TSTP Solution File: LCL301-3 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : LCL301-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n013.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 04:55:50 EDT 2022

% Result   : Unsatisfiable 3.49s 2.40s
% Output   : Proof 3.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   74
% Syntax   : Number of formulae    :  213 ( 108 unt;   9 typ;   0 def)
%            Number of atoms       :  500 (  95 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  527 ( 241   ~; 227   |;   0   &)
%                                         (  59 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :   11 (   3 avg)
%            Number of FOOLs       :   10 (  10 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   7   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-2 aty)
%            Number of variables   :  253 ( 234   !;   0   ?; 253   :)

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

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

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

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

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

tff(implies_type,type,
    implies: ( $i * $i ) > $i ).

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

tff(and_type,type,
    and: ( $i * $i ) > $i ).

tff(equivalent_type,type,
    equivalent: ( $i * $i ) > $i ).

tff(1,plain,
    ^ [Y: $i,X: $i] :
      refl(
        ( ( implies(X,Y) = or(not(X),Y) )
      <=> ( implies(X,Y) = or(not(X),Y) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
  <=> ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
  <=> ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',implies_definition) ).

tff(5,plain,
    ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
    | ( implies(not(or(not(not(p)),not(q))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))) = or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

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

tff(10,plain,
    or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))) = implies(not(or(not(not(p)),not(q))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))),
    inference(symmetry,[status(thm)],[9]) ).

tff(11,plain,
    ( axiom(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))))
  <=> axiom(implies(not(or(not(not(p)),not(q))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q)))))) ),
    inference(monotonicity,[status(thm)],[10]) ).

tff(12,plain,
    ( axiom(implies(not(or(not(not(p)),not(q))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))))
  <=> axiom(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q)))))) ),
    inference(symmetry,[status(thm)],[11]) ).

tff(13,plain,
    ^ [B: $i,A: $i] :
      refl(
        ( axiom(implies(A,or(B,A)))
      <=> axiom(implies(A,or(B,A))) )),
    inference(bind,[status(th)],]) ).

tff(14,plain,
    ( ! [B: $i,A: $i] : axiom(implies(A,or(B,A)))
  <=> ! [B: $i,A: $i] : axiom(implies(A,or(B,A))) ),
    inference(quant_intro,[status(thm)],[13]) ).

tff(15,plain,
    ( ! [B: $i,A: $i] : axiom(implies(A,or(B,A)))
  <=> ! [B: $i,A: $i] : axiom(implies(A,or(B,A))) ),
    inference(rewrite,[status(thm)],]) ).

tff(16,axiom,
    ! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_3) ).

tff(17,plain,
    ! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
    inference(modus_ponens,[status(thm)],[16,15]) ).

tff(18,plain,
    ! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
    inference(skolemize,[status(sab)],[17]) ).

tff(19,plain,
    ! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
    inference(modus_ponens,[status(thm)],[18,14]) ).

tff(20,plain,
    ( ~ ! [B: $i,A: $i] : axiom(implies(A,or(B,A)))
    | axiom(implies(not(or(not(not(p)),not(q))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q)))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(21,plain,
    axiom(implies(not(or(not(not(p)),not(q))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q)))))),
    inference(unit_resolution,[status(thm)],[20,19]) ).

tff(22,plain,
    axiom(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q)))))),
    inference(modus_ponens,[status(thm)],[21,12]) ).

tff(23,plain,
    ^ [Q: $i,P: $i] :
      refl(
        ( ( and(P,Q) = not(or(not(P),not(Q))) )
      <=> ( and(P,Q) = not(or(not(P),not(Q))) ) )),
    inference(bind,[status(th)],]) ).

tff(24,plain,
    ( ! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) )
  <=> ! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) ) ),
    inference(quant_intro,[status(thm)],[23]) ).

tff(25,plain,
    ( ! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) )
  <=> ! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(26,axiom,
    ! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL004-1.ax',and_defn) ).

tff(27,plain,
    ! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) ),
    inference(modus_ponens,[status(thm)],[26,25]) ).

tff(28,plain,
    ! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) ),
    inference(skolemize,[status(sab)],[27]) ).

tff(29,plain,
    ! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) ),
    inference(modus_ponens,[status(thm)],[28,24]) ).

tff(30,plain,
    ( ~ ! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) )
    | ( and(not(p),q) = not(or(not(not(p)),not(q))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(31,plain,
    and(not(p),q) = not(or(not(not(p)),not(q))),
    inference(unit_resolution,[status(thm)],[30,29]) ).

tff(32,plain,
    not(or(not(not(p)),not(q))) = and(not(p),q),
    inference(symmetry,[status(thm)],[31]) ).

tff(33,plain,
    ( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
    | ( implies(not(p),not(q)) = or(not(not(p)),not(q)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(34,plain,
    implies(not(p),not(q)) = or(not(not(p)),not(q)),
    inference(unit_resolution,[status(thm)],[33,7]) ).

tff(35,plain,
    not(implies(not(p),not(q))) = not(or(not(not(p)),not(q))),
    inference(monotonicity,[status(thm)],[34]) ).

tff(36,plain,
    not(or(not(not(p)),not(q))) = not(implies(not(p),not(q))),
    inference(symmetry,[status(thm)],[35]) ).

tff(37,plain,
    implies(not(or(not(not(p)),not(q))),not(or(not(not(p)),not(q)))) = implies(not(implies(not(p),not(q))),and(not(p),q)),
    inference(monotonicity,[status(thm)],[36,32]) ).

tff(38,plain,
    ( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
    | ( implies(not(or(not(not(p)),not(q))),not(or(not(not(p)),not(q)))) = or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(39,plain,
    implies(not(or(not(not(p)),not(q))),not(or(not(not(p)),not(q)))) = or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))),
    inference(unit_resolution,[status(thm)],[38,7]) ).

tff(40,plain,
    or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))) = implies(not(or(not(not(p)),not(q))),not(or(not(not(p)),not(q)))),
    inference(symmetry,[status(thm)],[39]) ).

tff(41,plain,
    or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))) = implies(not(implies(not(p),not(q))),and(not(p),q)),
    inference(transitivity,[status(thm)],[40,37]) ).

tff(42,plain,
    or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))) = or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),implies(not(implies(not(p),not(q))),and(not(p),q))),
    inference(monotonicity,[status(thm)],[41]) ).

tff(43,plain,
    implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))) = implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),implies(not(implies(not(p),not(q))),and(not(p),q)))),
    inference(monotonicity,[status(thm)],[42]) ).

tff(44,plain,
    ( theorem(implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))))
  <=> theorem(implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),implies(not(implies(not(p),not(q))),and(not(p),q))))) ),
    inference(monotonicity,[status(thm)],[43]) ).

tff(45,plain,
    ^ [B: $i,A: $i,C: $i] :
      refl(
        ( axiom(implies(or(A,or(B,C)),or(B,or(A,C))))
      <=> axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) )),
    inference(bind,[status(th)],]) ).

tff(46,plain,
    ( ! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C))))
  <=> ! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) ),
    inference(quant_intro,[status(thm)],[45]) ).

tff(47,plain,
    ( ! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C))))
  <=> ! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) ),
    inference(rewrite,[status(thm)],]) ).

tff(48,axiom,
    ! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_5) ).

tff(49,plain,
    ! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
    inference(modus_ponens,[status(thm)],[48,47]) ).

tff(50,plain,
    ! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
    inference(skolemize,[status(sab)],[49]) ).

tff(51,plain,
    ! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
    inference(modus_ponens,[status(thm)],[50,46]) ).

tff(52,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C))))
    | axiom(implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(53,plain,
    axiom(implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))))),
    inference(unit_resolution,[status(thm)],[52,51]) ).

tff(54,plain,
    ^ [X: $i] :
      refl(
        ( ( theorem(X)
          | ~ axiom(X) )
      <=> ( theorem(X)
          | ~ axiom(X) ) )),
    inference(bind,[status(th)],]) ).

tff(55,plain,
    ( ! [X: $i] :
        ( theorem(X)
        | ~ axiom(X) )
  <=> ! [X: $i] :
        ( theorem(X)
        | ~ axiom(X) ) ),
    inference(quant_intro,[status(thm)],[54]) ).

tff(56,plain,
    ( ! [X: $i] :
        ( theorem(X)
        | ~ axiom(X) )
  <=> ! [X: $i] :
        ( theorem(X)
        | ~ axiom(X) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(57,axiom,
    ! [X: $i] :
      ( theorem(X)
      | ~ axiom(X) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',rule_1) ).

tff(58,plain,
    ! [X: $i] :
      ( theorem(X)
      | ~ axiom(X) ),
    inference(modus_ponens,[status(thm)],[57,56]) ).

tff(59,plain,
    ! [X: $i] :
      ( theorem(X)
      | ~ axiom(X) ),
    inference(skolemize,[status(sab)],[58]) ).

tff(60,plain,
    ! [X: $i] :
      ( theorem(X)
      | ~ axiom(X) ),
    inference(modus_ponens,[status(thm)],[59,55]) ).

tff(61,plain,
    ( ( ~ ! [X: $i] :
            ( theorem(X)
            | ~ axiom(X) )
      | theorem(implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))))
      | ~ axiom(implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))))) )
  <=> ( ~ ! [X: $i] :
            ( theorem(X)
            | ~ axiom(X) )
      | theorem(implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))))
      | ~ axiom(implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(62,plain,
    ( ~ ! [X: $i] :
          ( theorem(X)
          | ~ axiom(X) )
    | theorem(implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))))
    | ~ axiom(implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(63,plain,
    ( ~ ! [X: $i] :
          ( theorem(X)
          | ~ axiom(X) )
    | theorem(implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))))
    | ~ axiom(implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))))) ),
    inference(modus_ponens,[status(thm)],[62,61]) ).

tff(64,plain,
    theorem(implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))))),
    inference(unit_resolution,[status(thm)],[63,60,53]) ).

tff(65,plain,
    theorem(implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),implies(not(implies(not(p),not(q))),and(not(p),q))))),
    inference(modus_ponens,[status(thm)],[64,44]) ).

tff(66,plain,
    ( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
    | ( implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q))))),implies(not(implies(not(p),not(q))),and(not(p),q))) = or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),implies(not(implies(not(p),not(q))),and(not(p),q))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(67,plain,
    implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q))))),implies(not(implies(not(p),not(q))),and(not(p),q))) = or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),implies(not(implies(not(p),not(q))),and(not(p),q))),
    inference(unit_resolution,[status(thm)],[66,7]) ).

tff(68,plain,
    ( theorem(implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q))))),implies(not(implies(not(p),not(q))),and(not(p),q))))
  <=> theorem(or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),implies(not(implies(not(p),not(q))),and(not(p),q)))) ),
    inference(monotonicity,[status(thm)],[67]) ).

tff(69,plain,
    ( ~ theorem(implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q))))),implies(not(implies(not(p),not(q))),and(not(p),q))))
  <=> ~ theorem(or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),implies(not(implies(not(p),not(q))),and(not(p),q)))) ),
    inference(monotonicity,[status(thm)],[68]) ).

tff(70,plain,
    ( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
    | ( implies(not(or(not(not(p)),not(q))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q))))) = or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(71,plain,
    implies(not(or(not(not(p)),not(q))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q))))) = or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q))))),
    inference(unit_resolution,[status(thm)],[70,7]) ).

tff(72,plain,
    or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q))))) = implies(not(or(not(not(p)),not(q))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q))))),
    inference(symmetry,[status(thm)],[71]) ).

tff(73,plain,
    ( theorem(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q))))))
  <=> theorem(implies(not(or(not(not(p)),not(q))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))) ),
    inference(monotonicity,[status(thm)],[72]) ).

tff(74,plain,
    ( theorem(implies(not(or(not(not(p)),not(q))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q))))))
  <=> theorem(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))) ),
    inference(symmetry,[status(thm)],[73]) ).

tff(75,plain,
    ( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
    | ( implies(not(q),not(p)) = or(not(not(q)),not(p)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(76,plain,
    implies(not(q),not(p)) = or(not(not(q)),not(p)),
    inference(unit_resolution,[status(thm)],[75,7]) ).

tff(77,plain,
    not(implies(not(q),not(p))) = not(or(not(not(q)),not(p))),
    inference(monotonicity,[status(thm)],[76]) ).

tff(78,plain,
    or(not(implies(not(q),not(p))),not(or(not(not(p)),not(q)))) = or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))),
    inference(monotonicity,[status(thm)],[77]) ).

tff(79,plain,
    implies(not(or(not(not(p)),not(q))),or(not(implies(not(q),not(p))),not(or(not(not(p)),not(q))))) = implies(not(or(not(not(p)),not(q))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q))))),
    inference(monotonicity,[status(thm)],[78]) ).

tff(80,plain,
    ( theorem(implies(not(or(not(not(p)),not(q))),or(not(implies(not(q),not(p))),not(or(not(not(p)),not(q))))))
  <=> theorem(implies(not(or(not(not(p)),not(q))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))) ),
    inference(monotonicity,[status(thm)],[79]) ).

tff(81,plain,
    ( ~ ! [B: $i,A: $i] : axiom(implies(A,or(B,A)))
    | axiom(implies(not(or(not(not(p)),not(q))),or(not(implies(not(q),not(p))),not(or(not(not(p)),not(q)))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(82,plain,
    axiom(implies(not(or(not(not(p)),not(q))),or(not(implies(not(q),not(p))),not(or(not(not(p)),not(q)))))),
    inference(unit_resolution,[status(thm)],[81,19]) ).

tff(83,plain,
    ( ( ~ ! [X: $i] :
            ( theorem(X)
            | ~ axiom(X) )
      | theorem(implies(not(or(not(not(p)),not(q))),or(not(implies(not(q),not(p))),not(or(not(not(p)),not(q))))))
      | ~ axiom(implies(not(or(not(not(p)),not(q))),or(not(implies(not(q),not(p))),not(or(not(not(p)),not(q)))))) )
  <=> ( ~ ! [X: $i] :
            ( theorem(X)
            | ~ axiom(X) )
      | theorem(implies(not(or(not(not(p)),not(q))),or(not(implies(not(q),not(p))),not(or(not(not(p)),not(q))))))
      | ~ axiom(implies(not(or(not(not(p)),not(q))),or(not(implies(not(q),not(p))),not(or(not(not(p)),not(q)))))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(84,plain,
    ( ~ ! [X: $i] :
          ( theorem(X)
          | ~ axiom(X) )
    | theorem(implies(not(or(not(not(p)),not(q))),or(not(implies(not(q),not(p))),not(or(not(not(p)),not(q))))))
    | ~ axiom(implies(not(or(not(not(p)),not(q))),or(not(implies(not(q),not(p))),not(or(not(not(p)),not(q)))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(85,plain,
    ( ~ ! [X: $i] :
          ( theorem(X)
          | ~ axiom(X) )
    | theorem(implies(not(or(not(not(p)),not(q))),or(not(implies(not(q),not(p))),not(or(not(not(p)),not(q))))))
    | ~ axiom(implies(not(or(not(not(p)),not(q))),or(not(implies(not(q),not(p))),not(or(not(not(p)),not(q)))))) ),
    inference(modus_ponens,[status(thm)],[84,83]) ).

tff(86,plain,
    theorem(implies(not(or(not(not(p)),not(q))),or(not(implies(not(q),not(p))),not(or(not(not(p)),not(q)))))),
    inference(unit_resolution,[status(thm)],[85,60,82]) ).

tff(87,plain,
    theorem(implies(not(or(not(not(p)),not(q))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),
    inference(modus_ponens,[status(thm)],[86,80]) ).

tff(88,plain,
    theorem(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),
    inference(modus_ponens,[status(thm)],[87,74]) ).

tff(89,plain,
    implies(not(implies(not(p),not(q))),and(not(p),q)) = implies(not(or(not(not(p)),not(q))),not(or(not(not(p)),not(q)))),
    inference(symmetry,[status(thm)],[37]) ).

tff(90,plain,
    implies(not(implies(not(p),not(q))),and(not(p),q)) = or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))),
    inference(transitivity,[status(thm)],[89,39]) ).

tff(91,plain,
    not(implies(not(implies(not(p),not(q))),and(not(p),q))) = not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),
    inference(monotonicity,[status(thm)],[90]) ).

tff(92,plain,
    not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))) = not(implies(not(implies(not(p),not(q))),and(not(p),q))),
    inference(symmetry,[status(thm)],[91]) ).

tff(93,plain,
    or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))) = or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))),
    inference(monotonicity,[status(thm)],[92]) ).

tff(94,plain,
    or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))) = or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))),
    inference(symmetry,[status(thm)],[93]) ).

tff(95,plain,
    ( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
    | ( implies(implies(not(implies(not(p),not(q))),and(not(p),q)),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))) = or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(96,plain,
    implies(implies(not(implies(not(p),not(q))),and(not(p),q)),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))) = or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))),
    inference(unit_resolution,[status(thm)],[95,7]) ).

tff(97,plain,
    implies(implies(not(implies(not(p),not(q))),and(not(p),q)),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))) = or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))),
    inference(transitivity,[status(thm)],[96,94]) ).

tff(98,plain,
    ( theorem(implies(implies(not(implies(not(p),not(q))),and(not(p),q)),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))))
  <=> theorem(or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))) ),
    inference(monotonicity,[status(thm)],[97]) ).

tff(99,plain,
    ( theorem(or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))))
  <=> theorem(implies(implies(not(implies(not(p),not(q))),and(not(p),q)),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))) ),
    inference(symmetry,[status(thm)],[98]) ).

tff(100,plain,
    ( ~ ! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) )
    | ( and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(not(implies(not(p),not(q))),and(not(p),q))) = not(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(101,plain,
    and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(not(implies(not(p),not(q))),and(not(p),q))) = not(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))),
    inference(unit_resolution,[status(thm)],[100,29]) ).

tff(102,plain,
    not(implies(not(p),not(q))) = and(not(p),q),
    inference(transitivity,[status(thm)],[35,32]) ).

tff(103,plain,
    and(not(p),q) = not(implies(not(p),not(q))),
    inference(transitivity,[status(thm)],[31,36]) ).

tff(104,plain,
    implies(and(not(p),q),not(implies(not(p),not(q)))) = implies(not(implies(not(p),not(q))),and(not(p),q)),
    inference(monotonicity,[status(thm)],[103,102]) ).

tff(105,plain,
    implies(not(implies(not(p),not(q))),and(not(p),q)) = implies(and(not(p),q),not(implies(not(p),not(q)))),
    inference(symmetry,[status(thm)],[104]) ).

tff(106,plain,
    and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(not(implies(not(p),not(q))),and(not(p),q))) = and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))),
    inference(monotonicity,[status(thm)],[105]) ).

tff(107,plain,
    and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))) = and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(not(implies(not(p),not(q))),and(not(p),q))),
    inference(symmetry,[status(thm)],[106]) ).

tff(108,plain,
    and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))) = not(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))),
    inference(transitivity,[status(thm)],[107,101]) ).

tff(109,plain,
    or(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))) = or(not(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))),
    inference(monotonicity,[status(thm)],[108]) ).

tff(110,plain,
    implies(or(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))),or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))) = implies(or(not(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))),or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))),
    inference(monotonicity,[status(thm)],[109]) ).

tff(111,plain,
    ( theorem(implies(or(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))),or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))))
  <=> theorem(implies(or(not(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))),or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))))) ),
    inference(monotonicity,[status(thm)],[110]) ).

tff(112,plain,
    ^ [B: $i,A: $i] :
      refl(
        ( axiom(implies(or(A,B),or(B,A)))
      <=> axiom(implies(or(A,B),or(B,A))) )),
    inference(bind,[status(th)],]) ).

tff(113,plain,
    ( ! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A)))
  <=> ! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))) ),
    inference(quant_intro,[status(thm)],[112]) ).

tff(114,plain,
    ( ! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A)))
  <=> ! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))) ),
    inference(rewrite,[status(thm)],]) ).

tff(115,axiom,
    ! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_4) ).

tff(116,plain,
    ! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
    inference(modus_ponens,[status(thm)],[115,114]) ).

tff(117,plain,
    ! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
    inference(skolemize,[status(sab)],[116]) ).

tff(118,plain,
    ! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
    inference(modus_ponens,[status(thm)],[117,113]) ).

tff(119,plain,
    ( ~ ! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A)))
    | axiom(implies(or(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))),or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(120,plain,
    axiom(implies(or(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))),or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))))),
    inference(unit_resolution,[status(thm)],[119,118]) ).

tff(121,plain,
    ( ( ~ ! [X: $i] :
            ( theorem(X)
            | ~ axiom(X) )
      | theorem(implies(or(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))),or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))))
      | ~ axiom(implies(or(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))),or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))))) )
  <=> ( ~ ! [X: $i] :
            ( theorem(X)
            | ~ axiom(X) )
      | theorem(implies(or(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))),or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))))
      | ~ axiom(implies(or(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))),or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(122,plain,
    ( ~ ! [X: $i] :
          ( theorem(X)
          | ~ axiom(X) )
    | theorem(implies(or(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))),or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))))
    | ~ axiom(implies(or(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))),or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(123,plain,
    ( ~ ! [X: $i] :
          ( theorem(X)
          | ~ axiom(X) )
    | theorem(implies(or(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))),or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))))
    | ~ axiom(implies(or(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))),or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))))) ),
    inference(modus_ponens,[status(thm)],[122,121]) ).

tff(124,plain,
    theorem(implies(or(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))),or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))))),
    inference(unit_resolution,[status(thm)],[123,60,120]) ).

tff(125,plain,
    theorem(implies(or(not(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))),or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))))),
    inference(modus_ponens,[status(thm)],[124,111]) ).

tff(126,plain,
    ( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
    | ( implies(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))) = or(not(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(127,plain,
    implies(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))) = or(not(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))),
    inference(unit_resolution,[status(thm)],[126,7]) ).

tff(128,plain,
    or(not(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))) = implies(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))),
    inference(symmetry,[status(thm)],[127]) ).

tff(129,plain,
    ( theorem(or(not(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))))
  <=> theorem(implies(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))))) ),
    inference(monotonicity,[status(thm)],[128]) ).

tff(130,plain,
    ( theorem(implies(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))))
  <=> theorem(or(not(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))))) ),
    inference(symmetry,[status(thm)],[129]) ).

tff(131,plain,
    implies(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))) = implies(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))),
    inference(monotonicity,[status(thm)],[91]) ).

tff(132,plain,
    ( theorem(implies(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))))
  <=> theorem(implies(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))))) ),
    inference(monotonicity,[status(thm)],[131]) ).

tff(133,plain,
    ^ [A: $i] :
      refl(
        ( axiom(implies(or(A,A),A))
      <=> axiom(implies(or(A,A),A)) )),
    inference(bind,[status(th)],]) ).

tff(134,plain,
    ( ! [A: $i] : axiom(implies(or(A,A),A))
  <=> ! [A: $i] : axiom(implies(or(A,A),A)) ),
    inference(quant_intro,[status(thm)],[133]) ).

tff(135,plain,
    ( ! [A: $i] : axiom(implies(or(A,A),A))
  <=> ! [A: $i] : axiom(implies(or(A,A),A)) ),
    inference(rewrite,[status(thm)],]) ).

tff(136,axiom,
    ! [A: $i] : axiom(implies(or(A,A),A)),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_2) ).

tff(137,plain,
    ! [A: $i] : axiom(implies(or(A,A),A)),
    inference(modus_ponens,[status(thm)],[136,135]) ).

tff(138,plain,
    ! [A: $i] : axiom(implies(or(A,A),A)),
    inference(skolemize,[status(sab)],[137]) ).

tff(139,plain,
    ! [A: $i] : axiom(implies(or(A,A),A)),
    inference(modus_ponens,[status(thm)],[138,134]) ).

tff(140,plain,
    ( ~ ! [A: $i] : axiom(implies(or(A,A),A))
    | axiom(implies(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(141,plain,
    axiom(implies(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))),
    inference(unit_resolution,[status(thm)],[140,139]) ).

tff(142,plain,
    ( ( ~ ! [X: $i] :
            ( theorem(X)
            | ~ axiom(X) )
      | theorem(implies(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))))
      | ~ axiom(implies(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))) )
  <=> ( ~ ! [X: $i] :
            ( theorem(X)
            | ~ axiom(X) )
      | theorem(implies(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))))
      | ~ axiom(implies(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(143,plain,
    ( ~ ! [X: $i] :
          ( theorem(X)
          | ~ axiom(X) )
    | theorem(implies(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))))
    | ~ axiom(implies(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(144,plain,
    ( ~ ! [X: $i] :
          ( theorem(X)
          | ~ axiom(X) )
    | theorem(implies(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))))
    | ~ axiom(implies(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))) ),
    inference(modus_ponens,[status(thm)],[143,142]) ).

tff(145,plain,
    theorem(implies(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))),
    inference(unit_resolution,[status(thm)],[144,60,141]) ).

tff(146,plain,
    theorem(implies(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q)))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))))),
    inference(modus_ponens,[status(thm)],[145,132]) ).

tff(147,plain,
    theorem(or(not(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))))),
    inference(modus_ponens,[status(thm)],[146,130]) ).

tff(148,plain,
    ^ [Y: $i,X: $i] :
      refl(
        ( ( theorem(X)
          | ~ theorem(Y)
          | ~ theorem(implies(Y,X)) )
      <=> ( theorem(X)
          | ~ theorem(Y)
          | ~ theorem(implies(Y,X)) ) )),
    inference(bind,[status(th)],]) ).

tff(149,plain,
    ( ! [Y: $i,X: $i] :
        ( theorem(X)
        | ~ theorem(Y)
        | ~ theorem(implies(Y,X)) )
  <=> ! [Y: $i,X: $i] :
        ( theorem(X)
        | ~ theorem(Y)
        | ~ theorem(implies(Y,X)) ) ),
    inference(quant_intro,[status(thm)],[148]) ).

tff(150,plain,
    ( ! [Y: $i,X: $i] :
        ( theorem(X)
        | ~ theorem(Y)
        | ~ theorem(implies(Y,X)) )
  <=> ! [Y: $i,X: $i] :
        ( theorem(X)
        | ~ theorem(Y)
        | ~ theorem(implies(Y,X)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(151,plain,
    ^ [Y: $i,X: $i] :
      rewrite(
        ( ( theorem(X)
          | ~ theorem(implies(Y,X))
          | ~ theorem(Y) )
      <=> ( theorem(X)
          | ~ theorem(Y)
          | ~ theorem(implies(Y,X)) ) )),
    inference(bind,[status(th)],]) ).

tff(152,plain,
    ( ! [Y: $i,X: $i] :
        ( theorem(X)
        | ~ theorem(implies(Y,X))
        | ~ theorem(Y) )
  <=> ! [Y: $i,X: $i] :
        ( theorem(X)
        | ~ theorem(Y)
        | ~ theorem(implies(Y,X)) ) ),
    inference(quant_intro,[status(thm)],[151]) ).

tff(153,axiom,
    ! [Y: $i,X: $i] :
      ( theorem(X)
      | ~ theorem(implies(Y,X))
      | ~ theorem(Y) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',rule_2) ).

tff(154,plain,
    ! [Y: $i,X: $i] :
      ( theorem(X)
      | ~ theorem(Y)
      | ~ theorem(implies(Y,X)) ),
    inference(modus_ponens,[status(thm)],[153,152]) ).

tff(155,plain,
    ! [Y: $i,X: $i] :
      ( theorem(X)
      | ~ theorem(Y)
      | ~ theorem(implies(Y,X)) ),
    inference(modus_ponens,[status(thm)],[154,150]) ).

tff(156,plain,
    ! [Y: $i,X: $i] :
      ( theorem(X)
      | ~ theorem(Y)
      | ~ theorem(implies(Y,X)) ),
    inference(skolemize,[status(sab)],[155]) ).

tff(157,plain,
    ! [Y: $i,X: $i] :
      ( theorem(X)
      | ~ theorem(Y)
      | ~ theorem(implies(Y,X)) ),
    inference(modus_ponens,[status(thm)],[156,149]) ).

tff(158,plain,
    ( ( ~ ! [Y: $i,X: $i] :
            ( theorem(X)
            | ~ theorem(Y)
            | ~ theorem(implies(Y,X)) )
      | theorem(or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))))
      | ~ theorem(or(not(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))))
      | ~ theorem(implies(or(not(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))),or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))))) )
  <=> ( ~ ! [Y: $i,X: $i] :
            ( theorem(X)
            | ~ theorem(Y)
            | ~ theorem(implies(Y,X)) )
      | theorem(or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))))
      | ~ theorem(or(not(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))))
      | ~ theorem(implies(or(not(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))),or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(159,plain,
    ( ~ ! [Y: $i,X: $i] :
          ( theorem(X)
          | ~ theorem(Y)
          | ~ theorem(implies(Y,X)) )
    | theorem(or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))))
    | ~ theorem(or(not(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))))
    | ~ theorem(implies(or(not(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))),or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(160,plain,
    ( ~ ! [Y: $i,X: $i] :
          ( theorem(X)
          | ~ theorem(Y)
          | ~ theorem(implies(Y,X)) )
    | theorem(or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))))
    | ~ theorem(or(not(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))))
    | ~ theorem(implies(or(not(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))),or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))))) ),
    inference(modus_ponens,[status(thm)],[159,158]) ).

tff(161,plain,
    ( theorem(or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))))
    | ~ theorem(or(not(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))))
    | ~ theorem(implies(or(not(or(not(implies(not(implies(not(p),not(q))),and(not(p),q))),not(implies(not(implies(not(p),not(q))),and(not(p),q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))),or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))))) ),
    inference(unit_resolution,[status(thm)],[160,157]) ).

tff(162,plain,
    theorem(or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))),
    inference(unit_resolution,[status(thm)],[161,147,125]) ).

tff(163,plain,
    theorem(implies(implies(not(implies(not(p),not(q))),and(not(p),q)),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))),
    inference(modus_ponens,[status(thm)],[162,99]) ).

tff(164,plain,
    ^ [Q: $i,P: $i] :
      refl(
        ( ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) )
      <=> ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ) )),
    inference(bind,[status(th)],]) ).

tff(165,plain,
    ( ! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) )
  <=> ! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ) ),
    inference(quant_intro,[status(thm)],[164]) ).

tff(166,plain,
    ( ! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) )
  <=> ! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(167,axiom,
    ! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL004-2.ax',equivalent_defn) ).

tff(168,plain,
    ! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ),
    inference(modus_ponens,[status(thm)],[167,166]) ).

tff(169,plain,
    ! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ),
    inference(skolemize,[status(sab)],[168]) ).

tff(170,plain,
    ! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ),
    inference(modus_ponens,[status(thm)],[169,165]) ).

tff(171,plain,
    ( ~ ! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) )
    | ( equivalent(not(implies(not(p),not(q))),and(not(p),q)) = and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(172,plain,
    equivalent(not(implies(not(p),not(q))),and(not(p),q)) = and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))),
    inference(unit_resolution,[status(thm)],[171,170]) ).

tff(173,plain,
    and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))) = equivalent(not(implies(not(p),not(q))),and(not(p),q)),
    inference(symmetry,[status(thm)],[172]) ).

tff(174,plain,
    ( theorem(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))
  <=> theorem(equivalent(not(implies(not(p),not(q))),and(not(p),q))) ),
    inference(monotonicity,[status(thm)],[173]) ).

tff(175,plain,
    ( theorem(equivalent(not(implies(not(p),not(q))),and(not(p),q)))
  <=> theorem(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))) ),
    inference(symmetry,[status(thm)],[174]) ).

tff(176,plain,
    ( ~ theorem(equivalent(not(implies(not(p),not(q))),and(not(p),q)))
  <=> ~ theorem(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))) ),
    inference(monotonicity,[status(thm)],[175]) ).

tff(177,plain,
    ( ~ theorem(equivalent(not(implies(not(p),not(q))),and(not(p),q)))
  <=> ~ theorem(equivalent(not(implies(not(p),not(q))),and(not(p),q))) ),
    inference(rewrite,[status(thm)],]) ).

tff(178,axiom,
    ~ theorem(equivalent(not(implies(not(p),not(q))),and(not(p),q))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

tff(179,plain,
    ~ theorem(equivalent(not(implies(not(p),not(q))),and(not(p),q))),
    inference(modus_ponens,[status(thm)],[178,177]) ).

tff(180,plain,
    ~ theorem(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q)))))),
    inference(modus_ponens,[status(thm)],[179,176]) ).

tff(181,plain,
    ( ( ~ ! [Y: $i,X: $i] :
            ( theorem(X)
            | ~ theorem(Y)
            | ~ theorem(implies(Y,X)) )
      | ~ theorem(implies(not(implies(not(p),not(q))),and(not(p),q)))
      | theorem(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))
      | ~ theorem(implies(implies(not(implies(not(p),not(q))),and(not(p),q)),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))) )
  <=> ( ~ ! [Y: $i,X: $i] :
            ( theorem(X)
            | ~ theorem(Y)
            | ~ theorem(implies(Y,X)) )
      | ~ theorem(implies(not(implies(not(p),not(q))),and(not(p),q)))
      | theorem(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))
      | ~ theorem(implies(implies(not(implies(not(p),not(q))),and(not(p),q)),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(182,plain,
    ( ( theorem(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))
      | ~ theorem(implies(not(implies(not(p),not(q))),and(not(p),q)))
      | ~ theorem(implies(implies(not(implies(not(p),not(q))),and(not(p),q)),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))) )
  <=> ( ~ theorem(implies(not(implies(not(p),not(q))),and(not(p),q)))
      | theorem(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))
      | ~ theorem(implies(implies(not(implies(not(p),not(q))),and(not(p),q)),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(183,plain,
    ( ( ~ ! [Y: $i,X: $i] :
            ( theorem(X)
            | ~ theorem(Y)
            | ~ theorem(implies(Y,X)) )
      | theorem(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))
      | ~ theorem(implies(not(implies(not(p),not(q))),and(not(p),q)))
      | ~ theorem(implies(implies(not(implies(not(p),not(q))),and(not(p),q)),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))) )
  <=> ( ~ ! [Y: $i,X: $i] :
            ( theorem(X)
            | ~ theorem(Y)
            | ~ theorem(implies(Y,X)) )
      | ~ theorem(implies(not(implies(not(p),not(q))),and(not(p),q)))
      | theorem(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))
      | ~ theorem(implies(implies(not(implies(not(p),not(q))),and(not(p),q)),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))) ) ),
    inference(monotonicity,[status(thm)],[182]) ).

tff(184,plain,
    ( ( ~ ! [Y: $i,X: $i] :
            ( theorem(X)
            | ~ theorem(Y)
            | ~ theorem(implies(Y,X)) )
      | theorem(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))
      | ~ theorem(implies(not(implies(not(p),not(q))),and(not(p),q)))
      | ~ theorem(implies(implies(not(implies(not(p),not(q))),and(not(p),q)),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))) )
  <=> ( ~ ! [Y: $i,X: $i] :
            ( theorem(X)
            | ~ theorem(Y)
            | ~ theorem(implies(Y,X)) )
      | ~ theorem(implies(not(implies(not(p),not(q))),and(not(p),q)))
      | theorem(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))
      | ~ theorem(implies(implies(not(implies(not(p),not(q))),and(not(p),q)),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))) ) ),
    inference(transitivity,[status(thm)],[183,181]) ).

tff(185,plain,
    ( ~ ! [Y: $i,X: $i] :
          ( theorem(X)
          | ~ theorem(Y)
          | ~ theorem(implies(Y,X)) )
    | theorem(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))
    | ~ theorem(implies(not(implies(not(p),not(q))),and(not(p),q)))
    | ~ theorem(implies(implies(not(implies(not(p),not(q))),and(not(p),q)),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(186,plain,
    ( ~ ! [Y: $i,X: $i] :
          ( theorem(X)
          | ~ theorem(Y)
          | ~ theorem(implies(Y,X)) )
    | ~ theorem(implies(not(implies(not(p),not(q))),and(not(p),q)))
    | theorem(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))
    | ~ theorem(implies(implies(not(implies(not(p),not(q))),and(not(p),q)),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))) ),
    inference(modus_ponens,[status(thm)],[185,184]) ).

tff(187,plain,
    ( ~ theorem(implies(not(implies(not(p),not(q))),and(not(p),q)))
    | theorem(and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))
    | ~ theorem(implies(implies(not(implies(not(p),not(q))),and(not(p),q)),and(implies(not(implies(not(p),not(q))),and(not(p),q)),implies(and(not(p),q),not(implies(not(p),not(q))))))) ),
    inference(unit_resolution,[status(thm)],[186,157]) ).

tff(188,plain,
    ~ theorem(implies(not(implies(not(p),not(q))),and(not(p),q))),
    inference(unit_resolution,[status(thm)],[187,180,163]) ).

tff(189,plain,
    ( ( ~ ! [Y: $i,X: $i] :
            ( theorem(X)
            | ~ theorem(Y)
            | ~ theorem(implies(Y,X)) )
      | theorem(implies(not(implies(not(p),not(q))),and(not(p),q)))
      | ~ theorem(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q))))))
      | ~ theorem(implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q))))),implies(not(implies(not(p),not(q))),and(not(p),q)))) )
  <=> ( ~ ! [Y: $i,X: $i] :
            ( theorem(X)
            | ~ theorem(Y)
            | ~ theorem(implies(Y,X)) )
      | theorem(implies(not(implies(not(p),not(q))),and(not(p),q)))
      | ~ theorem(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q))))))
      | ~ theorem(implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q))))),implies(not(implies(not(p),not(q))),and(not(p),q)))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(190,plain,
    ( ~ ! [Y: $i,X: $i] :
          ( theorem(X)
          | ~ theorem(Y)
          | ~ theorem(implies(Y,X)) )
    | theorem(implies(not(implies(not(p),not(q))),and(not(p),q)))
    | ~ theorem(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q))))))
    | ~ theorem(implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q))))),implies(not(implies(not(p),not(q))),and(not(p),q)))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(191,plain,
    ( ~ ! [Y: $i,X: $i] :
          ( theorem(X)
          | ~ theorem(Y)
          | ~ theorem(implies(Y,X)) )
    | theorem(implies(not(implies(not(p),not(q))),and(not(p),q)))
    | ~ theorem(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q))))))
    | ~ theorem(implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q))))),implies(not(implies(not(p),not(q))),and(not(p),q)))) ),
    inference(modus_ponens,[status(thm)],[190,189]) ).

tff(192,plain,
    ~ theorem(implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q))))),implies(not(implies(not(p),not(q))),and(not(p),q)))),
    inference(unit_resolution,[status(thm)],[191,157,188,88]) ).

tff(193,plain,
    ~ theorem(or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),implies(not(implies(not(p),not(q))),and(not(p),q)))),
    inference(modus_ponens,[status(thm)],[192,69]) ).

tff(194,plain,
    ( ( ~ ! [Y: $i,X: $i] :
            ( theorem(X)
            | ~ theorem(Y)
            | ~ theorem(implies(Y,X)) )
      | theorem(or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),implies(not(implies(not(p),not(q))),and(not(p),q))))
      | ~ theorem(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))))
      | ~ theorem(implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),implies(not(implies(not(p),not(q))),and(not(p),q))))) )
  <=> ( ~ ! [Y: $i,X: $i] :
            ( theorem(X)
            | ~ theorem(Y)
            | ~ theorem(implies(Y,X)) )
      | theorem(or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),implies(not(implies(not(p),not(q))),and(not(p),q))))
      | ~ theorem(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))))
      | ~ theorem(implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),implies(not(implies(not(p),not(q))),and(not(p),q))))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(195,plain,
    ( ~ ! [Y: $i,X: $i] :
          ( theorem(X)
          | ~ theorem(Y)
          | ~ theorem(implies(Y,X)) )
    | theorem(or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),implies(not(implies(not(p),not(q))),and(not(p),q))))
    | ~ theorem(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))))
    | ~ theorem(implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),implies(not(implies(not(p),not(q))),and(not(p),q))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(196,plain,
    ( ~ ! [Y: $i,X: $i] :
          ( theorem(X)
          | ~ theorem(Y)
          | ~ theorem(implies(Y,X)) )
    | theorem(or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),implies(not(implies(not(p),not(q))),and(not(p),q))))
    | ~ theorem(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))))
    | ~ theorem(implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),implies(not(implies(not(p),not(q))),and(not(p),q))))) ),
    inference(modus_ponens,[status(thm)],[195,194]) ).

tff(197,plain,
    ( theorem(or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),implies(not(implies(not(p),not(q))),and(not(p),q))))
    | ~ theorem(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))))
    | ~ theorem(implies(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),implies(not(implies(not(p),not(q))),and(not(p),q))))) ),
    inference(unit_resolution,[status(thm)],[196,157]) ).

tff(198,plain,
    ~ theorem(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q)))))),
    inference(unit_resolution,[status(thm)],[197,193,65]) ).

tff(199,plain,
    ( ( ~ ! [X: $i] :
            ( theorem(X)
            | ~ axiom(X) )
      | theorem(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))))
      | ~ axiom(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q)))))) )
  <=> ( ~ ! [X: $i] :
            ( theorem(X)
            | ~ axiom(X) )
      | theorem(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))))
      | ~ axiom(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q)))))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(200,plain,
    ( ~ ! [X: $i] :
          ( theorem(X)
          | ~ axiom(X) )
    | theorem(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))))
    | ~ axiom(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q)))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(201,plain,
    ( ~ ! [X: $i] :
          ( theorem(X)
          | ~ axiom(X) )
    | theorem(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))))
    | ~ axiom(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q)))))) ),
    inference(modus_ponens,[status(thm)],[200,199]) ).

tff(202,plain,
    ( theorem(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q))))))
    | ~ axiom(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q)))))) ),
    inference(unit_resolution,[status(thm)],[201,60]) ).

tff(203,plain,
    ~ axiom(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(or(not(not(p)),not(q)))),or(not(or(not(not(q)),not(p))),not(or(not(not(p)),not(q)))))),not(or(not(not(p)),not(q)))))),
    inference(unit_resolution,[status(thm)],[202,198]) ).

tff(204,plain,
    $false,
    inference(unit_resolution,[status(thm)],[203,22]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : LCL301-3 : TPTP v8.1.0. Released v2.3.0.
% 0.10/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.32  % Computer : n013.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Thu Sep  1 20:02:17 EDT 2022
% 0.12/0.32  % CPUTime  : 
% 0.17/0.32  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.17/0.32  Usage: tptp [options] [-file:]file
% 0.17/0.32    -h, -?       prints this message.
% 0.17/0.32    -smt2        print SMT-LIB2 benchmark.
% 0.17/0.32    -m, -model   generate model.
% 0.17/0.32    -p, -proof   generate proof.
% 0.17/0.32    -c, -core    generate unsat core of named formulas.
% 0.17/0.32    -st, -statistics display statistics.
% 0.17/0.32    -t:timeout   set timeout (in second).
% 0.17/0.32    -smt2status  display status in smt2 format instead of SZS.
% 0.17/0.32    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.17/0.32    -<param>:<value> configuration parameter and value.
% 0.17/0.32    -o:<output-file> file to place output in.
% 3.49/2.40  % SZS status Unsatisfiable
% 3.49/2.40  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------