%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV267-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:31:55 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of formulae : 29 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 113 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 142 ( 67 ~; 61 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 78 ( 69 !; 0 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_set_type,type,
tc_set: $i > $i ).
tff(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
tff(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
tff(v_G_type,type,
v_G: $i ).
tff(v_H_type,type,
v_H: $i ).
tff(1,plain,
^ [V_H: $i] :
refl(( c_lessequals(V_H,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
<=> c_lessequals(V_H,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_H: $i] : c_lessequals(V_H,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
<=> ! [V_H: $i] : c_lessequals(V_H,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_H: $i] : c_lessequals(V_H,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
<=> ! [V_H: $i] : c_lessequals(V_H,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_H: $i] : c_lessequals(V_H,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__increasing_0) ).
tff(5,plain,
! [V_H: $i] : c_lessequals(V_H,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_H: $i] : c_lessequals(V_H,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_H: $i] : c_lessequals(V_H,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_H: $i] : c_lessequals(V_H,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(v_G,c_Message_Oparts(v_G),tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
c_lessequals(v_G,c_Message_Oparts(v_G),tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
refl(( ( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) )
<=> ( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
trans(monotonicity(rewrite(( ( ~ c_lessequals(V_B,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
<=> ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ) )),
( ( ~ c_lessequals(V_B,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_lessequals(V_A,V_C,tc_set(T_a)) )
<=> ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a))
| c_lessequals(V_A,V_C,tc_set(T_a)) ) )),
rewrite(( ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a))
| c_lessequals(V_A,V_C,tc_set(T_a)) )
<=> ( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ) )),
( ( ~ c_lessequals(V_B,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_lessequals(V_A,V_C,tc_set(T_a)) )
<=> ( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( ~ c_lessequals(V_B,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_lessequals(V_A,V_C,tc_set(T_a)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( ~ c_lessequals(V_B,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_lessequals(V_A,V_C,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__trans_0) ).
tff(16,plain,
! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ~ c_lessequals(v_G,c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
<=> ~ c_lessequals(v_G,c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
~ c_lessequals(v_G,c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(22,plain,
~ c_lessequals(v_G,c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( c_lessequals(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
<=> c_lessequals(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
c_lessequals(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(25,plain,
c_lessequals(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) )
| c_lessequals(v_G,c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(v_G,c_Message_Oparts(v_G),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) )
| c_lessequals(v_G,c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(v_G,c_Message_Oparts(v_G),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) )
| c_lessequals(v_G,c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(v_G,c_Message_Oparts(v_G),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) )
| c_lessequals(v_G,c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(v_G,c_Message_Oparts(v_G),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
$false,
inference(unit_resolution,[status(thm)],[28,25,22,19,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV267-2 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n006.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 09:33:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Unsatisfiable
% 0.11/0.36 % SZS output start Proof
% See solution above
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------