TSTP Solution File: SYN713-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN713-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n009.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 : Thu Sep 29 23:57:02 EDT 2022

% Result   : Unsatisfiable 0.47s 0.54s
% Output   : Proof 0.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   95
% Syntax   : Number of formulae    :  164 (  44 unt;  38 typ;   0 def)
%            Number of atoms       :  579 (   0 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  741 ( 327   ~; 350   |;   0   &)
%                                         (  64 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of FOOLs       :   39 (  39 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   46 (  23   >;  23   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  14 usr;   1 prp; 0-3 aty)
%            Number of functors    :   28 (  28 usr;  15 con; 0-2 aty)
%            Number of variables   :  378 ( 335   !;   0   ?; 378   :)

% Comments : 
%------------------------------------------------------------------------------
tff(p4_type,type,
    p4: ( $i * $i ) > $o ).

tff(f11_type,type,
    f11: ( $i * $i ) > $i ).

tff(f14_type,type,
    f14: ( $i * $i ) > $i ).

tff(f23_type,type,
    f23: ( $i * $i ) > $i ).

tff(c77_type,type,
    c77: $i ).

tff(c74_type,type,
    c74: $i ).

tff(f17_type,type,
    f17: ( $i * $i ) > $i ).

tff(c67_type,type,
    c67: $i ).

tff(c66_type,type,
    c66: $i ).

tff(c65_type,type,
    c65: $i ).

tff(c68_type,type,
    c68: $i ).

tff(p10_type,type,
    p10: ( $i * $i ) > $o ).

tff(p12_type,type,
    p12: ( $i * $i ) > $o ).

tff(p13_type,type,
    p13: ( $i * $i ) > $o ).

tff(p58_type,type,
    p58: ( $i * $i ) > $o ).

tff(f19_type,type,
    f19: ( $i * $i ) > $i ).

tff(f22_type,type,
    f22: ( $i * $i ) > $i ).

tff(c69_type,type,
    c69: $i ).

tff(c70_type,type,
    c70: $i ).

tff(f31_type,type,
    f31: ( $i * $i ) > $i ).

tff(f33_type,type,
    f33: ( $i * $i ) > $i ).

tff(c76_type,type,
    c76: $i ).

tff(c75_type,type,
    c75: $i ).

tff(p59_type,type,
    p59: ( $i * $i ) > $o ).

tff(f35_type,type,
    f35: ( $i * $i ) > $i ).

tff(c73_type,type,
    c73: $i ).

tff(f38_type,type,
    f38: ( $i * $i ) > $i ).

tff(c72_type,type,
    c72: $i ).

tff(p9_type,type,
    p9: ( $i * $i ) > $o ).

tff(p40_type,type,
    p40: ( $i * $i ) > $o ).

tff(c64_type,type,
    c64: $i ).

tff(p56_type,type,
    p56: ( $i * $i ) > $o ).

tff(p57_type,type,
    p57: ( $i * $i ) > $o ).

tff(f26_type,type,
    f26: ( $i * $i ) > $i ).

tff(f41_type,type,
    f41: ( $i * $i ) > $i ).

tff(c78_type,type,
    c78: $i ).

tff(f28_type,type,
    f28: ( $i * $i ) > $i ).

tff(c71_type,type,
    c71: $i ).

tff(1,plain,
    ^ [X7: $i] :
      refl(
        ( p12(X7,X7)
      <=> p12(X7,X7) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [X7: $i] : p12(X7,X7)
  <=> ! [X7: $i] : p12(X7,X7) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [X7: $i] : p12(X7,X7)
  <=> ! [X7: $i] : p12(X7,X7) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [X7: $i] : p12(X7,X7),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_34) ).

tff(5,plain,
    ! [X7: $i] : p12(X7,X7),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [X7: $i] : p12(X7,X7),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [X7: $i] : p12(X7,X7),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [X7: $i] : p12(X7,X7)
    | p12(f17(c66,c67),f17(c66,c67)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    p12(f17(c66,c67),f17(c66,c67)),
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    ^ [X17: $i,X18: $i] :
      refl(
        ( ( ~ p59(f38(c72,X18),f35(c73,X17))
          | p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
          | p13(X17,f23(c74,X18)) )
      <=> ( ~ p59(f38(c72,X18),f35(c73,X17))
          | p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
          | p13(X17,f23(c74,X18)) ) )),
    inference(bind,[status(th)],]) ).

tff(11,plain,
    ( ! [X17: $i,X18: $i] :
        ( ~ p59(f38(c72,X18),f35(c73,X17))
        | p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
        | p13(X17,f23(c74,X18)) )
  <=> ! [X17: $i,X18: $i] :
        ( ~ p59(f38(c72,X18),f35(c73,X17))
        | p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
        | p13(X17,f23(c74,X18)) ) ),
    inference(quant_intro,[status(thm)],[10]) ).

tff(12,plain,
    ( ! [X17: $i,X18: $i] :
        ( ~ p59(f38(c72,X18),f35(c73,X17))
        | p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
        | p13(X17,f23(c74,X18)) )
  <=> ! [X17: $i,X18: $i] :
        ( ~ p59(f38(c72,X18),f35(c73,X17))
        | p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
        | p13(X17,f23(c74,X18)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(13,plain,
    ^ [X17: $i,X18: $i] :
      rewrite(
        ( ( p13(X17,f23(c74,X18))
          | p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
          | ~ p59(f38(c72,X18),f35(c73,X17)) )
      <=> ( ~ p59(f38(c72,X18),f35(c73,X17))
          | p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
          | p13(X17,f23(c74,X18)) ) )),
    inference(bind,[status(th)],]) ).

tff(14,plain,
    ( ! [X17: $i,X18: $i] :
        ( p13(X17,f23(c74,X18))
        | p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
        | ~ p59(f38(c72,X18),f35(c73,X17)) )
  <=> ! [X17: $i,X18: $i] :
        ( ~ p59(f38(c72,X18),f35(c73,X17))
        | p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
        | p13(X17,f23(c74,X18)) ) ),
    inference(quant_intro,[status(thm)],[13]) ).

tff(15,axiom,
    ! [X17: $i,X18: $i] :
      ( p13(X17,f23(c74,X18))
      | p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
      | ~ p59(f38(c72,X18),f35(c73,X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13_105) ).

tff(16,plain,
    ! [X17: $i,X18: $i] :
      ( ~ p59(f38(c72,X18),f35(c73,X17))
      | p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
      | p13(X17,f23(c74,X18)) ),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    ! [X17: $i,X18: $i] :
      ( ~ p59(f38(c72,X18),f35(c73,X17))
      | p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
      | p13(X17,f23(c74,X18)) ),
    inference(modus_ponens,[status(thm)],[16,12]) ).

tff(18,plain,
    ! [X17: $i,X18: $i] :
      ( ~ p59(f38(c72,X18),f35(c73,X17))
      | p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
      | p13(X17,f23(c74,X18)) ),
    inference(skolemize,[status(sab)],[17]) ).

tff(19,plain,
    ! [X17: $i,X18: $i] :
      ( ~ p59(f38(c72,X18),f35(c73,X17))
      | p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
      | p13(X17,f23(c74,X18)) ),
    inference(modus_ponens,[status(thm)],[18,11]) ).

tff(20,plain,
    ( ~ p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68))
  <=> ~ p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68)) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,axiom,
    ~ p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p58_80) ).

tff(22,plain,
    ~ p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68)),
    inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
    ( p59(f38(c72,c77),f35(c73,c68))
  <=> p59(f38(c72,c77),f35(c73,c68)) ),
    inference(rewrite,[status(thm)],]) ).

tff(24,axiom,
    p59(f38(c72,c77),f35(c73,c68)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p59_35) ).

tff(25,plain,
    p59(f38(c72,c77),f35(c73,c68)),
    inference(modus_ponens,[status(thm)],[24,23]) ).

tff(26,plain,
    ( ( ~ ! [X17: $i,X18: $i] :
            ( ~ p59(f38(c72,X18),f35(c73,X17))
            | p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
            | p13(X17,f23(c74,X18)) )
      | p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68))
      | ~ p59(f38(c72,c77),f35(c73,c68))
      | p13(c68,f23(c74,c77)) )
  <=> ( ~ ! [X17: $i,X18: $i] :
            ( ~ p59(f38(c72,X18),f35(c73,X17))
            | p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
            | p13(X17,f23(c74,X18)) )
      | p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68))
      | ~ p59(f38(c72,c77),f35(c73,c68))
      | p13(c68,f23(c74,c77)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(27,plain,
    ( ( ~ p59(f38(c72,c77),f35(c73,c68))
      | p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68))
      | p13(c68,f23(c74,c77)) )
  <=> ( p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68))
      | ~ p59(f38(c72,c77),f35(c73,c68))
      | p13(c68,f23(c74,c77)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(28,plain,
    ( ( ~ ! [X17: $i,X18: $i] :
            ( ~ p59(f38(c72,X18),f35(c73,X17))
            | p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
            | p13(X17,f23(c74,X18)) )
      | ~ p59(f38(c72,c77),f35(c73,c68))
      | p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68))
      | p13(c68,f23(c74,c77)) )
  <=> ( ~ ! [X17: $i,X18: $i] :
            ( ~ p59(f38(c72,X18),f35(c73,X17))
            | p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
            | p13(X17,f23(c74,X18)) )
      | p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68))
      | ~ p59(f38(c72,c77),f35(c73,c68))
      | p13(c68,f23(c74,c77)) ) ),
    inference(monotonicity,[status(thm)],[27]) ).

tff(29,plain,
    ( ( ~ ! [X17: $i,X18: $i] :
            ( ~ p59(f38(c72,X18),f35(c73,X17))
            | p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
            | p13(X17,f23(c74,X18)) )
      | ~ p59(f38(c72,c77),f35(c73,c68))
      | p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68))
      | p13(c68,f23(c74,c77)) )
  <=> ( ~ ! [X17: $i,X18: $i] :
            ( ~ p59(f38(c72,X18),f35(c73,X17))
            | p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
            | p13(X17,f23(c74,X18)) )
      | p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68))
      | ~ p59(f38(c72,c77),f35(c73,c68))
      | p13(c68,f23(c74,c77)) ) ),
    inference(transitivity,[status(thm)],[28,26]) ).

tff(30,plain,
    ( ~ ! [X17: $i,X18: $i] :
          ( ~ p59(f38(c72,X18),f35(c73,X17))
          | p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
          | p13(X17,f23(c74,X18)) )
    | ~ p59(f38(c72,c77),f35(c73,c68))
    | p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68))
    | p13(c68,f23(c74,c77)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(31,plain,
    ( ~ ! [X17: $i,X18: $i] :
          ( ~ p59(f38(c72,X18),f35(c73,X17))
          | p58(f31(f33(c75,c76),f23(c69,X18)),f19(f22(c70,c69),X17))
          | p13(X17,f23(c74,X18)) )
    | p58(f31(f33(c75,c76),f23(c69,c77)),f19(f22(c70,c69),c68))
    | ~ p59(f38(c72,c77),f35(c73,c68))
    | p13(c68,f23(c74,c77)) ),
    inference(modus_ponens,[status(thm)],[30,29]) ).

tff(32,plain,
    p13(c68,f23(c74,c77)),
    inference(unit_resolution,[status(thm)],[31,25,22,19]) ).

tff(33,plain,
    ^ [X6: $i,X4: $i,X3: $i,X5: $i] :
      refl(
        ( ( ~ p12(X3,X5)
          | ~ p13(X4,X6)
          | p10(f14(X3,X4),f14(X5,X6)) )
      <=> ( ~ p12(X3,X5)
          | ~ p13(X4,X6)
          | p10(f14(X3,X4),f14(X5,X6)) ) )),
    inference(bind,[status(th)],]) ).

tff(34,plain,
    ( ! [X6: $i,X4: $i,X3: $i,X5: $i] :
        ( ~ p12(X3,X5)
        | ~ p13(X4,X6)
        | p10(f14(X3,X4),f14(X5,X6)) )
  <=> ! [X6: $i,X4: $i,X3: $i,X5: $i] :
        ( ~ p12(X3,X5)
        | ~ p13(X4,X6)
        | p10(f14(X3,X4),f14(X5,X6)) ) ),
    inference(quant_intro,[status(thm)],[33]) ).

tff(35,plain,
    ( ! [X6: $i,X4: $i,X3: $i,X5: $i] :
        ( ~ p12(X3,X5)
        | ~ p13(X4,X6)
        | p10(f14(X3,X4),f14(X5,X6)) )
  <=> ! [X6: $i,X4: $i,X3: $i,X5: $i] :
        ( ~ p12(X3,X5)
        | ~ p13(X4,X6)
        | p10(f14(X3,X4),f14(X5,X6)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(36,plain,
    ^ [X6: $i,X4: $i,X3: $i,X5: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( p10(f14(X3,X4),f14(X5,X6))
              | ~ p12(X3,X5) )
          <=> ( ~ p12(X3,X5)
              | p10(f14(X3,X4),f14(X5,X6)) ) )),
          ( ( p10(f14(X3,X4),f14(X5,X6))
            | ~ p12(X3,X5)
            | ~ p13(X4,X6) )
        <=> ( ~ p12(X3,X5)
            | p10(f14(X3,X4),f14(X5,X6))
            | ~ p13(X4,X6) ) )),
        rewrite(
          ( ( ~ p12(X3,X5)
            | p10(f14(X3,X4),f14(X5,X6))
            | ~ p13(X4,X6) )
        <=> ( ~ p12(X3,X5)
            | ~ p13(X4,X6)
            | p10(f14(X3,X4),f14(X5,X6)) ) )),
        ( ( p10(f14(X3,X4),f14(X5,X6))
          | ~ p12(X3,X5)
          | ~ p13(X4,X6) )
      <=> ( ~ p12(X3,X5)
          | ~ p13(X4,X6)
          | p10(f14(X3,X4),f14(X5,X6)) ) )),
    inference(bind,[status(th)],]) ).

tff(37,plain,
    ( ! [X6: $i,X4: $i,X3: $i,X5: $i] :
        ( p10(f14(X3,X4),f14(X5,X6))
        | ~ p12(X3,X5)
        | ~ p13(X4,X6) )
  <=> ! [X6: $i,X4: $i,X3: $i,X5: $i] :
        ( ~ p12(X3,X5)
        | ~ p13(X4,X6)
        | p10(f14(X3,X4),f14(X5,X6)) ) ),
    inference(quant_intro,[status(thm)],[36]) ).

tff(38,axiom,
    ! [X6: $i,X4: $i,X3: $i,X5: $i] :
      ( p10(f14(X3,X4),f14(X5,X6))
      | ~ p12(X3,X5)
      | ~ p13(X4,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10_81) ).

tff(39,plain,
    ! [X6: $i,X4: $i,X3: $i,X5: $i] :
      ( ~ p12(X3,X5)
      | ~ p13(X4,X6)
      | p10(f14(X3,X4),f14(X5,X6)) ),
    inference(modus_ponens,[status(thm)],[38,37]) ).

tff(40,plain,
    ! [X6: $i,X4: $i,X3: $i,X5: $i] :
      ( ~ p12(X3,X5)
      | ~ p13(X4,X6)
      | p10(f14(X3,X4),f14(X5,X6)) ),
    inference(modus_ponens,[status(thm)],[39,35]) ).

tff(41,plain,
    ! [X6: $i,X4: $i,X3: $i,X5: $i] :
      ( ~ p12(X3,X5)
      | ~ p13(X4,X6)
      | p10(f14(X3,X4),f14(X5,X6)) ),
    inference(skolemize,[status(sab)],[40]) ).

tff(42,plain,
    ! [X6: $i,X4: $i,X3: $i,X5: $i] :
      ( ~ p12(X3,X5)
      | ~ p13(X4,X6)
      | p10(f14(X3,X4),f14(X5,X6)) ),
    inference(modus_ponens,[status(thm)],[41,34]) ).

tff(43,plain,
    ( ( ~ ! [X6: $i,X4: $i,X3: $i,X5: $i] :
            ( ~ p12(X3,X5)
            | ~ p13(X4,X6)
            | p10(f14(X3,X4),f14(X5,X6)) )
      | ~ p12(f17(c66,c67),f17(c66,c67))
      | ~ p13(c68,f23(c74,c77))
      | p10(f14(f17(c66,c67),c68),f14(f17(c66,c67),f23(c74,c77))) )
  <=> ( ~ ! [X6: $i,X4: $i,X3: $i,X5: $i] :
            ( ~ p12(X3,X5)
            | ~ p13(X4,X6)
            | p10(f14(X3,X4),f14(X5,X6)) )
      | ~ p12(f17(c66,c67),f17(c66,c67))
      | ~ p13(c68,f23(c74,c77))
      | p10(f14(f17(c66,c67),c68),f14(f17(c66,c67),f23(c74,c77))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(44,plain,
    ( ~ ! [X6: $i,X4: $i,X3: $i,X5: $i] :
          ( ~ p12(X3,X5)
          | ~ p13(X4,X6)
          | p10(f14(X3,X4),f14(X5,X6)) )
    | ~ p12(f17(c66,c67),f17(c66,c67))
    | ~ p13(c68,f23(c74,c77))
    | p10(f14(f17(c66,c67),c68),f14(f17(c66,c67),f23(c74,c77))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(45,plain,
    ( ~ ! [X6: $i,X4: $i,X3: $i,X5: $i] :
          ( ~ p12(X3,X5)
          | ~ p13(X4,X6)
          | p10(f14(X3,X4),f14(X5,X6)) )
    | ~ p12(f17(c66,c67),f17(c66,c67))
    | ~ p13(c68,f23(c74,c77))
    | p10(f14(f17(c66,c67),c68),f14(f17(c66,c67),f23(c74,c77))) ),
    inference(modus_ponens,[status(thm)],[44,43]) ).

tff(46,plain,
    p10(f14(f17(c66,c67),c68),f14(f17(c66,c67),f23(c74,c77))),
    inference(unit_resolution,[status(thm)],[45,42,32,9]) ).

tff(47,plain,
    ^ [X210: $i] :
      refl(
        ( p9(X210,X210)
      <=> p9(X210,X210) )),
    inference(bind,[status(th)],]) ).

tff(48,plain,
    ( ! [X210: $i] : p9(X210,X210)
  <=> ! [X210: $i] : p9(X210,X210) ),
    inference(quant_intro,[status(thm)],[47]) ).

tff(49,plain,
    ( ! [X210: $i] : p9(X210,X210)
  <=> ! [X210: $i] : p9(X210,X210) ),
    inference(rewrite,[status(thm)],]) ).

tff(50,axiom,
    ! [X210: $i] : p9(X210,X210),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9_2) ).

tff(51,plain,
    ! [X210: $i] : p9(X210,X210),
    inference(modus_ponens,[status(thm)],[50,49]) ).

tff(52,plain,
    ! [X210: $i] : p9(X210,X210),
    inference(skolemize,[status(sab)],[51]) ).

tff(53,plain,
    ! [X210: $i] : p9(X210,X210),
    inference(modus_ponens,[status(thm)],[52,48]) ).

tff(54,plain,
    ( ~ ! [X210: $i] : p9(X210,X210)
    | p9(c65,c65) ),
    inference(quant_inst,[status(thm)],]) ).

tff(55,plain,
    p9(c65,c65),
    inference(unit_resolution,[status(thm)],[54,53]) ).

tff(56,plain,
    ^ [X122: $i,X124: $i,X121: $i,X123: $i] :
      refl(
        ( ( ~ p9(X121,X123)
          | ~ p10(X122,X124)
          | p4(f11(X121,X122),f11(X123,X124)) )
      <=> ( ~ p9(X121,X123)
          | ~ p10(X122,X124)
          | p4(f11(X121,X122),f11(X123,X124)) ) )),
    inference(bind,[status(th)],]) ).

tff(57,plain,
    ( ! [X122: $i,X124: $i,X121: $i,X123: $i] :
        ( ~ p9(X121,X123)
        | ~ p10(X122,X124)
        | p4(f11(X121,X122),f11(X123,X124)) )
  <=> ! [X122: $i,X124: $i,X121: $i,X123: $i] :
        ( ~ p9(X121,X123)
        | ~ p10(X122,X124)
        | p4(f11(X121,X122),f11(X123,X124)) ) ),
    inference(quant_intro,[status(thm)],[56]) ).

tff(58,plain,
    ( ! [X122: $i,X124: $i,X121: $i,X123: $i] :
        ( ~ p9(X121,X123)
        | ~ p10(X122,X124)
        | p4(f11(X121,X122),f11(X123,X124)) )
  <=> ! [X122: $i,X124: $i,X121: $i,X123: $i] :
        ( ~ p9(X121,X123)
        | ~ p10(X122,X124)
        | p4(f11(X121,X122),f11(X123,X124)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(59,plain,
    ^ [X122: $i,X124: $i,X121: $i,X123: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( p4(f11(X121,X122),f11(X123,X124))
              | ~ p10(X122,X124) )
          <=> ( ~ p10(X122,X124)
              | p4(f11(X121,X122),f11(X123,X124)) ) )),
          ( ( p4(f11(X121,X122),f11(X123,X124))
            | ~ p10(X122,X124)
            | ~ p9(X121,X123) )
        <=> ( ~ p10(X122,X124)
            | p4(f11(X121,X122),f11(X123,X124))
            | ~ p9(X121,X123) ) )),
        rewrite(
          ( ( ~ p10(X122,X124)
            | p4(f11(X121,X122),f11(X123,X124))
            | ~ p9(X121,X123) )
        <=> ( ~ p9(X121,X123)
            | ~ p10(X122,X124)
            | p4(f11(X121,X122),f11(X123,X124)) ) )),
        ( ( p4(f11(X121,X122),f11(X123,X124))
          | ~ p10(X122,X124)
          | ~ p9(X121,X123) )
      <=> ( ~ p9(X121,X123)
          | ~ p10(X122,X124)
          | p4(f11(X121,X122),f11(X123,X124)) ) )),
    inference(bind,[status(th)],]) ).

tff(60,plain,
    ( ! [X122: $i,X124: $i,X121: $i,X123: $i] :
        ( p4(f11(X121,X122),f11(X123,X124))
        | ~ p10(X122,X124)
        | ~ p9(X121,X123) )
  <=> ! [X122: $i,X124: $i,X121: $i,X123: $i] :
        ( ~ p9(X121,X123)
        | ~ p10(X122,X124)
        | p4(f11(X121,X122),f11(X123,X124)) ) ),
    inference(quant_intro,[status(thm)],[59]) ).

tff(61,axiom,
    ! [X122: $i,X124: $i,X121: $i,X123: $i] :
      ( p4(f11(X121,X122),f11(X123,X124))
      | ~ p10(X122,X124)
      | ~ p9(X121,X123) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_87) ).

tff(62,plain,
    ! [X122: $i,X124: $i,X121: $i,X123: $i] :
      ( ~ p9(X121,X123)
      | ~ p10(X122,X124)
      | p4(f11(X121,X122),f11(X123,X124)) ),
    inference(modus_ponens,[status(thm)],[61,60]) ).

tff(63,plain,
    ! [X122: $i,X124: $i,X121: $i,X123: $i] :
      ( ~ p9(X121,X123)
      | ~ p10(X122,X124)
      | p4(f11(X121,X122),f11(X123,X124)) ),
    inference(modus_ponens,[status(thm)],[62,58]) ).

tff(64,plain,
    ! [X122: $i,X124: $i,X121: $i,X123: $i] :
      ( ~ p9(X121,X123)
      | ~ p10(X122,X124)
      | p4(f11(X121,X122),f11(X123,X124)) ),
    inference(skolemize,[status(sab)],[63]) ).

tff(65,plain,
    ! [X122: $i,X124: $i,X121: $i,X123: $i] :
      ( ~ p9(X121,X123)
      | ~ p10(X122,X124)
      | p4(f11(X121,X122),f11(X123,X124)) ),
    inference(modus_ponens,[status(thm)],[64,57]) ).

tff(66,plain,
    ( ( ~ ! [X122: $i,X124: $i,X121: $i,X123: $i] :
            ( ~ p9(X121,X123)
            | ~ p10(X122,X124)
            | p4(f11(X121,X122),f11(X123,X124)) )
      | ~ p9(c65,c65)
      | ~ p10(f14(f17(c66,c67),c68),f14(f17(c66,c67),f23(c74,c77)))
      | p4(f11(c65,f14(f17(c66,c67),c68)),f11(c65,f14(f17(c66,c67),f23(c74,c77)))) )
  <=> ( ~ ! [X122: $i,X124: $i,X121: $i,X123: $i] :
            ( ~ p9(X121,X123)
            | ~ p10(X122,X124)
            | p4(f11(X121,X122),f11(X123,X124)) )
      | ~ p9(c65,c65)
      | ~ p10(f14(f17(c66,c67),c68),f14(f17(c66,c67),f23(c74,c77)))
      | p4(f11(c65,f14(f17(c66,c67),c68)),f11(c65,f14(f17(c66,c67),f23(c74,c77)))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(67,plain,
    ( ~ ! [X122: $i,X124: $i,X121: $i,X123: $i] :
          ( ~ p9(X121,X123)
          | ~ p10(X122,X124)
          | p4(f11(X121,X122),f11(X123,X124)) )
    | ~ p9(c65,c65)
    | ~ p10(f14(f17(c66,c67),c68),f14(f17(c66,c67),f23(c74,c77)))
    | p4(f11(c65,f14(f17(c66,c67),c68)),f11(c65,f14(f17(c66,c67),f23(c74,c77)))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(68,plain,
    ( ~ ! [X122: $i,X124: $i,X121: $i,X123: $i] :
          ( ~ p9(X121,X123)
          | ~ p10(X122,X124)
          | p4(f11(X121,X122),f11(X123,X124)) )
    | ~ p9(c65,c65)
    | ~ p10(f14(f17(c66,c67),c68),f14(f17(c66,c67),f23(c74,c77)))
    | p4(f11(c65,f14(f17(c66,c67),c68)),f11(c65,f14(f17(c66,c67),f23(c74,c77)))) ),
    inference(modus_ponens,[status(thm)],[67,66]) ).

tff(69,plain,
    p4(f11(c65,f14(f17(c66,c67),c68)),f11(c65,f14(f17(c66,c67),f23(c74,c77)))),
    inference(unit_resolution,[status(thm)],[68,65,55,46]) ).

tff(70,plain,
    ^ [X129: $i] :
      refl(
        ( p40(X129,X129)
      <=> p40(X129,X129) )),
    inference(bind,[status(th)],]) ).

tff(71,plain,
    ( ! [X129: $i] : p40(X129,X129)
  <=> ! [X129: $i] : p40(X129,X129) ),
    inference(quant_intro,[status(thm)],[70]) ).

tff(72,plain,
    ( ! [X129: $i] : p40(X129,X129)
  <=> ! [X129: $i] : p40(X129,X129) ),
    inference(rewrite,[status(thm)],]) ).

tff(73,axiom,
    ! [X129: $i] : p40(X129,X129),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p40_14) ).

tff(74,plain,
    ! [X129: $i] : p40(X129,X129),
    inference(modus_ponens,[status(thm)],[73,72]) ).

tff(75,plain,
    ! [X129: $i] : p40(X129,X129),
    inference(skolemize,[status(sab)],[74]) ).

tff(76,plain,
    ! [X129: $i] : p40(X129,X129),
    inference(modus_ponens,[status(thm)],[75,71]) ).

tff(77,plain,
    ( ~ ! [X129: $i] : p40(X129,X129)
    | p40(c64,c64) ),
    inference(quant_inst,[status(thm)],]) ).

tff(78,plain,
    p40(c64,c64),
    inference(unit_resolution,[status(thm)],[77,76]) ).

tff(79,plain,
    ^ [X188: $i,X186: $i,X187: $i] :
      refl(
        ( ( ~ p57(f26(X186,X187),X188)
          | p57(f26(f28(c71,X186),X187),X188) )
      <=> ( ~ p57(f26(X186,X187),X188)
          | p57(f26(f28(c71,X186),X187),X188) ) )),
    inference(bind,[status(th)],]) ).

tff(80,plain,
    ( ! [X188: $i,X186: $i,X187: $i] :
        ( ~ p57(f26(X186,X187),X188)
        | p57(f26(f28(c71,X186),X187),X188) )
  <=> ! [X188: $i,X186: $i,X187: $i] :
        ( ~ p57(f26(X186,X187),X188)
        | p57(f26(f28(c71,X186),X187),X188) ) ),
    inference(quant_intro,[status(thm)],[79]) ).

tff(81,plain,
    ( ! [X188: $i,X186: $i,X187: $i] :
        ( ~ p57(f26(X186,X187),X188)
        | p57(f26(f28(c71,X186),X187),X188) )
  <=> ! [X188: $i,X186: $i,X187: $i] :
        ( ~ p57(f26(X186,X187),X188)
        | p57(f26(f28(c71,X186),X187),X188) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(82,plain,
    ^ [X188: $i,X186: $i,X187: $i] :
      rewrite(
        ( ( p57(f26(f28(c71,X186),X187),X188)
          | ~ p57(f26(X186,X187),X188) )
      <=> ( ~ p57(f26(X186,X187),X188)
          | p57(f26(f28(c71,X186),X187),X188) ) )),
    inference(bind,[status(th)],]) ).

tff(83,plain,
    ( ! [X188: $i,X186: $i,X187: $i] :
        ( p57(f26(f28(c71,X186),X187),X188)
        | ~ p57(f26(X186,X187),X188) )
  <=> ! [X188: $i,X186: $i,X187: $i] :
        ( ~ p57(f26(X186,X187),X188)
        | p57(f26(f28(c71,X186),X187),X188) ) ),
    inference(quant_intro,[status(thm)],[82]) ).

tff(84,axiom,
    ! [X188: $i,X186: $i,X187: $i] :
      ( p57(f26(f28(c71,X186),X187),X188)
      | ~ p57(f26(X186,X187),X188) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p57_74) ).

tff(85,plain,
    ! [X188: $i,X186: $i,X187: $i] :
      ( ~ p57(f26(X186,X187),X188)
      | p57(f26(f28(c71,X186),X187),X188) ),
    inference(modus_ponens,[status(thm)],[84,83]) ).

tff(86,plain,
    ! [X188: $i,X186: $i,X187: $i] :
      ( ~ p57(f26(X186,X187),X188)
      | p57(f26(f28(c71,X186),X187),X188) ),
    inference(modus_ponens,[status(thm)],[85,81]) ).

tff(87,plain,
    ! [X188: $i,X186: $i,X187: $i] :
      ( ~ p57(f26(X186,X187),X188)
      | p57(f26(f28(c71,X186),X187),X188) ),
    inference(skolemize,[status(sab)],[86]) ).

tff(88,plain,
    ! [X188: $i,X186: $i,X187: $i] :
      ( ~ p57(f26(X186,X187),X188)
      | p57(f26(f28(c71,X186),X187),X188) ),
    inference(modus_ponens,[status(thm)],[87,80]) ).

tff(89,plain,
    ( ~ p57(f26(f28(c71,f41(c78,c64)),c67),c77)
  <=> ~ p57(f26(f28(c71,f41(c78,c64)),c67),c77) ),
    inference(rewrite,[status(thm)],]) ).

tff(90,axiom,
    ~ p57(f26(f28(c71,f41(c78,c64)),c67),c77),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p57_39) ).

tff(91,plain,
    ~ p57(f26(f28(c71,f41(c78,c64)),c67),c77),
    inference(modus_ponens,[status(thm)],[90,89]) ).

tff(92,plain,
    ( ( ~ ! [X188: $i,X186: $i,X187: $i] :
            ( ~ p57(f26(X186,X187),X188)
            | p57(f26(f28(c71,X186),X187),X188) )
      | ~ p57(f26(f41(c78,c64),c67),c77)
      | p57(f26(f28(c71,f41(c78,c64)),c67),c77) )
  <=> ( ~ ! [X188: $i,X186: $i,X187: $i] :
            ( ~ p57(f26(X186,X187),X188)
            | p57(f26(f28(c71,X186),X187),X188) )
      | ~ p57(f26(f41(c78,c64),c67),c77)
      | p57(f26(f28(c71,f41(c78,c64)),c67),c77) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(93,plain,
    ( ~ ! [X188: $i,X186: $i,X187: $i] :
          ( ~ p57(f26(X186,X187),X188)
          | p57(f26(f28(c71,X186),X187),X188) )
    | ~ p57(f26(f41(c78,c64),c67),c77)
    | p57(f26(f28(c71,f41(c78,c64)),c67),c77) ),
    inference(quant_inst,[status(thm)],]) ).

tff(94,plain,
    ( ~ ! [X188: $i,X186: $i,X187: $i] :
          ( ~ p57(f26(X186,X187),X188)
          | p57(f26(f28(c71,X186),X187),X188) )
    | ~ p57(f26(f41(c78,c64),c67),c77)
    | p57(f26(f28(c71,f41(c78,c64)),c67),c77) ),
    inference(modus_ponens,[status(thm)],[93,92]) ).

tff(95,plain,
    ~ p57(f26(f41(c78,c64),c67),c77),
    inference(unit_resolution,[status(thm)],[94,91,88]) ).

tff(96,plain,
    ^ [X179: $i,X181: $i,X180: $i] :
      refl(
        ( ( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
          | p57(f26(f41(c78,X181),X179),X180) )
      <=> ( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
          | p57(f26(f41(c78,X181),X179),X180) ) )),
    inference(bind,[status(th)],]) ).

tff(97,plain,
    ( ! [X179: $i,X181: $i,X180: $i] :
        ( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
        | p57(f26(f41(c78,X181),X179),X180) )
  <=> ! [X179: $i,X181: $i,X180: $i] :
        ( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
        | p57(f26(f41(c78,X181),X179),X180) ) ),
    inference(quant_intro,[status(thm)],[96]) ).

tff(98,plain,
    ( ! [X179: $i,X181: $i,X180: $i] :
        ( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
        | p57(f26(f41(c78,X181),X179),X180) )
  <=> ! [X179: $i,X181: $i,X180: $i] :
        ( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
        | p57(f26(f41(c78,X181),X179),X180) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(99,plain,
    ^ [X179: $i,X181: $i,X180: $i] :
      rewrite(
        ( ( p57(f26(f41(c78,X181),X179),X180)
          | ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181) )
      <=> ( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
          | p57(f26(f41(c78,X181),X179),X180) ) )),
    inference(bind,[status(th)],]) ).

tff(100,plain,
    ( ! [X179: $i,X181: $i,X180: $i] :
        ( p57(f26(f41(c78,X181),X179),X180)
        | ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181) )
  <=> ! [X179: $i,X181: $i,X180: $i] :
        ( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
        | p57(f26(f41(c78,X181),X179),X180) ) ),
    inference(quant_intro,[status(thm)],[99]) ).

tff(101,axiom,
    ! [X179: $i,X181: $i,X180: $i] :
      ( p57(f26(f41(c78,X181),X179),X180)
      | ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p57_101) ).

tff(102,plain,
    ! [X179: $i,X181: $i,X180: $i] :
      ( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
      | p57(f26(f41(c78,X181),X179),X180) ),
    inference(modus_ponens,[status(thm)],[101,100]) ).

tff(103,plain,
    ! [X179: $i,X181: $i,X180: $i] :
      ( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
      | p57(f26(f41(c78,X181),X179),X180) ),
    inference(modus_ponens,[status(thm)],[102,98]) ).

tff(104,plain,
    ! [X179: $i,X181: $i,X180: $i] :
      ( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
      | p57(f26(f41(c78,X181),X179),X180) ),
    inference(skolemize,[status(sab)],[103]) ).

tff(105,plain,
    ! [X179: $i,X181: $i,X180: $i] :
      ( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
      | p57(f26(f41(c78,X181),X179),X180) ),
    inference(modus_ponens,[status(thm)],[104,97]) ).

tff(106,plain,
    ( ( ~ ! [X179: $i,X181: $i,X180: $i] :
            ( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
            | p57(f26(f41(c78,X181),X179),X180) )
      | ~ p56(f11(c65,f14(f17(c66,c67),f23(c74,c77))),c64)
      | p57(f26(f41(c78,c64),c67),c77) )
  <=> ( ~ ! [X179: $i,X181: $i,X180: $i] :
            ( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
            | p57(f26(f41(c78,X181),X179),X180) )
      | ~ p56(f11(c65,f14(f17(c66,c67),f23(c74,c77))),c64)
      | p57(f26(f41(c78,c64),c67),c77) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(107,plain,
    ( ~ ! [X179: $i,X181: $i,X180: $i] :
          ( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
          | p57(f26(f41(c78,X181),X179),X180) )
    | ~ p56(f11(c65,f14(f17(c66,c67),f23(c74,c77))),c64)
    | p57(f26(f41(c78,c64),c67),c77) ),
    inference(quant_inst,[status(thm)],]) ).

tff(108,plain,
    ( ~ ! [X179: $i,X181: $i,X180: $i] :
          ( ~ p56(f11(c65,f14(f17(c66,X179),f23(c74,X180))),X181)
          | p57(f26(f41(c78,X181),X179),X180) )
    | ~ p56(f11(c65,f14(f17(c66,c67),f23(c74,c77))),c64)
    | p57(f26(f41(c78,c64),c67),c77) ),
    inference(modus_ponens,[status(thm)],[107,106]) ).

tff(109,plain,
    ~ p56(f11(c65,f14(f17(c66,c67),f23(c74,c77))),c64),
    inference(unit_resolution,[status(thm)],[108,105,95]) ).

tff(110,plain,
    ^ [X175: $i,X176: $i,X178: $i,X177: $i] :
      refl(
        ( ( ~ p40(X178,X176)
          | ~ p4(X177,X175)
          | ~ p56(X177,X178)
          | p56(X175,X176) )
      <=> ( ~ p40(X178,X176)
          | ~ p4(X177,X175)
          | ~ p56(X177,X178)
          | p56(X175,X176) ) )),
    inference(bind,[status(th)],]) ).

tff(111,plain,
    ( ! [X175: $i,X176: $i,X178: $i,X177: $i] :
        ( ~ p40(X178,X176)
        | ~ p4(X177,X175)
        | ~ p56(X177,X178)
        | p56(X175,X176) )
  <=> ! [X175: $i,X176: $i,X178: $i,X177: $i] :
        ( ~ p40(X178,X176)
        | ~ p4(X177,X175)
        | ~ p56(X177,X178)
        | p56(X175,X176) ) ),
    inference(quant_intro,[status(thm)],[110]) ).

tff(112,plain,
    ( ! [X175: $i,X176: $i,X178: $i,X177: $i] :
        ( ~ p40(X178,X176)
        | ~ p4(X177,X175)
        | ~ p56(X177,X178)
        | p56(X175,X176) )
  <=> ! [X175: $i,X176: $i,X178: $i,X177: $i] :
        ( ~ p40(X178,X176)
        | ~ p4(X177,X175)
        | ~ p56(X177,X178)
        | p56(X175,X176) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(113,plain,
    ^ [X175: $i,X176: $i,X178: $i,X177: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( p56(X175,X176)
                  | ~ p40(X178,X176) )
              <=> ( ~ p40(X178,X176)
                  | p56(X175,X176) ) )),
              ( ( p56(X175,X176)
                | ~ p40(X178,X176)
                | ~ p56(X177,X178) )
            <=> ( ~ p40(X178,X176)
                | p56(X175,X176)
                | ~ p56(X177,X178) ) )),
            rewrite(
              ( ( ~ p40(X178,X176)
                | p56(X175,X176)
                | ~ p56(X177,X178) )
            <=> ( ~ p40(X178,X176)
                | ~ p56(X177,X178)
                | p56(X175,X176) ) )),
            ( ( p56(X175,X176)
              | ~ p40(X178,X176)
              | ~ p56(X177,X178) )
          <=> ( ~ p40(X178,X176)
              | ~ p56(X177,X178)
              | p56(X175,X176) ) )),
          ( ( p56(X175,X176)
            | ~ p40(X178,X176)
            | ~ p56(X177,X178)
            | ~ p4(X177,X175) )
        <=> ( ~ p40(X178,X176)
            | ~ p56(X177,X178)
            | p56(X175,X176)
            | ~ p4(X177,X175) ) )),
        rewrite(
          ( ( ~ p40(X178,X176)
            | ~ p56(X177,X178)
            | p56(X175,X176)
            | ~ p4(X177,X175) )
        <=> ( ~ p40(X178,X176)
            | ~ p4(X177,X175)
            | ~ p56(X177,X178)
            | p56(X175,X176) ) )),
        ( ( p56(X175,X176)
          | ~ p40(X178,X176)
          | ~ p56(X177,X178)
          | ~ p4(X177,X175) )
      <=> ( ~ p40(X178,X176)
          | ~ p4(X177,X175)
          | ~ p56(X177,X178)
          | p56(X175,X176) ) )),
    inference(bind,[status(th)],]) ).

tff(114,plain,
    ( ! [X175: $i,X176: $i,X178: $i,X177: $i] :
        ( p56(X175,X176)
        | ~ p40(X178,X176)
        | ~ p56(X177,X178)
        | ~ p4(X177,X175) )
  <=> ! [X175: $i,X176: $i,X178: $i,X177: $i] :
        ( ~ p40(X178,X176)
        | ~ p4(X177,X175)
        | ~ p56(X177,X178)
        | p56(X175,X176) ) ),
    inference(quant_intro,[status(thm)],[113]) ).

tff(115,axiom,
    ! [X175: $i,X176: $i,X178: $i,X177: $i] :
      ( p56(X175,X176)
      | ~ p40(X178,X176)
      | ~ p56(X177,X178)
      | ~ p4(X177,X175) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p56_76) ).

tff(116,plain,
    ! [X175: $i,X176: $i,X178: $i,X177: $i] :
      ( ~ p40(X178,X176)
      | ~ p4(X177,X175)
      | ~ p56(X177,X178)
      | p56(X175,X176) ),
    inference(modus_ponens,[status(thm)],[115,114]) ).

tff(117,plain,
    ! [X175: $i,X176: $i,X178: $i,X177: $i] :
      ( ~ p40(X178,X176)
      | ~ p4(X177,X175)
      | ~ p56(X177,X178)
      | p56(X175,X176) ),
    inference(modus_ponens,[status(thm)],[116,112]) ).

tff(118,plain,
    ! [X175: $i,X176: $i,X178: $i,X177: $i] :
      ( ~ p40(X178,X176)
      | ~ p4(X177,X175)
      | ~ p56(X177,X178)
      | p56(X175,X176) ),
    inference(skolemize,[status(sab)],[117]) ).

tff(119,plain,
    ! [X175: $i,X176: $i,X178: $i,X177: $i] :
      ( ~ p40(X178,X176)
      | ~ p4(X177,X175)
      | ~ p56(X177,X178)
      | p56(X175,X176) ),
    inference(modus_ponens,[status(thm)],[118,111]) ).

tff(120,plain,
    ( p56(f11(c65,f14(f17(c66,c67),c68)),c64)
  <=> p56(f11(c65,f14(f17(c66,c67),c68)),c64) ),
    inference(rewrite,[status(thm)],]) ).

tff(121,axiom,
    p56(f11(c65,f14(f17(c66,c67),c68)),c64),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p56_38) ).

tff(122,plain,
    p56(f11(c65,f14(f17(c66,c67),c68)),c64),
    inference(modus_ponens,[status(thm)],[121,120]) ).

tff(123,plain,
    ( ( ~ ! [X175: $i,X176: $i,X178: $i,X177: $i] :
            ( ~ p40(X178,X176)
            | ~ p4(X177,X175)
            | ~ p56(X177,X178)
            | p56(X175,X176) )
      | ~ p40(c64,c64)
      | ~ p4(f11(c65,f14(f17(c66,c67),c68)),f11(c65,f14(f17(c66,c67),f23(c74,c77))))
      | ~ p56(f11(c65,f14(f17(c66,c67),c68)),c64)
      | p56(f11(c65,f14(f17(c66,c67),f23(c74,c77))),c64) )
  <=> ( ~ ! [X175: $i,X176: $i,X178: $i,X177: $i] :
            ( ~ p40(X178,X176)
            | ~ p4(X177,X175)
            | ~ p56(X177,X178)
            | p56(X175,X176) )
      | ~ p40(c64,c64)
      | ~ p4(f11(c65,f14(f17(c66,c67),c68)),f11(c65,f14(f17(c66,c67),f23(c74,c77))))
      | ~ p56(f11(c65,f14(f17(c66,c67),c68)),c64)
      | p56(f11(c65,f14(f17(c66,c67),f23(c74,c77))),c64) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(124,plain,
    ( ~ ! [X175: $i,X176: $i,X178: $i,X177: $i] :
          ( ~ p40(X178,X176)
          | ~ p4(X177,X175)
          | ~ p56(X177,X178)
          | p56(X175,X176) )
    | ~ p40(c64,c64)
    | ~ p4(f11(c65,f14(f17(c66,c67),c68)),f11(c65,f14(f17(c66,c67),f23(c74,c77))))
    | ~ p56(f11(c65,f14(f17(c66,c67),c68)),c64)
    | p56(f11(c65,f14(f17(c66,c67),f23(c74,c77))),c64) ),
    inference(quant_inst,[status(thm)],]) ).

tff(125,plain,
    ( ~ ! [X175: $i,X176: $i,X178: $i,X177: $i] :
          ( ~ p40(X178,X176)
          | ~ p4(X177,X175)
          | ~ p56(X177,X178)
          | p56(X175,X176) )
    | ~ p40(c64,c64)
    | ~ p4(f11(c65,f14(f17(c66,c67),c68)),f11(c65,f14(f17(c66,c67),f23(c74,c77))))
    | ~ p56(f11(c65,f14(f17(c66,c67),c68)),c64)
    | p56(f11(c65,f14(f17(c66,c67),f23(c74,c77))),c64) ),
    inference(modus_ponens,[status(thm)],[124,123]) ).

tff(126,plain,
    $false,
    inference(unit_resolution,[status(thm)],[125,122,119,109,78,69]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SYN713-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.32  % Computer : n009.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Mon Sep  5 06:39:35 EDT 2022
% 0.12/0.32  % CPUTime  : 
% 0.12/0.33  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33  Usage: tptp [options] [-file:]file
% 0.12/0.33    -h, -?       prints this message.
% 0.12/0.33    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.33    -m, -model   generate model.
% 0.12/0.33    -p, -proof   generate proof.
% 0.12/0.33    -c, -core    generate unsat core of named formulas.
% 0.12/0.33    -st, -statistics display statistics.
% 0.12/0.33    -t:timeout   set timeout (in second).
% 0.12/0.33    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.33    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33    -<param>:<value> configuration parameter and value.
% 0.12/0.33    -o:<output-file> file to place output in.
% 0.47/0.54  % SZS status Unsatisfiable
% 0.47/0.54  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------