TSTP Solution File: SWW950+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW950+1 : TPTP v8.1.0. Released v7.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 21:00:21 EDT 2022
% Result : Theorem 0.21s 0.50s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 54
% Syntax : Number of formulae : 110 ( 24 unt; 11 typ; 0 def)
% Number of atoms : 478 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 605 ( 264 ~; 234 |; 32 &)
% ( 57 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 38 ( 38 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 7 >; 2 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 160 ( 140 !; 0 ?; 160 :)
% Comments :
%------------------------------------------------------------------------------
tff(pred_attacker_type,type,
pred_attacker: $i > $o ).
tff(constr_h_type,type,
constr_h: $i > $i ).
tff(constr_xor_type,type,
constr_xor: ( $i * $i ) > $i ).
tff(name_ki_type,type,
name_ki: $i ).
tff(name_k0x30_type,type,
name_k0x30: $i ).
tff(constr_ZERO_type,type,
constr_ZERO: $i ).
tff(tuple_T_out_2_type,type,
tuple_T_out_2: $i > $i ).
tff(tuple_T_in_1_type,type,
tuple_T_in_1: $i > $i ).
tff(tuple_T_in_3_type,type,
tuple_T_in_3: ( $i * $i ) > $i ).
tff(tuple_T_out_4_type,type,
tuple_T_out_4: $i > $i ).
tff(name_objective_type,type,
name_objective: $i ).
tff(1,plain,
^ [VAR_V_63: $i] :
refl(
( ( ~ pred_attacker(VAR_V_63)
| pred_attacker(tuple_T_in_1(VAR_V_63)) )
<=> ( ~ pred_attacker(VAR_V_63)
| pred_attacker(tuple_T_in_1(VAR_V_63)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [VAR_V_63: $i] :
( ~ pred_attacker(VAR_V_63)
| pred_attacker(tuple_T_in_1(VAR_V_63)) )
<=> ! [VAR_V_63: $i] :
( ~ pred_attacker(VAR_V_63)
| pred_attacker(tuple_T_in_1(VAR_V_63)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [VAR_V_63: $i] :
( ~ pred_attacker(VAR_V_63)
| pred_attacker(tuple_T_in_1(VAR_V_63)) )
<=> ! [VAR_V_63: $i] :
( ~ pred_attacker(VAR_V_63)
| pred_attacker(tuple_T_in_1(VAR_V_63)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
^ [VAR_V_63: $i] :
rewrite(
( ( pred_attacker(VAR_V_63)
=> pred_attacker(tuple_T_in_1(VAR_V_63)) )
<=> ( ~ pred_attacker(VAR_V_63)
| pred_attacker(tuple_T_in_1(VAR_V_63)) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [VAR_V_63: $i] :
( pred_attacker(VAR_V_63)
=> pred_attacker(tuple_T_in_1(VAR_V_63)) )
<=> ! [VAR_V_63: $i] :
( ~ pred_attacker(VAR_V_63)
| pred_attacker(tuple_T_in_1(VAR_V_63)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [VAR_V_63: $i] :
( pred_attacker(VAR_V_63)
=> pred_attacker(tuple_T_in_1(VAR_V_63)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax61) ).
tff(7,plain,
! [VAR_V_63: $i] :
( ~ pred_attacker(VAR_V_63)
| pred_attacker(tuple_T_in_1(VAR_V_63)) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [VAR_V_63: $i] :
( ~ pred_attacker(VAR_V_63)
| pred_attacker(tuple_T_in_1(VAR_V_63)) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [VAR_V_63: $i] :
( ~ pred_attacker(VAR_V_63)
| pred_attacker(tuple_T_in_1(VAR_V_63)) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [VAR_V_63: $i] :
( ~ pred_attacker(VAR_V_63)
| pred_attacker(tuple_T_in_1(VAR_V_63)) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( pred_attacker(constr_ZERO)
<=> pred_attacker(constr_ZERO) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
pred_attacker(constr_ZERO),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).
tff(13,plain,
pred_attacker(constr_ZERO),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [VAR_V_63: $i] :
( ~ pred_attacker(VAR_V_63)
| pred_attacker(tuple_T_in_1(VAR_V_63)) )
| ~ pred_attacker(constr_ZERO)
| pred_attacker(tuple_T_in_1(constr_ZERO)) )
<=> ( ~ ! [VAR_V_63: $i] :
( ~ pred_attacker(VAR_V_63)
| pred_attacker(tuple_T_in_1(VAR_V_63)) )
| ~ pred_attacker(constr_ZERO)
| pred_attacker(tuple_T_in_1(constr_ZERO)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [VAR_V_63: $i] :
( ~ pred_attacker(VAR_V_63)
| pred_attacker(tuple_T_in_1(VAR_V_63)) )
| ~ pred_attacker(constr_ZERO)
| pred_attacker(tuple_T_in_1(constr_ZERO)) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [VAR_V_63: $i] :
( ~ pred_attacker(VAR_V_63)
| pred_attacker(tuple_T_in_1(VAR_V_63)) )
| ~ pred_attacker(constr_ZERO)
| pred_attacker(tuple_T_in_1(constr_ZERO)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
pred_attacker(tuple_T_in_1(constr_ZERO)),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
^ [VAR_R_10X308: $i] :
refl(
( ( ~ pred_attacker(tuple_T_in_1(VAR_R_10X308))
| pred_attacker(tuple_T_out_2(constr_h(constr_xor(VAR_R_10X308,constr_xor(name_k0x30,name_ki))))) )
<=> ( ~ pred_attacker(tuple_T_in_1(VAR_R_10X308))
| pred_attacker(tuple_T_out_2(constr_h(constr_xor(VAR_R_10X308,constr_xor(name_k0x30,name_ki))))) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [VAR_R_10X308: $i] :
( ~ pred_attacker(tuple_T_in_1(VAR_R_10X308))
| pred_attacker(tuple_T_out_2(constr_h(constr_xor(VAR_R_10X308,constr_xor(name_k0x30,name_ki))))) )
<=> ! [VAR_R_10X308: $i] :
( ~ pred_attacker(tuple_T_in_1(VAR_R_10X308))
| pred_attacker(tuple_T_out_2(constr_h(constr_xor(VAR_R_10X308,constr_xor(name_k0x30,name_ki))))) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [VAR_R_10X308: $i] :
( ~ pred_attacker(tuple_T_in_1(VAR_R_10X308))
| pred_attacker(tuple_T_out_2(constr_h(constr_xor(VAR_R_10X308,constr_xor(name_k0x30,name_ki))))) )
<=> ! [VAR_R_10X308: $i] :
( ~ pred_attacker(tuple_T_in_1(VAR_R_10X308))
| pred_attacker(tuple_T_out_2(constr_h(constr_xor(VAR_R_10X308,constr_xor(name_k0x30,name_ki))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
^ [VAR_R_10X308: $i] :
rewrite(
( ( pred_attacker(tuple_T_in_1(VAR_R_10X308))
=> pred_attacker(tuple_T_out_2(constr_h(constr_xor(VAR_R_10X308,constr_xor(name_k0x30,name_ki))))) )
<=> ( ~ pred_attacker(tuple_T_in_1(VAR_R_10X308))
| pred_attacker(tuple_T_out_2(constr_h(constr_xor(VAR_R_10X308,constr_xor(name_k0x30,name_ki))))) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [VAR_R_10X308: $i] :
( pred_attacker(tuple_T_in_1(VAR_R_10X308))
=> pred_attacker(tuple_T_out_2(constr_h(constr_xor(VAR_R_10X308,constr_xor(name_k0x30,name_ki))))) )
<=> ! [VAR_R_10X308: $i] :
( ~ pred_attacker(tuple_T_in_1(VAR_R_10X308))
| pred_attacker(tuple_T_out_2(constr_h(constr_xor(VAR_R_10X308,constr_xor(name_k0x30,name_ki))))) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [VAR_R_10X308: $i] :
( pred_attacker(tuple_T_in_1(VAR_R_10X308))
=> pred_attacker(tuple_T_out_2(constr_h(constr_xor(VAR_R_10X308,constr_xor(name_k0x30,name_ki))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax73) ).
tff(24,plain,
! [VAR_R_10X308: $i] :
( ~ pred_attacker(tuple_T_in_1(VAR_R_10X308))
| pred_attacker(tuple_T_out_2(constr_h(constr_xor(VAR_R_10X308,constr_xor(name_k0x30,name_ki))))) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [VAR_R_10X308: $i] :
( ~ pred_attacker(tuple_T_in_1(VAR_R_10X308))
| pred_attacker(tuple_T_out_2(constr_h(constr_xor(VAR_R_10X308,constr_xor(name_k0x30,name_ki))))) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [VAR_R_10X308: $i] :
( ~ pred_attacker(tuple_T_in_1(VAR_R_10X308))
| pred_attacker(tuple_T_out_2(constr_h(constr_xor(VAR_R_10X308,constr_xor(name_k0x30,name_ki))))) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [VAR_R_10X308: $i] :
( ~ pred_attacker(tuple_T_in_1(VAR_R_10X308))
| pred_attacker(tuple_T_out_2(constr_h(constr_xor(VAR_R_10X308,constr_xor(name_k0x30,name_ki))))) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [VAR_R_10X308: $i] :
( ~ pred_attacker(tuple_T_in_1(VAR_R_10X308))
| pred_attacker(tuple_T_out_2(constr_h(constr_xor(VAR_R_10X308,constr_xor(name_k0x30,name_ki))))) )
| ~ pred_attacker(tuple_T_in_1(constr_ZERO))
| pred_attacker(tuple_T_out_2(constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))) )
<=> ( ~ ! [VAR_R_10X308: $i] :
( ~ pred_attacker(tuple_T_in_1(VAR_R_10X308))
| pred_attacker(tuple_T_out_2(constr_h(constr_xor(VAR_R_10X308,constr_xor(name_k0x30,name_ki))))) )
| ~ pred_attacker(tuple_T_in_1(constr_ZERO))
| pred_attacker(tuple_T_out_2(constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ~ ! [VAR_R_10X308: $i] :
( ~ pred_attacker(tuple_T_in_1(VAR_R_10X308))
| pred_attacker(tuple_T_out_2(constr_h(constr_xor(VAR_R_10X308,constr_xor(name_k0x30,name_ki))))) )
| ~ pred_attacker(tuple_T_in_1(constr_ZERO))
| pred_attacker(tuple_T_out_2(constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
( ~ ! [VAR_R_10X308: $i] :
( ~ pred_attacker(tuple_T_in_1(VAR_R_10X308))
| pred_attacker(tuple_T_out_2(constr_h(constr_xor(VAR_R_10X308,constr_xor(name_k0x30,name_ki))))) )
| ~ pred_attacker(tuple_T_in_1(constr_ZERO))
| pred_attacker(tuple_T_out_2(constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
pred_attacker(tuple_T_out_2(constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))),
inference(unit_resolution,[status(thm)],[30,27,17]) ).
tff(32,plain,
^ [VAR_V_44: $i] :
refl(
( ( pred_attacker(VAR_V_44)
| ~ pred_attacker(tuple_T_out_2(VAR_V_44)) )
<=> ( pred_attacker(VAR_V_44)
| ~ pred_attacker(tuple_T_out_2(VAR_V_44)) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [VAR_V_44: $i] :
( pred_attacker(VAR_V_44)
| ~ pred_attacker(tuple_T_out_2(VAR_V_44)) )
<=> ! [VAR_V_44: $i] :
( pred_attacker(VAR_V_44)
| ~ pred_attacker(tuple_T_out_2(VAR_V_44)) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [VAR_V_44: $i] :
( pred_attacker(VAR_V_44)
| ~ pred_attacker(tuple_T_out_2(VAR_V_44)) )
<=> ! [VAR_V_44: $i] :
( pred_attacker(VAR_V_44)
| ~ pred_attacker(tuple_T_out_2(VAR_V_44)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
^ [VAR_V_44: $i] :
rewrite(
( ( pred_attacker(tuple_T_out_2(VAR_V_44))
=> pred_attacker(VAR_V_44) )
<=> ( pred_attacker(VAR_V_44)
| ~ pred_attacker(tuple_T_out_2(VAR_V_44)) ) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [VAR_V_44: $i] :
( pred_attacker(tuple_T_out_2(VAR_V_44))
=> pred_attacker(VAR_V_44) )
<=> ! [VAR_V_44: $i] :
( pred_attacker(VAR_V_44)
| ~ pred_attacker(tuple_T_out_2(VAR_V_44)) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [VAR_V_44: $i] :
( pred_attacker(tuple_T_out_2(VAR_V_44))
=> pred_attacker(VAR_V_44) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).
tff(38,plain,
! [VAR_V_44: $i] :
( pred_attacker(VAR_V_44)
| ~ pred_attacker(tuple_T_out_2(VAR_V_44)) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [VAR_V_44: $i] :
( pred_attacker(VAR_V_44)
| ~ pred_attacker(tuple_T_out_2(VAR_V_44)) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [VAR_V_44: $i] :
( pred_attacker(VAR_V_44)
| ~ pred_attacker(tuple_T_out_2(VAR_V_44)) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [VAR_V_44: $i] :
( pred_attacker(VAR_V_44)
| ~ pred_attacker(tuple_T_out_2(VAR_V_44)) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ~ ! [VAR_V_44: $i] :
( pred_attacker(VAR_V_44)
| ~ pred_attacker(tuple_T_out_2(VAR_V_44)) )
| pred_attacker(constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))
| ~ pred_attacker(tuple_T_out_2(constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))) )
<=> ( ~ ! [VAR_V_44: $i] :
( pred_attacker(VAR_V_44)
| ~ pred_attacker(tuple_T_out_2(VAR_V_44)) )
| pred_attacker(constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))
| ~ pred_attacker(tuple_T_out_2(constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ~ ! [VAR_V_44: $i] :
( pred_attacker(VAR_V_44)
| ~ pred_attacker(tuple_T_out_2(VAR_V_44)) )
| pred_attacker(constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))
| ~ pred_attacker(tuple_T_out_2(constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( ~ ! [VAR_V_44: $i] :
( pred_attacker(VAR_V_44)
| ~ pred_attacker(tuple_T_out_2(VAR_V_44)) )
| pred_attacker(constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))
| ~ pred_attacker(tuple_T_out_2(constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
pred_attacker(constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki)))),
inference(unit_resolution,[status(thm)],[44,41,31]) ).
tff(46,plain,
( ~ pred_attacker(name_objective)
<=> ~ pred_attacker(name_objective) ),
inference(rewrite,[status(thm)],]) ).
tff(47,axiom,
~ pred_attacker(name_objective),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co0) ).
tff(48,plain,
~ pred_attacker(name_objective),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
^ [VAR_V_38: $i] :
refl(
( ( pred_attacker(VAR_V_38)
| ~ pred_attacker(tuple_T_out_4(VAR_V_38)) )
<=> ( pred_attacker(VAR_V_38)
| ~ pred_attacker(tuple_T_out_4(VAR_V_38)) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [VAR_V_38: $i] :
( pred_attacker(VAR_V_38)
| ~ pred_attacker(tuple_T_out_4(VAR_V_38)) )
<=> ! [VAR_V_38: $i] :
( pred_attacker(VAR_V_38)
| ~ pred_attacker(tuple_T_out_4(VAR_V_38)) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [VAR_V_38: $i] :
( pred_attacker(VAR_V_38)
| ~ pred_attacker(tuple_T_out_4(VAR_V_38)) )
<=> ! [VAR_V_38: $i] :
( pred_attacker(VAR_V_38)
| ~ pred_attacker(tuple_T_out_4(VAR_V_38)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
^ [VAR_V_38: $i] :
rewrite(
( ( pred_attacker(tuple_T_out_4(VAR_V_38))
=> pred_attacker(VAR_V_38) )
<=> ( pred_attacker(VAR_V_38)
| ~ pred_attacker(tuple_T_out_4(VAR_V_38)) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [VAR_V_38: $i] :
( pred_attacker(tuple_T_out_4(VAR_V_38))
=> pred_attacker(VAR_V_38) )
<=> ! [VAR_V_38: $i] :
( pred_attacker(VAR_V_38)
| ~ pred_attacker(tuple_T_out_4(VAR_V_38)) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,axiom,
! [VAR_V_38: $i] :
( pred_attacker(tuple_T_out_4(VAR_V_38))
=> pred_attacker(VAR_V_38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
tff(55,plain,
! [VAR_V_38: $i] :
( pred_attacker(VAR_V_38)
| ~ pred_attacker(tuple_T_out_4(VAR_V_38)) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [VAR_V_38: $i] :
( pred_attacker(VAR_V_38)
| ~ pred_attacker(tuple_T_out_4(VAR_V_38)) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
! [VAR_V_38: $i] :
( pred_attacker(VAR_V_38)
| ~ pred_attacker(tuple_T_out_4(VAR_V_38)) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [VAR_V_38: $i] :
( pred_attacker(VAR_V_38)
| ~ pred_attacker(tuple_T_out_4(VAR_V_38)) ),
inference(modus_ponens,[status(thm)],[57,50]) ).
tff(59,plain,
( ( ~ ! [VAR_V_38: $i] :
( pred_attacker(VAR_V_38)
| ~ pred_attacker(tuple_T_out_4(VAR_V_38)) )
| pred_attacker(name_objective)
| ~ pred_attacker(tuple_T_out_4(name_objective)) )
<=> ( ~ ! [VAR_V_38: $i] :
( pred_attacker(VAR_V_38)
| ~ pred_attacker(tuple_T_out_4(VAR_V_38)) )
| pred_attacker(name_objective)
| ~ pred_attacker(tuple_T_out_4(name_objective)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ~ ! [VAR_V_38: $i] :
( pred_attacker(VAR_V_38)
| ~ pred_attacker(tuple_T_out_4(VAR_V_38)) )
| pred_attacker(name_objective)
| ~ pred_attacker(tuple_T_out_4(name_objective)) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
( ~ ! [VAR_V_38: $i] :
( pred_attacker(VAR_V_38)
| ~ pred_attacker(tuple_T_out_4(VAR_V_38)) )
| pred_attacker(name_objective)
| ~ pred_attacker(tuple_T_out_4(name_objective)) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
~ pred_attacker(tuple_T_out_4(name_objective)),
inference(unit_resolution,[status(thm)],[61,58,48]) ).
tff(63,plain,
^ [VAR_A_143: $i,VAR_R_144: $i] :
refl(
( ( pred_attacker(tuple_T_out_4(name_objective))
| ~ pred_attacker(tuple_T_in_1(VAR_R_144))
| ~ pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki))))) )
<=> ( pred_attacker(tuple_T_out_4(name_objective))
| ~ pred_attacker(tuple_T_in_1(VAR_R_144))
| ~ pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki))))) ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [VAR_A_143: $i,VAR_R_144: $i] :
( pred_attacker(tuple_T_out_4(name_objective))
| ~ pred_attacker(tuple_T_in_1(VAR_R_144))
| ~ pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki))))) )
<=> ! [VAR_A_143: $i,VAR_R_144: $i] :
( pred_attacker(tuple_T_out_4(name_objective))
| ~ pred_attacker(tuple_T_in_1(VAR_R_144))
| ~ pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki))))) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
^ [VAR_A_143: $i,VAR_R_144: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki)))))
& pred_attacker(tuple_T_in_1(VAR_R_144)) )
<=> ~ ( ~ pred_attacker(tuple_T_in_1(VAR_R_144))
| ~ pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki))))) ) )),
( ~ ( pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki)))))
& pred_attacker(tuple_T_in_1(VAR_R_144)) )
<=> ~ ~ ( ~ pred_attacker(tuple_T_in_1(VAR_R_144))
| ~ pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki))))) ) )),
rewrite(
( ~ ~ ( ~ pred_attacker(tuple_T_in_1(VAR_R_144))
| ~ pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki))))) )
<=> ( ~ pred_attacker(tuple_T_in_1(VAR_R_144))
| ~ pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki))))) ) )),
( ~ ( pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki)))))
& pred_attacker(tuple_T_in_1(VAR_R_144)) )
<=> ( ~ pred_attacker(tuple_T_in_1(VAR_R_144))
| ~ pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki))))) ) )),
( ( pred_attacker(tuple_T_out_4(name_objective))
| ~ ( pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki)))))
& pred_attacker(tuple_T_in_1(VAR_R_144)) ) )
<=> ( pred_attacker(tuple_T_out_4(name_objective))
| ~ pred_attacker(tuple_T_in_1(VAR_R_144))
| ~ pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki))))) ) )),
rewrite(
( ( pred_attacker(tuple_T_out_4(name_objective))
| ~ pred_attacker(tuple_T_in_1(VAR_R_144))
| ~ pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki))))) )
<=> ( pred_attacker(tuple_T_out_4(name_objective))
| ~ pred_attacker(tuple_T_in_1(VAR_R_144))
| ~ pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki))))) ) )),
( ( pred_attacker(tuple_T_out_4(name_objective))
| ~ ( pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki)))))
& pred_attacker(tuple_T_in_1(VAR_R_144)) ) )
<=> ( pred_attacker(tuple_T_out_4(name_objective))
| ~ pred_attacker(tuple_T_in_1(VAR_R_144))
| ~ pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki))))) ) )),
inference(bind,[status(th)],]) ).
tff(66,plain,
( ! [VAR_A_143: $i,VAR_R_144: $i] :
( pred_attacker(tuple_T_out_4(name_objective))
| ~ ( pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki)))))
& pred_attacker(tuple_T_in_1(VAR_R_144)) ) )
<=> ! [VAR_A_143: $i,VAR_R_144: $i] :
( pred_attacker(tuple_T_out_4(name_objective))
| ~ pred_attacker(tuple_T_in_1(VAR_R_144))
| ~ pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki))))) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [VAR_A_143: $i,VAR_R_144: $i] :
( pred_attacker(tuple_T_out_4(name_objective))
| ~ ( pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki)))))
& pred_attacker(tuple_T_in_1(VAR_R_144)) ) )
<=> ! [VAR_A_143: $i,VAR_R_144: $i] :
( pred_attacker(tuple_T_out_4(name_objective))
| ~ ( pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki)))))
& pred_attacker(tuple_T_in_1(VAR_R_144)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
^ [VAR_A_143: $i,VAR_R_144: $i] :
rewrite(
( ( ( pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki)))))
& pred_attacker(tuple_T_in_1(VAR_R_144)) )
=> pred_attacker(tuple_T_out_4(name_objective)) )
<=> ( pred_attacker(tuple_T_out_4(name_objective))
| ~ ( pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki)))))
& pred_attacker(tuple_T_in_1(VAR_R_144)) ) ) )),
inference(bind,[status(th)],]) ).
tff(69,plain,
( ! [VAR_A_143: $i,VAR_R_144: $i] :
( ( pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki)))))
& pred_attacker(tuple_T_in_1(VAR_R_144)) )
=> pred_attacker(tuple_T_out_4(name_objective)) )
<=> ! [VAR_A_143: $i,VAR_R_144: $i] :
( pred_attacker(tuple_T_out_4(name_objective))
| ~ ( pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki)))))
& pred_attacker(tuple_T_in_1(VAR_R_144)) ) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,axiom,
! [VAR_A_143: $i,VAR_R_144: $i] :
( ( pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki)))))
& pred_attacker(tuple_T_in_1(VAR_R_144)) )
=> pred_attacker(tuple_T_out_4(name_objective)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax74) ).
tff(71,plain,
! [VAR_A_143: $i,VAR_R_144: $i] :
( pred_attacker(tuple_T_out_4(name_objective))
| ~ ( pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki)))))
& pred_attacker(tuple_T_in_1(VAR_R_144)) ) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
! [VAR_A_143: $i,VAR_R_144: $i] :
( pred_attacker(tuple_T_out_4(name_objective))
| ~ ( pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki)))))
& pred_attacker(tuple_T_in_1(VAR_R_144)) ) ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
! [VAR_A_143: $i,VAR_R_144: $i] :
( pred_attacker(tuple_T_out_4(name_objective))
| ~ ( pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki)))))
& pred_attacker(tuple_T_in_1(VAR_R_144)) ) ),
inference(skolemize,[status(sab)],[72]) ).
tff(74,plain,
! [VAR_A_143: $i,VAR_R_144: $i] :
( pred_attacker(tuple_T_out_4(name_objective))
| ~ pred_attacker(tuple_T_in_1(VAR_R_144))
| ~ pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki))))) ),
inference(modus_ponens,[status(thm)],[73,66]) ).
tff(75,plain,
! [VAR_A_143: $i,VAR_R_144: $i] :
( pred_attacker(tuple_T_out_4(name_objective))
| ~ pred_attacker(tuple_T_in_1(VAR_R_144))
| ~ pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki))))) ),
inference(modus_ponens,[status(thm)],[74,64]) ).
tff(76,plain,
( ( ~ ! [VAR_A_143: $i,VAR_R_144: $i] :
( pred_attacker(tuple_T_out_4(name_objective))
| ~ pred_attacker(tuple_T_in_1(VAR_R_144))
| ~ pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki))))) )
| pred_attacker(tuple_T_out_4(name_objective))
| ~ pred_attacker(tuple_T_in_1(constr_ZERO))
| ~ pred_attacker(tuple_T_in_3(constr_ZERO,constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))) )
<=> ( ~ ! [VAR_A_143: $i,VAR_R_144: $i] :
( pred_attacker(tuple_T_out_4(name_objective))
| ~ pred_attacker(tuple_T_in_1(VAR_R_144))
| ~ pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki))))) )
| pred_attacker(tuple_T_out_4(name_objective))
| ~ pred_attacker(tuple_T_in_1(constr_ZERO))
| ~ pred_attacker(tuple_T_in_3(constr_ZERO,constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
( ~ ! [VAR_A_143: $i,VAR_R_144: $i] :
( pred_attacker(tuple_T_out_4(name_objective))
| ~ pred_attacker(tuple_T_in_1(VAR_R_144))
| ~ pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki))))) )
| pred_attacker(tuple_T_out_4(name_objective))
| ~ pred_attacker(tuple_T_in_1(constr_ZERO))
| ~ pred_attacker(tuple_T_in_3(constr_ZERO,constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
( ~ ! [VAR_A_143: $i,VAR_R_144: $i] :
( pred_attacker(tuple_T_out_4(name_objective))
| ~ pred_attacker(tuple_T_in_1(VAR_R_144))
| ~ pred_attacker(tuple_T_in_3(VAR_A_143,constr_h(constr_xor(VAR_A_143,constr_xor(name_k0x30,name_ki))))) )
| pred_attacker(tuple_T_out_4(name_objective))
| ~ pred_attacker(tuple_T_in_1(constr_ZERO))
| ~ pred_attacker(tuple_T_in_3(constr_ZERO,constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
~ pred_attacker(tuple_T_in_3(constr_ZERO,constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))),
inference(unit_resolution,[status(thm)],[78,75,62,17]) ).
tff(80,plain,
^ [VAR_V_48: $i,VAR_V_49: $i] :
refl(
( ( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ pred_attacker(VAR_V_49)
| ~ pred_attacker(VAR_V_48) )
<=> ( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ pred_attacker(VAR_V_49)
| ~ pred_attacker(VAR_V_48) ) )),
inference(bind,[status(th)],]) ).
tff(81,plain,
( ! [VAR_V_48: $i,VAR_V_49: $i] :
( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ pred_attacker(VAR_V_49)
| ~ pred_attacker(VAR_V_48) )
<=> ! [VAR_V_48: $i,VAR_V_49: $i] :
( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ pred_attacker(VAR_V_49)
| ~ pred_attacker(VAR_V_48) ) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
^ [VAR_V_48: $i,VAR_V_49: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( pred_attacker(VAR_V_48)
& pred_attacker(VAR_V_49) )
<=> ~ ( ~ pred_attacker(VAR_V_49)
| ~ pred_attacker(VAR_V_48) ) )),
( ~ ( pred_attacker(VAR_V_48)
& pred_attacker(VAR_V_49) )
<=> ~ ~ ( ~ pred_attacker(VAR_V_49)
| ~ pred_attacker(VAR_V_48) ) )),
rewrite(
( ~ ~ ( ~ pred_attacker(VAR_V_49)
| ~ pred_attacker(VAR_V_48) )
<=> ( ~ pred_attacker(VAR_V_49)
| ~ pred_attacker(VAR_V_48) ) )),
( ~ ( pred_attacker(VAR_V_48)
& pred_attacker(VAR_V_49) )
<=> ( ~ pred_attacker(VAR_V_49)
| ~ pred_attacker(VAR_V_48) ) )),
( ( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ ( pred_attacker(VAR_V_48)
& pred_attacker(VAR_V_49) ) )
<=> ( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ pred_attacker(VAR_V_49)
| ~ pred_attacker(VAR_V_48) ) )),
rewrite(
( ( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ pred_attacker(VAR_V_49)
| ~ pred_attacker(VAR_V_48) )
<=> ( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ pred_attacker(VAR_V_49)
| ~ pred_attacker(VAR_V_48) ) )),
( ( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ ( pred_attacker(VAR_V_48)
& pred_attacker(VAR_V_49) ) )
<=> ( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ pred_attacker(VAR_V_49)
| ~ pred_attacker(VAR_V_48) ) )),
inference(bind,[status(th)],]) ).
tff(83,plain,
( ! [VAR_V_48: $i,VAR_V_49: $i] :
( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ ( pred_attacker(VAR_V_48)
& pred_attacker(VAR_V_49) ) )
<=> ! [VAR_V_48: $i,VAR_V_49: $i] :
( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ pred_attacker(VAR_V_49)
| ~ pred_attacker(VAR_V_48) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [VAR_V_48: $i,VAR_V_49: $i] :
( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ ( pred_attacker(VAR_V_48)
& pred_attacker(VAR_V_49) ) )
<=> ! [VAR_V_48: $i,VAR_V_49: $i] :
( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ ( pred_attacker(VAR_V_48)
& pred_attacker(VAR_V_49) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,plain,
^ [VAR_V_48: $i,VAR_V_49: $i] :
rewrite(
( ( ( pred_attacker(VAR_V_48)
& pred_attacker(VAR_V_49) )
=> pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49)) )
<=> ( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ ( pred_attacker(VAR_V_48)
& pred_attacker(VAR_V_49) ) ) )),
inference(bind,[status(th)],]) ).
tff(86,plain,
( ! [VAR_V_48: $i,VAR_V_49: $i] :
( ( pred_attacker(VAR_V_48)
& pred_attacker(VAR_V_49) )
=> pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49)) )
<=> ! [VAR_V_48: $i,VAR_V_49: $i] :
( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ ( pred_attacker(VAR_V_48)
& pred_attacker(VAR_V_49) ) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,axiom,
! [VAR_V_48: $i,VAR_V_49: $i] :
( ( pred_attacker(VAR_V_48)
& pred_attacker(VAR_V_49) )
=> pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).
tff(88,plain,
! [VAR_V_48: $i,VAR_V_49: $i] :
( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ ( pred_attacker(VAR_V_48)
& pred_attacker(VAR_V_49) ) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [VAR_V_48: $i,VAR_V_49: $i] :
( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ ( pred_attacker(VAR_V_48)
& pred_attacker(VAR_V_49) ) ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
! [VAR_V_48: $i,VAR_V_49: $i] :
( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ ( pred_attacker(VAR_V_48)
& pred_attacker(VAR_V_49) ) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [VAR_V_48: $i,VAR_V_49: $i] :
( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ pred_attacker(VAR_V_49)
| ~ pred_attacker(VAR_V_48) ),
inference(modus_ponens,[status(thm)],[90,83]) ).
tff(92,plain,
! [VAR_V_48: $i,VAR_V_49: $i] :
( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ pred_attacker(VAR_V_49)
| ~ pred_attacker(VAR_V_48) ),
inference(modus_ponens,[status(thm)],[91,81]) ).
tff(93,plain,
( ( ~ ! [VAR_V_48: $i,VAR_V_49: $i] :
( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ pred_attacker(VAR_V_49)
| ~ pred_attacker(VAR_V_48) )
| ~ pred_attacker(constr_ZERO)
| ~ pred_attacker(constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))
| pred_attacker(tuple_T_in_3(constr_ZERO,constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))) )
<=> ( ~ ! [VAR_V_48: $i,VAR_V_49: $i] :
( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ pred_attacker(VAR_V_49)
| ~ pred_attacker(VAR_V_48) )
| ~ pred_attacker(constr_ZERO)
| ~ pred_attacker(constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))
| pred_attacker(tuple_T_in_3(constr_ZERO,constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
( ( pred_attacker(tuple_T_in_3(constr_ZERO,constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki)))))
| ~ pred_attacker(constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))
| ~ pred_attacker(constr_ZERO) )
<=> ( ~ pred_attacker(constr_ZERO)
| ~ pred_attacker(constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))
| pred_attacker(tuple_T_in_3(constr_ZERO,constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,plain,
( ( ~ ! [VAR_V_48: $i,VAR_V_49: $i] :
( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ pred_attacker(VAR_V_49)
| ~ pred_attacker(VAR_V_48) )
| pred_attacker(tuple_T_in_3(constr_ZERO,constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki)))))
| ~ pred_attacker(constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))
| ~ pred_attacker(constr_ZERO) )
<=> ( ~ ! [VAR_V_48: $i,VAR_V_49: $i] :
( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ pred_attacker(VAR_V_49)
| ~ pred_attacker(VAR_V_48) )
| ~ pred_attacker(constr_ZERO)
| ~ pred_attacker(constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))
| pred_attacker(tuple_T_in_3(constr_ZERO,constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))) ) ),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
( ( ~ ! [VAR_V_48: $i,VAR_V_49: $i] :
( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ pred_attacker(VAR_V_49)
| ~ pred_attacker(VAR_V_48) )
| pred_attacker(tuple_T_in_3(constr_ZERO,constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki)))))
| ~ pred_attacker(constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))
| ~ pred_attacker(constr_ZERO) )
<=> ( ~ ! [VAR_V_48: $i,VAR_V_49: $i] :
( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ pred_attacker(VAR_V_49)
| ~ pred_attacker(VAR_V_48) )
| ~ pred_attacker(constr_ZERO)
| ~ pred_attacker(constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))
| pred_attacker(tuple_T_in_3(constr_ZERO,constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))) ) ),
inference(transitivity,[status(thm)],[95,93]) ).
tff(97,plain,
( ~ ! [VAR_V_48: $i,VAR_V_49: $i] :
( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ pred_attacker(VAR_V_49)
| ~ pred_attacker(VAR_V_48) )
| pred_attacker(tuple_T_in_3(constr_ZERO,constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki)))))
| ~ pred_attacker(constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))
| ~ pred_attacker(constr_ZERO) ),
inference(quant_inst,[status(thm)],]) ).
tff(98,plain,
( ~ ! [VAR_V_48: $i,VAR_V_49: $i] :
( pred_attacker(tuple_T_in_3(VAR_V_48,VAR_V_49))
| ~ pred_attacker(VAR_V_49)
| ~ pred_attacker(VAR_V_48) )
| ~ pred_attacker(constr_ZERO)
| ~ pred_attacker(constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))
| pred_attacker(tuple_T_in_3(constr_ZERO,constr_h(constr_xor(constr_ZERO,constr_xor(name_k0x30,name_ki))))) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
$false,
inference(unit_resolution,[status(thm)],[98,13,92,79,45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWW950+1 : TPTP v8.1.0. Released v7.4.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Sep 5 00:25:52 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.50 % SZS status Theorem
% 0.21/0.50 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------