TSTP Solution File: SWV883-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV883-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Thu Sep 29 15:24:50 EDT 2022
% Result : Unsatisfiable 1.01s 0.91s
% Output : Proof 1.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 114
% Syntax : Number of formulae : 237 ( 72 unt; 28 typ; 0 def)
% Number of atoms : 878 ( 209 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 1108 ( 490 ~; 518 |; 0 &)
% ( 100 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 51 ( 51 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 17 >; 20 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 11 con; 0-5 aty)
% Number of variables : 618 ( 553 !; 0 ?; 618 :)
% 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_Oimage_type,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(tc_Com_Opname_type,type,
tc_Com_Opname: $i ).
tff(v_U_type,type,
v_U: $i ).
tff(v_mgt__call_type,type,
v_mgt__call: $i ).
tff(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_pn_type,type,
v_pn: $i ).
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1_type,type,
c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_Finite__Set_Ofinite_type,type,
c_Finite__Set_Ofinite: ( $i * $i ) > $o ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(v_na_type,type,
v_na: $i ).
tff(c_Finite__Set_Ocard_type,type,
c_Finite__Set_Ocard: ( $i * $i ) > $i ).
tff(c_Suc_type,type,
c_Suc: $i > $i ).
tff(v_wt_type,type,
v_wt: $i > $o ).
tff(c_Option_Othe_type,type,
c_Option_Othe: ( $i * $i ) > $i ).
tff(tc_Com_Ocom_type,type,
tc_Com_Ocom: $i ).
tff(c_Com_Obody_type,type,
c_Com_Obody: $i > $i ).
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(v_mgt_type,type,
v_mgt: $i > $i ).
tff(v_P_type,type,
v_P: $i ).
tff(1,plain,
( c_in(v_pn,v_U,tc_Com_Opname)
<=> c_in(v_pn,v_U,tc_Com_Opname) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
c_in(v_pn,v_U,tc_Com_Opname),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(3,plain,
c_in(v_pn,v_U,tc_Com_Opname),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_a: $i,T_a: $i,V_A: $i] :
refl(
( ( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
<=> ( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [V_a: $i,T_a: $i,V_A: $i] :
rewrite(
( ( ( c_Set_Oinsert(V_a,V_A,T_a) = V_A )
| ~ c_in(V_a,V_A,T_a) )
<=> ( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] :
( ( c_Set_Oinsert(V_a,V_A,T_a) = V_A )
| ~ c_in(V_a,V_A,T_a) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V_a: $i,T_a: $i,V_A: $i] :
( ( c_Set_Oinsert(V_a,V_A,T_a) = V_A )
| ~ c_in(V_a,V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
tff(10,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(v_pn,v_U,tc_Com_Opname)
| ( c_Set_Oinsert(v_pn,v_U,tc_Com_Opname) = v_U ) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(v_pn,v_U,tc_Com_Opname)
| ( c_Set_Oinsert(v_pn,v_U,tc_Com_Opname) = v_U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(v_pn,v_U,tc_Com_Opname)
| ( c_Set_Oinsert(v_pn,v_U,tc_Com_Opname) = v_U ) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(v_pn,v_U,tc_Com_Opname)
| ( c_Set_Oinsert(v_pn,v_U,tc_Com_Opname) = v_U ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
c_Set_Oinsert(v_pn,v_U,tc_Com_Opname) = v_U,
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
c_Set_Oimage(v_mgt__call,c_Set_Oinsert(v_pn,v_U,tc_Com_Opname),tc_Com_Opname,t_a) = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
^ [T_b: $i,V_f: $i,V_a: $i,T_a: $i,V_B: $i] :
refl(
( ( c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) )
<=> ( c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [T_b: $i,V_f: $i,V_a: $i,T_a: $i,V_B: $i] : ( c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) )
<=> ! [T_b: $i,V_f: $i,V_a: $i,T_a: $i,V_B: $i] : ( c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [T_b: $i,V_f: $i,V_a: $i,T_a: $i,V_B: $i] : ( c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) )
<=> ! [T_b: $i,V_f: $i,V_a: $i,T_a: $i,V_B: $i] : ( c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
! [T_b: $i,V_f: $i,V_a: $i,T_a: $i,V_B: $i] : ( c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
tff(23,plain,
! [T_b: $i,V_f: $i,V_a: $i,T_a: $i,V_B: $i] : ( c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [T_b: $i,V_f: $i,V_a: $i,T_a: $i,V_B: $i] : ( c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [T_b: $i,V_f: $i,V_a: $i,T_a: $i,V_B: $i] : ( c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [T_b: $i,V_f: $i,V_a: $i,T_a: $i,V_B: $i] : ( c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) )
| ( c_Set_Oimage(v_mgt__call,c_Set_Oinsert(v_pn,v_U,tc_Com_Opname),tc_Com_Opname,t_a) = c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
c_Set_Oimage(v_mgt__call,c_Set_Oinsert(v_pn,v_U,tc_Com_Opname),tc_Com_Opname,t_a) = c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) = c_Set_Oimage(v_mgt__call,c_Set_Oinsert(v_pn,v_U,tc_Com_Opname),tc_Com_Opname,t_a),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),
inference(transitivity,[status(thm)],[28,18]) ).
tff(30,plain,
( c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_fun(t_a,tc_bool))
<=> c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a)
<=> ~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a) ),
inference(rewrite,[status(thm)],]) ).
tff(32,axiom,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
tff(33,plain,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
^ [V_x: $i,T_a: $i,V_A: $i] :
refl(
( ( ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) = V_A )
| c_in(V_x,V_A,T_a) )
<=> ( ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) = V_A )
| c_in(V_x,V_A,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [V_x: $i,T_a: $i,V_A: $i] :
( ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) = V_A )
| c_in(V_x,V_A,T_a) )
<=> ! [V_x: $i,T_a: $i,V_A: $i] :
( ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) = V_A )
| c_in(V_x,V_A,T_a) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [V_x: $i,T_a: $i,V_A: $i] :
( ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) = V_A )
| c_in(V_x,V_A,T_a) )
<=> ! [V_x: $i,T_a: $i,V_A: $i] :
( ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) = V_A )
| c_in(V_x,V_A,T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
! [V_x: $i,T_a: $i,V_A: $i] :
( ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) = V_A )
| c_in(V_x,V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
tff(38,plain,
! [V_x: $i,T_a: $i,V_A: $i] :
( ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) = V_A )
| c_in(V_x,V_A,T_a) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [V_x: $i,T_a: $i,V_A: $i] :
( ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) = V_A )
| c_in(V_x,V_A,T_a) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [V_x: $i,T_a: $i,V_A: $i] :
( ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) = V_A )
| c_in(V_x,V_A,T_a) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) = V_A )
| c_in(V_x,V_A,T_a) )
| ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)) = v_G )
| c_in(hAPP(v_mgt__call,v_pn),v_G,t_a) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) = V_A )
| c_in(V_x,V_A,T_a) )
| ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)) = v_G )
| c_in(hAPP(v_mgt__call,v_pn),v_G,t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) = V_A )
| c_in(V_x,V_A,T_a) )
| ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)) = v_G )
| c_in(hAPP(v_mgt__call,v_pn),v_G,t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) = V_A )
| c_in(V_x,V_A,T_a) )
| ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)) = v_G )
| c_in(hAPP(v_mgt__call,v_pn),v_G,t_a) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)) = v_G,
inference(unit_resolution,[status(thm)],[43,40,33]) ).
tff(45,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)),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(monotonicity,[status(thm)],[44]) ).
tff(46,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(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
inference(symmetry,[status(thm)],[45]) ).
tff(47,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(48,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(49,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)],[48,47]) ).
tff(50,plain,
c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(modus_ponens,[status(thm)],[49,46]) ).
tff(51,plain,
( c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
<=> c_Finite__Set_Ofinite(v_U,tc_Com_Opname) ),
inference(rewrite,[status(thm)],]) ).
tff(52,axiom,
c_Finite__Set_Ofinite(v_U,tc_Com_Opname),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(53,plain,
c_Finite__Set_Ofinite(v_U,tc_Com_Opname),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
^ [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
refl(
( ( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool)) )
<=> ( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool)) ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool)) )
<=> ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool)) )
<=> ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
^ [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
trans(
monotonicity(
rewrite(
( ( c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool)) )
<=> ( c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool)) ) )),
( ( c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a) )
<=> ( c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) )),
rewrite(
( ( c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a) )
<=> ( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool)) ) )),
( ( c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a) )
<=> ( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool)) ) )),
inference(bind,[status(th)],]) ).
tff(58,plain,
( ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a) )
<=> ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,axiom,
! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj_0) ).
tff(60,plain,
! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool)) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool)) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool)) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool)) ),
inference(modus_ponens,[status(thm)],[62,55]) ).
tff(64,plain,
( ( ~ ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,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))
| c_Finite__Set_Ofinite(v_G,t_a)
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname) )
<=> ( ~ ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,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))
| c_Finite__Set_Ofinite(v_G,t_a)
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ( ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
| c_Finite__Set_Ofinite(v_G,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(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| c_Finite__Set_Ofinite(v_G,t_a)
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
( ( ~ ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool)) )
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
| c_Finite__Set_Ofinite(v_G,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)) )
<=> ( ~ ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,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))
| c_Finite__Set_Ofinite(v_G,t_a)
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname) ) ),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
( ( ~ ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool)) )
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
| c_Finite__Set_Ofinite(v_G,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)) )
<=> ( ~ ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,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))
| c_Finite__Set_Ofinite(v_G,t_a)
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname) ) ),
inference(transitivity,[status(thm)],[66,64]) ).
tff(68,plain,
( ~ ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool)) )
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
| c_Finite__Set_Ofinite(v_G,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)) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
( ~ ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,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))
| c_Finite__Set_Ofinite(v_G,t_a)
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
c_Finite__Set_Ofinite(v_G,t_a),
inference(unit_resolution,[status(thm)],[69,63,53,49]) ).
tff(71,plain,
^ [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
refl(
( ( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| ( V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) ) )
<=> ( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| ( V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(72,plain,
( ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| ( V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) ) )
<=> ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| ( V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) ) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| ( V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) ) )
<=> ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| ( V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
^ [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
trans(
monotonicity(
rewrite(
( ( ( V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) )
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool)) )
<=> ( ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| ( V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) ) ) )),
( ( ( V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) )
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a) )
<=> ( ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| ( V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) )
| ~ c_Finite__Set_Ofinite(V_B,T_a) ) )),
rewrite(
( ( ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| ( V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) )
| ~ c_Finite__Set_Ofinite(V_B,T_a) )
<=> ( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| ( V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) ) ) )),
( ( ( V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) )
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),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_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| ( V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(75,plain,
( ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ( V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) )
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a) )
<=> ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| ( V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) ) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,axiom,
! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ( V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) )
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__image_2) ).
tff(77,plain,
! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| ( V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) ) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| ( V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) ) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| ( V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) ) ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| ( V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) ) ),
inference(modus_ponens,[status(thm)],[79,72]) ).
tff(81,plain,
( ( ~ ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| ( V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) ) )
| ~ c_Finite__Set_Ofinite(v_G,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))
| ( v_G = c_Set_Oimage(v_mgt__call,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),tc_Com_Opname,t_a) ) )
<=> ( ~ ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| ( V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) ) )
| ~ c_Finite__Set_Ofinite(v_G,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))
| ( v_G = c_Set_Oimage(v_mgt__call,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),tc_Com_Opname,t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
( ~ ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| ( V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) ) )
| ~ c_Finite__Set_Ofinite(v_G,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))
| ( v_G = c_Set_Oimage(v_mgt__call,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),tc_Com_Opname,t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(83,plain,
( ~ ! [T_b: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| ( V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) ) )
| ~ c_Finite__Set_Ofinite(v_G,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))
| ( v_G = c_Set_Oimage(v_mgt__call,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),tc_Com_Opname,t_a) ) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
v_G = c_Set_Oimage(v_mgt__call,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),tc_Com_Opname,t_a),
inference(unit_resolution,[status(thm)],[83,80,49,70]) ).
tff(85,plain,
c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a) = c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),tc_Com_Opname,t_a),t_a),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
( c_in(hAPP(v_mgt__call,v_pn),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a)
<=> c_in(hAPP(v_mgt__call,v_pn),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),tc_Com_Opname,t_a),t_a),t_a) ),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
( c_in(hAPP(v_mgt__call,v_pn),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),tc_Com_Opname,t_a),t_a),t_a)
<=> c_in(hAPP(v_mgt__call,v_pn),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) ),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
^ [V_x: $i,T_a: $i,V_B: $i] :
refl(
( c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a)
<=> c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a) )),
inference(bind,[status(th)],]) ).
tff(89,plain,
( ! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a)
<=> ! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,plain,
( ! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a)
<=> ! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a) ),
inference(rewrite,[status(thm)],]) ).
tff(91,axiom,
! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
tff(92,plain,
! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a),
inference(skolemize,[status(sab)],[92]) ).
tff(94,plain,
! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a),
inference(modus_ponens,[status(thm)],[93,89]) ).
tff(95,plain,
( ~ ! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a)
| c_in(hAPP(v_mgt__call,v_pn),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),tc_Com_Opname,t_a),t_a),t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(96,plain,
c_in(hAPP(v_mgt__call,v_pn),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),tc_Com_Opname,t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[95,94]) ).
tff(97,plain,
c_in(hAPP(v_mgt__call,v_pn),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a),
inference(modus_ponens,[status(thm)],[96,87]) ).
tff(98,plain,
^ [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
refl(
( ( ~ c_in(V_x,V_A,T_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) )
<=> ( ~ c_in(V_x,V_A,T_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ) )),
inference(bind,[status(th)],]) ).
tff(99,plain,
( ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) )
<=> ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[98]) ).
tff(100,plain,
( ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) )
<=> ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,plain,
^ [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
trans(
monotonicity(
rewrite(
( ( c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_A,T_a) )
<=> ( ~ c_in(V_x,V_A,T_a)
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ) )),
( ( c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_A,T_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) )
<=> ( ~ c_in(V_x,V_A,T_a)
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) ) )),
rewrite(
( ( ~ c_in(V_x,V_A,T_a)
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) )
<=> ( ~ c_in(V_x,V_A,T_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ) )),
( ( c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_A,T_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) )
<=> ( ~ c_in(V_x,V_A,T_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ) )),
inference(bind,[status(th)],]) ).
tff(102,plain,
( ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_A,T_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) )
<=> ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,axiom,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_A,T_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).
tff(104,plain,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[104,100]) ).
tff(106,plain,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ),
inference(skolemize,[status(sab)],[105]) ).
tff(107,plain,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[106,99]) ).
tff(108,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) )
| ~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_fun(t_a,tc_bool)) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) )
| ~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_fun(t_a,tc_bool)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(109,plain,
( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) )
| ~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_fun(t_a,tc_bool)) ),
inference(quant_inst,[status(thm)],]) ).
tff(110,plain,
( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_A,T_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) )
| ~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_fun(t_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
( ~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_fun(t_a,tc_bool)) ),
inference(unit_resolution,[status(thm)],[110,107]) ).
tff(112,plain,
c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_fun(t_a,tc_bool)),
inference(unit_resolution,[status(thm)],[111,97,50]) ).
tff(113,plain,
c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(modus_ponens,[status(thm)],[112,30]) ).
tff(114,plain,
( c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat)
<=> c_lessequals(c_Suc(v_na),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(115,axiom,
c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(116,plain,
c_lessequals(c_Suc(v_na),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)],[115,114]) ).
tff(117,plain,
^ [V_n: $i,V_m: $i] :
refl(
( ( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) )
<=> ( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) ) )),
inference(bind,[status(th)],]) ).
tff(118,plain,
( ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) )
<=> ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) ) ),
inference(quant_intro,[status(thm)],[117]) ).
tff(119,plain,
( ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) )
<=> ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(120,plain,
^ [V_n: $i,V_m: $i] :
rewrite(
( ( ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) )
| ~ c_lessequals(V_n,V_m,tc_nat) )
<=> ( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) ) )),
inference(bind,[status(th)],]) ).
tff(121,plain,
( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) )
| ~ c_lessequals(V_n,V_m,tc_nat) )
<=> ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) ) ),
inference(quant_intro,[status(thm)],[120]) ).
tff(122,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) )
| ~ c_lessequals(V_n,V_m,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).
tff(123,plain,
! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) ),
inference(modus_ponens,[status(thm)],[123,119]) ).
tff(125,plain,
! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) ),
inference(skolemize,[status(sab)],[124]) ).
tff(126,plain,
! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) ),
inference(modus_ponens,[status(thm)],[125,118]) ).
tff(127,plain,
( ( ~ ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) )
| ~ c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_Suc(v_na),tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat)) ) )
<=> ( ~ ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) )
| ~ c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_Suc(v_na),tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(128,plain,
( ~ ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) )
| ~ c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_Suc(v_na),tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
( ~ ! [V_n: $i,V_m: $i] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ) )
| ~ c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat)
| ( c_HOL_Ominus__class_Ominus(c_Suc(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_Suc(v_na),tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat)) ) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
c_HOL_Ominus__class_Ominus(c_Suc(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_Suc(v_na),tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat)),
inference(unit_resolution,[status(thm)],[129,126,116]) ).
tff(131,plain,
c_Suc(c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat)) = c_HOL_Ominus__class_Ominus(c_Suc(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_Suc(v_na),tc_nat),
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
( ( c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat) )
<=> ( c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(133,axiom,
c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(134,plain,
c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
c_Suc(c_Finite__Set_Ocard(v_G,t_a)) = c_Suc(c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat)),
inference(monotonicity,[status(thm)],[134]) ).
tff(136,plain,
^ [V_x: $i,T_a: $i,V_A: $i] :
refl(
( ( c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) )
<=> ( c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) ) )),
inference(bind,[status(th)],]) ).
tff(137,plain,
( ! [V_x: $i,T_a: $i,V_A: $i] :
( c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) )
<=> ! [V_x: $i,T_a: $i,V_A: $i] :
( c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) ) ),
inference(quant_intro,[status(thm)],[136]) ).
tff(138,plain,
( ! [V_x: $i,T_a: $i,V_A: $i] :
( c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) )
<=> ! [V_x: $i,T_a: $i,V_A: $i] :
( c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(139,plain,
^ [V_x: $i,T_a: $i,V_A: $i] :
rewrite(
( ( ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) )
| c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a) )
<=> ( c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) ) )),
inference(bind,[status(th)],]) ).
tff(140,plain,
( ! [V_x: $i,T_a: $i,V_A: $i] :
( ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) )
| c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a) )
<=> ! [V_x: $i,T_a: $i,V_A: $i] :
( c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) ) ),
inference(quant_intro,[status(thm)],[139]) ).
tff(141,axiom,
! [V_x: $i,T_a: $i,V_A: $i] :
( ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) )
| c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__if_1) ).
tff(142,plain,
! [V_x: $i,T_a: $i,V_A: $i] :
( c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) ),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
! [V_x: $i,T_a: $i,V_A: $i] :
( c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) ),
inference(modus_ponens,[status(thm)],[142,138]) ).
tff(144,plain,
! [V_x: $i,T_a: $i,V_A: $i] :
( c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) ),
inference(skolemize,[status(sab)],[143]) ).
tff(145,plain,
! [V_x: $i,T_a: $i,V_A: $i] :
( c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) ),
inference(modus_ponens,[status(thm)],[144,137]) ).
tff(146,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) )
| c_in(hAPP(v_mgt__call,v_pn),v_G,t_a)
| ~ c_Finite__Set_Ofinite(v_G,t_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) = c_Suc(c_Finite__Set_Ocard(v_G,t_a)) ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) )
| c_in(hAPP(v_mgt__call,v_pn),v_G,t_a)
| ~ c_Finite__Set_Ofinite(v_G,t_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) = c_Suc(c_Finite__Set_Ocard(v_G,t_a)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(147,plain,
( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) )
| c_in(hAPP(v_mgt__call,v_pn),v_G,t_a)
| ~ c_Finite__Set_Ofinite(v_G,t_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) = c_Suc(c_Finite__Set_Ocard(v_G,t_a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(148,plain,
( ~ ! [V_x: $i,T_a: $i,V_A: $i] :
( c_in(V_x,V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) )
| c_in(hAPP(v_mgt__call,v_pn),v_G,t_a)
| ~ c_Finite__Set_Ofinite(v_G,t_a)
| ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) = c_Suc(c_Finite__Set_Ocard(v_G,t_a)) ) ),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) = c_Suc(c_Finite__Set_Ocard(v_G,t_a)),
inference(unit_resolution,[status(thm)],[148,145,33,70]) ).
tff(150,plain,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) = c_HOL_Ominus__class_Ominus(c_Suc(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_Suc(v_na),tc_nat),
inference(transitivity,[status(thm)],[149,135,131]) ).
tff(151,plain,
( ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) )
<=> ( c_HOL_Ominus__class_Ominus(c_Suc(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_Suc(v_na),tc_nat) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) ),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
( ( c_HOL_Ominus__class_Ominus(c_Suc(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_Suc(v_na),tc_nat) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) )
<=> ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) ),
inference(symmetry,[status(thm)],[151]) ).
tff(153,plain,
^ [V_n: $i,V_m: $i] :
refl(
( ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) )
<=> ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ) )),
inference(bind,[status(th)],]) ).
tff(154,plain,
( ! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) )
<=> ! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ) ),
inference(quant_intro,[status(thm)],[153]) ).
tff(155,plain,
( ! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) )
<=> ! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(156,axiom,
! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
tff(157,plain,
! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ),
inference(skolemize,[status(sab)],[157]) ).
tff(159,plain,
! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ),
inference(modus_ponens,[status(thm)],[158,154]) ).
tff(160,plain,
( ~ ! [V_n: $i,V_m: $i] : ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) )
| ( c_HOL_Ominus__class_Ominus(c_Suc(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_Suc(v_na),tc_nat) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(161,plain,
c_HOL_Ominus__class_Ominus(c_Suc(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)),c_Suc(v_na),tc_nat) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat),
inference(unit_resolution,[status(thm)],[160,159]) ).
tff(162,plain,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat),
inference(modus_ponens,[status(thm)],[161,152]) ).
tff(163,plain,
^ [V_pn: $i] :
refl(
( ( ~ c_in(V_pn,v_U,tc_Com_Opname)
| v_wt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)) )
<=> ( ~ c_in(V_pn,v_U,tc_Com_Opname)
| v_wt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)) ) )),
inference(bind,[status(th)],]) ).
tff(164,plain,
( ! [V_pn: $i] :
( ~ c_in(V_pn,v_U,tc_Com_Opname)
| v_wt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)) )
<=> ! [V_pn: $i] :
( ~ c_in(V_pn,v_U,tc_Com_Opname)
| v_wt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)) ) ),
inference(quant_intro,[status(thm)],[163]) ).
tff(165,plain,
( ! [V_pn: $i] :
( ~ c_in(V_pn,v_U,tc_Com_Opname)
| v_wt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)) )
<=> ! [V_pn: $i] :
( ~ c_in(V_pn,v_U,tc_Com_Opname)
| v_wt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(166,plain,
^ [V_pn: $i] :
rewrite(
( ( v_wt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom))
| ~ c_in(V_pn,v_U,tc_Com_Opname) )
<=> ( ~ c_in(V_pn,v_U,tc_Com_Opname)
| v_wt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)) ) )),
inference(bind,[status(th)],]) ).
tff(167,plain,
( ! [V_pn: $i] :
( v_wt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom))
| ~ c_in(V_pn,v_U,tc_Com_Opname) )
<=> ! [V_pn: $i] :
( ~ c_in(V_pn,v_U,tc_Com_Opname)
| v_wt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)) ) ),
inference(quant_intro,[status(thm)],[166]) ).
tff(168,axiom,
! [V_pn: $i] :
( v_wt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom))
| ~ c_in(V_pn,v_U,tc_Com_Opname) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_assms_I4_J_0) ).
tff(169,plain,
! [V_pn: $i] :
( ~ c_in(V_pn,v_U,tc_Com_Opname)
| v_wt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)) ),
inference(modus_ponens,[status(thm)],[168,167]) ).
tff(170,plain,
! [V_pn: $i] :
( ~ c_in(V_pn,v_U,tc_Com_Opname)
| v_wt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)) ),
inference(modus_ponens,[status(thm)],[169,165]) ).
tff(171,plain,
! [V_pn: $i] :
( ~ c_in(V_pn,v_U,tc_Com_Opname)
| v_wt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)) ),
inference(skolemize,[status(sab)],[170]) ).
tff(172,plain,
! [V_pn: $i] :
( ~ c_in(V_pn,v_U,tc_Com_Opname)
| v_wt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)) ),
inference(modus_ponens,[status(thm)],[171,164]) ).
tff(173,plain,
( ( ~ ! [V_pn: $i] :
( ~ c_in(V_pn,v_U,tc_Com_Opname)
| v_wt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)) )
| ~ c_in(v_pn,v_U,tc_Com_Opname)
| v_wt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom)) )
<=> ( ~ ! [V_pn: $i] :
( ~ c_in(V_pn,v_U,tc_Com_Opname)
| v_wt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)) )
| ~ c_in(v_pn,v_U,tc_Com_Opname)
| v_wt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(174,plain,
( ~ ! [V_pn: $i] :
( ~ c_in(V_pn,v_U,tc_Com_Opname)
| v_wt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)) )
| ~ c_in(v_pn,v_U,tc_Com_Opname)
| v_wt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom)) ),
inference(quant_inst,[status(thm)],]) ).
tff(175,plain,
( ~ ! [V_pn: $i] :
( ~ c_in(V_pn,v_U,tc_Com_Opname)
| v_wt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)) )
| ~ c_in(v_pn,v_U,tc_Com_Opname)
| v_wt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom)) ),
inference(modus_ponens,[status(thm)],[174,173]) ).
tff(176,plain,
v_wt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom)),
inference(unit_resolution,[status(thm)],[175,172,3]) ).
tff(177,plain,
( ~ hBOOL(hAPP(hAPP(v_P,v_G),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),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_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ),
inference(rewrite,[status(thm)],]) ).
tff(178,axiom,
~ hBOOL(hAPP(hAPP(v_P,v_G),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
tff(179,plain,
~ hBOOL(hAPP(hAPP(v_P,v_G),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))),
inference(modus_ponens,[status(thm)],[178,177]) ).
tff(180,plain,
^ [V_pn: $i,V_G: $i] :
refl(
( ( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,V_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,V_pn),V_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)),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_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,V_pn),V_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ) )),
inference(bind,[status(th)],]) ).
tff(181,plain,
( ! [V_pn: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,V_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,V_pn),V_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) )
<=> ! [V_pn: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,V_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,V_pn),V_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ) ),
inference(quant_intro,[status(thm)],[180]) ).
tff(182,plain,
( ! [V_pn: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,V_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,V_pn),V_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) )
<=> ! [V_pn: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,V_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,V_pn),V_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(183,axiom,
! [V_pn: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,V_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,V_pn),V_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_assms_I2_J_0) ).
tff(184,plain,
! [V_pn: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,V_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,V_pn),V_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ),
inference(modus_ponens,[status(thm)],[183,182]) ).
tff(185,plain,
! [V_pn: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,V_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,V_pn),V_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ),
inference(skolemize,[status(sab)],[184]) ).
tff(186,plain,
! [V_pn: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,V_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,V_pn),V_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ),
inference(modus_ponens,[status(thm)],[185,181]) ).
tff(187,plain,
( ( ~ ! [V_pn: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,V_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,V_pn),V_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)),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_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) )
<=> ( ~ ! [V_pn: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,V_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,V_pn),V_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)),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_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(188,plain,
( ~ ! [V_pn: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,V_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,V_pn),V_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)),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_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(189,plain,
( ~ ! [V_pn: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),c_Set_Oinsert(hAPP(v_mgt__call,V_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,V_pn),V_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom)),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_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ),
inference(modus_ponens,[status(thm)],[188,187]) ).
tff(190,plain,
~ hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))),
inference(unit_resolution,[status(thm)],[189,186,179]) ).
tff(191,plain,
^ [V_c: $i,V_G: $i] :
refl(
( ( ~ 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_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) )
<=> ( ~ 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_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) ) )),
inference(bind,[status(th)],]) ).
tff(192,plain,
( ! [V_c: $i,V_G: $i] :
( ~ 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_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) )
<=> ! [V_c: $i,V_G: $i] :
( ~ 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_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) ) ),
inference(quant_intro,[status(thm)],[191]) ).
tff(193,plain,
( ! [V_c: $i,V_G: $i] :
( ~ 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_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) )
<=> ! [V_c: $i,V_G: $i] :
( ~ 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_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(194,plain,
^ [V_c: $i,V_G: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,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)) )
<=> ( ~ c_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) ) )),
( ( ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,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))
| 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_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) )
| 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))) ) )),
rewrite(
( ( ~ c_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) )
| 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)))
| ~ c_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) ) )),
( ( ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,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))
| 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)))
| ~ c_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) ) )),
( ( ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,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))
| 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(v_mgt(V_c),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),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_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) )
| ~ v_wt(V_c) ) )),
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_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) )
| ~ v_wt(V_c) )
<=> ( ~ 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_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) ) )),
( ( ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,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))
| 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) )
<=> ( ~ 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_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) ) )),
inference(bind,[status(th)],]) ).
tff(195,plain,
( ! [V_c: $i,V_G: $i] :
( ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,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))
| 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) )
<=> ! [V_c: $i,V_G: $i] :
( ~ 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_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) ) ),
inference(quant_intro,[status(thm)],[194]) ).
tff(196,axiom,
! [V_c: $i,V_G: $i] :
( ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,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))
| 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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_7) ).
tff(197,plain,
! [V_c: $i,V_G: $i] :
( ~ 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_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) ),
inference(modus_ponens,[status(thm)],[196,195]) ).
tff(198,plain,
! [V_c: $i,V_G: $i] :
( ~ 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_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) ),
inference(modus_ponens,[status(thm)],[197,193]) ).
tff(199,plain,
! [V_c: $i,V_G: $i] :
( ~ 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_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) ),
inference(skolemize,[status(sab)],[198]) ).
tff(200,plain,
! [V_c: $i,V_G: $i] :
( ~ 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_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) ),
inference(modus_ponens,[status(thm)],[199,192]) ).
tff(201,plain,
( ( ~ ! [V_c: $i,V_G: $i] :
( ~ 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_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) )
| hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom))
| ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) )
<=> ( ~ ! [V_c: $i,V_G: $i] :
( ~ 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_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) )
| hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom))
| ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(202,plain,
( ( ~ v_wt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom))
| hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) )
<=> ( hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom))
| ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(203,plain,
( ( ~ ! [V_c: $i,V_G: $i] :
( ~ 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_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) )
| ~ v_wt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom))
| hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) )
<=> ( ~ ! [V_c: $i,V_G: $i] :
( ~ 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_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) )
| hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom))
| ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) ) ),
inference(monotonicity,[status(thm)],[202]) ).
tff(204,plain,
( ( ~ ! [V_c: $i,V_G: $i] :
( ~ 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_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) )
| ~ v_wt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom))
| hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) )
<=> ( ~ ! [V_c: $i,V_G: $i] :
( ~ 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_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) )
| hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom))
| ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) ) ),
inference(transitivity,[status(thm)],[203,201]) ).
tff(205,plain,
( ~ ! [V_c: $i,V_G: $i] :
( ~ 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_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) )
| ~ v_wt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom))
| hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(206,plain,
( ~ ! [V_c: $i,V_G: $i] :
( ~ 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_lessequals(V_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(V_G,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) )
| hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ v_wt(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom))
| ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) ),
inference(modus_ponens,[status(thm)],[205,204]) ).
tff(207,plain,
( ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) ) ),
inference(unit_resolution,[status(thm)],[206,200,190,176]) ).
tff(208,plain,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(unit_resolution,[status(thm)],[207,162]) ).
tff(209,plain,
$false,
inference(unit_resolution,[status(thm)],[208,113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV883-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Sep 4 09:09:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 1.01/0.91 % SZS status Unsatisfiable
% 1.01/0.91 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------