TSTP Solution File: SWW473+2 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW473+2 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 20:58:55 EDT 2022
% Result : Theorem 0.65s 0.73s
% Output : Proof 0.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 65
% Syntax : Number of formulae : 120 ( 26 unt; 19 typ; 0 def)
% Number of atoms : 721 ( 84 equ)
% Maximal formula atoms : 20 ( 7 avg)
% Number of connectives : 906 ( 342 ~; 376 |; 20 &)
% ( 114 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 56 ( 56 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 12 >; 9 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 290 ( 258 !; 0 ?; 290 :)
% Comments :
%------------------------------------------------------------------------------
tff(hAPP_pname_a_type,type,
hAPP_pname_a: ( $i * $i ) > $i ).
tff(pn_type,type,
pn: $i ).
tff(mgt_call_type,type,
mgt_call: $i ).
tff(tptp_fun_X_1_70_type,type,
tptp_fun_X_1_70: ( $i * $i ) > $i ).
tff(image_pname_a_type,type,
image_pname_a: ( $i * $i ) > $i ).
tff(u_type,type,
u: $i ).
tff(insert_a_type,type,
insert_a: ( $i * $i ) > $i ).
tff(g_type,type,
g: $i ).
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_fun_a_bool_bool_type,type,
hAPP_fun_a_bool_bool: ( $i * $i ) > $i ).
tff(hAPP_a85458249l_bool_type,type,
hAPP_a85458249l_bool: ( $i * $i ) > $i ).
tff(member_a_type,type,
member_a: $i ).
tff(is_a_type,type,
is_a: $i > $o ).
tff(hAPP_f1631501043l_bool_type,type,
hAPP_f1631501043l_bool: ( $i * $i ) > $i ).
tff(ord_le1311769555a_bool_type,type,
ord_le1311769555a_bool: $i ).
tff(hAPP_f1664156314l_bool_type,type,
hAPP_f1664156314l_bool: ( $i * $i ) > $i ).
tff(hAPP_p338031245l_bool_type,type,
hAPP_p338031245l_bool: ( $i * $i ) > $i ).
tff(member_pname_type,type,
member_pname: $i ).
tff(is_pname_type,type,
is_pname: $i > $o ).
tff(1,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_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,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,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).
tff(3,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_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_6: $i,A_1: $i] :
refl(
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(A_1,B_6)),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(A_1,B_6)),B_6))
| ~ is_a(tptp_fun_X_1_70(A_1,B_6)) ) )
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(A_1,B_6)),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(A_1,B_6)),B_6))
| ~ is_a(tptp_fun_X_1_70(A_1,B_6)) ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [B_6: $i,A_1: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(A_1,B_6)),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(A_1,B_6)),B_6))
| ~ is_a(tptp_fun_X_1_70(A_1,B_6)) ) )
<=> ! [B_6: $i,A_1: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(A_1,B_6)),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(A_1,B_6)),B_6))
| ~ is_a(tptp_fun_X_1_70(A_1,B_6)) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [B_6: $i,A_1: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ ! [X_1: $i] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6))
| ~ is_a(X_1) ) )
<=> ! [B_6: $i,A_1: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ ! [X_1: $i] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6))
| ~ is_a(X_1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [B_6: $i,A_1: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [X_1: $i] :
trans(
monotonicity(
rewrite(
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6)) )
<=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6)) ) )),
( ( is_a(X_1)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6)) ) )
<=> ( is_a(X_1)
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6)) ) ) )),
rewrite(
( ( is_a(X_1)
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6)) ) )
<=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6))
| ~ is_a(X_1) ) )),
( ( is_a(X_1)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6)) ) )
<=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6))
| ~ is_a(X_1) ) ))),
( ! [X_1: $i] :
( is_a(X_1)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6)) ) )
<=> ! [X_1: $i] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6))
| ~ is_a(X_1) ) )),
( ( ! [X_1: $i] :
( is_a(X_1)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6)) ) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) )
<=> ( ! [X_1: $i] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6))
| ~ is_a(X_1) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ) )),
rewrite(
( ( ! [X_1: $i] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6))
| ~ is_a(X_1) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) )
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ ! [X_1: $i] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6))
| ~ is_a(X_1) ) ) )),
( ( ! [X_1: $i] :
( is_a(X_1)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6)) ) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) )
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ ! [X_1: $i] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6))
| ~ is_a(X_1) ) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [B_6: $i,A_1: $i] :
( ! [X_1: $i] :
( is_a(X_1)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6)) ) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) )
<=> ! [B_6: $i,A_1: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ ! [X_1: $i] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6))
| ~ is_a(X_1) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [B_6: $i,A_1: $i] :
( ! [X_1: $i] :
( is_a(X_1)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6)) ) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_359_subsetI) ).
tff(10,plain,
! [B_6: $i,A_1: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ ! [X_1: $i] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6))
| ~ is_a(X_1) ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [B_6: $i,A_1: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ ! [X_1: $i] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6))
| ~ is_a(X_1) ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [B_6: $i,A_1: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(A_1,B_6)),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(A_1,B_6)),B_6))
| ~ is_a(tptp_fun_X_1_70(A_1,B_6)) ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [B_6: $i,A_1: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(A_1,B_6)),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(A_1,B_6)),B_6))
| ~ is_a(tptp_fun_X_1_70(A_1,B_6)) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [B_6: $i,A_1: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(A_1,B_6)),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(A_1,B_6)),B_6))
| ~ is_a(tptp_fun_X_1_70(A_1,B_6)) ) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),insert_a(hAPP_pname_a(mgt_call,pn),g)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ is_a(tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))) ) )
<=> ( ~ ! [B_6: $i,A_1: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(A_1,B_6)),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(A_1,B_6)),B_6))
| ~ is_a(tptp_fun_X_1_70(A_1,B_6)) ) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),insert_a(hAPP_pname_a(mgt_call,pn),g)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ is_a(tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [B_6: $i,A_1: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(A_1,B_6)),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(A_1,B_6)),B_6))
| ~ is_a(tptp_fun_X_1_70(A_1,B_6)) ) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),insert_a(hAPP_pname_a(mgt_call,pn),g)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ is_a(tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [B_6: $i,A_1: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(A_1,B_6)),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(A_1,B_6)),B_6))
| ~ is_a(tptp_fun_X_1_70(A_1,B_6)) ) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),insert_a(hAPP_pname_a(mgt_call,pn),g)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ is_a(tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
~ ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),insert_a(hAPP_pname_a(mgt_call,pn),g)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ is_a(tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))) ),
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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),insert_a(hAPP_pname_a(mgt_call,pn),g)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ is_a(tptp_fun_X_1_70(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_1_70(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_1_70(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/sandbox2/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_1: $i,F: $i,X_3: $i,A_1: $i] :
refl(
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1)))
| ( B_1 != hAPP_pname_a(F,X_3) ) )
<=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1)))
| ( B_1 != hAPP_pname_a(F,X_3) ) ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [B_1: $i,F: $i,X_3: $i,A_1: $i] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1)))
| ( B_1 != hAPP_pname_a(F,X_3) ) )
<=> ! [B_1: $i,F: $i,X_3: $i,A_1: $i] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1)))
| ( B_1 != hAPP_pname_a(F,X_3) ) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [B_1: $i,F: $i,X_3: $i,A_1: $i] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1)))
| ( B_1 != hAPP_pname_a(F,X_3) ) )
<=> ! [B_1: $i,F: $i,X_3: $i,A_1: $i] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1)))
| ( B_1 != hAPP_pname_a(F,X_3) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
^ [B_1: $i,F: $i,X_3: $i,A_1: $i] :
trans(
monotonicity(
rewrite(
( ( ( B_1 = hAPP_pname_a(F,X_3) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1))) )
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1)))
| ( B_1 != hAPP_pname_a(F,X_3) ) ) )),
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
=> ( ( B_1 = hAPP_pname_a(F,X_3) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1))) ) )
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1)))
| ( B_1 != hAPP_pname_a(F,X_3) ) ) ) )),
rewrite(
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1)))
| ( B_1 != hAPP_pname_a(F,X_3) ) ) )
<=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1)))
| ( B_1 != hAPP_pname_a(F,X_3) ) ) )),
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
=> ( ( B_1 = hAPP_pname_a(F,X_3) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1))) ) )
<=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1)))
| ( B_1 != hAPP_pname_a(F,X_3) ) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [B_1: $i,F: $i,X_3: $i,A_1: $i] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
=> ( ( B_1 = hAPP_pname_a(F,X_3) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1))) ) )
<=> ! [B_1: $i,F: $i,X_3: $i,A_1: $i] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1)))
| ( B_1 != hAPP_pname_a(F,X_3) ) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,axiom,
! [B_1: $i,F: $i,X_3: $i,A_1: $i] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
=> ( ( B_1 = hAPP_pname_a(F,X_3) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_rev__image__eqI) ).
tff(29,plain,
! [B_1: $i,F: $i,X_3: $i,A_1: $i] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1)))
| ( B_1 != hAPP_pname_a(F,X_3) ) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [B_1: $i,F: $i,X_3: $i,A_1: $i] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1)))
| ( B_1 != hAPP_pname_a(F,X_3) ) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
! [B_1: $i,F: $i,X_3: $i,A_1: $i] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1)))
| ( B_1 != hAPP_pname_a(F,X_3) ) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [B_1: $i,F: $i,X_3: $i,A_1: $i] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1)))
| ( B_1 != hAPP_pname_a(F,X_3) ) ),
inference(modus_ponens,[status(thm)],[31,24]) ).
tff(33,plain,
( ( ~ ! [B_1: $i,F: $i,X_3: $i,A_1: $i] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1)))
| ( B_1 != hAPP_pname_a(F,X_3) ) )
| ~ 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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ( tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u)) != hAPP_pname_a(mgt_call,pn) ) )
<=> ( ~ ! [B_1: $i,F: $i,X_3: $i,A_1: $i] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1)))
| ( B_1 != hAPP_pname_a(F,X_3) ) )
| ~ 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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ( tptp_fun_X_1_70(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,
( ~ ! [B_1: $i,F: $i,X_3: $i,A_1: $i] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1)))
| ( B_1 != hAPP_pname_a(F,X_3) ) )
| ~ 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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ( tptp_fun_X_1_70(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(35,plain,
( ~ ! [B_1: $i,F: $i,X_3: $i,A_1: $i] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1)))
| ( B_1 != hAPP_pname_a(F,X_3) ) )
| ~ 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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ( tptp_fun_X_1_70(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)],[34,33]) ).
tff(36,plain,
tptp_fun_X_1_70(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)],[35,32,22,19]) ).
tff(37,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(38,axiom,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(39,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)],[38,37]) ).
tff(40,plain,
^ [X_3: $i,A_1: $i,B_6: $i] :
refl(
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) )
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [X_3: $i,A_1: $i,B_6: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) )
<=> ! [X_3: $i,A_1: $i,B_6: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [X_3: $i,A_1: $i,B_6: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) )
<=> ! [X_3: $i,A_1: $i,B_6: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
^ [X_3: $i,A_1: $i,B_6: $i] :
trans(
monotonicity(
rewrite(
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6)) )
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ) )),
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6)) ) )
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ) ) )),
rewrite(
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ) )
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ) )),
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6)) ) )
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [X_3: $i,A_1: $i,B_6: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6)) ) )
<=> ! [X_3: $i,A_1: $i,B_6: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,axiom,
! [X_3: $i,A_1: $i,B_6: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_in__mono) ).
tff(46,plain,
! [X_3: $i,A_1: $i,B_6: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [X_3: $i,A_1: $i,B_6: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
! [X_3: $i,A_1: $i,B_6: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [X_3: $i,A_1: $i,B_6: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ),
inference(modus_ponens,[status(thm)],[48,41]) ).
tff(50,plain,
( ( ~ ! [X_3: $i,A_1: $i,B_6: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) )
| ~ 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_1_70(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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),g)) )
<=> ( ~ ! [X_3: $i,A_1: $i,B_6: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) )
| ~ 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_1_70(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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),g)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(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_1_70(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_1_70(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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),g)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( ( ~ ! [X_3: $i,A_1: $i,B_6: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),g)) )
<=> ( ~ ! [X_3: $i,A_1: $i,B_6: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) )
| ~ 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_1_70(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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),g)) ) ),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
( ( ~ ! [X_3: $i,A_1: $i,B_6: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),g)) )
<=> ( ~ ! [X_3: $i,A_1: $i,B_6: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) )
| ~ 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_1_70(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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),g)) ) ),
inference(transitivity,[status(thm)],[52,50]) ).
tff(54,plain,
( ~ ! [X_3: $i,A_1: $i,B_6: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),g)) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
( ~ ! [X_3: $i,A_1: $i,B_6: $i] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) )
| ~ 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_1_70(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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),g)) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),g)),
inference(unit_resolution,[status(thm)],[55,49,39,19]) ).
tff(57,plain,
( ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),g))
| ( tptp_fun_X_1_70(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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),g))
| ( tptp_fun_X_1_70(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(58,plain,
~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),g))
| ( tptp_fun_X_1_70(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)],[57,56,36]) ).
tff(59,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),insert_a(hAPP_pname_a(mgt_call,pn),g)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ is_a(tptp_fun_X_1_70(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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),insert_a(hAPP_pname_a(mgt_call,pn),g))) ),
inference(tautology,[status(thm)],]) ).
tff(60,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),insert_a(hAPP_pname_a(mgt_call,pn),g))),
inference(unit_resolution,[status(thm)],[59,17]) ).
tff(61,plain,
( ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),insert_a(hAPP_pname_a(mgt_call,pn),g)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),g))
| ( tptp_fun_X_1_70(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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),insert_a(hAPP_pname_a(mgt_call,pn),g)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),g))
| ( tptp_fun_X_1_70(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(62,plain,
~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),insert_a(hAPP_pname_a(mgt_call,pn),g)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),g))
| ( tptp_fun_X_1_70(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)],[61,60,58]) ).
tff(63,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),insert_a(hAPP_pname_a(mgt_call,pn),g)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),image_pname_a(mgt_call,u)))
| ~ is_a(tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u)))
| is_a(tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))) ),
inference(tautology,[status(thm)],]) ).
tff(64,plain,
is_a(tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),
inference(unit_resolution,[status(thm)],[63,17]) ).
tff(65,plain,
( is_pname(pn)
<=> is_pname(pn) ),
inference(rewrite,[status(thm)],]) ).
tff(66,axiom,
is_pname(pn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_pn) ).
tff(67,plain,
is_pname(pn),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
^ [B_1_1: $i,B_2_1: $i] :
refl(
( ( is_a(hAPP_pname_a(B_1_1,B_2_1))
| ~ is_pname(B_2_1) )
<=> ( is_a(hAPP_pname_a(B_1_1,B_2_1))
| ~ is_pname(B_2_1) ) )),
inference(bind,[status(th)],]) ).
tff(69,plain,
( ! [B_1_1: $i,B_2_1: $i] :
( is_a(hAPP_pname_a(B_1_1,B_2_1))
| ~ is_pname(B_2_1) )
<=> ! [B_1_1: $i,B_2_1: $i] :
( is_a(hAPP_pname_a(B_1_1,B_2_1))
| ~ is_pname(B_2_1) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ! [B_1_1: $i,B_2_1: $i] :
( is_a(hAPP_pname_a(B_1_1,B_2_1))
| ~ is_pname(B_2_1) )
<=> ! [B_1_1: $i,B_2_1: $i] :
( is_a(hAPP_pname_a(B_1_1,B_2_1))
| ~ is_pname(B_2_1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
^ [B_1_1: $i,B_2_1: $i] :
rewrite(
( ( is_pname(B_2_1)
=> is_a(hAPP_pname_a(B_1_1,B_2_1)) )
<=> ( is_a(hAPP_pname_a(B_1_1,B_2_1))
| ~ is_pname(B_2_1) ) )),
inference(bind,[status(th)],]) ).
tff(72,plain,
( ! [B_1_1: $i,B_2_1: $i] :
( is_pname(B_2_1)
=> is_a(hAPP_pname_a(B_1_1,B_2_1)) )
<=> ! [B_1_1: $i,B_2_1: $i] :
( is_a(hAPP_pname_a(B_1_1,B_2_1))
| ~ is_pname(B_2_1) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,axiom,
! [B_1_1: $i,B_2_1: $i] :
( is_pname(B_2_1)
=> is_a(hAPP_pname_a(B_1_1,B_2_1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000t__a) ).
tff(74,plain,
! [B_1_1: $i,B_2_1: $i] :
( is_a(hAPP_pname_a(B_1_1,B_2_1))
| ~ is_pname(B_2_1) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [B_1_1: $i,B_2_1: $i] :
( is_a(hAPP_pname_a(B_1_1,B_2_1))
| ~ is_pname(B_2_1) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
! [B_1_1: $i,B_2_1: $i] :
( is_a(hAPP_pname_a(B_1_1,B_2_1))
| ~ is_pname(B_2_1) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [B_1_1: $i,B_2_1: $i] :
( is_a(hAPP_pname_a(B_1_1,B_2_1))
| ~ is_pname(B_2_1) ),
inference(modus_ponens,[status(thm)],[76,69]) ).
tff(78,plain,
( ( ~ ! [B_1_1: $i,B_2_1: $i] :
( is_a(hAPP_pname_a(B_1_1,B_2_1))
| ~ is_pname(B_2_1) )
| is_a(hAPP_pname_a(mgt_call,pn))
| ~ is_pname(pn) )
<=> ( ~ ! [B_1_1: $i,B_2_1: $i] :
( is_a(hAPP_pname_a(B_1_1,B_2_1))
| ~ is_pname(B_2_1) )
| is_a(hAPP_pname_a(mgt_call,pn))
| ~ is_pname(pn) ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,plain,
( ~ ! [B_1_1: $i,B_2_1: $i] :
( is_a(hAPP_pname_a(B_1_1,B_2_1))
| ~ is_pname(B_2_1) )
| is_a(hAPP_pname_a(mgt_call,pn))
| ~ is_pname(pn) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
( ~ ! [B_1_1: $i,B_2_1: $i] :
( is_a(hAPP_pname_a(B_1_1,B_2_1))
| ~ is_pname(B_2_1) )
| is_a(hAPP_pname_a(mgt_call,pn))
| ~ is_pname(pn) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
is_a(hAPP_pname_a(mgt_call,pn)),
inference(unit_resolution,[status(thm)],[80,77,67]) ).
tff(82,plain,
^ [A_3: $i,B_1: $i,A_1: $i] :
refl(
( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) )
| ~ is_a(A_3)
| ~ is_a(B_1) )
<=> ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) )
| ~ is_a(A_3)
| ~ is_a(B_1) ) )),
inference(bind,[status(th)],]) ).
tff(83,plain,
( ! [A_3: $i,B_1: $i,A_1: $i] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) )
| ~ is_a(A_3)
| ~ is_a(B_1) )
<=> ! [A_3: $i,B_1: $i,A_1: $i] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) )
| ~ is_a(A_3)
| ~ is_a(B_1) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
^ [A_3: $i,B_1: $i,A_1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( is_a(A_3)
& is_a(B_1) )
<=> ~ ( ~ is_a(A_3)
| ~ is_a(B_1) ) )),
( ~ ( is_a(A_3)
& is_a(B_1) )
<=> ~ ~ ( ~ is_a(A_3)
| ~ is_a(B_1) ) )),
rewrite(
( ~ ~ ( ~ is_a(A_3)
| ~ is_a(B_1) )
<=> ( ~ is_a(A_3)
| ~ is_a(B_1) ) )),
( ~ ( is_a(A_3)
& is_a(B_1) )
<=> ( ~ is_a(A_3)
| ~ is_a(B_1) ) )),
( ( ~ ( is_a(A_3)
& is_a(B_1) )
| ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) ) )
<=> ( ~ is_a(A_3)
| ~ is_a(B_1)
| ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) ) ) )),
rewrite(
( ( ~ is_a(A_3)
| ~ is_a(B_1)
| ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) ) )
<=> ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) )
| ~ is_a(A_3)
| ~ is_a(B_1) ) )),
( ( ~ ( is_a(A_3)
& is_a(B_1) )
| ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) ) )
<=> ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) )
| ~ is_a(A_3)
| ~ is_a(B_1) ) )),
inference(bind,[status(th)],]) ).
tff(85,plain,
( ! [A_3: $i,B_1: $i,A_1: $i] :
( ~ ( is_a(A_3)
& is_a(B_1) )
| ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) ) )
<=> ! [A_3: $i,B_1: $i,A_1: $i] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) )
| ~ is_a(A_3)
| ~ is_a(B_1) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,plain,
( ! [A_3: $i,B_1: $i,A_1: $i] :
( ~ ( is_a(A_3)
& is_a(B_1) )
| ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) ) )
<=> ! [A_3: $i,B_1: $i,A_1: $i] :
( ~ ( is_a(A_3)
& is_a(B_1) )
| ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
^ [A_3: $i,B_1: $i,A_1: $i] :
trans(
monotonicity(
rewrite(
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( ( A_3 = B_1 )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1)) ) )
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) ) )),
( ( ( is_a(A_3)
& is_a(B_1) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( ( A_3 = B_1 )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1)) ) ) )
<=> ( ( is_a(A_3)
& is_a(B_1) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) ) ) )),
rewrite(
( ( ( is_a(A_3)
& is_a(B_1) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) ) )
<=> ( ~ ( is_a(A_3)
& is_a(B_1) )
| ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) ) ) )),
( ( ( is_a(A_3)
& is_a(B_1) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( ( A_3 = B_1 )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1)) ) ) )
<=> ( ~ ( is_a(A_3)
& is_a(B_1) )
| ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(88,plain,
( ! [A_3: $i,B_1: $i,A_1: $i] :
( ( is_a(A_3)
& is_a(B_1) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( ( A_3 = B_1 )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1)) ) ) )
<=> ! [A_3: $i,B_1: $i,A_1: $i] :
( ~ ( is_a(A_3)
& is_a(B_1) )
| ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) ) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,axiom,
! [A_3: $i,B_1: $i,A_1: $i] :
( ( is_a(A_3)
& is_a(B_1) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( ( A_3 = B_1 )
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_insert__iff) ).
tff(90,plain,
! [A_3: $i,B_1: $i,A_1: $i] :
( ~ ( is_a(A_3)
& is_a(B_1) )
| ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) ) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
! [A_3: $i,B_1: $i,A_1: $i] :
( ~ ( is_a(A_3)
& is_a(B_1) )
| ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) ) ),
inference(modus_ponens,[status(thm)],[90,86]) ).
tff(92,plain,
! [A_3: $i,B_1: $i,A_1: $i] :
( ~ ( is_a(A_3)
& is_a(B_1) )
| ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) ) ),
inference(skolemize,[status(sab)],[91]) ).
tff(93,plain,
! [A_3: $i,B_1: $i,A_1: $i] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) )
| ~ is_a(A_3)
| ~ is_a(B_1) ),
inference(modus_ponens,[status(thm)],[92,85]) ).
tff(94,plain,
! [A_3: $i,B_1: $i,A_1: $i] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) )
| ~ is_a(A_3)
| ~ is_a(B_1) ),
inference(modus_ponens,[status(thm)],[93,83]) ).
tff(95,plain,
( ( ~ ! [A_3: $i,B_1: $i,A_1: $i] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) )
| ~ is_a(A_3)
| ~ is_a(B_1) )
| ~ is_a(hAPP_pname_a(mgt_call,pn))
| ~ is_a(tptp_fun_X_1_70(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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),insert_a(hAPP_pname_a(mgt_call,pn),g)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),g))
| ( tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u)) = hAPP_pname_a(mgt_call,pn) ) ) ) )
<=> ( ~ ! [A_3: $i,B_1: $i,A_1: $i] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) )
| ~ is_a(A_3)
| ~ is_a(B_1) )
| ~ is_a(hAPP_pname_a(mgt_call,pn))
| ~ is_a(tptp_fun_X_1_70(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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),insert_a(hAPP_pname_a(mgt_call,pn),g)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),g))
| ( tptp_fun_X_1_70(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(96,plain,
( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),insert_a(hAPP_pname_a(mgt_call,pn),g)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),g))
| ( tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u)) = hAPP_pname_a(mgt_call,pn) ) ) )
| ~ is_a(tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u)))
| ~ is_a(hAPP_pname_a(mgt_call,pn)) )
<=> ( ~ is_a(hAPP_pname_a(mgt_call,pn))
| ~ is_a(tptp_fun_X_1_70(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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),insert_a(hAPP_pname_a(mgt_call,pn),g)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),g))
| ( tptp_fun_X_1_70(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(97,plain,
( ( ~ ! [A_3: $i,B_1: $i,A_1: $i] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) )
| ~ is_a(A_3)
| ~ is_a(B_1) )
| ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),insert_a(hAPP_pname_a(mgt_call,pn),g)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),g))
| ( tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u)) = hAPP_pname_a(mgt_call,pn) ) ) )
| ~ is_a(tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u)))
| ~ is_a(hAPP_pname_a(mgt_call,pn)) )
<=> ( ~ ! [A_3: $i,B_1: $i,A_1: $i] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) )
| ~ is_a(A_3)
| ~ is_a(B_1) )
| ~ is_a(hAPP_pname_a(mgt_call,pn))
| ~ is_a(tptp_fun_X_1_70(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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),insert_a(hAPP_pname_a(mgt_call,pn),g)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),g))
| ( tptp_fun_X_1_70(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)],[96]) ).
tff(98,plain,
( ( ~ ! [A_3: $i,B_1: $i,A_1: $i] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) )
| ~ is_a(A_3)
| ~ is_a(B_1) )
| ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),insert_a(hAPP_pname_a(mgt_call,pn),g)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),g))
| ( tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u)) = hAPP_pname_a(mgt_call,pn) ) ) )
| ~ is_a(tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u)))
| ~ is_a(hAPP_pname_a(mgt_call,pn)) )
<=> ( ~ ! [A_3: $i,B_1: $i,A_1: $i] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) )
| ~ is_a(A_3)
| ~ is_a(B_1) )
| ~ is_a(hAPP_pname_a(mgt_call,pn))
| ~ is_a(tptp_fun_X_1_70(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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),insert_a(hAPP_pname_a(mgt_call,pn),g)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),g))
| ( tptp_fun_X_1_70(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)],[97,95]) ).
tff(99,plain,
( ~ ! [A_3: $i,B_1: $i,A_1: $i] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) )
| ~ is_a(A_3)
| ~ is_a(B_1) )
| ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),insert_a(hAPP_pname_a(mgt_call,pn),g)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),g))
| ( tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u)) = hAPP_pname_a(mgt_call,pn) ) ) )
| ~ is_a(tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u)))
| ~ is_a(hAPP_pname_a(mgt_call,pn)) ),
inference(quant_inst,[status(thm)],]) ).
tff(100,plain,
( ~ ! [A_3: $i,B_1: $i,A_1: $i] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
| ( A_3 = B_1 ) ) )
| ~ is_a(A_3)
| ~ is_a(B_1) )
| ~ is_a(hAPP_pname_a(mgt_call,pn))
| ~ is_a(tptp_fun_X_1_70(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_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),insert_a(hAPP_pname_a(mgt_call,pn),g)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,tptp_fun_X_1_70(insert_a(hAPP_pname_a(mgt_call,pn),g),image_pname_a(mgt_call,u))),g))
| ( tptp_fun_X_1_70(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)],[99,98]) ).
tff(101,plain,
$false,
inference(unit_resolution,[status(thm)],[100,94,81,64,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW473+2 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Sep 4 18:19:18 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.65/0.73 % SZS status Theorem
% 0.65/0.73 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------