TSTP Solution File: SWW961+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW961+1 : TPTP v8.1.0. Released v7.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 Sep 29 21:00:23 EDT 2022
% Result : Theorem 157.44s 101.68s
% Output : Proof 157.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 78
% Number of leaves : 117
% Syntax : Number of formulae : 422 ( 311 unt; 28 typ; 0 def)
% Number of atoms : 487 ( 481 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 164 ( 76 ~; 72 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 27 ( 20 >; 7 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 8 con; 0-2 aty)
% Number of variables : 261 ( 250 !; 0 ?; 261 :)
% Comments :
%------------------------------------------------------------------------------
tff(name_skB_type,type,
name_skB: $i ).
tff(name_A_type,type,
name_A: $i ).
tff(constr_assoc_pair_2_get_0x30_type,type,
constr_assoc_pair_2_get_0x30: $i > $i ).
tff(tuple_assoc_pair_type,type,
tuple_assoc_pair: ( $i * $i ) > $i ).
tff(tuple_client_B_in_2_type,type,
tuple_client_B_in_2: $i > $i ).
tff(tuple_out_2_type,type,
tuple_out_2: $i > $i ).
tff(constr_pkey_type,type,
constr_pkey: $i > $i ).
tff(tuple_client_B_in_3_type,type,
tuple_client_B_in_3: $i > $i ).
tff(name_skS_type,type,
name_skS: $i ).
tff(constr_assoc_pair_2_get_1_type,type,
constr_assoc_pair_2_get_1: $i > $i ).
tff(constr_tuple_2_get_1_bitstring_type,type,
constr_tuple_2_get_1_bitstring: $i > $i ).
tff(tuple_2_type,type,
tuple_2: ( $i * $i ) > $i ).
tff(tuple_out_1_type,type,
tuple_out_1: $i > $i ).
tff(tuple_keys_type,type,
tuple_keys: ( $i * $i ) > $i ).
tff(name_c_type,type,
name_c: $i ).
tff(constr_enc_type,type,
constr_enc: ( $i * $i ) > $i ).
tff(tuple_client_A_out_5_type,type,
tuple_client_A_out_5: $i > $i ).
tff(tuple_key_retrieval_server_out_2_type,type,
tuple_key_retrieval_server_out_2: $i > $i ).
tff(tuple_client_B_in_5_type,type,
tuple_client_B_in_5: $i > $i ).
tff(constr_aenc_type,type,
constr_aenc: ( $i * $i ) > $i ).
tff(name_skA_type,type,
name_skA: $i ).
tff(tuple_client_B_out_1_type,type,
tuple_client_B_out_1: ( $i * $i ) > $i ).
tff(name_B_type,type,
name_B: $i ).
tff(constr_tuple_2_get_0x30_type,type,
constr_tuple_2_get_0x30: $i > $i ).
tff(tuple_out_3_type,type,
tuple_out_3: $i > $i ).
tff(constr_CONST_0x30_type,type,
constr_CONST_0x30: $i ).
tff(tuple_client_A_out_1_type,type,
tuple_client_A_out_1: ( $i * $i ) > $i ).
tff(name_I_type,type,
name_I: $i ).
tff(1,plain,
^ [VAR_X0X30_9: $i,VAR_X1_10X30: $i] :
refl(
( ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
<=> ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
<=> ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
<=> ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax86) ).
tff(5,plain,
! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))))) = name_skB ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))))) = name_skB,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_out_2(constr_pkey(name_skB)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(11,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_out_2(constr_pkey(name_skB)),
inference(unit_resolution,[status(thm)],[10,7]) ).
tff(12,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),
inference(unit_resolution,[status(thm)],[12,7]) ).
tff(14,plain,
^ [VAR_X0X30_11: $i,VAR_X1_12: $i] :
refl(
( ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 )
<=> ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 )
<=> ! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 )
<=> ! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,axiom,
! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax85) ).
tff(18,plain,
! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
( ~ ! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 )
| ( constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS))))) = tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS))))) = tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(unit_resolution,[status(thm)],[21,20]) ).
tff(23,plain,
^ [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] :
refl(
( ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) )
<=> ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] : ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) )
<=> ! [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] : ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] : ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) )
<=> ! [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] : ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,axiom,
! [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] : ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax82) ).
tff(27,plain,
! [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] : ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] : ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] : ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
( ~ ! [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] : ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) )
| ( tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS))))) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS)))) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS))))),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
( ~ ! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 )
| ( constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_client_B_in_3(constr_pkey(name_skS)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_client_B_in_3(constr_pkey(name_skS)),
inference(unit_resolution,[status(thm)],[34,20]) ).
tff(36,plain,
tuple_client_B_in_3(constr_pkey(name_skS)) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
tuple_client_B_in_3(constr_pkey(name_skS)) = tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(transitivity,[status(thm)],[36,33,22]) ).
tff(38,plain,
tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
( ~ ! [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] : ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) )
| ( tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(unit_resolution,[status(thm)],[40,29]) ).
tff(42,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(transitivity,[status(thm)],[42,39]) ).
tff(44,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS)))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_3(constr_pkey(name_skS)))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_client_B_in_3(constr_pkey(name_skS)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_client_B_in_3(constr_pkey(name_skS)),
inference(unit_resolution,[status(thm)],[46,7]) ).
tff(48,plain,
tuple_client_B_in_3(constr_pkey(name_skS)) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS))) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS))))),
inference(symmetry,[status(thm)],[22]) ).
tff(50,plain,
tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),
inference(transitivity,[status(thm)],[49,32,35,48,45,13]) ).
tff(51,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS)))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))) = tuple_client_B_in_3(constr_pkey(name_skS)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))) = tuple_client_B_in_3(constr_pkey(name_skS)),
inference(unit_resolution,[status(thm)],[53,7]) ).
tff(55,plain,
tuple_client_B_in_3(constr_pkey(name_skS)) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
tuple_client_B_in_3(constr_pkey(name_skS)) = tuple_out_2(constr_pkey(name_skB)),
inference(transitivity,[status(thm)],[55,52,11]) ).
tff(57,plain,
tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_out_2(constr_pkey(name_skB))),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_out_2(constr_pkey(name_skB))) = tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(symmetry,[status(thm)],[57]) ).
tff(59,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_out_2(constr_pkey(name_skB))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_out_2(constr_pkey(name_skB))),
inference(unit_resolution,[status(thm)],[59,7]) ).
tff(61,plain,
tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_client_B_in_3(constr_pkey(name_skS)),
inference(transitivity,[status(thm)],[49,32,35]) ).
tff(62,plain,
tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
( ~ ! [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] : ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) )
| ( tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(unit_resolution,[status(thm)],[63,29]) ).
tff(65,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(transitivity,[status(thm)],[65,62]) ).
tff(67,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS)))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS)))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),
inference(unit_resolution,[status(thm)],[69,7]) ).
tff(71,plain,
tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))) = tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(transitivity,[status(thm)],[71,68,60,58]) ).
tff(73,plain,
tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))) = tuple_assoc_pair(name_skB,tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
tuple_assoc_pair(name_skB,tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
( ~ ! [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] : ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) )
| ( tuple_assoc_pair(name_skB,tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,plain,
tuple_assoc_pair(name_skB,tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(unit_resolution,[status(thm)],[75,29]) ).
tff(77,plain,
tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(name_skB,tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),
inference(transitivity,[status(thm)],[77,74]) ).
tff(79,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))) = tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(transitivity,[status(thm)],[73,76,80]) ).
tff(82,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))))),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(unit_resolution,[status(thm)],[84,7]) ).
tff(86,plain,
tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
^ [VAR_X0X30_7: $i,VAR_X1_8: $i] :
refl(
( ( constr_tuple_2_get_1_bitstring(tuple_2(VAR_X0X30_7,VAR_X1_8)) = VAR_X1_8 )
<=> ( constr_tuple_2_get_1_bitstring(tuple_2(VAR_X0X30_7,VAR_X1_8)) = VAR_X1_8 ) )),
inference(bind,[status(th)],]) ).
tff(88,plain,
( ! [VAR_X0X30_7: $i,VAR_X1_8: $i] : ( constr_tuple_2_get_1_bitstring(tuple_2(VAR_X0X30_7,VAR_X1_8)) = VAR_X1_8 )
<=> ! [VAR_X0X30_7: $i,VAR_X1_8: $i] : ( constr_tuple_2_get_1_bitstring(tuple_2(VAR_X0X30_7,VAR_X1_8)) = VAR_X1_8 ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
( ! [VAR_X0X30_7: $i,VAR_X1_8: $i] : ( constr_tuple_2_get_1_bitstring(tuple_2(VAR_X0X30_7,VAR_X1_8)) = VAR_X1_8 )
<=> ! [VAR_X0X30_7: $i,VAR_X1_8: $i] : ( constr_tuple_2_get_1_bitstring(tuple_2(VAR_X0X30_7,VAR_X1_8)) = VAR_X1_8 ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,axiom,
! [VAR_X0X30_7: $i,VAR_X1_8: $i] : ( constr_tuple_2_get_1_bitstring(tuple_2(VAR_X0X30_7,VAR_X1_8)) = VAR_X1_8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax87) ).
tff(91,plain,
! [VAR_X0X30_7: $i,VAR_X1_8: $i] : ( constr_tuple_2_get_1_bitstring(tuple_2(VAR_X0X30_7,VAR_X1_8)) = VAR_X1_8 ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
! [VAR_X0X30_7: $i,VAR_X1_8: $i] : ( constr_tuple_2_get_1_bitstring(tuple_2(VAR_X0X30_7,VAR_X1_8)) = VAR_X1_8 ),
inference(skolemize,[status(sab)],[91]) ).
tff(93,plain,
! [VAR_X0X30_7: $i,VAR_X1_8: $i] : ( constr_tuple_2_get_1_bitstring(tuple_2(VAR_X0X30_7,VAR_X1_8)) = VAR_X1_8 ),
inference(modus_ponens,[status(thm)],[92,88]) ).
tff(94,plain,
( ~ ! [VAR_X0X30_7: $i,VAR_X1_8: $i] : ( constr_tuple_2_get_1_bitstring(tuple_2(VAR_X0X30_7,VAR_X1_8)) = VAR_X1_8 )
| ( constr_tuple_2_get_1_bitstring(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))) = tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
constr_tuple_2_get_1_bitstring(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))) = tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(unit_resolution,[status(thm)],[94,93]) ).
tff(96,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),tuple_key_retrieval_server_out_2(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)))) = constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),tuple_key_retrieval_server_out_2(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)))) = constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),
inference(unit_resolution,[status(thm)],[96,7]) ).
tff(98,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),
inference(unit_resolution,[status(thm)],[98,7]) ).
tff(100,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(name_A,tuple_client_B_out_1(name_B,name_A))) = name_A ) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(name_A,tuple_client_B_out_1(name_B,name_A))) = name_A,
inference(unit_resolution,[status(thm)],[100,7]) ).
tff(102,plain,
( ~ ! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 )
| ( constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A))) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(103,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A))) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A),
inference(unit_resolution,[status(thm)],[102,20]) ).
tff(104,plain,
tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_out_2(constr_pkey(name_skB))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(symmetry,[status(thm)],[60]) ).
tff(105,plain,
tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),
inference(transitivity,[status(thm)],[57,104,67,70]) ).
tff(106,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS))),name_A) = tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),name_A),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
( ~ ! [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] : ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) )
| ( tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A)) = tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS))),name_A) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A)) = tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_client_B_in_3(constr_pkey(name_skS))),name_A),
inference(unit_resolution,[status(thm)],[107,29]) ).
tff(109,plain,
tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A)) = tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),name_A),
inference(transitivity,[status(thm)],[108,106]) ).
tff(110,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A))) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),name_A)),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),name_A)) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A))),
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
( ~ ! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 )
| ( constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),name_A)) = name_A ) ),
inference(quant_inst,[status(thm)],]) ).
tff(113,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),name_A)) = name_A,
inference(unit_resolution,[status(thm)],[112,20]) ).
tff(114,plain,
name_A = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB))),name_A)),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
name_A = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A),
inference(transitivity,[status(thm)],[114,111,103]) ).
tff(116,plain,
tuple_assoc_pair(name_A,tuple_client_B_out_1(name_B,name_A)) = tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A),tuple_client_B_out_1(name_B,name_A)),
inference(monotonicity,[status(thm)],[115]) ).
tff(117,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A),tuple_client_B_out_1(name_B,name_A)) = tuple_assoc_pair(name_A,tuple_client_B_out_1(name_B,name_A)),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A),tuple_client_B_out_1(name_B,name_A))) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(name_A,tuple_client_B_out_1(name_B,name_A))),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(name_A,tuple_client_B_out_1(name_B,name_A))) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A),tuple_client_B_out_1(name_B,name_A))),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
( ~ ! [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] : ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) )
| ( tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(name_A,tuple_client_B_out_1(name_B,name_A))) = tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A),tuple_client_B_out_1(name_B,name_A)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(121,plain,
tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(name_A,tuple_client_B_out_1(name_B,name_A))) = tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A),tuple_client_B_out_1(name_B,name_A)),
inference(unit_resolution,[status(thm)],[120,29]) ).
tff(122,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A),tuple_client_B_out_1(name_B,name_A)) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(name_A,tuple_client_B_out_1(name_B,name_A))),
inference(symmetry,[status(thm)],[121]) ).
tff(123,plain,
tuple_assoc_pair(name_A,tuple_client_B_out_1(name_B,name_A)) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A),tuple_client_B_out_1(name_B,name_A))),
inference(transitivity,[status(thm)],[116,122,119]) ).
tff(124,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(name_A,tuple_client_B_out_1(name_B,name_A))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A),tuple_client_B_out_1(name_B,name_A)))),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A),tuple_client_B_out_1(name_B,name_A)))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(name_A,tuple_client_B_out_1(name_B,name_A))),
inference(symmetry,[status(thm)],[124]) ).
tff(126,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A),tuple_client_B_out_1(name_B,name_A)))) = tuple_client_B_in_3(constr_pkey(name_skS)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(127,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A),tuple_client_B_out_1(name_B,name_A)))) = tuple_client_B_in_3(constr_pkey(name_skS)),
inference(unit_resolution,[status(thm)],[126,7]) ).
tff(128,plain,
tuple_client_B_in_3(constr_pkey(name_skS)) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A),tuple_client_B_out_1(name_B,name_A)))),
inference(symmetry,[status(thm)],[127]) ).
tff(129,plain,
tuple_client_B_in_3(constr_pkey(name_skS)) = name_A,
inference(transitivity,[status(thm)],[128,125,101]) ).
tff(130,plain,
tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_out_1(name_B,name_A)) = tuple_assoc_pair(name_A,tuple_client_B_out_1(name_B,name_A)),
inference(monotonicity,[status(thm)],[129]) ).
tff(131,plain,
tuple_assoc_pair(name_A,tuple_client_B_out_1(name_B,name_A)) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_out_1(name_B,name_A)),
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
( ~ ! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 )
| ( constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A),tuple_client_B_out_1(name_B,name_A)))) = tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A),tuple_client_B_out_1(name_B,name_A)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(133,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A),tuple_client_B_out_1(name_B,name_A)))) = tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A),tuple_client_B_out_1(name_B,name_A)),
inference(unit_resolution,[status(thm)],[132,20]) ).
tff(134,plain,
tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A),tuple_client_B_out_1(name_B,name_A))) = tuple_assoc_pair(name_A,tuple_client_B_out_1(name_B,name_A)),
inference(transitivity,[status(thm)],[118,121,117]) ).
tff(135,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A),tuple_client_B_out_1(name_B,name_A)))) = constr_assoc_pair_2_get_1(tuple_assoc_pair(name_A,tuple_client_B_out_1(name_B,name_A))),
inference(monotonicity,[status(thm)],[134]) ).
tff(136,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(name_A,tuple_client_B_out_1(name_B,name_A))) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),name_A),tuple_client_B_out_1(name_B,name_A)))),
inference(symmetry,[status(thm)],[135]) ).
tff(137,plain,
( ~ ! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 )
| ( constr_assoc_pair_2_get_1(tuple_assoc_pair(name_A,tuple_client_B_out_1(name_B,name_A))) = tuple_client_B_out_1(name_B,name_A) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(name_A,tuple_client_B_out_1(name_B,name_A))) = tuple_client_B_out_1(name_B,name_A),
inference(unit_resolution,[status(thm)],[137,20]) ).
tff(139,plain,
tuple_client_B_out_1(name_B,name_A) = constr_assoc_pair_2_get_1(tuple_assoc_pair(name_A,tuple_client_B_out_1(name_B,name_A))),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
tuple_client_B_out_1(name_B,name_A) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_out_1(name_B,name_A)),
inference(transitivity,[status(thm)],[139,136,133,117,131]) ).
tff(141,plain,
tuple_assoc_pair(tuple_client_B_out_1(name_B,name_A),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))) = tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_out_1(name_B,name_A)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),
inference(monotonicity,[status(thm)],[140]) ).
tff(142,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_out_1(name_B,name_A)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))) = tuple_assoc_pair(tuple_client_B_out_1(name_B,name_A),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
( ~ ! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 )
| ( constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_out_1(name_B,name_A)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))))) = tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_out_1(name_B,name_A)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(144,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_out_1(name_B,name_A)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))))) = tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_out_1(name_B,name_A)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),
inference(unit_resolution,[status(thm)],[143,20]) ).
tff(145,plain,
( ~ ! [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] : ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) )
| ( tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_client_B_out_1(name_B,name_A),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_out_1(name_B,name_A)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(146,plain,
tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_client_B_out_1(name_B,name_A),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_out_1(name_B,name_A)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),
inference(unit_resolution,[status(thm)],[145,29]) ).
tff(147,plain,
tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_out_1(name_B,name_A)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_client_B_out_1(name_B,name_A),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))),
inference(monotonicity,[status(thm)],[142]) ).
tff(148,plain,
tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_out_1(name_B,name_A)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = tuple_assoc_pair(tuple_client_B_out_1(name_B,name_A),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),
inference(transitivity,[status(thm)],[147,146,142]) ).
tff(149,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_out_1(name_B,name_A)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))))) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_out_1(name_B,name_A),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))),
inference(monotonicity,[status(thm)],[148]) ).
tff(150,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_out_1(name_B,name_A),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_out_1(name_B,name_A)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))))),
inference(symmetry,[status(thm)],[149]) ).
tff(151,plain,
( ~ ! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 )
| ( constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_out_1(name_B,name_A),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(152,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_out_1(name_B,name_A),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),
inference(unit_resolution,[status(thm)],[151,20]) ).
tff(153,plain,
tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_out_1(name_B,name_A),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))),
inference(symmetry,[status(thm)],[152]) ).
tff(154,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(155,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),
inference(unit_resolution,[status(thm)],[154,7]) ).
tff(156,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_out_1(name_B,name_A),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = tuple_client_B_out_1(name_B,name_A) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(157,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_out_1(name_B,name_A),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = tuple_client_B_out_1(name_B,name_A),
inference(unit_resolution,[status(thm)],[156,7]) ).
tff(158,plain,
tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_client_B_out_1(name_B,name_A),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_out_1(name_B,name_A)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))),
inference(symmetry,[status(thm)],[147]) ).
tff(159,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_out_1(name_B,name_A)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_client_B_out_1(name_B,name_A),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))),
inference(symmetry,[status(thm)],[146]) ).
tff(160,plain,
tuple_assoc_pair(tuple_client_B_out_1(name_B,name_A),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_out_1(name_B,name_A)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))),
inference(transitivity,[status(thm)],[141,159,158]) ).
tff(161,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_out_1(name_B,name_A),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_out_1(name_B,name_A)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))))),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_out_1(name_B,name_A)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_out_1(name_B,name_A),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))),
inference(symmetry,[status(thm)],[161]) ).
tff(163,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_out_1(name_B,name_A)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))))) = tuple_client_B_in_3(constr_pkey(name_skS)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(164,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_out_1(name_B,name_A)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))))) = tuple_client_B_in_3(constr_pkey(name_skS)),
inference(unit_resolution,[status(thm)],[163,7]) ).
tff(165,plain,
tuple_client_B_in_3(constr_pkey(name_skS)) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_out_1(name_B,name_A)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))))),
inference(symmetry,[status(thm)],[164]) ).
tff(166,plain,
tuple_client_B_in_3(constr_pkey(name_skS)) = tuple_client_B_out_1(name_B,name_A),
inference(transitivity,[status(thm)],[165,162,157]) ).
tff(167,plain,
tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))) = tuple_assoc_pair(tuple_client_B_out_1(name_B,name_A),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),
inference(monotonicity,[status(thm)],[166]) ).
tff(168,plain,
tuple_assoc_pair(tuple_client_B_out_1(name_B,name_A),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),
inference(transitivity,[status(thm)],[153,150,144,142,168]) ).
tff(170,plain,
tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))) = tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),
inference(symmetry,[status(thm)],[170]) ).
tff(172,plain,
( ~ ! [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] : ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) )
| ( tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(173,plain,
tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),
inference(unit_resolution,[status(thm)],[172,29]) ).
tff(174,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))) = tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))),
inference(symmetry,[status(thm)],[173]) ).
tff(175,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))) = tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),
inference(transitivity,[status(thm)],[174,171]) ).
tff(176,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))),
inference(monotonicity,[status(thm)],[175]) ).
tff(177,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_client_B_in_3(constr_pkey(name_skS))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(178,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(unit_resolution,[status(thm)],[177,7]) ).
tff(179,plain,
tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_client_B_in_3(constr_pkey(name_skS))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))),
inference(symmetry,[status(thm)],[178]) ).
tff(180,plain,
tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_client_B_out_1(name_B,name_A),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),
inference(transitivity,[status(thm)],[179,176,155,153,150,144,142]) ).
tff(181,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_client_B_in_3(constr_pkey(name_skS)))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_out_1(name_B,name_A),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))),
inference(monotonicity,[status(thm)],[180]) ).
tff(182,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_out_1(name_B,name_A),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
tuple_client_B_in_3(constr_pkey(name_skS)) = tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),
inference(transitivity,[status(thm)],[165,162,182,99]) ).
tff(184,plain,
tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))) = tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))),
inference(monotonicity,[status(thm)],[183]) ).
tff(185,plain,
tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))),
inference(symmetry,[status(thm)],[184]) ).
tff(186,plain,
tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))) = tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))),
inference(monotonicity,[status(thm)],[169]) ).
tff(187,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))) = tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))),
inference(symmetry,[status(thm)],[186]) ).
tff(188,plain,
( ~ ! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 )
| ( constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))))) = tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(189,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))))) = tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))),
inference(unit_resolution,[status(thm)],[188,20]) ).
tff(190,plain,
( ~ ! [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] : ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) )
| ( tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))))) = tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(191,plain,
tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))))) = tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))),
inference(unit_resolution,[status(thm)],[190,29]) ).
tff(192,plain,
tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))))) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))))),
inference(monotonicity,[status(thm)],[187]) ).
tff(193,plain,
tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))))) = tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))),
inference(transitivity,[status(thm)],[192,191,187]) ).
tff(194,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))))) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))))),
inference(monotonicity,[status(thm)],[193]) ).
tff(195,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))))) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))))),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
( ~ ! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 )
| ( constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))))) = constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(197,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))))) = constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),
inference(unit_resolution,[status(thm)],[196,20]) ).
tff(198,plain,
constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))))),
inference(symmetry,[status(thm)],[197]) ).
tff(199,plain,
constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))),
inference(transitivity,[status(thm)],[198,195,189,187,185]) ).
tff(200,plain,
tuple_assoc_pair(constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),tuple_key_retrieval_server_out_2(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c))) = tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))),tuple_key_retrieval_server_out_2(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c))),
inference(monotonicity,[status(thm)],[199]) ).
tff(201,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))),tuple_key_retrieval_server_out_2(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c))) = tuple_assoc_pair(constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),tuple_key_retrieval_server_out_2(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c))),
inference(symmetry,[status(thm)],[200]) ).
tff(202,plain,
tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))),tuple_key_retrieval_server_out_2(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)))) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),tuple_key_retrieval_server_out_2(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)))),
inference(monotonicity,[status(thm)],[201]) ).
tff(203,plain,
tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),tuple_key_retrieval_server_out_2(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)))) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))),tuple_key_retrieval_server_out_2(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)))),
inference(symmetry,[status(thm)],[202]) ).
tff(204,plain,
( ~ ! [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] : ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) )
| ( tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),tuple_key_retrieval_server_out_2(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)))) = tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))),tuple_key_retrieval_server_out_2(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(205,plain,
tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),tuple_key_retrieval_server_out_2(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)))) = tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))),tuple_key_retrieval_server_out_2(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c))),
inference(unit_resolution,[status(thm)],[204,29]) ).
tff(206,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))),tuple_key_retrieval_server_out_2(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c))) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),tuple_key_retrieval_server_out_2(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)))),
inference(symmetry,[status(thm)],[205]) ).
tff(207,plain,
tuple_assoc_pair(constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),tuple_key_retrieval_server_out_2(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c))) = tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))),tuple_key_retrieval_server_out_2(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)))),
inference(transitivity,[status(thm)],[200,206,203]) ).
tff(208,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),tuple_key_retrieval_server_out_2(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))),tuple_key_retrieval_server_out_2(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c))))),
inference(monotonicity,[status(thm)],[207]) ).
tff(209,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))),tuple_key_retrieval_server_out_2(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c))))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),tuple_key_retrieval_server_out_2(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)))),
inference(symmetry,[status(thm)],[208]) ).
tff(210,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))),tuple_key_retrieval_server_out_2(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c))))) = tuple_client_B_in_3(constr_pkey(name_skS)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(211,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))),tuple_key_retrieval_server_out_2(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c))))) = tuple_client_B_in_3(constr_pkey(name_skS)),
inference(unit_resolution,[status(thm)],[210,7]) ).
tff(212,plain,
tuple_client_B_in_3(constr_pkey(name_skS)) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))),tuple_key_retrieval_server_out_2(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c))))),
inference(symmetry,[status(thm)],[211]) ).
tff(213,plain,
( ~ ! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 )
| ( constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_client_B_in_3(constr_pkey(name_skS)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(214,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_client_B_in_3(constr_pkey(name_skS)),
inference(unit_resolution,[status(thm)],[213,20]) ).
tff(215,plain,
^ [VAR_X0X30_0X30: $i,VAR_X1_0X30: $i] :
refl(
( ( constr_tuple_2_get_0x30(tuple_2(VAR_X0X30_0X30,VAR_X1_0X30)) = VAR_X0X30_0X30 )
<=> ( constr_tuple_2_get_0x30(tuple_2(VAR_X0X30_0X30,VAR_X1_0X30)) = VAR_X0X30_0X30 ) )),
inference(bind,[status(th)],]) ).
tff(216,plain,
( ! [VAR_X0X30_0X30: $i,VAR_X1_0X30: $i] : ( constr_tuple_2_get_0x30(tuple_2(VAR_X0X30_0X30,VAR_X1_0X30)) = VAR_X0X30_0X30 )
<=> ! [VAR_X0X30_0X30: $i,VAR_X1_0X30: $i] : ( constr_tuple_2_get_0x30(tuple_2(VAR_X0X30_0X30,VAR_X1_0X30)) = VAR_X0X30_0X30 ) ),
inference(quant_intro,[status(thm)],[215]) ).
tff(217,plain,
( ! [VAR_X0X30_0X30: $i,VAR_X1_0X30: $i] : ( constr_tuple_2_get_0x30(tuple_2(VAR_X0X30_0X30,VAR_X1_0X30)) = VAR_X0X30_0X30 )
<=> ! [VAR_X0X30_0X30: $i,VAR_X1_0X30: $i] : ( constr_tuple_2_get_0x30(tuple_2(VAR_X0X30_0X30,VAR_X1_0X30)) = VAR_X0X30_0X30 ) ),
inference(rewrite,[status(thm)],]) ).
tff(218,axiom,
! [VAR_X0X30_0X30: $i,VAR_X1_0X30: $i] : ( constr_tuple_2_get_0x30(tuple_2(VAR_X0X30_0X30,VAR_X1_0X30)) = VAR_X0X30_0X30 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax88) ).
tff(219,plain,
! [VAR_X0X30_0X30: $i,VAR_X1_0X30: $i] : ( constr_tuple_2_get_0x30(tuple_2(VAR_X0X30_0X30,VAR_X1_0X30)) = VAR_X0X30_0X30 ),
inference(modus_ponens,[status(thm)],[218,217]) ).
tff(220,plain,
! [VAR_X0X30_0X30: $i,VAR_X1_0X30: $i] : ( constr_tuple_2_get_0x30(tuple_2(VAR_X0X30_0X30,VAR_X1_0X30)) = VAR_X0X30_0X30 ),
inference(skolemize,[status(sab)],[219]) ).
tff(221,plain,
! [VAR_X0X30_0X30: $i,VAR_X1_0X30: $i] : ( constr_tuple_2_get_0x30(tuple_2(VAR_X0X30_0X30,VAR_X1_0X30)) = VAR_X0X30_0X30 ),
inference(modus_ponens,[status(thm)],[220,216]) ).
tff(222,plain,
( ~ ! [VAR_X0X30_0X30: $i,VAR_X1_0X30: $i] : ( constr_tuple_2_get_0x30(tuple_2(VAR_X0X30_0X30,VAR_X1_0X30)) = VAR_X0X30_0X30 )
| ( constr_tuple_2_get_0x30(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))) = tuple_client_B_in_3(constr_pkey(name_skS)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(223,plain,
constr_tuple_2_get_0x30(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))) = tuple_client_B_in_3(constr_pkey(name_skS)),
inference(unit_resolution,[status(thm)],[222,221]) ).
tff(224,plain,
( ~ ! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 )
| ( constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))))) = tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(225,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))))) = tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),
inference(unit_resolution,[status(thm)],[224,20]) ).
tff(226,plain,
( ~ ! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 )
| ( constr_assoc_pair_2_get_1(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))) = constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(227,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))) = constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),
inference(unit_resolution,[status(thm)],[226,20]) ).
tff(228,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(229,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(unit_resolution,[status(thm)],[228,7]) ).
tff(230,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_out_1(name_B,name_A)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_assoc_pair(tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_out_1(name_B,name_A)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))))),
inference(symmetry,[status(thm)],[144]) ).
tff(231,plain,
tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))) = tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))),
inference(transitivity,[status(thm)],[167,141,230,149,152]) ).
tff(232,plain,
tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),
inference(monotonicity,[status(thm)],[231]) ).
tff(233,plain,
( ~ ! [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] : ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) )
| ( tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = tuple_assoc_pair(tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(234,plain,
tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = tuple_assoc_pair(tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),
inference(unit_resolution,[status(thm)],[233,29]) ).
tff(235,plain,
tuple_assoc_pair(tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))) = tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_assoc_pair(tuple_client_B_in_3(constr_pkey(name_skS)),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))),
inference(symmetry,[status(thm)],[234]) ).
tff(236,plain,
tuple_assoc_pair(tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))) = tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB)))))),
inference(transitivity,[status(thm)],[235,232]) ).
tff(237,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))),
inference(monotonicity,[status(thm)],[236]) ).
tff(238,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))),
inference(symmetry,[status(thm)],[237]) ).
tff(239,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(240,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))) = constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),
inference(unit_resolution,[status(thm)],[239,7]) ).
tff(241,plain,
constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_5(constr_aenc(name_skA,constr_pkey(tuple_out_2(constr_pkey(name_skB))))))),
inference(symmetry,[status(thm)],[240]) ).
tff(242,plain,
constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))) = tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(transitivity,[status(thm)],[241,238,229]) ).
tff(243,plain,
tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))) = tuple_assoc_pair(constr_pkey(name_skS),tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(monotonicity,[status(thm)],[242]) ).
tff(244,plain,
tuple_assoc_pair(constr_pkey(name_skS),tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),
inference(symmetry,[status(thm)],[243]) ).
tff(245,plain,
( ~ ! [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] : ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) )
| ( tuple_assoc_pair(constr_pkey(name_skS),tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(246,plain,
tuple_assoc_pair(constr_pkey(name_skS),tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(unit_resolution,[status(thm)],[245,29]) ).
tff(247,plain,
tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(constr_pkey(name_skS),tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(symmetry,[status(thm)],[246]) ).
tff(248,plain,
tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),
inference(transitivity,[status(thm)],[247,244]) ).
tff(249,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(monotonicity,[status(thm)],[248]) ).
tff(250,plain,
tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(symmetry,[status(thm)],[249]) ).
tff(251,plain,
tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(transitivity,[status(thm)],[243,246,250]) ).
tff(252,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(monotonicity,[status(thm)],[251]) ).
tff(253,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))) = constr_assoc_pair_2_get_1(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))),
inference(symmetry,[status(thm)],[252]) ).
tff(254,plain,
( ~ ! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 )
| ( constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_client_B_in_3(constr_pkey(name_skS)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(255,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_client_B_in_3(constr_pkey(name_skS)),
inference(unit_resolution,[status(thm)],[254,20]) ).
tff(256,plain,
tuple_client_B_in_3(constr_pkey(name_skS)) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(symmetry,[status(thm)],[255]) ).
tff(257,plain,
tuple_client_B_in_3(constr_pkey(name_skS)) = constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),
inference(transitivity,[status(thm)],[256,253,227]) ).
tff(258,plain,
tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),
inference(monotonicity,[status(thm)],[257]) ).
tff(259,plain,
tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(symmetry,[status(thm)],[258]) ).
tff(260,plain,
tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(monotonicity,[status(thm)],[242]) ).
tff(261,plain,
tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),
inference(symmetry,[status(thm)],[260]) ).
tff(262,plain,
( ~ ! [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] : ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) )
| ( tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(263,plain,
tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(unit_resolution,[status(thm)],[262,29]) ).
tff(264,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_assoc_pair(constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(symmetry,[status(thm)],[263]) ).
tff(265,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(266,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(unit_resolution,[status(thm)],[265,7]) ).
tff(267,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),
inference(transitivity,[status(thm)],[264,261]) ).
tff(268,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(monotonicity,[status(thm)],[267]) ).
tff(269,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),
inference(transitivity,[status(thm)],[268,264,261]) ).
tff(270,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))),
inference(monotonicity,[status(thm)],[269]) ).
tff(271,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(symmetry,[status(thm)],[270]) ).
tff(272,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))) = tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(273,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))) = tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),
inference(unit_resolution,[status(thm)],[272,7]) ).
tff(274,plain,
tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))),
inference(symmetry,[status(thm)],[273]) ).
tff(275,plain,
tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(transitivity,[status(thm)],[274,271,266,264,261,259]) ).
tff(276,plain,
tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))) = tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(monotonicity,[status(thm)],[275]) ).
tff(277,plain,
tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))),
inference(symmetry,[status(thm)],[276]) ).
tff(278,plain,
( ~ ! [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] : ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) )
| ( tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))),tuple_client_B_in_3(constr_pkey(name_skS))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(279,plain,
tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(unit_resolution,[status(thm)],[278,29]) ).
tff(280,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(symmetry,[status(thm)],[279]) ).
tff(281,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))),
inference(transitivity,[status(thm)],[280,277]) ).
tff(282,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(monotonicity,[status(thm)],[281]) ).
tff(283,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(symmetry,[status(thm)],[282]) ).
tff(284,plain,
tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))) = tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(transitivity,[status(thm)],[276,279,283]) ).
tff(285,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))))) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(monotonicity,[status(thm)],[284]) ).
tff(286,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))))),
inference(symmetry,[status(thm)],[285]) ).
tff(287,plain,
( ~ ! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 )
| ( constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_client_B_in_3(constr_pkey(name_skS)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(288,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_client_B_in_3(constr_pkey(name_skS)),
inference(unit_resolution,[status(thm)],[287,20]) ).
tff(289,plain,
tuple_client_B_in_3(constr_pkey(name_skS)) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(symmetry,[status(thm)],[288]) ).
tff(290,plain,
constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),tuple_key_retrieval_server_out_2(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)))),
inference(symmetry,[status(thm)],[97]) ).
tff(291,plain,
constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))) = tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),
inference(transitivity,[status(thm)],[290,208,211,289,286,225]) ).
tff(292,plain,
constr_tuple_2_get_0x30(constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))) = constr_tuple_2_get_0x30(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))),
inference(monotonicity,[status(thm)],[291]) ).
tff(293,plain,
( ~ ! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 )
| ( constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_assoc_pair_2_get_0x30(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_client_B_in_3(constr_pkey(name_skS)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(294,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_assoc_pair_2_get_0x30(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_client_B_in_3(constr_pkey(name_skS)),
inference(unit_resolution,[status(thm)],[293,20]) ).
tff(295,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))) = constr_pkey(name_skS) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(296,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))) = constr_pkey(name_skS),
inference(unit_resolution,[status(thm)],[295,7]) ).
tff(297,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),
inference(transitivity,[status(thm)],[249,247,244]) ).
tff(298,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))),
inference(monotonicity,[status(thm)],[297]) ).
tff(299,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(300,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(unit_resolution,[status(thm)],[299,7]) ).
tff(301,plain,
tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(symmetry,[status(thm)],[300]) ).
tff(302,plain,
tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))) = constr_pkey(name_skS),
inference(transitivity,[status(thm)],[243,246,301,298,296]) ).
tff(303,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))) = constr_assoc_pair_2_get_0x30(constr_pkey(name_skS)),
inference(monotonicity,[status(thm)],[302]) ).
tff(304,plain,
constr_pkey(name_skS) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))),
inference(symmetry,[status(thm)],[296]) ).
tff(305,plain,
constr_pkey(name_skS) = constr_assoc_pair_2_get_0x30(constr_pkey(name_skS)),
inference(transitivity,[status(thm)],[304,303]) ).
tff(306,plain,
tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_pkey(name_skS)) = tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_assoc_pair_2_get_0x30(constr_pkey(name_skS))),
inference(monotonicity,[status(thm)],[305]) ).
tff(307,plain,
tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_assoc_pair_2_get_0x30(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_pkey(name_skS)),
inference(symmetry,[status(thm)],[306]) ).
tff(308,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_assoc_pair_2_get_0x30(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_pkey(name_skS)),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(monotonicity,[status(thm)],[307]) ).
tff(309,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_pkey(name_skS)),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_assoc_pair_2_get_0x30(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(symmetry,[status(thm)],[308]) ).
tff(310,plain,
( ~ ! [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] : ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) )
| ( tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_assoc_pair(constr_pkey(name_skS),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_pkey(name_skS)),tuple_client_B_in_3(constr_pkey(name_skS))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(311,plain,
tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_assoc_pair(constr_pkey(name_skS),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_pkey(name_skS)),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(unit_resolution,[status(thm)],[310,29]) ).
tff(312,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(symmetry,[status(thm)],[298]) ).
tff(313,plain,
constr_pkey(name_skS) = tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),
inference(transitivity,[status(thm)],[304,312,300,247,244]) ).
tff(314,plain,
tuple_assoc_pair(constr_pkey(name_skS),tuple_client_B_in_3(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skS),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(monotonicity,[status(thm)],[313]) ).
tff(315,plain,
tuple_assoc_pair(constr_pkey(name_skS),tuple_client_B_in_3(constr_pkey(name_skS))) = constr_assoc_pair_2_get_0x30(constr_pkey(name_skS)),
inference(transitivity,[status(thm)],[314,301,298,303]) ).
tff(316,plain,
tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_assoc_pair(constr_pkey(name_skS),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_assoc_pair_2_get_0x30(constr_pkey(name_skS))),
inference(monotonicity,[status(thm)],[315]) ).
tff(317,plain,
tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_assoc_pair_2_get_0x30(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),tuple_assoc_pair(constr_pkey(name_skS),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(symmetry,[status(thm)],[316]) ).
tff(318,plain,
tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_assoc_pair_2_get_0x30(constr_pkey(name_skS))) = tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_assoc_pair_2_get_0x30(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(transitivity,[status(thm)],[317,311,309]) ).
tff(319,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_assoc_pair_2_get_0x30(constr_pkey(name_skS)))) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_assoc_pair_2_get_0x30(constr_pkey(name_skS))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(monotonicity,[status(thm)],[318]) ).
tff(320,plain,
( ~ ! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 )
| ( constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_assoc_pair_2_get_0x30(constr_pkey(name_skS)))) = constr_assoc_pair_2_get_0x30(constr_pkey(name_skS)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(321,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_assoc_pair_2_get_0x30(constr_pkey(name_skS)))) = constr_assoc_pair_2_get_0x30(constr_pkey(name_skS)),
inference(unit_resolution,[status(thm)],[320,20]) ).
tff(322,plain,
constr_assoc_pair_2_get_0x30(constr_pkey(name_skS)) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS)))),constr_assoc_pair_2_get_0x30(constr_pkey(name_skS)))),
inference(symmetry,[status(thm)],[321]) ).
tff(323,plain,
constr_pkey(name_skS) = constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),
inference(transitivity,[status(thm)],[304,303,322,319,294,212,209,97]) ).
tff(324,plain,
constr_tuple_2_get_0x30(constr_pkey(name_skS)) = constr_tuple_2_get_0x30(constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))),
inference(monotonicity,[status(thm)],[323]) ).
tff(325,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))))) = constr_tuple_2_get_0x30(constr_pkey(name_skS)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(326,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))))) = constr_tuple_2_get_0x30(constr_pkey(name_skS)),
inference(unit_resolution,[status(thm)],[325,7]) ).
tff(327,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))))) = tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(328,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))))) = tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),
inference(unit_resolution,[status(thm)],[327,7]) ).
tff(329,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB))) = tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(330,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB))) = tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)),
inference(unit_resolution,[status(thm)],[329,7]) ).
tff(331,plain,
( ~ ! [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] : ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) )
| ( tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB))) = tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(332,plain,
tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB))) = tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)),
inference(unit_resolution,[status(thm)],[331,29]) ).
tff(333,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)) = tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB))),
inference(symmetry,[status(thm)],[332]) ).
tff(334,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)))),
inference(monotonicity,[status(thm)],[333]) ).
tff(335,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB))),
inference(symmetry,[status(thm)],[334]) ).
tff(336,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)))) = tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(337,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)))) = tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(unit_resolution,[status(thm)],[336,7]) ).
tff(338,plain,
tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)))),
inference(symmetry,[status(thm)],[337]) ).
tff(339,plain,
( ~ ! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 )
| ( constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))))) = tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(340,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))))) = tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(unit_resolution,[status(thm)],[339,20]) ).
tff(341,plain,
( ~ ! [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] : ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) )
| ( tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))))) = tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(342,plain,
tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))))) = tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),
inference(unit_resolution,[status(thm)],[341,29]) ).
tff(343,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))))) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))))),
inference(monotonicity,[status(thm)],[342]) ).
tff(344,plain,
( ~ ! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 )
| ( constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))))) = tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(345,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))))) = tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),
inference(unit_resolution,[status(thm)],[344,20]) ).
tff(346,plain,
tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))))),
inference(symmetry,[status(thm)],[345]) ).
tff(347,plain,
tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))) = tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)),
inference(transitivity,[status(thm)],[346,343,340,338,335,330]) ).
tff(348,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB))),
inference(monotonicity,[status(thm)],[347]) ).
tff(349,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))))),
inference(symmetry,[status(thm)],[348]) ).
tff(350,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB))) = tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(351,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB))) = tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(unit_resolution,[status(thm)],[350,7]) ).
tff(352,plain,
tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB))),
inference(symmetry,[status(thm)],[351]) ).
tff(353,plain,
tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),
inference(transitivity,[status(thm)],[352,349,328]) ).
tff(354,plain,
tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))) = tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)),
inference(monotonicity,[status(thm)],[353,353]) ).
tff(355,plain,
tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)) = tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),
inference(symmetry,[status(thm)],[354]) ).
tff(356,plain,
( ~ ! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 )
| ( constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)))) = tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(357,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)))) = tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)),
inference(unit_resolution,[status(thm)],[356,20]) ).
tff(358,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)))) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB))),
inference(monotonicity,[status(thm)],[332]) ).
tff(359,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB))) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_assoc_pair(tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)))),
inference(symmetry,[status(thm)],[358]) ).
tff(360,plain,
( ~ ! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 )
| ( constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB))) = tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(361,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB))) = tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB),
inference(unit_resolution,[status(thm)],[360,20]) ).
tff(362,plain,
tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB)),tuple_2(tuple_client_A_out_1(name_A,name_I),name_skB))),
inference(symmetry,[status(thm)],[361]) ).
tff(363,plain,
tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))) = tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),
inference(transitivity,[status(thm)],[352,349,328,362,359,357,355]) ).
tff(364,plain,
tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))) = tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))))),
inference(monotonicity,[status(thm)],[363]) ).
tff(365,plain,
tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))))) = tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),
inference(symmetry,[status(thm)],[364]) ).
tff(366,plain,
( ~ ! [VAR_X_17: $i,VAR_Y_18: $i,VAR_Z_0X30: $i] : ( tuple_assoc_pair(VAR_X_17,tuple_assoc_pair(VAR_Y_18,VAR_Z_0X30)) = tuple_assoc_pair(tuple_assoc_pair(VAR_X_17,VAR_Y_18),VAR_Z_0X30) )
| ( tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))))) = tuple_assoc_pair(tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(367,plain,
tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))))) = tuple_assoc_pair(tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),
inference(unit_resolution,[status(thm)],[366,29]) ).
tff(368,plain,
tuple_assoc_pair(tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))) = tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_assoc_pair(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))))),
inference(symmetry,[status(thm)],[367]) ).
tff(369,plain,
tuple_assoc_pair(tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))) = tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),
inference(transitivity,[status(thm)],[368,365]) ).
tff(370,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))) = tuple_assoc_pair(tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),
inference(monotonicity,[status(thm)],[369]) ).
tff(371,plain,
tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))) = tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),
inference(transitivity,[status(thm)],[370,368,365]) ).
tff(372,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))))),
inference(monotonicity,[status(thm)],[371]) ).
tff(373,plain,
( ~ ! [VAR_X0X30_9: $i,VAR_X1_10X30: $i] : ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(VAR_X0X30_9,VAR_X1_10X30)) = VAR_X0X30_9 )
| ( constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))))) = tuple_assoc_pair(tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(374,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))))) = tuple_assoc_pair(tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),
inference(unit_resolution,[status(thm)],[373,7]) ).
tff(375,plain,
tuple_assoc_pair(tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))))),
inference(symmetry,[status(thm)],[374]) ).
tff(376,plain,
tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))) = tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS))),
inference(transitivity,[status(thm)],[364,367,375,372,326,324,292,223,36,33,22]) ).
tff(377,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))))) = constr_assoc_pair_2_get_1(tuple_assoc_pair(tuple_out_2(constr_pkey(name_skB)),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(monotonicity,[status(thm)],[376]) ).
tff(378,plain,
( ~ ! [VAR_X0X30_11: $i,VAR_X1_12: $i] : ( constr_assoc_pair_2_get_1(tuple_assoc_pair(VAR_X0X30_11,VAR_X1_12)) = VAR_X1_12 )
| ( constr_assoc_pair_2_get_1(tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))))) = tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(379,plain,
constr_assoc_pair_2_get_1(tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))))) = tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))),
inference(unit_resolution,[status(thm)],[378,20]) ).
tff(380,plain,
tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))) = constr_assoc_pair_2_get_1(tuple_assoc_pair(constr_tuple_2_get_0x30(constr_pkey(name_skS)),tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))))),
inference(symmetry,[status(thm)],[379]) ).
tff(381,plain,
tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS)))) = constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB))),
inference(transitivity,[status(thm)],[380,377,214,212,209,97]) ).
tff(382,plain,
constr_tuple_2_get_1_bitstring(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))) = constr_tuple_2_get_1_bitstring(constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))),
inference(monotonicity,[status(thm)],[381]) ).
tff(383,plain,
constr_tuple_2_get_1_bitstring(constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))) = constr_tuple_2_get_1_bitstring(tuple_2(tuple_out_1(tuple_keys(tuple_out_2(constr_pkey(name_skB)),name_c)),tuple_assoc_pair(tuple_assoc_pair(name_skB,tuple_client_B_in_2(tuple_out_2(constr_pkey(name_skB)))),tuple_client_B_in_3(constr_pkey(name_skS))))),
inference(symmetry,[status(thm)],[382]) ).
tff(384,plain,
constr_tuple_2_get_1_bitstring(constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))) = constr_tuple_2_get_1_bitstring(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))),
inference(monotonicity,[status(thm)],[291]) ).
tff(385,plain,
constr_tuple_2_get_1_bitstring(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))) = constr_tuple_2_get_1_bitstring(constr_enc(tuple_client_A_out_5(constr_pkey(name_skS)),tuple_out_2(constr_pkey(name_skB)))),
inference(symmetry,[status(thm)],[384]) ).
tff(386,plain,
( ~ ! [VAR_X0X30_7: $i,VAR_X1_8: $i] : ( constr_tuple_2_get_1_bitstring(tuple_2(VAR_X0X30_7,VAR_X1_8)) = VAR_X1_8 )
| ( constr_tuple_2_get_1_bitstring(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))) = constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(387,plain,
constr_tuple_2_get_1_bitstring(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))) = constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))),
inference(unit_resolution,[status(thm)],[386,93]) ).
tff(388,plain,
constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))) = constr_tuple_2_get_1_bitstring(tuple_2(tuple_client_B_in_3(constr_pkey(name_skS)),constr_enc(constr_CONST_0x30,tuple_out_3(constr_pkey(name_skS))))),
inference(symmetry,[status(thm)],[387]) ).
tff(389,plain,
name_A = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(name_A,tuple_client_B_out_1(name_B,name_A))),
inference(symmetry,[status(thm)],[101]) ).
tff(390,plain,
name_A = name_skB,
inference(transitivity,[status(thm)],[389,124,127,256,253,227,388,385,383,95,86,83,9]) ).
tff(391,plain,
( ( name_A != name_skB )
<=> ( name_A != name_skB ) ),
inference(rewrite,[status(thm)],]) ).
tff(392,axiom,
name_A != name_skB,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
tff(393,plain,
name_A != name_skB,
inference(modus_ponens,[status(thm)],[392,391]) ).
tff(394,plain,
$false,
inference(unit_resolution,[status(thm)],[393,390]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW961+1 : TPTP v8.1.0. Released v7.4.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Sep 5 00:25:29 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 157.44/101.68 % SZS status Theorem
% 157.44/101.68 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------