TSTP Solution File: NUM415^1 by LEO-II---1.7.0

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%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : NUM415^1 : TPTP v8.1.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% 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  : 600s
% DateTime : Mon Jul 18 11:49:32 EDT 2022

% Result   : Theorem 27.25s 27.47s
% Output   : CNFRefutation 27.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   31
% Syntax   : Number of formulae    :   44 (  28 unt;  16 typ;  14 def)
%            Number of atoms       :   52 (  38 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :  428 (   3   ~;   0   |;   0   &; 425   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    1 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   99 (  99   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  16 usr;   3 con; 0-4 aty)
%            Number of variables   :   53 (  51   ^   2   !;   0   ?;  53   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_eight,type,
    eight: ( $i > $i ) > $i > $i ).

thf(tp_five,type,
    five: ( $i > $i ) > $i > $i ).

thf(tp_four,type,
    four: ( $i > $i ) > $i > $i ).

thf(tp_mult,type,
    mult: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).

thf(tp_nine,type,
    nine: ( $i > $i ) > $i > $i ).

thf(tp_one,type,
    one: ( $i > $i ) > $i > $i ).

thf(tp_plus,type,
    plus: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).

thf(tp_sK1_SV1,type,
    sK1_SV1: $i > $i ).

thf(tp_sK2_SV2,type,
    sK2_SV2: $i ).

thf(tp_seven,type,
    seven: ( $i > $i ) > $i > $i ).

thf(tp_six,type,
    six: ( $i > $i ) > $i > $i ).

thf(tp_succ,type,
    succ: ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).

thf(tp_ten,type,
    ten: ( $i > $i ) > $i > $i ).

thf(tp_three,type,
    three: ( $i > $i ) > $i > $i ).

thf(tp_two,type,
    two: ( $i > $i ) > $i > $i ).

thf(tp_zero,type,
    zero: ( $i > $i ) > $i > $i ).

thf(eight,definition,
    ( eight
    = ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',eight) ).

thf(five,definition,
    ( five
    = ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',five) ).

thf(four,definition,
    ( four
    = ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',four) ).

thf(mult,definition,
    ( mult
    = ( ^ [M: ( $i > $i ) > $i > $i,N: ( $i > $i ) > $i > $i,X: $i > $i,Y: $i] : ( M @ ( N @ X ) @ Y ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mult) ).

thf(nine,definition,
    ( nine
    = ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',nine) ).

thf(one,definition,
    ( one
    = ( ^ [X: $i > $i,Y: $i] : ( X @ Y ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',one) ).

thf(plus,definition,
    ( plus
    = ( ^ [M: ( $i > $i ) > $i > $i,N: ( $i > $i ) > $i > $i,X: $i > $i,Y: $i] : ( M @ X @ ( N @ X @ Y ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus) ).

thf(seven,definition,
    ( seven
    = ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',seven) ).

thf(six,definition,
    ( six
    = ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',six) ).

thf(succ,definition,
    ( succ
    = ( ^ [N: ( $i > $i ) > $i > $i,X: $i > $i,Y: $i] : ( X @ ( N @ X @ Y ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ) ).

thf(ten,definition,
    ( ten
    = ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ten) ).

thf(three,definition,
    ( three
    = ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ Y ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',three) ).

thf(two,definition,
    ( two
    = ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ Y ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',two) ).

thf(zero,definition,
    ( zero
    = ( ^ [X: $i > $i,Y: $i] : Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero) ).

thf(1,conjecture,
    ( ( mult @ two @ ( plus @ three @ seven ) )
    = ( mult @ ( mult @ two @ five ) @ ( plus @ one @ one ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).

thf(2,negated_conjecture,
    ( ( ( mult @ two @ ( plus @ three @ seven ) )
      = ( mult @ ( mult @ two @ five ) @ ( plus @ one @ one ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ( ( mult @ two @ ( plus @ three @ seven ) )
       != ( mult @ ( mult @ two @ five ) @ ( plus @ one @ one ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ( ( mult @ two @ ( plus @ three @ seven ) )
       != ( mult @ ( mult @ two @ five ) @ ( plus @ one @ one ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ( ( ^ [SX0: $i > $i,SX1: $i] : ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ SX1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( ^ [SX0: $i > $i,SX1: $i] : ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ SX1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4,eight,five,four,mult,nine,one,plus,seven,six,succ,ten,three,two,zero]) ).

thf(6,plain,
    ( ( ( ^ [SX0: $i > $i,SX1: $i] : ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ SX1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( ^ [SX0: $i > $i,SX1: $i] : ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ SX1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ! [SV1: $i > $i] :
          ( ( ^ [SY0: $i] : ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ SY0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          = ( ^ [SY1: $i] : ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ SY1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_equal_neg,[status(thm)],[6]) ).

thf(8,plain,
    ( ( ( ^ [SX0: $i > $i,SX1: $i] : ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ SX1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( ^ [SX0: $i > $i,SX1: $i] : ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ SX1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_equal_neg,[status(thm)],[6]) ).

thf(9,plain,
    ( ( ( ^ [SY2: $i] : ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ SY2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( ^ [SY3: $i] : ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ SY3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[7]) ).

thf(10,plain,
    ( ( ! [SV2: $i] :
          ( ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ SV2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          = ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ SV2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_equal_neg,[status(thm)],[9]) ).

thf(11,plain,
    ( ( ( ^ [SY2: $i] : ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ SY2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( ^ [SY3: $i] : ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ SY3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_equal_neg,[status(thm)],[9]) ).

thf(12,plain,
    ( ( ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ sK2_SV2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ sK2_SV2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[10]) ).

thf(13,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[8,12,11]) ).

thf(14,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : NUM415^1 : TPTP v8.1.0. Released v3.6.0.
% 0.04/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34  % Computer : n007.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  : 600
% 0.12/0.34  % DateTime : Thu Jul  7 05:04:59 EDT 2022
% 0.12/0.35  % CPUTime  : 
% 0.12/0.35  
% 0.12/0.35   No.of.Axioms: 0
% 0.12/0.35  
% 0.12/0.35   Length.of.Defs: 2009
% 0.12/0.35  
% 0.12/0.35   Contains.Choice.Funs: false
% 0.12/0.36  (rf:0,axioms:0,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)
% 27.25/27.47  ********************************
% 27.25/27.47  *   All subproblems solved!    *
% 27.25/27.47  ********************************
% 27.25/27.47  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:13,loop_count:0,foatp_calls:1,translation:fof_full)
% 27.25/27.47  
% 27.25/27.47  %**** Beginning of derivation protocol ****
% 27.25/27.47  % SZS output start CNFRefutation
% See solution above
% 27.25/27.47  
% 27.25/27.47  %**** End of derivation protocol ****
% 27.25/27.47  %**** no. of clauses in derivation: 14 ****
% 27.25/27.47  %**** clause counter: 13 ****
% 27.25/27.47  
% 27.25/27.47  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:13,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------