%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV277-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:31:58 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 19
% Syntax : Number of formulae : 40 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 166 ( 78 ~; 73 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-1 aty)
% Number of variables : 104 ( 93 !; 0 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_set_type,type,
tc_set: $i > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_Message_OkeysFor_type,type,
c_Message_OkeysFor: $i > $i ).
tff(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
tff(v_H_type,type,
v_H: $i ).
tff(c_Message_Oanalz_type,type,
c_Message_Oanalz: $i > $i ).
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(v_K_type,type,
v_K: $i ).
tff(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
tff(1,plain,
( c_in(v_K,c_Message_OkeysFor(c_Message_Oanalz(v_H)),tc_nat)
<=> c_in(v_K,c_Message_OkeysFor(c_Message_Oanalz(v_H)),tc_nat) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
c_in(v_K,c_Message_OkeysFor(c_Message_Oanalz(v_H)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(3,plain,
c_in(v_K,c_Message_OkeysFor(c_Message_Oanalz(v_H)),tc_nat),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(v_H)),tc_nat)
<=> ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(v_H)),tc_nat) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(v_H)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(6,plain,
~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(v_H)),tc_nat),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
refl(( ( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) )
<=> ( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
rewrite(( ( ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a) )
<=> ( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
tff(13,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) )
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(v_H)),tc_nat)
| ~ c_lessequals(c_Message_OkeysFor(c_Message_Oanalz(v_H)),c_Message_OkeysFor(c_Message_Oparts(v_H)),tc_set(tc_nat))
| ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oanalz(v_H)),tc_nat) )
<=> ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) )
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(v_H)),tc_nat)
| ~ c_lessequals(c_Message_OkeysFor(c_Message_Oanalz(v_H)),c_Message_OkeysFor(c_Message_Oparts(v_H)),tc_set(tc_nat))
| ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oanalz(v_H)),tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) )
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(v_H)),tc_nat)
| ~ c_lessequals(c_Message_OkeysFor(c_Message_Oanalz(v_H)),c_Message_OkeysFor(c_Message_Oparts(v_H)),tc_set(tc_nat))
| ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oanalz(v_H)),tc_nat) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) )
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(v_H)),tc_nat)
| ~ c_lessequals(c_Message_OkeysFor(c_Message_Oanalz(v_H)),c_Message_OkeysFor(c_Message_Oparts(v_H)),tc_set(tc_nat))
| ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oanalz(v_H)),tc_nat) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
~ c_lessequals(c_Message_OkeysFor(c_Message_Oanalz(v_H)),c_Message_OkeysFor(c_Message_Oparts(v_H)),tc_set(tc_nat)),
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
tff(21,plain,
^ [V_H: $i] :
refl(( c_lessequals(c_Message_Oanalz(V_H),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
<=> c_lessequals(c_Message_Oanalz(V_H),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [V_H: $i] : c_lessequals(c_Message_Oanalz(V_H),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
<=> ! [V_H: $i] : c_lessequals(c_Message_Oanalz(V_H),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [V_H: $i] : c_lessequals(c_Message_Oanalz(V_H),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
<=> ! [V_H: $i] : c_lessequals(c_Message_Oanalz(V_H),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [V_H: $i] : c_lessequals(c_Message_Oanalz(V_H),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__subset__parts_0) ).
tff(25,plain,
! [V_H: $i] : c_lessequals(c_Message_Oanalz(V_H),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [V_H: $i] : c_lessequals(c_Message_Oanalz(V_H),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [V_H: $i] : c_lessequals(c_Message_Oanalz(V_H),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [V_H: $i] : c_lessequals(c_Message_Oanalz(V_H),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(v_H),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
c_lessequals(c_Message_Oanalz(v_H),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
^ [V_H: $i,V_G: $i] :
refl(( ( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_OkeysFor(V_G),c_Message_OkeysFor(V_H),tc_set(tc_nat)) )
<=> ( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_OkeysFor(V_G),c_Message_OkeysFor(V_H),tc_set(tc_nat)) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_OkeysFor(V_G),c_Message_OkeysFor(V_H),tc_set(tc_nat)) )
<=> ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_OkeysFor(V_G),c_Message_OkeysFor(V_H),tc_set(tc_nat)) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_OkeysFor(V_G),c_Message_OkeysFor(V_H),tc_set(tc_nat)) )
<=> ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_OkeysFor(V_G),c_Message_OkeysFor(V_H),tc_set(tc_nat)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_OkeysFor(V_G),c_Message_OkeysFor(V_H),tc_set(tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__mono_0) ).
tff(34,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_OkeysFor(V_G),c_Message_OkeysFor(V_H),tc_set(tc_nat)) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_OkeysFor(V_G),c_Message_OkeysFor(V_H),tc_set(tc_nat)) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_OkeysFor(V_G),c_Message_OkeysFor(V_H),tc_set(tc_nat)) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_OkeysFor(V_G),c_Message_OkeysFor(V_H),tc_set(tc_nat)) )
| ~ c_lessequals(c_Message_Oanalz(v_H),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_OkeysFor(c_Message_Oanalz(v_H)),c_Message_OkeysFor(c_Message_Oparts(v_H)),tc_set(tc_nat)) )
<=> ( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_OkeysFor(V_G),c_Message_OkeysFor(V_H),tc_set(tc_nat)) )
| ~ c_lessequals(c_Message_Oanalz(v_H),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_OkeysFor(c_Message_Oanalz(v_H)),c_Message_OkeysFor(c_Message_Oparts(v_H)),tc_set(tc_nat)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_OkeysFor(V_G),c_Message_OkeysFor(V_H),tc_set(tc_nat)) )
| ~ c_lessequals(c_Message_Oanalz(v_H),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_OkeysFor(c_Message_Oanalz(v_H)),c_Message_OkeysFor(c_Message_Oparts(v_H)),tc_set(tc_nat)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_OkeysFor(V_G),c_Message_OkeysFor(V_H),tc_set(tc_nat)) )
| ~ c_lessequals(c_Message_Oanalz(v_H),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_OkeysFor(c_Message_Oanalz(v_H)),c_Message_OkeysFor(c_Message_Oparts(v_H)),tc_set(tc_nat)) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
$false,
inference(unit_resolution,[status(thm)],[39,36,29,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV277-2 : TPTP v9.0.0. Released v3.2.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:34:55 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.37 % SZS status Unsatisfiable
% 0.20/0.37 % SZS output start Proof
% See solution above
% 0.20/0.38 % E exiting
%------------------------------------------------------------------------------