TSTP Solution File: SYN224-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN224-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n014.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 23:54:16 EDT 2022

% Result   : Unsatisfiable 0.18s 0.47s
% Output   : Proof 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   50
% Syntax   : Number of formulae    :   95 (  26 unt;  12 typ;   0 def)
%            Number of atoms       :  433 (   0 equ)
%            Maximal formula atoms :   12 (   5 avg)
%            Number of connectives :  595 ( 280   ~; 266   |;   0   &)
%                                         (  49 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :   35 (  35 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (   9   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :   17 (  15 usr;   2 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :  162 ( 144   !;   0   ?; 162   :)

% Comments : 
%------------------------------------------------------------------------------
tff(l3_type,type,
    l3: ( $i * $i ) > $o ).

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

tff(r2_type,type,
    r2: $i > $o ).

tff(r1_type,type,
    r1: $i > $o ).

tff(q1_type,type,
    q1: ( $i * $i * $i ) > $o ).

tff(d_type,type,
    d: $i ).

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

tff(n0_type,type,
    n0: ( $i * $i ) > $o ).

tff(p0_type,type,
    p0: ( $i * $i ) > $o ).

tff(q0_type,type,
    q0: ( $i * $i ) > $o ).

tff(s0_type,type,
    s0: $i > $o ).

tff(l0_type,type,
    l0: $i > $o ).

tff(1,plain,
    ^ [B: $i] :
      refl(
        ( ( l3(B,B)
          | ~ r2(B) )
      <=> ( l3(B,B)
          | ~ r2(B) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [B: $i] :
        ( l3(B,B)
        | ~ r2(B) )
  <=> ! [B: $i] :
        ( l3(B,B)
        | ~ r2(B) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [B: $i] :
        ( l3(B,B)
        | ~ r2(B) )
  <=> ! [B: $i] :
        ( l3(B,B)
        | ~ r2(B) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [B: $i] :
      ( l3(B,B)
      | ~ r2(B) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_218) ).

tff(5,plain,
    ! [B: $i] :
      ( l3(B,B)
      | ~ r2(B) ),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [B: $i] :
      ( l3(B,B)
      | ~ r2(B) ),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [B: $i] :
      ( l3(B,B)
      | ~ r2(B) ),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ^ [B: $i,A: $i,J: $i,C: $i] :
      refl(
        ( ( ~ p0(C,J)
          | ~ n0(B,A)
          | q1(J,A,J) )
      <=> ( ~ p0(C,J)
          | ~ n0(B,A)
          | q1(J,A,J) ) )),
    inference(bind,[status(th)],]) ).

tff(9,plain,
    ( ! [B: $i,A: $i,J: $i,C: $i] :
        ( ~ p0(C,J)
        | ~ n0(B,A)
        | q1(J,A,J) )
  <=> ! [B: $i,A: $i,J: $i,C: $i] :
        ( ~ p0(C,J)
        | ~ n0(B,A)
        | q1(J,A,J) ) ),
    inference(quant_intro,[status(thm)],[8]) ).

tff(10,plain,
    ( ! [B: $i,A: $i,J: $i,C: $i] :
        ( ~ p0(C,J)
        | ~ n0(B,A)
        | q1(J,A,J) )
  <=> ! [B: $i,A: $i,J: $i,C: $i] :
        ( ~ p0(C,J)
        | ~ n0(B,A)
        | q1(J,A,J) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(11,plain,
    ^ [B: $i,A: $i,J: $i,C: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( q1(J,A,J)
              | ~ n0(B,A) )
          <=> ( ~ n0(B,A)
              | q1(J,A,J) ) )),
          ( ( q1(J,A,J)
            | ~ n0(B,A)
            | ~ p0(C,J) )
        <=> ( ~ n0(B,A)
            | q1(J,A,J)
            | ~ p0(C,J) ) )),
        rewrite(
          ( ( ~ n0(B,A)
            | q1(J,A,J)
            | ~ p0(C,J) )
        <=> ( ~ p0(C,J)
            | ~ n0(B,A)
            | q1(J,A,J) ) )),
        ( ( q1(J,A,J)
          | ~ n0(B,A)
          | ~ p0(C,J) )
      <=> ( ~ p0(C,J)
          | ~ n0(B,A)
          | q1(J,A,J) ) )),
    inference(bind,[status(th)],]) ).

tff(12,plain,
    ( ! [B: $i,A: $i,J: $i,C: $i] :
        ( q1(J,A,J)
        | ~ n0(B,A)
        | ~ p0(C,J) )
  <=> ! [B: $i,A: $i,J: $i,C: $i] :
        ( ~ p0(C,J)
        | ~ n0(B,A)
        | q1(J,A,J) ) ),
    inference(quant_intro,[status(thm)],[11]) ).

tff(13,axiom,
    ! [B: $i,A: $i,J: $i,C: $i] :
      ( q1(J,A,J)
      | ~ n0(B,A)
      | ~ p0(C,J) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_092) ).

tff(14,plain,
    ! [B: $i,A: $i,J: $i,C: $i] :
      ( ~ p0(C,J)
      | ~ n0(B,A)
      | q1(J,A,J) ),
    inference(modus_ponens,[status(thm)],[13,12]) ).

tff(15,plain,
    ! [B: $i,A: $i,J: $i,C: $i] :
      ( ~ p0(C,J)
      | ~ n0(B,A)
      | q1(J,A,J) ),
    inference(modus_ponens,[status(thm)],[14,10]) ).

tff(16,plain,
    ! [B: $i,A: $i,J: $i,C: $i] :
      ( ~ p0(C,J)
      | ~ n0(B,A)
      | q1(J,A,J) ),
    inference(skolemize,[status(sab)],[15]) ).

tff(17,plain,
    ! [B: $i,A: $i,J: $i,C: $i] :
      ( ~ p0(C,J)
      | ~ n0(B,A)
      | q1(J,A,J) ),
    inference(modus_ponens,[status(thm)],[16,9]) ).

tff(18,plain,
    ( p0(b,d)
  <=> p0(b,d) ),
    inference(rewrite,[status(thm)],]) ).

tff(19,axiom,
    p0(b,d),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_10) ).

tff(20,plain,
    p0(b,d),
    inference(modus_ponens,[status(thm)],[19,18]) ).

tff(21,plain,
    ( n0(d,b)
  <=> n0(d,b) ),
    inference(rewrite,[status(thm)],]) ).

tff(22,axiom,
    n0(d,b),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_7) ).

tff(23,plain,
    n0(d,b),
    inference(modus_ponens,[status(thm)],[22,21]) ).

tff(24,plain,
    ( ( ~ ! [B: $i,A: $i,J: $i,C: $i] :
            ( ~ p0(C,J)
            | ~ n0(B,A)
            | q1(J,A,J) )
      | ~ p0(b,d)
      | ~ n0(d,b)
      | q1(d,b,d) )
  <=> ( ~ ! [B: $i,A: $i,J: $i,C: $i] :
            ( ~ p0(C,J)
            | ~ n0(B,A)
            | q1(J,A,J) )
      | ~ p0(b,d)
      | ~ n0(d,b)
      | q1(d,b,d) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(25,plain,
    ( ~ ! [B: $i,A: $i,J: $i,C: $i] :
          ( ~ p0(C,J)
          | ~ n0(B,A)
          | q1(J,A,J) )
    | ~ p0(b,d)
    | ~ n0(d,b)
    | q1(d,b,d) ),
    inference(quant_inst,[status(thm)],]) ).

tff(26,plain,
    ( ~ ! [B: $i,A: $i,J: $i,C: $i] :
          ( ~ p0(C,J)
          | ~ n0(B,A)
          | q1(J,A,J) )
    | ~ p0(b,d)
    | ~ n0(d,b)
    | q1(d,b,d) ),
    inference(modus_ponens,[status(thm)],[25,24]) ).

tff(27,plain,
    q1(d,b,d),
    inference(unit_resolution,[status(thm)],[26,23,20,17]) ).

tff(28,plain,
    ^ [D: $i,E: $i] :
      refl(
        ( ( ~ q0(D,E)
          | ~ q1(d,E,d)
          | r1(D) )
      <=> ( ~ q0(D,E)
          | ~ q1(d,E,d)
          | r1(D) ) )),
    inference(bind,[status(th)],]) ).

tff(29,plain,
    ( ! [D: $i,E: $i] :
        ( ~ q0(D,E)
        | ~ q1(d,E,d)
        | r1(D) )
  <=> ! [D: $i,E: $i] :
        ( ~ q0(D,E)
        | ~ q1(d,E,d)
        | r1(D) ) ),
    inference(quant_intro,[status(thm)],[28]) ).

tff(30,plain,
    ( ! [D: $i,E: $i] :
        ( ~ q0(D,E)
        | ~ q1(d,E,d)
        | r1(D) )
  <=> ! [D: $i,E: $i] :
        ( ~ q0(D,E)
        | ~ q1(d,E,d)
        | r1(D) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(31,plain,
    ^ [D: $i,E: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              iff_true(asserted(s0(d)),
                ( s0(d)
              <=> $true )),
              ( ~ s0(d)
            <=> ~ $true )),
            rewrite(
              ( ~ $true
            <=> $false )),
            ( ~ s0(d)
          <=> $false )),
          ( ( ~ q0(D,E)
            | ~ s0(d)
            | ~ q1(d,E,d)
            | r1(D) )
        <=> ( ~ q0(D,E)
            | $false
            | ~ q1(d,E,d)
            | r1(D) ) )),
        rewrite(
          ( ( ~ q0(D,E)
            | $false
            | ~ q1(d,E,d)
            | r1(D) )
        <=> ( ~ q0(D,E)
            | ~ q1(d,E,d)
            | r1(D) ) )),
        ( ( ~ q0(D,E)
          | ~ s0(d)
          | ~ q1(d,E,d)
          | r1(D) )
      <=> ( ~ q0(D,E)
          | ~ q1(d,E,d)
          | r1(D) ) )),
    inference(bind,[status(th)],]) ).

tff(32,plain,
    ( ! [D: $i,E: $i] :
        ( ~ q0(D,E)
        | ~ s0(d)
        | ~ q1(d,E,d)
        | r1(D) )
  <=> ! [D: $i,E: $i] :
        ( ~ q0(D,E)
        | ~ q1(d,E,d)
        | r1(D) ) ),
    inference(quant_intro,[status(thm)],[31]) ).

tff(33,plain,
    ^ [D: $i,E: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( r1(D)
              | ~ q0(D,E)
              | ~ s0(d) )
          <=> ( ~ q0(D,E)
              | ~ s0(d)
              | r1(D) ) )),
          ( ( r1(D)
            | ~ q0(D,E)
            | ~ s0(d)
            | ~ q1(d,E,d) )
        <=> ( ~ q0(D,E)
            | ~ s0(d)
            | r1(D)
            | ~ q1(d,E,d) ) )),
        rewrite(
          ( ( ~ q0(D,E)
            | ~ s0(d)
            | r1(D)
            | ~ q1(d,E,d) )
        <=> ( ~ q0(D,E)
            | ~ s0(d)
            | ~ q1(d,E,d)
            | r1(D) ) )),
        ( ( r1(D)
          | ~ q0(D,E)
          | ~ s0(d)
          | ~ q1(d,E,d) )
      <=> ( ~ q0(D,E)
          | ~ s0(d)
          | ~ q1(d,E,d)
          | r1(D) ) )),
    inference(bind,[status(th)],]) ).

tff(34,plain,
    ( ! [D: $i,E: $i] :
        ( r1(D)
        | ~ q0(D,E)
        | ~ s0(d)
        | ~ q1(d,E,d) )
  <=> ! [D: $i,E: $i] :
        ( ~ q0(D,E)
        | ~ s0(d)
        | ~ q1(d,E,d)
        | r1(D) ) ),
    inference(quant_intro,[status(thm)],[33]) ).

tff(35,axiom,
    ! [D: $i,E: $i] :
      ( r1(D)
      | ~ q0(D,E)
      | ~ s0(d)
      | ~ q1(d,E,d) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_124) ).

tff(36,plain,
    ! [D: $i,E: $i] :
      ( ~ q0(D,E)
      | ~ s0(d)
      | ~ q1(d,E,d)
      | r1(D) ),
    inference(modus_ponens,[status(thm)],[35,34]) ).

tff(37,plain,
    ! [D: $i,E: $i] :
      ( ~ q0(D,E)
      | ~ q1(d,E,d)
      | r1(D) ),
    inference(modus_ponens,[status(thm)],[36,32]) ).

tff(38,plain,
    ! [D: $i,E: $i] :
      ( ~ q0(D,E)
      | ~ q1(d,E,d)
      | r1(D) ),
    inference(modus_ponens,[status(thm)],[37,30]) ).

tff(39,plain,
    ! [D: $i,E: $i] :
      ( ~ q0(D,E)
      | ~ q1(d,E,d)
      | r1(D) ),
    inference(skolemize,[status(sab)],[38]) ).

tff(40,plain,
    ! [D: $i,E: $i] :
      ( ~ q0(D,E)
      | ~ q1(d,E,d)
      | r1(D) ),
    inference(modus_ponens,[status(thm)],[39,29]) ).

tff(41,plain,
    ( q0(a,b)
  <=> q0(a,b) ),
    inference(rewrite,[status(thm)],]) ).

tff(42,axiom,
    q0(a,b),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_36) ).

tff(43,plain,
    q0(a,b),
    inference(modus_ponens,[status(thm)],[42,41]) ).

tff(44,plain,
    ( ( ~ ! [D: $i,E: $i] :
            ( ~ q0(D,E)
            | ~ q1(d,E,d)
            | r1(D) )
      | r1(a)
      | ~ q1(d,b,d)
      | ~ q0(a,b) )
  <=> ( ~ ! [D: $i,E: $i] :
            ( ~ q0(D,E)
            | ~ q1(d,E,d)
            | r1(D) )
      | r1(a)
      | ~ q1(d,b,d)
      | ~ q0(a,b) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(45,plain,
    ( ( ~ q0(a,b)
      | ~ q1(d,b,d)
      | r1(a) )
  <=> ( r1(a)
      | ~ q1(d,b,d)
      | ~ q0(a,b) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(46,plain,
    ( ( ~ ! [D: $i,E: $i] :
            ( ~ q0(D,E)
            | ~ q1(d,E,d)
            | r1(D) )
      | ~ q0(a,b)
      | ~ q1(d,b,d)
      | r1(a) )
  <=> ( ~ ! [D: $i,E: $i] :
            ( ~ q0(D,E)
            | ~ q1(d,E,d)
            | r1(D) )
      | r1(a)
      | ~ q1(d,b,d)
      | ~ q0(a,b) ) ),
    inference(monotonicity,[status(thm)],[45]) ).

tff(47,plain,
    ( ( ~ ! [D: $i,E: $i] :
            ( ~ q0(D,E)
            | ~ q1(d,E,d)
            | r1(D) )
      | ~ q0(a,b)
      | ~ q1(d,b,d)
      | r1(a) )
  <=> ( ~ ! [D: $i,E: $i] :
            ( ~ q0(D,E)
            | ~ q1(d,E,d)
            | r1(D) )
      | r1(a)
      | ~ q1(d,b,d)
      | ~ q0(a,b) ) ),
    inference(transitivity,[status(thm)],[46,44]) ).

tff(48,plain,
    ( ~ ! [D: $i,E: $i] :
          ( ~ q0(D,E)
          | ~ q1(d,E,d)
          | r1(D) )
    | ~ q0(a,b)
    | ~ q1(d,b,d)
    | r1(a) ),
    inference(quant_inst,[status(thm)],]) ).

tff(49,plain,
    ( ~ ! [D: $i,E: $i] :
          ( ~ q0(D,E)
          | ~ q1(d,E,d)
          | r1(D) )
    | r1(a)
    | ~ q1(d,b,d)
    | ~ q0(a,b) ),
    inference(modus_ponens,[status(thm)],[48,47]) ).

tff(50,plain,
    r1(a),
    inference(unit_resolution,[status(thm)],[49,43,40,27]) ).

tff(51,plain,
    ^ [G: $i] :
      refl(
        ( ( ~ l0(G)
          | ~ r1(G)
          | r2(G) )
      <=> ( ~ l0(G)
          | ~ r1(G)
          | r2(G) ) )),
    inference(bind,[status(th)],]) ).

tff(52,plain,
    ( ! [G: $i] :
        ( ~ l0(G)
        | ~ r1(G)
        | r2(G) )
  <=> ! [G: $i] :
        ( ~ l0(G)
        | ~ r1(G)
        | r2(G) ) ),
    inference(quant_intro,[status(thm)],[51]) ).

tff(53,plain,
    ( ! [G: $i] :
        ( ~ l0(G)
        | ~ r1(G)
        | r2(G) )
  <=> ! [G: $i] :
        ( ~ l0(G)
        | ~ r1(G)
        | r2(G) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(54,plain,
    ^ [G: $i] :
      rewrite(
        ( ( r2(G)
          | ~ r1(G)
          | ~ l0(G) )
      <=> ( ~ l0(G)
          | ~ r1(G)
          | r2(G) ) )),
    inference(bind,[status(th)],]) ).

tff(55,plain,
    ( ! [G: $i] :
        ( r2(G)
        | ~ r1(G)
        | ~ l0(G) )
  <=> ! [G: $i] :
        ( ~ l0(G)
        | ~ r1(G)
        | r2(G) ) ),
    inference(quant_intro,[status(thm)],[54]) ).

tff(56,axiom,
    ! [G: $i] :
      ( r2(G)
      | ~ r1(G)
      | ~ l0(G) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_188) ).

tff(57,plain,
    ! [G: $i] :
      ( ~ l0(G)
      | ~ r1(G)
      | r2(G) ),
    inference(modus_ponens,[status(thm)],[56,55]) ).

tff(58,plain,
    ! [G: $i] :
      ( ~ l0(G)
      | ~ r1(G)
      | r2(G) ),
    inference(modus_ponens,[status(thm)],[57,53]) ).

tff(59,plain,
    ! [G: $i] :
      ( ~ l0(G)
      | ~ r1(G)
      | r2(G) ),
    inference(skolemize,[status(sab)],[58]) ).

tff(60,plain,
    ! [G: $i] :
      ( ~ l0(G)
      | ~ r1(G)
      | r2(G) ),
    inference(modus_ponens,[status(thm)],[59,52]) ).

tff(61,plain,
    ( l0(a)
  <=> l0(a) ),
    inference(rewrite,[status(thm)],]) ).

tff(62,axiom,
    l0(a),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_20) ).

tff(63,plain,
    l0(a),
    inference(modus_ponens,[status(thm)],[62,61]) ).

tff(64,plain,
    ( ( ~ ! [G: $i] :
            ( ~ l0(G)
            | ~ r1(G)
            | r2(G) )
      | ~ l0(a)
      | ~ r1(a)
      | r2(a) )
  <=> ( ~ ! [G: $i] :
            ( ~ l0(G)
            | ~ r1(G)
            | r2(G) )
      | ~ l0(a)
      | ~ r1(a)
      | r2(a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(65,plain,
    ( ~ ! [G: $i] :
          ( ~ l0(G)
          | ~ r1(G)
          | r2(G) )
    | ~ l0(a)
    | ~ r1(a)
    | r2(a) ),
    inference(quant_inst,[status(thm)],]) ).

tff(66,plain,
    ( ~ ! [G: $i] :
          ( ~ l0(G)
          | ~ r1(G)
          | r2(G) )
    | ~ l0(a)
    | ~ r1(a)
    | r2(a) ),
    inference(modus_ponens,[status(thm)],[65,64]) ).

tff(67,plain,
    r2(a),
    inference(unit_resolution,[status(thm)],[66,63,60,50]) ).

tff(68,plain,
    ( ( ~ ! [B: $i] :
            ( l3(B,B)
            | ~ r2(B) )
      | ~ r2(a)
      | l3(a,a) )
  <=> ( ~ ! [B: $i] :
            ( l3(B,B)
            | ~ r2(B) )
      | ~ r2(a)
      | l3(a,a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(69,plain,
    ( ( l3(a,a)
      | ~ r2(a) )
  <=> ( ~ r2(a)
      | l3(a,a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(70,plain,
    ( ( ~ ! [B: $i] :
            ( l3(B,B)
            | ~ r2(B) )
      | l3(a,a)
      | ~ r2(a) )
  <=> ( ~ ! [B: $i] :
            ( l3(B,B)
            | ~ r2(B) )
      | ~ r2(a)
      | l3(a,a) ) ),
    inference(monotonicity,[status(thm)],[69]) ).

tff(71,plain,
    ( ( ~ ! [B: $i] :
            ( l3(B,B)
            | ~ r2(B) )
      | l3(a,a)
      | ~ r2(a) )
  <=> ( ~ ! [B: $i] :
            ( l3(B,B)
            | ~ r2(B) )
      | ~ r2(a)
      | l3(a,a) ) ),
    inference(transitivity,[status(thm)],[70,68]) ).

tff(72,plain,
    ( ~ ! [B: $i] :
          ( l3(B,B)
          | ~ r2(B) )
    | l3(a,a)
    | ~ r2(a) ),
    inference(quant_inst,[status(thm)],]) ).

tff(73,plain,
    ( ~ ! [B: $i] :
          ( l3(B,B)
          | ~ r2(B) )
    | ~ r2(a)
    | l3(a,a) ),
    inference(modus_ponens,[status(thm)],[72,71]) ).

tff(74,plain,
    l3(a,a),
    inference(unit_resolution,[status(thm)],[73,67,7]) ).

tff(75,plain,
    ^ [X: $i] :
      refl(
        ( ~ l3(a,X)
      <=> ~ l3(a,X) )),
    inference(bind,[status(th)],]) ).

tff(76,plain,
    ( ! [X: $i] : ~ l3(a,X)
  <=> ! [X: $i] : ~ l3(a,X) ),
    inference(quant_intro,[status(thm)],[75]) ).

tff(77,plain,
    ( ! [X: $i] : ~ l3(a,X)
  <=> ! [X: $i] : ~ l3(a,X) ),
    inference(rewrite,[status(thm)],]) ).

tff(78,axiom,
    ! [X: $i] : ~ l3(a,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

tff(79,plain,
    ! [X: $i] : ~ l3(a,X),
    inference(modus_ponens,[status(thm)],[78,77]) ).

tff(80,plain,
    ! [X: $i] : ~ l3(a,X),
    inference(skolemize,[status(sab)],[79]) ).

tff(81,plain,
    ! [X: $i] : ~ l3(a,X),
    inference(modus_ponens,[status(thm)],[80,76]) ).

tff(82,plain,
    ( ~ ! [X: $i] : ~ l3(a,X)
    | ~ l3(a,a) ),
    inference(quant_inst,[status(thm)],]) ).

tff(83,plain,
    $false,
    inference(unit_resolution,[status(thm)],[82,81,74]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10  % Problem  : SYN224-1 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.11  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.32  % Computer : n014.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit : 300
% 0.10/0.32  % WCLimit  : 300
% 0.10/0.32  % DateTime : Mon Sep  5 02:14:44 EDT 2022
% 0.10/0.32  % CPUTime  : 
% 0.10/0.32  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.32  Usage: tptp [options] [-file:]file
% 0.10/0.32    -h, -?       prints this message.
% 0.10/0.32    -smt2        print SMT-LIB2 benchmark.
% 0.10/0.32    -m, -model   generate model.
% 0.10/0.32    -p, -proof   generate proof.
% 0.10/0.32    -c, -core    generate unsat core of named formulas.
% 0.10/0.32    -st, -statistics display statistics.
% 0.10/0.32    -t:timeout   set timeout (in second).
% 0.10/0.32    -smt2status  display status in smt2 format instead of SZS.
% 0.10/0.32    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.32    -<param>:<value> configuration parameter and value.
% 0.10/0.32    -o:<output-file> file to place output in.
% 0.18/0.47  % SZS status Unsatisfiable
% 0.18/0.47  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------