%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV258-2 : 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 05:31:53 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.36s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 25
% Syntax : Number of formulae : 55 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 202 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 269 ( 127 ~; 120 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 5 ( 5 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 : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 156 ( 142 !; 0 ?; 156 :)
% 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_H_type,type,
v_H: $i ).
tff(c_insert_type,type,
c_insert: ( $i * $i * $i ) > $i ).
tff(v_X_type,type,
v_X: $i ).
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(1,plain,
^ [V_H: $i,V_G: $i] :
refl(( ( ~ c_lessequals(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)) )
<=> ( ~ c_lessequals(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(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(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)) )
<=> ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(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(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(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)) )
<=> ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(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(4,axiom,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(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)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__subset__iff_1) ).
tff(5,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(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(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(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(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(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(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
<=> ~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(10,plain,
~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(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)) )
| ~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)) )
<=> ( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(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)) )
| ~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(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)) )
| ~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(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)) )
| ~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,plain,
^ [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
refl(( ( c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_x,V_B,T_a) )
<=> ( c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_x,V_B,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_x,V_B,T_a) )
<=> ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_x,V_B,T_a) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_x,V_B,T_a) )
<=> ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_x,V_B,T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
^ [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
rewrite(( ( ~ c_in(V_x,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) )
<=> ( c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_x,V_B,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) )
<=> ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_x,V_B,T_a) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,axiom,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_2) ).
tff(21,plain,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_x,V_B,T_a) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_x,V_B,T_a) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_x,V_B,T_a) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_x,V_B,T_a) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
( c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg)
<=> c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(27,plain,
c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_x,V_B,T_a) )
| ~ c_lessequals(v_H,c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| ~ c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_x,V_B,T_a) )
| ~ c_lessequals(v_H,c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| ~ c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ( c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(v_H,c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| ~ c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg) )
<=> ( ~ c_lessequals(v_H,c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| ~ c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_x,V_B,T_a) )
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(v_H,c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| ~ c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_x,V_B,T_a) )
| ~ c_lessequals(v_H,c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| ~ c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_x,V_B,T_a) )
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(v_H,c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| ~ c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_x,V_B,T_a) )
| ~ c_lessequals(v_H,c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| ~ c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
tff(32,plain,
( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_x,V_B,T_a) )
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(v_H,c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| ~ c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_x,V_B,T_a) )
| ~ c_lessequals(v_H,c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| ~ c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
~ c_lessequals(v_H,c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[33,27,24,14]) ).
tff(35,plain,
^ [V_H: $i,V_G: $i] :
refl(( ( ~ c_lessequals(c_Message_Oparts(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)) )
<=> ( ~ c_lessequals(c_Message_Oparts(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(bind,[status(th)],[]) ).
tff(36,plain,
( ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(c_Message_Oparts(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)) )
<=> ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(c_Message_Oparts(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(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(c_Message_Oparts(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)) )
<=> ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(c_Message_Oparts(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(38,axiom,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(c_Message_Oparts(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)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__subset__iff_0) ).
tff(39,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(c_Message_Oparts(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(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(c_Message_Oparts(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(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(c_Message_Oparts(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(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(c_Message_Oparts(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)) )
| ~ c_lessequals(c_Message_Oparts(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)) )
<=> ( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(c_Message_Oparts(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)) )
| ~ c_lessequals(c_Message_Oparts(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(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(c_Message_Oparts(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)) )
| ~ c_lessequals(c_Message_Oparts(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(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(c_Message_Oparts(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)) )
| ~ c_lessequals(c_Message_Oparts(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(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
( ~ c_lessequals(c_Message_Oparts(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(unit_resolution,[status(thm)],[44,41]) ).
tff(46,plain,
~ c_lessequals(c_Message_Oparts(v_H),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[45,34]) ).
tff(47,plain,
^ [T_a: $i,V_A: $i] :
refl(( c_lessequals(V_A,V_A,tc_set(T_a))
<=> c_lessequals(V_A,V_A,tc_set(T_a)) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [T_a: $i,V_A: $i] : c_lessequals(V_A,V_A,tc_set(T_a))
<=> ! [T_a: $i,V_A: $i] : c_lessequals(V_A,V_A,tc_set(T_a)) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [T_a: $i,V_A: $i] : c_lessequals(V_A,V_A,tc_set(T_a))
<=> ! [T_a: $i,V_A: $i] : c_lessequals(V_A,V_A,tc_set(T_a)) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
! [T_a: $i,V_A: $i] : c_lessequals(V_A,V_A,tc_set(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
tff(51,plain,
! [T_a: $i,V_A: $i] : c_lessequals(V_A,V_A,tc_set(T_a)),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [T_a: $i,V_A: $i] : c_lessequals(V_A,V_A,tc_set(T_a)),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [T_a: $i,V_A: $i] : c_lessequals(V_A,V_A,tc_set(T_a)),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
( ~ ! [T_a: $i,V_A: $i] : c_lessequals(V_A,V_A,tc_set(T_a))
| c_lessequals(c_Message_Oparts(v_H),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
$false,
inference(unit_resolution,[status(thm)],[54,53,46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV258-2 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.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 09:32:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.36 % SZS status Unsatisfiable
% 0.19/0.36 % SZS output start Proof
% See solution above
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------