi4 tptp.pi) (Z2 tptp.pi)) (@ (@ P Z2) (@ (@ tptp.late_FreeR FreeRes2) Pi4))) (@ (@ P Z) Residual)))))
% 0.25/0.69 (assert (forall ((Rel tptp.set_Pr1834926343_pi_pi) (Q tptp.pi) (X tptp.name) (P tptp.pi) (C3 tptp.late_freeRes)) (=> (@ tptp.eqvt_pi Rel) (=> (forall ((Q2 tptp.pi) (A3 tptp.name)) (=> (@ (@ tptp.late_transitions Q) (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR A3) X)) Q2)) (=> (not (= A3 X)) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR (@ tptp.late_BoundOutputS A3)) X) P6)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P6) Q2)) Rel)))))) (=> (forall ((Q2 tptp.pi) (A3 tptp.late_subject) (Y3 tptp.name)) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR A3) Y3) Q2)) (=> (@ (@ tptp.fresh_717452603ubject X) A3) (=> (not (= X Y3)) (=> (@ (@ tptp.fresh_1641682979reeRes Y3) C3) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR A3) Y3) P6)) (@ (@ (@ (@ (@ tptp.strong2129052853vative P6) (@ (@ tptp.res X) Q2)) A3) Y3) Rel)))))))) (=> (forall ((Q2 tptp.pi) (Alpha tptp.late_freeRes)) (=> (@ (@ tptp.late_transitions Q) (@ (@ tptp.late_FreeR Alpha) Q2)) (=> (@ (@ tptp.fresh_1641682979reeRes X) Alpha) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR Alpha) P6)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P6) (@ (@ tptp.res X) Q2))) Rel)))))) (@ (@ (@ tptp.strong743114133lation P) Rel) (@ (@ tptp.res X) Q))))))))
% 0.25/0.69 (assert (forall ((Rel tptp.set_Pr1834926343_pi_pi) (Q tptp.pi) (X tptp.name) (P tptp.pi) (C3 tptp.produc1141751126_pi_pi)) (=> (@ tptp.eqvt_pi Rel) (=> (forall ((Q2 tptp.pi) (A3 tptp.name)) (=> (@ (@ tptp.late_transitions Q) (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR A3) X)) Q2)) (=> (not (= A3 X)) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR (@ tptp.late_BoundOutputS A3)) X) P6)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P6) Q2)) Rel)))))) (=> (forall ((Q2 tptp.pi) (A3 tptp.late_subject) (Y3 tptp.name)) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR A3) Y3) Q2)) (=> (@ (@ tptp.fresh_717452603ubject X) A3) (=> (not (= X Y3)) (=> (@ (@ tptp.fresh_1376661020_pi_pi Y3) C3) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR A3) Y3) P6)) (@ (@ (@ (@ (@ tptp.strong2129052853vative P6) (@ (@ tptp.res X) Q2)) A3) Y3) Rel)))))))) (=> (forall ((Q2 tptp.pi) (Alpha tptp.late_freeRes)) (=> (@ (@ tptp.late_transitions Q) (@ (@ tptp.late_FreeR Alpha) Q2)) (=> (@ (@ tptp.fresh_1641682979reeRes X) Alpha) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR Alpha) P6)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P6) (@ (@ tptp.res X) Q2))) Rel)))))) (@ (@ (@ tptp.strong743114133lation P) Rel) (@ (@ tptp.res X) Q))))))))
% 0.25/0.69 (assert (forall ((Rel tptp.set_Pr1834926343_pi_pi) (Q tptp.pi) (X tptp.name) (P tptp.pi) (C3 tptp.name)) (=> (@ tptp.eqvt_pi Rel) (=> (forall ((Q2 tptp.pi) (A3 tptp.name)) (=> (@ (@ tptp.late_transitions Q) (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR A3) X)) Q2)) (=> (not (= A3 X)) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR (@ tptp.late_BoundOutputS A3)) X) P6)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P6) Q2)) Rel)))))) (=> (forall ((Q2 tptp.pi) (A3 tptp.late_subject) (Y3 tptp.name)) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR A3) Y3) Q2)) (=> (@ (@ tptp.fresh_717452603ubject X) A3) (=> (not (= X Y3)) (=> (@ (@ tptp.fresh_name_name Y3) C3) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR A3) Y3) P6)) (@ (@ (@ (@ (@ tptp.strong2129052853vative P6) (@ (@ tptp.res X) Q2)) A3) Y3) Rel)))))))) (=> (forall ((Q2 tptp.pi) (Alpha tptp.late_freeRes)) (=> (@ (@ tptp.late_transitions Q) (@ (@ tptp.late_FreeR Alpha) Q2)) (=> (@ (@ tptp.fresh_1641682979reeRes X) Alpha) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR Alpha) P6)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P6) (@ (@ tptp.res X) Q2))) Rel)))))) (@ (@ (@ tptp.strong743114133lation P) Rel) (@ (@ tptp.res X) Q))))))))
% 0.25/0.69 (assert (forall ((Rel tptp.set_Pr1834926343_pi_pi) (Q tptp.pi) (X tptp.name) (P tptp.pi) (C3 tptp.pi)) (=> (@ tptp.eqvt_pi Rel) (=> (forall ((Q2 tptp.pi) (A3 tptp.name)) (=> (@ (@ tptp.late_transitions Q) (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR A3) X)) Q2)) (=> (not (= A3 X)) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR (@ tptp.late_BoundOutputS A3)) X) P6)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P6) Q2)) Rel)))))) (=> (forall ((Q2 tptp.pi) (A3 tptp.late_subject) (Y3 tptp.name)) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR A3) Y3) Q2)) (=> (@ (@ tptp.fresh_717452603ubject X) A3) (=> (not (= X Y3)) (=> (@ (@ tptp.fresh_name_pi Y3) C3) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR A3) Y3) P6)) (@ (@ (@ (@ (@ tptp.strong2129052853vative P6) (@ (@ tptp.res X) Q2)) A3) Y3) Rel)))))))) (=> (forall ((Q2 tptp.pi) (Alpha tptp.late_freeRes)) (=> (@ (@ tptp.late_transitions Q) (@ (@ tptp.late_FreeR Alpha) Q2)) (=> (@ (@ tptp.fresh_1641682979reeRes X) Alpha) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR Alpha) P6)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P6) (@ (@ tptp.res X) Q2))) Rel)))))) (@ (@ (@ tptp.strong743114133lation P) Rel) (@ (@ tptp.res X) Q))))))))
% 0.25/0.69 (assert (forall ((X tptp.name) (A tptp.name) (Y tptp.name) (P tptp.pi) (B tptp.name) (Z tptp.name) (P3 tptp.pi)) (not (@ (@ tptp.late_transitions (@ (@ tptp.res X) (@ (@ (@ tptp.input A) Y) P))) (@ (@ (@ tptp.late_BoundR (@ tptp.late_BoundOutputS B)) Z) P3)))))
% 0.25/0.69 (assert (forall ((X tptp.name) (P tptp.pi) (A tptp.name) (B tptp.name) (P3 tptp.pi)) (not (@ (@ tptp.late_transitions (@ (@ tptp.res X) (@ tptp.tau P))) (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR A) B)) P3)))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X32 tptp.late_subject) (X1 tptp.name) (X2 tptp.pi)) (= (@ (@ tptp.fresh_81631222sidual A) (@ (@ (@ tptp.late_BoundR X32) X1) X2)) (and (@ (@ tptp.fresh_717452603ubject A) X32) (@ (@ tptp.fresh_543891186ion_pi A) (@ (@ tptp.abs_fun_name_pi X1) X2))))))
% 0.25/0.69 (assert (forall ((P tptp.pi)) (@ (@ tptp.late_transitions (@ tptp.tau P)) (@ (@ tptp.late_FreeR tptp.late_TauR) P))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (Rs tptp.late_residual)) (=> (@ (@ tptp.late_transitions (@ tptp.tau P)) Rs) (not (forall ((P5 tptp.pi)) (=> (= (@ tptp.tau P) (@ tptp.tau P5)) (not (= Rs (@ (@ tptp.late_FreeR tptp.late_TauR) P5)))))))))
% 0.25/0.69 (assert (forall ((X2 tptp.name) (X1 tptp.name) (Y2 tptp.name) (Y1 tptp.name)) (= (= (@ (@ tptp.late_OutputR X2) X1) (@ (@ tptp.late_OutputR Y2) Y1)) (and (= X2 Y2) (= X1 Y1)))))
% 0.25/0.69 (assert (forall ((X1 tptp.name) (Y1 tptp.name)) (= (= (@ tptp.late_BoundOutputS X1) (@ tptp.late_BoundOutputS Y1)) (= X1 Y1))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X1 tptp.name)) (= (@ (@ tptp.fresh_717452603ubject A) (@ tptp.late_BoundOutputS X1)) (@ (@ tptp.fresh_name_name A) X1))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X2 tptp.name) (X1 tptp.name)) (let ((_let_1 (@ tptp.fresh_name_name A))) (= (@ (@ tptp.fresh_1641682979reeRes A) (@ (@ tptp.late_OutputR X2) X1)) (and (@ _let_1 X2) (@ _let_1 X1))))))
% 0.25/0.69 (assert (forall ((A tptp.name)) (@ (@ tptp.fresh_1641682979reeRes A) tptp.late_TauR)))
% 0.25/0.69 (assert (forall ((A tptp.name) (X1 tptp.name) (X2 tptp.pi)) (= (@ (@ tptp.fresh_name_pi A) (@ (@ tptp.res X1) X2)) (@ (@ tptp.fresh_543891186ion_pi A) (@ (@ tptp.abs_fun_name_pi X1) X2)))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X32 tptp.name) (X1 tptp.name) (X2 tptp.pi)) (= (@ (@ tptp.fresh_name_pi A) (@ (@ (@ tptp.input X32) X1) X2)) (and (@ (@ tptp.fresh_name_name A) X32) (@ (@ tptp.fresh_543891186ion_pi A) (@ (@ tptp.abs_fun_name_pi X1) X2))))))
% 0.25/0.69 (assert (forall ((Name12 tptp.name) (Name22 tptp.name)) (not (= (@ (@ tptp.late_OutputR Name12) Name22) tptp.late_TauR))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X tptp.name) (Y tptp.name)) (let ((_let_1 (@ tptp.abs_fun_name_name A))) (= (= (@ _let_1 X) (@ _let_1 Y)) (= X Y)))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X tptp.produc1141751126_pi_pi) (Y tptp.produc1141751126_pi_pi)) (let ((_let_1 (@ tptp.abs_fu385186459_pi_pi A))) (= (= (@ _let_1 X) (@ _let_1 Y)) (= X Y)))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X tptp.late_freeRes) (Y tptp.late_freeRes)) (let ((_let_1 (@ tptp.abs_fu681348580reeRes A))) (= (= (@ _let_1 X) (@ _let_1 Y)) (= X Y)))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X tptp.pi) (Y tptp.pi)) (let ((_let_1 (@ tptp.abs_fun_name_pi A))) (= (= (@ _let_1 X) (@ _let_1 Y)) (= X Y)))))
% 0.25/0.69 (assert (forall ((P (-> tptp.late_freeRes Bool)) (FreeRes3 tptp.late_freeRes)) (=> (forall ((Name13 tptp.name) (Name23 tptp.name)) (@ P (@ (@ tptp.late_OutputR Name13) Name23))) (=> (@ P tptp.late_TauR) (@ P FreeRes3)))))
% 0.25/0.69 (assert (forall ((X1 tptp.name) (X2 tptp.pi) (Y1 tptp.name) (Y2 tptp.pi)) (= (= (@ (@ tptp.res X1) X2) (@ (@ tptp.res Y1) Y2)) (= (@ (@ tptp.abs_fun_name_pi X1) X2) (@ (@ tptp.abs_fun_name_pi Y1) Y2)))))
% 0.25/0.69 (assert (forall ((X32 tptp.late_subject) (X1 tptp.name) (X2 tptp.pi) (Y32 tptp.late_subject) (Y1 tptp.name) (Y2 tptp.pi)) (= (= (@ (@ (@ tptp.late_BoundR X32) X1) X2) (@ (@ (@ tptp.late_BoundR Y32) Y1) Y2)) (and (= X32 Y32) (= (@ (@ tptp.abs_fun_name_pi X1) X2) (@ (@ tptp.abs_fun_name_pi Y1) Y2))))))
% 0.25/0.69 (assert (forall ((B tptp.name) (A tptp.name) (X tptp.late_freeRes)) (= (@ (@ tptp.fresh_785364841reeRes B) (@ (@ tptp.abs_fu681348580reeRes A) X)) (or (= B A) (@ (@ tptp.fresh_1641682979reeRes B) X)))))
% 0.25/0.69 (assert (forall ((B tptp.name) (A tptp.name) (X tptp.produc1141751126_pi_pi)) (= (@ (@ tptp.fresh_2065563522_pi_pi B) (@ (@ tptp.abs_fu385186459_pi_pi A) X)) (or (= B A) (@ (@ tptp.fresh_1376661020_pi_pi B) X)))))
% 0.25/0.69 (assert (forall ((B tptp.name) (A tptp.name) (X tptp.name)) (= (@ (@ tptp.fresh_1093033124n_name B) (@ (@ tptp.abs_fun_name_name A) X)) (or (= B A) (@ (@ tptp.fresh_name_name B) X)))))
% 0.25/0.69 (assert (forall ((B tptp.name) (A tptp.name) (X tptp.pi)) (= (@ (@ tptp.fresh_543891186ion_pi B) (@ (@ tptp.abs_fun_name_pi A) X)) (or (= B A) (@ (@ tptp.fresh_name_pi B) X)))))
% 0.25/0.69 (assert (forall ((B tptp.name) (A tptp.name) (X tptp.late_freeRes)) (= (@ (@ tptp.fresh_785364841reeRes B) (@ (@ tptp.abs_fu681348580reeRes A) X)) (or (= B A) (@ (@ tptp.fresh_1641682979reeRes B) X)))))
% 0.25/0.69 (assert (forall ((B tptp.name) (A tptp.name) (X tptp.produc1141751126_pi_pi)) (= (@ (@ tptp.fresh_2065563522_pi_pi B) (@ (@ tptp.abs_fu385186459_pi_pi A) X)) (or (= B A) (@ (@ tptp.fresh_1376661020_pi_pi B) X)))))
% 0.25/0.69 (assert (forall ((B tptp.name) (A tptp.name) (X tptp.name)) (= (@ (@ tptp.fresh_1093033124n_name B) (@ (@ tptp.abs_fun_name_name A) X)) (or (= B A) (@ (@ tptp.fresh_name_name B) X)))))
% 0.25/0.69 (assert (forall ((B tptp.name) (A tptp.name) (X tptp.pi)) (= (@ (@ tptp.fresh_543891186ion_pi B) (@ (@ tptp.abs_fun_name_pi A) X)) (or (= B A) (@ (@ tptp.fresh_name_pi B) X)))))
% 0.25/0.69 (assert (forall ((X32 tptp.name) (X1 tptp.name) (X2 tptp.pi) (Y32 tptp.name) (Y1 tptp.name) (Y2 tptp.pi)) (= (= (@ (@ (@ tptp.input X32) X1) X2) (@ (@ (@ tptp.input Y32) Y1) Y2)) (and (= X32 Y32) (= (@ (@ tptp.abs_fun_name_pi X1) X2) (@ (@ tptp.abs_fun_name_pi Y1) Y2))))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (A tptp.name) (B tptp.name) (P3 tptp.pi)) (=> (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR A) B)) P3)) (=> (not (= A B)) (@ (@ tptp.late_transitions (@ (@ tptp.res B) P)) (@ (@ (@ tptp.late_BoundR (@ tptp.late_BoundOutputS A)) B) P3))))))
% 0.25/0.69 (assert (forall ((X tptp.name) (P tptp.pi) (Rs tptp.late_residual)) (=> (@ (@ tptp.late_transitions (@ (@ tptp.res X) P)) Rs) (=> (forall ((P5 tptp.pi) (A3 tptp.name) (B3 tptp.name)) (=> (= (@ (@ tptp.res X) P) (@ (@ tptp.res B3) P5)) (forall ((P4 tptp.pi)) (=> (= Rs (@ (@ (@ tptp.late_BoundR (@ tptp.late_BoundOutputS A3)) B3) P4)) (=> (@ (@ tptp.late_transitions P5) (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR A3) B3)) P4)) (= A3 B3)))))) (=> (forall ((P5 tptp.pi) (A3 tptp.late_subject) (X3 tptp.name) (P4 tptp.pi) (Y3 tptp.name)) (let ((_let_1 (@ (@ tptp.late_BoundR A3) X3))) (let ((_let_2 (@ tptp.res Y3))) (=> (= (@ (@ tptp.res X) P) (@ _let_2 P5)) (=> (= Rs (@ _let_1 (@ _let_2 P4))) (=> (@ (@ tptp.late_transitions P5) (@ _let_1 P4)) (=> (@ (@ tptp.fresh_717452603ubject Y3) A3) (=> (not (= Y3 X3)) (=> (@ (@ tptp.fresh_name_pi X3) P5) (not (@ (@ tptp.fresh_717452603ubject X3) A3))))))))))) (not (forall ((P5 tptp.pi) (Alpha tptp.late_freeRes) (P4 tptp.pi) (Y3 tptp.name)) (let ((_let_1 (@ tptp.late_FreeR Alpha))) (let ((_let_2 (@ tptp.res Y3))) (=> (= (@ (@ tptp.res X) P) (@ _let_2 P5)) (=> (= Rs (@ _let_1 (@ _let_2 P4))) (=> (@ (@ tptp.late_transitions P5) (@ _let_1 P4)) (not (@ (@ tptp.fresh_1641682979reeRes Y3) Alpha))))))))))))))
% 0.25/0.69 (assert (forall ((X5 tptp.name) (P tptp.pi) (A tptp.late_subject) (Y4 tptp.name) (P3 tptp.pi)) (=> (@ (@ tptp.late_transitions (@ (@ tptp.res X5) P)) (@ (@ (@ tptp.late_BoundR A) Y4) P3)) (=> (forall ((P5 tptp.pi) (A3 tptp.name) (B3 tptp.name)) (=> (= (@ (@ tptp.res X5) P) (@ (@ tptp.res B3) P5)) (forall ((P4 tptp.pi)) (=> (= (@ (@ (@ tptp.late_BoundR A) Y4) P3) (@ (@ (@ tptp.late_BoundR (@ tptp.late_BoundOutputS A3)) B3) P4)) (=> (@ (@ tptp.late_transitions P5) (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR A3) B3)) P4)) (= A3 B3)))))) (not (forall ((P5 tptp.pi) (A3 tptp.late_subject) (X3 tptp.name) (P4 tptp.pi) (Y3 tptp.name)) (let ((_let_1 (@ (@ tptp.late_BoundR A3) X3))) (let ((_let_2 (@ tptp.res Y3))) (=> (= (@ (@ tptp.res X5) P) (@ _let_2 P5)) (=> (= (@ (@ (@ tptp.late_BoundR A) Y4) P3) (@ _let_1 (@ _let_2 P4))) (=> (@ (@ tptp.late_transitions P5) (@ _let_1 P4)) (=> (@ (@ tptp.fresh_717452603ubject Y3) A3) (=> (not (= Y3 X3)) (=> (@ (@ tptp.fresh_name_pi X3) P5) (not (@ (@ tptp.fresh_717452603ubject X3) A3))))))))))))))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (A tptp.name) (B tptp.name) (P3 tptp.pi)) (not (@ (@ tptp.late_transitions (@ tptp.tau P)) (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR A) B)) P3)))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X tptp.name) (P tptp.pi) (B tptp.name) (Y tptp.name) (P3 tptp.pi)) (not (@ (@ tptp.late_transitions (@ (@ (@ tptp.input A) X) P)) (@ (@ (@ tptp.late_BoundR (@ tptp.late_BoundOutputS B)) Y) P3)))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (Alpha2 tptp.late_freeRes) (P3 tptp.pi) (Prop (-> tptp.late_freeRes tptp.pi Bool))) (=> (@ (@ tptp.late_transitions (@ tptp.tau P)) (@ (@ tptp.late_FreeR Alpha2) P3)) (=> (=> (= Alpha2 tptp.late_TauR) (=> (= P P3) (@ (@ Prop tptp.late_TauR) P))) (@ (@ Prop Alpha2) P3)))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (A tptp.name) (Y tptp.name) (P3 tptp.pi) (Q tptp.pi) (X tptp.name) (Q3 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi Y))) (let ((_let_2 (@ tptp.fresh_name_pi X))) (=> (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR (@ tptp.late_BoundOutputS A)) Y) P3)) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR (@ tptp.late_InputS A)) X) Q3)) (=> (@ _let_2 P) (=> (@ _let_2 Q) (=> (@ _let_1 P) (=> (@ _let_1 Q) (=> (not (= X A)) (=> (@ _let_2 P3) (=> (not (= Y A)) (=> (@ _let_1 Q3) (=> (not (= X Y)) (@ (@ tptp.late_transitions (@ (@ tptp.par P) Q)) (@ (@ tptp.late_FreeR tptp.late_TauR) (@ (@ tptp.res Y) (@ (@ tptp.par P3) (@ (@ (@ tptp.subs Q3) X) Y))))))))))))))))))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (A tptp.name) (X tptp.name) (P3 tptp.pi) (Q tptp.pi) (Y tptp.name) (Q3 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi Y))) (let ((_let_2 (@ tptp.fresh_name_pi X))) (=> (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR (@ tptp.late_InputS A)) X) P3)) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR (@ tptp.late_BoundOutputS A)) Y) Q3)) (=> (@ _let_2 P) (=> (@ _let_2 Q) (=> (@ _let_1 P) (=> (@ _let_1 Q) (=> (not (= X A)) (=> (@ _let_2 Q3) (=> (not (= Y A)) (=> (@ _let_1 P3) (=> (not (= X Y)) (@ (@ tptp.late_transitions (@ (@ tptp.par P) Q)) (@ (@ tptp.late_FreeR tptp.late_TauR) (@ (@ tptp.res Y) (@ (@ tptp.par (@ (@ (@ tptp.subs P3) X) Y)) Q3)))))))))))))))))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (A tptp.name) (Y tptp.name) (P3 tptp.pi) (Q tptp.pi) (X tptp.name) (Q3 tptp.pi)) (=> (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR (@ tptp.late_BoundOutputS A)) Y) P3)) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR (@ tptp.late_InputS A)) X) Q3)) (=> (@ (@ tptp.fresh_name_pi Y) Q) (@ (@ tptp.late_transitions (@ (@ tptp.par P) Q)) (@ (@ tptp.late_FreeR tptp.late_TauR) (@ (@ tptp.res Y) (@ (@ tptp.par P3) (@ (@ (@ tptp.subs Q3) X) Y))))))))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (A tptp.name) (X tptp.name) (P3 tptp.pi) (Q tptp.pi) (Y tptp.name) (Q3 tptp.pi)) (=> (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR (@ tptp.late_InputS A)) X) P3)) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR (@ tptp.late_BoundOutputS A)) Y) Q3)) (=> (@ (@ tptp.fresh_name_pi Y) P) (@ (@ tptp.late_transitions (@ (@ tptp.par P) Q)) (@ (@ tptp.late_FreeR tptp.late_TauR) (@ (@ tptp.res Y) (@ (@ tptp.par (@ (@ (@ tptp.subs P3) X) Y)) Q3)))))))))
% 0.25/0.69 (assert (= tptp.fresh_name_name (lambda ((A5 tptp.name) (B4 tptp.name)) (not (= A5 B4)))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X1 tptp.name)) (= (@ (@ tptp.fresh_717452603ubject A) (@ tptp.late_InputS X1)) (@ (@ tptp.fresh_name_name A) X1))))
% 0.25/0.69 (assert (forall ((P (-> tptp.late_subject Bool)) (Subject tptp.late_subject)) (=> (forall ((Name4 tptp.name)) (@ P (@ tptp.late_InputS Name4))) (=> (forall ((Name4 tptp.name)) (@ P (@ tptp.late_BoundOutputS Name4))) (@ P Subject)))))
% 0.25/0.69 (assert (forall ((Name3 tptp.name) (Name tptp.name)) (not (= (@ tptp.late_InputS Name3) (@ tptp.late_BoundOutputS Name)))))
% 0.25/0.69 (assert (forall ((A tptp.name) (X tptp.name) (P tptp.pi)) (@ (@ tptp.late_transitions (@ (@ (@ tptp.input A) X) P)) (@ (@ (@ tptp.late_BoundR (@ tptp.late_InputS A)) X) P))))
% 0.25/0.69 (assert (forall ((X tptp.name) (A tptp.name) (P tptp.pi)) (=> (not (= X A)) (@ (@ tptp.late_transitions (@ (@ (@ tptp.input A) X) P)) (@ (@ (@ tptp.late_BoundR (@ tptp.late_InputS A)) X) P)))))
% 0.25/0.69 (assert (forall ((A tptp.name) (B tptp.name) (P tptp.pi) (Rs tptp.late_residual)) (=> (@ (@ tptp.late_transitions (@ (@ (@ tptp.input A) B) P)) Rs) (not (forall ((X3 tptp.name) (A3 tptp.name) (P5 tptp.pi)) (=> (and (= A A3) (= (@ (@ tptp.abs_fun_name_pi B) P) (@ (@ tptp.abs_fun_name_pi X3) P5))) (=> (= Rs (@ (@ (@ tptp.late_BoundR (@ tptp.late_InputS A3)) X3) P5)) (= X3 A3))))))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (A tptp.name) (X tptp.name) (P3 tptp.pi) (Q tptp.pi) (B tptp.name) (Q3 tptp.pi)) (=> (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR (@ tptp.late_InputS A)) X) P3)) (=> (@ (@ tptp.late_transitions Q) (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR A) B)) Q3)) (@ (@ tptp.late_transitions (@ (@ tptp.par P) Q)) (@ (@ tptp.late_FreeR tptp.late_TauR) (@ (@ tptp.par (@ (@ (@ tptp.subs P3) X) B)) Q3)))))))
% 0.25/0.69 (assert (forall ((P tptp.pi) (A tptp.name) (B tptp.name) (P3 tptp.pi) (Q tptp.pi) (X tptp.name) (Q3 tptp.pi)) (=> (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR A) B)) P3)) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR (@ tptp.late_InputS A)) X) Q3)) (@ (@ tptp.late_transitions (@ (@ tptp.par P) Q)) (@ (@ tptp.late_FreeR tptp.late_TauR) (@ (@ tptp.par P3) (@ (@ (@ tptp.subs Q3) X) B))))))))
% 0.25/0.70 (assert (forall ((P tptp.pi) (A tptp.name) (B tptp.name) (P3 tptp.pi) (Q tptp.pi) (X tptp.name) (Q3 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi X))) (=> (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR A) B)) P3)) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR (@ tptp.late_InputS A)) X) Q3)) (=> (@ _let_1 P) (=> (@ _let_1 Q) (=> (not (= X A)) (=> (not (= X B)) (=> (@ _let_1 P3) (@ (@ tptp.late_transitions (@ (@ tptp.par P) Q)) (@ (@ tptp.late_FreeR tptp.late_TauR) (@ (@ tptp.par P3) (@ (@ (@ tptp.subs Q3) X) B))))))))))))))
% 0.25/0.70 (assert (forall ((P tptp.pi) (A tptp.name) (X tptp.name) (P3 tptp.pi) (Q tptp.pi) (B tptp.name) (Q3 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi X))) (=> (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR (@ tptp.late_InputS A)) X) P3)) (=> (@ (@ tptp.late_transitions Q) (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR A) B)) Q3)) (=> (@ _let_1 P) (=> (@ _let_1 Q) (=> (not (= X A)) (=> (not (= X B)) (=> (@ _let_1 Q3) (@ (@ tptp.late_transitions (@ (@ tptp.par P) Q)) (@ (@ tptp.late_FreeR tptp.late_TauR) (@ (@ tptp.par (@ (@ (@ tptp.subs P3) X) B)) Q3)))))))))))))
% 0.25/0.70 (assert (forall ((X1 tptp.name) (Y1 tptp.name)) (= (= (@ tptp.late_InputS X1) (@ tptp.late_InputS Y1)) (= X1 Y1))))
% 0.25/0.70 (assert (forall ((X2 tptp.name) (Y2 tptp.name)) (= (= (@ tptp.late_BoundOutputS X2) (@ tptp.late_BoundOutputS Y2)) (= X2 Y2))))
% 0.25/0.70 (assert (forall ((X11 tptp.name) (X12 tptp.name) (Y11 tptp.name) (Y12 tptp.name)) (= (= (@ (@ tptp.late_OutputR X11) X12) (@ (@ tptp.late_OutputR Y11) Y12)) (and (= X11 Y11) (= X12 Y12)))))
% 0.25/0.70 (assert (forall ((Y tptp.late_freeRes)) (=> (forall ((X112 tptp.name) (X122 tptp.name)) (not (= Y (@ (@ tptp.late_OutputR X112) X122)))) (= Y tptp.late_TauR))))
% 0.25/0.70 (assert (forall ((X11 tptp.name) (X12 tptp.name)) (not (= (@ (@ tptp.late_OutputR X11) X12) tptp.late_TauR))))
% 0.25/0.70 (assert (forall ((X1 tptp.name) (X2 tptp.name)) (not (= (@ tptp.late_InputS X1) (@ tptp.late_BoundOutputS X2)))))
% 0.25/0.70 (assert (forall ((Y tptp.late_subject)) (=> (forall ((X13 tptp.name)) (not (= Y (@ tptp.late_InputS X13)))) (not (forall ((X22 tptp.name)) (not (= Y (@ tptp.late_BoundOutputS X22))))))))
% 0.25/0.70 (assert (forall ((X tptp.name) (A tptp.name) (B tptp.name) (P tptp.pi) (P3 tptp.pi)) (not (@ (@ tptp.late_transitions (@ (@ tptp.res X) (@ (@ (@ tptp.output A) B) P))) (@ (@ tptp.late_FreeR tptp.late_TauR) P3)))))
% 0.25/0.70 (assert (forall ((X tptp.name) (A tptp.name) (B tptp.name) (P tptp.pi) (C tptp.name) (Y tptp.name) (P3 tptp.pi)) (not (@ (@ tptp.late_transitions (@ (@ tptp.res X) (@ (@ (@ tptp.output A) B) P))) (@ (@ (@ tptp.late_BoundR (@ tptp.late_InputS C)) Y) P3)))))
% 0.25/0.70 (assert (forall ((X tptp.name) (A tptp.name) (P tptp.pi) (B tptp.name) (Y tptp.name) (P3 tptp.pi)) (not (@ (@ tptp.late_transitions (@ (@ tptp.res X) (@ (@ (@ tptp.output A) X) P))) (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR B) Y)) P3)))))
% 0.25/0.70 (assert (forall ((A tptp.name) (X32 tptp.name) (X2 tptp.name) (X1 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi A))) (let ((_let_2 (@ tptp.fresh_name_name A))) (= (@ _let_1 (@ (@ (@ tptp.output X32) X2) X1)) (and (@ _let_2 X32) (@ _let_2 X2) (@ _let_1 X1)))))))
% 0.25/0.70 (assert (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Name tptp.name) (Pi tptp.pi)) (not (= (@ (@ (@ tptp.output Name12) Name22) Pi3) (@ (@ tptp.res Name) Pi)))))
% 0.25/0.70 (assert (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Pi12 tptp.pi) (Pi22 tptp.pi)) (not (= (@ (@ (@ tptp.output Name12) Name22) Pi3) (@ (@ tptp.par Pi12) Pi22)))))
% 0.25/0.70 (assert (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Name1 tptp.name) (Name2 tptp.name) (Pi tptp.pi)) (not (= (@ (@ (@ tptp.output Name12) Name22) Pi3) (@ (@ (@ tptp.input Name1) Name2) Pi)))))
% 0.25/0.70 (assert (forall ((Name1 tptp.name) (Name2 tptp.name) (Pi tptp.pi)) (not (= tptp.piNil (@ (@ (@ tptp.output Name1) Name2) Pi)))))
% 0.25/0.70 (assert (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Pi tptp.pi)) (not (= (@ (@ (@ tptp.output Name12) Name22) Pi3) (@ tptp.tau Pi)))))
% 0.25/0.70 (assert (forall ((X32 tptp.name) (X2 tptp.name) (X1 tptp.pi) (Y32 tptp.name) (Y2 tptp.name) (Y1 tptp.pi)) (= (= (@ (@ (@ tptp.output X32) X2) X1) (@ (@ (@ tptp.output Y32) Y2) Y1)) (and (= X32 Y32) (= X2 Y2) (= X1 Y1)))))
% 0.25/0.70 (assert (forall ((X tptp.name) (B tptp.name) (P tptp.pi) (Rs tptp.late_residual)) (not (@ (@ tptp.late_transitions (@ (@ tptp.res X) (@ (@ (@ tptp.output X) B) P))) Rs))))
% 0.25/0.70 (assert (forall ((A tptp.name) (B tptp.name) (P tptp.pi) (C tptp.late_subject) (X tptp.name) (P3 tptp.pi)) (not (@ (@ tptp.late_transitions (@ (@ (@ tptp.output A) B) P)) (@ (@ (@ tptp.late_BoundR C) X) P3)))))
% 0.25/0.70 (assert (forall ((Rel tptp.set_Pr1834926343_pi_pi) (A tptp.name) (B tptp.name) (P tptp.pi)) (not (@ (@ (@ tptp.strong743114133lation tptp.piNil) Rel) (@ (@ (@ tptp.output A) B) P)))))
% 0.25/0.70 (assert (forall ((A tptp.name) (B tptp.name) (P tptp.pi) (Alpha2 tptp.late_freeRes) (P3 tptp.pi) (Prop (-> tptp.late_freeRes tptp.pi Bool))) (let ((_let_1 (@ (@ tptp.late_OutputR A) B))) (=> (@ (@ tptp.late_transitions (@ (@ (@ tptp.output A) B) P)) (@ (@ tptp.late_FreeR Alpha2) P3)) (=> (=> (= Alpha2 _let_1) (=> (= P P3) (@ (@ Prop _let_1) P))) (@ (@ Prop Alpha2) P3))))))
% 0.25/0.70 (assert (forall ((A tptp.name) (B tptp.name) (P tptp.pi) (Rs tptp.late_residual)) (=> (@ (@ tptp.late_transitions (@ (@ (@ tptp.output A) B) P)) Rs) (not (forall ((A3 tptp.name) (B3 tptp.name) (P5 tptp.pi)) (=> (and (= A A3) (= B B3) (= P P5)) (not (= Rs (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR A3) B3)) P5)))))))))
% 0.25/0.70 (assert (forall ((A tptp.name) (B tptp.name) (P tptp.pi) (C tptp.name) (D tptp.name) (P3 tptp.pi)) (=> (@ (@ tptp.late_transitions (@ (@ (@ tptp.output A) B) P)) (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR C) D)) P3)) (not (or (not (= A C)) (not (= B D)))))))
% 0.25/0.70 (assert (forall ((A tptp.name) (B tptp.name) (P tptp.pi)) (@ (@ tptp.late_transitions (@ (@ (@ tptp.output A) B) P)) (@ (@ tptp.late_FreeR (@ (@ tptp.late_OutputR A) B)) P))))
% 0.25/0.70 (assert (forall ((A tptp.name) (B tptp.name) (P tptp.pi) (P3 tptp.pi)) (not (@ (@ tptp.late_transitions (@ (@ (@ tptp.output A) B) P)) (@ (@ tptp.late_FreeR tptp.late_TauR) P3)))))
% 0.25/0.70 (assert (forall ((A tptp.name) (B tptp.name) (P tptp.pi) (Alpha2 tptp.late_freeRes) (P3 tptp.pi)) (=> (@ (@ tptp.late_transitions (@ (@ (@ tptp.output A) B) P)) (@ (@ tptp.late_FreeR Alpha2) P3)) (not (or (@ (@ tptp.fresh_1641682979reeRes A) Alpha2) (@ (@ tptp.fresh_1641682979reeRes B) Alpha2))))))
% 0.25/0.70 (assert (forall ((A tptp.name) (B tptp.name) (P tptp.pi) (C tptp.name) (D tptp.name)) (= (@ (@ (@ tptp.subs (@ (@ (@ tptp.output A) B) P)) C) D) (@ (@ (@ tptp.output (@ (@ (@ tptp.subst_name A) C) D)) (@ (@ (@ tptp.subst_name B) C) D)) (@ (@ (@ tptp.subs P) C) D)))))
% 0.25/0.70 (assert (forall ((X tptp.name) (A tptp.name) (C tptp.name) (D tptp.name) (P tptp.pi)) (=> (not (= X A)) (=> (not (= X C)) (=> (not (= X D)) (= (@ (@ (@ tptp.subs (@ (@ (@ tptp.input A) X) P)) C) D) (@ (@ (@ tptp.input (@ (@ (@ tptp.subst_name A) C) D)) X) (@ (@ (@ tptp.subs P) C) D))))))))
% 0.25/0.70 (assert (forall ((X tptp.name) (B tptp.name) (C tptp.name) (A tptp.name) (P tptp.pi)) (=> (not (= X B)) (=> (not (= X C)) (= (@ (@ (@ tptp.subs (@ (@ (@ tptp.input A) X) P)) B) C) (@ (@ (@ tptp.input (@ (@ (@ tptp.subst_name A) B) C)) X) (@ (@ (@ tptp.subs P) B) C)))))))
% 0.25/0.70 (assert (= tptp.subst_name (lambda ((A5 tptp.name) (B4 tptp.name) (C4 tptp.name)) (@ (@ (@ tptp.if_name (= A5 B4)) C4) A5))))
% 0.25/0.70 (assert (forall ((A tptp.name) (B tptp.name) (P tptp.pi) (C tptp.name) (D tptp.name)) (= (@ (@ (@ tptp.subs (@ (@ (@ tptp.mismatch A) B) P)) C) D) (@ (@ (@ tptp.mismatch (@ (@ (@ tptp.subst_name A) C) D)) (@ (@ (@ tptp.subst_name B) C) D)) (@ (@ (@ tptp.subs P) C) D)))))
% 0.25/0.70 (assert (forall ((A tptp.name) (B tptp.name) (P tptp.pi) (C tptp.name) (D tptp.name)) (= (@ (@ (@ tptp.subs (@ (@ (@ tptp.match A) B) P)) C) D) (@ (@ (@ tptp.match (@ (@ (@ tptp.subst_name A) C) D)) (@ (@ (@ tptp.subst_name B) C) D)) (@ (@ (@ tptp.subs P) C) D)))))
% 0.25/0.70 (assert (forall ((A tptp.name) (X32 tptp.name) (X2 tptp.name) (X1 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi A))) (let ((_let_2 (@ tptp.fresh_name_name A))) (= (@ _let_1 (@ (@ (@ tptp.match X32) X2) X1)) (and (@ _let_2 X32) (@ _let_2 X2) (@ _let_1 X1)))))))
% 0.25/0.70 (assert (forall ((A tptp.name) (X32 tptp.name) (X2 tptp.name) (X1 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi A))) (let ((_let_2 (@ tptp.fresh_name_name A))) (= (@ _let_1 (@ (@ (@ tptp.mismatch X32) X2) X1)) (and (@ _let_2 X32) (@ _let_2 X2) (@ _let_1 X1)))))))
% 0.25/0.70 (assert (forall ((A tptp.name) (B tptp.name) (P tptp.pi) (Rs tptp.late_residual) (F (-> tptp.name tptp.name Bool))) (let ((_let_1 (@ F A))) (=> (@ (@ tptp.late_transitions (@ (@ (@ tptp.match A) B) P)) Rs) (=> (=> (@ (@ tptp.late_transitions P) Rs) (=> (= A B) (@ _let_1 A))) (@ _let_1 B))))))
% 0.25/0.70 (assert (forall ((A tptp.name) (B tptp.name) (P tptp.pi) (Rs tptp.late_residual)) (=> (@ (@ tptp.late_transitions (@ (@ (@ tptp.match A) B) P)) Rs) (= A B))))
% 0.25/0.70 (assert (forall ((A tptp.name) (B tptp.name) (P tptp.pi) (Rs tptp.late_residual)) (=> (@ (@ tptp.late_transitions (@ (@ (@ tptp.match A) B) P)) Rs) (not (forall ((P5 tptp.pi)) (=> (and (= B A) (= P P5)) (not (@ (@ tptp.late_transitions P5) Rs))))))))
% 0.25/0.70 (assert (forall ((A tptp.name) (B tptp.name) (P tptp.pi) (Rs tptp.late_residual) (F (-> tptp.name tptp.name Bool))) (let ((_let_1 (@ (@ F A) B))) (=> (@ (@ tptp.late_transitions (@ (@ (@ tptp.mismatch A) B) P)) Rs) (=> (=> (@ (@ tptp.late_transitions P) Rs) (=> (not (= A B)) _let_1)) _let_1)))))
% 0.25/0.70 (assert (forall ((A tptp.name) (P tptp.pi) (Rs tptp.late_residual)) (not (@ (@ tptp.late_transitions (@ (@ (@ tptp.mismatch A) A) P)) Rs))))
% 0.25/0.70 (assert (forall ((A tptp.name) (B tptp.name) (P tptp.pi) (Rs tptp.late_residual)) (=> (@ (@ tptp.late_transitions (@ (@ (@ tptp.mismatch A) B) P)) Rs) (not (forall ((P5 tptp.pi) (A3 tptp.name) (B3 tptp.name)) (=> (and (= A A3) (= B B3) (= P P5)) (=> (@ (@ tptp.late_transitions P5) Rs) (= A3 B3))))))))
% 0.25/0.70 (assert (forall ((P tptp.pi) (Rs tptp.late_residual) (B tptp.name)) (=> (@ (@ tptp.late_transitions P) Rs) (@ (@ tptp.late_transitions (@ (@ (@ tptp.match B) B) P)) Rs))))
% 0.25/0.70 (assert (forall ((P tptp.pi) (Rs tptp.late_residual) (A tptp.name) (B tptp.name)) (=> (@ (@ tptp.late_transitions P) Rs) (=> (not (= A B)) (@ (@ tptp.late_transitions (@ (@ (@ tptp.mismatch A) B) P)) Rs)))))
% 0.25/0.70 (assert (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Name tptp.name) (Pi tptp.pi)) (not (= (@ (@ (@ tptp.match Name12) Name22) Pi3) (@ (@ tptp.res Name) Pi)))))
% 0.25/0.70 (assert (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Name tptp.name) (Pi tptp.pi)) (not (= (@ (@ (@ tptp.mismatch Name12) Name22) Pi3) (@ (@ tptp.res Name) Pi)))))
% 0.25/0.70 (assert (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Pi12 tptp.pi) (Pi22 tptp.pi)) (not (= (@ (@ (@ tptp.match Name12) Name22) Pi3) (@ (@ tptp.par Pi12) Pi22)))))
% 0.25/0.70 (assert (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Pi12 tptp.pi) (Pi22 tptp.pi)) (not (= (@ (@ (@ tptp.mismatch Name12) Name22) Pi3) (@ (@ tptp.par Pi12) Pi22)))))
% 0.25/0.70 (assert (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Name1 tptp.name) (Name2 tptp.name) (Pi tptp.pi)) (not (= (@ (@ (@ tptp.input Name12) Name22) Pi3) (@ (@ (@ tptp.match Name1) Name2) Pi)))))
% 0.25/0.70 (assert (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Name1 tptp.name) (Name2 tptp.name) (Pi tptp.pi)) (not (= (@ (@ (@ tptp.input Name12) Name22) Pi3) (@ (@ (@ tptp.mismatch Name1) Name2) Pi)))))
% 0.25/0.70 (assert (forall ((Name1 tptp.name) (Name2 tptp.name) (Pi tptp.pi)) (not (= tptp.piNil (@ (@ (@ tptp.match Name1) Name2) Pi)))))
% 0.25/0.70 (assert (forall ((Name1 tptp.name) (Name2 tptp.name) (Pi tptp.pi)) (not (= tptp.piNil (@ (@ (@ tptp.mismatch Name1) Name2) Pi)))))
% 0.25/0.70 (assert (forall ((Pi3 tptp.pi) (Name1 tptp.name) (Name2 tptp.name) (Pi tptp.pi)) (not (= (@ tptp.tau Pi3) (@ (@ (@ tptp.match Name1) Name2) Pi)))))
% 0.25/0.70 (assert (forall ((Pi3 tptp.pi) (Name1 tptp.name) (Name2 tptp.name) (Pi tptp.pi)) (not (= (@ tptp.tau Pi3) (@ (@ (@ tptp.mismatch Name1) Name2) Pi)))))
% 0.25/0.70 (assert (forall ((X32 tptp.name) (X2 tptp.name) (X1 tptp.pi) (Y32 tptp.name) (Y2 tptp.name) (Y1 tptp.pi)) (= (= (@ (@ (@ tptp.mismatch X32) X2) X1) (@ (@ (@ tptp.mismatch Y32) Y2) Y1)) (and (= X32 Y32) (= X2 Y2) (= X1 Y1)))))
% 0.25/0.70 (assert (forall ((X32 tptp.name) (X2 tptp.name) (X1 tptp.pi) (Y32 tptp.name) (Y2 tptp.name) (Y1 tptp.pi)) (= (= (@ (@ (@ tptp.match X32) X2) X1) (@ (@ (@ tptp.match Y32) Y2) Y1)) (and (= X32 Y32) (= X2 Y2) (= X1 Y1)))))
% 0.25/0.70 (assert (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Name1 tptp.name) (Name2 tptp.name) (Pi tptp.pi)) (not (= (@ (@ (@ tptp.match Name12) Name22) Pi3) (@ (@ (@ tptp.mismatch Name1) Name2) Pi)))))
% 0.25/0.70 (assert (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Name1 tptp.name) (Name2 tptp.name) (Pi tptp.pi)) (not (= (@ (@ (@ tptp.output Name12) Name22) Pi3) (@ (@ (@ tptp.match Name1) Name2) Pi)))))
% 0.25/0.70 (assert (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Name1 tptp.name) (Name2 tptp.name) (Pi tptp.pi)) (not (= (@ (@ (@ tptp.output Name12) Name22) Pi3) (@ (@ (@ tptp.mismatch Name1) Name2) Pi)))))
% 0.25/0.70 (assert (forall ((A tptp.name) (B tptp.name) (Rel tptp.set_Pr1834926343_pi_pi) (P tptp.pi)) (=> (not (= A B)) (@ (@ (@ tptp.strong743114133lation tptp.piNil) Rel) (@ (@ (@ tptp.match A) B) P)))))
% 0.25/0.70 (assert (forall ((Rel tptp.set_Pr1834926343_pi_pi) (A tptp.name) (P tptp.pi)) (@ (@ (@ tptp.strong743114133lation tptp.piNil) Rel) (@ (@ (@ tptp.mismatch A) A) P))))
% 0.25/0.70 (assert (forall ((P (-> tptp.late_freeRes tptp.pi Bool)) (Z tptp.late_freeRes) (Pi3 tptp.pi)) (=> (forall ((Z2 tptp.late_freeRes)) (@ (@ P Z2) tptp.piNil)) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.late_freeRes)) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.output Name13) Name23) Pi4)))) (=> (forall ((Pi4 tptp.pi) (Z2 tptp.late_freeRes)) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ tptp.tau Pi4)))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.late_freeRes)) (=> (@ (@ tptp.fresh_1641682979reeRes Name23) Z2) (=> (@ (@ tptp.fresh_name_name Name23) Name13) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.input Name13) Name23) Pi4)))))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.late_freeRes)) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.match Name13) Name23) Pi4)))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.late_freeRes)) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.mismatch Name13) Name23) Pi4)))) (=> (forall ((Pi13 tptp.pi) (Pi23 tptp.pi) (Z2 tptp.late_freeRes)) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi13)) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi23)) (@ (@ P Z2) (@ (@ tptp.sum Pi13) Pi23))))) (=> (forall ((Pi13 tptp.pi) (Pi23 tptp.pi) (Z2 tptp.late_freeRes)) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi13)) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi23)) (@ (@ P Z2) (@ (@ tptp.par Pi13) Pi23))))) (=> (forall ((Name4 tptp.name) (Pi4 tptp.pi) (Z2 tptp.late_freeRes)) (=> (@ (@ tptp.fresh_1641682979reeRes Name4) Z2) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ tptp.res Name4) Pi4))))) (=> (forall ((Pi4 tptp.pi) (Z2 tptp.late_freeRes)) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ tptp.bang Pi4)))) (@ (@ P Z) Pi3)))))))))))))
% 0.25/0.70 (assert (forall ((P (-> tptp.produc1141751126_pi_pi tptp.pi Bool)) (Z tptp.produc1141751126_pi_pi) (Pi3 tptp.pi)) (=> (forall ((Z2 tptp.produc1141751126_pi_pi)) (@ (@ P Z2) tptp.piNil)) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.output Name13) Name23) Pi4)))) (=> (forall ((Pi4 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ tptp.tau Pi4)))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (@ (@ tptp.fresh_1376661020_pi_pi Name23) Z2) (=> (@ (@ tptp.fresh_name_name Name23) Name13) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.input Name13) Name23) Pi4)))))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.match Name13) Name23) Pi4)))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.mismatch Name13) Name23) Pi4)))) (=> (forall ((Pi13 tptp.pi) (Pi23 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi13)) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi23)) (@ (@ P Z2) (@ (@ tptp.sum Pi13) Pi23))))) (=> (forall ((Pi13 tptp.pi) (Pi23 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi13)) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi23)) (@ (@ P Z2) (@ (@ tptp.par Pi13) Pi23))))) (=> (forall ((Name4 tptp.name) (Pi4 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (@ (@ tptp.fresh_1376661020_pi_pi Name4) Z2) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ tptp.res Name4) Pi4))))) (=> (forall ((Pi4 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ tptp.bang Pi4)))) (@ (@ P Z) Pi3)))))))))))))
% 0.25/0.70 (assert (forall ((P (-> tptp.name tptp.pi Bool)) (Z tptp.name) (Pi3 tptp.pi)) (=> (forall ((Z2 tptp.name)) (@ (@ P Z2) tptp.piNil)) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.name)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.output Name13) Name23) Pi4)))) (=> (forall ((Pi4 tptp.pi) (Z2 tptp.name)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ tptp.tau Pi4)))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.name)) (let ((_let_1 (@ tptp.fresh_name_name Name23))) (=> (@ _let_1 Z2) (=> (@ _let_1 Name13) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.input Name13) Name23) Pi4))))))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.name)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.match Name13) Name23) Pi4)))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.name)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.mismatch Name13) Name23) Pi4)))) (=> (forall ((Pi13 tptp.pi) (Pi23 tptp.pi) (Z2 tptp.name)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi13)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi23)) (@ (@ P Z2) (@ (@ tptp.sum Pi13) Pi23))))) (=> (forall ((Pi13 tptp.pi) (Pi23 tptp.pi) (Z2 tptp.name)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi13)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi23)) (@ (@ P Z2) (@ (@ tptp.par Pi13) Pi23))))) (=> (forall ((Name4 tptp.name) (Pi4 tptp.pi) (Z2 tptp.name)) (=> (@ (@ tptp.fresh_name_name Name4) Z2) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ tptp.res Name4) Pi4))))) (=> (forall ((Pi4 tptp.pi) (Z2 tptp.name)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ tptp.bang Pi4)))) (@ (@ P Z) Pi3)))))))))))))
% 0.25/0.70 (assert (forall ((P (-> tptp.pi tptp.pi Bool)) (Z tptp.pi) (Pi3 tptp.pi)) (=> (forall ((Z2 tptp.pi)) (@ (@ P Z2) tptp.piNil)) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.pi)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.output Name13) Name23) Pi4)))) (=> (forall ((Pi4 tptp.pi) (Z2 tptp.pi)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ tptp.tau Pi4)))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.pi)) (=> (@ (@ tptp.fresh_name_pi Name23) Z2) (=> (@ (@ tptp.fresh_name_name Name23) Name13) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.input Name13) Name23) Pi4)))))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.pi)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.match Name13) Name23) Pi4)))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.pi)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.mismatch Name13) Name23) Pi4)))) (=> (forall ((Pi13 tptp.pi) (Pi23 tptp.pi) (Z2 tptp.pi)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi13)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi23)) (@ (@ P Z2) (@ (@ tptp.sum Pi13) Pi23))))) (=> (forall ((Pi13 tptp.pi) (Pi23 tptp.pi) (Z2 tptp.pi)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi13)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi23)) (@ (@ P Z2) (@ (@ tptp.par Pi13) Pi23))))) (=> (forall ((Name4 tptp.name) (Pi4 tptp.pi) (Z2 tptp.pi)) (=> (@ (@ tptp.fresh_name_pi Name4) Z2) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ tptp.res Name4) Pi4))))) (=> (forall ((Pi4 tptp.pi) (Z2 tptp.pi)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ tptp.bang Pi4)))) (@ (@ P Z) Pi3)))))))))))))
% 0.25/0.70 (assert (forall ((P (-> tptp.late_freeRes tptp.pi Bool)) (Z tptp.late_freeRes) (Pi3 tptp.pi)) (=> (forall ((Z2 tptp.late_freeRes)) (@ (@ P Z2) tptp.piNil)) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.late_freeRes)) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.output Name13) Name23) Pi4)))) (=> (forall ((Pi4 tptp.pi) (Z2 tptp.late_freeRes)) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ tptp.tau Pi4)))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.late_freeRes)) (=> (@ (@ tptp.fresh_1641682979reeRes Name23) Z2) (=> (@ (@ tptp.fresh_name_name Name23) Name13) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.input Name13) Name23) Pi4)))))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.late_freeRes)) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.match Name13) Name23) Pi4)))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.late_freeRes)) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.mismatch Name13) Name23) Pi4)))) (=> (forall ((Pi13 tptp.pi) (Pi23 tptp.pi) (Z2 tptp.late_freeRes)) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi13)) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi23)) (@ (@ P Z2) (@ (@ tptp.sum Pi13) Pi23))))) (=> (forall ((Pi13 tptp.pi) (Pi23 tptp.pi) (Z2 tptp.late_freeRes)) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi13)) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi23)) (@ (@ P Z2) (@ (@ tptp.par Pi13) Pi23))))) (=> (forall ((Name4 tptp.name) (Pi4 tptp.pi) (Z2 tptp.late_freeRes)) (=> (@ (@ tptp.fresh_1641682979reeRes Name4) Z2) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ tptp.res Name4) Pi4))))) (=> (forall ((Pi4 tptp.pi) (Z2 tptp.late_freeRes)) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ tptp.bang Pi4)))) (@ (@ P Z) Pi3)))))))))))))
% 0.25/0.70 (assert (forall ((P (-> tptp.produc1141751126_pi_pi tptp.pi Bool)) (Z tptp.produc1141751126_pi_pi) (Pi3 tptp.pi)) (=> (forall ((Z2 tptp.produc1141751126_pi_pi)) (@ (@ P Z2) tptp.piNil)) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.output Name13) Name23) Pi4)))) (=> (forall ((Pi4 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ tptp.tau Pi4)))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (@ (@ tptp.fresh_1376661020_pi_pi Name23) Z2) (=> (@ (@ tptp.fresh_name_name Name23) Name13) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.input Name13) Name23) Pi4)))))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.match Name13) Name23) Pi4)))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.mismatch Name13) Name23) Pi4)))) (=> (forall ((Pi13 tptp.pi) (Pi23 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi13)) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi23)) (@ (@ P Z2) (@ (@ tptp.sum Pi13) Pi23))))) (=> (forall ((Pi13 tptp.pi) (Pi23 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi13)) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi23)) (@ (@ P Z2) (@ (@ tptp.par Pi13) Pi23))))) (=> (forall ((Name4 tptp.name) (Pi4 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (@ (@ tptp.fresh_1376661020_pi_pi Name4) Z2) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ tptp.res Name4) Pi4))))) (=> (forall ((Pi4 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ tptp.bang Pi4)))) (@ (@ P Z) Pi3)))))))))))))
% 0.25/0.70 (assert (forall ((P (-> tptp.name tptp.pi Bool)) (Z tptp.name) (Pi3 tptp.pi)) (=> (forall ((Z2 tptp.name)) (@ (@ P Z2) tptp.piNil)) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.name)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.output Name13) Name23) Pi4)))) (=> (forall ((Pi4 tptp.pi) (Z2 tptp.name)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ tptp.tau Pi4)))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.name)) (let ((_let_1 (@ tptp.fresh_name_name Name23))) (=> (@ _let_1 Z2) (=> (@ _let_1 Name13) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.input Name13) Name23) Pi4))))))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.name)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.match Name13) Name23) Pi4)))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.name)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.mismatch Name13) Name23) Pi4)))) (=> (forall ((Pi13 tptp.pi) (Pi23 tptp.pi) (Z2 tptp.name)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi13)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi23)) (@ (@ P Z2) (@ (@ tptp.sum Pi13) Pi23))))) (=> (forall ((Pi13 tptp.pi) (Pi23 tptp.pi) (Z2 tptp.name)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi13)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi23)) (@ (@ P Z2) (@ (@ tptp.par Pi13) Pi23))))) (=> (forall ((Name4 tptp.name) (Pi4 tptp.pi) (Z2 tptp.name)) (=> (@ (@ tptp.fresh_name_name Name4) Z2) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ tptp.res Name4) Pi4))))) (=> (forall ((Pi4 tptp.pi) (Z2 tptp.name)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ tptp.bang Pi4)))) (@ (@ P Z) Pi3)))))))))))))
% 0.25/0.70 (assert (forall ((P (-> tptp.pi tptp.pi Bool)) (Z tptp.pi) (Pi3 tptp.pi)) (=> (forall ((Z2 tptp.pi)) (@ (@ P Z2) tptp.piNil)) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.pi)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.output Name13) Name23) Pi4)))) (=> (forall ((Pi4 tptp.pi) (Z2 tptp.pi)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ tptp.tau Pi4)))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.pi)) (=> (@ (@ tptp.fresh_name_pi Name23) Z2) (=> (@ (@ tptp.fresh_name_name Name23) Name13) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.input Name13) Name23) Pi4)))))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.pi)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.match Name13) Name23) Pi4)))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.pi)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.mismatch Name13) Name23) Pi4)))) (=> (forall ((Pi13 tptp.pi) (Pi23 tptp.pi) (Z2 tptp.pi)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi13)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi23)) (@ (@ P Z2) (@ (@ tptp.sum Pi13) Pi23))))) (=> (forall ((Pi13 tptp.pi) (Pi23 tptp.pi) (Z2 tptp.pi)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi13)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi23)) (@ (@ P Z2) (@ (@ tptp.par Pi13) Pi23))))) (=> (forall ((Name4 tptp.name) (Pi4 tptp.pi) (Z2 tptp.pi)) (=> (@ (@ tptp.fresh_name_pi Name4) Z2) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ tptp.res Name4) Pi4))))) (=> (forall ((Pi4 tptp.pi) (Z2 tptp.pi)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ tptp.bang Pi4)))) (@ (@ P Z) Pi3)))))))))))))
% 0.25/0.70 (assert (forall ((A tptp.name) (X1 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi A))) (= (@ _let_1 (@ tptp.bang X1)) (@ _let_1 X1)))))
% 0.25/0.70 (assert (forall ((A tptp.name) (X2 tptp.pi) (X1 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi A))) (= (@ _let_1 (@ (@ tptp.sum X2) X1)) (and (@ _let_1 X2) (@ _let_1 X1))))))
% 0.25/0.70 (assert (forall ((P tptp.pi) (C tptp.name) (D tptp.name)) (= (@ (@ (@ tptp.subs (@ tptp.bang P)) C) D) (@ tptp.bang (@ (@ (@ tptp.subs P) C) D)))))
% 0.25/0.70 (assert (forall ((P tptp.pi) (Q tptp.pi) (C tptp.name) (D tptp.name)) (= (@ (@ (@ tptp.subs (@ (@ tptp.sum P) Q)) C) D) (@ (@ tptp.sum (@ (@ (@ tptp.subs P) C) D)) (@ (@ (@ tptp.subs Q) C) D)))))
% 0.25/0.70 (assert (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Pi tptp.pi)) (not (= (@ (@ (@ tptp.mismatch Name12) Name22) Pi3) (@ tptp.bang Pi)))))
% 0.25/0.70 (assert (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Pi12 tptp.pi) (Pi22 tptp.pi)) (not (= (@ (@ (@ tptp.mismatch Name12) Name22) Pi3) (@ (@ tptp.sum Pi12) Pi22)))))
% 0.25/0.70 (assert (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Pi tptp.pi)) (not (= (@ (@ (@ tptp.match Name12) Name22) Pi3) (@ tptp.bang Pi)))))
% 0.25/0.70 (assert (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Pi12 tptp.pi) (Pi22 tptp.pi)) (not (= (@ (@ (@ tptp.match Name12) Name22) Pi3) (@ (@ tptp.sum Pi12) Pi22)))))
% 0.25/0.70 (assert (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Pi tptp.pi)) (not (= (@ (@ (@ tptp.output Name12) Name22) Pi3) (@ tptp.bang Pi)))))
% 0.25/0.70 (assert (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Pi12 tptp.pi) (Pi22 tptp.pi)) (not (= (@ (@ (@ tptp.output Name12) Name22) Pi3) (@ (@ tptp.sum Pi12) Pi22)))))
% 0.25/0.70 (assert (forall ((Name3 tptp.name) (Pi3 tptp.pi) (Pi tptp.pi)) (not (= (@ (@ tptp.res Name3) Pi3) (@ tptp.bang Pi)))))
% 0.25/0.70 (assert (forall ((Pi1 tptp.pi) (Pi2 tptp.pi) (Pi tptp.pi)) (not (= (@ (@ tptp.par Pi1) Pi2) (@ tptp.bang Pi)))))
% 0.25/0.70 (assert (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Pi tptp.pi)) (not (= (@ (@ (@ tptp.input Name12) Name22) Pi3) (@ tptp.bang Pi)))))
% 0.25/0.70 (assert (forall ((Pi tptp.pi)) (not (= tptp.piNil (@ tptp.bang Pi)))))
% 0.25/0.70 (assert (forall ((Q tptp.pi) (Rs tptp.late_residual) (P tptp.pi)) (=> (@ (@ tptp.late_transitions Q) Rs) (@ (@ tptp.late_transitions (@ (@ tptp.sum P) Q)) Rs))))
% 0.25/0.70 (assert (forall ((P tptp.pi) (Rs tptp.late_residual) (Q tptp.pi)) (=> (@ (@ tptp.late_transitions P) Rs) (@ (@ tptp.late_transitions (@ (@ tptp.sum P) Q)) Rs))))
% 0.25/0.70 (assert (forall ((P tptp.pi) (Q tptp.pi) (Rs tptp.late_residual)) (=> (@ (@ tptp.late_transitions (@ (@ tptp.sum P) Q)) Rs) (=> (not (@ (@ tptp.late_transitions P) Rs)) (@ (@ tptp.late_transitions Q) Rs)))))
% 0.25/0.70 (assert (forall ((P tptp.pi) (Q tptp.pi) (Rs tptp.late_residual)) (=> (@ (@ tptp.late_transitions (@ (@ tptp.sum P) Q)) Rs) (=> (not (@ (@ tptp.late_transitions P) Rs)) (@ (@ tptp.late_transitions Q) Rs)))))
% 0.25/0.70 (assert (forall ((Pi3 tptp.pi) (Pi tptp.pi)) (not (= (@ tptp.tau Pi3) (@ tptp.bang Pi)))))
% 0.25/0.70 (assert (forall ((Pi1 tptp.pi) (Pi2 tptp.pi) (Name tptp.name) (Pi tptp.pi)) (not (= (@ (@ tptp.sum Pi1) Pi2) (@ (@ tptp.res Name) Pi)))))
% 0.25/0.70 (assert (forall ((Pi1 tptp.pi) (Pi2 tptp.pi) (Pi12 tptp.pi) (Pi22 tptp.pi)) (not (= (@ (@ tptp.sum Pi1) Pi2) (@ (@ tptp.par Pi12) Pi22)))))
% 0.25/0.70 (assert (forall ((Pi1 tptp.pi) (Pi2 tptp.pi) (Pi tptp.pi)) (not (= (@ (@ tptp.sum Pi1) Pi2) (@ tptp.bang Pi)))))
% 0.25/0.70 (assert (forall ((X2 tptp.pi) (X1 tptp.pi) (Y2 tptp.pi) (Y1 tptp.pi)) (= (= (@ (@ tptp.sum X2) X1) (@ (@ tptp.sum Y2) Y1)) (and (= X2 Y2) (= X1 Y1)))))
% 0.25/0.70 (assert (forall ((X1 tptp.pi) (Y1 tptp.pi)) (= (= (@ tptp.bang X1) (@ tptp.bang Y1)) (= X1 Y1))))
% 0.25/0.70 (assert (forall ((Pi3 tptp.pi) (Pi12 tptp.pi) (Pi22 tptp.pi)) (not (= (@ tptp.tau Pi3) (@ (@ tptp.sum Pi12) Pi22)))))
% 0.25/0.70 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 0.25/0.70 (assert (forall ((X tptp.name) (Y tptp.name)) (= (@ (@ (@ tptp.if_name false) X) Y) Y)))
% 0.25/0.70 (assert (forall ((X tptp.name) (Y tptp.name)) (= (@ (@ (@ tptp.if_name true) X) Y) X)))
% 0.25/0.70 (assert (let ((_let_1 (@ tptp.res tptp.x))) (not (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi (@ (@ (@ tptp.subs (@ _let_1 (@ (@ tptp.par tptp.p2) tptp.q))) tptp.y) tptp.u)) (@ (@ tptp.par (@ (@ (@ tptp.subs tptp.p2) tptp.y) tptp.u)) (@ (@ (@ tptp.subs (@ _let_1 tptp.q)) tptp.y) tptp.u)))) tptp.rel))))
% 0.85/1.03 (set-info :filename cvc5---1.0.5_26572)
% 0.85/1.03 (check-sat-assuming ( true ))
% 0.85/1.03 ------- get file name : TPTP file name is ITP188^1
% 0.85/1.03 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_26572.smt2...
% 0.85/1.03 --- Run --ho-elim --full-saturate-quant at 10...
% 0.85/1.03 % SZS status Theorem for ITP188^1
% 0.85/1.03 % SZS output start Proof for ITP188^1
% 0.85/1.03 (
% 0.85/1.03 (let ((_let_1 (@ tptp.res tptp.x))) (let ((_let_2 (@ _let_1 tptp.q))) (let ((_let_3 (@ (@ (@ tptp.subs _let_2) tptp.y) tptp.u))) (let ((_let_4 (@ (@ (@ tptp.subs tptp.p2) tptp.y) tptp.u))) (let ((_let_5 (@ tptp.par _let_4))) (let ((_let_6 (@ (@ tptp.par tptp.p2) tptp.q))) (let ((_let_7 (@ _let_1 _let_6))) (let ((_let_8 (@ (@ (@ tptp.subs _let_7) tptp.y) tptp.u))) (let ((_let_9 (not (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi _let_8) (@ _let_5 _let_3))) tptp.rel)))) (let ((_let_10 (@ (@ tptp.late_BoundR tptp.aa) tptp.y))) (let ((_let_11 (@ tptp.par tptp.p))) (let ((_let_12 (@ _let_11 tptp.q))) (let ((_let_13 (@ _let_1 _let_12))) (let ((_let_14 (@ _let_11 _let_2))) (let ((_let_15 (@ tptp.fresh_name_pi tptp.y))) (let ((_let_16 (@ tptp.fresh_name_pi tptp.x))) (let ((_let_17 (forall ((Y tptp.name) (R tptp.pi) (S tptp.pi)) (let ((_let_1 (@ tptp.res Y))) (let ((_let_2 (@ tptp.par R))) (=> (@ (@ tptp.fresh_name_pi Y) R) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi (@ _let_1 (@ _let_2 S))) (@ _let_2 (@ _let_1 S)))) tptp.rel))))))) (let ((_let_18 (@ (@ (@ tptp.subs tptp.q) tptp.y) tptp.u))) (let ((_let_19 (= _let_8 (@ _let_1 (@ _let_5 _let_18))))) (let ((_let_20 (@ _let_16 _let_4))) (let ((_let_21 (= _let_3 (@ _let_1 _let_18)))) (let ((_let_22 (forall ((Y tptp.name) (R tptp.pi) (S tptp.pi)) (let ((_let_1 (ho_14 k_13 Y))) (let ((_let_2 (ho_21 k_20 R))) (or (not (ho_18 (ho_17 k_16 Y) R)) (ho_8 (ho_7 k_6 (ho_24 (ho_23 k_22 (ho_15 _let_1 (ho_15 _let_2 S))) (ho_15 _let_2 (ho_15 _let_1 S)))) tptp.rel))))))) (let ((_let_23 (ho_12 (ho_11 (ho_10 k_9 tptp.q) tptp.y) tptp.u))) (let ((_let_24 (ho_14 k_13 tptp.x))) (let ((_let_25 (ho_15 _let_24 _let_23))) (let ((_let_26 (ho_12 (ho_11 (ho_10 k_9 tptp.p2) tptp.y) tptp.u))) (let ((_let_27 (ho_21 k_20 _let_26))) (let ((_let_28 (ho_15 _let_24 (ho_15 _let_27 _let_23)))) (let ((_let_29 (ho_8 (ho_7 k_6 (ho_24 (ho_23 k_22 _let_28) (ho_15 _let_27 _let_25))) tptp.rel))) (let ((_let_30 (ho_18 (ho_17 k_16 tptp.x) _let_26))) (let ((_let_31 (not _let_30))) (let ((_let_32 (or _let_31 _let_29))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_17)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Y tptp.name) (R tptp.pi) (S tptp.pi)) (let ((_let_1 (@ tptp.res Y))) (let ((_let_2 (@ tptp.par R))) (or (not (@ (@ tptp.fresh_name_pi Y) R)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi (@ _let_1 (@ _let_2 S))) (@ _let_2 (@ _let_1 S)))) tptp.rel))))) _let_22))))))) (let ((_let_34 (not _let_32))) (let ((_let_35 (ho_12 (ho_11 (ho_10 k_9 (ho_15 _let_24 (ho_15 (ho_21 k_20 tptp.p2) tptp.q))) tptp.y) tptp.u))) (let ((_let_36 (= _let_28 _let_35))) (let ((_let_37 (ho_12 (ho_11 (ho_10 k_9 (ho_15 _let_24 tptp.q)) tptp.y) tptp.u))) (let ((_let_38 (= _let_25 _let_37))) (let ((_let_39 (ho_8 (ho_7 k_6 (ho_24 (ho_23 k_22 _let_35) (ho_15 _let_27 _let_37))) tptp.rel))) (let ((_let_40 (not _let_29))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_19)) (PREPROCESS :args ((= _let_19 _let_36)))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_21)) (PREPROCESS :args ((= _let_21 _let_38)))))) (let ((_let_43 (not _let_39))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_9)) (PREPROCESS :args ((= _let_9 _let_43)))))) (let ((_let_45 (not _let_36))) (let ((_let_46 (not _let_38))) (let ((_let_47 (and _let_38 _let_36 _let_43))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (tptp.x _let_26 _let_23 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_22))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_31 _let_29 _let_34))) (EQ_RESOLVE (ASSUME :args (_let_20)) (PREPROCESS :args ((= _let_20 _let_30)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_47)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_44 _let_41 _let_42) (SCOPE (FALSE_ELIM (TRANS (CONG (CONG (REFL :args (k_6)) (CONG (CONG (REFL :args (k_22)) (SYMM (SYMM _let_41)) :args (APPLY_UF ho_23)) (CONG (REFL :args (_let_27)) (SYMM (SYMM _let_42)) :args (APPLY_UF ho_15)) :args (APPLY_UF ho_24)) :args (APPLY_UF ho_7)) (REFL :args (tptp.rel)) :args (APPLY_UF ho_8)) (FALSE_INTRO _let_44))) :args (_let_43 _let_36 _let_38))) :args (_let_38 _let_36 _let_43))) :args (true _let_47)) (CONG (REFL :args (_let_46)) (REFL :args (_let_45)) (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_39))) (REFL :args (_let_40)) :args (or))) :args ((or _let_39 _let_46 _let_45 _let_40))) _let_44 _let_42 _let_41 :args (_let_40 true _let_39 false _let_38 false _let_36)) :args (_let_34 false _let_30 true _let_29)) _let_33 :args (false true _let_32 false _let_22)) :args ((not (= tptp.x tptp.u)) _let_21 (not (= tptp.y tptp.x)) _let_20 (@ tptp.eqvt_pi tptp.rel) _let_19 (@ _let_15 tptp.q) (@ _let_16 tptp.p2) _let_17 (forall ((Y tptp.name) (R tptp.pi) (Z tptp.name) (S tptp.pi)) (let ((_let_1 (@ tptp.res Y))) (let ((_let_2 (@ tptp.par R))) (let ((_let_3 (@ tptp.res Z))) (=> (@ (@ tptp.fresh_name_pi Y) R) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi (@ _let_1 (@ _let_3 (@ _let_2 S)))) (@ _let_3 (@ _let_2 (@ _let_1 S))))) tptp.rel)))))) (@ _let_15 _let_2) (@ _let_16 tptp.p) (@ _let_15 _let_14) (@ _let_15 _let_13) (forall ((P tptp.pi) (Q tptp.pi) (C tptp.name) (D tptp.name)) (= (@ (@ (@ tptp.subs (@ (@ tptp.par P) Q)) C) D) (@ (@ tptp.par (@ (@ (@ tptp.subs P) C) D)) (@ (@ (@ tptp.subs Q) C) D)))) (forall ((X tptp.name) (C tptp.name) (D tptp.name) (P tptp.pi)) (let ((_let_1 (@ tptp.res X))) (=> (not (= X C)) (=> (not (= X D)) (= (@ (@ (@ tptp.subs (@ _let_1 P)) C) D) (@ _let_1 (@ (@ (@ tptp.subs P) C) D))))))) (forall ((P tptp.pi) (A tptp.name)) (= (@ (@ (@ tptp.subs P) A) A) P)) (forall ((X1 (-> tptp.name tptp.noption_pi)) (X2 tptp.late_freeRes) (Y1 (-> tptp.name tptp.noption_pi)) (Y2 tptp.late_freeRes)) (= (= (@ (@ tptp.produc1505598906reeRes X1) X2) (@ (@ tptp.produc1505598906reeRes Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((X1 (-> tptp.name tptp.noption_pi)) (X2 tptp.produc1141751126_pi_pi) (Y1 (-> tptp.name tptp.noption_pi)) (Y2 tptp.produc1141751126_pi_pi)) (= (= (@ (@ tptp.produc1275980869_pi_pi X1) X2) (@ (@ tptp.produc1275980869_pi_pi Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((X1 (-> tptp.name tptp.noption_pi)) (X2 tptp.name) (Y1 (-> tptp.name tptp.noption_pi)) (Y2 tptp.name)) (= (= (@ (@ tptp.produc540578151i_name X1) X2) (@ (@ tptp.produc540578151i_name Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((X1 (-> tptp.name tptp.noption_pi)) (X2 tptp.pi) (Y1 (-> tptp.name tptp.noption_pi)) (Y2 tptp.pi)) (= (= (@ (@ tptp.produc1820286517_pi_pi X1) X2) (@ (@ tptp.produc1820286517_pi_pi Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((X1 (-> tptp.name tptp.noption_pi)) (X2 (-> tptp.name tptp.noption_pi)) (Y1 (-> tptp.name tptp.noption_pi)) (Y2 (-> tptp.name tptp.noption_pi))) (= (= (@ (@ tptp.produc1342893193ion_pi X1) X2) (@ (@ tptp.produc1342893193ion_pi Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((X1 tptp.pi) (X2 tptp.pi) (Y1 tptp.pi) (Y2 tptp.pi)) (= (= (@ (@ tptp.product_Pair_pi_pi X1) X2) (@ (@ tptp.product_Pair_pi_pi Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((X1 tptp.name) (X2 tptp.product_prod_pi_pi) (Y1 tptp.name) (Y2 tptp.product_prod_pi_pi)) (= (= (@ (@ tptp.produc235456326_pi_pi X1) X2) (@ (@ tptp.produc235456326_pi_pi Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((A (-> tptp.name tptp.noption_pi)) (B tptp.late_freeRes) (A2 (-> tptp.name tptp.noption_pi)) (B2 tptp.late_freeRes)) (= (= (@ (@ tptp.produc1505598906reeRes A) B) (@ (@ tptp.produc1505598906reeRes A2) B2)) (and (= A A2) (= B B2)))) (forall ((A (-> tptp.name tptp.noption_pi)) (B tptp.produc1141751126_pi_pi) (A2 (-> tptp.name tptp.noption_pi)) (B2 tptp.produc1141751126_pi_pi)) (= (= (@ (@ tptp.produc1275980869_pi_pi A) B) (@ (@ tptp.produc1275980869_pi_pi A2) B2)) (and (= A A2) (= B B2)))) (forall ((A (-> tptp.name tptp.noption_pi)) (B tptp.name) (A2 (-> tptp.name tptp.noption_pi)) (B2 tptp.name)) (= (= (@ (@ tptp.produc540578151i_name A) B) (@ (@ tptp.produc540578151i_name A2) B2)) (and (= A A2) (= B B2)))) (forall ((A (-> tptp.name tptp.noption_pi)) (B tptp.pi) (A2 (-> tptp.name tptp.noption_pi)) (B2 tptp.pi)) (= (= (@ (@ tptp.produc1820286517_pi_pi A) B) (@ (@ tptp.produc1820286517_pi_pi A2) B2)) (and (= A A2) (= B B2)))) (forall ((A (-> tptp.name tptp.noption_pi)) (B (-> tptp.name tptp.noption_pi)) (A2 (-> tptp.name tptp.noption_pi)) (B2 (-> tptp.name tptp.noption_pi))) (= (= (@ (@ tptp.produc1342893193ion_pi A) B) (@ (@ tptp.produc1342893193ion_pi A2) B2)) (and (= A A2) (= B B2)))) (forall ((A tptp.pi) (B tptp.pi) (A2 tptp.pi) (B2 tptp.pi)) (= (= (@ (@ tptp.product_Pair_pi_pi A) B) (@ (@ tptp.product_Pair_pi_pi A2) B2)) (and (= A A2) (= B B2)))) (forall ((A tptp.name) (B tptp.product_prod_pi_pi) (A2 tptp.name) (B2 tptp.product_prod_pi_pi)) (= (= (@ (@ tptp.produc235456326_pi_pi A) B) (@ (@ tptp.produc235456326_pi_pi A2) B2)) (and (= A A2) (= B B2)))) (forall ((Pi1 tptp.pi) (Pi2 tptp.pi) (Name tptp.name) (Pi tptp.pi)) (not (= (@ (@ tptp.par Pi1) Pi2) (@ (@ tptp.res Name) Pi)))) (@ _let_15 tptp.p) (@ (@ tptp.fresh_1376661020_pi_pi tptp.y) (@ (@ tptp.produc235456326_pi_pi tptp.x) (@ (@ tptp.product_Pair_pi_pi tptp.p) tptp.q))) (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P tptp.pi) (Q tptp.pi)) (=> (forall ((R2 tptp.pi) (S2 tptp.pi)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi (@ (@ tptp.par R2) S2)) (@ (@ tptp.par S2) R2))) Rel)) (=> (forall ((R2 tptp.pi) (S2 tptp.pi) (X3 tptp.name)) (let ((_let_1 (@ tptp.res X3))) (=> (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi R2) S2)) Rel) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi (@ _let_1 R2)) (@ _let_1 S2))) Rel)))) (@ (@ (@ tptp.strong743114133lation (@ (@ tptp.par P) Q)) Rel) (@ (@ tptp.par Q) P))))) (forall ((B tptp.name) (P tptp.pi) (A tptp.name)) (=> (@ (@ tptp.fresh_name_pi B) P) (= (@ (@ tptp.res A) P) (@ (@ tptp.res B) (@ (@ (@ tptp.subs P) A) B))))) (forall ((B tptp.name) (P tptp.pi) (A tptp.name)) (=> (@ (@ tptp.fresh_name_pi B) P) (= (@ (@ (@ tptp.subs (@ (@ tptp.res A) P)) A) B) (@ (@ tptp.res B) (@ (@ (@ tptp.subs P) A) B))))) (@ (@ tptp.fresh_717452603ubject tptp.y) tptp.aa) (@ (@ tptp.fresh_717452603ubject tptp.x) tptp.aa) (forall ((A tptp.name) (X2 tptp.pi) (X1 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi A))) (= (@ _let_1 (@ (@ tptp.par X2) X1)) (and (@ _let_1 X2) (@ _let_1 X1))))) (forall ((X tptp.late_freeRes)) (not (forall ((C2 tptp.name)) (not (@ (@ tptp.fresh_1641682979reeRes C2) X))))) (forall ((X tptp.produc1141751126_pi_pi)) (not (forall ((C2 tptp.name)) (not (@ (@ tptp.fresh_1376661020_pi_pi C2) X))))) (forall ((X tptp.name)) (not (forall ((C2 tptp.name)) (not (@ (@ tptp.fresh_name_name C2) X))))) (forall ((X tptp.pi)) (not (forall ((C2 tptp.name)) (not (@ (@ tptp.fresh_name_pi C2) X))))) (forall ((A tptp.name) (P tptp.pi)) (@ (@ tptp.fresh_name_pi A) (@ (@ tptp.res A) P))) (forall ((A tptp.name) (B tptp.name) (P tptp.pi)) (=> (not (= A B)) (@ (@ tptp.fresh_name_pi A) (@ (@ (@ tptp.subs P) A) B)))) (forall ((A tptp.name) (P tptp.pi) (C tptp.name) (B tptp.name)) (let ((_let_1 (@ tptp.fresh_name_pi A))) (=> (@ _let_1 P) (=> (not (= A C)) (@ _let_1 (@ (@ (@ tptp.subs P) B) C)))))) (forall ((A tptp.name) (P tptp.pi) (B tptp.name)) (=> (@ (@ tptp.fresh_name_pi A) P) (= (@ (@ (@ tptp.subs P) A) B) P))) (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P tptp.pi) (Q tptp.pi) (R tptp.pi)) (let ((_let_1 (@ tptp.par P))) (=> (forall ((S2 tptp.pi) (T tptp.pi) (U tptp.pi)) (let ((_let_1 (@ tptp.par S2))) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi (@ (@ tptp.par (@ _let_1 T)) U)) (@ _let_1 (@ (@ tptp.par T) U)))) Rel))) (=> (forall ((S2 tptp.pi) (T tptp.pi) (X3 tptp.name)) (let ((_let_1 (@ tptp.res X3))) (=> (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi S2) T)) Rel) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi (@ _let_1 S2)) (@ _let_1 T))) Rel)))) (=> (forall ((S2 tptp.pi) (T tptp.pi) (U tptp.pi) (X3 tptp.name)) (let ((_let_1 (@ tptp.res X3))) (let ((_let_2 (@ tptp.par S2))) (=> (@ (@ tptp.fresh_name_pi X3) S2) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi (@ _let_1 (@ (@ tptp.par (@ _let_2 T)) U))) (@ _let_2 (@ _let_1 (@ (@ tptp.par T) U))))) Rel))))) (=> (forall ((S2 tptp.pi) (T tptp.pi) (U tptp.pi) (X3 tptp.name)) (let ((_let_1 (@ tptp.par S2))) (let ((_let_2 (@ tptp.res X3))) (=> (@ (@ tptp.fresh_name_pi X3) U) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi (@ (@ tptp.par (@ _let_2 (@ _let_1 T))) U)) (@ _let_2 (@ _let_1 (@ (@ tptp.par T) U))))) Rel))))) (@ (@ (@ tptp.strong743114133lation (@ (@ tptp.par (@ _let_1 Q)) R)) Rel) (@ _let_1 (@ (@ tptp.par Q) R))))))))) (forall ((P (-> tptp.produc1834551554reeRes Bool)) (Prod tptp.produc1834551554reeRes)) (=> (forall ((A3 (-> tptp.name tptp.noption_pi)) (B3 tptp.late_freeRes)) (@ P (@ (@ tptp.produc1505598906reeRes A3) B3))) (@ P Prod))) (forall ((P (-> tptp.produc53907987_pi_pi Bool)) (Prod tptp.produc53907987_pi_pi)) (=> (forall ((A3 (-> tptp.name tptp.noption_pi)) (B3 tptp.produc1141751126_pi_pi)) (@ P (@ (@ tptp.produc1275980869_pi_pi A3) B3))) (@ P Prod))) (forall ((P (-> tptp.produc405342261i_name Bool)) (Prod tptp.produc405342261i_name)) (=> (forall ((A3 (-> tptp.name tptp.noption_pi)) (B3 tptp.name)) (@ P (@ (@ tptp.produc540578151i_name A3) B3))) (@ P Prod))) (forall ((P (-> tptp.produc629157763_pi_pi Bool)) (Prod tptp.produc629157763_pi_pi)) (=> (forall ((A3 (-> tptp.name tptp.noption_pi)) (B3 tptp.pi)) (@ P (@ (@ tptp.produc1820286517_pi_pi A3) B3))) (@ P Prod))) (forall ((P (-> tptp.produc1462499409ion_pi Bool)) (Prod tptp.produc1462499409ion_pi)) (=> (forall ((A3 (-> tptp.name tptp.noption_pi)) (B3 (-> tptp.name tptp.noption_pi))) (@ P (@ (@ tptp.produc1342893193ion_pi A3) B3))) (@ P Prod))) (forall ((P (-> tptp.product_prod_pi_pi Bool)) (Prod tptp.product_prod_pi_pi)) (=> (forall ((A3 tptp.pi) (B3 tptp.pi)) (@ P (@ (@ 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(@ _let_2 (@ (@ tptp.par P4) Q4))) (=> (@ (@ tptp.late_transitions P5) (@ _let_2 P4)) (=> (@ _let_1 P5) (=> (@ _let_1 Q4) (not (@ (@ tptp.fresh_717452603ubject X3) A3)))))))))) (not (forall ((Q4 tptp.pi) (A3 tptp.late_subject) (X3 tptp.name) (Q2 tptp.pi) (P5 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi X3))) (let ((_let_2 (@ (@ tptp.late_BoundR A3) X3))) (let ((_let_3 (@ tptp.par P5))) (=> (= (@ (@ tptp.par P) Q) (@ _let_3 Q4)) (=> (= (@ (@ (@ tptp.late_BoundR B) Y) P3) (@ _let_2 (@ _let_3 Q2))) (=> (@ (@ tptp.late_transitions Q4) (@ _let_2 Q2)) (=> (@ _let_1 P5) (=> (@ _let_1 Q4) (not (@ (@ tptp.fresh_717452603ubject X3) A3))))))))))))))) (forall ((P tptp.pi) (Rel tptp.set_Pr1834926343_pi_pi) (Q tptp.pi) (A tptp.late_subject) (X tptp.name) (Q3 tptp.pi)) (=> (@ (@ (@ tptp.strong743114133lation P) Rel) Q) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR A) X) Q3)) (=> (@ (@ tptp.fresh_name_pi X) P) (exists ((P4 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR A) X) P4)) (@ (@ (@ (@ (@ tptp.strong2129052853vative P4) Q3) A) X) Rel))))))) (forall ((Rel tptp.set_Pr1834926343_pi_pi) (Q tptp.pi) (P tptp.pi) (C3 tptp.late_freeRes)) (=> (@ tptp.eqvt_pi Rel) (=> (forall ((A3 tptp.late_subject) (X3 tptp.name) (Q2 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi X3))) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR A3) X3) Q2)) (=> (@ _let_1 P) (=> (@ _let_1 Q) (=> (@ (@ tptp.fresh_717452603ubject X3) A3) (=> (@ (@ tptp.fresh_1641682979reeRes X3) C3) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR A3) X3) P6)) (@ (@ (@ (@ (@ tptp.strong2129052853vative P6) Q2) A3) X3) Rel)))))))))) (=> (forall ((Alpha tptp.late_freeRes) (Q2 tptp.pi)) (=> (@ (@ tptp.late_transitions Q) (@ (@ tptp.late_FreeR Alpha) Q2)) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR Alpha) P6)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P6) Q2)) Rel))))) (@ (@ (@ tptp.strong743114133lation P) Rel) Q))))) (forall ((Rel tptp.set_Pr1834926343_pi_pi) (Q tptp.pi) (P tptp.pi) (C3 tptp.produc1141751126_pi_pi)) (=> (@ tptp.eqvt_pi Rel) (=> (forall ((A3 tptp.late_subject) (X3 tptp.name) (Q2 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi X3))) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR A3) X3) Q2)) (=> (@ _let_1 P) (=> (@ _let_1 Q) (=> (@ (@ tptp.fresh_717452603ubject X3) A3) (=> (@ (@ tptp.fresh_1376661020_pi_pi X3) C3) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR A3) X3) P6)) (@ (@ (@ (@ (@ tptp.strong2129052853vative P6) Q2) A3) X3) Rel)))))))))) (=> (forall ((Alpha tptp.late_freeRes) (Q2 tptp.pi)) (=> (@ (@ tptp.late_transitions Q) (@ (@ tptp.late_FreeR Alpha) Q2)) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR Alpha) P6)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P6) Q2)) Rel))))) (@ (@ (@ tptp.strong743114133lation P) Rel) Q))))) (forall ((Rel tptp.set_Pr1834926343_pi_pi) (Q tptp.pi) (P tptp.pi) (C3 tptp.name)) (=> (@ tptp.eqvt_pi Rel) (=> (forall ((A3 tptp.late_subject) (X3 tptp.name) (Q2 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi X3))) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR A3) X3) Q2)) (=> (@ _let_1 P) (=> (@ _let_1 Q) (=> (@ (@ tptp.fresh_717452603ubject X3) A3) (=> (@ (@ tptp.fresh_name_name X3) C3) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR A3) X3) P6)) (@ (@ (@ (@ (@ tptp.strong2129052853vative P6) Q2) A3) X3) Rel)))))))))) (=> (forall ((Alpha tptp.late_freeRes) (Q2 tptp.pi)) (=> (@ (@ tptp.late_transitions Q) (@ (@ tptp.late_FreeR Alpha) Q2)) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR Alpha) P6)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P6) Q2)) Rel))))) (@ (@ (@ tptp.strong743114133lation P) Rel) Q))))) (forall ((Rel tptp.set_Pr1834926343_pi_pi) (Q tptp.pi) (P tptp.pi) (C3 tptp.pi)) (=> (@ tptp.eqvt_pi Rel) (=> (forall ((A3 tptp.late_subject) (X3 tptp.name) (Q2 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi X3))) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR A3) X3) Q2)) (=> (@ _let_1 P) (=> (@ _let_1 Q) (=> (@ (@ tptp.fresh_717452603ubject X3) A3) (=> (@ _let_1 C3) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR A3) X3) P6)) (@ (@ (@ (@ (@ tptp.strong2129052853vative P6) Q2) A3) X3) Rel)))))))))) (=> (forall ((Alpha tptp.late_freeRes) (Q2 tptp.pi)) (=> (@ (@ tptp.late_transitions Q) (@ (@ tptp.late_FreeR Alpha) Q2)) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR Alpha) P6)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P6) Q2)) Rel))))) (@ (@ (@ tptp.strong743114133lation P) Rel) Q))))) (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P tptp.pi)) (=> (forall ((Q4 tptp.pi)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi (@ (@ tptp.par Q4) tptp.piNil)) Q4)) Rel)) (@ (@ (@ tptp.strong743114133lation (@ (@ tptp.par P) tptp.piNil)) Rel) P))) (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P tptp.pi)) (=> (forall ((Q4 tptp.pi)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi Q4) (@ (@ tptp.par Q4) tptp.piNil))) Rel)) (@ (@ (@ tptp.strong743114133lation P) Rel) (@ (@ tptp.par P) tptp.piNil)))) (forall ((A tptp.name) (X tptp.name) (P tptp.pi) (B tptp.late_subject) (Y tptp.name) (P3 tptp.pi)) (=> (@ (@ tptp.late_transitions (@ (@ (@ tptp.input A) X) P)) (@ (@ (@ tptp.late_BoundR B) Y) P3)) (not (@ (@ tptp.fresh_717452603ubject A) B)))) (forall ((X tptp.name) (P tptp.pi) (A tptp.late_subject) (Y tptp.name) (P3 tptp.pi)) (not (@ (@ tptp.late_transitions (@ (@ tptp.res X) (@ tptp.tau P))) (@ (@ (@ tptp.late_BoundR A) Y) P3)))) (forall ((A tptp.name)) (@ (@ tptp.fresh_name_pi A) tptp.piNil)) (forall ((A tptp.name) (X1 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi A))) (= (@ _let_1 (@ tptp.tau X1)) (@ _let_1 X1)))) (forall ((C tptp.name) (D tptp.name)) (= (@ (@ (@ tptp.subs tptp.piNil) C) D) tptp.piNil)) (forall ((P tptp.pi) (C tptp.name) (D tptp.name)) (= (@ (@ (@ tptp.subs (@ tptp.tau P)) C) D) (@ tptp.tau (@ (@ (@ tptp.subs P) C) D)))) (forall ((A tptp.name) (X2 tptp.late_freeRes) (X1 tptp.pi)) (= (@ (@ tptp.fresh_81631222sidual A) (@ (@ tptp.late_FreeR X2) X1)) (and (@ (@ tptp.fresh_1641682979reeRes A) X2) (@ (@ tptp.fresh_name_pi A) X1)))) (forall ((A tptp.name) (X tptp.name) (P tptp.pi) (Alpha2 tptp.late_freeRes) (P3 tptp.pi)) (not (@ (@ tptp.late_transitions (@ (@ (@ tptp.input A) X) P)) (@ (@ tptp.late_FreeR Alpha2) P3)))) (forall ((X2 tptp.late_freeRes) (X1 tptp.pi) (Y2 tptp.late_freeRes) (Y1 tptp.pi)) (= (= (@ (@ tptp.late_FreeR X2) X1) (@ (@ tptp.late_FreeR Y2) Y1)) (and (= X2 Y2) (= X1 Y1)))) (forall ((Rel tptp.set_Pr1834926343_pi_pi) (A tptp.name) (X tptp.name) (P tptp.pi)) (not (@ (@ (@ tptp.strong743114133lation tptp.piNil) Rel) (@ (@ (@ tptp.input A) X) P)))) (forall ((Rel tptp.set_Pr1834926343_pi_pi) (P tptp.pi)) (not (@ (@ (@ tptp.strong743114133lation tptp.piNil) Rel) (@ tptp.tau P)))) (forall ((Pi tptp.pi)) (not (= tptp.piNil (@ tptp.tau Pi)))) (forall ((Name1 tptp.name) (Name2 tptp.name) (Pi tptp.pi)) (not (= tptp.piNil (@ (@ (@ tptp.input Name1) Name2) Pi)))) (forall ((Pi3 tptp.pi) (Name1 tptp.name) (Name2 tptp.name) (Pi tptp.pi)) (not (= (@ tptp.tau Pi3) (@ (@ (@ tptp.input Name1) Name2) Pi)))) (forall ((X1 tptp.pi) (Y1 tptp.pi)) (= (= (@ tptp.tau X1) (@ tptp.tau Y1)) (= X1 Y1))) (forall ((X tptp.name) (A tptp.name) (Y tptp.name) (P tptp.pi) (Alpha2 tptp.late_freeRes) (P3 tptp.pi)) (not (@ (@ tptp.late_transitions (@ (@ tptp.res X) (@ (@ (@ tptp.input A) Y) P))) (@ (@ tptp.late_FreeR Alpha2) P3)))) (forall ((Subject tptp.late_subject) (Name3 tptp.name) (Pi3 tptp.pi) (FreeRes tptp.late_freeRes) (Pi tptp.pi)) (not (= (@ (@ (@ tptp.late_BoundR Subject) Name3) Pi3) (@ (@ tptp.late_FreeR FreeRes) Pi)))) (forall ((P (-> tptp.late_residual Bool)) (Residual tptp.late_residual)) (=> (forall ((Subject2 tptp.late_subject) (Name4 tptp.name) (Pi4 tptp.pi)) (@ P (@ (@ (@ tptp.late_BoundR Subject2) Name4) Pi4))) (=> (forall ((FreeRes2 tptp.late_freeRes) (Pi4 tptp.pi)) (@ P (@ (@ tptp.late_FreeR FreeRes2) Pi4))) (@ P Residual)))) (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Name tptp.name) (Pi tptp.pi)) (not (= (@ (@ (@ tptp.input Name12) Name22) Pi3) (@ (@ tptp.res Name) Pi)))) (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Pi12 tptp.pi) (Pi22 tptp.pi)) (not (= (@ (@ (@ tptp.input Name12) Name22) Pi3) (@ (@ tptp.par Pi12) Pi22)))) (forall ((Pi3 tptp.pi) (Name tptp.name) (Pi tptp.pi)) (not (= (@ tptp.tau Pi3) (@ (@ tptp.res Name) Pi)))) (forall ((Pi3 tptp.pi) (Pi12 tptp.pi) (Pi22 tptp.pi)) (not (= (@ tptp.tau Pi3) (@ (@ tptp.par Pi12) Pi22)))) (forall ((Rs tptp.late_residual)) (not (@ (@ tptp.late_transitions tptp.piNil) Rs))) (forall ((Rs tptp.late_residual)) (not (@ (@ tptp.late_transitions tptp.piNil) Rs))) (forall ((Name tptp.name) (Pi tptp.pi)) (not (= tptp.piNil (@ (@ tptp.res Name) Pi)))) (forall ((Pi12 tptp.pi) (Pi22 tptp.pi)) (not (= tptp.piNil (@ (@ tptp.par Pi12) Pi22)))) (forall ((P tptp.pi) (Rel tptp.set_Pr1834926343_pi_pi)) (@ (@ (@ tptp.strong743114133lation P) Rel) tptp.piNil)) (forall ((P tptp.pi) (Alpha2 tptp.late_freeRes) (P3 tptp.pi) (Y tptp.name)) (let ((_let_1 (@ tptp.res Y))) (let ((_let_2 (@ tptp.late_FreeR Alpha2))) (=> (@ (@ tptp.late_transitions P) (@ _let_2 P3)) (=> (@ (@ tptp.fresh_1641682979reeRes Y) Alpha2) (@ (@ tptp.late_transitions (@ _let_1 P)) (@ _let_2 (@ _let_1 P3)))))))) (forall ((X tptp.name) (P tptp.pi) (Alpha2 tptp.late_freeRes) (P3 tptp.pi)) (=> (@ (@ tptp.late_transitions (@ (@ tptp.res X) P)) (@ (@ tptp.late_FreeR Alpha2) P3)) (not (forall ((P5 tptp.pi) (Alpha tptp.late_freeRes) (P4 tptp.pi) (Y3 tptp.name)) (let ((_let_1 (@ tptp.late_FreeR Alpha))) (let ((_let_2 (@ tptp.res Y3))) (=> (= (@ (@ tptp.res X) P) (@ _let_2 P5)) (=> (= (@ (@ tptp.late_FreeR Alpha2) P3) (@ _let_1 (@ _let_2 P4))) (=> (@ (@ tptp.late_transitions P5) (@ _let_1 P4)) (not (@ (@ tptp.fresh_1641682979reeRes Y3) Alpha))))))))))) (forall ((X tptp.name) (P tptp.pi) (Alpha2 tptp.late_freeRes) (XP tptp.pi) (F (-> tptp.pi Bool))) (=> (@ (@ tptp.late_transitions (@ (@ tptp.res X) P)) (@ (@ tptp.late_FreeR Alpha2) XP)) (=> (forall ((P4 tptp.pi)) (=> (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR Alpha2) P4)) (=> (@ (@ tptp.fresh_1641682979reeRes X) Alpha2) (@ F (@ (@ tptp.res X) P4))))) (@ F XP)))) (forall ((P tptp.pi) (Alpha2 tptp.late_freeRes) (P3 tptp.pi) (Q tptp.pi)) (let ((_let_1 (@ tptp.late_FreeR Alpha2))) (=> (@ (@ tptp.late_transitions P) (@ _let_1 P3)) (@ (@ tptp.late_transitions (@ (@ tptp.par P) Q)) (@ _let_1 (@ (@ tptp.par P3) Q)))))) (forall ((Q tptp.pi) (Alpha2 tptp.late_freeRes) (Q3 tptp.pi) (P tptp.pi)) (let ((_let_1 (@ tptp.par P))) (let ((_let_2 (@ tptp.late_FreeR Alpha2))) (=> (@ (@ tptp.late_transitions Q) (@ _let_2 Q3)) (@ (@ tptp.late_transitions (@ _let_1 Q)) (@ _let_2 (@ _let_1 Q3))))))) (forall ((P tptp.pi) (Alpha2 tptp.late_freeRes) (P3 tptp.pi) (Y tptp.name)) (=> (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR Alpha2) P3)) (=> (@ (@ tptp.fresh_name_pi Y) P) (@ (@ tptp.fresh_1641682979reeRes Y) Alpha2)))) (forall ((P tptp.pi) (Alpha2 tptp.late_freeRes) (P3 tptp.pi) (Y tptp.name)) (let ((_let_1 (@ tptp.fresh_name_pi Y))) (=> (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR Alpha2) P3)) (=> (@ _let_1 P) (@ _let_1 P3))))) (forall ((P tptp.pi) (Rel tptp.set_Pr1834926343_pi_pi) (Q tptp.pi) (Alpha2 tptp.late_freeRes) (Q3 tptp.pi)) (=> (@ (@ (@ tptp.strong743114133lation P) Rel) Q) (=> (@ (@ tptp.late_transitions Q) (@ (@ tptp.late_FreeR Alpha2) Q3)) (exists ((P4 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR Alpha2) P4)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P4) Q3)) Rel)))))) (forall ((X tptp.name) (Y tptp.name) (P tptp.pi) (Rs tptp.late_residual)) (not (@ (@ tptp.late_transitions (@ (@ tptp.res X) (@ (@ (@ tptp.input X) Y) P))) Rs))) (forall ((Q tptp.pi) (P tptp.pi) (Rel tptp.set_Pr1834926343_pi_pi)) (=> (forall ((A3 tptp.late_subject) (Y3 tptp.name) (Q2 tptp.pi)) (=> (@ (@ tptp.late_transitions Q) (@ (@ (@ tptp.late_BoundR A3) Y3) Q2)) (=> (@ (@ tptp.fresh_name_pi Y3) P) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ (@ tptp.late_BoundR A3) Y3) P6)) (@ (@ (@ (@ (@ tptp.strong2129052853vative P6) Q2) A3) Y3) Rel)))))) (=> (forall ((Alpha tptp.late_freeRes) (Q2 tptp.pi)) (=> (@ (@ tptp.late_transitions Q) (@ (@ tptp.late_FreeR Alpha) Q2)) (exists ((P6 tptp.pi)) (and (@ (@ tptp.late_transitions P) (@ (@ tptp.late_FreeR Alpha) P6)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P6) Q2)) Rel))))) (@ (@ (@ tptp.strong743114133lation P) Rel) Q)))) (= tptp.strong743114133lation (lambda ((P7 tptp.pi) (Rel2 tptp.set_Pr1834926343_pi_pi) (Q5 tptp.pi)) (and (forall ((A5 tptp.late_subject) (X4 tptp.name) (Q6 tptp.pi)) (=> (and (@ (@ tptp.late_transitions Q5) (@ (@ (@ tptp.late_BoundR A5) X4) Q6)) (@ (@ tptp.fresh_name_pi X4) P7)) (exists ((P8 tptp.pi)) (and (@ (@ tptp.late_transitions P7) (@ (@ (@ tptp.late_BoundR A5) X4) P8)) (@ (@ (@ (@ (@ tptp.strong2129052853vative P8) Q6) A5) X4) Rel2))))) (forall ((Alpha3 tptp.late_freeRes) (Q6 tptp.pi)) (=> (@ (@ tptp.late_transitions Q5) (@ (@ tptp.late_FreeR Alpha3) Q6)) (exists ((P8 tptp.pi)) (and (@ (@ tptp.late_transitions P7) (@ (@ tptp.late_FreeR Alpha3) P8)) (@ (@ tptp.member558706512_pi_pi (@ (@ tptp.product_Pair_pi_pi P8) Q6)) Rel2)))))))) (forall ((P tptp.pi) (A tptp.late_subject) (X tptp.name) (P3 tptp.pi)) (not (@ (@ tptp.late_transitions (@ tptp.tau P)) (@ (@ (@ tptp.late_BoundR A) X) P3)))) (forall ((X tptp.name) (Rs tptp.late_residual)) (not (@ (@ tptp.late_transitions (@ (@ tptp.res X) tptp.piNil)) Rs))) (forall ((P (-> tptp.late_freeRes tptp.late_residual Bool)) (Z tptp.late_freeRes) (Residual tptp.late_residual)) (=> (forall ((Subject2 tptp.late_subject) (Name4 tptp.name) (Pi4 tptp.pi) (Z2 tptp.late_freeRes)) (=> (@ (@ tptp.fresh_1641682979reeRes Name4) Z2) (=> (@ (@ tptp.fresh_717452603ubject Name4) Subject2) (@ (@ P Z2) (@ (@ (@ tptp.late_BoundR Subject2) Name4) Pi4))))) (=> (forall ((FreeRes2 tptp.late_freeRes) (Pi4 tptp.pi) (Z2 tptp.late_freeRes)) (@ (@ P Z2) (@ (@ tptp.late_FreeR FreeRes2) Pi4))) (@ (@ P Z) Residual)))) (forall ((P (-> tptp.produc1141751126_pi_pi tptp.late_residual Bool)) (Z tptp.produc1141751126_pi_pi) (Residual tptp.late_residual)) (=> (forall ((Subject2 tptp.late_subject) (Name4 tptp.name) (Pi4 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (@ (@ tptp.fresh_1376661020_pi_pi Name4) Z2) (=> (@ (@ tptp.fresh_717452603ubject Name4) Subject2) (@ (@ P Z2) (@ (@ (@ tptp.late_BoundR Subject2) Name4) Pi4))))) (=> (forall ((FreeRes2 tptp.late_freeRes) (Pi4 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (@ (@ P Z2) (@ (@ tptp.late_FreeR FreeRes2) Pi4))) (@ (@ P Z) Residual)))) (forall ((P (-> 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(forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.late_freeRes)) (=> (@ (@ tptp.fresh_1641682979reeRes Name23) Z2) (=> (@ (@ tptp.fresh_name_name Name23) Name13) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.input Name13) Name23) Pi4)))))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.late_freeRes)) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.match Name13) Name23) Pi4)))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.late_freeRes)) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.mismatch Name13) Name23) Pi4)))) (=> (forall ((Pi13 tptp.pi) (Pi23 tptp.pi) (Z2 tptp.late_freeRes)) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi13)) (=> (forall ((Za tptp.late_freeRes)) (@ (@ P Za) Pi23)) (@ (@ P Z2) (@ (@ tptp.sum Pi13) Pi23))))) (=> (forall ((Pi13 tptp.pi) (Pi23 tptp.pi) (Z2 tptp.late_freeRes)) (=> (forall 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((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ tptp.tau Pi4)))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (@ (@ tptp.fresh_1376661020_pi_pi Name23) Z2) (=> (@ (@ tptp.fresh_name_name Name23) Name13) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.input Name13) Name23) Pi4)))))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.match Name13) Name23) Pi4)))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.mismatch Name13) Name23) Pi4)))) (=> (forall ((Pi13 tptp.pi) (Pi23 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi13)) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi23)) (@ (@ P Z2) (@ (@ tptp.sum Pi13) Pi23))))) (=> (forall ((Pi13 tptp.pi) (Pi23 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi13)) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi23)) (@ (@ P Z2) (@ (@ tptp.par Pi13) Pi23))))) (=> (forall ((Name4 tptp.name) (Pi4 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (@ (@ tptp.fresh_1376661020_pi_pi Name4) Z2) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ tptp.res Name4) Pi4))))) (=> (forall ((Pi4 tptp.pi) (Z2 tptp.produc1141751126_pi_pi)) (=> (forall ((Za tptp.produc1141751126_pi_pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ tptp.bang Pi4)))) (@ (@ P Z) Pi3)))))))))))) (forall ((P (-> tptp.name tptp.pi Bool)) (Z tptp.name) (Pi3 tptp.pi)) (=> (forall ((Z2 tptp.name)) (@ (@ P Z2) tptp.piNil)) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.name)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.output Name13) Name23) Pi4)))) (=> (forall ((Pi4 tptp.pi) (Z2 tptp.name)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ tptp.tau Pi4)))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.name)) (let ((_let_1 (@ tptp.fresh_name_name Name23))) (=> (@ _let_1 Z2) (=> (@ _let_1 Name13) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.input Name13) Name23) Pi4))))))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.name)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.match Name13) Name23) Pi4)))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.name)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.mismatch Name13) Name23) Pi4)))) (=> (forall ((Pi13 tptp.pi) (Pi23 tptp.pi) (Z2 tptp.name)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi13)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi23)) (@ (@ P Z2) (@ (@ tptp.sum Pi13) Pi23))))) (=> (forall ((Pi13 tptp.pi) (Pi23 tptp.pi) (Z2 tptp.name)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi13)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi23)) (@ (@ P Z2) (@ (@ tptp.par Pi13) Pi23))))) (=> (forall ((Name4 tptp.name) (Pi4 tptp.pi) (Z2 tptp.name)) (=> (@ (@ tptp.fresh_name_name Name4) Z2) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ tptp.res Name4) Pi4))))) (=> (forall ((Pi4 tptp.pi) (Z2 tptp.name)) (=> (forall ((Za tptp.name)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ tptp.bang Pi4)))) (@ (@ P Z) Pi3)))))))))))) (forall ((P (-> tptp.pi tptp.pi Bool)) (Z tptp.pi) (Pi3 tptp.pi)) (=> (forall ((Z2 tptp.pi)) (@ (@ P Z2) tptp.piNil)) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.pi)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.output Name13) Name23) Pi4)))) (=> (forall ((Pi4 tptp.pi) (Z2 tptp.pi)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ tptp.tau Pi4)))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.pi)) (=> (@ (@ tptp.fresh_name_pi Name23) Z2) (=> (@ (@ tptp.fresh_name_name Name23) Name13) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.input Name13) Name23) Pi4)))))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.pi)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.match Name13) Name23) Pi4)))) (=> (forall ((Name13 tptp.name) (Name23 tptp.name) (Pi4 tptp.pi) (Z2 tptp.pi)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ (@ tptp.mismatch Name13) Name23) Pi4)))) (=> (forall ((Pi13 tptp.pi) (Pi23 tptp.pi) (Z2 tptp.pi)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi13)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi23)) (@ (@ P Z2) (@ (@ tptp.sum Pi13) Pi23))))) (=> (forall ((Pi13 tptp.pi) (Pi23 tptp.pi) (Z2 tptp.pi)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi13)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi23)) (@ (@ P Z2) (@ (@ tptp.par Pi13) Pi23))))) (=> (forall ((Name4 tptp.name) (Pi4 tptp.pi) (Z2 tptp.pi)) (=> (@ (@ tptp.fresh_name_pi Name4) Z2) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ (@ tptp.res Name4) Pi4))))) (=> (forall ((Pi4 tptp.pi) (Z2 tptp.pi)) (=> (forall ((Za tptp.pi)) (@ (@ P Za) Pi4)) (@ (@ P Z2) (@ tptp.bang Pi4)))) (@ (@ P Z) Pi3)))))))))))) (forall ((A tptp.name) (X1 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi A))) (= (@ _let_1 (@ tptp.bang X1)) (@ _let_1 X1)))) (forall ((A tptp.name) (X2 tptp.pi) (X1 tptp.pi)) (let ((_let_1 (@ tptp.fresh_name_pi A))) (= (@ _let_1 (@ (@ tptp.sum X2) X1)) (and (@ _let_1 X2) (@ _let_1 X1))))) (forall ((P tptp.pi) (C tptp.name) (D tptp.name)) (= (@ (@ (@ tptp.subs (@ tptp.bang P)) C) D) (@ tptp.bang (@ (@ (@ tptp.subs P) C) D)))) (forall ((P tptp.pi) (Q tptp.pi) (C tptp.name) (D tptp.name)) (= (@ (@ (@ tptp.subs (@ (@ tptp.sum P) Q)) C) D) (@ (@ tptp.sum (@ (@ (@ tptp.subs P) C) D)) (@ (@ (@ tptp.subs Q) C) D)))) (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Pi tptp.pi)) (not (= (@ (@ (@ tptp.mismatch Name12) Name22) Pi3) (@ tptp.bang Pi)))) (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Pi12 tptp.pi) (Pi22 tptp.pi)) (not (= (@ (@ (@ tptp.mismatch Name12) Name22) Pi3) (@ (@ tptp.sum Pi12) Pi22)))) (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Pi tptp.pi)) (not (= (@ (@ (@ tptp.match Name12) Name22) Pi3) (@ tptp.bang Pi)))) (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Pi12 tptp.pi) (Pi22 tptp.pi)) (not (= (@ (@ (@ tptp.match Name12) Name22) Pi3) (@ (@ tptp.sum Pi12) Pi22)))) (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Pi tptp.pi)) (not (= (@ (@ (@ tptp.output Name12) Name22) Pi3) (@ tptp.bang Pi)))) (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Pi12 tptp.pi) (Pi22 tptp.pi)) (not (= (@ (@ (@ tptp.output Name12) Name22) Pi3) (@ (@ tptp.sum Pi12) Pi22)))) (forall ((Name3 tptp.name) (Pi3 tptp.pi) (Pi tptp.pi)) (not (= (@ (@ tptp.res Name3) Pi3) (@ tptp.bang Pi)))) (forall ((Pi1 tptp.pi) (Pi2 tptp.pi) (Pi tptp.pi)) (not (= (@ (@ tptp.par Pi1) Pi2) (@ tptp.bang Pi)))) (forall ((Name12 tptp.name) (Name22 tptp.name) (Pi3 tptp.pi) (Pi tptp.pi)) (not (= (@ (@ (@ tptp.input Name12) Name22) Pi3) (@ tptp.bang Pi)))) (forall ((Pi tptp.pi)) (not (= tptp.piNil (@ tptp.bang Pi)))) (forall ((Q tptp.pi) (Rs tptp.late_residual) (P tptp.pi)) (=> (@ (@ tptp.late_transitions Q) Rs) (@ (@ tptp.late_transitions (@ (@ tptp.sum P) Q)) Rs))) (forall ((P tptp.pi) (Rs tptp.late_residual) (Q tptp.pi)) (=> (@ (@ tptp.late_transitions P) Rs) (@ (@ tptp.late_transitions (@ (@ tptp.sum P) Q)) Rs))) (forall ((P tptp.pi) (Q tptp.pi) (Rs tptp.late_residual)) (=> (@ (@ tptp.late_transitions (@ (@ tptp.sum P) Q)) Rs) (=> (not (@ (@ tptp.late_transitions P) Rs)) (@ (@ tptp.late_transitions Q) Rs)))) (forall ((P tptp.pi) (Q tptp.pi) (Rs tptp.late_residual)) (=> (@ (@ tptp.late_transitions (@ (@ tptp.sum P) Q)) Rs) (=> (not (@ (@ tptp.late_transitions P) Rs)) (@ (@ tptp.late_transitions Q) Rs)))) (forall ((Pi3 tptp.pi) (Pi tptp.pi)) (not (= (@ tptp.tau Pi3) (@ tptp.bang Pi)))) (forall ((Pi1 tptp.pi) (Pi2 tptp.pi) (Name tptp.name) (Pi tptp.pi)) (not (= (@ (@ tptp.sum Pi1) Pi2) (@ (@ tptp.res Name) Pi)))) (forall ((Pi1 tptp.pi) (Pi2 tptp.pi) (Pi12 tptp.pi) (Pi22 tptp.pi)) (not (= (@ (@ tptp.sum Pi1) Pi2) (@ (@ tptp.par Pi12) Pi22)))) (forall ((Pi1 tptp.pi) (Pi2 tptp.pi) (Pi tptp.pi)) (not (= (@ (@ tptp.sum Pi1) Pi2) (@ tptp.bang Pi)))) (forall ((X2 tptp.pi) (X1 tptp.pi) (Y2 tptp.pi) (Y1 tptp.pi)) (= (= (@ (@ tptp.sum X2) X1) (@ (@ tptp.sum Y2) Y1)) (and (= X2 Y2) (= X1 Y1)))) (forall ((X1 tptp.pi) (Y1 tptp.pi)) (= (= (@ tptp.bang X1) (@ tptp.bang Y1)) (= X1 Y1))) (forall ((Pi3 tptp.pi) (Pi12 tptp.pi) (Pi22 tptp.pi)) (not (= (@ tptp.tau Pi3) (@ (@ tptp.sum Pi12) Pi22)))) (forall ((P Bool)) (or (= P true) (= P false))) (forall ((X tptp.name) (Y tptp.name)) (= (@ (@ (@ tptp.if_name false) X) Y) Y)) (forall ((X tptp.name) (Y tptp.name)) (= (@ (@ (@ tptp.if_name true) X) Y) X)) _let_9 true))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.85/1.04 )
% 0.85/1.04 % SZS output end Proof for ITP188^1
% 0.85/1.04 % cvc5---1.0.5 exiting
% 0.85/1.04 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------