TSTP Solution File: SYN113-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN113-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n027.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 23:53:47 EDT 2022

% Result   : Unsatisfiable 0.80s 0.76s
% Output   : Proof 0.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   53
% Syntax   : Number of formulae    :  101 (  23 unt;  13 typ;   0 def)
%            Number of atoms       :  404 (   0 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  538 ( 247   ~; 240   |;   0   &)
%                                         (  51 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :   25 (  25 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (   9   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  13 usr;   2 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :  179 ( 159   !;   0   ?; 179   :)

% Comments : 
%------------------------------------------------------------------------------
tff(m1_type,type,
    m1: ( $i * $i * $i ) > $o ).

tff(e_type,type,
    e: $i ).

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

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

tff(r0_type,type,
    r0: $i > $o ).

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

tff(k2_type,type,
    k2: ( $i * $i ) > $o ).

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

tff(k0_type,type,
    k0: $i > $o ).

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

tff(k1_type,type,
    k1: $i > $o ).

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

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

tff(1,plain,
    ^ [I: $i,H: $i,G: $i] :
      refl(
        ( ( ~ r0(G)
          | ~ p0(I,H)
          | m1(G,H,G) )
      <=> ( ~ r0(G)
          | ~ p0(I,H)
          | m1(G,H,G) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [I: $i,H: $i,G: $i] :
        ( ~ r0(G)
        | ~ p0(I,H)
        | m1(G,H,G) )
  <=> ! [I: $i,H: $i,G: $i] :
        ( ~ r0(G)
        | ~ p0(I,H)
        | m1(G,H,G) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [I: $i,H: $i,G: $i] :
        ( ~ r0(G)
        | ~ p0(I,H)
        | m1(G,H,G) )
  <=> ! [I: $i,H: $i,G: $i] :
        ( ~ r0(G)
        | ~ p0(I,H)
        | m1(G,H,G) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,plain,
    ^ [I: $i,H: $i,G: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( m1(G,H,G)
              | ~ p0(I,H) )
          <=> ( ~ p0(I,H)
              | m1(G,H,G) ) )),
          ( ( m1(G,H,G)
            | ~ p0(I,H)
            | ~ r0(G) )
        <=> ( ~ p0(I,H)
            | m1(G,H,G)
            | ~ r0(G) ) )),
        rewrite(
          ( ( ~ p0(I,H)
            | m1(G,H,G)
            | ~ r0(G) )
        <=> ( ~ r0(G)
            | ~ p0(I,H)
            | m1(G,H,G) ) )),
        ( ( m1(G,H,G)
          | ~ p0(I,H)
          | ~ r0(G) )
      <=> ( ~ r0(G)
          | ~ p0(I,H)
          | m1(G,H,G) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [I: $i,H: $i,G: $i] :
        ( m1(G,H,G)
        | ~ p0(I,H)
        | ~ r0(G) )
  <=> ! [I: $i,H: $i,G: $i] :
        ( ~ r0(G)
        | ~ p0(I,H)
        | m1(G,H,G) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,axiom,
    ! [I: $i,H: $i,G: $i] :
      ( m1(G,H,G)
      | ~ p0(I,H)
      | ~ r0(G) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_007) ).

tff(7,plain,
    ! [I: $i,H: $i,G: $i] :
      ( ~ r0(G)
      | ~ p0(I,H)
      | m1(G,H,G) ),
    inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
    ! [I: $i,H: $i,G: $i] :
      ( ~ r0(G)
      | ~ p0(I,H)
      | m1(G,H,G) ),
    inference(modus_ponens,[status(thm)],[7,3]) ).

tff(9,plain,
    ! [I: $i,H: $i,G: $i] :
      ( ~ r0(G)
      | ~ p0(I,H)
      | m1(G,H,G) ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [I: $i,H: $i,G: $i] :
      ( ~ r0(G)
      | ~ p0(I,H)
      | m1(G,H,G) ),
    inference(modus_ponens,[status(thm)],[9,2]) ).

tff(11,plain,
    ( r0(e)
  <=> r0(e) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,axiom,
    r0(e),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_13) ).

tff(13,plain,
    r0(e),
    inference(modus_ponens,[status(thm)],[12,11]) ).

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

tff(15,axiom,
    p0(b,d),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_10) ).

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

tff(17,plain,
    ( ( ~ ! [I: $i,H: $i,G: $i] :
            ( ~ r0(G)
            | ~ p0(I,H)
            | m1(G,H,G) )
      | ~ r0(e)
      | ~ p0(b,d)
      | m1(e,d,e) )
  <=> ( ~ ! [I: $i,H: $i,G: $i] :
            ( ~ r0(G)
            | ~ p0(I,H)
            | m1(G,H,G) )
      | ~ r0(e)
      | ~ p0(b,d)
      | m1(e,d,e) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(18,plain,
    ( ~ ! [I: $i,H: $i,G: $i] :
          ( ~ r0(G)
          | ~ p0(I,H)
          | m1(G,H,G) )
    | ~ r0(e)
    | ~ p0(b,d)
    | m1(e,d,e) ),
    inference(quant_inst,[status(thm)],]) ).

tff(19,plain,
    ( ~ ! [I: $i,H: $i,G: $i] :
          ( ~ r0(G)
          | ~ p0(I,H)
          | m1(G,H,G) )
    | ~ r0(e)
    | ~ p0(b,d)
    | m1(e,d,e) ),
    inference(modus_ponens,[status(thm)],[18,17]) ).

tff(20,plain,
    m1(e,d,e),
    inference(unit_resolution,[status(thm)],[19,16,13,10]) ).

tff(21,plain,
    ^ [A: $i,J: $i] :
      refl(
        ( ( ~ q1(A,J,J)
          | k2(J,J) )
      <=> ( ~ q1(A,J,J)
          | k2(J,J) ) )),
    inference(bind,[status(th)],]) ).

tff(22,plain,
    ( ! [A: $i,J: $i] :
        ( ~ q1(A,J,J)
        | k2(J,J) )
  <=> ! [A: $i,J: $i] :
        ( ~ q1(A,J,J)
        | k2(J,J) ) ),
    inference(quant_intro,[status(thm)],[21]) ).

tff(23,plain,
    ( ! [A: $i,J: $i] :
        ( ~ q1(A,J,J)
        | k2(J,J) )
  <=> ! [A: $i,J: $i] :
        ( ~ q1(A,J,J)
        | k2(J,J) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(24,plain,
    ^ [A: $i,J: $i] :
      rewrite(
        ( ( k2(J,J)
          | ~ q1(A,J,J) )
      <=> ( ~ q1(A,J,J)
          | k2(J,J) ) )),
    inference(bind,[status(th)],]) ).

tff(25,plain,
    ( ! [A: $i,J: $i] :
        ( k2(J,J)
        | ~ q1(A,J,J) )
  <=> ! [A: $i,J: $i] :
        ( ~ q1(A,J,J)
        | k2(J,J) ) ),
    inference(quant_intro,[status(thm)],[24]) ).

tff(26,axiom,
    ! [A: $i,J: $i] :
      ( k2(J,J)
      | ~ q1(A,J,J) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_129) ).

tff(27,plain,
    ! [A: $i,J: $i] :
      ( ~ q1(A,J,J)
      | k2(J,J) ),
    inference(modus_ponens,[status(thm)],[26,25]) ).

tff(28,plain,
    ! [A: $i,J: $i] :
      ( ~ q1(A,J,J)
      | k2(J,J) ),
    inference(modus_ponens,[status(thm)],[27,23]) ).

tff(29,plain,
    ! [A: $i,J: $i] :
      ( ~ q1(A,J,J)
      | k2(J,J) ),
    inference(skolemize,[status(sab)],[28]) ).

tff(30,plain,
    ! [A: $i,J: $i] :
      ( ~ q1(A,J,J)
      | k2(J,J) ),
    inference(modus_ponens,[status(thm)],[29,22]) ).

tff(31,plain,
    ( q1(d,d,d)
  <=> q1(d,d,d) ),
    inference(rewrite,[status(thm)],]) ).

tff(32,plain,
    ( ( $false
      | $false
      | q1(d,d,d) )
  <=> q1(d,d,d) ),
    inference(rewrite,[status(thm)],]) ).

tff(33,plain,
    ( ~ $true
  <=> $false ),
    inference(rewrite,[status(thm)],]) ).

tff(34,axiom,
    k0(e),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_28) ).

tff(35,plain,
    ( k0(e)
  <=> $true ),
    inference(iff_true,[status(thm)],[34]) ).

tff(36,plain,
    ( ~ k0(e)
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[35]) ).

tff(37,plain,
    ( ~ k0(e)
  <=> $false ),
    inference(transitivity,[status(thm)],[36,33]) ).

tff(38,axiom,
    s0(d),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_1) ).

tff(39,plain,
    ( s0(d)
  <=> $true ),
    inference(iff_true,[status(thm)],[38]) ).

tff(40,plain,
    ( ~ s0(d)
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[39]) ).

tff(41,plain,
    ( ~ s0(d)
  <=> $false ),
    inference(transitivity,[status(thm)],[40,33]) ).

tff(42,plain,
    ( ( ~ s0(d)
      | ~ k0(e)
      | q1(d,d,d) )
  <=> ( $false
      | $false
      | q1(d,d,d) ) ),
    inference(monotonicity,[status(thm)],[41,37]) ).

tff(43,plain,
    ( ( ~ s0(d)
      | ~ k0(e)
      | q1(d,d,d) )
  <=> q1(d,d,d) ),
    inference(transitivity,[status(thm)],[42,32]) ).

tff(44,plain,
    ( ( ~ s0(d)
      | ~ k0(e)
      | q1(d,d,d) )
  <=> ( ~ s0(d)
      | ~ k0(e)
      | q1(d,d,d) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(45,plain,
    ( ( ~ k0(e)
      | q1(d,d,d)
      | ~ s0(d) )
  <=> ( ~ s0(d)
      | ~ k0(e)
      | q1(d,d,d) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(46,plain,
    ( ( q1(d,d,d)
      | ~ k0(e) )
  <=> ( ~ k0(e)
      | q1(d,d,d) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(47,plain,
    ( ( q1(d,d,d)
      | ~ k0(e)
      | ~ s0(d) )
  <=> ( ~ k0(e)
      | q1(d,d,d)
      | ~ s0(d) ) ),
    inference(monotonicity,[status(thm)],[46]) ).

tff(48,plain,
    ( ( q1(d,d,d)
      | ~ k0(e)
      | ~ s0(d) )
  <=> ( ~ s0(d)
      | ~ k0(e)
      | q1(d,d,d) ) ),
    inference(transitivity,[status(thm)],[47,45]) ).

tff(49,axiom,
    ( q1(d,d,d)
    | ~ k0(e)
    | ~ s0(d) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_117) ).

tff(50,plain,
    ( ~ s0(d)
    | ~ k0(e)
    | q1(d,d,d) ),
    inference(modus_ponens,[status(thm)],[49,48]) ).

tff(51,plain,
    ( ~ s0(d)
    | ~ k0(e)
    | q1(d,d,d) ),
    inference(modus_ponens,[status(thm)],[50,44]) ).

tff(52,plain,
    q1(d,d,d),
    inference(modus_ponens,[status(thm)],[51,43]) ).

tff(53,plain,
    q1(d,d,d),
    inference(modus_ponens,[status(thm)],[52,31]) ).

tff(54,plain,
    ( ( ~ ! [A: $i,J: $i] :
            ( ~ q1(A,J,J)
            | k2(J,J) )
      | ~ q1(d,d,d)
      | k2(d,d) )
  <=> ( ~ ! [A: $i,J: $i] :
            ( ~ q1(A,J,J)
            | k2(J,J) )
      | ~ q1(d,d,d)
      | k2(d,d) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(55,plain,
    ( ~ ! [A: $i,J: $i] :
          ( ~ q1(A,J,J)
          | k2(J,J) )
    | ~ q1(d,d,d)
    | k2(d,d) ),
    inference(quant_inst,[status(thm)],]) ).

tff(56,plain,
    ( ~ ! [A: $i,J: $i] :
          ( ~ q1(A,J,J)
          | k2(J,J) )
    | ~ q1(d,d,d)
    | k2(d,d) ),
    inference(modus_ponens,[status(thm)],[55,54]) ).

tff(57,plain,
    k2(d,d),
    inference(unit_resolution,[status(thm)],[56,53,30]) ).

tff(58,plain,
    ( ~ k2(e,d)
  <=> ~ k2(e,d) ),
    inference(rewrite,[status(thm)],]) ).

tff(59,axiom,
    ~ k2(e,d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

tff(60,plain,
    ~ k2(e,d),
    inference(modus_ponens,[status(thm)],[59,58]) ).

tff(61,plain,
    ^ [I: $i,J: $i] :
      refl(
        ( ( k1(I)
          | ~ n0(J,I) )
      <=> ( k1(I)
          | ~ n0(J,I) ) )),
    inference(bind,[status(th)],]) ).

tff(62,plain,
    ( ! [I: $i,J: $i] :
        ( k1(I)
        | ~ n0(J,I) )
  <=> ! [I: $i,J: $i] :
        ( k1(I)
        | ~ n0(J,I) ) ),
    inference(quant_intro,[status(thm)],[61]) ).

tff(63,plain,
    ( ! [I: $i,J: $i] :
        ( k1(I)
        | ~ n0(J,I) )
  <=> ! [I: $i,J: $i] :
        ( k1(I)
        | ~ n0(J,I) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(64,axiom,
    ! [I: $i,J: $i] :
      ( k1(I)
      | ~ n0(J,I) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_001) ).

tff(65,plain,
    ! [I: $i,J: $i] :
      ( k1(I)
      | ~ n0(J,I) ),
    inference(modus_ponens,[status(thm)],[64,63]) ).

tff(66,plain,
    ! [I: $i,J: $i] :
      ( k1(I)
      | ~ n0(J,I) ),
    inference(skolemize,[status(sab)],[65]) ).

tff(67,plain,
    ! [I: $i,J: $i] :
      ( k1(I)
      | ~ n0(J,I) ),
    inference(modus_ponens,[status(thm)],[66,62]) ).

tff(68,plain,
    ( n0(c,d)
  <=> n0(c,d) ),
    inference(rewrite,[status(thm)],]) ).

tff(69,axiom,
    n0(c,d),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_34) ).

tff(70,plain,
    n0(c,d),
    inference(modus_ponens,[status(thm)],[69,68]) ).

tff(71,plain,
    ( ( ~ ! [I: $i,J: $i] :
            ( k1(I)
            | ~ n0(J,I) )
      | k1(d)
      | ~ n0(c,d) )
  <=> ( ~ ! [I: $i,J: $i] :
            ( k1(I)
            | ~ n0(J,I) )
      | k1(d)
      | ~ n0(c,d) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(72,plain,
    ( ~ ! [I: $i,J: $i] :
          ( k1(I)
          | ~ n0(J,I) )
    | k1(d)
    | ~ n0(c,d) ),
    inference(quant_inst,[status(thm)],]) ).

tff(73,plain,
    ( ~ ! [I: $i,J: $i] :
          ( k1(I)
          | ~ n0(J,I) )
    | k1(d)
    | ~ n0(c,d) ),
    inference(modus_ponens,[status(thm)],[72,71]) ).

tff(74,plain,
    k1(d),
    inference(unit_resolution,[status(thm)],[73,70,67]) ).

tff(75,plain,
    ^ [D: $i,E: $i,F: $i,C: $i] :
      refl(
        ( ( ~ k1(F)
          | ~ k2(F,D)
          | ~ m1(E,D,C)
          | k2(C,D) )
      <=> ( ~ k1(F)
          | ~ k2(F,D)
          | ~ m1(E,D,C)
          | k2(C,D) ) )),
    inference(bind,[status(th)],]) ).

tff(76,plain,
    ( ! [D: $i,E: $i,F: $i,C: $i] :
        ( ~ k1(F)
        | ~ k2(F,D)
        | ~ m1(E,D,C)
        | k2(C,D) )
  <=> ! [D: $i,E: $i,F: $i,C: $i] :
        ( ~ k1(F)
        | ~ k2(F,D)
        | ~ m1(E,D,C)
        | k2(C,D) ) ),
    inference(quant_intro,[status(thm)],[75]) ).

tff(77,plain,
    ( ! [D: $i,E: $i,F: $i,C: $i] :
        ( ~ k1(F)
        | ~ k2(F,D)
        | ~ m1(E,D,C)
        | k2(C,D) )
  <=> ! [D: $i,E: $i,F: $i,C: $i] :
        ( ~ k1(F)
        | ~ k2(F,D)
        | ~ m1(E,D,C)
        | k2(C,D) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(78,plain,
    ^ [D: $i,E: $i,F: $i,C: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( k2(C,D)
                  | ~ m1(E,D,C) )
              <=> ( ~ m1(E,D,C)
                  | k2(C,D) ) )),
              ( ( k2(C,D)
                | ~ m1(E,D,C)
                | ~ k1(F) )
            <=> ( ~ m1(E,D,C)
                | k2(C,D)
                | ~ k1(F) ) )),
            rewrite(
              ( ( ~ m1(E,D,C)
                | k2(C,D)
                | ~ k1(F) )
            <=> ( ~ k1(F)
                | ~ m1(E,D,C)
                | k2(C,D) ) )),
            ( ( k2(C,D)
              | ~ m1(E,D,C)
              | ~ k1(F) )
          <=> ( ~ k1(F)
              | ~ m1(E,D,C)
              | k2(C,D) ) )),
          ( ( k2(C,D)
            | ~ m1(E,D,C)
            | ~ k1(F)
            | ~ k2(F,D) )
        <=> ( ~ k1(F)
            | ~ m1(E,D,C)
            | k2(C,D)
            | ~ k2(F,D) ) )),
        rewrite(
          ( ( ~ k1(F)
            | ~ m1(E,D,C)
            | k2(C,D)
            | ~ k2(F,D) )
        <=> ( ~ k1(F)
            | ~ k2(F,D)
            | ~ m1(E,D,C)
            | k2(C,D) ) )),
        ( ( k2(C,D)
          | ~ m1(E,D,C)
          | ~ k1(F)
          | ~ k2(F,D) )
      <=> ( ~ k1(F)
          | ~ k2(F,D)
          | ~ m1(E,D,C)
          | k2(C,D) ) )),
    inference(bind,[status(th)],]) ).

tff(79,plain,
    ( ! [D: $i,E: $i,F: $i,C: $i] :
        ( k2(C,D)
        | ~ m1(E,D,C)
        | ~ k1(F)
        | ~ k2(F,D) )
  <=> ! [D: $i,E: $i,F: $i,C: $i] :
        ( ~ k1(F)
        | ~ k2(F,D)
        | ~ m1(E,D,C)
        | k2(C,D) ) ),
    inference(quant_intro,[status(thm)],[78]) ).

tff(80,axiom,
    ! [D: $i,E: $i,F: $i,C: $i] :
      ( k2(C,D)
      | ~ m1(E,D,C)
      | ~ k1(F)
      | ~ k2(F,D) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_127) ).

tff(81,plain,
    ! [D: $i,E: $i,F: $i,C: $i] :
      ( ~ k1(F)
      | ~ k2(F,D)
      | ~ m1(E,D,C)
      | k2(C,D) ),
    inference(modus_ponens,[status(thm)],[80,79]) ).

tff(82,plain,
    ! [D: $i,E: $i,F: $i,C: $i] :
      ( ~ k1(F)
      | ~ k2(F,D)
      | ~ m1(E,D,C)
      | k2(C,D) ),
    inference(modus_ponens,[status(thm)],[81,77]) ).

tff(83,plain,
    ! [D: $i,E: $i,F: $i,C: $i] :
      ( ~ k1(F)
      | ~ k2(F,D)
      | ~ m1(E,D,C)
      | k2(C,D) ),
    inference(skolemize,[status(sab)],[82]) ).

tff(84,plain,
    ! [D: $i,E: $i,F: $i,C: $i] :
      ( ~ k1(F)
      | ~ k2(F,D)
      | ~ m1(E,D,C)
      | k2(C,D) ),
    inference(modus_ponens,[status(thm)],[83,76]) ).

tff(85,plain,
    ( ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
            ( ~ k1(F)
            | ~ k2(F,D)
            | ~ m1(E,D,C)
            | k2(C,D) )
      | ~ k1(d)
      | ~ k2(d,d)
      | ~ m1(e,d,e)
      | k2(e,d) )
  <=> ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
            ( ~ k1(F)
            | ~ k2(F,D)
            | ~ m1(E,D,C)
            | k2(C,D) )
      | ~ k1(d)
      | ~ k2(d,d)
      | ~ m1(e,d,e)
      | k2(e,d) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(86,plain,
    ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
          ( ~ k1(F)
          | ~ k2(F,D)
          | ~ m1(E,D,C)
          | k2(C,D) )
    | ~ k1(d)
    | ~ k2(d,d)
    | ~ m1(e,d,e)
    | k2(e,d) ),
    inference(quant_inst,[status(thm)],]) ).

tff(87,plain,
    ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
          ( ~ k1(F)
          | ~ k2(F,D)
          | ~ m1(E,D,C)
          | k2(C,D) )
    | ~ k1(d)
    | ~ k2(d,d)
    | ~ m1(e,d,e)
    | k2(e,d) ),
    inference(modus_ponens,[status(thm)],[86,85]) ).

tff(88,plain,
    $false,
    inference(unit_resolution,[status(thm)],[87,84,74,60,57,20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : SYN113-1 : TPTP v8.1.0. Released v1.1.0.
% 0.08/0.15  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.16/0.37  % Computer : n027.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Mon Sep  5 02:06:52 EDT 2022
% 0.16/0.37  % CPUTime  : 
% 0.16/0.37  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.37  Usage: tptp [options] [-file:]file
% 0.16/0.37    -h, -?       prints this message.
% 0.16/0.37    -smt2        print SMT-LIB2 benchmark.
% 0.16/0.37    -m, -model   generate model.
% 0.16/0.37    -p, -proof   generate proof.
% 0.16/0.37    -c, -core    generate unsat core of named formulas.
% 0.16/0.37    -st, -statistics display statistics.
% 0.16/0.37    -t:timeout   set timeout (in second).
% 0.16/0.37    -smt2status  display status in smt2 format instead of SZS.
% 0.16/0.37    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.37    -<param>:<value> configuration parameter and value.
% 0.16/0.37    -o:<output-file> file to place output in.
% 0.80/0.76  % SZS status Unsatisfiable
% 0.80/0.76  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------