TSTP Solution File: SWW473_3 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW473_3 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 20:58:56 EDT 2022
% Result : Theorem 5.87s 4.15s
% Output : Proof 5.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 54
% Syntax : Number of formulae : 96 ( 19 unt; 19 typ; 0 def)
% Number of atoms : 429 ( 63 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 537 ( 214 ~; 228 |; 0 &)
% ( 61 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 29 ( 29 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 21 ( 11 >; 10 *; 0 +; 0 <<)
% Number of predicates : 22 ( 20 usr; 14 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-2 aty)
% Number of variables : 239 ( 214 !; 0 ?; 239 :)
% Comments :
%------------------------------------------------------------------------------
tff(hAPP_pname_a_type,type,
hAPP_pname_a: ( fun_pname_a * pname ) > x_a ).
tff(pn_type,type,
pn: pname ).
tff(mgt_call_type,type,
mgt_call: fun_pname_a ).
tff(tptp_fun_X_2_76_type,type,
tptp_fun_X_2_76: ( fun_a_bool * fun_a_bool ) > x_a ).
tff(image_pname_a_type,type,
image_pname_a: ( fun_pname_a * fun_pname_bool ) > fun_a_bool ).
tff(u_type,type,
u: fun_pname_bool ).
tff(hAPP_f2050579477a_bool_type,type,
hAPP_f2050579477a_bool: ( fun_fu1731003005a_bool * fun_a_bool ) > fun_a_bool ).
tff(g_type,type,
g: fun_a_bool ).
tff(hAPP_a1206381875a_bool_type,type,
hAPP_a1206381875a_bool: ( fun_a_1752562919a_bool * x_a ) > fun_fu1731003005a_bool ).
tff(insert_a_type,type,
insert_a: fun_a_1752562919a_bool ).
tff(hBOOL_type,type,
hBOOL: bool > $o ).
tff(hAPP_fun_a_bool_bool_type,type,
hAPP_fun_a_bool_bool: ( fun_fun_a_bool_bool * fun_a_bool ) > bool ).
tff(hAPP_a85458249l_bool_type,type,
hAPP_a85458249l_bool: ( fun_a_1255737515l_bool * x_a ) > fun_fun_a_bool_bool ).
tff(member_a_type,type,
member_a: fun_a_1255737515l_bool ).
tff(hAPP_f1631501043l_bool_type,type,
hAPP_f1631501043l_bool: ( fun_fu1471507361l_bool * fun_a_bool ) > fun_fun_a_bool_bool ).
tff(ord_le1311769555a_bool_type,type,
ord_le1311769555a_bool: fun_fu1471507361l_bool ).
tff(hAPP_f1664156314l_bool_type,type,
hAPP_f1664156314l_bool: ( fun_fu1430349052l_bool * fun_pname_bool ) > bool ).
tff(hAPP_p338031245l_bool_type,type,
hAPP_p338031245l_bool: ( fun_pn422929397l_bool * pname ) > fun_fu1430349052l_bool ).
tff(member_pname_type,type,
member_pname: fun_pn422929397l_bool ).
tff(1,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u)))
<=> ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6) ).
tff(3,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [B: fun_a_bool,A: fun_a_bool] :
refl(
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(A,B)),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(A,B)),A)) ) )
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(A,B)),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(A,B)),A)) ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [B: fun_a_bool,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(A,B)),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(A,B)),A)) ) )
<=> ! [B: fun_a_bool,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(A,B)),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(A,B)),A)) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [B: fun_a_bool,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ ! [X_2: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) ) )
<=> ! [B: fun_a_bool,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ ! [X_2: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [B: fun_a_bool,A: fun_a_bool] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [X_2: x_a] :
rewrite(
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B)) )
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) ) ))),
( ! [X_2: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B)) )
<=> ! [X_2: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) ) )),
( ( ! [X_2: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B)) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) )
<=> ( ! [X_2: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) ) )),
rewrite(
( ( ! [X_2: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) )
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ ! [X_2: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) ) ) )),
( ( ! [X_2: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B)) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) )
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ ! [X_2: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) ) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [B: fun_a_bool,A: fun_a_bool] :
( ! [X_2: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B)) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) )
<=> ! [B: fun_a_bool,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ ! [X_2: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [B: fun_a_bool,A: fun_a_bool] :
( ! [X_2: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B)) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_479_subsetI) ).
tff(10,plain,
! [B: fun_a_bool,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ ! [X_2: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [B: fun_a_bool,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ ! [X_2: x_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [B: fun_a_bool,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(A,B)),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(A,B)),A)) ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [B: fun_a_bool,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(A,B)),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(A,B)),A)) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [B: fun_a_bool,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(A,B)),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(A,B)),A)) ) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u)))
| ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g))) ) )
<=> ( ~ ! [B: fun_a_bool,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(A,B)),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(A,B)),A)) ) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u)))
| ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [B: fun_a_bool,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(A,B)),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(A,B)),A)) ) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u)))
| ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [B: fun_a_bool,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(A,B)),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(A,B)),A)) ) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u)))
| ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g))) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g))) ),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u))) ),
inference(tautology,[status(thm)],]) ).
tff(19,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u))),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
tff(22,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
^ [B_3: x_a,F: fun_pname_a,X_1: pname,A: fun_pname_bool] :
refl(
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
| ( B_3 != hAPP_pname_a(F,X_1) ) )
<=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
| ( B_3 != hAPP_pname_a(F,X_1) ) ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [B_3: x_a,F: fun_pname_a,X_1: pname,A: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
| ( B_3 != hAPP_pname_a(F,X_1) ) )
<=> ! [B_3: x_a,F: fun_pname_a,X_1: pname,A: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
| ( B_3 != hAPP_pname_a(F,X_1) ) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [B_3: x_a,F: fun_pname_a,X_1: pname,A: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
| ( B_3 != hAPP_pname_a(F,X_1) ) )
<=> ! [B_3: x_a,F: fun_pname_a,X_1: pname,A: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
| ( B_3 != hAPP_pname_a(F,X_1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
^ [B_3: x_a,F: fun_pname_a,X_1: pname,A: fun_pname_bool] :
trans(
monotonicity(
rewrite(
( ( ( B_3 = hAPP_pname_a(F,X_1) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A))) )
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
| ( B_3 != hAPP_pname_a(F,X_1) ) ) )),
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> ( ( B_3 = hAPP_pname_a(F,X_1) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A))) ) )
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
| ( B_3 != hAPP_pname_a(F,X_1) ) ) ) )),
rewrite(
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
| ( B_3 != hAPP_pname_a(F,X_1) ) ) )
<=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
| ( B_3 != hAPP_pname_a(F,X_1) ) ) )),
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> ( ( B_3 = hAPP_pname_a(F,X_1) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A))) ) )
<=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
| ( B_3 != hAPP_pname_a(F,X_1) ) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [B_3: x_a,F: fun_pname_a,X_1: pname,A: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> ( ( B_3 = hAPP_pname_a(F,X_1) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A))) ) )
<=> ! [B_3: x_a,F: fun_pname_a,X_1: pname,A: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
| ( B_3 != hAPP_pname_a(F,X_1) ) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,axiom,
! [B_3: x_a,F: fun_pname_a,X_1: pname,A: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> ( ( B_3 = hAPP_pname_a(F,X_1) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_436_rev__image__eqI) ).
tff(29,plain,
! [B_3: x_a,F: fun_pname_a,X_1: pname,A: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
| ( B_3 != hAPP_pname_a(F,X_1) ) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [B_3: x_a,F: fun_pname_a,X_1: pname,A: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
| ( B_3 != hAPP_pname_a(F,X_1) ) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
! [B_3: x_a,F: fun_pname_a,X_1: pname,A: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
| ( B_3 != hAPP_pname_a(F,X_1) ) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [B_3: x_a,F: fun_pname_a,X_1: pname,A: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
| ( B_3 != hAPP_pname_a(F,X_1) ) ),
inference(modus_ponens,[status(thm)],[31,24]) ).
tff(33,plain,
( ( ~ ! [B_3: x_a,F: fun_pname_a,X_1: pname,A: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
| ( B_3 != hAPP_pname_a(F,X_1) ) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u))
| ( tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u)) != hAPP_pname_a(mgt_call,pn) ) )
<=> ( ~ ! [B_3: x_a,F: fun_pname_a,X_1: pname,A: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
| ( B_3 != hAPP_pname_a(F,X_1) ) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u))
| ( tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u)) != hAPP_pname_a(mgt_call,pn) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ( tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u)) != hAPP_pname_a(mgt_call,pn) ) )
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u))
| ( tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u)) != hAPP_pname_a(mgt_call,pn) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ( ~ ! [B_3: x_a,F: fun_pname_a,X_1: pname,A: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
| ( B_3 != hAPP_pname_a(F,X_1) ) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ( tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u)) != hAPP_pname_a(mgt_call,pn) ) )
<=> ( ~ ! [B_3: x_a,F: fun_pname_a,X_1: pname,A: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
| ( B_3 != hAPP_pname_a(F,X_1) ) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u))
| ( tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u)) != hAPP_pname_a(mgt_call,pn) ) ) ),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( ( ~ ! [B_3: x_a,F: fun_pname_a,X_1: pname,A: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
| ( B_3 != hAPP_pname_a(F,X_1) ) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ( tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u)) != hAPP_pname_a(mgt_call,pn) ) )
<=> ( ~ ! [B_3: x_a,F: fun_pname_a,X_1: pname,A: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
| ( B_3 != hAPP_pname_a(F,X_1) ) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u))
| ( tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u)) != hAPP_pname_a(mgt_call,pn) ) ) ),
inference(transitivity,[status(thm)],[35,33]) ).
tff(37,plain,
( ~ ! [B_3: x_a,F: fun_pname_a,X_1: pname,A: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
| ( B_3 != hAPP_pname_a(F,X_1) ) )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ( tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u)) != hAPP_pname_a(mgt_call,pn) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(38,plain,
( ~ ! [B_3: x_a,F: fun_pname_a,X_1: pname,A: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
| ( B_3 != hAPP_pname_a(F,X_1) ) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u))
| ( tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u)) != hAPP_pname_a(mgt_call,pn) ) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u)) != hAPP_pname_a(mgt_call,pn),
inference(unit_resolution,[status(thm)],[38,32,22,19]) ).
tff(40,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)))
<=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))) ),
inference(rewrite,[status(thm)],]) ).
tff(41,axiom,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(42,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
^ [X_1: x_a,A: fun_a_bool,B: fun_a_bool] :
refl(
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) )
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [X_1: x_a,A: fun_a_bool,B: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) )
<=> ! [X_1: x_a,A: fun_a_bool,B: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [X_1: x_a,A: fun_a_bool,B: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) )
<=> ! [X_1: x_a,A: fun_a_bool,B: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
^ [X_1: x_a,A: fun_a_bool,B: fun_a_bool] :
trans(
monotonicity(
rewrite(
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B)) )
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) ) )),
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B)) ) )
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) ) ) )),
rewrite(
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) ) )
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) ) )),
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B)) ) )
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [X_1: x_a,A: fun_a_bool,B: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B)) ) )
<=> ! [X_1: x_a,A: fun_a_bool,B: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,axiom,
! [X_1: x_a,A: fun_a_bool,B: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_415_in__mono) ).
tff(49,plain,
! [X_1: x_a,A: fun_a_bool,B: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [X_1: x_a,A: fun_a_bool,B: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
! [X_1: x_a,A: fun_a_bool,B: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [X_1: x_a,A: fun_a_bool,B: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) ),
inference(modus_ponens,[status(thm)],[51,44]) ).
tff(53,plain,
( ( ~ ! [X_1: x_a,A: fun_a_bool,B: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),g)) )
<=> ( ~ ! [X_1: x_a,A: fun_a_bool,B: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),g)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),g)) )
<=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),g)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
( ( ~ ! [X_1: x_a,A: fun_a_bool,B: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),g)) )
<=> ( ~ ! [X_1: x_a,A: fun_a_bool,B: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),g)) ) ),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ( ~ ! [X_1: x_a,A: fun_a_bool,B: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),g)) )
<=> ( ~ ! [X_1: x_a,A: fun_a_bool,B: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),g)) ) ),
inference(transitivity,[status(thm)],[55,53]) ).
tff(57,plain,
( ~ ! [X_1: x_a,A: fun_a_bool,B: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),g)) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
( ~ ! [X_1: x_a,A: fun_a_bool,B: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),g)) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),g)),
inference(unit_resolution,[status(thm)],[58,52,42,19]) ).
tff(60,plain,
( ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),g))
| ( tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u)) = hAPP_pname_a(mgt_call,pn) ) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),g))
| ( tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u)) = hAPP_pname_a(mgt_call,pn) ) ),
inference(tautology,[status(thm)],]) ).
tff(61,plain,
~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),g))
| ( tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u)) = hAPP_pname_a(mgt_call,pn) ) ),
inference(unit_resolution,[status(thm)],[60,59,39]) ).
tff(62,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g))) ),
inference(tautology,[status(thm)],]) ).
tff(63,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g))),
inference(unit_resolution,[status(thm)],[62,17]) ).
tff(64,plain,
( ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),g))
| ( tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u)) = hAPP_pname_a(mgt_call,pn) ) ) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),g))
| ( tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u)) = hAPP_pname_a(mgt_call,pn) ) ),
inference(tautology,[status(thm)],]) ).
tff(65,plain,
~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),g))
| ( tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u)) = hAPP_pname_a(mgt_call,pn) ) ) ),
inference(unit_resolution,[status(thm)],[64,63,61]) ).
tff(66,plain,
^ [A_2: x_a,B_3: x_a,A: fun_a_bool] :
refl(
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),A)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A))
| ( A_2 = B_3 ) ) )
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),A)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A))
| ( A_2 = B_3 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(67,plain,
( ! [A_2: x_a,B_3: x_a,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),A)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A))
| ( A_2 = B_3 ) ) )
<=> ! [A_2: x_a,B_3: x_a,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),A)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A))
| ( A_2 = B_3 ) ) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [A_2: x_a,B_3: x_a,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),A)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A))
| ( A_2 = B_3 ) ) )
<=> ! [A_2: x_a,B_3: x_a,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),A)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A))
| ( A_2 = B_3 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
^ [A_2: x_a,B_3: x_a,A: fun_a_bool] :
rewrite(
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),A)))
<=> ( ( A_2 = B_3 )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A)) ) )
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),A)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A))
| ( A_2 = B_3 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(70,plain,
( ! [A_2: x_a,B_3: x_a,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),A)))
<=> ( ( A_2 = B_3 )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A)) ) )
<=> ! [A_2: x_a,B_3: x_a,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),A)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A))
| ( A_2 = B_3 ) ) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,axiom,
! [A_2: x_a,B_3: x_a,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),A)))
<=> ( ( A_2 = B_3 )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_384_insert__iff) ).
tff(72,plain,
! [A_2: x_a,B_3: x_a,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),A)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A))
| ( A_2 = B_3 ) ) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [A_2: x_a,B_3: x_a,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),A)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A))
| ( A_2 = B_3 ) ) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
! [A_2: x_a,B_3: x_a,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),A)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A))
| ( A_2 = B_3 ) ) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [A_2: x_a,B_3: x_a,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),A)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A))
| ( A_2 = B_3 ) ) ),
inference(modus_ponens,[status(thm)],[74,67]) ).
tff(76,plain,
( ~ ! [A_2: x_a,B_3: x_a,A: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),A)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A))
| ( A_2 = B_3 ) ) )
| ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),g))
| ( tptp_fun_X_2_76(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u)) = hAPP_pname_a(mgt_call,pn) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(77,plain,
$false,
inference(unit_resolution,[status(thm)],[76,75,65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW473_3 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Sep 4 18:36:05 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.20/0.35 Usage: tptp [options] [-file:]file
% 0.20/0.35 -h, -? prints this message.
% 0.20/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.20/0.35 -m, -model generate model.
% 0.20/0.35 -p, -proof generate proof.
% 0.20/0.35 -c, -core generate unsat core of named formulas.
% 0.20/0.35 -st, -statistics display statistics.
% 0.20/0.35 -t:timeout set timeout (in second).
% 0.20/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.20/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.20/0.35 -<param>:<value> configuration parameter and value.
% 0.20/0.35 -o:<output-file> file to place output in.
% 5.87/4.15 % SZS status Theorem
% 5.87/4.15 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------