%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV877-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:36:15 AM UTC 2025
% Result : Unsatisfiable 0.90s 1.12s
% Output : Proof 1.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 94
% Syntax : Number of formulae : 235 ( 82 unt; 0 typ; 0 def)
% Number of atoms : 877 ( 182 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 1086 ( 486 ~; 500 |; 0 &)
% ( 100 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 42 ( 42 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-4 aty)
% Number of variables : 683 ( 609 !; 0 ?; 683 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
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(v_G_type,type,
v_G: $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_mgt__call_type,type,
v_mgt__call: $i ).
tff(v_U_type,type,
v_U: $i ).
tff(v_P_type,type,
v_P: $i ).
tff(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $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(c_Finite__Set_Ofinite_type,type,
c_Finite__Set_Ofinite: ( $i * $i ) > $o ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_Finite__Set_Ocard_type,type,
c_Finite__Set_Ocard: ( $i * $i ) > $i ).
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(v_mgt_type,type,
v_mgt: $i > $i ).
tff(v_c_type,type,
v_c: $i ).
tff(v_wt_type,type,
v_wt: $i > $o ).
tff(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(c_Lattices_Olower__semilattice__class_Oinf_type,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i ).
tff(class_Lattices_Olower__semilattice_type,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(class_Lattices_Olattice_type,type,
class_Lattices_Olattice: $i > $o ).
tff(1,plain,
( c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
<=> c_Finite__Set_Ofinite(v_U,tc_Com_Opname) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
c_Finite__Set_Ofinite(v_U,tc_Com_Opname),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(3,plain,
c_Finite__Set_Ofinite(v_U,tc_Com_Opname),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
refl(( ( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
<=> ( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
<=> ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
<=> ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
rewrite(( ( c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b)
| ~ c_Finite__Set_Ofinite(V_F,T_a) )
<=> ( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b)
| ~ c_Finite__Set_Ofinite(V_F,T_a) )
<=> ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b)
| ~ c_Finite__Set_Ofinite(V_F,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
tff(10,plain,
! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
| c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) )
<=> ( ~ ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
| c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
| c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
| c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
( ( c_Finite__Set_Ocard(v_G,t_a) = c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) )
<=> ( c_Finite__Set_Ocard(v_G,t_a) = c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
c_Finite__Set_Ocard(v_G,t_a) = c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(20,plain,
c_Finite__Set_Ocard(v_G,t_a) = c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) = c_Finite__Set_Ocard(v_G,t_a),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
( c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Finite__Set_Ocard(v_G,t_a),tc_nat)
<=> c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat) ),
inference(monotonicity,[status(thm)],[21,20]) ).
tff(23,plain,
( c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat)
<=> c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Finite__Set_Ocard(v_G,t_a),tc_nat) ),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
( c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
<=> c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
c_lessequals(v_G,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_1) ).
tff(26,plain,
c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
refl(( ( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat) )
<=> ( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
trans(monotonicity(rewrite(( ( c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat)
| ~ 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_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat) ) )),
( ( c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a) )
<=> ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat)
| ~ c_Finite__Set_Ofinite(V_B,T_a) ) )),
rewrite(( ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat)
| ~ c_Finite__Set_Ofinite(V_B,T_a) )
<=> ( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat) ) )),
( ( c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a) )
<=> ( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,axiom,
! [T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__mono_0) ).
tff(33,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat) )
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat) )
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat) )
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat) )
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ~ c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat) ),
inference(unit_resolution,[status(thm)],[39,36,26]) ).
tff(41,plain,
c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
inference(unit_resolution,[status(thm)],[40,17]) ).
tff(42,plain,
c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Finite__Set_Ocard(v_G,t_a),tc_nat),
inference(modus_ponens,[status(thm)],[41,23]) ).
tff(43,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
refl(( ( ( V_A = V_B )
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) )
<=> ( ( V_A = V_B )
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) ) )),
inference(bind,[status(th)],[]) ).
tff(44,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( V_A = V_B )
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) )
<=> ( ( V_A = V_B )
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) ) )),
( ( ( V_A = V_B )
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
<=> ( ( V_A = V_B )
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) )),
rewrite(( ( ( V_A = V_B )
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
<=> ( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) ) )),
( ( ( V_A = V_B )
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
<=> ( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) ) )),
( ( ( V_A = V_B )
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a) )
<=> ( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat)
| ~ c_Finite__Set_Ofinite(V_B,T_a) ) )),
rewrite(( ( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat)
| ~ c_Finite__Set_Ofinite(V_B,T_a) )
<=> ( ( V_A = V_B )
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) ) )),
( ( ( V_A = V_B )
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a) )
<=> ( ( V_A = V_B )
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,axiom,
! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__seteq_0) ).
tff(49,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) ),
inference(modus_ponens,[status(thm)],[51,44]) ).
tff(53,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) )
| ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) )
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| ~ c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Finite__Set_Ocard(v_G,t_a),tc_nat) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) )
| ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) )
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| ~ c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Finite__Set_Ocard(v_G,t_a),tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ( ( v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) )
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Finite__Set_Ocard(v_G,t_a),tc_nat) )
<=> ( ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) )
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| ~ c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Finite__Set_Ocard(v_G,t_a),tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) )
| ( v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) )
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Finite__Set_Ocard(v_G,t_a),tc_nat) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) )
| ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) )
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| ~ c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Finite__Set_Ocard(v_G,t_a),tc_nat) ) ),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) )
| ( v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) )
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Finite__Set_Ocard(v_G,t_a),tc_nat) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) )
| ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) )
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| ~ c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Finite__Set_Ocard(v_G,t_a),tc_nat) ) ),
inference(transitivity,[status(thm)],[55,53]) ).
tff(57,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) )
| ( v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) )
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Finite__Set_Ocard(v_G,t_a),tc_nat) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) )
| ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) )
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| ~ c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Finite__Set_Ocard(v_G,t_a),tc_nat) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
( ( v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) )
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
| ~ c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Finite__Set_Ocard(v_G,t_a),tc_nat) ),
inference(unit_resolution,[status(thm)],[58,52,26]) ).
tff(60,plain,
v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),
inference(unit_resolution,[status(thm)],[59,42,17]) ).
tff(61,plain,
c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) = v_G,
inference(symmetry,[status(thm)],[60]) ).
tff(62,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(63,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_4) ).
tff(64,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)],[63,62]) ).
tff(65,plain,
( v_wt(v_c)
<=> v_wt(v_c) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,axiom,
v_wt(v_c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(67,plain,
v_wt(v_c),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,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(69,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)],[68]) ).
tff(70,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(71,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(72,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)],[71]) ).
tff(73,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(74,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)],[73,72]) ).
tff(75,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)],[74,70]) ).
tff(76,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)],[75]) ).
tff(77,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)],[76,69]) ).
tff(78,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,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) )
| 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(79,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,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_inst,[status(thm)],[]) ).
tff(80,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,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)],[79,78]) ).
tff(81,plain,
c_in(v_sko__local__Xassms__3__1(v_G,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname),
inference(unit_resolution,[status(thm)],[80,77,67,64]) ).
tff(82,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(83,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)],[82]) ).
tff(84,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(85,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(86,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)],[85]) ).
tff(87,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(88,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)],[87,86]) ).
tff(89,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)],[88,84]) ).
tff(90,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)],[89]) ).
tff(91,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)],[90,83]) ).
tff(92,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(v_G,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(v_G,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(v_G,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(v_G,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(93,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(v_G,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(v_G,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(94,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(v_G,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(v_G,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)],[93,92]) ).
tff(95,plain,
c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(v_G,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)],[94,91,81]) ).
tff(96,plain,
c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(v_G,v_P,v_U,v_mgt__call)),v_G,t_a) = c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(v_G,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)],[60]) ).
tff(97,plain,
c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(v_G,v_P,v_U,v_mgt__call)),v_G,t_a) = v_G,
inference(transitivity,[status(thm)],[96,95,61]) ).
tff(98,plain,
( c_lessequals(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),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(v_G,v_P,v_U,v_mgt__call)),v_G,t_a),tc_fun(t_a,tc_bool))
<=> c_lessequals(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_G,tc_fun(t_a,tc_bool)) ),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
( c_lessequals(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_G,tc_fun(t_a,tc_bool))
<=> c_lessequals(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),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(v_G,v_P,v_U,v_mgt__call)),v_G,t_a),tc_fun(t_a,tc_bool)) ),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
( ~ c_lessequals(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_G,tc_fun(t_a,tc_bool))
<=> ~ c_lessequals(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),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(v_G,v_P,v_U,v_mgt__call)),v_G,t_a),tc_fun(t_a,tc_bool)) ),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,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(102,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)],[101]) ).
tff(103,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(104,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(105,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)],[104]) ).
tff(106,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(107,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)],[106,105]) ).
tff(108,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)],[107,103]) ).
tff(109,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)],[108]) ).
tff(110,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)],[109,102]) ).
tff(111,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,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))) )
| 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(112,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,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_inst,[status(thm)],[]) ).
tff(113,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,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)],[112,111]) ).
tff(114,plain,
~ 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(unit_resolution,[status(thm)],[113,110,67,64]) ).
tff(115,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(116,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)],[115]) ).
tff(117,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(118,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(119,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)],[118,117]) ).
tff(120,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)],[119]) ).
tff(121,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)],[120,116]) ).
tff(122,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,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)))
| ~ c_lessequals(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_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)) )
| 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)))
| ~ c_lessequals(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_G,tc_fun(t_a,tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(123,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,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)))
| ~ c_lessequals(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_G,tc_fun(t_a,tc_bool)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(124,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,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)))
| ~ c_lessequals(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_G,tc_fun(t_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
~ c_lessequals(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_G,tc_fun(t_a,tc_bool)),
inference(unit_resolution,[status(thm)],[124,121,114]) ).
tff(126,plain,
~ c_lessequals(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),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(v_G,v_P,v_U,v_mgt__call)),v_G,t_a),tc_fun(t_a,tc_bool)),
inference(modus_ponens,[status(thm)],[125,100]) ).
tff(127,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
refl(( ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,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_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) )),
inference(bind,[status(th)],[]) ).
tff(128,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[127]) ).
tff(129,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(130,axiom,
! [T_a: $i,V_B: $i,V_A: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,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_Diff__disjoint_0) ).
tff(131,plain,
! [T_a: $i,V_B: $i,V_A: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
! [T_a: $i,V_B: $i,V_A: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(skolemize,[status(sab)],[131]) ).
tff(133,plain,
! [T_a: $i,V_B: $i,V_A: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[132,128]) ).
tff(134,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,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_G),c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_G,tc_fun(t_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(135,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_G,tc_fun(t_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),
inference(unit_resolution,[status(thm)],[134,133]) ).
tff(136,plain,
^ [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
refl(( ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_B),tc_fun(T_a,tc_bool)) )
<=> ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_B),tc_fun(T_a,tc_bool)) ) )),
inference(bind,[status(th)],[]) ).
tff(137,plain,
( ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_B),tc_fun(T_a,tc_bool)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_B),tc_fun(T_a,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[136]) ).
tff(138,plain,
( ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_B),tc_fun(T_a,tc_bool)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_B),tc_fun(T_a,tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(139,axiom,
! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_B),tc_fun(T_a,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).
tff(140,plain,
! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_B),tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[139,138]) ).
tff(141,plain,
! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_B),tc_fun(T_a,tc_bool)) ),
inference(skolemize,[status(sab)],[140]) ).
tff(142,plain,
! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_B),tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[141,137]) ).
tff(143,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_B),tc_fun(T_a,tc_bool)) )
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_G,tc_fun(t_a,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),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)),v_G),v_G),tc_fun(t_a,tc_bool)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(144,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_G,tc_fun(t_a,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),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)),v_G),v_G),tc_fun(t_a,tc_bool)),
inference(unit_resolution,[status(thm)],[143,142]) ).
tff(145,plain,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),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)),v_G),v_G),tc_fun(t_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_G,tc_fun(t_a,tc_bool))),
inference(symmetry,[status(thm)],[144]) ).
tff(146,plain,
( class_Lattices_Olattice(tc_bool)
<=> class_Lattices_Olattice(tc_bool) ),
inference(rewrite,[status(thm)],[]) ).
tff(147,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
tff(148,plain,
class_Lattices_Olattice(tc_bool),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,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(150,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)],[149]) ).
tff(151,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(152,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(153,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)],[152,151]) ).
tff(154,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)],[153]) ).
tff(155,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)],[154,150]) ).
tff(156,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(157,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(158,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)],[157,156]) ).
tff(159,plain,
class_Lattices_Olower__semilattice(tc_fun(t_a,tc_bool)),
inference(unit_resolution,[status(thm)],[158,155,148]) ).
tff(160,plain,
^ [V_x: $i,T_a: $i] :
refl(( ( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_x) = V_x ) )
<=> ( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_x) = V_x ) ) )),
inference(bind,[status(th)],[]) ).
tff(161,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_x) = V_x ) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_x) = V_x ) ) ),
inference(quant_intro,[status(thm)],[160]) ).
tff(162,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_x) = V_x ) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_x) = V_x ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(163,axiom,
! [V_x: $i,T_a: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_x) = V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
tff(164,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_x) = V_x ) ),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_x) = V_x ) ),
inference(skolemize,[status(sab)],[164]) ).
tff(166,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_x) = V_x ) ),
inference(modus_ponens,[status(thm)],[165,161]) ).
tff(167,plain,
( ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_x) = V_x ) )
| ~ class_Lattices_Olower__semilattice(tc_fun(t_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),v_G) = v_G ) )
<=> ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_x) = V_x ) )
| ~ class_Lattices_Olower__semilattice(tc_fun(t_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),v_G) = v_G ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(168,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_x) = V_x ) )
| ~ class_Lattices_Olower__semilattice(tc_fun(t_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),v_G) = v_G ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(169,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Lattices_Olower__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_x) = V_x ) )
| ~ class_Lattices_Olower__semilattice(tc_fun(t_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),v_G) = v_G ) ),
inference(modus_ponens,[status(thm)],[168,167]) ).
tff(170,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),v_G) = v_G,
inference(unit_resolution,[status(thm)],[169,166,159]) ).
tff(171,plain,
v_G = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),v_G),
inference(symmetry,[status(thm)],[170]) ).
tff(172,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
refl(( ( ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_B ) )
<=> ( ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_B ) ) )),
inference(bind,[status(th)],[]) ).
tff(173,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_B ) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_B ) ) ),
inference(quant_intro,[status(thm)],[172]) ).
tff(174,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_B ) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_B ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(175,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
rewrite(( ( ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_B )
| ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool)) )
<=> ( ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_B ) ) )),
inference(bind,[status(th)],[]) ).
tff(176,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_B )
| ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_B ) ) ),
inference(quant_intro,[status(thm)],[175]) ).
tff(177,axiom,
! [T_a: $i,V_B: $i,V_A: $i] :
( ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_B )
| ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
tff(178,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_B ) ),
inference(modus_ponens,[status(thm)],[177,176]) ).
tff(179,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_B ) ),
inference(modus_ponens,[status(thm)],[178,174]) ).
tff(180,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_B ) ),
inference(skolemize,[status(sab)],[179]) ).
tff(181,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_B ) ),
inference(modus_ponens,[status(thm)],[180,173]) ).
tff(182,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_B ) )
| ~ c_lessequals(v_G,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)),v_G) = v_G ) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_B ) )
| ~ c_lessequals(v_G,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)),v_G) = v_G ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(183,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_B ) )
| ~ c_lessequals(v_G,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)),v_G) = v_G ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(184,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_B ) )
| ~ c_lessequals(v_G,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)),v_G) = v_G ) ),
inference(modus_ponens,[status(thm)],[183,182]) ).
tff(185,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)),v_G) = v_G,
inference(unit_resolution,[status(thm)],[184,181,26]) ).
tff(186,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)),v_G) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),v_G),
inference(transitivity,[status(thm)],[185,171]) ).
tff(187,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
refl(( ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A ) )
<=> ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A ) ) )),
inference(bind,[status(th)],[]) ).
tff(188,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A ) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A ) ) ),
inference(quant_intro,[status(thm)],[187]) ).
tff(189,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A ) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(190,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
rewrite(( ( ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A )
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
<=> ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A ) ) )),
inference(bind,[status(th)],[]) ).
tff(191,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A )
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A ) ) ),
inference(quant_intro,[status(thm)],[190]) ).
tff(192,axiom,
! [T_a: $i,V_B: $i,V_A: $i] :
( ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A )
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
tff(193,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A ) ),
inference(modus_ponens,[status(thm)],[192,191]) ).
tff(194,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A ) ),
inference(modus_ponens,[status(thm)],[193,189]) ).
tff(195,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A ) ),
inference(skolemize,[status(sab)],[194]) ).
tff(196,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A ) ),
inference(modus_ponens,[status(thm)],[195,188]) ).
tff(197,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A ) )
| ~ c_lessequals(v_G,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)),v_G),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)) = v_G ) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A ) )
| ~ c_lessequals(v_G,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)),v_G),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)) = v_G ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(198,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A ) )
| ~ c_lessequals(v_G,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)),v_G),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)) = v_G ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(199,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A ) )
| ~ c_lessequals(v_G,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)),v_G),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)) = v_G ) ),
inference(modus_ponens,[status(thm)],[198,197]) ).
tff(200,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)) = v_G,
inference(unit_resolution,[status(thm)],[199,196,26]) ).
tff(201,plain,
v_G = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),
inference(symmetry,[status(thm)],[200]) ).
tff(202,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)),v_G) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),
inference(transitivity,[status(thm)],[185,201]) ).
tff(203,plain,
c_HOL_Ominus__class_Ominus(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)),v_G),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)),v_G),tc_fun(t_a,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),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)),v_G),v_G),tc_fun(t_a,tc_bool)),
inference(monotonicity,[status(thm)],[202,186]) ).
tff(204,plain,
v_G = 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)),v_G),
inference(symmetry,[status(thm)],[185]) ).
tff(205,plain,
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)),v_G),
inference(transitivity,[status(thm)],[61,204]) ).
tff(206,plain,
c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_G,tc_fun(t_a,tc_bool)) = c_HOL_Ominus__class_Ominus(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)),v_G),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)),v_G),tc_fun(t_a,tc_bool)),
inference(monotonicity,[status(thm)],[205,204]) ).
tff(207,plain,
c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_G,tc_fun(t_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),
inference(transitivity,[status(thm)],[206,203,145,135]) ).
tff(208,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_G,tc_fun(t_a,tc_bool)),v_G,tc_fun(t_a,tc_bool))
<=> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_G,tc_fun(t_a,tc_bool)) ),
inference(monotonicity,[status(thm)],[207]) ).
tff(209,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_G,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),v_G,tc_fun(t_a,tc_bool)),v_G,tc_fun(t_a,tc_bool)) ),
inference(monotonicity,[status(thm)],[61]) ).
tff(210,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(211,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)],[210]) ).
tff(212,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(213,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(214,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)],[213,212]) ).
tff(215,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)],[214]) ).
tff(216,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)],[215,211]) ).
tff(217,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),v_G,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(218,plain,
c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_G,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)],[217,216]) ).
tff(219,plain,
c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_G,tc_fun(t_a,tc_bool)),v_G,tc_fun(t_a,tc_bool)),
inference(modus_ponens,[status(thm)],[218,209]) ).
tff(220,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_G,tc_fun(t_a,tc_bool)),
inference(modus_ponens,[status(thm)],[219,208]) ).
tff(221,plain,
^ [V_D: $i,V_a: $i,T_a: $i,V_C: $i] :
refl(( ( ~ c_lessequals(V_C,V_D,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_a,V_C,T_a),c_Set_Oinsert(V_a,V_D,T_a),tc_fun(T_a,tc_bool)) )
<=> ( ~ c_lessequals(V_C,V_D,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_a,V_C,T_a),c_Set_Oinsert(V_a,V_D,T_a),tc_fun(T_a,tc_bool)) ) )),
inference(bind,[status(th)],[]) ).
tff(222,plain,
( ! [V_D: $i,V_a: $i,T_a: $i,V_C: $i] :
( ~ c_lessequals(V_C,V_D,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_a,V_C,T_a),c_Set_Oinsert(V_a,V_D,T_a),tc_fun(T_a,tc_bool)) )
<=> ! [V_D: $i,V_a: $i,T_a: $i,V_C: $i] :
( ~ c_lessequals(V_C,V_D,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_a,V_C,T_a),c_Set_Oinsert(V_a,V_D,T_a),tc_fun(T_a,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[221]) ).
tff(223,plain,
( ! [V_D: $i,V_a: $i,T_a: $i,V_C: $i] :
( ~ c_lessequals(V_C,V_D,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_a,V_C,T_a),c_Set_Oinsert(V_a,V_D,T_a),tc_fun(T_a,tc_bool)) )
<=> ! [V_D: $i,V_a: $i,T_a: $i,V_C: $i] :
( ~ c_lessequals(V_C,V_D,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_a,V_C,T_a),c_Set_Oinsert(V_a,V_D,T_a),tc_fun(T_a,tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(224,plain,
^ [V_D: $i,V_a: $i,T_a: $i,V_C: $i] :
rewrite(( ( c_lessequals(c_Set_Oinsert(V_a,V_C,T_a),c_Set_Oinsert(V_a,V_D,T_a),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_C,V_D,tc_fun(T_a,tc_bool)) )
<=> ( ~ c_lessequals(V_C,V_D,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_a,V_C,T_a),c_Set_Oinsert(V_a,V_D,T_a),tc_fun(T_a,tc_bool)) ) )),
inference(bind,[status(th)],[]) ).
tff(225,plain,
( ! [V_D: $i,V_a: $i,T_a: $i,V_C: $i] :
( c_lessequals(c_Set_Oinsert(V_a,V_C,T_a),c_Set_Oinsert(V_a,V_D,T_a),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_C,V_D,tc_fun(T_a,tc_bool)) )
<=> ! [V_D: $i,V_a: $i,T_a: $i,V_C: $i] :
( ~ c_lessequals(V_C,V_D,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_a,V_C,T_a),c_Set_Oinsert(V_a,V_D,T_a),tc_fun(T_a,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[224]) ).
tff(226,axiom,
! [V_D: $i,V_a: $i,T_a: $i,V_C: $i] :
( c_lessequals(c_Set_Oinsert(V_a,V_C,T_a),c_Set_Oinsert(V_a,V_D,T_a),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_C,V_D,tc_fun(T_a,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
tff(227,plain,
! [V_D: $i,V_a: $i,T_a: $i,V_C: $i] :
( ~ c_lessequals(V_C,V_D,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_a,V_C,T_a),c_Set_Oinsert(V_a,V_D,T_a),tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[226,225]) ).
tff(228,plain,
! [V_D: $i,V_a: $i,T_a: $i,V_C: $i] :
( ~ c_lessequals(V_C,V_D,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_a,V_C,T_a),c_Set_Oinsert(V_a,V_D,T_a),tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[227,223]) ).
tff(229,plain,
! [V_D: $i,V_a: $i,T_a: $i,V_C: $i] :
( ~ c_lessequals(V_C,V_D,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_a,V_C,T_a),c_Set_Oinsert(V_a,V_D,T_a),tc_fun(T_a,tc_bool)) ),
inference(skolemize,[status(sab)],[228]) ).
tff(230,plain,
! [V_D: $i,V_a: $i,T_a: $i,V_C: $i] :
( ~ c_lessequals(V_C,V_D,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_a,V_C,T_a),c_Set_Oinsert(V_a,V_D,T_a),tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[229,222]) ).
tff(231,plain,
( ( ~ ! [V_D: $i,V_a: $i,T_a: $i,V_C: $i] :
( ~ c_lessequals(V_C,V_D,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_a,V_C,T_a),c_Set_Oinsert(V_a,V_D,T_a),tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_G,tc_fun(t_a,tc_bool))
| c_lessequals(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),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(v_G,v_P,v_U,v_mgt__call)),v_G,t_a),tc_fun(t_a,tc_bool)) )
<=> ( ~ ! [V_D: $i,V_a: $i,T_a: $i,V_C: $i] :
( ~ c_lessequals(V_C,V_D,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_a,V_C,T_a),c_Set_Oinsert(V_a,V_D,T_a),tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_G,tc_fun(t_a,tc_bool))
| c_lessequals(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),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(v_G,v_P,v_U,v_mgt__call)),v_G,t_a),tc_fun(t_a,tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(232,plain,
( ~ ! [V_D: $i,V_a: $i,T_a: $i,V_C: $i] :
( ~ c_lessequals(V_C,V_D,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_a,V_C,T_a),c_Set_Oinsert(V_a,V_D,T_a),tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_G,tc_fun(t_a,tc_bool))
| c_lessequals(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),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(v_G,v_P,v_U,v_mgt__call)),v_G,t_a),tc_fun(t_a,tc_bool)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(233,plain,
( ~ ! [V_D: $i,V_a: $i,T_a: $i,V_C: $i] :
( ~ c_lessequals(V_C,V_D,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_a,V_C,T_a),c_Set_Oinsert(V_a,V_D,T_a),tc_fun(T_a,tc_bool)) )
| ~ c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_G,tc_fun(t_a,tc_bool))
| c_lessequals(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),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(v_G,v_P,v_U,v_mgt__call)),v_G,t_a),tc_fun(t_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[232,231]) ).
tff(234,plain,
c_lessequals(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),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(v_G,v_P,v_U,v_mgt__call)),v_G,t_a),tc_fun(t_a,tc_bool)),
inference(unit_resolution,[status(thm)],[233,230,220]) ).
tff(235,plain,
$false,
inference(unit_resolution,[status(thm)],[234,126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SWV877-1 : TPTP v9.0.0. Released v4.1.0.
% 0.13/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 10:59:41 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.90/1.12 % SZS status Unsatisfiable
% 0.90/1.12 % SZS output start Proof
% See solution above
% 1.00/1.18 % E exiting
%------------------------------------------------------------------------------