TSTP Solution File: SWV879-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV879-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 15:24:49 EDT 2022
% Result : Unsatisfiable 0.82s 0.84s
% Output : Proof 0.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 63
% Syntax : Number of formulae : 134 ( 49 unt; 19 typ; 0 def)
% Number of atoms : 316 ( 119 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 353 ( 162 ~; 153 |; 0 &)
% ( 38 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 12 >; 13 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-4 aty)
% Number of variables : 293 ( 263 !; 0 ?; 293 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Set_Oimage_type,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(tc_Com_Opname_type,type,
tc_Com_Opname: $i ).
tff(v_U_type,type,
v_U: $i ).
tff(v_mgt__call_type,type,
v_mgt__call: $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_bool_type,type,
tc_bool: $i ).
tff(c_Set_Oinsert_type,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(c_Lattices_Oupper__semilattice__class_Osup_type,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i ).
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $i ).
tff(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(v_P_type,type,
v_P: $i ).
tff(class_Lattices_Oupper__semilattice_type,type,
class_Lattices_Oupper__semilattice: $i > $o ).
tff(class_Lattices_Olattice_type,type,
class_Lattices_Olattice: $i > $o ).
tff(1,plain,
( hBOOL(c_in(v_x,v_U,tc_Com_Opname))
<=> hBOOL(c_in(v_x,v_U,tc_Com_Opname)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
hBOOL(c_in(v_x,v_U,tc_Com_Opname)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(3,plain,
hBOOL(c_in(v_x,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(
( ( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
<=> ( ~ hBOOL(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] :
( ~ hBOOL(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] :
( ~ hBOOL(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] :
( ~ hBOOL(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] :
( ~ hBOOL(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 )
| ~ hBOOL(c_in(V_a,V_A,T_a)) )
<=> ( ~ hBOOL(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 )
| ~ hBOOL(c_in(V_a,V_A,T_a)) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(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 )
| ~ hBOOL(c_in(V_a,V_A,T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
tff(10,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(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] :
( ~ hBOOL(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] :
( ~ hBOOL(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] :
( ~ hBOOL(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] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ hBOOL(c_in(v_x,v_U,tc_Com_Opname))
| ( c_Set_Oinsert(v_x,v_U,tc_Com_Opname) = v_U ) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ hBOOL(c_in(v_x,v_U,tc_Com_Opname))
| ( c_Set_Oinsert(v_x,v_U,tc_Com_Opname) = v_U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ hBOOL(c_in(v_x,v_U,tc_Com_Opname))
| ( c_Set_Oinsert(v_x,v_U,tc_Com_Opname) = v_U ) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ hBOOL(c_in(v_x,v_U,tc_Com_Opname))
| ( c_Set_Oinsert(v_x,v_U,tc_Com_Opname) = v_U ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
c_Set_Oinsert(v_x,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_x,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/sandbox2/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_x,v_U,tc_Com_Opname),tc_Com_Opname,t_a) = c_Set_Oinsert(hAPP(v_mgt__call,v_x),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_x,v_U,tc_Com_Opname),tc_Com_Opname,t_a) = c_Set_Oinsert(hAPP(v_mgt__call,v_x),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_x),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_x,v_U,tc_Com_Opname),tc_Com_Opname,t_a),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
^ [V_a: $i,T_a: $i,V_A: $i] :
refl(
( ( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) )
<=> ( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
^ [V_a: $i,T_a: $i,V_A: $i] :
rewrite(
( ( ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A )
| ~ hBOOL(c_in(V_a,V_A,T_a)) )
<=> ( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] :
( ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A )
| ~ hBOOL(c_in(V_a,V_A,T_a)) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,axiom,
! [V_a: $i,T_a: $i,V_A: $i] :
( ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A )
| ~ hBOOL(c_in(V_a,V_A,T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff_0) ).
tff(35,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) )
| ~ hBOOL(c_in(v_x,v_U,tc_Com_Opname))
| ( c_Set_Oinsert(v_x,c_HOL_Ominus__class_Ominus(v_U,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname) = v_U ) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) )
| ~ hBOOL(c_in(v_x,v_U,tc_Com_Opname))
| ( c_Set_Oinsert(v_x,c_HOL_Ominus__class_Ominus(v_U,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname) = v_U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) )
| ~ hBOOL(c_in(v_x,v_U,tc_Com_Opname))
| ( c_Set_Oinsert(v_x,c_HOL_Ominus__class_Ominus(v_U,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname) = v_U ) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) )
| ~ hBOOL(c_in(v_x,v_U,tc_Com_Opname))
| ( c_Set_Oinsert(v_x,c_HOL_Ominus__class_Ominus(v_U,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname) = v_U ) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
c_Set_Oinsert(v_x,c_HOL_Ominus__class_Ominus(v_U,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname) = v_U,
inference(unit_resolution,[status(thm)],[41,38,3]) ).
tff(43,plain,
v_U = c_Set_Oinsert(v_x,c_HOL_Ominus__class_Ominus(v_U,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) = c_Set_Oimage(v_mgt__call,c_Set_Oinsert(v_x,c_HOL_Ominus__class_Ominus(v_U,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_Com_Opname,t_a),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
c_Set_Oimage(v_mgt__call,c_Set_Oinsert(v_x,c_HOL_Ominus__class_Ominus(v_U,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_Com_Opname,t_a) = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),
inference(symmetry,[status(thm)],[44]) ).
tff(46,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_x,c_HOL_Ominus__class_Ominus(v_U,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_Com_Opname,t_a) = c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Set_Oimage(v_mgt__call,c_HOL_Ominus__class_Ominus(v_U,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a),t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
c_Set_Oimage(v_mgt__call,c_Set_Oinsert(v_x,c_HOL_Ominus__class_Ominus(v_U,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_Com_Opname,t_a) = c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Set_Oimage(v_mgt__call,c_HOL_Ominus__class_Ominus(v_U,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a),t_a),
inference(unit_resolution,[status(thm)],[46,25]) ).
tff(48,plain,
c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Set_Oimage(v_mgt__call,c_HOL_Ominus__class_Ominus(v_U,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a),t_a) = c_Set_Oimage(v_mgt__call,c_Set_Oinsert(v_x,c_HOL_Ominus__class_Ominus(v_U,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_Com_Opname,t_a),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Set_Oimage(v_mgt__call,c_HOL_Ominus__class_Ominus(v_U,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a),t_a) = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),
inference(transitivity,[status(thm)],[48,45]) ).
tff(50,plain,
c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Set_Oimage(v_mgt__call,c_HOL_Ominus__class_Ominus(v_U,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a),t_a),t_a) = c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
^ [V_a: $i,T_a: $i,V_A: $i] :
refl(
( ( c_Set_Oinsert(V_a,V_A,T_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),V_A) )
<=> ( c_Set_Oinsert(V_a,V_A,T_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),V_A) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),V_A) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),V_A) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),V_A) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),V_A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,axiom,
! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),V_A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
tff(55,plain,
! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),V_A) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),V_A) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),V_A) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),V_A) )
| ( c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Set_Oimage(v_mgt__call,c_HOL_Ominus__class_Ominus(v_U,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a),t_a),t_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Set_Oimage(v_mgt__call,c_HOL_Ominus__class_Ominus(v_U,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a),t_a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Set_Oimage(v_mgt__call,c_HOL_Ominus__class_Ominus(v_U,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a),t_a),t_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Set_Oimage(v_mgt__call,c_HOL_Ominus__class_Ominus(v_U,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a),t_a)),
inference(unit_resolution,[status(thm)],[58,57]) ).
tff(60,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Set_Oimage(v_mgt__call,c_HOL_Ominus__class_Ominus(v_U,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a),t_a)) = c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Set_Oimage(v_mgt__call,c_HOL_Ominus__class_Ominus(v_U,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a),t_a),t_a),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) = c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Set_Oimage(v_mgt__call,c_HOL_Ominus__class_Ominus(v_U,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a),t_a),
inference(transitivity,[status(thm)],[44,47]) ).
tff(62,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),V_A) )
| ( c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),
inference(unit_resolution,[status(thm)],[62,57]) ).
tff(64,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))) = c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Set_Oimage(v_mgt__call,c_HOL_Ominus__class_Ominus(v_U,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a),t_a)),
inference(monotonicity,[status(thm)],[65,61]) ).
tff(67,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)) = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),
inference(transitivity,[status(thm)],[66,60,50,28,18]) ).
tff(68,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
<=> c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
inference(monotonicity,[status(thm)],[64]) ).
tff(69,plain,
( c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
<=> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
( ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
<=> ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
<=> ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ),
inference(rewrite,[status(thm)],]) ).
tff(72,axiom,
~ hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(73,plain,
~ hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
^ [V_ts: $i,V_G: $i] :
refl(
( ( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) )
<=> ( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) ) )),
inference(bind,[status(th)],]) ).
tff(75,plain,
( ! [V_ts: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) )
<=> ! [V_ts: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
( ! [V_ts: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) )
<=> ! [V_ts: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,axiom,
! [V_ts: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_assms_I1_J_0) ).
tff(78,plain,
! [V_ts: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
! [V_ts: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [V_ts: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[79,75]) ).
tff(81,plain,
( ( ~ ! [V_ts: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) )
| hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) )
<=> ( ~ ! [V_ts: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) )
| hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
( ~ ! [V_ts: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) )
| hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
inference(quant_inst,[status(thm)],]) ).
tff(83,plain,
( ~ ! [V_ts: $i,V_G: $i] :
( hBOOL(hAPP(hAPP(v_P,V_G),V_ts))
| ~ c_lessequals(V_ts,V_G,tc_fun(t_a,tc_bool)) )
| hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
| ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(unit_resolution,[status(thm)],[83,80,73]) ).
tff(85,plain,
~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(modus_ponens,[status(thm)],[84,70]) ).
tff(86,plain,
( class_Lattices_Olattice(tc_bool)
<=> class_Lattices_Olattice(tc_bool) ),
inference(rewrite,[status(thm)],]) ).
tff(87,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
tff(88,plain,
class_Lattices_Olattice(tc_bool),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
^ [T_1: $i,T_2: $i] :
refl(
( ( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
<=> ( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [T_1: $i,T_2: $i] :
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
<=> ! [T_1: $i,T_2: $i] :
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [T_1: $i,T_2: $i] :
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
<=> ! [T_1: $i,T_2: $i] :
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,axiom,
! [T_1: $i,T_2: $i] :
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
tff(93,plain,
! [T_1: $i,T_2: $i] :
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
! [T_1: $i,T_2: $i] :
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ),
inference(skolemize,[status(sab)],[93]) ).
tff(95,plain,
! [T_1: $i,T_2: $i] :
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ),
inference(modus_ponens,[status(thm)],[94,90]) ).
tff(96,plain,
( ( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
| class_Lattices_Oupper__semilattice(tc_fun(t_a,tc_bool))
| ~ class_Lattices_Olattice(tc_bool) )
<=> ( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
| class_Lattices_Oupper__semilattice(tc_fun(t_a,tc_bool))
| ~ class_Lattices_Olattice(tc_bool) ) ),
inference(rewrite,[status(thm)],]) ).
tff(97,plain,
( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
| class_Lattices_Oupper__semilattice(tc_fun(t_a,tc_bool))
| ~ class_Lattices_Olattice(tc_bool) ),
inference(quant_inst,[status(thm)],]) ).
tff(98,plain,
( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
| class_Lattices_Oupper__semilattice(tc_fun(t_a,tc_bool))
| ~ class_Lattices_Olattice(tc_bool) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
class_Lattices_Oupper__semilattice(tc_fun(t_a,tc_bool)),
inference(unit_resolution,[status(thm)],[98,95,88]) ).
tff(100,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(
( ( c_lessequals(V_x,V_y,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) != V_y ) )
<=> ( c_lessequals(V_x,V_y,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) != V_y ) ) )),
inference(bind,[status(th)],]) ).
tff(101,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) != V_y ) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) != V_y ) ) ),
inference(quant_intro,[status(thm)],[100]) ).
tff(102,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) != V_y ) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) != V_y ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
rewrite(
( ( ~ class_Lattices_Oupper__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) != V_y )
| c_lessequals(V_x,V_y,T_a) )
<=> ( c_lessequals(V_x,V_y,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) != V_y ) ) )),
inference(bind,[status(th)],]) ).
tff(104,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oupper__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) != V_y )
| c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) != V_y ) ) ),
inference(quant_intro,[status(thm)],[103]) ).
tff(105,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oupper__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) != V_y )
| c_lessequals(V_x,V_y,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
tff(106,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) != V_y ) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) != V_y ) ),
inference(modus_ponens,[status(thm)],[106,102]) ).
tff(108,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) != V_y ) ),
inference(skolemize,[status(sab)],[107]) ).
tff(109,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) != V_y ) ),
inference(modus_ponens,[status(thm)],[108,101]) ).
tff(110,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) != V_y ) )
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ class_Lattices_Oupper__semilattice(tc_fun(t_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)) != c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) != V_y ) )
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ class_Lattices_Oupper__semilattice(tc_fun(t_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)) != c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(111,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) != V_y ) )
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ class_Lattices_Oupper__semilattice(tc_fun(t_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)) != c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(112,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a)
| ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) != V_y ) )
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ~ class_Lattices_Oupper__semilattice(tc_fun(t_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)) != c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) ) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
| ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)) != c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) ) ),
inference(unit_resolution,[status(thm)],[112,109,99]) ).
tff(114,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)) != c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),
inference(unit_resolution,[status(thm)],[113,85]) ).
tff(115,plain,
$false,
inference(unit_resolution,[status(thm)],[114,67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWV879-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n009.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 09:07:05 EDT 2022
% 0.12/0.33 % 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.
% 0.82/0.84 % SZS status Unsatisfiable
% 0.82/0.84 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------