TSTP Solution File: SWV878-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV878-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 15:24:49 EDT 2022
% Result : Unsatisfiable 0.97s 0.91s
% Output : Proof 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 82
% Syntax : Number of formulae : 164 ( 49 unt; 23 typ; 0 def)
% Number of atoms : 501 ( 59 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 610 ( 270 ~; 280 |; 0 &)
% ( 60 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 20 ( 20 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 15 >; 17 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-4 aty)
% Number of variables : 408 ( 367 !; 0 ?; 408 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(t_a_type,type,
t_a: $i ).
tff(c_Set_Oinsert_type,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(c_Set_Oimage_type,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(tc_Com_Opname_type,type,
tc_Com_Opname: $i ).
tff(v_U_type,type,
v_U: $i ).
tff(v_mgt__call_type,type,
v_mgt__call: $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_sko__local__Xassms__3__1_type,type,
v_sko__local__Xassms__3__1: ( $i * $i * $i * $i ) > $i ).
tff(v_P_type,type,
v_P: $i ).
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_bool_type,type,
tc_bool: $i ).
tff(v_mgt_type,type,
v_mgt: $i > $i ).
tff(v_c_type,type,
v_c: $i ).
tff(v_G_type,type,
v_G: $i ).
tff(v_wt_type,type,
v_wt: $i > $o ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(c_HOL_Ouminus__class_Ouminus_type,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(c_Lattices_Olower__semilattice__class_Oinf_type,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i ).
tff(class_Lattices_Oboolean__algebra_type,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(1,plain,
( ~ hBOOL(hAPP(hAPP(v_P,v_G),c_Set_Oinsert(v_mgt(v_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
<=> ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(v_mgt(v_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ hBOOL(hAPP(hAPP(v_P,v_G),c_Set_Oinsert(v_mgt(v_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
<=> ~ hBOOL(hAPP(hAPP(v_P,v_G),c_Set_Oinsert(v_mgt(v_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
~ hBOOL(hAPP(hAPP(v_P,v_G),c_Set_Oinsert(v_mgt(v_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
tff(4,plain,
~ hBOOL(hAPP(hAPP(v_P,v_G),c_Set_Oinsert(v_mgt(v_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
~ hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(v_mgt(v_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
( v_wt(v_c)
<=> v_wt(v_c) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
v_wt(v_c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(8,plain,
v_wt(v_c),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
^ [V_c: $i,V_G: $i] :
refl(
( ( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| c_in(v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ~ v_wt(V_c) )
<=> ( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| c_in(v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ~ v_wt(V_c) ) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| c_in(v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ~ v_wt(V_c) )
<=> ! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| c_in(v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ~ v_wt(V_c) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
( ! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| c_in(v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ~ v_wt(V_c) )
<=> ! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| c_in(v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ~ v_wt(V_c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
^ [V_c: $i,V_G: $i] :
rewrite(
( ( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| c_in(v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ~ v_wt(V_c) )
<=> ( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| c_in(v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ~ v_wt(V_c) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| c_in(v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ~ v_wt(V_c) )
<=> ! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| c_in(v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ~ v_wt(V_c) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,axiom,
! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| c_in(v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ~ v_wt(V_c) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_assms_I3_J_0) ).
tff(15,plain,
! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| c_in(v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ~ v_wt(V_c) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| c_in(v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ~ v_wt(V_c) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| c_in(v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ~ v_wt(V_c) ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| c_in(v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ~ v_wt(V_c) ),
inference(modus_ponens,[status(thm)],[17,10]) ).
tff(19,plain,
( ( ~ ! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| c_in(v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ~ v_wt(V_c) )
| hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(v_mgt(v_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| c_in(v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ~ v_wt(v_c) )
<=> ( ~ ! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| c_in(v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ~ v_wt(V_c) )
| hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(v_mgt(v_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| c_in(v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ~ v_wt(v_c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
( ~ ! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| c_in(v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ~ v_wt(V_c) )
| hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(v_mgt(v_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| c_in(v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ~ v_wt(v_c) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
( ~ ! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| c_in(v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ~ v_wt(V_c) )
| hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(v_mgt(v_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| c_in(v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ~ v_wt(v_c) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
c_in(v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call),v_U,tc_Com_Opname),
inference(unit_resolution,[status(thm)],[21,18,8,5]) ).
tff(23,plain,
^ [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
refl(
( ( ~ c_in(V_x,V_A,T_a)
| ( c_Set_Oinsert(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Set_Oimage(V_f,V_A,T_a,T_b) ) )
<=> ( ~ c_in(V_x,V_A,T_a)
| ( c_Set_Oinsert(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Set_Oimage(V_f,V_A,T_a,T_b) ) ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| ( c_Set_Oinsert(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Set_Oimage(V_f,V_A,T_a,T_b) ) )
<=> ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| ( c_Set_Oinsert(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Set_Oimage(V_f,V_A,T_a,T_b) ) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| ( c_Set_Oinsert(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Set_Oimage(V_f,V_A,T_a,T_b) ) )
<=> ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| ( c_Set_Oinsert(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Set_Oimage(V_f,V_A,T_a,T_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
^ [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
rewrite(
( ( ( c_Set_Oinsert(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Set_Oimage(V_f,V_A,T_a,T_b) )
| ~ c_in(V_x,V_A,T_a) )
<=> ( ~ c_in(V_x,V_A,T_a)
| ( c_Set_Oinsert(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Set_Oimage(V_f,V_A,T_a,T_b) ) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ( c_Set_Oinsert(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Set_Oimage(V_f,V_A,T_a,T_b) )
| ~ c_in(V_x,V_A,T_a) )
<=> ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| ( c_Set_Oinsert(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Set_Oimage(V_f,V_A,T_a,T_b) ) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,axiom,
! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ( c_Set_Oinsert(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Set_Oimage(V_f,V_A,T_a,T_b) )
| ~ c_in(V_x,V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).
tff(29,plain,
! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| ( c_Set_Oinsert(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Set_Oimage(V_f,V_A,T_a,T_b) ) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| ( c_Set_Oinsert(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Set_Oimage(V_f,V_A,T_a,T_b) ) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| ( c_Set_Oinsert(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Set_Oimage(V_f,V_A,T_a,T_b) ) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| ( c_Set_Oinsert(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Set_Oimage(V_f,V_A,T_a,T_b) ) ),
inference(modus_ponens,[status(thm)],[31,24]) ).
tff(33,plain,
( ( ~ ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| ( c_Set_Oinsert(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Set_Oimage(V_f,V_A,T_a,T_b) ) )
| ~ c_in(v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ( c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) ) )
<=> ( ~ ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| ( c_Set_Oinsert(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Set_Oimage(V_f,V_A,T_a,T_b) ) )
| ~ c_in(v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ( c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ~ ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| ( c_Set_Oinsert(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Set_Oimage(V_f,V_A,T_a,T_b) ) )
| ~ c_in(v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ( c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
( ~ ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| ( c_Set_Oinsert(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Set_Oimage(V_f,V_A,T_a,T_b) ) )
| ~ c_in(v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
| ( c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) ) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),
inference(unit_resolution,[status(thm)],[35,32,22]) ).
tff(37,plain,
( c_in(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),t_a)
<=> c_in(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( c_in(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
<=> c_in(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),t_a) ),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
( ~ c_in(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
<=> ~ c_in(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),t_a) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( class_Lattices_Oboolean__algebra(tc_bool)
<=> class_Lattices_Oboolean__algebra(tc_bool) ),
inference(rewrite,[status(thm)],]) ).
tff(41,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
tff(42,plain,
class_Lattices_Oboolean__algebra(tc_bool),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
^ [T_1: $i,T_2: $i] :
refl(
( ( class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))
| ~ class_Lattices_Oboolean__algebra(T_1) )
<=> ( class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))
| ~ class_Lattices_Oboolean__algebra(T_1) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [T_1: $i,T_2: $i] :
( class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))
| ~ class_Lattices_Oboolean__algebra(T_1) )
<=> ! [T_1: $i,T_2: $i] :
( class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))
| ~ class_Lattices_Oboolean__algebra(T_1) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [T_1: $i,T_2: $i] :
( class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))
| ~ class_Lattices_Oboolean__algebra(T_1) )
<=> ! [T_1: $i,T_2: $i] :
( class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))
| ~ class_Lattices_Oboolean__algebra(T_1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
! [T_1: $i,T_2: $i] :
( class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))
| ~ class_Lattices_Oboolean__algebra(T_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
tff(47,plain,
! [T_1: $i,T_2: $i] :
( class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))
| ~ class_Lattices_Oboolean__algebra(T_1) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [T_1: $i,T_2: $i] :
( class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))
| ~ class_Lattices_Oboolean__algebra(T_1) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [T_1: $i,T_2: $i] :
( class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))
| ~ class_Lattices_Oboolean__algebra(T_1) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))
| ~ class_Lattices_Oboolean__algebra(T_1) )
| class_Lattices_Oboolean__algebra(tc_fun(t_a,tc_bool))
| ~ class_Lattices_Oboolean__algebra(tc_bool) )
<=> ( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))
| ~ class_Lattices_Oboolean__algebra(T_1) )
| class_Lattices_Oboolean__algebra(tc_fun(t_a,tc_bool))
| ~ class_Lattices_Oboolean__algebra(tc_bool) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))
| ~ class_Lattices_Oboolean__algebra(T_1) )
| class_Lattices_Oboolean__algebra(tc_fun(t_a,tc_bool))
| ~ class_Lattices_Oboolean__algebra(tc_bool) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))
| ~ class_Lattices_Oboolean__algebra(T_1) )
| class_Lattices_Oboolean__algebra(tc_fun(t_a,tc_bool))
| ~ class_Lattices_Oboolean__algebra(tc_bool) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
class_Lattices_Oboolean__algebra(tc_fun(t_a,tc_bool)),
inference(unit_resolution,[status(thm)],[52,49,42]) ).
tff(54,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(
( ( ~ class_Lattices_Oboolean__algebra(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),c_HOL_Ouminus__class_Ouminus(V_y,T_a)) ) )
<=> ( ~ class_Lattices_Oboolean__algebra(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),c_HOL_Ouminus__class_Ouminus(V_y,T_a)) ) ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oboolean__algebra(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),c_HOL_Ouminus__class_Ouminus(V_y,T_a)) ) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oboolean__algebra(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),c_HOL_Ouminus__class_Ouminus(V_y,T_a)) ) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oboolean__algebra(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),c_HOL_Ouminus__class_Ouminus(V_y,T_a)) ) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oboolean__algebra(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),c_HOL_Ouminus__class_Ouminus(V_y,T_a)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oboolean__algebra(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),c_HOL_Ouminus__class_Ouminus(V_y,T_a)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__eq_0) ).
tff(58,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oboolean__algebra(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),c_HOL_Ouminus__class_Ouminus(V_y,T_a)) ) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oboolean__algebra(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),c_HOL_Ouminus__class_Ouminus(V_y,T_a)) ) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oboolean__algebra(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),c_HOL_Ouminus__class_Ouminus(V_y,T_a)) ) ),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oboolean__algebra(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),c_HOL_Ouminus__class_Ouminus(V_y,T_a)) ) )
| ~ class_Lattices_Oboolean__algebra(tc_fun(t_a,tc_bool))
| ( c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))) ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oboolean__algebra(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),c_HOL_Ouminus__class_Ouminus(V_y,T_a)) ) )
| ~ class_Lattices_Oboolean__algebra(tc_fun(t_a,tc_bool))
| ( c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oboolean__algebra(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),c_HOL_Ouminus__class_Ouminus(V_y,T_a)) ) )
| ~ class_Lattices_Oboolean__algebra(tc_fun(t_a,tc_bool))
| ( c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oboolean__algebra(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),c_HOL_Ouminus__class_Ouminus(V_y,T_a)) ) )
| ~ class_Lattices_Oboolean__algebra(tc_fun(t_a,tc_bool))
| ( c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))) ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))),
inference(unit_resolution,[status(thm)],[63,60,53]) ).
tff(65,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
^ [T_a: $i,V_A: $i] :
refl(
( ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
<=> ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) )),
inference(bind,[status(th)],]) ).
tff(67,plain,
( ! [T_a: $i,V_A: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
<=> ! [T_a: $i,V_A: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [T_a: $i,V_A: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
<=> ! [T_a: $i,V_A: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,axiom,
! [T_a: $i,V_A: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__disjoint_0) ).
tff(70,plain,
! [T_a: $i,V_A: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [T_a: $i,V_A: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [T_a: $i,V_A: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
( ~ ! [T_a: $i,V_A: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(74,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),
inference(unit_resolution,[status(thm)],[73,72]) ).
tff(75,plain,
c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(transitivity,[status(thm)],[75,65]) ).
tff(77,plain,
( c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
<=> c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
<=> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
inference(symmetry,[status(thm)],[77]) ).
tff(79,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
refl(
( c_lessequals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool))
<=> c_lessequals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) )),
inference(bind,[status(th)],]) ).
tff(80,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] : c_lessequals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool))
<=> ! [T_a: $i,V_B: $i,V_A: $i] : c_lessequals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] : c_lessequals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool))
<=> ! [T_a: $i,V_B: $i,V_A: $i] : c_lessequals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) ),
inference(rewrite,[status(thm)],]) ).
tff(82,axiom,
! [T_a: $i,V_B: $i,V_A: $i] : c_lessequals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
tff(83,plain,
! [T_a: $i,V_B: $i,V_A: $i] : c_lessequals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
! [T_a: $i,V_B: $i,V_A: $i] : c_lessequals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)),
inference(skolemize,[status(sab)],[83]) ).
tff(85,plain,
! [T_a: $i,V_B: $i,V_A: $i] : c_lessequals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)),
inference(modus_ponens,[status(thm)],[84,80]) ).
tff(86,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : c_lessequals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
inference(quant_inst,[status(thm)],]) ).
tff(87,plain,
c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(unit_resolution,[status(thm)],[86,85]) ).
tff(88,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(modus_ponens,[status(thm)],[87,78]) ).
tff(89,plain,
^ [V_c: $i,V_G: $i] :
refl(
( ( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(V_c)
| ~ hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) )
<=> ( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(V_c)
| ~ hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(V_c)
| ~ hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) )
<=> ! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(V_c)
| ~ hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(V_c)
| ~ hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) )
<=> ! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(V_c)
| ~ hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
^ [V_c: $i,V_G: $i] :
rewrite(
( ( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(V_c) )
<=> ( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(V_c)
| ~ hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(V_c) )
<=> ! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(V_c)
| ~ hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,axiom,
! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(V_c) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_assms_I3_J_1) ).
tff(95,plain,
! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(V_c)
| ~ hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(V_c)
| ~ hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(V_c)
| ~ hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(V_c)
| ~ hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,plain,
( ( ~ ! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(V_c)
| ~ hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) )
| hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(v_mgt(v_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(v_c)
| ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) )
<=> ( ~ ! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(V_c)
| ~ hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) )
| hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(v_mgt(v_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(v_c)
| ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ~ ! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(V_c)
| ~ hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) )
| hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(v_mgt(v_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(v_c)
| ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
( ~ ! [V_c: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(V_c)
| ~ hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(V_G,v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) )
| hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(v_mgt(v_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(v_c)
| ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
~ hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))),
inference(unit_resolution,[status(thm)],[101,98,8,5]) ).
tff(103,plain,
^ [V_ts: $i,V_G: $i] :
refl(
( ( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) )
<=> ( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) ) )),
inference(bind,[status(th)],]) ).
tff(104,plain,
( ! [V_ts: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) )
<=> ! [V_ts: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[103]) ).
tff(105,plain,
( ! [V_ts: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) )
<=> ! [V_ts: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(106,axiom,
! [V_ts: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_assms_I1_J_0) ).
tff(107,plain,
! [V_ts: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
! [V_ts: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) ),
inference(skolemize,[status(sab)],[107]) ).
tff(109,plain,
! [V_ts: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[108,104]) ).
tff(110,plain,
( ( ~ ! [V_ts: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) )
| hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) )
<=> ( ~ ! [V_ts: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) )
| hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(111,plain,
( ~ ! [V_ts: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) )
| hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
inference(quant_inst,[status(thm)],]) ).
tff(112,plain,
( ~ ! [V_ts: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) )
| hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(unit_resolution,[status(thm)],[112,109,102]) ).
tff(114,plain,
^ [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
refl(
( ( ~ c_in(V_x,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
<=> ( ~ c_in(V_x,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ) )),
inference(bind,[status(th)],]) ).
tff(115,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_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
<=> ! [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_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[114]) ).
tff(116,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_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
<=> ! [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_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,plain,
^ [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
trans(
monotonicity(
rewrite(
( ( c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
<=> ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ) )),
( ( c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a) )
<=> ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a) ) )),
rewrite(
( ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a) )
<=> ( ~ c_in(V_x,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ) )),
( ( c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a) )
<=> ( ~ c_in(V_x,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ) )),
inference(bind,[status(th)],]) ).
tff(118,plain,
( ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a) )
<=> ! [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_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[117]) ).
tff(119,axiom,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
tff(120,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_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,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_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[120,116]) ).
tff(122,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_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ),
inference(skolemize,[status(sab)],[121]) ).
tff(123,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_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[122,115]) ).
tff(124,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_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_in(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) )
<=> ( ~ ! [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_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_in(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(125,plain,
( ( ~ c_in(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| ~ c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) )
<=> ( c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_in(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(126,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_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
| ~ c_in(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| ~ c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) )
<=> ( ~ ! [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_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_in(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ) ),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,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_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
| ~ c_in(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| ~ c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) )
<=> ( ~ ! [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_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_in(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ) ),
inference(transitivity,[status(thm)],[126,124]) ).
tff(128,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_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
| ~ c_in(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| ~ c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,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_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_in(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
~ c_in(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),
inference(unit_resolution,[status(thm)],[129,123,113,88]) ).
tff(131,plain,
~ c_in(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),t_a),
inference(modus_ponens,[status(thm)],[130,39]) ).
tff(132,plain,
^ [V_x: $i,T_a: $i,V_B: $i] :
refl(
( c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a)
<=> c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a) )),
inference(bind,[status(th)],]) ).
tff(133,plain,
( ! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a)
<=> ! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a) ),
inference(quant_intro,[status(thm)],[132]) ).
tff(134,plain,
( ! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a)
<=> ! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a) ),
inference(rewrite,[status(thm)],]) ).
tff(135,axiom,
! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
tff(136,plain,
! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a),
inference(modus_ponens,[status(thm)],[135,134]) ).
tff(137,plain,
! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a),
inference(skolemize,[status(sab)],[136]) ).
tff(138,plain,
! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a),
inference(modus_ponens,[status(thm)],[137,133]) ).
tff(139,plain,
( ~ ! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a)
| c_in(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(140,plain,
c_in(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_P,v_U,v_mgt__call)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[139,138]) ).
tff(141,plain,
$false,
inference(unit_resolution,[status(thm)],[140,131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV878-1 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n028.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Sep 4 09:18:09 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.97/0.91 % SZS status Unsatisfiable
% 0.97/0.91 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------