TSTP Solution File: SYN211-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN211-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n022.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 23:54:13 EDT 2022

% Result   : Unsatisfiable 0.21s 0.50s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   52
% Syntax   : Number of formulae    :  101 (  22 unt;  11 typ;   0 def)
%            Number of atoms       :  379 (   0 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  509 ( 236   ~; 232   |;   0   &)
%                                         (  41 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :   16 (  16 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (   8   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  12 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :  234 ( 211   !;   0   ?; 234   :)

% Comments : 
%------------------------------------------------------------------------------
tff(p3_type,type,
    p3: ( $i * $i * $i ) > $o ).

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

tff(n2_type,type,
    n2: $i > $o ).

tff(p1_type,type,
    p1: ( $i * $i * $i ) > $o ).

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

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

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

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

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

tff(l1_type,type,
    l1: ( $i * $i ) > $o ).

tff(s4_type,type,
    s4: $i > $o ).

tff(1,plain,
    ^ [B: $i,C: $i] :
      refl(
        ( ( ~ p0(C,B)
          | p1(B,B,B) )
      <=> ( ~ p0(C,B)
          | p1(B,B,B) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [B: $i,C: $i] :
        ( ~ p0(C,B)
        | p1(B,B,B) )
  <=> ! [B: $i,C: $i] :
        ( ~ p0(C,B)
        | p1(B,B,B) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [B: $i,C: $i] :
        ( ~ p0(C,B)
        | p1(B,B,B) )
  <=> ! [B: $i,C: $i] :
        ( ~ p0(C,B)
        | p1(B,B,B) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,plain,
    ^ [B: $i,C: $i] :
      rewrite(
        ( ( p1(B,B,B)
          | ~ p0(C,B) )
      <=> ( ~ p0(C,B)
          | p1(B,B,B) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [B: $i,C: $i] :
        ( p1(B,B,B)
        | ~ p0(C,B) )
  <=> ! [B: $i,C: $i] :
        ( ~ p0(C,B)
        | p1(B,B,B) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,axiom,
    ! [B: $i,C: $i] :
      ( p1(B,B,B)
      | ~ p0(C,B) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_085) ).

tff(7,plain,
    ! [B: $i,C: $i] :
      ( ~ p0(C,B)
      | p1(B,B,B) ),
    inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
    ! [B: $i,C: $i] :
      ( ~ p0(C,B)
      | p1(B,B,B) ),
    inference(modus_ponens,[status(thm)],[7,3]) ).

tff(9,plain,
    ! [B: $i,C: $i] :
      ( ~ p0(C,B)
      | p1(B,B,B) ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [B: $i,C: $i] :
      ( ~ p0(C,B)
      | p1(B,B,B) ),
    inference(modus_ponens,[status(thm)],[9,2]) ).

tff(11,plain,
    ( p0(b,d)
  <=> p0(b,d) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,axiom,
    p0(b,d),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_10) ).

tff(13,plain,
    p0(b,d),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    ( ( ~ ! [B: $i,C: $i] :
            ( ~ p0(C,B)
            | p1(B,B,B) )
      | ~ p0(b,d)
      | p1(d,d,d) )
  <=> ( ~ ! [B: $i,C: $i] :
            ( ~ p0(C,B)
            | p1(B,B,B) )
      | ~ p0(b,d)
      | p1(d,d,d) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,plain,
    ( ~ ! [B: $i,C: $i] :
          ( ~ p0(C,B)
          | p1(B,B,B) )
    | ~ p0(b,d)
    | p1(d,d,d) ),
    inference(quant_inst,[status(thm)],]) ).

tff(16,plain,
    ( ~ ! [B: $i,C: $i] :
          ( ~ p0(C,B)
          | p1(B,B,B) )
    | ~ p0(b,d)
    | p1(d,d,d) ),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    p1(d,d,d),
    inference(unit_resolution,[status(thm)],[16,13,10]) ).

tff(18,plain,
    ^ [B: $i,A: $i,C: $i] :
      refl(
        ( ( n2(A)
          | ~ p1(B,C,A) )
      <=> ( n2(A)
          | ~ p1(B,C,A) ) )),
    inference(bind,[status(th)],]) ).

tff(19,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( n2(A)
        | ~ p1(B,C,A) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( n2(A)
        | ~ p1(B,C,A) ) ),
    inference(quant_intro,[status(thm)],[18]) ).

tff(20,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( n2(A)
        | ~ p1(B,C,A) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( n2(A)
        | ~ p1(B,C,A) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,axiom,
    ! [B: $i,A: $i,C: $i] :
      ( n2(A)
      | ~ p1(B,C,A) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_137) ).

tff(22,plain,
    ! [B: $i,A: $i,C: $i] :
      ( n2(A)
      | ~ p1(B,C,A) ),
    inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
    ! [B: $i,A: $i,C: $i] :
      ( n2(A)
      | ~ p1(B,C,A) ),
    inference(skolemize,[status(sab)],[22]) ).

tff(24,plain,
    ! [B: $i,A: $i,C: $i] :
      ( n2(A)
      | ~ p1(B,C,A) ),
    inference(modus_ponens,[status(thm)],[23,19]) ).

tff(25,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( n2(A)
            | ~ p1(B,C,A) )
      | n2(d)
      | ~ p1(d,d,d) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( n2(A)
            | ~ p1(B,C,A) )
      | n2(d)
      | ~ p1(d,d,d) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(26,plain,
    ( ~ ! [B: $i,A: $i,C: $i] :
          ( n2(A)
          | ~ p1(B,C,A) )
    | n2(d)
    | ~ p1(d,d,d) ),
    inference(quant_inst,[status(thm)],]) ).

tff(27,plain,
    ( ~ ! [B: $i,A: $i,C: $i] :
          ( n2(A)
          | ~ p1(B,C,A) )
    | n2(d)
    | ~ p1(d,d,d) ),
    inference(modus_ponens,[status(thm)],[26,25]) ).

tff(28,plain,
    n2(d),
    inference(unit_resolution,[status(thm)],[27,24,17]) ).

tff(29,plain,
    ^ [H: $i] :
      refl(
        ( ( ~ k1(H)
          | ~ n2(H)
          | p3(H,H,H) )
      <=> ( ~ k1(H)
          | ~ n2(H)
          | p3(H,H,H) ) )),
    inference(bind,[status(th)],]) ).

tff(30,plain,
    ( ! [H: $i] :
        ( ~ k1(H)
        | ~ n2(H)
        | p3(H,H,H) )
  <=> ! [H: $i] :
        ( ~ k1(H)
        | ~ n2(H)
        | p3(H,H,H) ) ),
    inference(quant_intro,[status(thm)],[29]) ).

tff(31,plain,
    ( ! [H: $i] :
        ( ~ k1(H)
        | ~ n2(H)
        | p3(H,H,H) )
  <=> ! [H: $i] :
        ( ~ k1(H)
        | ~ n2(H)
        | p3(H,H,H) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(32,plain,
    ^ [H: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( p3(H,H,H)
              | ~ k1(H) )
          <=> ( ~ k1(H)
              | p3(H,H,H) ) )),
          ( ( p3(H,H,H)
            | ~ k1(H)
            | ~ n2(H) )
        <=> ( ~ k1(H)
            | p3(H,H,H)
            | ~ n2(H) ) )),
        rewrite(
          ( ( ~ k1(H)
            | p3(H,H,H)
            | ~ n2(H) )
        <=> ( ~ k1(H)
            | ~ n2(H)
            | p3(H,H,H) ) )),
        ( ( p3(H,H,H)
          | ~ k1(H)
          | ~ n2(H) )
      <=> ( ~ k1(H)
          | ~ n2(H)
          | p3(H,H,H) ) )),
    inference(bind,[status(th)],]) ).

tff(33,plain,
    ( ! [H: $i] :
        ( p3(H,H,H)
        | ~ k1(H)
        | ~ n2(H) )
  <=> ! [H: $i] :
        ( ~ k1(H)
        | ~ n2(H)
        | p3(H,H,H) ) ),
    inference(quant_intro,[status(thm)],[32]) ).

tff(34,axiom,
    ! [H: $i] :
      ( p3(H,H,H)
      | ~ k1(H)
      | ~ n2(H) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_249) ).

tff(35,plain,
    ! [H: $i] :
      ( ~ k1(H)
      | ~ n2(H)
      | p3(H,H,H) ),
    inference(modus_ponens,[status(thm)],[34,33]) ).

tff(36,plain,
    ! [H: $i] :
      ( ~ k1(H)
      | ~ n2(H)
      | p3(H,H,H) ),
    inference(modus_ponens,[status(thm)],[35,31]) ).

tff(37,plain,
    ! [H: $i] :
      ( ~ k1(H)
      | ~ n2(H)
      | p3(H,H,H) ),
    inference(skolemize,[status(sab)],[36]) ).

tff(38,plain,
    ! [H: $i] :
      ( ~ k1(H)
      | ~ n2(H)
      | p3(H,H,H) ),
    inference(modus_ponens,[status(thm)],[37,30]) ).

tff(39,plain,
    ^ [I: $i,J: $i] :
      refl(
        ( ( k1(I)
          | ~ n0(J,I) )
      <=> ( k1(I)
          | ~ n0(J,I) ) )),
    inference(bind,[status(th)],]) ).

tff(40,plain,
    ( ! [I: $i,J: $i] :
        ( k1(I)
        | ~ n0(J,I) )
  <=> ! [I: $i,J: $i] :
        ( k1(I)
        | ~ n0(J,I) ) ),
    inference(quant_intro,[status(thm)],[39]) ).

tff(41,plain,
    ( ! [I: $i,J: $i] :
        ( k1(I)
        | ~ n0(J,I) )
  <=> ! [I: $i,J: $i] :
        ( k1(I)
        | ~ n0(J,I) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(42,axiom,
    ! [I: $i,J: $i] :
      ( k1(I)
      | ~ n0(J,I) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_001) ).

tff(43,plain,
    ! [I: $i,J: $i] :
      ( k1(I)
      | ~ n0(J,I) ),
    inference(modus_ponens,[status(thm)],[42,41]) ).

tff(44,plain,
    ! [I: $i,J: $i] :
      ( k1(I)
      | ~ n0(J,I) ),
    inference(skolemize,[status(sab)],[43]) ).

tff(45,plain,
    ! [I: $i,J: $i] :
      ( k1(I)
      | ~ n0(J,I) ),
    inference(modus_ponens,[status(thm)],[44,40]) ).

tff(46,plain,
    ( n0(c,d)
  <=> n0(c,d) ),
    inference(rewrite,[status(thm)],]) ).

tff(47,axiom,
    n0(c,d),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_34) ).

tff(48,plain,
    n0(c,d),
    inference(modus_ponens,[status(thm)],[47,46]) ).

tff(49,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(50,plain,
    ( ~ ! [I: $i,J: $i] :
          ( k1(I)
          | ~ n0(J,I) )
    | k1(d)
    | ~ n0(c,d) ),
    inference(quant_inst,[status(thm)],]) ).

tff(51,plain,
    ( ~ ! [I: $i,J: $i] :
          ( k1(I)
          | ~ n0(J,I) )
    | k1(d)
    | ~ n0(c,d) ),
    inference(modus_ponens,[status(thm)],[50,49]) ).

tff(52,plain,
    k1(d),
    inference(unit_resolution,[status(thm)],[51,48,45]) ).

tff(53,plain,
    ( ( ~ ! [H: $i] :
            ( ~ k1(H)
            | ~ n2(H)
            | p3(H,H,H) )
      | ~ k1(d)
      | ~ n2(d)
      | p3(d,d,d) )
  <=> ( ~ ! [H: $i] :
            ( ~ k1(H)
            | ~ n2(H)
            | p3(H,H,H) )
      | ~ k1(d)
      | ~ n2(d)
      | p3(d,d,d) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(54,plain,
    ( ~ ! [H: $i] :
          ( ~ k1(H)
          | ~ n2(H)
          | p3(H,H,H) )
    | ~ k1(d)
    | ~ n2(d)
    | p3(d,d,d) ),
    inference(quant_inst,[status(thm)],]) ).

tff(55,plain,
    ( ~ ! [H: $i] :
          ( ~ k1(H)
          | ~ n2(H)
          | p3(H,H,H) )
    | ~ k1(d)
    | ~ n2(d)
    | p3(d,d,d) ),
    inference(modus_ponens,[status(thm)],[54,53]) ).

tff(56,plain,
    p3(d,d,d),
    inference(unit_resolution,[status(thm)],[55,52,38,28]) ).

tff(57,plain,
    ^ [H: $i,G: $i] :
      refl(
        ( ( ~ n0(H,G)
          | l1(G,G) )
      <=> ( ~ n0(H,G)
          | l1(G,G) ) )),
    inference(bind,[status(th)],]) ).

tff(58,plain,
    ( ! [H: $i,G: $i] :
        ( ~ n0(H,G)
        | l1(G,G) )
  <=> ! [H: $i,G: $i] :
        ( ~ n0(H,G)
        | l1(G,G) ) ),
    inference(quant_intro,[status(thm)],[57]) ).

tff(59,plain,
    ( ! [H: $i,G: $i] :
        ( ~ n0(H,G)
        | l1(G,G) )
  <=> ! [H: $i,G: $i] :
        ( ~ n0(H,G)
        | l1(G,G) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(60,plain,
    ^ [H: $i,G: $i] :
      rewrite(
        ( ( l1(G,G)
          | ~ n0(H,G) )
      <=> ( ~ n0(H,G)
          | l1(G,G) ) )),
    inference(bind,[status(th)],]) ).

tff(61,plain,
    ( ! [H: $i,G: $i] :
        ( l1(G,G)
        | ~ n0(H,G) )
  <=> ! [H: $i,G: $i] :
        ( ~ n0(H,G)
        | l1(G,G) ) ),
    inference(quant_intro,[status(thm)],[60]) ).

tff(62,axiom,
    ! [H: $i,G: $i] :
      ( l1(G,G)
      | ~ n0(H,G) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_002) ).

tff(63,plain,
    ! [H: $i,G: $i] :
      ( ~ n0(H,G)
      | l1(G,G) ),
    inference(modus_ponens,[status(thm)],[62,61]) ).

tff(64,plain,
    ! [H: $i,G: $i] :
      ( ~ n0(H,G)
      | l1(G,G) ),
    inference(modus_ponens,[status(thm)],[63,59]) ).

tff(65,plain,
    ! [H: $i,G: $i] :
      ( ~ n0(H,G)
      | l1(G,G) ),
    inference(skolemize,[status(sab)],[64]) ).

tff(66,plain,
    ! [H: $i,G: $i] :
      ( ~ n0(H,G)
      | l1(G,G) ),
    inference(modus_ponens,[status(thm)],[65,58]) ).

tff(67,plain,
    ( ( ~ ! [H: $i,G: $i] :
            ( ~ n0(H,G)
            | l1(G,G) )
      | ~ n0(c,d)
      | l1(d,d) )
  <=> ( ~ ! [H: $i,G: $i] :
            ( ~ n0(H,G)
            | l1(G,G) )
      | ~ n0(c,d)
      | l1(d,d) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(68,plain,
    ( ~ ! [H: $i,G: $i] :
          ( ~ n0(H,G)
          | l1(G,G) )
    | ~ n0(c,d)
    | l1(d,d) ),
    inference(quant_inst,[status(thm)],]) ).

tff(69,plain,
    ( ~ ! [H: $i,G: $i] :
          ( ~ n0(H,G)
          | l1(G,G) )
    | ~ n0(c,d)
    | l1(d,d) ),
    inference(modus_ponens,[status(thm)],[68,67]) ).

tff(70,plain,
    l1(d,d),
    inference(unit_resolution,[status(thm)],[69,48,66]) ).

tff(71,plain,
    ( ~ s4(d)
  <=> ~ s4(d) ),
    inference(rewrite,[status(thm)],]) ).

tff(72,axiom,
    ~ s4(d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

tff(73,plain,
    ~ s4(d),
    inference(modus_ponens,[status(thm)],[72,71]) ).

tff(74,plain,
    ^ [B: $i,D: $i,A: $i,C: $i] :
      refl(
        ( ( ~ l1(A,C)
          | ~ p3(B,C,D)
          | s4(A) )
      <=> ( ~ l1(A,C)
          | ~ p3(B,C,D)
          | s4(A) ) )),
    inference(bind,[status(th)],]) ).

tff(75,plain,
    ( ! [B: $i,D: $i,A: $i,C: $i] :
        ( ~ l1(A,C)
        | ~ p3(B,C,D)
        | s4(A) )
  <=> ! [B: $i,D: $i,A: $i,C: $i] :
        ( ~ l1(A,C)
        | ~ p3(B,C,D)
        | s4(A) ) ),
    inference(quant_intro,[status(thm)],[74]) ).

tff(76,plain,
    ( ! [B: $i,D: $i,A: $i,C: $i] :
        ( ~ l1(A,C)
        | ~ p3(B,C,D)
        | s4(A) )
  <=> ! [B: $i,D: $i,A: $i,C: $i] :
        ( ~ l1(A,C)
        | ~ p3(B,C,D)
        | s4(A) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(77,plain,
    ^ [B: $i,D: $i,A: $i,C: $i] :
      rewrite(
        ( ( s4(A)
          | ~ p3(B,C,D)
          | ~ l1(A,C) )
      <=> ( ~ l1(A,C)
          | ~ p3(B,C,D)
          | s4(A) ) )),
    inference(bind,[status(th)],]) ).

tff(78,plain,
    ( ! [B: $i,D: $i,A: $i,C: $i] :
        ( s4(A)
        | ~ p3(B,C,D)
        | ~ l1(A,C) )
  <=> ! [B: $i,D: $i,A: $i,C: $i] :
        ( ~ l1(A,C)
        | ~ p3(B,C,D)
        | s4(A) ) ),
    inference(quant_intro,[status(thm)],[77]) ).

tff(79,axiom,
    ! [B: $i,D: $i,A: $i,C: $i] :
      ( s4(A)
      | ~ p3(B,C,D)
      | ~ l1(A,C) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_299) ).

tff(80,plain,
    ! [B: $i,D: $i,A: $i,C: $i] :
      ( ~ l1(A,C)
      | ~ p3(B,C,D)
      | s4(A) ),
    inference(modus_ponens,[status(thm)],[79,78]) ).

tff(81,plain,
    ! [B: $i,D: $i,A: $i,C: $i] :
      ( ~ l1(A,C)
      | ~ p3(B,C,D)
      | s4(A) ),
    inference(modus_ponens,[status(thm)],[80,76]) ).

tff(82,plain,
    ! [B: $i,D: $i,A: $i,C: $i] :
      ( ~ l1(A,C)
      | ~ p3(B,C,D)
      | s4(A) ),
    inference(skolemize,[status(sab)],[81]) ).

tff(83,plain,
    ! [B: $i,D: $i,A: $i,C: $i] :
      ( ~ l1(A,C)
      | ~ p3(B,C,D)
      | s4(A) ),
    inference(modus_ponens,[status(thm)],[82,75]) ).

tff(84,plain,
    ( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
            ( ~ l1(A,C)
            | ~ p3(B,C,D)
            | s4(A) )
      | s4(d)
      | ~ l1(d,d)
      | ~ p3(d,d,d) )
  <=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
            ( ~ l1(A,C)
            | ~ p3(B,C,D)
            | s4(A) )
      | s4(d)
      | ~ l1(d,d)
      | ~ p3(d,d,d) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(85,plain,
    ( ( ~ l1(d,d)
      | ~ p3(d,d,d)
      | s4(d) )
  <=> ( s4(d)
      | ~ l1(d,d)
      | ~ p3(d,d,d) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(86,plain,
    ( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
            ( ~ l1(A,C)
            | ~ p3(B,C,D)
            | s4(A) )
      | ~ l1(d,d)
      | ~ p3(d,d,d)
      | s4(d) )
  <=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
            ( ~ l1(A,C)
            | ~ p3(B,C,D)
            | s4(A) )
      | s4(d)
      | ~ l1(d,d)
      | ~ p3(d,d,d) ) ),
    inference(monotonicity,[status(thm)],[85]) ).

tff(87,plain,
    ( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
            ( ~ l1(A,C)
            | ~ p3(B,C,D)
            | s4(A) )
      | ~ l1(d,d)
      | ~ p3(d,d,d)
      | s4(d) )
  <=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
            ( ~ l1(A,C)
            | ~ p3(B,C,D)
            | s4(A) )
      | s4(d)
      | ~ l1(d,d)
      | ~ p3(d,d,d) ) ),
    inference(transitivity,[status(thm)],[86,84]) ).

tff(88,plain,
    ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
          ( ~ l1(A,C)
          | ~ p3(B,C,D)
          | s4(A) )
    | ~ l1(d,d)
    | ~ p3(d,d,d)
    | s4(d) ),
    inference(quant_inst,[status(thm)],]) ).

tff(89,plain,
    ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
          ( ~ l1(A,C)
          | ~ p3(B,C,D)
          | s4(A) )
    | s4(d)
    | ~ l1(d,d)
    | ~ p3(d,d,d) ),
    inference(modus_ponens,[status(thm)],[88,87]) ).

tff(90,plain,
    $false,
    inference(unit_resolution,[status(thm)],[89,83,73,70,56]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYN211-1 : 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 : n022.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 02:10:54 EDT 2022
% 0.14/0.35  % 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
%------------------------------------------------------------------------------