TSTP Solution File: SCT171+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SCT171+1 : TPTP v8.1.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n020.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 : Tue Sep 20 03:41:50 EDT 2022

% Result   : Theorem 0.20s 0.46s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   40 (   4 unt;  27 typ;   0 def)
%            Number of atoms       :   26 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   18 (   5   ~;   0   |;   0   &)
%                                         (  13 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   26 (  14   >;  12   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   2 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: $i > $o ).

tff(hAPP_f745298353l_bool_type,type,
    hAPP_f745298353l_bool: ( $i * $i ) > $i ).

tff(hAPP_f695124765t_bool_type,type,
    hAPP_f695124765t_bool: ( $i * $i ) > $i ).

tff(p_type,type,
    p: $i ).

tff(f_type,type,
    f: $i ).

tff(member1056080916le_alt_type,type,
    member1056080916le_alt: $i > $i ).

tff(produc171383831le_alt_type,type,
    produc171383831le_alt: ( $i * $i ) > $i ).

tff(d_type,type,
    d: $i ).

tff(c_type,type,
    c: $i ).

tff(cOMBS_867867294t_bool_type,type,
    cOMBS_867867294t_bool: ( $i * $i ) > $i ).

tff(cOMBC_1778077589t_bool_type,type,
    cOMBC_1778077589t_bool: ( $i * $i ) > $i ).

tff(e_type,type,
    e: $i ).

tff(cOMBB_1292070696e_indi_type,type,
    cOMBB_1292070696e_indi: ( $i * $i ) > $i ).

tff(arrow_2077223396_mkbot_type,type,
    arrow_2077223396_mkbot: $i ).

tff(cOMBS_102864562t_bool_type,type,
    cOMBS_102864562t_bool: ( $i * $i ) > $i ).

tff(cOMBC_493523632t_bool_type,type,
    cOMBC_493523632t_bool: ( $i * $i ) > $i ).

tff(cOMBB_69933763e_indi_type,type,
    cOMBB_69933763e_indi: ( $i * $i ) > $i ).

tff(arrow_812378712_above_type,type,
    arrow_812378712_above: $i ).

tff(cOMBB_963584201e_indi_type,type,
    cOMBB_963584201e_indi: ( $i * $i ) > $i ).

tff(cOMBC_277798809t_bool_type,type,
    cOMBC_277798809t_bool: ( $i * $i ) > $i ).

tff(n_type,type,
    n: $i ).

tff(cOMBB_317992461e_indi_type,type,
    cOMBB_317992461e_indi: ( $i * $i ) > $i ).

tff(h_type,type,
    h: $i ).

tff(fequal_nat_type,type,
    fequal_nat: $i ).

tff(if_fun1419651289t_bool_type,type,
    if_fun1419651289t_bool: $i ).

tff(arrow_78446834_mktop_type,type,
    arrow_78446834_mktop: $i ).

tff(ord_less_nat_type,type,
    ord_less_nat: $i ).

tff(1,plain,
    ( ~ $true
  <=> $false ),
    inference(rewrite,[status(thm)],]) ).

tff(2,plain,
    ( ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p)))
    <=> $true )
  <=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p))) ),
    inference(rewrite,[status(thm)],]) ).

tff(3,axiom,
    hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),n)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop,p),e)),cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat,h),n)),cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above,p),c),e)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot,p),e)))))),
    file('/export/starexec/sandbox/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(4,plain,
    ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),n)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop,p),e)),cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat,h),n)),cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above,p),c),e)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot,p),e))))))
  <=> $true ),
    inference(iff_true,[status(thm)],[3]) ).

tff(5,plain,
    ( ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p)))
    <=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),n)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop,p),e)),cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat,h),n)),cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above,p),c),e)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot,p),e)))))) )
  <=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p)))
    <=> $true ) ),
    inference(monotonicity,[status(thm)],[4]) ).

tff(6,plain,
    ( ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p)))
    <=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),n)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop,p),e)),cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat,h),n)),cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above,p),c),e)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot,p),e)))))) )
  <=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p))) ),
    inference(transitivity,[status(thm)],[5,2]) ).

tff(7,axiom,
    ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p)))
  <=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),n)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop,p),e)),cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat,h),n)),cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above,p),c),e)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot,p),e)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_PW) ).

tff(8,plain,
    hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p))),
    inference(modus_ponens,[status(thm)],[7,6]) ).

tff(9,plain,
    ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p)))
  <=> $true ),
    inference(iff_true,[status(thm)],[8]) ).

tff(10,plain,
    ( ~ hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p)))
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[9]) ).

tff(11,plain,
    ( ~ hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p)))
  <=> $false ),
    inference(transitivity,[status(thm)],[10,1]) ).

tff(12,axiom,
    ~ hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

tff(13,plain,
    $false,
    inference(modus_ponens,[status(thm)],[12,11]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SCT171+1 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n020.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sat Sep  3 00:47:44 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 0.20/0.46  % SZS status Theorem
% 0.20/0.46  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------