TSTP Solution File: SWW473+6 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW473+6 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 1.51s 1.29s
% Output : Proof 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 39
% Syntax : Number of formulae : 68 ( 18 unt; 15 typ; 0 def)
% Number of atoms : 224 ( 52 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 296 ( 136 ~; 99 |; 7 &)
% ( 43 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 8 >; 6 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-4 aty)
% Number of variables : 222 ( 198 !; 0 ?; 222 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i * $i * $i ) > $i ).
tff(u_type,type,
u: $i ).
tff(mgt_call_type,type,
mgt_call: $i ).
tff(image_type,type,
image: ( $i * $i ) > $i ).
tff(x_a_type,type,
x_a: $i ).
tff(pname_type,type,
pname: $i ).
tff(fun_type,type,
fun: ( $i * $i ) > $i ).
tff(bool_type,type,
bool: $i ).
tff(pn_type,type,
pn: $i ).
tff(member_type,type,
member: $i > $i ).
tff(g_type,type,
g: $i ).
tff(ord_less_eq_type,type,
ord_less_eq: $i > $i ).
tff(insert_type,type,
insert: $i > $i ).
tff(ti_type,type,
ti: ( $i * $i ) > $i ).
tff(1,plain,
^ [X_b: $i,X_1: $i,A_3: $i,B_2: $i] :
refl(
( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2))
<=> ~ ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ) )
<=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2))
<=> ~ ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X_b: $i,X_1: $i,A_3: $i,B_2: $i] :
( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2))
<=> ~ ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ) )
<=> ! [X_b: $i,X_1: $i,A_3: $i,B_2: $i] :
( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2))
<=> ~ ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X_b: $i,X_1: $i,A_3: $i,B_2: $i] :
rewrite(
( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2))
<=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
& hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ) )
<=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2))
<=> ~ ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [X_b: $i,X_1: $i,A_3: $i,B_2: $i] :
( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2))
<=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
& hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ) )
<=> ! [X_b: $i,X_1: $i,A_3: $i,B_2: $i] :
( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2))
<=> ~ ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X_b: $i,X_1: $i,A_3: $i,B_2: $i] :
( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2))
<=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
& hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ) )
<=> ! [X_b: $i,X_1: $i,A_3: $i,B_2: $i] :
( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2))
<=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
& hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
! [X_b: $i,X_1: $i,A_3: $i,B_2: $i] :
( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2))
<=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
& hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_insert__subset) ).
tff(7,plain,
! [X_b: $i,X_1: $i,A_3: $i,B_2: $i] :
( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2))
<=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
& hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X_b: $i,X_1: $i,A_3: $i,B_2: $i] :
( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2))
<=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
& hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ) ),
inference(skolemize,[status(sab)],[7]) ).
tff(9,plain,
! [X_b: $i,X_1: $i,A_3: $i,B_2: $i] :
( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2))
<=> ~ ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ) ),
inference(modus_ponens,[status(thm)],[8,4]) ).
tff(10,plain,
! [X_b: $i,X_1: $i,A_3: $i,B_2: $i] :
( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2))
<=> ~ ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ ! [X_b: $i,X_1: $i,A_3: $i,B_2: $i] :
( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2))
<=> ~ ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ) )
| ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
<=> ~ ( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
<=> ~ ( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) ) ),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
<=> ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6) ).
tff(15,plain,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
( ~ ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
<=> ~ ( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) ) )
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) ),
inference(tautology,[status(thm)],]) ).
tff(17,plain,
( ~ ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
<=> ~ ( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) ) )
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) ),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) ),
inference(unit_resolution,[status(thm)],[17,12]) ).
tff(19,plain,
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
<=> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) ),
inference(rewrite,[status(thm)],]) ).
tff(20,axiom,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(21,plain,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
( ~ ( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) )
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) ),
inference(tautology,[status(thm)],]) ).
tff(23,plain,
( ~ ( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) )
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) ),
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(unit_resolution,[status(thm)],[23,18]) ).
tff(25,plain,
^ [X_c: $i,X_a: $i,B_1_1: $i,B_2_1: $i] :
refl(
( ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) )
<=> ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [X_c: $i,X_a: $i,B_1_1: $i,B_2_1: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) )
<=> ! [X_c: $i,X_a: $i,B_1_1: $i,B_2_1: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [X_c: $i,X_a: $i,B_1_1: $i,B_2_1: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) )
<=> ! [X_c: $i,X_a: $i,B_1_1: $i,B_2_1: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,axiom,
! [X_c: $i,X_a: $i,B_1_1: $i,B_2_1: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
tff(29,plain,
! [X_c: $i,X_a: $i,B_1_1: $i,B_2_1: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [X_c: $i,X_a: $i,B_1_1: $i,B_2_1: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [X_c: $i,X_a: $i,B_1_1: $i,B_2_1: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
( ~ ! [X_c: $i,X_a: $i,B_1_1: $i,B_2_1: $i] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) )
| ( ti(x_a,hAPP(pname,x_a,mgt_call,pn)) = hAPP(pname,x_a,mgt_call,pn) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
ti(x_a,hAPP(pname,x_a,mgt_call,pn)) = hAPP(pname,x_a,mgt_call,pn),
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,plain,
( hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u))
<=> hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
tff(36,plain,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
^ [X_c: $i,X_b: $i,B: $i,F: $i,X_1: $i,A_3: $i] :
refl(
( ( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
| ( ti(X_c,B) != hAPP(X_b,X_c,F,X_1) ) )
<=> ( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
| ( ti(X_c,B) != hAPP(X_b,X_c,F,X_1) ) ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [X_c: $i,X_b: $i,B: $i,F: $i,X_1: $i,A_3: $i] :
( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
| ( ti(X_c,B) != hAPP(X_b,X_c,F,X_1) ) )
<=> ! [X_c: $i,X_b: $i,B: $i,F: $i,X_1: $i,A_3: $i] :
( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
| ( ti(X_c,B) != hAPP(X_b,X_c,F,X_1) ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [X_c: $i,X_b: $i,B: $i,F: $i,X_1: $i,A_3: $i] :
( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
| ( ti(X_c,B) != hAPP(X_b,X_c,F,X_1) ) )
<=> ! [X_c: $i,X_b: $i,B: $i,F: $i,X_1: $i,A_3: $i] :
( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
| ( ti(X_c,B) != hAPP(X_b,X_c,F,X_1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
^ [X_c: $i,X_b: $i,B: $i,F: $i,X_1: $i,A_3: $i] :
trans(
monotonicity(
rewrite(
( ( ( ti(X_c,B) = hAPP(X_b,X_c,F,X_1) )
=> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))) )
<=> ( ( ti(X_c,B) != hAPP(X_b,X_c,F,X_1) )
| hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))) ) )),
( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
=> ( ( ti(X_c,B) = hAPP(X_b,X_c,F,X_1) )
=> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))) ) )
<=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
=> ( ( ti(X_c,B) != hAPP(X_b,X_c,F,X_1) )
| hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))) ) ) )),
rewrite(
( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
=> ( ( ti(X_c,B) != hAPP(X_b,X_c,F,X_1) )
| hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))) ) )
<=> ( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
| ( ti(X_c,B) != hAPP(X_b,X_c,F,X_1) ) ) )),
( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
=> ( ( ti(X_c,B) = hAPP(X_b,X_c,F,X_1) )
=> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))) ) )
<=> ( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
| ( ti(X_c,B) != hAPP(X_b,X_c,F,X_1) ) ) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [X_c: $i,X_b: $i,B: $i,F: $i,X_1: $i,A_3: $i] :
( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
=> ( ( ti(X_c,B) = hAPP(X_b,X_c,F,X_1) )
=> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))) ) )
<=> ! [X_c: $i,X_b: $i,B: $i,F: $i,X_1: $i,A_3: $i] :
( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
| ( ti(X_c,B) != hAPP(X_b,X_c,F,X_1) ) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,axiom,
! [X_c: $i,X_b: $i,B: $i,F: $i,X_1: $i,A_3: $i] :
( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
=> ( ( ti(X_c,B) = hAPP(X_b,X_c,F,X_1) )
=> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_rev__image__eqI) ).
tff(43,plain,
! [X_c: $i,X_b: $i,B: $i,F: $i,X_1: $i,A_3: $i] :
( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
| ( ti(X_c,B) != hAPP(X_b,X_c,F,X_1) ) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [X_c: $i,X_b: $i,B: $i,F: $i,X_1: $i,A_3: $i] :
( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
| ( ti(X_c,B) != hAPP(X_b,X_c,F,X_1) ) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
! [X_c: $i,X_b: $i,B: $i,F: $i,X_1: $i,A_3: $i] :
( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
| ( ti(X_c,B) != hAPP(X_b,X_c,F,X_1) ) ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [X_c: $i,X_b: $i,B: $i,F: $i,X_1: $i,A_3: $i] :
( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
| ( ti(X_c,B) != hAPP(X_b,X_c,F,X_1) ) ),
inference(modus_ponens,[status(thm)],[45,38]) ).
tff(47,plain,
( ( ~ ! [X_c: $i,X_b: $i,B: $i,F: $i,X_1: $i,A_3: $i] :
( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
| ( ti(X_c,B) != hAPP(X_b,X_c,F,X_1) ) )
| ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ( ti(x_a,hAPP(pname,x_a,mgt_call,pn)) != hAPP(pname,x_a,mgt_call,pn) ) )
<=> ( ~ ! [X_c: $i,X_b: $i,B: $i,F: $i,X_1: $i,A_3: $i] :
( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
| ( ti(X_c,B) != hAPP(X_b,X_c,F,X_1) ) )
| ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ( ti(x_a,hAPP(pname,x_a,mgt_call,pn)) != hAPP(pname,x_a,mgt_call,pn) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
( ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u))
| ( ti(x_a,hAPP(pname,x_a,mgt_call,pn)) != hAPP(pname,x_a,mgt_call,pn) ) )
<=> ( ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ( ti(x_a,hAPP(pname,x_a,mgt_call,pn)) != hAPP(pname,x_a,mgt_call,pn) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ( ~ ! [X_c: $i,X_b: $i,B: $i,F: $i,X_1: $i,A_3: $i] :
( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
| ( ti(X_c,B) != hAPP(X_b,X_c,F,X_1) ) )
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u))
| ( ti(x_a,hAPP(pname,x_a,mgt_call,pn)) != hAPP(pname,x_a,mgt_call,pn) ) )
<=> ( ~ ! [X_c: $i,X_b: $i,B: $i,F: $i,X_1: $i,A_3: $i] :
( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
| ( ti(X_c,B) != hAPP(X_b,X_c,F,X_1) ) )
| ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ( ti(x_a,hAPP(pname,x_a,mgt_call,pn)) != hAPP(pname,x_a,mgt_call,pn) ) ) ),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
( ( ~ ! [X_c: $i,X_b: $i,B: $i,F: $i,X_1: $i,A_3: $i] :
( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
| ( ti(X_c,B) != hAPP(X_b,X_c,F,X_1) ) )
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u))
| ( ti(x_a,hAPP(pname,x_a,mgt_call,pn)) != hAPP(pname,x_a,mgt_call,pn) ) )
<=> ( ~ ! [X_c: $i,X_b: $i,B: $i,F: $i,X_1: $i,A_3: $i] :
( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
| ( ti(X_c,B) != hAPP(X_b,X_c,F,X_1) ) )
| ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ( ti(x_a,hAPP(pname,x_a,mgt_call,pn)) != hAPP(pname,x_a,mgt_call,pn) ) ) ),
inference(transitivity,[status(thm)],[49,47]) ).
tff(51,plain,
( ~ ! [X_c: $i,X_b: $i,B: $i,F: $i,X_1: $i,A_3: $i] :
( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
| ( ti(X_c,B) != hAPP(X_b,X_c,F,X_1) ) )
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u))
| ( ti(x_a,hAPP(pname,x_a,mgt_call,pn)) != hAPP(pname,x_a,mgt_call,pn) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
( ~ ! [X_c: $i,X_b: $i,B: $i,F: $i,X_1: $i,A_3: $i] :
( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
| ( ti(X_c,B) != hAPP(X_b,X_c,F,X_1) ) )
| ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ( ti(x_a,hAPP(pname,x_a,mgt_call,pn)) != hAPP(pname,x_a,mgt_call,pn) ) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
$false,
inference(unit_resolution,[status(thm)],[52,46,36,33,24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW473+6 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Sep 4 18:18:49 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 1.51/1.29 % SZS status Theorem
% 1.51/1.29 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------