TSTP Solution File: SWV259-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV259-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 11.72s 7.82s
% Output : Proof 11.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 37
% Syntax : Number of formulae : 70 ( 12 unt; 9 typ; 0 def)
% Number of atoms : 214 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 251 ( 103 ~; 124 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 6 >; 8 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 194 ( 180 !; 0 ?; 194 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
tff(c_insert_type,type,
c_insert: ( $i * $i * $i ) > $i ).
tff(v_H_type,type,
v_H: $i ).
tff(v_X_type,type,
v_X: $i ).
tff(c_Main_OsubsetI__1_type,type,
c_Main_OsubsetI__1: ( $i * $i * $i ) > $i ).
tff(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_set_type,type,
tc_set: $i > $i ).
tff(1,plain,
( ~ c_lessequals(c_Message_Oparts(v_H),c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
<=> ~ c_lessequals(c_Message_Oparts(v_H),c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ c_lessequals(c_Message_Oparts(v_H),c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(3,plain,
~ c_lessequals(c_Message_Oparts(v_H),c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,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(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)) )
<=> ! [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)],[4]) ).
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)) )
<=> ! [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(7,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(8,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)],[7,6]) ).
tff(9,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)],[8]) ).
tff(10,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)],[9,5]) ).
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(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(v_H),c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),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(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(v_H),c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),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(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(v_H),c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),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(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(v_H),c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ c_lessequals(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
refl(
( ( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
<=> ( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',cls_Set_OsubsetI_1) ).
tff(19,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
| ~ c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg)
| c_lessequals(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
| ~ c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg)
| c_lessequals(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
| ~ c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg)
| c_lessequals(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
| ~ c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg)
| c_lessequals(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
~ c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[24,21,14]) ).
tff(26,plain,
^ [V_H: $i,V_X: $i] :
refl(
( ( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,axiom,
! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV005-0.ax',cls_Message_Oparts_OInj_0) ).
tff(30,plain,
! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg)
| c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg) )
<=> ( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg)
| c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg)
| c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg)
| c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
~ c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[35,32,25]) ).
tff(37,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
refl(
( ( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
<=> ( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,axiom,
! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',cls_Set_OsubsetI_0) ).
tff(41,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
| c_lessequals(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),v_H,tc_Message_Omsg) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
| c_lessequals(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),v_H,tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ( c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),v_H,tc_Message_Omsg)
| c_lessequals(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) )
<=> ( c_lessequals(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),v_H,tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
| c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),v_H,tc_Message_Omsg)
| c_lessequals(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
| c_lessequals(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),v_H,tc_Message_Omsg) ) ),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
| c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),v_H,tc_Message_Omsg)
| c_lessequals(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
| c_lessequals(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),v_H,tc_Message_Omsg) ) ),
inference(transitivity,[status(thm)],[46,44]) ).
tff(48,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
| c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),v_H,tc_Message_Omsg)
| c_lessequals(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
| c_lessequals(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),v_H,tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),v_H,tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[49,43,14]) ).
tff(51,plain,
^ [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
refl(
( ( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_insert(V_b,V_A,T_a),T_a) )
<=> ( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_insert(V_b,V_A,T_a),T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_insert(V_b,V_A,T_a),T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,axiom,
! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Set_Oinsert__iff_2) ).
tff(55,plain,
! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_insert(V_b,V_A,T_a),T_a) )
| ~ c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),v_H,tc_Message_Omsg)
| c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_insert(V_b,V_A,T_a),T_a) )
| ~ c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),v_H,tc_Message_Omsg)
| c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_insert(V_b,V_A,T_a),T_a) )
| ~ c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),v_H,tc_Message_Omsg)
| c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_insert(V_b,V_A,T_a),T_a) )
| ~ c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),v_H,tc_Message_Omsg)
| c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
$false,
inference(unit_resolution,[status(thm)],[60,57,50,36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV259-1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 02:00:45 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 11.72/7.82 % SZS status Unsatisfiable
% 11.72/7.82 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------