TSTP Solution File: SWW473_3 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWW473_3 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n007.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 : Fri Sep 1 00:39:22 EDT 2023
% Result : Theorem 28.58s 4.75s
% Output : CNFRefutation 28.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 97 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 528 ( 44 equ)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 161 ( 68 ~; 63 |; 13 &)
% ( 12 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 338 ( 338 fml; 0 var)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 37 ( 35 usr; 20 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 136 ( 7 sgn; 89 !; 3 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
tff(f379,axiom,
! [X8: x_a,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X2))
<=> hBOOL(hAPP_a_bool(X2,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_378_mem__def) ).
tff(f380,axiom,
! [X8: pname,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X2))
<=> hBOOL(hAPP_pname_bool(X2,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_379_mem__def) ).
tff(f382,axiom,
! [X10: fun_nat_bool] : ( collect_nat(X10) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_381_Collect__def) ).
tff(f437,axiom,
! [X28: x_a,X6: fun_pname_a,X8: pname,X2: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X2))
=> ( ( hAPP_pname_a(X6,X8) = X28 )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X28),image_pname_a(X6,X2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_436_rev__image__eqI) ).
tff(f454,axiom,
! [X8: x_a,X2: fun_a_bool,X7: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X2)),X7))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X7))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_453_insert__subset) ).
tff(f523,axiom,
! [X10: fun_nat_bool] :
( ( collect_nat(X10) = bot_bot_fun_nat_bool )
<=> ! [X27: nat] : ~ hBOOL(hAPP_nat_bool(X10,X27)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_522_empty__Collect__eq) ).
tff(f536,axiom,
! [X8: nat] :
( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X8))
<=> hBOOL(bot_bot_bool) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_535_bot__apply) ).
tff(f540,axiom,
bot_bot_fun_nat_bool = collect_nat(cOMBK_bool_nat(fFalse)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_539_empty__def) ).
tff(f542,axiom,
! [X27: nat] :
( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X27))
<=> hBOOL(bot_bot_bool) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_541_bot__fun__def) ).
tff(f1230,axiom,
! [X156: bool,X157: nat] : ( hAPP_nat_bool(cOMBK_bool_nat(X156),X157) = X156 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U) ).
tff(f1304,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(f1307,axiom,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
tff(f1309,conjecture,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).
tff(f1310,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
inference(negated_conjecture,[],[f1309]) ).
tff(f1688,plain,
! [X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
<=> hBOOL(hAPP_a_bool(X1,X0)) ),
inference(rectify,[],[f379]) ).
tff(f1689,plain,
! [X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
<=> hBOOL(hAPP_pname_bool(X1,X0)) ),
inference(rectify,[],[f380]) ).
tff(f1691,plain,
! [X0: fun_nat_bool] : ( collect_nat(X0) = X0 ),
inference(rectify,[],[f382]) ).
tff(f1746,plain,
! [X0: x_a,X1: fun_pname_a,X2: pname,X3: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
=> ( ( hAPP_pname_a(X1,X2) = X0 )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X3))) ) ),
inference(rectify,[],[f437]) ).
tff(f1763,plain,
! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ) ),
inference(rectify,[],[f454]) ).
tff(f1828,plain,
! [X0: fun_nat_bool] :
( ( bot_bot_fun_nat_bool = collect_nat(X0) )
<=> ! [X1: nat] : ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
inference(rectify,[],[f523]) ).
tff(f1841,plain,
! [X0: nat] :
( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X0))
<=> hBOOL(bot_bot_bool) ),
inference(rectify,[],[f536]) ).
tff(f1844,plain,
! [X0: nat] :
( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X0))
<=> hBOOL(bot_bot_bool) ),
inference(rectify,[],[f542]) ).
tff(f2502,plain,
! [X0: bool,X1: nat] : ( hAPP_nat_bool(cOMBK_bool_nat(X0),X1) = X0 ),
inference(rectify,[],[f1230]) ).
tff(f2575,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
inference(flattening,[],[f1310]) ).
tff(f3159,plain,
! [X0: x_a,X1: fun_pname_a,X2: pname,X3: fun_pname_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X3)))
| ( hAPP_pname_a(X1,X2) != X0 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3)) ),
inference(ennf_transformation,[],[f1746]) ).
tff(f3160,plain,
! [X0: x_a,X1: fun_pname_a,X2: pname,X3: fun_pname_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X3)))
| ( hAPP_pname_a(X1,X2) != X0 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3)) ),
inference(flattening,[],[f3159]) ).
tff(f3872,plain,
! [X0: x_a,X1: fun_a_bool] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ hBOOL(hAPP_a_bool(X1,X0)) )
& ( hBOOL(hAPP_a_bool(X1,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ) ),
inference(nnf_transformation,[],[f1688]) ).
tff(f3873,plain,
! [X0: pname,X1: fun_pname_bool] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_pname_bool(X1,X0)) )
& ( hBOOL(hAPP_pname_bool(X1,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ) ),
inference(nnf_transformation,[],[f1689]) ).
tff(f3914,plain,
! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
& ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2)) ) ),
inference(nnf_transformation,[],[f1763]) ).
tff(f3915,plain,
! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
& ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2)) ) ),
inference(flattening,[],[f3914]) ).
tff(f3981,plain,
! [X0: fun_nat_bool] :
( ( ( bot_bot_fun_nat_bool = collect_nat(X0) )
| ? [X1: nat] : hBOOL(hAPP_nat_bool(X0,X1)) )
& ( ! [X1: nat] : ~ hBOOL(hAPP_nat_bool(X0,X1))
| ( bot_bot_fun_nat_bool != collect_nat(X0) ) ) ),
inference(nnf_transformation,[],[f1828]) ).
tff(f3982,plain,
! [X0: fun_nat_bool] :
( ( ( bot_bot_fun_nat_bool = collect_nat(X0) )
| ? [X1: nat] : hBOOL(hAPP_nat_bool(X0,X1)) )
& ( ! [X2: nat] : ~ hBOOL(hAPP_nat_bool(X0,X2))
| ( bot_bot_fun_nat_bool != collect_nat(X0) ) ) ),
inference(rectify,[],[f3981]) ).
tff(f3983,plain,
! [X0: fun_nat_bool] :
( ? [X1: nat] : hBOOL(hAPP_nat_bool(X0,X1))
=> hBOOL(hAPP_nat_bool(X0,sK95(X0))) ),
introduced(choice_axiom,[]) ).
tff(f3984,plain,
! [X0: fun_nat_bool] :
( ( ( bot_bot_fun_nat_bool = collect_nat(X0) )
| hBOOL(hAPP_nat_bool(X0,sK95(X0))) )
& ( ! [X2: nat] : ~ hBOOL(hAPP_nat_bool(X0,X2))
| ( bot_bot_fun_nat_bool != collect_nat(X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK95])],[f3982,f3983]) ).
tff(f4021,plain,
! [X0: nat] :
( ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X0))
| ~ hBOOL(bot_bot_bool) )
& ( hBOOL(bot_bot_bool)
| ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X0)) ) ),
inference(nnf_transformation,[],[f1841]) ).
tff(f4024,plain,
! [X0: nat] :
( ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X0))
| ~ hBOOL(bot_bot_bool) )
& ( hBOOL(bot_bot_bool)
| ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X0)) ) ),
inference(nnf_transformation,[],[f1844]) ).
tff(f4994,plain,
! [X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_a_bool(X1,X0))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ),
inference(cnf_transformation,[],[f3872]) ).
tff(f4995,plain,
! [X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
| ~ hBOOL(hAPP_a_bool(X1,X0)) ),
inference(cnf_transformation,[],[f3872]) ).
tff(f4996,plain,
! [X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_pname_bool(X1,X0))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ),
inference(cnf_transformation,[],[f3873]) ).
tff(f4997,plain,
! [X0: pname,X1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
| ~ hBOOL(hAPP_pname_bool(X1,X0)) ),
inference(cnf_transformation,[],[f3873]) ).
tff(f4999,plain,
! [X0: fun_nat_bool] : ( collect_nat(X0) = X0 ),
inference(cnf_transformation,[],[f1691]) ).
tff(f5081,plain,
! [X2: pname,X3: fun_pname_bool,X0: x_a,X1: fun_pname_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X3)))
| ( hAPP_pname_a(X1,X2) != X0 )
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3)) ),
inference(cnf_transformation,[],[f3160]) ).
tff(f5103,plain,
! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ),
inference(cnf_transformation,[],[f3915]) ).
tff(f5203,plain,
! [X2: nat,X0: fun_nat_bool] :
( ~ hBOOL(hAPP_nat_bool(X0,X2))
| ( bot_bot_fun_nat_bool != collect_nat(X0) ) ),
inference(cnf_transformation,[],[f3984]) ).
tff(f5204,plain,
! [X0: fun_nat_bool] :
( ( bot_bot_fun_nat_bool = collect_nat(X0) )
| hBOOL(hAPP_nat_bool(X0,sK95(X0))) ),
inference(cnf_transformation,[],[f3984]) ).
tff(f5227,plain,
! [X0: nat] :
( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X0))
| ~ hBOOL(bot_bot_bool) ),
inference(cnf_transformation,[],[f4021]) ).
tff(f5233,plain,
bot_bot_fun_nat_bool = collect_nat(cOMBK_bool_nat(fFalse)),
inference(cnf_transformation,[],[f540]) ).
tff(f5236,plain,
! [X0: nat] :
( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X0))
| ~ hBOOL(bot_bot_bool) ),
inference(cnf_transformation,[],[f4024]) ).
tff(f6353,plain,
! [X0: bool,X1: nat] : ( hAPP_nat_bool(cOMBK_bool_nat(X0),X1) = X0 ),
inference(cnf_transformation,[],[f2502]) ).
tff(f6427,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
inference(cnf_transformation,[],[f1304]) ).
tff(f6430,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(cnf_transformation,[],[f1307]) ).
tff(f6432,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
inference(cnf_transformation,[],[f2575]) ).
tff(f6652,plain,
! [X2: pname,X3: fun_pname_bool,X1: fun_pname_a] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X1,X2)),image_pname_a(X1,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3)) ),
inference(equality_resolution,[],[f5081]) ).
cnf(c_571,plain,
( ~ hBOOL(hAPP_a_bool(X0_22,X0_13))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),X0_22)) ),
inference(cnf_transformation,[],[f4995]) ).
cnf(c_572,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),X0_22))
| hBOOL(hAPP_a_bool(X0_22,X0_13)) ),
inference(cnf_transformation,[],[f4994]) ).
cnf(c_573,plain,
( ~ hBOOL(hAPP_pname_bool(X0_35,X0_15))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0_15),X0_35)) ),
inference(cnf_transformation,[],[f4997]) ).
cnf(c_574,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0_15),X0_35))
| hBOOL(hAPP_pname_bool(X0_35,X0_15)) ),
inference(cnf_transformation,[],[f4996]) ).
cnf(c_576,plain,
collect_nat(X0_65) = X0_65,
inference(cnf_transformation,[],[f4999]) ).
cnf(c_658,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0_15),X0_35))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0_33,X0_15)),image_pname_a(X0_33,X0_35))) ),
inference(cnf_transformation,[],[f6652]) ).
cnf(c_678,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),X0_22))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1_22),X0_22))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0_13),X1_22)),X0_22)) ),
inference(cnf_transformation,[],[f5103]) ).
cnf(c_780,plain,
( collect_nat(X0_65) = bot_bot_fun_nat_bool
| hBOOL(hAPP_nat_bool(X0_65,sK95(X0_65))) ),
inference(cnf_transformation,[],[f5204]) ).
cnf(c_781,plain,
( collect_nat(X0_65) != bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_nat_bool(X0_65,X0_18)) ),
inference(cnf_transformation,[],[f5203]) ).
cnf(c_803,plain,
( ~ hBOOL(bot_bot_bool)
| hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X0_18)) ),
inference(cnf_transformation,[],[f5227]) ).
cnf(c_810,plain,
collect_nat(cOMBK_bool_nat(fFalse)) = bot_bot_fun_nat_bool,
inference(cnf_transformation,[],[f5233]) ).
cnf(c_812,plain,
( ~ hBOOL(bot_bot_bool)
| hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X0_18)) ),
inference(cnf_transformation,[],[f5236]) ).
cnf(c_1892,plain,
hAPP_nat_bool(cOMBK_bool_nat(X0_16),X0_18) = X0_16,
inference(cnf_transformation,[],[f6353]) ).
cnf(c_1966,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
inference(cnf_transformation,[],[f6427]) ).
cnf(c_1969,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(cnf_transformation,[],[f6430]) ).
cnf(c_1971,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
inference(cnf_transformation,[],[f6432]) ).
cnf(c_1972,plain,
collect_nat(bot_bot_fun_nat_bool) = bot_bot_fun_nat_bool,
inference(instantiation,[status(thm)],[c_576]) ).
cnf(c_2004,plain,
( ~ hBOOL(bot_bot_bool)
| hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,zero_zero_nat)) ),
inference(instantiation,[status(thm)],[c_812]) ).
cnf(c_2108,plain,
( collect_nat(bot_bot_fun_nat_bool) != bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,zero_zero_nat)) ),
inference(instantiation,[status(thm)],[c_781]) ).
cnf(c_2899,plain,
~ hBOOL(bot_bot_bool),
inference(global_subsumption_just,[status(thm)],[c_803,c_1972,c_2004,c_2108]) ).
cnf(c_3002,plain,
( ~ hBOOL(hAPP_a_bool(X0_22,X0_13))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),X0_22)) ),
inference(prop_impl_just,[status(thm)],[c_571]) ).
cnf(c_3668,plain,
( ~ hBOOL(hAPP_pname_bool(X0_35,X0_15))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0_33,X0_15)),image_pname_a(X0_33,X0_35))) ),
inference(prop_impl_just,[status(thm)],[c_573,c_658]) ).
cnf(c_3764,plain,
( collect_nat(X0_65) = bot_bot_fun_nat_bool
| hBOOL(hAPP_nat_bool(X0_65,sK95(X0_65))) ),
inference(prop_impl_just,[status(thm)],[c_780]) ).
cnf(c_6863,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_22),X1_22))
| ~ hBOOL(hAPP_a_bool(X1_22,X0_13))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0_13),X0_22)),X1_22)) ),
inference(bin_hyper_res,[status(thm)],[c_678,c_3002]) ).
cnf(c_14138,plain,
cOMBK_bool_nat(fFalse) = bot_bot_fun_nat_bool,
inference(demodulation,[status(thm)],[c_810,c_576]) ).
cnf(c_14235,plain,
( X0_65 = bot_bot_fun_nat_bool
| hBOOL(hAPP_nat_bool(X0_65,sK95(X0_65))) ),
inference(light_normalisation,[status(thm)],[c_3764,c_576]) ).
cnf(c_39220,plain,
( ~ hBOOL(hAPP_pname_bool(X0_35,X0_15))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0_33,X0_15)),image_pname_a(X0_33,X0_35))) ),
inference(prop_impl_just,[status(thm)],[c_3668]) ).
cnf(c_39708,plain,
( hBOOL(hAPP_nat_bool(X0_65,sK95(X0_65)))
| X0_65 = bot_bot_fun_nat_bool ),
inference(prop_impl_just,[status(thm)],[c_14235]) ).
cnf(c_39709,plain,
( X0_65 = bot_bot_fun_nat_bool
| hBOOL(hAPP_nat_bool(X0_65,sK95(X0_65))) ),
inference(renaming,[status(thm)],[c_39708]) ).
cnf(c_68686,plain,
( ~ hBOOL(hAPP_a_bool(image_pname_a(mgt_call,u),hAPP_pname_a(mgt_call,pn)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))) ),
inference(superposition,[status(thm)],[c_6863,c_1971]) ).
cnf(c_68693,plain,
~ hBOOL(hAPP_a_bool(image_pname_a(mgt_call,u),hAPP_pname_a(mgt_call,pn))),
inference(global_subsumption_just,[status(thm)],[c_68686,c_1966,c_68686]) ).
cnf(c_68713,plain,
hAPP_nat_bool(bot_bot_fun_nat_bool,X0_18) = fFalse,
inference(superposition,[status(thm)],[c_14138,c_1892]) ).
cnf(c_69617,plain,
( cOMBK_bool_nat(X0_16) = bot_bot_fun_nat_bool
| hBOOL(X0_16) ),
inference(superposition,[status(thm)],[c_1892,c_39709]) ).
cnf(c_69641,plain,
cOMBK_bool_nat(bot_bot_bool) = bot_bot_fun_nat_bool,
inference(superposition,[status(thm)],[c_69617,c_2899]) ).
cnf(c_69657,plain,
cOMBK_bool_nat(hAPP_a_bool(image_pname_a(mgt_call,u),hAPP_pname_a(mgt_call,pn))) = bot_bot_fun_nat_bool,
inference(superposition,[status(thm)],[c_69617,c_68693]) ).
cnf(c_69703,plain,
hAPP_a_bool(image_pname_a(mgt_call,u),hAPP_pname_a(mgt_call,pn)) = hAPP_nat_bool(bot_bot_fun_nat_bool,X0_18),
inference(superposition,[status(thm)],[c_69657,c_1892]) ).
cnf(c_69704,plain,
hAPP_a_bool(image_pname_a(mgt_call,u),hAPP_pname_a(mgt_call,pn)) = fFalse,
inference(light_normalisation,[status(thm)],[c_69703,c_68713]) ).
cnf(c_69746,plain,
hAPP_nat_bool(bot_bot_fun_nat_bool,X0_18) = bot_bot_bool,
inference(superposition,[status(thm)],[c_69641,c_1892]) ).
cnf(c_69747,plain,
bot_bot_bool = fFalse,
inference(demodulation,[status(thm)],[c_68713,c_69746]) ).
cnf(c_69843,plain,
hAPP_a_bool(image_pname_a(mgt_call,u),hAPP_pname_a(mgt_call,pn)) = bot_bot_bool,
inference(light_normalisation,[status(thm)],[c_69704,c_69747]) ).
cnf(c_72333,plain,
( ~ hBOOL(hAPP_pname_bool(X0_35,X0_15))
| hBOOL(hAPP_a_bool(image_pname_a(X0_33,X0_35),hAPP_pname_a(X0_33,X0_15))) ),
inference(superposition,[status(thm)],[c_39220,c_572]) ).
cnf(c_72384,plain,
hBOOL(hAPP_pname_bool(u,pn)),
inference(superposition,[status(thm)],[c_1969,c_574]) ).
cnf(c_91322,plain,
( ~ hBOOL(hAPP_pname_bool(u,pn))
| hBOOL(bot_bot_bool) ),
inference(superposition,[status(thm)],[c_69843,c_72333]) ).
cnf(c_91329,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_91322,c_2899,c_72384]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWW473_3 : TPTP v8.1.2. Released v5.3.0.
% 0.08/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 19:36:27 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 28.58/4.75 % SZS status Started for theBenchmark.p
% 28.58/4.75 % SZS status Theorem for theBenchmark.p
% 28.58/4.75
% 28.58/4.75 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 28.58/4.75
% 28.58/4.75 ------ iProver source info
% 28.58/4.75
% 28.58/4.75 git: date: 2023-05-31 18:12:56 +0000
% 28.58/4.75 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 28.58/4.75 git: non_committed_changes: false
% 28.58/4.75 git: last_make_outside_of_git: false
% 28.58/4.75
% 28.58/4.75 ------ Parsing...
% 28.58/4.75 ------ Clausification by vclausify_rel & Parsing by iProver...------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 28.58/4.75
% 28.58/4.75
% 28.58/4.75 ------ Preprocessing... sup_sim: 339 pe_s pe:1:0s pe:2:0s pe_e sup_sim: 1 pe_s pe_e sup_sim: 0 pe_s pe_e
% 28.58/4.75
% 28.58/4.75 ------ Preprocessing...------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 28.58/4.75 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 28.58/4.75
% 28.58/4.75
% 28.58/4.75 ------ Preprocessing...
% 28.58/4.75 ------ Proving...
% 28.58/4.75 ------ Problem Properties
% 28.58/4.75
% 28.58/4.75
% 28.58/4.75 clauses 1398
% 28.58/4.75 conjectures 1
% 28.58/4.75 EPR 4
% 28.58/4.75 Horn 1062
% 28.58/4.75 unary 285
% 28.58/4.75 binary 501
% 28.58/4.75 lits 3409
% 28.58/4.75 lits eq 725
% 28.58/4.75 fd_pure 1
% 28.58/4.75 fd_pseudo 0
% 28.58/4.75 fd_cond 86
% 28.58/4.75 fd_pseudo_cond 78
% 28.58/4.75 AC symbols 0
% 28.58/4.75
% 28.58/4.75 ------ Schedule dynamic 5 is on
% 28.58/4.75
% 28.58/4.75 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 28.58/4.75
% 28.58/4.75
% 28.58/4.75 ------
% 28.58/4.75 Current options:
% 28.58/4.75 ------
% 28.58/4.75
% 28.58/4.75
% 28.58/4.75
% 28.58/4.75
% 28.58/4.75 ------ Proving...
% 28.58/4.75
% 28.58/4.75
% 28.58/4.75 % SZS status Theorem for theBenchmark.p
% 28.58/4.75
% 28.58/4.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 28.58/4.75
% 28.58/4.75
%------------------------------------------------------------------------------