%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW961+1 : TPTP v9.0.0. Released v7.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 : Sat Jun 21 05:37:43 AM UTC 2025
% Result : Theorem 3.10s 3.28s
% Output : Proof 3.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 31
% Syntax : Number of formulae : 78 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 199 ( 34 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 197 ( 84 ~; 75 |; 0 &)
% ( 29 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 137 ( 122 !; 0 ?; 137 :)
% Comments :
%------------------------------------------------------------------------------
tff(pred_attacker_type,type,
pred_attacker: $i > $o ).
tff(constr_pkey_type,type,
constr_pkey: $i > $i ).
tff(name_skA_type,type,
name_skA: $i ).
tff(tuple_assoc_pair_type,type,
tuple_assoc_pair: ( $i * $i ) > $i ).
tff(tuple_2_type,type,
tuple_2: ( $i * $i ) > $i ).
tff(name_objective_type,type,
name_objective: $i ).
tff(constr_assoc_pair_2_get_0x30_type,type,
constr_assoc_pair_2_get_0x30: $i > $i ).
tff(tuple_out_1_type,type,
tuple_out_1: $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(tuple_assoc_pair(constr_pkey(name_skA),tuple_2(name_objective,name_objective)),name_skA)) = tuple_assoc_pair(constr_pkey(name_skA),tuple_2(name_objective,name_objective)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skA),tuple_2(name_objective,name_objective)),name_skA)) = tuple_assoc_pair(constr_pkey(name_skA),tuple_2(name_objective,name_objective)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,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(14,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)],[13,12]) ).
tff(15,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)],[14]) ).
tff(16,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)],[15,11]) ).
tff(17,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_skA),tuple_assoc_pair(tuple_2(name_objective,name_objective),name_skA)) = tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skA),tuple_2(name_objective,name_objective)),name_skA) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
tuple_assoc_pair(constr_pkey(name_skA),tuple_assoc_pair(tuple_2(name_objective,name_objective),name_skA)) = tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skA),tuple_2(name_objective,name_objective)),name_skA),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skA),tuple_2(name_objective,name_objective)),name_skA) = tuple_assoc_pair(constr_pkey(name_skA),tuple_assoc_pair(tuple_2(name_objective,name_objective),name_skA)),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skA),tuple_2(name_objective,name_objective)),name_skA)) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(constr_pkey(name_skA),tuple_assoc_pair(tuple_2(name_objective,name_objective),name_skA))),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(constr_pkey(name_skA),tuple_assoc_pair(tuple_2(name_objective,name_objective),name_skA))) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(tuple_assoc_pair(constr_pkey(name_skA),tuple_2(name_objective,name_objective)),name_skA)),
inference(symmetry,[status(thm)],[20]) ).
tff(22,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_skA),tuple_assoc_pair(tuple_2(name_objective,name_objective),name_skA))) = constr_pkey(name_skA) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
constr_assoc_pair_2_get_0x30(tuple_assoc_pair(constr_pkey(name_skA),tuple_assoc_pair(tuple_2(name_objective,name_objective),name_skA))) = constr_pkey(name_skA),
inference(unit_resolution,[status(thm)],[22,7]) ).
tff(24,plain,
constr_pkey(name_skA) = constr_assoc_pair_2_get_0x30(tuple_assoc_pair(constr_pkey(name_skA),tuple_assoc_pair(tuple_2(name_objective,name_objective),name_skA))),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
constr_pkey(name_skA) = tuple_assoc_pair(constr_pkey(name_skA),tuple_2(name_objective,name_objective)),
inference(transitivity,[status(thm)],[24,21,9]) ).
tff(26,plain,
( pred_attacker(constr_pkey(name_skA))
<=> pred_attacker(tuple_assoc_pair(constr_pkey(name_skA),tuple_2(name_objective,name_objective))) ),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
( pred_attacker(tuple_assoc_pair(constr_pkey(name_skA),tuple_2(name_objective,name_objective)))
<=> pred_attacker(constr_pkey(name_skA)) ),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
( ~ pred_attacker(tuple_assoc_pair(constr_pkey(name_skA),tuple_2(name_objective,name_objective)))
<=> ~ pred_attacker(constr_pkey(name_skA)) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( ~ pred_attacker(name_objective)
<=> ~ pred_attacker(name_objective) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
~ pred_attacker(name_objective),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co0) ).
tff(31,plain,
~ pred_attacker(name_objective),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
^ [VAR_V_260X30: $i,VAR_V_261: $i] :
refl(( ( pred_attacker(VAR_V_260X30)
| ~ pred_attacker(tuple_2(VAR_V_260X30,VAR_V_261)) )
<=> ( pred_attacker(VAR_V_260X30)
| ~ pred_attacker(tuple_2(VAR_V_260X30,VAR_V_261)) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [VAR_V_260X30: $i,VAR_V_261: $i] :
( pred_attacker(VAR_V_260X30)
| ~ pred_attacker(tuple_2(VAR_V_260X30,VAR_V_261)) )
<=> ! [VAR_V_260X30: $i,VAR_V_261: $i] :
( pred_attacker(VAR_V_260X30)
| ~ pred_attacker(tuple_2(VAR_V_260X30,VAR_V_261)) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [VAR_V_260X30: $i,VAR_V_261: $i] :
( pred_attacker(VAR_V_260X30)
| ~ pred_attacker(tuple_2(VAR_V_260X30,VAR_V_261)) )
<=> ! [VAR_V_260X30: $i,VAR_V_261: $i] :
( pred_attacker(VAR_V_260X30)
| ~ pred_attacker(tuple_2(VAR_V_260X30,VAR_V_261)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
^ [VAR_V_260X30: $i,VAR_V_261: $i] :
rewrite(( ( pred_attacker(tuple_2(VAR_V_260X30,VAR_V_261))
=> pred_attacker(VAR_V_260X30) )
<=> ( pred_attacker(VAR_V_260X30)
| ~ pred_attacker(tuple_2(VAR_V_260X30,VAR_V_261)) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [VAR_V_260X30: $i,VAR_V_261: $i] :
( pred_attacker(tuple_2(VAR_V_260X30,VAR_V_261))
=> pred_attacker(VAR_V_260X30) )
<=> ! [VAR_V_260X30: $i,VAR_V_261: $i] :
( pred_attacker(VAR_V_260X30)
| ~ pred_attacker(tuple_2(VAR_V_260X30,VAR_V_261)) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [VAR_V_260X30: $i,VAR_V_261: $i] :
( pred_attacker(tuple_2(VAR_V_260X30,VAR_V_261))
=> pred_attacker(VAR_V_260X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax153) ).
tff(38,plain,
! [VAR_V_260X30: $i,VAR_V_261: $i] :
( pred_attacker(VAR_V_260X30)
| ~ pred_attacker(tuple_2(VAR_V_260X30,VAR_V_261)) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [VAR_V_260X30: $i,VAR_V_261: $i] :
( pred_attacker(VAR_V_260X30)
| ~ pred_attacker(tuple_2(VAR_V_260X30,VAR_V_261)) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [VAR_V_260X30: $i,VAR_V_261: $i] :
( pred_attacker(VAR_V_260X30)
| ~ pred_attacker(tuple_2(VAR_V_260X30,VAR_V_261)) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [VAR_V_260X30: $i,VAR_V_261: $i] :
( pred_attacker(VAR_V_260X30)
| ~ pred_attacker(tuple_2(VAR_V_260X30,VAR_V_261)) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ~ ! [VAR_V_260X30: $i,VAR_V_261: $i] :
( pred_attacker(VAR_V_260X30)
| ~ pred_attacker(tuple_2(VAR_V_260X30,VAR_V_261)) )
| pred_attacker(name_objective)
| ~ pred_attacker(tuple_2(name_objective,name_objective)) )
<=> ( ~ ! [VAR_V_260X30: $i,VAR_V_261: $i] :
( pred_attacker(VAR_V_260X30)
| ~ pred_attacker(tuple_2(VAR_V_260X30,VAR_V_261)) )
| pred_attacker(name_objective)
| ~ pred_attacker(tuple_2(name_objective,name_objective)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [VAR_V_260X30: $i,VAR_V_261: $i] :
( pred_attacker(VAR_V_260X30)
| ~ pred_attacker(tuple_2(VAR_V_260X30,VAR_V_261)) )
| pred_attacker(name_objective)
| ~ pred_attacker(tuple_2(name_objective,name_objective)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [VAR_V_260X30: $i,VAR_V_261: $i] :
( pred_attacker(VAR_V_260X30)
| ~ pred_attacker(tuple_2(VAR_V_260X30,VAR_V_261)) )
| pred_attacker(name_objective)
| ~ pred_attacker(tuple_2(name_objective,name_objective)) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
~ pred_attacker(tuple_2(name_objective,name_objective)),
inference(unit_resolution,[status(thm)],[44,41,31]) ).
tff(46,plain,
^ [VAR_V_235: $i,VAR_V_236: $i] :
refl(( ( pred_attacker(VAR_V_236)
| ~ pred_attacker(tuple_assoc_pair(VAR_V_235,VAR_V_236)) )
<=> ( pred_attacker(VAR_V_236)
| ~ pred_attacker(tuple_assoc_pair(VAR_V_235,VAR_V_236)) ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [VAR_V_235: $i,VAR_V_236: $i] :
( pred_attacker(VAR_V_236)
| ~ pred_attacker(tuple_assoc_pair(VAR_V_235,VAR_V_236)) )
<=> ! [VAR_V_235: $i,VAR_V_236: $i] :
( pred_attacker(VAR_V_236)
| ~ pred_attacker(tuple_assoc_pair(VAR_V_235,VAR_V_236)) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [VAR_V_235: $i,VAR_V_236: $i] :
( pred_attacker(VAR_V_236)
| ~ pred_attacker(tuple_assoc_pair(VAR_V_235,VAR_V_236)) )
<=> ! [VAR_V_235: $i,VAR_V_236: $i] :
( pred_attacker(VAR_V_236)
| ~ pred_attacker(tuple_assoc_pair(VAR_V_235,VAR_V_236)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
^ [VAR_V_235: $i,VAR_V_236: $i] :
rewrite(( ( pred_attacker(tuple_assoc_pair(VAR_V_235,VAR_V_236))
=> pred_attacker(VAR_V_236) )
<=> ( pred_attacker(VAR_V_236)
| ~ pred_attacker(tuple_assoc_pair(VAR_V_235,VAR_V_236)) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [VAR_V_235: $i,VAR_V_236: $i] :
( pred_attacker(tuple_assoc_pair(VAR_V_235,VAR_V_236))
=> pred_attacker(VAR_V_236) )
<=> ! [VAR_V_235: $i,VAR_V_236: $i] :
( pred_attacker(VAR_V_236)
| ~ pred_attacker(tuple_assoc_pair(VAR_V_235,VAR_V_236)) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,axiom,
! [VAR_V_235: $i,VAR_V_236: $i] :
( pred_attacker(tuple_assoc_pair(VAR_V_235,VAR_V_236))
=> pred_attacker(VAR_V_236) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax144) ).
tff(52,plain,
! [VAR_V_235: $i,VAR_V_236: $i] :
( pred_attacker(VAR_V_236)
| ~ pred_attacker(tuple_assoc_pair(VAR_V_235,VAR_V_236)) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [VAR_V_235: $i,VAR_V_236: $i] :
( pred_attacker(VAR_V_236)
| ~ pred_attacker(tuple_assoc_pair(VAR_V_235,VAR_V_236)) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
! [VAR_V_235: $i,VAR_V_236: $i] :
( pred_attacker(VAR_V_236)
| ~ pred_attacker(tuple_assoc_pair(VAR_V_235,VAR_V_236)) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [VAR_V_235: $i,VAR_V_236: $i] :
( pred_attacker(VAR_V_236)
| ~ pred_attacker(tuple_assoc_pair(VAR_V_235,VAR_V_236)) ),
inference(modus_ponens,[status(thm)],[54,47]) ).
tff(56,plain,
( ( ~ ! [VAR_V_235: $i,VAR_V_236: $i] :
( pred_attacker(VAR_V_236)
| ~ pred_attacker(tuple_assoc_pair(VAR_V_235,VAR_V_236)) )
| pred_attacker(tuple_2(name_objective,name_objective))
| ~ pred_attacker(tuple_assoc_pair(constr_pkey(name_skA),tuple_2(name_objective,name_objective))) )
<=> ( ~ ! [VAR_V_235: $i,VAR_V_236: $i] :
( pred_attacker(VAR_V_236)
| ~ pred_attacker(tuple_assoc_pair(VAR_V_235,VAR_V_236)) )
| pred_attacker(tuple_2(name_objective,name_objective))
| ~ pred_attacker(tuple_assoc_pair(constr_pkey(name_skA),tuple_2(name_objective,name_objective))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
( ~ ! [VAR_V_235: $i,VAR_V_236: $i] :
( pred_attacker(VAR_V_236)
| ~ pred_attacker(tuple_assoc_pair(VAR_V_235,VAR_V_236)) )
| pred_attacker(tuple_2(name_objective,name_objective))
| ~ pred_attacker(tuple_assoc_pair(constr_pkey(name_skA),tuple_2(name_objective,name_objective))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [VAR_V_235: $i,VAR_V_236: $i] :
( pred_attacker(VAR_V_236)
| ~ pred_attacker(tuple_assoc_pair(VAR_V_235,VAR_V_236)) )
| pred_attacker(tuple_2(name_objective,name_objective))
| ~ pred_attacker(tuple_assoc_pair(constr_pkey(name_skA),tuple_2(name_objective,name_objective))) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
~ pred_attacker(tuple_assoc_pair(constr_pkey(name_skA),tuple_2(name_objective,name_objective))),
inference(unit_resolution,[status(thm)],[58,55,45]) ).
tff(60,plain,
~ pred_attacker(constr_pkey(name_skA)),
inference(modus_ponens,[status(thm)],[59,28]) ).
tff(61,plain,
( pred_attacker(tuple_out_1(constr_pkey(name_skA)))
<=> pred_attacker(tuple_out_1(constr_pkey(name_skA))) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,axiom,
pred_attacker(tuple_out_1(constr_pkey(name_skA))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax165) ).
tff(63,plain,
pred_attacker(tuple_out_1(constr_pkey(name_skA))),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
^ [VAR_V_73: $i] :
refl(( ( pred_attacker(VAR_V_73)
| ~ pred_attacker(tuple_out_1(VAR_V_73)) )
<=> ( pred_attacker(VAR_V_73)
| ~ pred_attacker(tuple_out_1(VAR_V_73)) ) )),
inference(bind,[status(th)],[]) ).
tff(65,plain,
( ! [VAR_V_73: $i] :
( pred_attacker(VAR_V_73)
| ~ pred_attacker(tuple_out_1(VAR_V_73)) )
<=> ! [VAR_V_73: $i] :
( pred_attacker(VAR_V_73)
| ~ pred_attacker(tuple_out_1(VAR_V_73)) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [VAR_V_73: $i] :
( pred_attacker(VAR_V_73)
| ~ pred_attacker(tuple_out_1(VAR_V_73)) )
<=> ! [VAR_V_73: $i] :
( pred_attacker(VAR_V_73)
| ~ pred_attacker(tuple_out_1(VAR_V_73)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
^ [VAR_V_73: $i] :
rewrite(( ( pred_attacker(tuple_out_1(VAR_V_73))
=> pred_attacker(VAR_V_73) )
<=> ( pred_attacker(VAR_V_73)
| ~ pred_attacker(tuple_out_1(VAR_V_73)) ) )),
inference(bind,[status(th)],[]) ).
tff(68,plain,
( ! [VAR_V_73: $i] :
( pred_attacker(tuple_out_1(VAR_V_73))
=> pred_attacker(VAR_V_73) )
<=> ! [VAR_V_73: $i] :
( pred_attacker(VAR_V_73)
| ~ pred_attacker(tuple_out_1(VAR_V_73)) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,axiom,
! [VAR_V_73: $i] :
( pred_attacker(tuple_out_1(VAR_V_73))
=> pred_attacker(VAR_V_73) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax100) ).
tff(70,plain,
! [VAR_V_73: $i] :
( pred_attacker(VAR_V_73)
| ~ pred_attacker(tuple_out_1(VAR_V_73)) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [VAR_V_73: $i] :
( pred_attacker(VAR_V_73)
| ~ pred_attacker(tuple_out_1(VAR_V_73)) ),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
! [VAR_V_73: $i] :
( pred_attacker(VAR_V_73)
| ~ pred_attacker(tuple_out_1(VAR_V_73)) ),
inference(skolemize,[status(sab)],[71]) ).
tff(73,plain,
! [VAR_V_73: $i] :
( pred_attacker(VAR_V_73)
| ~ pred_attacker(tuple_out_1(VAR_V_73)) ),
inference(modus_ponens,[status(thm)],[72,65]) ).
tff(74,plain,
( ( ~ ! [VAR_V_73: $i] :
( pred_attacker(VAR_V_73)
| ~ pred_attacker(tuple_out_1(VAR_V_73)) )
| pred_attacker(constr_pkey(name_skA))
| ~ pred_attacker(tuple_out_1(constr_pkey(name_skA))) )
<=> ( ~ ! [VAR_V_73: $i] :
( pred_attacker(VAR_V_73)
| ~ pred_attacker(tuple_out_1(VAR_V_73)) )
| pred_attacker(constr_pkey(name_skA))
| ~ pred_attacker(tuple_out_1(constr_pkey(name_skA))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
( ~ ! [VAR_V_73: $i] :
( pred_attacker(VAR_V_73)
| ~ pred_attacker(tuple_out_1(VAR_V_73)) )
| pred_attacker(constr_pkey(name_skA))
| ~ pred_attacker(tuple_out_1(constr_pkey(name_skA))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
( ~ ! [VAR_V_73: $i] :
( pred_attacker(VAR_V_73)
| ~ pred_attacker(tuple_out_1(VAR_V_73)) )
| pred_attacker(constr_pkey(name_skA))
| ~ pred_attacker(tuple_out_1(constr_pkey(name_skA))) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
pred_attacker(constr_pkey(name_skA)),
inference(unit_resolution,[status(thm)],[76,73,63]) ).
tff(78,plain,
$false,
inference(unit_resolution,[status(thm)],[77,60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW961+1 : TPTP v9.0.0. Released v7.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:15:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 3.10/3.28 % SZS status Theorem
% 3.10/3.28 % SZS output start Proof
% See solution above
% 3.10/3.29 % E exiting
%------------------------------------------------------------------------------