TSTP Solution File: SWV258-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV258-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 15:10:39 EDT 2022
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 32
% Syntax : Number of formulae : 59 ( 17 unt; 8 typ; 0 def)
% Number of atoms : 170 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 215 ( 101 ~; 95 |; 0 &)
% ( 19 <=>; 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 : 11 ( 5 >; 6 *; 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 : 140 ( 126 !; 0 ?; 140 :)
% 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,
^ [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(2,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)],[1]) ).
tff(3,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(4,axiom,
! [T_a: $i,V_A: $i] : c_lessequals(V_A,V_A,tc_set(T_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
tff(5,plain,
! [T_a: $i,V_A: $i] : c_lessequals(V_A,V_A,tc_set(T_a)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [T_a: $i,V_A: $i] : c_lessequals(V_A,V_A,tc_set(T_a)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [T_a: $i,V_A: $i] : c_lessequals(V_A,V_A,tc_set(T_a)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,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(9,plain,
c_lessequals(c_Message_Oparts(v_H),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(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)) )
<=> ! [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)],[10]) ).
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)) )
<=> ! [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(13,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/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__subset__iff_1) ).
tff(14,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)],[13,12]) ).
tff(15,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)],[14]) ).
tff(16,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)],[15,11]) ).
tff(17,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(18,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/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(19,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)],[18,17]) ).
tff(20,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(21,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(22,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)],[21,20]) ).
tff(23,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)],[22,19,16]) ).
tff(24,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(25,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)],[24]) ).
tff(26,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(27,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(28,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)],[27]) ).
tff(29,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/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_2) ).
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) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
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) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
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) ),
inference(skolemize,[status(sab)],[31]) ).
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) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,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(35,axiom,
c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(36,plain,
c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,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(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(rewrite,[status(thm)],]) ).
tff(38,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(39,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(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
~ c_lessequals(v_H,c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[39,36,33,23]) ).
tff(41,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(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)) )
<=> ! [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)],[41]) ).
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)) )
<=> ! [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(44,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/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__subset__iff_0) ).
tff(45,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)],[44,43]) ).
tff(46,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)],[45]) ).
tff(47,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)],[46,42]) ).
tff(48,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(49,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(50,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)],[49,48]) ).
tff(51,plain,
$false,
inference(unit_resolution,[status(thm)],[50,47,40,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.11 % Problem : SWV258-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Sep 4 02:00:59 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.20/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.20/0.34 Usage: tptp [options] [-file:]file
% 0.20/0.34 -h, -? prints this message.
% 0.20/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.20/0.34 -m, -model generate model.
% 0.20/0.34 -p, -proof generate proof.
% 0.20/0.34 -c, -core generate unsat core of named formulas.
% 0.20/0.34 -st, -statistics display statistics.
% 0.20/0.34 -t:timeout set timeout (in second).
% 0.20/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.20/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.20/0.34 -<param>:<value> configuration parameter and value.
% 0.20/0.34 -o:<output-file> file to place output in.
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------