TSTP Solution File: SYN299-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN299-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n026.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 23:54:35 EDT 2022

% Result   : Unsatisfiable 0.21s 0.50s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   53
% Syntax   : Number of formulae    :  101 (  28 unt;  12 typ;   0 def)
%            Number of atoms       :  421 (   0 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  572 ( 268   ~; 260   |;   0   &)
%                                         (  44 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :   28 (  28 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (   8   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  12 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :  210 ( 186   !;   0   ?; 210   :)

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

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

tff(s1_type,type,
    s1: $i > $o ).

tff(q2_type,type,
    q2: ( $i * $i * $i ) > $o ).

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

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

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

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

tff(s2_type,type,
    s2: $i > $o ).

tff(s3_type,type,
    s3: ( $i * $i ) > $o ).

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

tff(m0_type,type,
    m0: ( $i * $i * $i ) > $o ).

tff(1,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(2,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)],[1]) ).

tff(3,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(4,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(5,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)],[4]) ).

tff(6,axiom,
    ! [B: $i,A: $i,J: $i,C: $i] :
      ( q1(J,A,J)
      | ~ n0(B,A)
      | ~ p0(C,J) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_092) ).

tff(7,plain,
    ! [B: $i,A: $i,J: $i,C: $i] :
      ( ~ p0(C,J)
      | ~ n0(B,A)
      | q1(J,A,J) ),
    inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
    ! [B: $i,A: $i,J: $i,C: $i] :
      ( ~ p0(C,J)
      | ~ n0(B,A)
      | q1(J,A,J) ),
    inference(modus_ponens,[status(thm)],[7,3]) ).

tff(9,plain,
    ! [B: $i,A: $i,J: $i,C: $i] :
      ( ~ p0(C,J)
      | ~ n0(B,A)
      | q1(J,A,J) ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [B: $i,A: $i,J: $i,C: $i] :
      ( ~ p0(C,J)
      | ~ n0(B,A)
      | q1(J,A,J) ),
    inference(modus_ponens,[status(thm)],[9,2]) ).

tff(11,plain,
    ( n0(d,c)
  <=> n0(d,c) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,axiom,
    n0(d,c),
    file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_26) ).

tff(13,plain,
    n0(d,c),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    ( p0(c,b)
  <=> p0(c,b) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,axiom,
    p0(c,b),
    file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_18) ).

tff(16,plain,
    p0(c,b),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    ( ( ~ ! [B: $i,A: $i,J: $i,C: $i] :
            ( ~ p0(C,J)
            | ~ n0(B,A)
            | q1(J,A,J) )
      | ~ p0(c,b)
      | ~ n0(d,c)
      | q1(b,c,b) )
  <=> ( ~ ! [B: $i,A: $i,J: $i,C: $i] :
            ( ~ p0(C,J)
            | ~ n0(B,A)
            | q1(J,A,J) )
      | ~ p0(c,b)
      | ~ n0(d,c)
      | q1(b,c,b) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(18,plain,
    ( ~ ! [B: $i,A: $i,J: $i,C: $i] :
          ( ~ p0(C,J)
          | ~ n0(B,A)
          | q1(J,A,J) )
    | ~ p0(c,b)
    | ~ n0(d,c)
    | q1(b,c,b) ),
    inference(quant_inst,[status(thm)],]) ).

tff(19,plain,
    ( ~ ! [B: $i,A: $i,J: $i,C: $i] :
          ( ~ p0(C,J)
          | ~ n0(B,A)
          | q1(J,A,J) )
    | ~ p0(c,b)
    | ~ n0(d,c)
    | q1(b,c,b) ),
    inference(modus_ponens,[status(thm)],[18,17]) ).

tff(20,plain,
    q1(b,c,b),
    inference(unit_resolution,[status(thm)],[19,16,13,10]) ).

tff(21,plain,
    ^ [B: $i,C: $i] :
      refl(
        ( ( ~ q1(C,c,B)
          | q2(B,B,B) )
      <=> ( ~ q1(C,c,B)
          | q2(B,B,B) ) )),
    inference(bind,[status(th)],]) ).

tff(22,plain,
    ( ! [B: $i,C: $i] :
        ( ~ q1(C,c,B)
        | q2(B,B,B) )
  <=> ! [B: $i,C: $i] :
        ( ~ q1(C,c,B)
        | q2(B,B,B) ) ),
    inference(quant_intro,[status(thm)],[21]) ).

tff(23,plain,
    ( ! [B: $i,C: $i] :
        ( ~ q1(C,c,B)
        | q2(B,B,B) )
  <=> ! [B: $i,C: $i] :
        ( ~ q1(C,c,B)
        | q2(B,B,B) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(24,plain,
    ^ [B: $i,C: $i] :
      rewrite(
        ( ( q2(B,B,B)
          | ~ q1(C,c,B) )
      <=> ( ~ q1(C,c,B)
          | q2(B,B,B) ) )),
    inference(bind,[status(th)],]) ).

tff(25,plain,
    ( ! [B: $i,C: $i] :
        ( q2(B,B,B)
        | ~ q1(C,c,B) )
  <=> ! [B: $i,C: $i] :
        ( ~ q1(C,c,B)
        | q2(B,B,B) ) ),
    inference(quant_intro,[status(thm)],[24]) ).

tff(26,axiom,
    ! [B: $i,C: $i] :
      ( q2(B,B,B)
      | ~ q1(C,c,B) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_184) ).

tff(27,plain,
    ! [B: $i,C: $i] :
      ( ~ q1(C,c,B)
      | q2(B,B,B) ),
    inference(modus_ponens,[status(thm)],[26,25]) ).

tff(28,plain,
    ! [B: $i,C: $i] :
      ( ~ q1(C,c,B)
      | q2(B,B,B) ),
    inference(modus_ponens,[status(thm)],[27,23]) ).

tff(29,plain,
    ! [B: $i,C: $i] :
      ( ~ q1(C,c,B)
      | q2(B,B,B) ),
    inference(skolemize,[status(sab)],[28]) ).

tff(30,plain,
    ! [B: $i,C: $i] :
      ( ~ q1(C,c,B)
      | q2(B,B,B) ),
    inference(modus_ponens,[status(thm)],[29,22]) ).

tff(31,plain,
    ( ( ~ ! [B: $i,C: $i] :
            ( ~ q1(C,c,B)
            | q2(B,B,B) )
      | ~ q1(b,c,b)
      | q2(b,b,b) )
  <=> ( ~ ! [B: $i,C: $i] :
            ( ~ q1(C,c,B)
            | q2(B,B,B) )
      | ~ q1(b,c,b)
      | q2(b,b,b) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(32,plain,
    ( ~ ! [B: $i,C: $i] :
          ( ~ q1(C,c,B)
          | q2(B,B,B) )
    | ~ q1(b,c,b)
    | q2(b,b,b) ),
    inference(quant_inst,[status(thm)],]) ).

tff(33,plain,
    ( ~ ! [B: $i,C: $i] :
          ( ~ q1(C,c,B)
          | q2(B,B,B) )
    | ~ q1(b,c,b)
    | q2(b,b,b) ),
    inference(modus_ponens,[status(thm)],[32,31]) ).

tff(34,plain,
    q2(b,b,b),
    inference(unit_resolution,[status(thm)],[33,30,20]) ).

tff(35,plain,
    ( ~ s3(b,a)
  <=> ~ s3(b,a) ),
    inference(rewrite,[status(thm)],]) ).

tff(36,axiom,
    ~ s3(b,a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).

tff(37,plain,
    ~ s3(b,a),
    inference(modus_ponens,[status(thm)],[36,35]) ).

tff(38,plain,
    ^ [I: $i,B: $i,A: $i,J: $i] :
      refl(
        ( ( ~ s2(I)
          | ~ m0(A,B,J)
          | ~ q2(A,I,A)
          | s3(I,J) )
      <=> ( ~ s2(I)
          | ~ m0(A,B,J)
          | ~ q2(A,I,A)
          | s3(I,J) ) )),
    inference(bind,[status(th)],]) ).

tff(39,plain,
    ( ! [I: $i,B: $i,A: $i,J: $i] :
        ( ~ s2(I)
        | ~ m0(A,B,J)
        | ~ q2(A,I,A)
        | s3(I,J) )
  <=> ! [I: $i,B: $i,A: $i,J: $i] :
        ( ~ s2(I)
        | ~ m0(A,B,J)
        | ~ q2(A,I,A)
        | s3(I,J) ) ),
    inference(quant_intro,[status(thm)],[38]) ).

tff(40,plain,
    ( ! [I: $i,B: $i,A: $i,J: $i] :
        ( ~ s2(I)
        | ~ m0(A,B,J)
        | ~ q2(A,I,A)
        | s3(I,J) )
  <=> ! [I: $i,B: $i,A: $i,J: $i] :
        ( ~ s2(I)
        | ~ m0(A,B,J)
        | ~ q2(A,I,A)
        | s3(I,J) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(41,plain,
    ^ [I: $i,B: $i,A: $i,J: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( s3(I,J)
                  | ~ q2(A,I,A) )
              <=> ( ~ q2(A,I,A)
                  | s3(I,J) ) )),
              ( ( s3(I,J)
                | ~ q2(A,I,A)
                | ~ s2(I) )
            <=> ( ~ q2(A,I,A)
                | s3(I,J)
                | ~ s2(I) ) )),
            rewrite(
              ( ( ~ q2(A,I,A)
                | s3(I,J)
                | ~ s2(I) )
            <=> ( ~ s2(I)
                | ~ q2(A,I,A)
                | s3(I,J) ) )),
            ( ( s3(I,J)
              | ~ q2(A,I,A)
              | ~ s2(I) )
          <=> ( ~ s2(I)
              | ~ q2(A,I,A)
              | s3(I,J) ) )),
          ( ( s3(I,J)
            | ~ q2(A,I,A)
            | ~ s2(I)
            | ~ m0(A,B,J) )
        <=> ( ~ s2(I)
            | ~ q2(A,I,A)
            | s3(I,J)
            | ~ m0(A,B,J) ) )),
        rewrite(
          ( ( ~ s2(I)
            | ~ q2(A,I,A)
            | s3(I,J)
            | ~ m0(A,B,J) )
        <=> ( ~ s2(I)
            | ~ m0(A,B,J)
            | ~ q2(A,I,A)
            | s3(I,J) ) )),
        ( ( s3(I,J)
          | ~ q2(A,I,A)
          | ~ s2(I)
          | ~ m0(A,B,J) )
      <=> ( ~ s2(I)
          | ~ m0(A,B,J)
          | ~ q2(A,I,A)
          | s3(I,J) ) )),
    inference(bind,[status(th)],]) ).

tff(42,plain,
    ( ! [I: $i,B: $i,A: $i,J: $i] :
        ( s3(I,J)
        | ~ q2(A,I,A)
        | ~ s2(I)
        | ~ m0(A,B,J) )
  <=> ! [I: $i,B: $i,A: $i,J: $i] :
        ( ~ s2(I)
        | ~ m0(A,B,J)
        | ~ q2(A,I,A)
        | s3(I,J) ) ),
    inference(quant_intro,[status(thm)],[41]) ).

tff(43,axiom,
    ! [I: $i,B: $i,A: $i,J: $i] :
      ( s3(I,J)
      | ~ q2(A,I,A)
      | ~ s2(I)
      | ~ m0(A,B,J) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_273) ).

tff(44,plain,
    ! [I: $i,B: $i,A: $i,J: $i] :
      ( ~ s2(I)
      | ~ m0(A,B,J)
      | ~ q2(A,I,A)
      | s3(I,J) ),
    inference(modus_ponens,[status(thm)],[43,42]) ).

tff(45,plain,
    ! [I: $i,B: $i,A: $i,J: $i] :
      ( ~ s2(I)
      | ~ m0(A,B,J)
      | ~ q2(A,I,A)
      | s3(I,J) ),
    inference(modus_ponens,[status(thm)],[44,40]) ).

tff(46,plain,
    ! [I: $i,B: $i,A: $i,J: $i] :
      ( ~ s2(I)
      | ~ m0(A,B,J)
      | ~ q2(A,I,A)
      | s3(I,J) ),
    inference(skolemize,[status(sab)],[45]) ).

tff(47,plain,
    ! [I: $i,B: $i,A: $i,J: $i] :
      ( ~ s2(I)
      | ~ m0(A,B,J)
      | ~ q2(A,I,A)
      | s3(I,J) ),
    inference(modus_ponens,[status(thm)],[46,39]) ).

tff(48,plain,
    ( m0(b,a,a)
  <=> m0(b,a,a) ),
    inference(rewrite,[status(thm)],]) ).

tff(49,axiom,
    m0(b,a,a),
    file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_38) ).

tff(50,plain,
    m0(b,a,a),
    inference(modus_ponens,[status(thm)],[49,48]) ).

tff(51,plain,
    ( ( ~ ! [I: $i,B: $i,A: $i,J: $i] :
            ( ~ s2(I)
            | ~ m0(A,B,J)
            | ~ q2(A,I,A)
            | s3(I,J) )
      | ~ s2(b)
      | ~ m0(b,a,a)
      | ~ q2(b,b,b)
      | s3(b,a) )
  <=> ( ~ ! [I: $i,B: $i,A: $i,J: $i] :
            ( ~ s2(I)
            | ~ m0(A,B,J)
            | ~ q2(A,I,A)
            | s3(I,J) )
      | ~ s2(b)
      | ~ m0(b,a,a)
      | ~ q2(b,b,b)
      | s3(b,a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(52,plain,
    ( ~ ! [I: $i,B: $i,A: $i,J: $i] :
          ( ~ s2(I)
          | ~ m0(A,B,J)
          | ~ q2(A,I,A)
          | s3(I,J) )
    | ~ s2(b)
    | ~ m0(b,a,a)
    | ~ q2(b,b,b)
    | s3(b,a) ),
    inference(quant_inst,[status(thm)],]) ).

tff(53,plain,
    ( ~ ! [I: $i,B: $i,A: $i,J: $i] :
          ( ~ s2(I)
          | ~ m0(A,B,J)
          | ~ q2(A,I,A)
          | s3(I,J) )
    | ~ s2(b)
    | ~ m0(b,a,a)
    | ~ q2(b,b,b)
    | s3(b,a) ),
    inference(modus_ponens,[status(thm)],[52,51]) ).

tff(54,plain,
    ( ~ s2(b)
    | ~ q2(b,b,b) ),
    inference(unit_resolution,[status(thm)],[53,50,47,37]) ).

tff(55,plain,
    ~ s2(b),
    inference(unit_resolution,[status(thm)],[54,34]) ).

tff(56,plain,
    ^ [H: $i] :
      refl(
        ( ( ~ s1(b)
          | s2(H)
          | ~ q2(b,H,b) )
      <=> ( ~ s1(b)
          | s2(H)
          | ~ q2(b,H,b) ) )),
    inference(bind,[status(th)],]) ).

tff(57,plain,
    ( ! [H: $i] :
        ( ~ s1(b)
        | s2(H)
        | ~ q2(b,H,b) )
  <=> ! [H: $i] :
        ( ~ s1(b)
        | s2(H)
        | ~ q2(b,H,b) ) ),
    inference(quant_intro,[status(thm)],[56]) ).

tff(58,plain,
    ( ! [H: $i] :
        ( ~ s1(b)
        | s2(H)
        | ~ q2(b,H,b) )
  <=> ! [H: $i] :
        ( ~ s1(b)
        | s2(H)
        | ~ q2(b,H,b) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(59,plain,
    ^ [H: $i] :
      rewrite(
        ( ( s2(H)
          | ~ q2(b,H,b)
          | ~ s1(b) )
      <=> ( ~ s1(b)
          | s2(H)
          | ~ q2(b,H,b) ) )),
    inference(bind,[status(th)],]) ).

tff(60,plain,
    ( ! [H: $i] :
        ( s2(H)
        | ~ q2(b,H,b)
        | ~ s1(b) )
  <=> ! [H: $i] :
        ( ~ s1(b)
        | s2(H)
        | ~ q2(b,H,b) ) ),
    inference(quant_intro,[status(thm)],[59]) ).

tff(61,axiom,
    ! [H: $i] :
      ( s2(H)
      | ~ q2(b,H,b)
      | ~ s1(b) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_189) ).

tff(62,plain,
    ! [H: $i] :
      ( ~ s1(b)
      | s2(H)
      | ~ q2(b,H,b) ),
    inference(modus_ponens,[status(thm)],[61,60]) ).

tff(63,plain,
    ! [H: $i] :
      ( ~ s1(b)
      | s2(H)
      | ~ q2(b,H,b) ),
    inference(modus_ponens,[status(thm)],[62,58]) ).

tff(64,plain,
    ! [H: $i] :
      ( ~ s1(b)
      | s2(H)
      | ~ q2(b,H,b) ),
    inference(skolemize,[status(sab)],[63]) ).

tff(65,plain,
    ! [H: $i] :
      ( ~ s1(b)
      | s2(H)
      | ~ q2(b,H,b) ),
    inference(modus_ponens,[status(thm)],[64,57]) ).

tff(66,plain,
    ( ( ~ ! [H: $i] :
            ( ~ s1(b)
            | s2(H)
            | ~ q2(b,H,b) )
      | ~ s1(b)
      | s2(b)
      | ~ q2(b,b,b) )
  <=> ( ~ ! [H: $i] :
            ( ~ s1(b)
            | s2(H)
            | ~ q2(b,H,b) )
      | ~ s1(b)
      | s2(b)
      | ~ q2(b,b,b) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(67,plain,
    ( ~ ! [H: $i] :
          ( ~ s1(b)
          | s2(H)
          | ~ q2(b,H,b) )
    | ~ s1(b)
    | s2(b)
    | ~ q2(b,b,b) ),
    inference(quant_inst,[status(thm)],]) ).

tff(68,plain,
    ( ~ ! [H: $i] :
          ( ~ s1(b)
          | s2(H)
          | ~ q2(b,H,b) )
    | ~ s1(b)
    | s2(b)
    | ~ q2(b,b,b) ),
    inference(modus_ponens,[status(thm)],[67,66]) ).

tff(69,plain,
    ~ s1(b),
    inference(unit_resolution,[status(thm)],[68,65,55,34]) ).

tff(70,plain,
    ^ [I: $i] :
      refl(
        ( ( s1(I)
          | ~ p0(I,I) )
      <=> ( s1(I)
          | ~ p0(I,I) ) )),
    inference(bind,[status(th)],]) ).

tff(71,plain,
    ( ! [I: $i] :
        ( s1(I)
        | ~ p0(I,I) )
  <=> ! [I: $i] :
        ( s1(I)
        | ~ p0(I,I) ) ),
    inference(quant_intro,[status(thm)],[70]) ).

tff(72,plain,
    ( ! [I: $i] :
        ( s1(I)
        | ~ p0(I,I) )
  <=> ! [I: $i] :
        ( s1(I)
        | ~ p0(I,I) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(73,axiom,
    ! [I: $i] :
      ( s1(I)
      | ~ p0(I,I) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_125) ).

tff(74,plain,
    ! [I: $i] :
      ( s1(I)
      | ~ p0(I,I) ),
    inference(modus_ponens,[status(thm)],[73,72]) ).

tff(75,plain,
    ! [I: $i] :
      ( s1(I)
      | ~ p0(I,I) ),
    inference(skolemize,[status(sab)],[74]) ).

tff(76,plain,
    ! [I: $i] :
      ( s1(I)
      | ~ p0(I,I) ),
    inference(modus_ponens,[status(thm)],[75,71]) ).

tff(77,plain,
    ( ( ~ ! [I: $i] :
            ( s1(I)
            | ~ p0(I,I) )
      | s1(b)
      | ~ p0(b,b) )
  <=> ( ~ ! [I: $i] :
            ( s1(I)
            | ~ p0(I,I) )
      | s1(b)
      | ~ p0(b,b) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(78,plain,
    ( ~ ! [I: $i] :
          ( s1(I)
          | ~ p0(I,I) )
    | s1(b)
    | ~ p0(b,b) ),
    inference(quant_inst,[status(thm)],]) ).

tff(79,plain,
    ( ~ ! [I: $i] :
          ( s1(I)
          | ~ p0(I,I) )
    | s1(b)
    | ~ p0(b,b) ),
    inference(modus_ponens,[status(thm)],[78,77]) ).

tff(80,plain,
    ~ p0(b,b),
    inference(unit_resolution,[status(thm)],[79,76,69]) ).

tff(81,plain,
    ^ [X: $i] :
      refl(
        ( p0(b,X)
      <=> p0(b,X) )),
    inference(bind,[status(th)],]) ).

tff(82,plain,
    ( ! [X: $i] : p0(b,X)
  <=> ! [X: $i] : p0(b,X) ),
    inference(quant_intro,[status(thm)],[81]) ).

tff(83,plain,
    ( ! [X: $i] : p0(b,X)
  <=> ! [X: $i] : p0(b,X) ),
    inference(rewrite,[status(thm)],]) ).

tff(84,axiom,
    ! [X: $i] : p0(b,X),
    file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_14) ).

tff(85,plain,
    ! [X: $i] : p0(b,X),
    inference(modus_ponens,[status(thm)],[84,83]) ).

tff(86,plain,
    ! [X: $i] : p0(b,X),
    inference(skolemize,[status(sab)],[85]) ).

tff(87,plain,
    ! [X: $i] : p0(b,X),
    inference(modus_ponens,[status(thm)],[86,82]) ).

tff(88,plain,
    ( ~ ! [X: $i] : p0(b,X)
    | p0(b,b) ),
    inference(quant_inst,[status(thm)],]) ).

tff(89,plain,
    $false,
    inference(unit_resolution,[status(thm)],[88,87,80]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SYN299-1 : TPTP v8.1.0. Released v1.1.0.
% 0.12/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34  % Computer : n026.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Mon Sep  5 02:38:10 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35  Usage: tptp [options] [-file:]file
% 0.14/0.35    -h, -?       prints this message.
% 0.14/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.35    -m, -model   generate model.
% 0.14/0.35    -p, -proof   generate proof.
% 0.14/0.35    -c, -core    generate unsat core of named formulas.
% 0.14/0.35    -st, -statistics display statistics.
% 0.14/0.35    -t:timeout   set timeout (in second).
% 0.14/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35    -<param>:<value> configuration parameter and value.
% 0.14/0.35    -o:<output-file> file to place output in.
% 0.21/0.50  % SZS status Unsatisfiable
% 0.21/0.50  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------