TSTP Solution File: NUM765^1 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM765^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n017.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 May 21 02:13:19 EDT 2024

% Result   : Theorem 0.11s 0.35s
% Output   : Refutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   27
% Syntax   : Number of formulae    :   93 (   3 unt;  17 typ;   0 def)
%            Number of atoms       :  855 ( 117 equ;   0 cnn)
%            Maximal formula atoms :    4 (  11 avg)
%            Number of connectives :  234 ( 115   ~;  67   |;   5   &;   0   @)
%                                         (   4 <=>;  43  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   24 (  23   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :   23 (  20 usr;  10 con; 0-6 aty)
%            Number of variables   :   90 (   0   ^  84   !;   0   ?;  90   :)
%                                         (   6  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    frac: $tType ).

thf(type_def_6,type,
    sTfun: ( $tType * $tType ) > $tType ).

thf(func_def_0,type,
    frac: $tType ).

thf(func_def_1,type,
    x: frac ).

thf(func_def_2,type,
    y: frac ).

thf(func_def_3,type,
    z: frac ).

thf(func_def_4,type,
    u: frac ).

thf(func_def_5,type,
    moref: frac > frac > $o ).

thf(func_def_6,type,
    eq: frac > frac > $o ).

thf(func_def_8,type,
    pf: frac > frac > frac ).

thf(func_def_12,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_13,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_14,type,
    vAND: $o > $o > $o ).

thf(func_def_15,type,
    vOR: $o > $o > $o ).

thf(func_def_16,type,
    vIMP: $o > $o > $o ).

thf(func_def_17,type,
    vNOT: $o > $o ).

thf(func_def_18,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(f147,plain,
    $false,
    inference(avatar_sat_refutation,[],[f88,f97,f104,f115,f129,f146]) ).

thf(f146,plain,
    ( ~ spl0_1
    | ~ spl0_4 ),
    inference(avatar_contradiction_clause,[],[f145]) ).

thf(f145,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(trivial_inequality_removal,[],[f142]) ).

thf(f142,plain,
    ( ( $true != $true )
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(superposition,[],[f141,f96]) ).

thf(f96,plain,
    ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) = $true )
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f94]) ).

thf(f94,plain,
    ( spl0_4
  <=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

thf(f141,plain,
    ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) != $true )
    | ~ spl0_1 ),
    inference(trivial_inequality_removal,[],[f140]) ).

thf(f140,plain,
    ( ( $true != $true )
    | ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) != $true )
    | ~ spl0_1 ),
    inference(forward_demodulation,[],[f139,f83]) ).

thf(f83,plain,
    ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,x),y) = $true )
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f81]) ).

thf(f81,plain,
    ( spl0_1
  <=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,x),y) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

thf(f139,plain,
    ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) != $true )
    | ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,x),y) != $true ) ),
    inference(trivial_inequality_removal,[],[f138]) ).

thf(f138,plain,
    ( ( $true != $true )
    | ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) != $true )
    | ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,x),y) != $true ) ),
    inference(superposition,[],[f41,f50]) ).

thf(f50,plain,
    ! [X2: frac,X3: frac,X0: frac,X1: frac] :
      ( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) )
      | ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3) )
      | ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X0),X1) ) ),
    inference(cnf_transformation,[],[f40]) ).

thf(f40,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) )
      | ( ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3) )
        & ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X2),X3) ) )
      | ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X0),X1) ) ),
    inference(flattening,[],[f39]) ).

thf(f39,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) )
      | ( ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3) )
        & ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X2),X3) ) )
      | ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X0),X1) ) ),
    inference(ennf_transformation,[],[f30]) ).

thf(f30,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X0),X1) )
     => ( ( ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X2),X3) )
         => ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3) ) )
       => ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) ) ) ),
    inference(flattening,[],[f24]) ).

thf(f24,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X0),X1) )
     => ( ( ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X2),X3) )
         => ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3) ) )
       => ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) ) ) ),
    inference(fool_elimination,[],[f23]) ).

thf(f23,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X0),X1)
     => ( ( ~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X2),X3)
         => vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3) )
       => vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) ) ),
    inference(rectify,[],[f5]) ).

thf(f5,axiom,
    ! [X1: frac,X2: frac,X3: frac,X4: frac] :
      ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X1),X2)
     => ( ( ~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X3),X4)
         => vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X3),X4) )
       => vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X2),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz65b) ).

thf(f41,plain,
    vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u)) != $true,
    inference(cnf_transformation,[],[f31]) ).

thf(f31,plain,
    ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u)) != $true )
    & ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u)) != $true ) ),
    inference(ennf_transformation,[],[f25]) ).

thf(f25,plain,
    ~ ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u)) != $true )
     => ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u)) = $true ) ),
    inference(flattening,[],[f12]) ).

thf(f12,plain,
    ~ ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u)) != $true )
     => ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u)) = $true ) ),
    inference(fool_elimination,[],[f11]) ).

thf(f11,plain,
    ~ ( ~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u))
     => vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u)) ),
    inference(rectify,[],[f8]) ).

thf(f8,negated_conjecture,
    ~ ( ~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u))
     => vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u)) ),
    inference(negated_conjecture,[],[f7]) ).

thf(f7,conjecture,
    ( ~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u))
   => vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz66) ).

thf(f129,plain,
    ( ~ spl0_2
    | ~ spl0_4 ),
    inference(avatar_contradiction_clause,[],[f128]) ).

thf(f128,plain,
    ( $false
    | ~ spl0_2
    | ~ spl0_4 ),
    inference(trivial_inequality_removal,[],[f125]) ).

thf(f125,plain,
    ( ( $true != $true )
    | ~ spl0_2
    | ~ spl0_4 ),
    inference(superposition,[],[f124,f96]) ).

thf(f124,plain,
    ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) != $true )
    | ~ spl0_2 ),
    inference(trivial_inequality_removal,[],[f123]) ).

thf(f123,plain,
    ( ( $true != $true )
    | ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) != $true )
    | ~ spl0_2 ),
    inference(forward_demodulation,[],[f122,f87]) ).

thf(f87,plain,
    ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) = $true )
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f85]) ).

thf(f85,plain,
    ( spl0_2
  <=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

thf(f122,plain,
    ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) != $true )
    | ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) != $true ) ),
    inference(trivial_inequality_removal,[],[f121]) ).

thf(f121,plain,
    ( ( $true != $true )
    | ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) != $true )
    | ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) != $true ) ),
    inference(superposition,[],[f42,f48]) ).

thf(f48,plain,
    ! [X2: frac,X3: frac,X0: frac,X1: frac] :
      ( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) )
      | ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3) )
      | ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1) ) ),
    inference(cnf_transformation,[],[f38]) ).

thf(f38,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) )
      | ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3) )
      | ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1) ) ),
    inference(flattening,[],[f37]) ).

thf(f37,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) )
      | ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3) )
      | ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1) ) ),
    inference(ennf_transformation,[],[f22]) ).

thf(f22,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1) )
     => ( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3) )
       => ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) ) ) ),
    inference(fool_elimination,[],[f21]) ).

thf(f21,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1)
     => ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X2),X3)
       => vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) ) ),
    inference(rectify,[],[f4]) ).

thf(f4,axiom,
    ! [X1: frac,X2: frac,X3: frac,X4: frac] :
      ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X1),X2)
     => ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X3),X4)
       => vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X2),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz56) ).

thf(f42,plain,
    vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,x),z)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,y),u)) != $true,
    inference(cnf_transformation,[],[f31]) ).

thf(f115,plain,
    ( ~ spl0_2
    | ~ spl0_3 ),
    inference(avatar_contradiction_clause,[],[f114]) ).

thf(f114,plain,
    ( $false
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(trivial_inequality_removal,[],[f111]) ).

thf(f111,plain,
    ( ( $true != $true )
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(superposition,[],[f110,f87]) ).

thf(f110,plain,
    ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) != $true )
    | ~ spl0_3 ),
    inference(trivial_inequality_removal,[],[f109]) ).

thf(f109,plain,
    ( ( $true != $true )
    | ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) != $true )
    | ~ spl0_3 ),
    inference(forward_demodulation,[],[f108,f92]) ).

thf(f92,plain,
    ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,z),u) = $true )
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f90]) ).

thf(f90,plain,
    ( spl0_3
  <=> ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,z),u) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

thf(f108,plain,
    ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,z),u) != $true )
    | ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) != $true ) ),
    inference(trivial_inequality_removal,[],[f107]) ).

thf(f107,plain,
    ( ( $true != $true )
    | ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,z),u) != $true )
    | ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) != $true ) ),
    inference(superposition,[],[f41,f47]) ).

thf(f47,plain,
    ! [X2: frac,X3: frac,X0: frac,X1: frac] :
      ( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) )
      | ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X2),X3) )
      | ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1) ) ),
    inference(cnf_transformation,[],[f36]) ).

thf(f36,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) )
      | ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X2),X3) )
      | ( ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1) )
        & ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X0),X1) ) ) ),
    inference(flattening,[],[f35]) ).

thf(f35,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) )
      | ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X2),X3) )
      | ( ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1) )
        & ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X0),X1) ) ) ),
    inference(ennf_transformation,[],[f29]) ).

thf(f29,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( ( ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X0),X1) )
       => ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1) ) )
     => ( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X2),X3) )
       => ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) ) ) ),
    inference(flattening,[],[f20]) ).

thf(f20,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( ( ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X0),X1) )
       => ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1) ) )
     => ( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X2),X3) )
       => ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) ) ) ),
    inference(fool_elimination,[],[f19]) ).

thf(f19,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( ( ~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X0),X1)
       => vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X0),X1) )
     => ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X2),X3)
       => vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) ) ),
    inference(rectify,[],[f6]) ).

thf(f6,axiom,
    ! [X1: frac,X2: frac,X3: frac,X4: frac] :
      ( ( ~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X1),X2)
       => vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,X1),X2) )
     => ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X3),X4)
       => vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X2),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz65a) ).

thf(f104,plain,
    ( ~ spl0_1
    | ~ spl0_3 ),
    inference(avatar_split_clause,[],[f103,f90,f81]) ).

thf(f103,plain,
    ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,z),u) != $true )
    | ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,x),y) != $true ) ),
    inference(trivial_inequality_removal,[],[f102]) ).

thf(f102,plain,
    ( ( $true != $true )
    | ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,z),u) != $true )
    | ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,x),y) != $true ) ),
    inference(superposition,[],[f41,f46]) ).

thf(f46,plain,
    ! [X2: frac,X3: frac,X0: frac,X1: frac] :
      ( ( $true = vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X0),X2)),vAPP(frac,frac,vAPP(frac,sTfun(frac,frac),pf,X1),X3)) )
      | ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X2),X3) )
      | ( $true != vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,X0),X1) ) ),
    inference(cnf_transformation,[],[f36]) ).

thf(f97,plain,
    ( spl0_3
    | spl0_4 ),
    inference(avatar_split_clause,[],[f44,f94,f90]) ).

thf(f44,plain,
    ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) = $true )
    | ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,z),u) = $true ) ),
    inference(cnf_transformation,[],[f33]) ).

thf(f33,plain,
    ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) = $true )
    | ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,z),u) = $true ) ),
    inference(ennf_transformation,[],[f27]) ).

thf(f27,plain,
    ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,z),u) != $true )
   => ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) = $true ) ),
    inference(flattening,[],[f16]) ).

thf(f16,plain,
    ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,z),u) != $true )
   => ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) = $true ) ),
    inference(fool_elimination,[],[f15]) ).

thf(f15,plain,
    ( ~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,z),u)
   => vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) ),
    inference(rectify,[],[f2]) ).

thf(f2,axiom,
    ( ~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,z),u)
   => vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,z),u) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',n) ).

thf(f88,plain,
    ( spl0_1
    | spl0_2 ),
    inference(avatar_split_clause,[],[f43,f85,f81]) ).

thf(f43,plain,
    ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) = $true )
    | ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,x),y) = $true ) ),
    inference(cnf_transformation,[],[f32]) ).

thf(f32,plain,
    ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) = $true )
    | ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,x),y) = $true ) ),
    inference(ennf_transformation,[],[f26]) ).

thf(f26,plain,
    ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,x),y) != $true )
   => ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) = $true ) ),
    inference(flattening,[],[f14]) ).

thf(f14,plain,
    ( ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,x),y) != $true )
   => ( vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) = $true ) ),
    inference(fool_elimination,[],[f13]) ).

thf(f13,plain,
    ( ~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,x),y)
   => vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) ),
    inference(rectify,[],[f1]) ).

thf(f1,axiom,
    ( ~ vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),moref,x),y)
   => vAPP(frac,$o,vAPP(frac,sTfun(frac,$o),eq,x),y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem    : NUM765^1 : TPTP v8.2.0. Released v3.7.0.
% 0.09/0.12  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32  % Computer : n017.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Mon May 20 03:56:52 EDT 2024
% 0.11/0.32  % CPUTime    : 
% 0.11/0.33  % (7103)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.34  % (7105)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.34  % (7107)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.11/0.34  % (7108)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.11/0.34  % (7109)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.11/0.34  % (7106)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.11/0.34  % (7110)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.11/0.34  % (7106)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.11/0.34  % (7107)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.11/0.34  % Exception at run slice level% Exception at run slice level% Exception at run slice level
% 0.11/0.34  
% 0.11/0.34  User error: User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructsFinite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.34  
% 0.11/0.34  
% 0.11/0.34  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.34  % (7104)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.11/0.35  % Exception at run slice level
% 0.11/0.35  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.35  % (7106)First to succeed.
% 0.11/0.35  % (7106)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-7103"
% 0.11/0.35  % (7106)Refutation found. Thanks to Tanya!
% 0.11/0.35  % SZS status Theorem for theBenchmark
% 0.11/0.35  % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.35  % (7106)------------------------------
% 0.11/0.35  % (7106)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.11/0.35  % (7106)Termination reason: Refutation
% 0.11/0.35  
% 0.11/0.35  % (7106)Memory used [KB]: 852
% 0.11/0.35  % (7106)Time elapsed: 0.009 s
% 0.11/0.35  % (7106)Instructions burned: 15 (million)
% 0.11/0.35  % (7103)Success in time 0.022 s
%------------------------------------------------------------------------------