TSTP Solution File: SYN310-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN310-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n004.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 23:54:38 EDT 2022

% Result   : Unsatisfiable 0.13s 0.39s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   46
% Syntax   : Number of formulae    :   88 (  20 unt;   6 typ;   0 def)
%            Number of atoms       :  296 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  400 ( 190   ~; 184   |;   0   &)
%                                         (  26 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of FOOLs       :    4 (   4 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   3   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-1 aty)
%            Number of variables   :  252 ( 240   !;   0   ?; 252   :)

% Comments : 
%------------------------------------------------------------------------------
tff(p_type,type,
    p: ( $i * $i * $i ) > $o ).

tff(g_type,type,
    g: $i > $i ).

tff(b_type,type,
    b: $i ).

tff(a_type,type,
    a: $i ).

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

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

tff(1,plain,
    ( p(f(g(a)),f(g(b)),f(g(c)))
  <=> p(f(g(a)),f(g(b)),f(g(c))) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    p(f(g(a)),f(g(b)),f(g(c))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause6) ).

tff(3,plain,
    p(f(g(a)),f(g(b)),f(g(c))),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ^ [X: $i,X2: $i,X1: $i] :
      refl(
        ( ( ~ p(f(X),X1,X2)
          | p(X,X1,X2) )
      <=> ( ~ p(f(X),X1,X2)
          | p(X,X1,X2) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [X: $i,X2: $i,X1: $i] :
        ( ~ p(f(X),X1,X2)
        | p(X,X1,X2) )
  <=> ! [X: $i,X2: $i,X1: $i] :
        ( ~ p(f(X),X1,X2)
        | p(X,X1,X2) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,plain,
    ( ! [X: $i,X2: $i,X1: $i] :
        ( ~ p(f(X),X1,X2)
        | p(X,X1,X2) )
  <=> ! [X: $i,X2: $i,X1: $i] :
        ( ~ p(f(X),X1,X2)
        | p(X,X1,X2) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(7,axiom,
    ! [X: $i,X2: $i,X1: $i] :
      ( ~ p(f(X),X1,X2)
      | p(X,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause4) ).

tff(8,plain,
    ! [X: $i,X2: $i,X1: $i] :
      ( ~ p(f(X),X1,X2)
      | p(X,X1,X2) ),
    inference(modus_ponens,[status(thm)],[7,6]) ).

tff(9,plain,
    ! [X: $i,X2: $i,X1: $i] :
      ( ~ p(f(X),X1,X2)
      | p(X,X1,X2) ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [X: $i,X2: $i,X1: $i] :
      ( ~ p(f(X),X1,X2)
      | p(X,X1,X2) ),
    inference(modus_ponens,[status(thm)],[9,5]) ).

tff(11,plain,
    ( ( ~ ! [X: $i,X2: $i,X1: $i] :
            ( ~ p(f(X),X1,X2)
            | p(X,X1,X2) )
      | ~ p(f(g(a)),f(g(b)),f(g(c)))
      | p(g(a),f(g(b)),f(g(c))) )
  <=> ( ~ ! [X: $i,X2: $i,X1: $i] :
            ( ~ p(f(X),X1,X2)
            | p(X,X1,X2) )
      | ~ p(f(g(a)),f(g(b)),f(g(c)))
      | p(g(a),f(g(b)),f(g(c))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,plain,
    ( ~ ! [X: $i,X2: $i,X1: $i] :
          ( ~ p(f(X),X1,X2)
          | p(X,X1,X2) )
    | ~ p(f(g(a)),f(g(b)),f(g(c)))
    | p(g(a),f(g(b)),f(g(c))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(13,plain,
    ( ~ ! [X: $i,X2: $i,X1: $i] :
          ( ~ p(f(X),X1,X2)
          | p(X,X1,X2) )
    | ~ p(f(g(a)),f(g(b)),f(g(c)))
    | p(g(a),f(g(b)),f(g(c))) ),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    p(g(a),f(g(b)),f(g(c))),
    inference(unit_resolution,[status(thm)],[13,10,3]) ).

tff(15,plain,
    ^ [X: $i,X2: $i,X1: $i] :
      refl(
        ( ( ~ p(X2,X1,X)
          | p(X,X1,X2) )
      <=> ( ~ p(X2,X1,X)
          | p(X,X1,X2) ) )),
    inference(bind,[status(th)],]) ).

tff(16,plain,
    ( ! [X: $i,X2: $i,X1: $i] :
        ( ~ p(X2,X1,X)
        | p(X,X1,X2) )
  <=> ! [X: $i,X2: $i,X1: $i] :
        ( ~ p(X2,X1,X)
        | p(X,X1,X2) ) ),
    inference(quant_intro,[status(thm)],[15]) ).

tff(17,plain,
    ( ! [X: $i,X2: $i,X1: $i] :
        ( ~ p(X2,X1,X)
        | p(X,X1,X2) )
  <=> ! [X: $i,X2: $i,X1: $i] :
        ( ~ p(X2,X1,X)
        | p(X,X1,X2) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(18,axiom,
    ! [X: $i,X2: $i,X1: $i] :
      ( ~ p(X2,X1,X)
      | p(X,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause1) ).

tff(19,plain,
    ! [X: $i,X2: $i,X1: $i] :
      ( ~ p(X2,X1,X)
      | p(X,X1,X2) ),
    inference(modus_ponens,[status(thm)],[18,17]) ).

tff(20,plain,
    ! [X: $i,X2: $i,X1: $i] :
      ( ~ p(X2,X1,X)
      | p(X,X1,X2) ),
    inference(skolemize,[status(sab)],[19]) ).

tff(21,plain,
    ! [X: $i,X2: $i,X1: $i] :
      ( ~ p(X2,X1,X)
      | p(X,X1,X2) ),
    inference(modus_ponens,[status(thm)],[20,16]) ).

tff(22,plain,
    ( ( ~ ! [X: $i,X2: $i,X1: $i] :
            ( ~ p(X2,X1,X)
            | p(X,X1,X2) )
      | ~ p(g(a),f(g(b)),f(g(c)))
      | p(f(g(c)),f(g(b)),g(a)) )
  <=> ( ~ ! [X: $i,X2: $i,X1: $i] :
            ( ~ p(X2,X1,X)
            | p(X,X1,X2) )
      | ~ p(g(a),f(g(b)),f(g(c)))
      | p(f(g(c)),f(g(b)),g(a)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(23,plain,
    ( ~ ! [X: $i,X2: $i,X1: $i] :
          ( ~ p(X2,X1,X)
          | p(X,X1,X2) )
    | ~ p(g(a),f(g(b)),f(g(c)))
    | p(f(g(c)),f(g(b)),g(a)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(24,plain,
    ( ~ ! [X: $i,X2: $i,X1: $i] :
          ( ~ p(X2,X1,X)
          | p(X,X1,X2) )
    | ~ p(g(a),f(g(b)),f(g(c)))
    | p(f(g(c)),f(g(b)),g(a)) ),
    inference(modus_ponens,[status(thm)],[23,22]) ).

tff(25,plain,
    p(f(g(c)),f(g(b)),g(a)),
    inference(unit_resolution,[status(thm)],[24,21,14]) ).

tff(26,plain,
    ( ( ~ ! [X: $i,X2: $i,X1: $i] :
            ( ~ p(f(X),X1,X2)
            | p(X,X1,X2) )
      | ~ p(f(g(c)),f(g(b)),g(a))
      | p(g(c),f(g(b)),g(a)) )
  <=> ( ~ ! [X: $i,X2: $i,X1: $i] :
            ( ~ p(f(X),X1,X2)
            | p(X,X1,X2) )
      | ~ p(f(g(c)),f(g(b)),g(a))
      | p(g(c),f(g(b)),g(a)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(27,plain,
    ( ~ ! [X: $i,X2: $i,X1: $i] :
          ( ~ p(f(X),X1,X2)
          | p(X,X1,X2) )
    | ~ p(f(g(c)),f(g(b)),g(a))
    | p(g(c),f(g(b)),g(a)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(28,plain,
    ( ~ ! [X: $i,X2: $i,X1: $i] :
          ( ~ p(f(X),X1,X2)
          | p(X,X1,X2) )
    | ~ p(f(g(c)),f(g(b)),g(a))
    | p(g(c),f(g(b)),g(a)) ),
    inference(modus_ponens,[status(thm)],[27,26]) ).

tff(29,plain,
    p(g(c),f(g(b)),g(a)),
    inference(unit_resolution,[status(thm)],[28,10,25]) ).

tff(30,plain,
    ^ [X: $i,X2: $i,X1: $i] :
      refl(
        ( ( ~ p(X,X1,g(X2))
          | p(X,X1,X2) )
      <=> ( ~ p(X,X1,g(X2))
          | p(X,X1,X2) ) )),
    inference(bind,[status(th)],]) ).

tff(31,plain,
    ( ! [X: $i,X2: $i,X1: $i] :
        ( ~ p(X,X1,g(X2))
        | p(X,X1,X2) )
  <=> ! [X: $i,X2: $i,X1: $i] :
        ( ~ p(X,X1,g(X2))
        | p(X,X1,X2) ) ),
    inference(quant_intro,[status(thm)],[30]) ).

tff(32,plain,
    ( ! [X: $i,X2: $i,X1: $i] :
        ( ~ p(X,X1,g(X2))
        | p(X,X1,X2) )
  <=> ! [X: $i,X2: $i,X1: $i] :
        ( ~ p(X,X1,g(X2))
        | p(X,X1,X2) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(33,axiom,
    ! [X: $i,X2: $i,X1: $i] :
      ( ~ p(X,X1,g(X2))
      | p(X,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause3) ).

tff(34,plain,
    ! [X: $i,X2: $i,X1: $i] :
      ( ~ p(X,X1,g(X2))
      | p(X,X1,X2) ),
    inference(modus_ponens,[status(thm)],[33,32]) ).

tff(35,plain,
    ! [X: $i,X2: $i,X1: $i] :
      ( ~ p(X,X1,g(X2))
      | p(X,X1,X2) ),
    inference(skolemize,[status(sab)],[34]) ).

tff(36,plain,
    ! [X: $i,X2: $i,X1: $i] :
      ( ~ p(X,X1,g(X2))
      | p(X,X1,X2) ),
    inference(modus_ponens,[status(thm)],[35,31]) ).

tff(37,plain,
    ( ( ~ ! [X: $i,X2: $i,X1: $i] :
            ( ~ p(X,X1,g(X2))
            | p(X,X1,X2) )
      | ~ p(g(c),f(g(b)),g(a))
      | p(g(c),f(g(b)),a) )
  <=> ( ~ ! [X: $i,X2: $i,X1: $i] :
            ( ~ p(X,X1,g(X2))
            | p(X,X1,X2) )
      | ~ p(g(c),f(g(b)),g(a))
      | p(g(c),f(g(b)),a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(38,plain,
    ( ~ ! [X: $i,X2: $i,X1: $i] :
          ( ~ p(X,X1,g(X2))
          | p(X,X1,X2) )
    | ~ p(g(c),f(g(b)),g(a))
    | p(g(c),f(g(b)),a) ),
    inference(quant_inst,[status(thm)],]) ).

tff(39,plain,
    ( ~ ! [X: $i,X2: $i,X1: $i] :
          ( ~ p(X,X1,g(X2))
          | p(X,X1,X2) )
    | ~ p(g(c),f(g(b)),g(a))
    | p(g(c),f(g(b)),a) ),
    inference(modus_ponens,[status(thm)],[38,37]) ).

tff(40,plain,
    p(g(c),f(g(b)),a),
    inference(unit_resolution,[status(thm)],[39,36,29]) ).

tff(41,plain,
    ( ( ~ ! [X: $i,X2: $i,X1: $i] :
            ( ~ p(X2,X1,X)
            | p(X,X1,X2) )
      | ~ p(g(c),f(g(b)),a)
      | p(a,f(g(b)),g(c)) )
  <=> ( ~ ! [X: $i,X2: $i,X1: $i] :
            ( ~ p(X2,X1,X)
            | p(X,X1,X2) )
      | ~ p(g(c),f(g(b)),a)
      | p(a,f(g(b)),g(c)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(42,plain,
    ( ~ ! [X: $i,X2: $i,X1: $i] :
          ( ~ p(X2,X1,X)
          | p(X,X1,X2) )
    | ~ p(g(c),f(g(b)),a)
    | p(a,f(g(b)),g(c)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(43,plain,
    ( ~ ! [X: $i,X2: $i,X1: $i] :
          ( ~ p(X2,X1,X)
          | p(X,X1,X2) )
    | ~ p(g(c),f(g(b)),a)
    | p(a,f(g(b)),g(c)) ),
    inference(modus_ponens,[status(thm)],[42,41]) ).

tff(44,plain,
    p(a,f(g(b)),g(c)),
    inference(unit_resolution,[status(thm)],[43,21,40]) ).

tff(45,plain,
    ( ( ~ ! [X: $i,X2: $i,X1: $i] :
            ( ~ p(X,X1,g(X2))
            | p(X,X1,X2) )
      | ~ p(a,f(g(b)),g(c))
      | p(a,f(g(b)),c) )
  <=> ( ~ ! [X: $i,X2: $i,X1: $i] :
            ( ~ p(X,X1,g(X2))
            | p(X,X1,X2) )
      | ~ p(a,f(g(b)),g(c))
      | p(a,f(g(b)),c) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(46,plain,
    ( ~ ! [X: $i,X2: $i,X1: $i] :
          ( ~ p(X,X1,g(X2))
          | p(X,X1,X2) )
    | ~ p(a,f(g(b)),g(c))
    | p(a,f(g(b)),c) ),
    inference(quant_inst,[status(thm)],]) ).

tff(47,plain,
    ( ~ ! [X: $i,X2: $i,X1: $i] :
          ( ~ p(X,X1,g(X2))
          | p(X,X1,X2) )
    | ~ p(a,f(g(b)),g(c))
    | p(a,f(g(b)),c) ),
    inference(modus_ponens,[status(thm)],[46,45]) ).

tff(48,plain,
    p(a,f(g(b)),c),
    inference(unit_resolution,[status(thm)],[47,36,44]) ).

tff(49,plain,
    ^ [X: $i,X2: $i,X1: $i] :
      refl(
        ( ( ~ p(X1,X,X2)
          | p(X,X1,X2) )
      <=> ( ~ p(X1,X,X2)
          | p(X,X1,X2) ) )),
    inference(bind,[status(th)],]) ).

tff(50,plain,
    ( ! [X: $i,X2: $i,X1: $i] :
        ( ~ p(X1,X,X2)
        | p(X,X1,X2) )
  <=> ! [X: $i,X2: $i,X1: $i] :
        ( ~ p(X1,X,X2)
        | p(X,X1,X2) ) ),
    inference(quant_intro,[status(thm)],[49]) ).

tff(51,plain,
    ( ! [X: $i,X2: $i,X1: $i] :
        ( ~ p(X1,X,X2)
        | p(X,X1,X2) )
  <=> ! [X: $i,X2: $i,X1: $i] :
        ( ~ p(X1,X,X2)
        | p(X,X1,X2) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(52,axiom,
    ! [X: $i,X2: $i,X1: $i] :
      ( ~ p(X1,X,X2)
      | p(X,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause2) ).

tff(53,plain,
    ! [X: $i,X2: $i,X1: $i] :
      ( ~ p(X1,X,X2)
      | p(X,X1,X2) ),
    inference(modus_ponens,[status(thm)],[52,51]) ).

tff(54,plain,
    ! [X: $i,X2: $i,X1: $i] :
      ( ~ p(X1,X,X2)
      | p(X,X1,X2) ),
    inference(skolemize,[status(sab)],[53]) ).

tff(55,plain,
    ! [X: $i,X2: $i,X1: $i] :
      ( ~ p(X1,X,X2)
      | p(X,X1,X2) ),
    inference(modus_ponens,[status(thm)],[54,50]) ).

tff(56,plain,
    ( ( ~ ! [X: $i,X2: $i,X1: $i] :
            ( ~ p(X1,X,X2)
            | p(X,X1,X2) )
      | ~ p(a,f(g(b)),c)
      | p(f(g(b)),a,c) )
  <=> ( ~ ! [X: $i,X2: $i,X1: $i] :
            ( ~ p(X1,X,X2)
            | p(X,X1,X2) )
      | ~ p(a,f(g(b)),c)
      | p(f(g(b)),a,c) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(57,plain,
    ( ~ ! [X: $i,X2: $i,X1: $i] :
          ( ~ p(X1,X,X2)
          | p(X,X1,X2) )
    | ~ p(a,f(g(b)),c)
    | p(f(g(b)),a,c) ),
    inference(quant_inst,[status(thm)],]) ).

tff(58,plain,
    ( ~ ! [X: $i,X2: $i,X1: $i] :
          ( ~ p(X1,X,X2)
          | p(X,X1,X2) )
    | ~ p(a,f(g(b)),c)
    | p(f(g(b)),a,c) ),
    inference(modus_ponens,[status(thm)],[57,56]) ).

tff(59,plain,
    p(f(g(b)),a,c),
    inference(unit_resolution,[status(thm)],[58,55,48]) ).

tff(60,plain,
    ( ( ~ ! [X: $i,X2: $i,X1: $i] :
            ( ~ p(f(X),X1,X2)
            | p(X,X1,X2) )
      | ~ p(f(g(b)),a,c)
      | p(g(b),a,c) )
  <=> ( ~ ! [X: $i,X2: $i,X1: $i] :
            ( ~ p(f(X),X1,X2)
            | p(X,X1,X2) )
      | ~ p(f(g(b)),a,c)
      | p(g(b),a,c) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(61,plain,
    ( ~ ! [X: $i,X2: $i,X1: $i] :
          ( ~ p(f(X),X1,X2)
          | p(X,X1,X2) )
    | ~ p(f(g(b)),a,c)
    | p(g(b),a,c) ),
    inference(quant_inst,[status(thm)],]) ).

tff(62,plain,
    ( ~ ! [X: $i,X2: $i,X1: $i] :
          ( ~ p(f(X),X1,X2)
          | p(X,X1,X2) )
    | ~ p(f(g(b)),a,c)
    | p(g(b),a,c) ),
    inference(modus_ponens,[status(thm)],[61,60]) ).

tff(63,plain,
    p(g(b),a,c),
    inference(unit_resolution,[status(thm)],[62,10,59]) ).

tff(64,plain,
    ( ( ~ ! [X: $i,X2: $i,X1: $i] :
            ( ~ p(X2,X1,X)
            | p(X,X1,X2) )
      | ~ p(g(b),a,c)
      | p(c,a,g(b)) )
  <=> ( ~ ! [X: $i,X2: $i,X1: $i] :
            ( ~ p(X2,X1,X)
            | p(X,X1,X2) )
      | ~ p(g(b),a,c)
      | p(c,a,g(b)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(65,plain,
    ( ~ ! [X: $i,X2: $i,X1: $i] :
          ( ~ p(X2,X1,X)
          | p(X,X1,X2) )
    | ~ p(g(b),a,c)
    | p(c,a,g(b)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(66,plain,
    ( ~ ! [X: $i,X2: $i,X1: $i] :
          ( ~ p(X2,X1,X)
          | p(X,X1,X2) )
    | ~ p(g(b),a,c)
    | p(c,a,g(b)) ),
    inference(modus_ponens,[status(thm)],[65,64]) ).

tff(67,plain,
    p(c,a,g(b)),
    inference(unit_resolution,[status(thm)],[66,21,63]) ).

tff(68,plain,
    ( ~ p(a,b,c)
  <=> ~ p(a,b,c) ),
    inference(rewrite,[status(thm)],]) ).

tff(69,axiom,
    ~ p(a,b,c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause5) ).

tff(70,plain,
    ~ p(a,b,c),
    inference(modus_ponens,[status(thm)],[69,68]) ).

tff(71,plain,
    ( ( ~ ! [X: $i,X2: $i,X1: $i] :
            ( ~ p(X1,X,X2)
            | p(X,X1,X2) )
      | ~ p(b,a,c)
      | p(a,b,c) )
  <=> ( ~ ! [X: $i,X2: $i,X1: $i] :
            ( ~ p(X1,X,X2)
            | p(X,X1,X2) )
      | ~ p(b,a,c)
      | p(a,b,c) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(72,plain,
    ( ~ ! [X: $i,X2: $i,X1: $i] :
          ( ~ p(X1,X,X2)
          | p(X,X1,X2) )
    | ~ p(b,a,c)
    | p(a,b,c) ),
    inference(quant_inst,[status(thm)],]) ).

tff(73,plain,
    ( ~ ! [X: $i,X2: $i,X1: $i] :
          ( ~ p(X1,X,X2)
          | p(X,X1,X2) )
    | ~ p(b,a,c)
    | p(a,b,c) ),
    inference(modus_ponens,[status(thm)],[72,71]) ).

tff(74,plain,
    ~ p(b,a,c),
    inference(unit_resolution,[status(thm)],[73,55,70]) ).

tff(75,plain,
    ( ( ~ ! [X: $i,X2: $i,X1: $i] :
            ( ~ p(X2,X1,X)
            | p(X,X1,X2) )
      | ~ p(c,a,b)
      | p(b,a,c) )
  <=> ( ~ ! [X: $i,X2: $i,X1: $i] :
            ( ~ p(X2,X1,X)
            | p(X,X1,X2) )
      | ~ p(c,a,b)
      | p(b,a,c) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(76,plain,
    ( ~ ! [X: $i,X2: $i,X1: $i] :
          ( ~ p(X2,X1,X)
          | p(X,X1,X2) )
    | ~ p(c,a,b)
    | p(b,a,c) ),
    inference(quant_inst,[status(thm)],]) ).

tff(77,plain,
    ( ~ ! [X: $i,X2: $i,X1: $i] :
          ( ~ p(X2,X1,X)
          | p(X,X1,X2) )
    | ~ p(c,a,b)
    | p(b,a,c) ),
    inference(modus_ponens,[status(thm)],[76,75]) ).

tff(78,plain,
    ~ p(c,a,b),
    inference(unit_resolution,[status(thm)],[77,21,74]) ).

tff(79,plain,
    ( ( ~ ! [X: $i,X2: $i,X1: $i] :
            ( ~ p(X,X1,g(X2))
            | p(X,X1,X2) )
      | ~ p(c,a,g(b))
      | p(c,a,b) )
  <=> ( ~ ! [X: $i,X2: $i,X1: $i] :
            ( ~ p(X,X1,g(X2))
            | p(X,X1,X2) )
      | ~ p(c,a,g(b))
      | p(c,a,b) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(80,plain,
    ( ~ ! [X: $i,X2: $i,X1: $i] :
          ( ~ p(X,X1,g(X2))
          | p(X,X1,X2) )
    | ~ p(c,a,g(b))
    | p(c,a,b) ),
    inference(quant_inst,[status(thm)],]) ).

tff(81,plain,
    ( ~ ! [X: $i,X2: $i,X1: $i] :
          ( ~ p(X,X1,g(X2))
          | p(X,X1,X2) )
    | ~ p(c,a,g(b))
    | p(c,a,b) ),
    inference(modus_ponens,[status(thm)],[80,79]) ).

tff(82,plain,
    $false,
    inference(unit_resolution,[status(thm)],[81,36,78,67]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN310-1 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n004.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon Sep  5 02:23:19 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 0.13/0.39  % SZS status Unsatisfiable
% 0.13/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------