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Leo-III---1.8.0.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : NUM436+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 08:08:50 AM UTC 2026

% Result   : Theorem 121.50s 49.57s
% Output   : Refutation 121.81s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   57 (  16 unt;   0 typ;   1 def)
%            Number of atoms       :  184 (  56 equ;   0 cnn)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  676 (  83   ~;  66   |;  50   &; 475   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  14 usr;  10 con; 0-3 aty)
%            Number of variables   :   36 (   0   ^;  27   !;   8   ?;  36   :)
%                                         (   0  !>;   0  ?*;   0  @-;   1  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(aInteger0_decl,type,
    aInteger0: $i > $o ).

thf(aDivisorOf0_decl,type,
    aDivisorOf0: $i > $i > $o ).

thf(sz00_decl,type,
    sz00: $i ).

thf(sdtasdt0_decl,type,
    sdtasdt0: $i > $i > $i ).

thf(sdteqdtlpzmzozddtrp0_decl,type,
    sdteqdtlpzmzozddtrp0: $i > $i > $i > $o ).

thf(sdtpldt0_decl,type,
    sdtpldt0: $i > $i > $i ).

thf(smndt0_decl,type,
    smndt0: $i > $i ).

thf(xp_decl,type,
    xp: $i ).

thf(xa_decl,type,
    xa: $i ).

thf(xb_decl,type,
    xb: $i ).

thf(xq_decl,type,
    xq: $i ).

thf(xm_decl,type,
    xm: $i ).

thf(sk1_decl,type,
    sk1: $o ).

thf(sk3_decl,type,
    sk3: $i ).

thf(sk3_def,definition,
    ( sk3
    = ( @+[A: $i] :
          ( ( ( A @ ( xq @ ( xp @ sdtasdt0 ) @ sdtasdt0 ) )
            = ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
          & ( A @ aInteger0 ) ) ) ) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ aInteger0 )
        & ( A @ aInteger0 ) )
     => ( B @ ( A @ sdtasdt0 ) @ aInteger0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).

thf(46,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ aInteger0 )
        & ( A @ aInteger0 ) )
     => ( B @ ( A @ sdtasdt0 ) @ aInteger0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(47,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ sdtasdt0 ) @ aInteger0 )
      | ~ ( B @ aInteger0 )
      | ~ ( A @ aInteger0 ) ),
    inference(cnf,[status(esa)],[46]) ).

thf(11,axiom,
    ( ( xq @ ( xp @ sdtasdt0 ) @ ( xb @ ( xa @ sdteqdtlpzmzozddtrp0 ) ) )
    & ( xb @ smndt0 @ ( xa @ sdtpldt0 ) @ ( xq @ ( xp @ sdtasdt0 ) @ aDivisorOf0 ) )
    & ? [A: $i] :
        ( ( ( A @ ( xq @ ( xp @ sdtasdt0 ) @ sdtasdt0 ) )
          = ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
        & ( A @ aInteger0 ) )
    & ( ( xq @ ( xp @ sdtasdt0 ) )
     != sz00 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1003) ).

thf(78,plain,
    ( ( xq @ ( xp @ sdtasdt0 ) @ ( xb @ ( xa @ sdteqdtlpzmzozddtrp0 ) ) )
    & ( xb @ smndt0 @ ( xa @ sdtpldt0 ) @ ( xq @ ( xp @ sdtasdt0 ) @ aDivisorOf0 ) )
    & ? [A: $i] :
        ( ( ( A @ ( xq @ ( xp @ sdtasdt0 ) @ sdtasdt0 ) )
          = ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
        & ( A @ aInteger0 ) )
    & ( ( xq @ ( xp @ sdtasdt0 ) )
     != sz00 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(79,plain,
    ( ( xq @ ( xp @ sdtasdt0 ) @ ( xb @ ( xa @ sdteqdtlpzmzozddtrp0 ) ) )
    & ( xb @ smndt0 @ ( xa @ sdtpldt0 ) @ ( xq @ ( xp @ sdtasdt0 ) @ aDivisorOf0 ) )
    & ( ( sk3 @ ( xq @ ( xp @ sdtasdt0 ) @ sdtasdt0 ) )
      = ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
    & ( sk3 @ aInteger0 )
    & ( ( xq @ ( xp @ sdtasdt0 ) )
     != sz00 ) ),
    inference(cnf,[status(esa)],[78]) ).

thf(84,plain,
    ( ( sk3 @ ( xq @ ( xp @ sdtasdt0 ) @ sdtasdt0 ) )
    = ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) ),
    inference(cnfConj,[status(thm)],[79]) ).

thf(85,plain,
    ( ( xb @ smndt0 @ ( xa @ sdtpldt0 ) )
    = ( sk3 @ ( xq @ ( xp @ sdtasdt0 ) @ sdtasdt0 ) ) ),
    inference(lifteq,[status(thm)],[84]) ).

thf(13,axiom,
    ( ( ( xb @ smndt0 @ ( xa @ sdtpldt0 ) )
      = ( xm @ ( xp @ sdtasdt0 ) @ ( xq @ sdtasdt0 ) ) )
    & ( ( xm @ ( xq @ sdtasdt0 ) @ ( xp @ sdtasdt0 ) )
      = ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1071) ).

thf(93,plain,
    ( ( ( xb @ smndt0 @ ( xa @ sdtpldt0 ) )
      = ( xm @ ( xp @ sdtasdt0 ) @ ( xq @ sdtasdt0 ) ) )
    & ( ( xm @ ( xq @ sdtasdt0 ) @ ( xp @ sdtasdt0 ) )
      = ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(94,plain,
    ( ( ( xb @ smndt0 @ ( xa @ sdtpldt0 ) )
      = ( xm @ ( xp @ sdtasdt0 ) @ ( xq @ sdtasdt0 ) ) )
    & ( ( xm @ ( xq @ sdtasdt0 ) @ ( xp @ sdtasdt0 ) )
      = ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) ) ),
    inference(cnf,[status(esa)],[93]) ).

thf(95,plain,
    ( ( xm @ ( xq @ sdtasdt0 ) @ ( xp @ sdtasdt0 ) )
    = ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) ),
    inference(cnfConj,[status(thm)],[94]) ).

thf(97,plain,
    ( ( xb @ smndt0 @ ( xa @ sdtpldt0 ) )
    = ( xm @ ( xq @ sdtasdt0 ) @ ( xp @ sdtasdt0 ) ) ),
    inference(lifteq,[status(thm)],[95]) ).

thf(280,plain,
    ( ( sk3 @ ( xq @ ( xp @ sdtasdt0 ) @ sdtasdt0 ) )
    = ( xm @ ( xq @ sdtasdt0 ) @ ( xp @ sdtasdt0 ) ) ),
    inference(rewrite,[status(thm)],[97,85]) ).

thf(281,plain,
    ( ( xb @ smndt0 @ ( xa @ sdtpldt0 ) )
    = ( xm @ ( xq @ sdtasdt0 ) @ ( xp @ sdtasdt0 ) ) ),
    inference(rewrite,[status(thm)],[85,280]) ).

thf(96,plain,
    ( ( xb @ smndt0 @ ( xa @ sdtpldt0 ) )
    = ( xm @ ( xp @ sdtasdt0 ) @ ( xq @ sdtasdt0 ) ) ),
    inference(cnfConj,[status(thm)],[94]) ).

thf(98,plain,
    ( ( xb @ smndt0 @ ( xa @ sdtpldt0 ) )
    = ( xm @ ( xp @ sdtasdt0 ) @ ( xq @ sdtasdt0 ) ) ),
    inference(lifteq,[status(thm)],[96]) ).

thf(2551,plain,
    ( ( xm @ ( xp @ sdtasdt0 ) @ ( xq @ sdtasdt0 ) )
    = ( xm @ ( xq @ sdtasdt0 ) @ ( xp @ sdtasdt0 ) ) ),
    inference(rewrite,[status(thm)],[281,98]) ).

thf(1,conjecture,
    ( ( ( xq @ ( xb @ ( xa @ sdteqdtlpzmzozddtrp0 ) ) )
      | ( xb @ smndt0 @ ( xa @ sdtpldt0 ) @ ( xq @ aDivisorOf0 ) )
      | ? [A: $i] :
          ( ( ( A @ ( xq @ sdtasdt0 ) )
            = ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
          & ( A @ aInteger0 ) ) )
    & ( ( xp @ ( xb @ ( xa @ sdteqdtlpzmzozddtrp0 ) ) )
      | ( xb @ smndt0 @ ( xa @ sdtpldt0 ) @ ( xp @ aDivisorOf0 ) )
      | ? [A: $i] :
          ( ( ( A @ ( xp @ sdtasdt0 ) )
            = ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
          & ( A @ aInteger0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

thf(2,negated_conjecture,
    ~ ( ( ( xq @ ( xb @ ( xa @ sdteqdtlpzmzozddtrp0 ) ) )
        | ( xb @ smndt0 @ ( xa @ sdtpldt0 ) @ ( xq @ aDivisorOf0 ) )
        | ? [A: $i] :
            ( ( ( A @ ( xq @ sdtasdt0 ) )
              = ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
            & ( A @ aInteger0 ) ) )
      & ( ( xp @ ( xb @ ( xa @ sdteqdtlpzmzozddtrp0 ) ) )
        | ( xb @ smndt0 @ ( xa @ sdtpldt0 ) @ ( xp @ aDivisorOf0 ) )
        | ? [A: $i] :
            ( ( ( A @ ( xp @ sdtasdt0 ) )
              = ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
            & ( A @ aInteger0 ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(29,plain,
    ~ ( ( ( xq @ ( xb @ ( xa @ sdteqdtlpzmzozddtrp0 ) ) )
        | ( xb @ smndt0 @ ( xa @ sdtpldt0 ) @ ( xq @ aDivisorOf0 ) )
        | ? [A: $i] :
            ( ( ( A @ ( xq @ sdtasdt0 ) )
              = ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
            & ( A @ aInteger0 ) ) )
      & ( ( xp @ ( xb @ ( xa @ sdteqdtlpzmzozddtrp0 ) ) )
        | ( xb @ smndt0 @ ( xa @ sdtpldt0 ) @ ( xp @ aDivisorOf0 ) )
        | ? [A: $i] :
            ( ( ( A @ ( xp @ sdtasdt0 ) )
              = ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
            & ( A @ aInteger0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(30,plain,
    ! [B: $i,A: $i] :
      ( ( ~ ( xq @ ( xb @ ( xa @ sdteqdtlpzmzozddtrp0 ) ) )
        | sk1 )
      & ( ~ ( xb @ smndt0 @ ( xa @ sdtpldt0 ) @ ( xq @ aDivisorOf0 ) )
        | sk1 )
      & ( ( ( B @ ( xq @ sdtasdt0 ) )
         != ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
        | ~ ( B @ aInteger0 )
        | sk1 )
      & ( ~ sk1
        | ~ ( xp @ ( xb @ ( xa @ sdteqdtlpzmzozddtrp0 ) ) ) )
      & ( ~ sk1
        | ~ ( xb @ smndt0 @ ( xa @ sdtpldt0 ) @ ( xp @ aDivisorOf0 ) ) )
      & ( ~ sk1
        | ( ( A @ ( xp @ sdtasdt0 ) )
         != ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
        | ~ ( A @ aInteger0 ) ) ),
    inference(cnf,[status(esa)],[29]) ).

thf(32,plain,
    ! [A: $i] :
      ( ( ( A @ ( xq @ sdtasdt0 ) )
       != ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
      | ~ ( A @ aInteger0 )
      | sk1 ),
    inference(cnfConj,[status(thm)],[30]) ).

thf(38,plain,
    ! [A: $i] :
      ( ~ ( A @ aInteger0 )
      | sk1
      | ( ( A @ ( xq @ sdtasdt0 ) )
       != ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) ) ),
    inference(lifteq,[status(thm)],[32]) ).

thf(39,plain,
    ! [A: $i] :
      ( ~ ( A @ aInteger0 )
      | sk1
      | ( ( A @ ( xq @ sdtasdt0 ) )
       != ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) ) ),
    inference(simp,[status(thm)],[38]) ).

thf(278,plain,
    ! [A: $i] :
      ( ~ ( A @ aInteger0 )
      | sk1
      | ( ( A @ ( xq @ sdtasdt0 ) )
       != ( sk3 @ ( xq @ ( xp @ sdtasdt0 ) @ sdtasdt0 ) ) ) ),
    inference(rewrite,[status(thm)],[39,85]) ).

thf(90365,plain,
    ! [A: $i] :
      ( ~ ( A @ aInteger0 )
      | sk1
      | ( ( A @ ( xq @ sdtasdt0 ) )
       != ( xm @ ( xq @ sdtasdt0 ) @ ( xp @ sdtasdt0 ) ) ) ),
    inference(rewrite,[status(thm)],[278,280]) ).

thf(90612,plain,
    ! [A: $i] :
      ( ( ( xm @ ( xp @ sdtasdt0 ) @ ( xq @ sdtasdt0 ) )
       != ( A @ ( xq @ sdtasdt0 ) ) )
      | ~ ( A @ aInteger0 )
      | sk1
      | ( ( xm @ ( xq @ sdtasdt0 ) @ ( xp @ sdtasdt0 ) )
       != ( xm @ ( xq @ sdtasdt0 ) @ ( xp @ sdtasdt0 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2551,90365]) ).

thf(90613,plain,
    ! [A: $i] :
      ( ( ( xm @ ( xp @ sdtasdt0 ) @ ( xq @ sdtasdt0 ) )
       != ( A @ ( xq @ sdtasdt0 ) ) )
      | ~ ( A @ aInteger0 )
      | sk1 ),
    inference(simp,[status(thm)],[90612]) ).

thf(90614,plain,
    ( ~ ( xm @ ( xp @ sdtasdt0 ) @ aInteger0 )
    | sk1 ),
    inference(pattern_uni,[status(thm)],[90613:[bind(A,$thf( xm @ ( xp @ sdtasdt0 ) ))]]) ).

thf(33,plain,
    ! [A: $i] :
      ( ~ sk1
      | ( ( A @ ( xp @ sdtasdt0 ) )
       != ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
      | ~ ( A @ aInteger0 ) ),
    inference(cnfConj,[status(thm)],[30]) ).

thf(37,plain,
    ! [A: $i] :
      ( ~ sk1
      | ~ ( A @ aInteger0 )
      | ( ( A @ ( xp @ sdtasdt0 ) )
       != ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) ) ),
    inference(lifteq,[status(thm)],[33]) ).

thf(274,plain,
    ! [A: $i] :
      ( ~ sk1
      | ~ ( A @ aInteger0 )
      | ( ( A @ ( xp @ sdtasdt0 ) )
       != ( sk3 @ ( xq @ ( xp @ sdtasdt0 ) @ sdtasdt0 ) ) ) ),
    inference(rewrite,[status(thm)],[37,85]) ).

thf(74507,plain,
    ! [A: $i] :
      ( ~ sk1
      | ~ ( A @ aInteger0 )
      | ( ( A @ ( xp @ sdtasdt0 ) )
       != ( xm @ ( xq @ sdtasdt0 ) @ ( xp @ sdtasdt0 ) ) ) ),
    inference(rewrite,[status(thm)],[274,280]) ).

thf(74509,plain,
    ( ~ ( xm @ ( xq @ sdtasdt0 ) @ aInteger0 )
    | ~ sk1 ),
    inference(pattern_uni,[status(thm)],[74507:[bind(A,$thf( xm @ ( xq @ sdtasdt0 ) ))]]) ).

thf(129070,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ sdtasdt0 ) @ aInteger0 )
       != ( xm @ ( xq @ sdtasdt0 ) @ aInteger0 ) )
      | ~ $true
      | ~ sk1
      | ~ ( B @ aInteger0 )
      | ~ ( A @ aInteger0 ) ),
    inference(paramod_ordered,[status(thm)],[47,74509]) ).

thf(129071,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ sdtasdt0 ) @ aInteger0 )
       != ( xm @ ( xq @ sdtasdt0 ) @ aInteger0 ) )
      | ~ sk1
      | ~ ( B @ aInteger0 )
      | ~ ( A @ aInteger0 ) ),
    inference(simp,[status(thm)],[129070]) ).

thf(129072,plain,
    ( ~ sk1
    | ~ ( xm @ aInteger0 )
    | ~ ( xq @ aInteger0 ) ),
    inference(pattern_uni,[status(thm)],[129071:[bind(A,$thf( xq )),bind(B,$thf( xm ))]]) ).

thf(25,axiom,
    ( ( ( xm @ ( xq @ ( xp @ sdtasdt0 ) @ sdtasdt0 ) )
      = ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
    & ( xm @ aInteger0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1032) ).

thf(143,plain,
    ( ( ( xm @ ( xq @ ( xp @ sdtasdt0 ) @ sdtasdt0 ) )
      = ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
    & ( xm @ aInteger0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(144,plain,
    ( ( ( xm @ ( xq @ ( xp @ sdtasdt0 ) @ sdtasdt0 ) )
      = ( xb @ smndt0 @ ( xa @ sdtpldt0 ) ) )
    & ( xm @ aInteger0 ) ),
    inference(cnf,[status(esa)],[143]) ).

thf(145,plain,
    xm @ aInteger0,
    inference(cnfConj,[status(thm)],[144]) ).

thf(23,axiom,
    ( ( xq != sz00 )
    & ( xq @ aInteger0 )
    & ( xp != sz00 )
    & ( xp @ aInteger0 )
    & ( xb @ aInteger0 )
    & ( xa @ aInteger0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__979) ).

thf(127,plain,
    ( ( xq != sz00 )
    & ( xq @ aInteger0 )
    & ( xp != sz00 )
    & ( xp @ aInteger0 )
    & ( xb @ aInteger0 )
    & ( xa @ aInteger0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(128,plain,
    ( ( xq != sz00 )
    & ( xq @ aInteger0 )
    & ( xp != sz00 )
    & ( xp @ aInteger0 )
    & ( xb @ aInteger0 )
    & ( xa @ aInteger0 ) ),
    inference(cnf,[status(esa)],[127]) ).

thf(134,plain,
    xq @ aInteger0,
    inference(cnfConj,[status(thm)],[128]) ).

thf(172555,plain,
    ( ~ sk1
    | ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[129072,145,134]) ).

thf(172556,plain,
    ~ sk1,
    inference(simp,[status(thm)],[172555]) ).

thf(172571,plain,
    ( ~ ( xm @ ( xp @ sdtasdt0 ) @ aInteger0 )
    | $false ),
    inference(rewrite,[status(thm)],[90614,172556]) ).

thf(172572,plain,
    ~ ( xm @ ( xp @ sdtasdt0 ) @ aInteger0 ),
    inference(simp,[status(thm)],[172571]) ).

thf(173292,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ sdtasdt0 ) @ aInteger0 )
       != ( xm @ ( xp @ sdtasdt0 ) @ aInteger0 ) )
      | ~ $true
      | ~ ( B @ aInteger0 )
      | ~ ( A @ aInteger0 ) ),
    inference(paramod_ordered,[status(thm)],[47,172572]) ).

thf(173293,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ sdtasdt0 ) @ aInteger0 )
       != ( xm @ ( xp @ sdtasdt0 ) @ aInteger0 ) )
      | ~ ( B @ aInteger0 )
      | ~ ( A @ aInteger0 ) ),
    inference(simp,[status(thm)],[173292]) ).

thf(173294,plain,
    ( ~ ( xm @ aInteger0 )
    | ~ ( xp @ aInteger0 ) ),
    inference(pattern_uni,[status(thm)],[173293:[bind(A,$thf( xp )),bind(B,$thf( xm ))]]) ).

thf(133,plain,
    xp @ aInteger0,
    inference(cnfConj,[status(thm)],[128]) ).

thf(177343,plain,
    ( ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[173294,145,133]) ).

thf(177344,plain,
    $false,
    inference(simp,[status(thm)],[177343]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05  % Problem  : NUM436+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.12  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.23/0.49  % Computer : n007.cluster.edu
% 0.23/0.49  % Model    : x86_64 x86_64
% 0.23/0.49  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.49  % Memory   : 8046.5625MB
% 0.23/0.49  % OS       : Linux 6.8.0-71-generic
% 0.23/0.49  % CPULimit : 300
% 0.23/0.49  % WCLimit  : 300
% 0.23/0.49  % DateTime : Sat Sep 26 02:41:39 UTC 2026
% 0.23/0.50  % CPUTime  : 
% 0.23/0.50  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.45/1.34  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.98/1.64  % [INFO] 	 Parsing done (300ms). 
% 1.98/1.67  % [INFO] 	 Running in sequential loop mode. 
% 3.09/2.25  % [INFO] 	 eprover registered as external prover. 
% 3.09/2.26  % [INFO] 	 Scanning for conjecture ... 
% 3.30/2.38  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 3.48/2.40  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 3.48/2.46  % [INFO] 	 Found a conjecture (or negated_conjecture) and 26 axioms. Running axiom selection ... 
% 3.67/2.58  % [INFO] 	 Axiom selection finished. Selected 26 axioms (removed 0 axioms). 
% 3.67/2.59  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 3.87/2.61  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 3.87/2.65  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 3.87/2.67  % [INFO] 	 Type checking passed. 
% 3.87/2.67  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 121.50/49.56  % [INFO] 	 Killing All external provers ... 
% 121.50/49.57  % Time passed: 48863ms (effective reasoning time: 47887ms)
% 121.50/49.57  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 121.50/49.57  % Axioms used in derivation (5): m__1071, m__1003, mIntMult, m__979, m__1032
% 121.50/49.57  % No. of inferences in proof: 56
% 121.50/49.57  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 48863 ms resp. 47887 ms w/o parsing
% 121.81/49.62  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 121.81/49.62  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------