%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SCT171_1 : TPTP v9.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 : Sat Jun 21 05:24:36 AM UTC 2025
% Result : Theorem 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of formulae : 13 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 18 ( 7 ~; 3 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 21 ( 20 usr; 20 prp; 0-1 aty)
% Number of functors : 26 ( 26 usr; 13 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: bool > $o ).
tff(hAPP_f1944886577l_bool_type,type,
hAPP_f1944886577l_bool: ( fun_fu383145951l_bool * fun_Pr1639951081t_bool ) > bool ).
tff(hAPP_f718157575t_bool_type,type,
hAPP_f718157575t_bool: ( fun_fu50365883t_bool * fun_Ar2047178847t_bool ) > fun_Pr1639951081t_bool ).
tff(p_type,type,
p: fun_Ar2047178847t_bool ).
tff(f_type,type,
f: fun_fu50365883t_bool ).
tff(member1484933012le_alt_type,type,
member1484933012le_alt: produc624534567le_alt > fun_fu383145951l_bool ).
tff(produc170576535le_alt_type,type,
produc170576535le_alt: ( arrow_1621810872le_alt * arrow_1621810872le_alt ) > produc624534567le_alt ).
tff(d_type,type,
d: arrow_1621810872le_alt ).
tff(c_type,type,
c: arrow_1621810872le_alt ).
tff(cOMBS_1688227464t_bool_type,type,
cOMBS_1688227464t_bool: ( fun_Ar2040671475t_bool * fun_Ar2047178847t_bool ) > fun_Ar2047178847t_bool ).
tff(cOMBC_377836265t_bool_type,type,
cOMBC_377836265t_bool: ( fun_Ar1757019876t_bool * arrow_1621810872le_alt ) > fun_Ar2047178847t_bool ).
tff(e_type,type,
e: arrow_1621810872le_alt ).
tff(cOMBB_1932856316e_indi_type,type,
cOMBB_1932856316e_indi: ( fun_fu1760369922t_bool * fun_Ar2047178847t_bool ) > fun_Ar1757019876t_bool ).
tff(arrow_1126550734_mkbot_type,type,
arrow_1126550734_mkbot: fun_fu1760369922t_bool ).
tff(cOMBS_1833320732t_bool_type,type,
cOMBS_1833320732t_bool: ( fun_Ar2100459655t_bool * fun_Ar2047178847t_bool ) > fun_Ar2040671475t_bool ).
tff(cOMBC_1994570734t_bool_type,type,
cOMBC_1994570734t_bool: ( fun_Ar2079322857t_bool * arrow_1621810872le_alt ) > fun_Ar1757019876t_bool ).
tff(cOMBB_715840641e_indi_type,type,
cOMBB_715840641e_indi: ( fun_fu193278215t_bool * fun_Ar2047178847t_bool ) > fun_Ar2079322857t_bool ).
tff(arrow_2009189698_above_type,type,
arrow_2009189698_above: fun_fu193278215t_bool ).
tff(cOMBB_124649523e_indi_type,type,
cOMBB_124649523e_indi: ( fun_bo292969573t_bool * fun_Ar1871347069i_bool ) > fun_Ar2100459655t_bool ).
tff(cOMBC_998415407t_bool_type,type,
cOMBC_998415407t_bool: ( fun_Ar156616864t_bool * nat ) > fun_Ar1871347069i_bool ).
tff(n_type,type,
n: nat ).
tff(cOMBB_1514803447e_indi_type,type,
cOMBB_1514803447e_indi: ( fun_nat_fun_nat_bool * fun_Ar2035712896di_nat ) > fun_Ar156616864t_bool ).
tff(h_type,type,
h: fun_Ar2035712896di_nat ).
tff(fequal_nat_type,type,
fequal_nat: fun_nat_fun_nat_bool ).
tff(if_fun95824985t_bool_type,type,
if_fun95824985t_bool: fun_bo292969573t_bool ).
tff(arrow_1275257820_mktop_type,type,
arrow_1275257820_mktop: fun_fu1760369922t_bool ).
tff(ord_less_nat_type,type,
ord_less_nat: fun_nat_fun_nat_bool ).
tff(1,plain,
( ~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,p)))
<=> ~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,p))) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,p))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(3,plain,
~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,p))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(ord_less_nat,h),n)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1275257820_mktop,p),e)),cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(fequal_nat,h),n)),cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_2009189698_above,p),c),e)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1126550734_mkbot,p),e))))))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(ord_less_nat,h),n)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1275257820_mktop,p),e)),cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(fequal_nat,h),n)),cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_2009189698_above,p),c),e)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1126550734_mkbot,p),e)))))) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(ord_less_nat,h),n)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1275257820_mktop,p),e)),cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(fequal_nat,h),n)),cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_2009189698_above,p),c),e)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1126550734_mkbot,p),e)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).
tff(6,plain,
hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(ord_less_nat,h),n)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1275257820_mktop,p),e)),cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(fequal_nat,h),n)),cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_2009189698_above,p),c),e)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1126550734_mkbot,p),e)))))),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,p)))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(ord_less_nat,h),n)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1275257820_mktop,p),e)),cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(fequal_nat,h),n)),cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_2009189698_above,p),c),e)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1126550734_mkbot,p),e)))))) )
<=> ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,p)))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(ord_less_nat,h),n)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1275257820_mktop,p),e)),cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(fequal_nat,h),n)),cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_2009189698_above,p),c),e)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1126550734_mkbot,p),e)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,p)))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(ord_less_nat,h),n)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1275257820_mktop,p),e)),cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(fequal_nat,h),n)),cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_2009189698_above,p),c),e)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1126550734_mkbot,p),e)))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_PW) ).
tff(9,plain,
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,p)))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(ord_less_nat,h),n)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1275257820_mktop,p),e)),cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(fequal_nat,h),n)),cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_2009189698_above,p),c),e)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1126550734_mkbot,p),e)))))) ),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,p)))
| ~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(ord_less_nat,h),n)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1275257820_mktop,p),e)),cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(fequal_nat,h),n)),cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_2009189698_above,p),c),e)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1126550734_mkbot,p),e))))))
| ~ ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,p)))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(ord_less_nat,h),n)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1275257820_mktop,p),e)),cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(fequal_nat,h),n)),cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_2009189698_above,p),c),e)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1126550734_mkbot,p),e)))))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(11,plain,
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,p)))
| ~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(ord_less_nat,h),n)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1275257820_mktop,p),e)),cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(fequal_nat,h),n)),cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_2009189698_above,p),c),e)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1126550734_mkbot,p),e)))))) ),
inference(unit_resolution,[status(thm)],[10,9]) ).
tff(12,plain,
hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,p))),
inference(unit_resolution,[status(thm)],[11,6]) ).
tff(13,plain,
$false,
inference(unit_resolution,[status(thm)],[12,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SCT171_1 : TPTP v9.0.0. Released v5.3.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 03:58:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 % SZS output start Proof
% See solution above
% 0.19/0.48 % E exiting
%------------------------------------------------------------------------------