%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV880-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:36:16 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.53s
% Output : Proof 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 69
% Syntax : Number of formulae : 169 ( 61 unt; 0 typ; 0 def)
% Number of atoms : 582 ( 240 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 697 ( 306 ~; 326 |; 0 &)
% ( 65 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 22 ( 22 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 524 ( 474 !; 0 ?; 524 :)
% Comments :
%------------------------------------------------------------------------------
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(t_a_type,type,
t_a: $i ).
tff(c_Set_Oinsert_type,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_pn_type,type,
v_pn: $i ).
tff(v_mgt__call_type,type,
v_mgt__call: $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(c_Lattices_Olower__semilattice__class_Oinf_type,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(class_Lattices_Olattice_type,type,
class_Lattices_Olattice: $i > $o ).
tff(class_Lattices_Olower__semilattice_type,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(1,plain,
( class_Lattices_Olattice(tc_bool)
<=> class_Lattices_Olattice(tc_bool) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
tff(3,plain,
class_Lattices_Olattice(tc_bool),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [T_1: $i,T_2: $i] :
refl(( ( class_Lattices_Olattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
<=> ( class_Lattices_Olattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [T_1: $i,T_2: $i] :
( class_Lattices_Olattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
<=> ! [T_1: $i,T_2: $i] :
( class_Lattices_Olattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [T_1: $i,T_2: $i] :
( class_Lattices_Olattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
<=> ! [T_1: $i,T_2: $i] :
( class_Lattices_Olattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [T_1: $i,T_2: $i] :
( class_Lattices_Olattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
tff(8,plain,
! [T_1: $i,T_2: $i] :
( class_Lattices_Olattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [T_1: $i,T_2: $i] :
( class_Lattices_Olattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [T_1: $i,T_2: $i] :
( class_Lattices_Olattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Olattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
| class_Lattices_Olattice(tc_fun(t_a,tc_bool))
| ~ class_Lattices_Olattice(tc_bool) )
<=> ( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Olattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
| class_Lattices_Olattice(tc_fun(t_a,tc_bool))
| ~ class_Lattices_Olattice(tc_bool) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Olattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
| class_Lattices_Olattice(tc_fun(t_a,tc_bool))
| ~ class_Lattices_Olattice(tc_bool) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Olattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
| class_Lattices_Olattice(tc_fun(t_a,tc_bool))
| ~ class_Lattices_Olattice(tc_bool) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
class_Lattices_Olattice(tc_fun(t_a,tc_bool)),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(( ( ~ class_Lattices_Olattice(T_a)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y),V_x,T_a) )
<=> ( ~ class_Lattices_Olattice(T_a)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y),V_x,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y),V_x,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y),V_x,T_a) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y),V_x,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y),V_x,T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y),V_x,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
tff(19,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y),V_x,T_a) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y),V_x,T_a) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y),V_x,T_a) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y),V_x,T_a) )
| ~ class_Lattices_Olattice(tc_fun(t_a,tc_bool))
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y),V_x,T_a) )
| ~ class_Lattices_Olattice(tc_fun(t_a,tc_bool))
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y),V_x,T_a) )
| ~ class_Lattices_Olattice(tc_fun(t_a,tc_bool))
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y),V_x,T_a) )
| ~ class_Lattices_Olattice(tc_fun(t_a,tc_bool))
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)),
inference(unit_resolution,[status(thm)],[24,21,14]) ).
tff(26,plain,
^ [T_1: $i,T_2: $i] :
refl(( ( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
<=> ( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
<=> ! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
<=> ! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
tff(30,plain,
! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
| class_Lattices_Olower__semilattice(tc_fun(t_a,tc_bool))
| ~ class_Lattices_Olattice(tc_bool) )
<=> ( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
| class_Lattices_Olower__semilattice(tc_fun(t_a,tc_bool))
| ~ class_Lattices_Olattice(tc_bool) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
| class_Lattices_Olower__semilattice(tc_fun(t_a,tc_bool))
| ~ class_Lattices_Olattice(tc_bool) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
| class_Lattices_Olower__semilattice(tc_fun(t_a,tc_bool))
| ~ class_Lattices_Olattice(tc_bool) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
class_Lattices_Olower__semilattice(tc_fun(t_a,tc_bool)),
inference(unit_resolution,[status(thm)],[35,32,3]) ).
tff(37,plain,
( ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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_pn),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(38,axiom,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(39,plain,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)],[38,37]) ).
tff(40,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(( ( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != V_x ) )
<=> ( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != V_x ) ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != V_x ) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != V_x ) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != V_x ) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != V_x ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
rewrite(( ( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != V_x )
| c_lessequals(V_x,V_y,T_a) )
<=> ( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != V_x ) ) )),
inference(bind,[status(th)],[]) ).
tff(44,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != V_x )
| c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != V_x ) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != V_x )
| c_lessequals(V_x,V_y,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
tff(46,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != V_x ) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != V_x ) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != V_x ) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != V_x ) ),
inference(modus_ponens,[status(thm)],[48,41]) ).
tff(50,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != V_x ) )
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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))
| ~ class_Lattices_Olower__semilattice(tc_fun(t_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) != c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != V_x ) )
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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))
| ~ class_Lattices_Olower__semilattice(tc_fun(t_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) != c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ( ~ class_Lattices_Olower__semilattice(tc_fun(t_a,tc_bool))
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) != c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) ) )
<=> ( c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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))
| ~ class_Lattices_Olower__semilattice(tc_fun(t_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) != c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != V_x ) )
| ~ class_Lattices_Olower__semilattice(tc_fun(t_a,tc_bool))
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) != c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != V_x ) )
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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))
| ~ class_Lattices_Olower__semilattice(tc_fun(t_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) != c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) ) ) ),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != V_x ) )
| ~ class_Lattices_Olower__semilattice(tc_fun(t_a,tc_bool))
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) != c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != V_x ) )
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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))
| ~ class_Lattices_Olower__semilattice(tc_fun(t_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) != c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) ) ) ),
inference(transitivity,[status(thm)],[52,50]) ).
tff(54,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != V_x ) )
| ~ class_Lattices_Olower__semilattice(tc_fun(t_a,tc_bool))
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) != c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != V_x ) )
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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))
| ~ class_Lattices_Olower__semilattice(tc_fun(t_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) != c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) ) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
( ~ class_Lattices_Olower__semilattice(tc_fun(t_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) != c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) ) ),
inference(unit_resolution,[status(thm)],[55,49,39]) ).
tff(57,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) != c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),
inference(unit_resolution,[status(thm)],[56,36]) ).
tff(58,plain,
^ [V_x: $i,T_a: $i,V_A: $i] :
refl(( ( ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool))
| ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ) )
<=> ( ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool))
| ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(59,plain,
( ! [V_x: $i,T_a: $i,V_A: $i] :
( ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool))
| ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ) )
<=> ! [V_x: $i,T_a: $i,V_A: $i] :
( ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool))
| ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [V_x: $i,T_a: $i,V_A: $i] :
( ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool))
| ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ) )
<=> ! [V_x: $i,T_a: $i,V_A: $i] :
( ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool))
| ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
^ [V_x: $i,T_a: $i,V_A: $i] :
trans(monotonicity(rewrite(( ( ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) )
| ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) )
<=> ( ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ) ) )),
( ( ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) )
| ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) )
<=> ( ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) ) )),
rewrite(( ( ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) )
<=> ( ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool))
| ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ) ) )),
( ( ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) )
| ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) )
<=> ( ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool))
| ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(62,plain,
( ! [V_x: $i,T_a: $i,V_A: $i] :
( ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) )
| ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) )
<=> ! [V_x: $i,T_a: $i,V_A: $i] :
( ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool))
| ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,axiom,
! [V_x: $i,T_a: $i,V_A: $i] :
( ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) )
| ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
tff(64,plain,
! [V_x: $i,T_a: $i,V_A: $i] :
( ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool))
| ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [V_x: $i,T_a: $i,V_A: $i] :
( ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool))
| ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
! [V_x: $i,T_a: $i,V_A: $i] :
( ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool))
| ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [V_x: $i,T_a: $i,V_A: $i] :
( ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool))
| ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ) ),
inference(modus_ponens,[status(thm)],[66,59]) ).
tff(68,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool))
| ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ) )
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) = c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) )
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) = c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)) )
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool))
| ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ) )
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) = c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) )
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) = c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)) )
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
( ( ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) = c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)) )
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) = c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) ) )
<=> ( ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) = c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) )
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) = c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)) )
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool))
| ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ) )
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) = c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)) )
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) = c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool))
| ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ) )
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) = c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) )
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) = c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)) )
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)) ) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool))
| ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ) )
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) = c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)) )
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) = c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool))
| ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ) )
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) = c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) )
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) = c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)) )
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)) ) ),
inference(transitivity,[status(thm)],[70,68]) ).
tff(72,plain,
( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool))
| ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ) )
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) = c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)) )
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) = c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( ( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool))
| ( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ) )
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) = c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) )
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) = c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)) )
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) = c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),
inference(unit_resolution,[status(thm)],[73,67,57,25]) ).
tff(75,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(( ( ~ class_Lattices_Olattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_x) ) )
<=> ( ~ class_Lattices_Olattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_x) ) ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_x) ) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_x) ) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_x) ) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_x) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_x) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
tff(79,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_x) ) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_x) ) ),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_x) ) ),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_x) ) )
| ~ class_Lattices_Olattice(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_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_x) ) )
| ~ class_Lattices_Olattice(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_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_x) ) )
| ~ class_Lattices_Olattice(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_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_x) ) )
| ~ class_Lattices_Olattice(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_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) ) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,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_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)),
inference(unit_resolution,[status(thm)],[84,81,14]) ).
tff(86,plain,
( c_in(v_pn,v_U,tc_Com_Opname)
<=> c_in(v_pn,v_U,tc_Com_Opname) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,axiom,
c_in(v_pn,v_U,tc_Com_Opname),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(88,plain,
c_in(v_pn,v_U,tc_Com_Opname),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
^ [V_a: $i,T_a: $i,V_A: $i] :
refl(( ( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
<=> ( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) )),
inference(bind,[status(th)],[]) ).
tff(90,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
^ [V_a: $i,T_a: $i,V_A: $i] :
rewrite(( ( ( c_Set_Oinsert(V_a,V_A,T_a) = V_A )
| ~ c_in(V_a,V_A,T_a) )
<=> ( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) )),
inference(bind,[status(th)],[]) ).
tff(93,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] :
( ( c_Set_Oinsert(V_a,V_A,T_a) = V_A )
| ~ c_in(V_a,V_A,T_a) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,axiom,
! [V_a: $i,T_a: $i,V_A: $i] :
( ( c_Set_Oinsert(V_a,V_A,T_a) = V_A )
| ~ c_in(V_a,V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
tff(95,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(v_pn,v_U,tc_Com_Opname)
| ( c_Set_Oinsert(v_pn,v_U,tc_Com_Opname) = v_U ) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(v_pn,v_U,tc_Com_Opname)
| ( c_Set_Oinsert(v_pn,v_U,tc_Com_Opname) = v_U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(v_pn,v_U,tc_Com_Opname)
| ( c_Set_Oinsert(v_pn,v_U,tc_Com_Opname) = v_U ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(v_pn,v_U,tc_Com_Opname)
| ( c_Set_Oinsert(v_pn,v_U,tc_Com_Opname) = v_U ) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
c_Set_Oinsert(v_pn,v_U,tc_Com_Opname) = v_U,
inference(unit_resolution,[status(thm)],[101,98,88]) ).
tff(103,plain,
c_Set_Oimage(v_mgt__call,c_Set_Oinsert(v_pn,v_U,tc_Com_Opname),tc_Com_Opname,t_a) = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
^ [T_b: $i,V_f: $i,V_a: $i,T_a: $i,V_B: $i] :
refl(( ( c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) )
<=> ( c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(105,plain,
( ! [T_b: $i,V_f: $i,V_a: $i,T_a: $i,V_B: $i] : ( c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) )
<=> ! [T_b: $i,V_f: $i,V_a: $i,T_a: $i,V_B: $i] : ( c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,plain,
( ! [T_b: $i,V_f: $i,V_a: $i,T_a: $i,V_B: $i] : ( c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) )
<=> ! [T_b: $i,V_f: $i,V_a: $i,T_a: $i,V_B: $i] : ( c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,axiom,
! [T_b: $i,V_f: $i,V_a: $i,T_a: $i,V_B: $i] : ( c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
tff(108,plain,
! [T_b: $i,V_f: $i,V_a: $i,T_a: $i,V_B: $i] : ( c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
! [T_b: $i,V_f: $i,V_a: $i,T_a: $i,V_B: $i] : ( c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) ),
inference(skolemize,[status(sab)],[108]) ).
tff(110,plain,
! [T_b: $i,V_f: $i,V_a: $i,T_a: $i,V_B: $i] : ( c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[109,105]) ).
tff(111,plain,
( ~ ! [T_b: $i,V_f: $i,V_a: $i,T_a: $i,V_B: $i] : ( c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) )
| ( c_Set_Oimage(v_mgt__call,c_Set_Oinsert(v_pn,v_U,tc_Com_Opname),tc_Com_Opname,t_a) = c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
c_Set_Oimage(v_mgt__call,c_Set_Oinsert(v_pn,v_U,tc_Com_Opname),tc_Com_Opname,t_a) = c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),
inference(unit_resolution,[status(thm)],[111,110]) ).
tff(113,plain,
c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) = c_Set_Oimage(v_mgt__call,c_Set_Oinsert(v_pn,v_U,tc_Com_Opname),tc_Com_Opname,t_a),
inference(symmetry,[status(thm)],[112]) ).
tff(114,plain,
c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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(transitivity,[status(thm)],[113,103]) ).
tff(115,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)) = 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)),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)) = 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_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),
inference(monotonicity,[status(thm)],[115]) ).
tff(117,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(118,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)],[117]) ).
tff(119,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(120,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(121,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)],[120,119]) ).
tff(122,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)],[121]) ).
tff(123,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)],[122,118]) ).
tff(124,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_pn),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(125,plain,
c_in(hAPP(v_mgt__call,v_pn),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),t_a),
inference(unit_resolution,[status(thm)],[124,123]) ).
tff(126,plain,
^ [V_a: $i,T_a: $i,V_B: $i,V_C: $i] :
refl(( ( ~ c_in(V_a,V_C,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_B,T_a)),V_C) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),T_a) ) )
<=> ( ~ c_in(V_a,V_C,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_B,T_a)),V_C) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(127,plain,
( ! [V_a: $i,T_a: $i,V_B: $i,V_C: $i] :
( ~ c_in(V_a,V_C,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_B,T_a)),V_C) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),T_a) ) )
<=> ! [V_a: $i,T_a: $i,V_B: $i,V_C: $i] :
( ~ c_in(V_a,V_C,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_B,T_a)),V_C) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),T_a) ) ) ),
inference(quant_intro,[status(thm)],[126]) ).
tff(128,plain,
( ! [V_a: $i,T_a: $i,V_B: $i,V_C: $i] :
( ~ c_in(V_a,V_C,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_B,T_a)),V_C) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),T_a) ) )
<=> ! [V_a: $i,T_a: $i,V_B: $i,V_C: $i] :
( ~ c_in(V_a,V_C,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_B,T_a)),V_C) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,plain,
^ [V_a: $i,T_a: $i,V_B: $i,V_C: $i] :
rewrite(( ( ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_B,T_a)),V_C) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),T_a) )
| ~ c_in(V_a,V_C,T_a) )
<=> ( ~ c_in(V_a,V_C,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_B,T_a)),V_C) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(130,plain,
( ! [V_a: $i,T_a: $i,V_B: $i,V_C: $i] :
( ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_B,T_a)),V_C) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),T_a) )
| ~ c_in(V_a,V_C,T_a) )
<=> ! [V_a: $i,T_a: $i,V_B: $i,V_C: $i] :
( ~ c_in(V_a,V_C,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_B,T_a)),V_C) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),T_a) ) ) ),
inference(quant_intro,[status(thm)],[129]) ).
tff(131,axiom,
! [V_a: $i,T_a: $i,V_B: $i,V_C: $i] :
( ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_B,T_a)),V_C) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),T_a) )
| ~ c_in(V_a,V_C,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
tff(132,plain,
! [V_a: $i,T_a: $i,V_B: $i,V_C: $i] :
( ~ c_in(V_a,V_C,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_B,T_a)),V_C) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),T_a) ) ),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
! [V_a: $i,T_a: $i,V_B: $i,V_C: $i] :
( ~ c_in(V_a,V_C,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_B,T_a)),V_C) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),T_a) ) ),
inference(modus_ponens,[status(thm)],[132,128]) ).
tff(134,plain,
! [V_a: $i,T_a: $i,V_B: $i,V_C: $i] :
( ~ c_in(V_a,V_C,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_B,T_a)),V_C) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),T_a) ) ),
inference(skolemize,[status(sab)],[133]) ).
tff(135,plain,
! [V_a: $i,T_a: $i,V_B: $i,V_C: $i] :
( ~ c_in(V_a,V_C,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_B,T_a)),V_C) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),T_a) ) ),
inference(modus_ponens,[status(thm)],[134,127]) ).
tff(136,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_B: $i,V_C: $i] :
( ~ c_in(V_a,V_C,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_B,T_a)),V_C) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),T_a) ) )
| ~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),t_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)) = c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),t_a) ) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_B: $i,V_C: $i] :
( ~ c_in(V_a,V_C,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_B,T_a)),V_C) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),T_a) ) )
| ~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),t_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)) = c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(137,plain,
( ~ ! [V_a: $i,T_a: $i,V_B: $i,V_C: $i] :
( ~ c_in(V_a,V_C,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_B,T_a)),V_C) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),T_a) ) )
| ~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),t_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)) = c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(138,plain,
( ~ ! [V_a: $i,T_a: $i,V_B: $i,V_C: $i] :
( ~ c_in(V_a,V_C,T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_B,T_a)),V_C) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),T_a) ) )
| ~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),t_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)) = c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),t_a) ) ),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)) = c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),t_a),
inference(unit_resolution,[status(thm)],[138,135,125]) ).
tff(140,plain,
c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),t_a) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),
inference(symmetry,[status(thm)],[139]) ).
tff(141,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) = 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_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),
inference(symmetry,[status(thm)],[85]) ).
tff(142,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(( ( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) ) )
<=> ( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(143,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) ) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) ) ) ),
inference(quant_intro,[status(thm)],[142]) ).
tff(144,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) ) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(145,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
tff(146,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) ) ),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) ) ),
inference(skolemize,[status(sab)],[146]) ).
tff(148,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) ) ),
inference(modus_ponens,[status(thm)],[147,143]) ).
tff(149,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) ) )
| ~ class_Lattices_Olower__semilattice(tc_fun(t_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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))) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) ) )
| ~ class_Lattices_Olower__semilattice(tc_fun(t_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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))) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(150,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) ) )
| ~ class_Lattices_Olower__semilattice(tc_fun(t_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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))) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(151,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) ) )
| ~ class_Lattices_Olower__semilattice(tc_fun(t_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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))) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) ) ),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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))) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)),
inference(unit_resolution,[status(thm)],[151,148,36]) ).
tff(153,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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))) = 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_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),
inference(transitivity,[status(thm)],[152,141]) ).
tff(154,plain,
c_Set_Oinsert(hAPP(v_mgt__call,v_pn),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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))),t_a) = c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),t_a),
inference(monotonicity,[status(thm)],[153]) ).
tff(155,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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))),
inference(symmetry,[status(thm)],[152]) ).
tff(156,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_Oinsert(hAPP(v_mgt__call,v_pn),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)),
inference(symmetry,[status(thm)],[74]) ).
tff(157,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_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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))),
inference(transitivity,[status(thm)],[156,155]) ).
tff(158,plain,
c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) = c_Set_Oinsert(hAPP(v_mgt__call,v_pn),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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))),t_a),
inference(monotonicity,[status(thm)],[157]) ).
tff(159,plain,
c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) = c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),
inference(transitivity,[status(thm)],[158,154,140,116,85,74]) ).
tff(160,plain,
^ [V_a: $i,T_a: $i,V_A: $i] :
refl(( ( c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
<=> ( c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) )),
inference(bind,[status(th)],[]) ).
tff(161,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[160]) ).
tff(162,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(163,axiom,
! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
tff(164,plain,
! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(skolemize,[status(sab)],[164]) ).
tff(166,plain,
! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[165,161]) ).
tff(167,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
| ( c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) != c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(168,plain,
c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) != c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),
inference(unit_resolution,[status(thm)],[167,166]) ).
tff(169,plain,
$false,
inference(unit_resolution,[status(thm)],[168,159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV880-1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.32 % Computer : n007.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Fri Jun 20 11:00:35 EDT 2025
% 0.13/0.32 % CPUTime :
% 0.19/0.53 % SZS status Unsatisfiable
% 0.19/0.53 % SZS output start Proof
% See solution above
% 0.41/0.58 % E exiting
%------------------------------------------------------------------------------