TSTP Solution File: LCL188-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : LCL188-1 : TPTP v8.1.0. Released v1.1.0.
% 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 : Sun Sep 18 04:55:17 EDT 2022

% Result   : Unsatisfiable 72.71s 46.44s
% Output   : Proof 72.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   36
% Syntax   : Number of formulae    :   75 (  23 unt;   6 typ;   0 def)
%            Number of atoms       :  279 (   0 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  381 ( 178   ~; 174   |;   0   &)
%                                         (  29 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of FOOLs       :    7 (   7 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   4   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-1 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :  170 ( 154   !;   0   ?; 170   :)

% Comments : 
%------------------------------------------------------------------------------
tff(axiom_type,type,
    axiom: $i > $o ).

tff(or_type,type,
    or: ( $i * $i ) > $i ).

tff(q_type,type,
    q: $i ).

tff(not_type,type,
    not: $i > $i ).

tff(p_type,type,
    p: $i ).

tff(theorem_type,type,
    theorem: $i > $o ).

tff(1,plain,
    ^ [B: $i,A: $i,C: $i] :
      refl(
        ( axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))
      <=> axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))
  <=> ! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))
  <=> ! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL003-0.ax',axiom_1_5) ).

tff(5,plain,
    ! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))
    | axiom(or(not(or(not(or(p,q)),or(p,q))),or(p,or(not(or(p,q)),q)))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    axiom(or(not(or(not(or(p,q)),or(p,q))),or(p,or(not(or(p,q)),q)))),
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    ^ [B: $i,A: $i] :
      refl(
        ( axiom(or(not(or(A,B)),or(B,A)))
      <=> axiom(or(not(or(A,B)),or(B,A))) )),
    inference(bind,[status(th)],]) ).

tff(11,plain,
    ( ! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A)))
  <=> ! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A))) ),
    inference(quant_intro,[status(thm)],[10]) ).

tff(12,plain,
    ( ! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A)))
  <=> ! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A))) ),
    inference(rewrite,[status(thm)],]) ).

tff(13,axiom,
    ! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A))),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL003-0.ax',axiom_1_4) ).

tff(14,plain,
    ! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A))),
    inference(modus_ponens,[status(thm)],[13,12]) ).

tff(15,plain,
    ! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A))),
    inference(skolemize,[status(sab)],[14]) ).

tff(16,plain,
    ! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A))),
    inference(modus_ponens,[status(thm)],[15,11]) ).

tff(17,plain,
    ( ~ ! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A)))
    | axiom(or(not(or(q,p)),or(p,q))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(18,plain,
    axiom(or(not(or(q,p)),or(p,q))),
    inference(unit_resolution,[status(thm)],[17,16]) ).

tff(19,plain,
    ^ [X: $i] :
      refl(
        ( ( theorem(X)
          | ~ axiom(X) )
      <=> ( theorem(X)
          | ~ axiom(X) ) )),
    inference(bind,[status(th)],]) ).

tff(20,plain,
    ( ! [X: $i] :
        ( theorem(X)
        | ~ axiom(X) )
  <=> ! [X: $i] :
        ( theorem(X)
        | ~ axiom(X) ) ),
    inference(quant_intro,[status(thm)],[19]) ).

tff(21,plain,
    ( ! [X: $i] :
        ( theorem(X)
        | ~ axiom(X) )
  <=> ! [X: $i] :
        ( theorem(X)
        | ~ axiom(X) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(22,axiom,
    ! [X: $i] :
      ( theorem(X)
      | ~ axiom(X) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL003-0.ax',rule_1) ).

tff(23,plain,
    ! [X: $i] :
      ( theorem(X)
      | ~ axiom(X) ),
    inference(modus_ponens,[status(thm)],[22,21]) ).

tff(24,plain,
    ! [X: $i] :
      ( theorem(X)
      | ~ axiom(X) ),
    inference(skolemize,[status(sab)],[23]) ).

tff(25,plain,
    ! [X: $i] :
      ( theorem(X)
      | ~ axiom(X) ),
    inference(modus_ponens,[status(thm)],[24,20]) ).

tff(26,plain,
    ( ( ~ ! [X: $i] :
            ( theorem(X)
            | ~ axiom(X) )
      | theorem(or(not(or(q,p)),or(p,q)))
      | ~ axiom(or(not(or(q,p)),or(p,q))) )
  <=> ( ~ ! [X: $i] :
            ( theorem(X)
            | ~ axiom(X) )
      | theorem(or(not(or(q,p)),or(p,q)))
      | ~ axiom(or(not(or(q,p)),or(p,q))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(27,plain,
    ( ~ ! [X: $i] :
          ( theorem(X)
          | ~ axiom(X) )
    | theorem(or(not(or(q,p)),or(p,q)))
    | ~ axiom(or(not(or(q,p)),or(p,q))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(28,plain,
    ( ~ ! [X: $i] :
          ( theorem(X)
          | ~ axiom(X) )
    | theorem(or(not(or(q,p)),or(p,q)))
    | ~ axiom(or(not(or(q,p)),or(p,q))) ),
    inference(modus_ponens,[status(thm)],[27,26]) ).

tff(29,plain,
    theorem(or(not(or(q,p)),or(p,q))),
    inference(unit_resolution,[status(thm)],[28,25,18]) ).

tff(30,plain,
    ( ~ ! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A)))
    | axiom(or(not(or(p,q)),or(q,p))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(31,plain,
    axiom(or(not(or(p,q)),or(q,p))),
    inference(unit_resolution,[status(thm)],[30,16]) ).

tff(32,plain,
    ^ [Z: $i,Y: $i,X: $i] :
      refl(
        ( ( ~ theorem(or(not(Y),Z))
          | ~ axiom(or(not(X),Y))
          | theorem(or(not(X),Z)) )
      <=> ( ~ theorem(or(not(Y),Z))
          | ~ axiom(or(not(X),Y))
          | theorem(or(not(X),Z)) ) )),
    inference(bind,[status(th)],]) ).

tff(33,plain,
    ( ! [Z: $i,Y: $i,X: $i] :
        ( ~ theorem(or(not(Y),Z))
        | ~ axiom(or(not(X),Y))
        | theorem(or(not(X),Z)) )
  <=> ! [Z: $i,Y: $i,X: $i] :
        ( ~ theorem(or(not(Y),Z))
        | ~ axiom(or(not(X),Y))
        | theorem(or(not(X),Z)) ) ),
    inference(quant_intro,[status(thm)],[32]) ).

tff(34,plain,
    ( ! [Z: $i,Y: $i,X: $i] :
        ( ~ theorem(or(not(Y),Z))
        | ~ axiom(or(not(X),Y))
        | theorem(or(not(X),Z)) )
  <=> ! [Z: $i,Y: $i,X: $i] :
        ( ~ theorem(or(not(Y),Z))
        | ~ axiom(or(not(X),Y))
        | theorem(or(not(X),Z)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(35,plain,
    ^ [Z: $i,Y: $i,X: $i] :
      rewrite(
        ( ( theorem(or(not(X),Z))
          | ~ axiom(or(not(X),Y))
          | ~ theorem(or(not(Y),Z)) )
      <=> ( ~ theorem(or(not(Y),Z))
          | ~ axiom(or(not(X),Y))
          | theorem(or(not(X),Z)) ) )),
    inference(bind,[status(th)],]) ).

tff(36,plain,
    ( ! [Z: $i,Y: $i,X: $i] :
        ( theorem(or(not(X),Z))
        | ~ axiom(or(not(X),Y))
        | ~ theorem(or(not(Y),Z)) )
  <=> ! [Z: $i,Y: $i,X: $i] :
        ( ~ theorem(or(not(Y),Z))
        | ~ axiom(or(not(X),Y))
        | theorem(or(not(X),Z)) ) ),
    inference(quant_intro,[status(thm)],[35]) ).

tff(37,axiom,
    ! [Z: $i,Y: $i,X: $i] :
      ( theorem(or(not(X),Z))
      | ~ axiom(or(not(X),Y))
      | ~ theorem(or(not(Y),Z)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL003-0.ax',rule_3) ).

tff(38,plain,
    ! [Z: $i,Y: $i,X: $i] :
      ( ~ theorem(or(not(Y),Z))
      | ~ axiom(or(not(X),Y))
      | theorem(or(not(X),Z)) ),
    inference(modus_ponens,[status(thm)],[37,36]) ).

tff(39,plain,
    ! [Z: $i,Y: $i,X: $i] :
      ( ~ theorem(or(not(Y),Z))
      | ~ axiom(or(not(X),Y))
      | theorem(or(not(X),Z)) ),
    inference(modus_ponens,[status(thm)],[38,34]) ).

tff(40,plain,
    ! [Z: $i,Y: $i,X: $i] :
      ( ~ theorem(or(not(Y),Z))
      | ~ axiom(or(not(X),Y))
      | theorem(or(not(X),Z)) ),
    inference(skolemize,[status(sab)],[39]) ).

tff(41,plain,
    ! [Z: $i,Y: $i,X: $i] :
      ( ~ theorem(or(not(Y),Z))
      | ~ axiom(or(not(X),Y))
      | theorem(or(not(X),Z)) ),
    inference(modus_ponens,[status(thm)],[40,33]) ).

tff(42,plain,
    ( ( ~ ! [Z: $i,Y: $i,X: $i] :
            ( ~ theorem(or(not(Y),Z))
            | ~ axiom(or(not(X),Y))
            | theorem(or(not(X),Z)) )
      | ~ axiom(or(not(or(p,q)),or(q,p)))
      | ~ theorem(or(not(or(q,p)),or(p,q)))
      | theorem(or(not(or(p,q)),or(p,q))) )
  <=> ( ~ ! [Z: $i,Y: $i,X: $i] :
            ( ~ theorem(or(not(Y),Z))
            | ~ axiom(or(not(X),Y))
            | theorem(or(not(X),Z)) )
      | ~ axiom(or(not(or(p,q)),or(q,p)))
      | ~ theorem(or(not(or(q,p)),or(p,q)))
      | theorem(or(not(or(p,q)),or(p,q))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(43,plain,
    ( ( ~ theorem(or(not(or(q,p)),or(p,q)))
      | ~ axiom(or(not(or(p,q)),or(q,p)))
      | theorem(or(not(or(p,q)),or(p,q))) )
  <=> ( ~ axiom(or(not(or(p,q)),or(q,p)))
      | ~ theorem(or(not(or(q,p)),or(p,q)))
      | theorem(or(not(or(p,q)),or(p,q))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(44,plain,
    ( ( ~ ! [Z: $i,Y: $i,X: $i] :
            ( ~ theorem(or(not(Y),Z))
            | ~ axiom(or(not(X),Y))
            | theorem(or(not(X),Z)) )
      | ~ theorem(or(not(or(q,p)),or(p,q)))
      | ~ axiom(or(not(or(p,q)),or(q,p)))
      | theorem(or(not(or(p,q)),or(p,q))) )
  <=> ( ~ ! [Z: $i,Y: $i,X: $i] :
            ( ~ theorem(or(not(Y),Z))
            | ~ axiom(or(not(X),Y))
            | theorem(or(not(X),Z)) )
      | ~ axiom(or(not(or(p,q)),or(q,p)))
      | ~ theorem(or(not(or(q,p)),or(p,q)))
      | theorem(or(not(or(p,q)),or(p,q))) ) ),
    inference(monotonicity,[status(thm)],[43]) ).

tff(45,plain,
    ( ( ~ ! [Z: $i,Y: $i,X: $i] :
            ( ~ theorem(or(not(Y),Z))
            | ~ axiom(or(not(X),Y))
            | theorem(or(not(X),Z)) )
      | ~ theorem(or(not(or(q,p)),or(p,q)))
      | ~ axiom(or(not(or(p,q)),or(q,p)))
      | theorem(or(not(or(p,q)),or(p,q))) )
  <=> ( ~ ! [Z: $i,Y: $i,X: $i] :
            ( ~ theorem(or(not(Y),Z))
            | ~ axiom(or(not(X),Y))
            | theorem(or(not(X),Z)) )
      | ~ axiom(or(not(or(p,q)),or(q,p)))
      | ~ theorem(or(not(or(q,p)),or(p,q)))
      | theorem(or(not(or(p,q)),or(p,q))) ) ),
    inference(transitivity,[status(thm)],[44,42]) ).

tff(46,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] :
          ( ~ theorem(or(not(Y),Z))
          | ~ axiom(or(not(X),Y))
          | theorem(or(not(X),Z)) )
    | ~ theorem(or(not(or(q,p)),or(p,q)))
    | ~ axiom(or(not(or(p,q)),or(q,p)))
    | theorem(or(not(or(p,q)),or(p,q))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(47,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] :
          ( ~ theorem(or(not(Y),Z))
          | ~ axiom(or(not(X),Y))
          | theorem(or(not(X),Z)) )
    | ~ axiom(or(not(or(p,q)),or(q,p)))
    | ~ theorem(or(not(or(q,p)),or(p,q)))
    | theorem(or(not(or(p,q)),or(p,q))) ),
    inference(modus_ponens,[status(thm)],[46,45]) ).

tff(48,plain,
    ( ~ theorem(or(not(or(q,p)),or(p,q)))
    | theorem(or(not(or(p,q)),or(p,q))) ),
    inference(unit_resolution,[status(thm)],[47,41,31]) ).

tff(49,plain,
    theorem(or(not(or(p,q)),or(p,q))),
    inference(unit_resolution,[status(thm)],[48,29]) ).

tff(50,plain,
    ( ~ theorem(or(p,or(not(or(p,q)),q)))
  <=> ~ theorem(or(p,or(not(or(p,q)),q))) ),
    inference(rewrite,[status(thm)],]) ).

tff(51,axiom,
    ~ theorem(or(p,or(not(or(p,q)),q))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).

tff(52,plain,
    ~ theorem(or(p,or(not(or(p,q)),q))),
    inference(modus_ponens,[status(thm)],[51,50]) ).

tff(53,plain,
    ^ [Y: $i,X: $i] :
      refl(
        ( ( theorem(X)
          | ~ theorem(Y)
          | ~ axiom(or(not(Y),X)) )
      <=> ( theorem(X)
          | ~ theorem(Y)
          | ~ axiom(or(not(Y),X)) ) )),
    inference(bind,[status(th)],]) ).

tff(54,plain,
    ( ! [Y: $i,X: $i] :
        ( theorem(X)
        | ~ theorem(Y)
        | ~ axiom(or(not(Y),X)) )
  <=> ! [Y: $i,X: $i] :
        ( theorem(X)
        | ~ theorem(Y)
        | ~ axiom(or(not(Y),X)) ) ),
    inference(quant_intro,[status(thm)],[53]) ).

tff(55,plain,
    ( ! [Y: $i,X: $i] :
        ( theorem(X)
        | ~ theorem(Y)
        | ~ axiom(or(not(Y),X)) )
  <=> ! [Y: $i,X: $i] :
        ( theorem(X)
        | ~ theorem(Y)
        | ~ axiom(or(not(Y),X)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(56,plain,
    ^ [Y: $i,X: $i] :
      rewrite(
        ( ( theorem(X)
          | ~ axiom(or(not(Y),X))
          | ~ theorem(Y) )
      <=> ( theorem(X)
          | ~ theorem(Y)
          | ~ axiom(or(not(Y),X)) ) )),
    inference(bind,[status(th)],]) ).

tff(57,plain,
    ( ! [Y: $i,X: $i] :
        ( theorem(X)
        | ~ axiom(or(not(Y),X))
        | ~ theorem(Y) )
  <=> ! [Y: $i,X: $i] :
        ( theorem(X)
        | ~ theorem(Y)
        | ~ axiom(or(not(Y),X)) ) ),
    inference(quant_intro,[status(thm)],[56]) ).

tff(58,axiom,
    ! [Y: $i,X: $i] :
      ( theorem(X)
      | ~ axiom(or(not(Y),X))
      | ~ theorem(Y) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL003-0.ax',rule_2) ).

tff(59,plain,
    ! [Y: $i,X: $i] :
      ( theorem(X)
      | ~ theorem(Y)
      | ~ axiom(or(not(Y),X)) ),
    inference(modus_ponens,[status(thm)],[58,57]) ).

tff(60,plain,
    ! [Y: $i,X: $i] :
      ( theorem(X)
      | ~ theorem(Y)
      | ~ axiom(or(not(Y),X)) ),
    inference(modus_ponens,[status(thm)],[59,55]) ).

tff(61,plain,
    ! [Y: $i,X: $i] :
      ( theorem(X)
      | ~ theorem(Y)
      | ~ axiom(or(not(Y),X)) ),
    inference(skolemize,[status(sab)],[60]) ).

tff(62,plain,
    ! [Y: $i,X: $i] :
      ( theorem(X)
      | ~ theorem(Y)
      | ~ axiom(or(not(Y),X)) ),
    inference(modus_ponens,[status(thm)],[61,54]) ).

tff(63,plain,
    ( ( ~ ! [Y: $i,X: $i] :
            ( theorem(X)
            | ~ theorem(Y)
            | ~ axiom(or(not(Y),X)) )
      | theorem(or(p,or(not(or(p,q)),q)))
      | ~ axiom(or(not(or(not(or(p,q)),or(p,q))),or(p,or(not(or(p,q)),q))))
      | ~ theorem(or(not(or(p,q)),or(p,q))) )
  <=> ( ~ ! [Y: $i,X: $i] :
            ( theorem(X)
            | ~ theorem(Y)
            | ~ axiom(or(not(Y),X)) )
      | theorem(or(p,or(not(or(p,q)),q)))
      | ~ axiom(or(not(or(not(or(p,q)),or(p,q))),or(p,or(not(or(p,q)),q))))
      | ~ theorem(or(not(or(p,q)),or(p,q))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(64,plain,
    ( ( theorem(or(p,or(not(or(p,q)),q)))
      | ~ theorem(or(not(or(p,q)),or(p,q)))
      | ~ axiom(or(not(or(not(or(p,q)),or(p,q))),or(p,or(not(or(p,q)),q)))) )
  <=> ( theorem(or(p,or(not(or(p,q)),q)))
      | ~ axiom(or(not(or(not(or(p,q)),or(p,q))),or(p,or(not(or(p,q)),q))))
      | ~ theorem(or(not(or(p,q)),or(p,q))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(65,plain,
    ( ( ~ ! [Y: $i,X: $i] :
            ( theorem(X)
            | ~ theorem(Y)
            | ~ axiom(or(not(Y),X)) )
      | theorem(or(p,or(not(or(p,q)),q)))
      | ~ theorem(or(not(or(p,q)),or(p,q)))
      | ~ axiom(or(not(or(not(or(p,q)),or(p,q))),or(p,or(not(or(p,q)),q)))) )
  <=> ( ~ ! [Y: $i,X: $i] :
            ( theorem(X)
            | ~ theorem(Y)
            | ~ axiom(or(not(Y),X)) )
      | theorem(or(p,or(not(or(p,q)),q)))
      | ~ axiom(or(not(or(not(or(p,q)),or(p,q))),or(p,or(not(or(p,q)),q))))
      | ~ theorem(or(not(or(p,q)),or(p,q))) ) ),
    inference(monotonicity,[status(thm)],[64]) ).

tff(66,plain,
    ( ( ~ ! [Y: $i,X: $i] :
            ( theorem(X)
            | ~ theorem(Y)
            | ~ axiom(or(not(Y),X)) )
      | theorem(or(p,or(not(or(p,q)),q)))
      | ~ theorem(or(not(or(p,q)),or(p,q)))
      | ~ axiom(or(not(or(not(or(p,q)),or(p,q))),or(p,or(not(or(p,q)),q)))) )
  <=> ( ~ ! [Y: $i,X: $i] :
            ( theorem(X)
            | ~ theorem(Y)
            | ~ axiom(or(not(Y),X)) )
      | theorem(or(p,or(not(or(p,q)),q)))
      | ~ axiom(or(not(or(not(or(p,q)),or(p,q))),or(p,or(not(or(p,q)),q))))
      | ~ theorem(or(not(or(p,q)),or(p,q))) ) ),
    inference(transitivity,[status(thm)],[65,63]) ).

tff(67,plain,
    ( ~ ! [Y: $i,X: $i] :
          ( theorem(X)
          | ~ theorem(Y)
          | ~ axiom(or(not(Y),X)) )
    | theorem(or(p,or(not(or(p,q)),q)))
    | ~ theorem(or(not(or(p,q)),or(p,q)))
    | ~ axiom(or(not(or(not(or(p,q)),or(p,q))),or(p,or(not(or(p,q)),q)))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(68,plain,
    ( ~ ! [Y: $i,X: $i] :
          ( theorem(X)
          | ~ theorem(Y)
          | ~ axiom(or(not(Y),X)) )
    | theorem(or(p,or(not(or(p,q)),q)))
    | ~ axiom(or(not(or(not(or(p,q)),or(p,q))),or(p,or(not(or(p,q)),q))))
    | ~ theorem(or(not(or(p,q)),or(p,q))) ),
    inference(modus_ponens,[status(thm)],[67,66]) ).

tff(69,plain,
    $false,
    inference(unit_resolution,[status(thm)],[68,62,52,49,9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : LCL188-1 : TPTP v8.1.0. Released v1.1.0.
% 0.00/0.11  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32  % Computer : n004.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Thu Sep  1 18:33:34 EDT 2022
% 0.11/0.32  % CPUTime  : 
% 0.11/0.32  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32  Usage: tptp [options] [-file:]file
% 0.11/0.32    -h, -?       prints this message.
% 0.11/0.32    -smt2        print SMT-LIB2 benchmark.
% 0.11/0.32    -m, -model   generate model.
% 0.11/0.32    -p, -proof   generate proof.
% 0.11/0.32    -c, -core    generate unsat core of named formulas.
% 0.11/0.32    -st, -statistics display statistics.
% 0.11/0.32    -t:timeout   set timeout (in second).
% 0.11/0.32    -smt2status  display status in smt2 format instead of SZS.
% 0.11/0.32    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32    -<param>:<value> configuration parameter and value.
% 0.11/0.32    -o:<output-file> file to place output in.
% 72.71/46.44  % SZS status Unsatisfiable
% 72.71/46.44  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------