TSTP Solution File: LCL297-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL297-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 04:55:49 EDT 2022
% Result : Unsatisfiable 2.54s 1.88s
% Output : Proof 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 74
% Syntax : Number of formulae : 215 ( 110 unt; 9 typ; 0 def)
% Number of atoms : 502 ( 97 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(p),not(q))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))) = or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
implies(not(or(not(p),not(q))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))) = or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))) = implies(not(or(not(p),not(q))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( axiom(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))))
<=> axiom(implies(not(or(not(p),not(q))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q)))))) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( axiom(implies(not(or(not(p),not(q))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))))
<=> axiom(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(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(p),not(q))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q)))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
axiom(implies(not(or(not(p),not(q))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q)))))),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
axiom(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(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(p,q) = not(or(not(p),not(q))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
and(p,q) = not(or(not(p),not(q))),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
not(or(not(p),not(q))) = and(p,q),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(p,not(q)) = or(not(p),not(q)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
implies(p,not(q)) = or(not(p),not(q)),
inference(unit_resolution,[status(thm)],[33,7]) ).
tff(35,plain,
not(implies(p,not(q))) = not(or(not(p),not(q))),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
not(or(not(p),not(q))) = not(implies(p,not(q))),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
implies(not(or(not(p),not(q))),not(or(not(p),not(q)))) = implies(not(implies(p,not(q))),and(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(p),not(q))),not(or(not(p),not(q)))) = or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
implies(not(or(not(p),not(q))),not(or(not(p),not(q)))) = or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))),
inference(unit_resolution,[status(thm)],[38,7]) ).
tff(40,plain,
or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))) = implies(not(or(not(p),not(q))),not(or(not(p),not(q)))),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))) = implies(not(implies(p,not(q))),and(p,q)),
inference(transitivity,[status(thm)],[40,37]) ).
tff(42,plain,
or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))) = or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),implies(not(implies(p,not(q))),and(p,q))),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
implies(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))) = implies(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),implies(not(implies(p,not(q))),and(p,q)))),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( theorem(implies(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))))
<=> theorem(implies(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),implies(not(implies(p,not(q))),and(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(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
axiom(implies(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),or(not(not(or(not(p),not(q)))),not(or(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(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))))
| ~ axiom(implies(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))))
| ~ axiom(implies(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))))
| ~ axiom(implies(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),or(not(not(or(not(p),not(q)))),not(or(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(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))))
| ~ axiom(implies(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))))) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
theorem(implies(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))))),
inference(unit_resolution,[status(thm)],[63,60,53]) ).
tff(65,plain,
theorem(implies(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),implies(not(implies(p,not(q))),and(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(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q))))),implies(not(implies(p,not(q))),and(p,q))) = or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),implies(not(implies(p,not(q))),and(p,q))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
implies(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q))))),implies(not(implies(p,not(q))),and(p,q))) = or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),implies(not(implies(p,not(q))),and(p,q))),
inference(unit_resolution,[status(thm)],[66,7]) ).
tff(68,plain,
( theorem(implies(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q))))),implies(not(implies(p,not(q))),and(p,q))))
<=> theorem(or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),implies(not(implies(p,not(q))),and(p,q)))) ),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
( ~ theorem(implies(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q))))),implies(not(implies(p,not(q))),and(p,q))))
<=> ~ theorem(or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),implies(not(implies(p,not(q))),and(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(p),not(q))),or(not(or(not(not(q)),p)),not(or(not(p),not(q))))) = or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
implies(not(or(not(p),not(q))),or(not(or(not(not(q)),p)),not(or(not(p),not(q))))) = or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q))))),
inference(unit_resolution,[status(thm)],[70,7]) ).
tff(72,plain,
or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q))))) = implies(not(or(not(p),not(q))),or(not(or(not(not(q)),p)),not(or(not(p),not(q))))),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
( theorem(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q))))))
<=> theorem(implies(not(or(not(p),not(q))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))) ),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
( theorem(implies(not(or(not(p),not(q))),or(not(or(not(not(q)),p)),not(or(not(p),not(q))))))
<=> theorem(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(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),p) = or(not(not(q)),p) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,plain,
implies(not(q),p) = or(not(not(q)),p),
inference(unit_resolution,[status(thm)],[75,7]) ).
tff(77,plain,
or(not(not(q)),p) = implies(not(q),p),
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
not(or(not(not(q)),p)) = not(implies(not(q),p)),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
not(implies(not(q),p)) = not(or(not(not(q)),p)),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
or(not(implies(not(q),p)),not(or(not(p),not(q)))) = or(not(or(not(not(q)),p)),not(or(not(p),not(q)))),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
implies(not(or(not(p),not(q))),or(not(implies(not(q),p)),not(or(not(p),not(q))))) = implies(not(or(not(p),not(q))),or(not(or(not(not(q)),p)),not(or(not(p),not(q))))),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
( theorem(implies(not(or(not(p),not(q))),or(not(implies(not(q),p)),not(or(not(p),not(q))))))
<=> theorem(implies(not(or(not(p),not(q))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))) ),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
( ~ ! [B: $i,A: $i] : axiom(implies(A,or(B,A)))
| axiom(implies(not(or(not(p),not(q))),or(not(implies(not(q),p)),not(or(not(p),not(q)))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
axiom(implies(not(or(not(p),not(q))),or(not(implies(not(q),p)),not(or(not(p),not(q)))))),
inference(unit_resolution,[status(thm)],[83,19]) ).
tff(85,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(not(or(not(p),not(q))),or(not(implies(not(q),p)),not(or(not(p),not(q))))))
| ~ axiom(implies(not(or(not(p),not(q))),or(not(implies(not(q),p)),not(or(not(p),not(q)))))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(not(or(not(p),not(q))),or(not(implies(not(q),p)),not(or(not(p),not(q))))))
| ~ axiom(implies(not(or(not(p),not(q))),or(not(implies(not(q),p)),not(or(not(p),not(q)))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(not(or(not(p),not(q))),or(not(implies(not(q),p)),not(or(not(p),not(q))))))
| ~ axiom(implies(not(or(not(p),not(q))),or(not(implies(not(q),p)),not(or(not(p),not(q)))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(87,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(not(or(not(p),not(q))),or(not(implies(not(q),p)),not(or(not(p),not(q))))))
| ~ axiom(implies(not(or(not(p),not(q))),or(not(implies(not(q),p)),not(or(not(p),not(q)))))) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
theorem(implies(not(or(not(p),not(q))),or(not(implies(not(q),p)),not(or(not(p),not(q)))))),
inference(unit_resolution,[status(thm)],[87,60,84]) ).
tff(89,plain,
theorem(implies(not(or(not(p),not(q))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),
inference(modus_ponens,[status(thm)],[88,82]) ).
tff(90,plain,
theorem(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),
inference(modus_ponens,[status(thm)],[89,74]) ).
tff(91,plain,
implies(not(implies(p,not(q))),and(p,q)) = implies(not(or(not(p),not(q))),not(or(not(p),not(q)))),
inference(symmetry,[status(thm)],[37]) ).
tff(92,plain,
implies(not(implies(p,not(q))),and(p,q)) = or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))),
inference(transitivity,[status(thm)],[91,39]) ).
tff(93,plain,
not(implies(not(implies(p,not(q))),and(p,q))) = not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))) = not(implies(not(implies(p,not(q))),and(p,q))),
inference(symmetry,[status(thm)],[93]) ).
tff(95,plain,
or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))) = or(not(implies(not(implies(p,not(q))),and(p,q))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
or(not(implies(not(implies(p,not(q))),and(p,q))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))) = or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(implies(not(implies(p,not(q))),and(p,q)),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))) = or(not(implies(not(implies(p,not(q))),and(p,q))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(98,plain,
implies(implies(not(implies(p,not(q))),and(p,q)),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))) = or(not(implies(not(implies(p,not(q))),and(p,q))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))),
inference(unit_resolution,[status(thm)],[97,7]) ).
tff(99,plain,
implies(implies(not(implies(p,not(q))),and(p,q)),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))) = or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))),
inference(transitivity,[status(thm)],[98,96]) ).
tff(100,plain,
( theorem(implies(implies(not(implies(p,not(q))),and(p,q)),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))))
<=> theorem(or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))) ),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
( theorem(or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))))
<=> theorem(implies(implies(not(implies(p,not(q))),and(p,q)),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))) ),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
( ~ ! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) )
| ( and(implies(not(implies(p,not(q))),and(p,q)),implies(not(implies(p,not(q))),and(p,q))) = not(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(103,plain,
and(implies(not(implies(p,not(q))),and(p,q)),implies(not(implies(p,not(q))),and(p,q))) = not(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q))))),
inference(unit_resolution,[status(thm)],[102,29]) ).
tff(104,plain,
not(implies(p,not(q))) = and(p,q),
inference(transitivity,[status(thm)],[35,32]) ).
tff(105,plain,
and(p,q) = not(implies(p,not(q))),
inference(transitivity,[status(thm)],[31,36]) ).
tff(106,plain,
implies(and(p,q),not(implies(p,not(q)))) = implies(not(implies(p,not(q))),and(p,q)),
inference(monotonicity,[status(thm)],[105,104]) ).
tff(107,plain,
implies(not(implies(p,not(q))),and(p,q)) = implies(and(p,q),not(implies(p,not(q)))),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
and(implies(not(implies(p,not(q))),and(p,q)),implies(not(implies(p,not(q))),and(p,q))) = and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))) = and(implies(not(implies(p,not(q))),and(p,q)),implies(not(implies(p,not(q))),and(p,q))),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))) = not(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q))))),
inference(transitivity,[status(thm)],[109,103]) ).
tff(111,plain,
or(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))) = or(not(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
implies(or(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))),or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))) = implies(or(not(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))),or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
( theorem(implies(or(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))),or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))))
<=> theorem(implies(or(not(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))),or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))))) ),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,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(115,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)],[114]) ).
tff(116,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(117,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(118,plain,
! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
inference(skolemize,[status(sab)],[118]) ).
tff(120,plain,
! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
inference(modus_ponens,[status(thm)],[119,115]) ).
tff(121,plain,
( ~ ! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A)))
| axiom(implies(or(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))),or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(122,plain,
axiom(implies(or(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))),or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))))),
inference(unit_resolution,[status(thm)],[121,120]) ).
tff(123,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))),or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))))
| ~ axiom(implies(or(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))),or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))),or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))))
| ~ axiom(implies(or(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))),or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))),or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))))
| ~ axiom(implies(or(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))),or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(125,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))),or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))))
| ~ axiom(implies(or(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))),or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))))) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
theorem(implies(or(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))),or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))))),
inference(unit_resolution,[status(thm)],[125,60,122]) ).
tff(127,plain,
theorem(implies(or(not(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))),or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))))),
inference(modus_ponens,[status(thm)],[126,113]) ).
tff(128,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q)))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))) = or(not(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
implies(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q)))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))) = or(not(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))),
inference(unit_resolution,[status(thm)],[128,7]) ).
tff(130,plain,
or(not(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))) = implies(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q)))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))),
inference(symmetry,[status(thm)],[129]) ).
tff(131,plain,
( theorem(or(not(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))))
<=> theorem(implies(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q)))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))))) ),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
( theorem(implies(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q)))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))))
<=> theorem(or(not(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))))) ),
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
implies(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q)))),not(implies(not(implies(p,not(q))),and(p,q)))) = implies(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q)))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))),
inference(monotonicity,[status(thm)],[93]) ).
tff(134,plain,
( theorem(implies(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q)))),not(implies(not(implies(p,not(q))),and(p,q)))))
<=> theorem(implies(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q)))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))))) ),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
^ [A: $i] :
refl(
( axiom(implies(or(A,A),A))
<=> axiom(implies(or(A,A),A)) )),
inference(bind,[status(th)],]) ).
tff(136,plain,
( ! [A: $i] : axiom(implies(or(A,A),A))
<=> ! [A: $i] : axiom(implies(or(A,A),A)) ),
inference(quant_intro,[status(thm)],[135]) ).
tff(137,plain,
( ! [A: $i] : axiom(implies(or(A,A),A))
<=> ! [A: $i] : axiom(implies(or(A,A),A)) ),
inference(rewrite,[status(thm)],]) ).
tff(138,axiom,
! [A: $i] : axiom(implies(or(A,A),A)),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_2) ).
tff(139,plain,
! [A: $i] : axiom(implies(or(A,A),A)),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
! [A: $i] : axiom(implies(or(A,A),A)),
inference(skolemize,[status(sab)],[139]) ).
tff(141,plain,
! [A: $i] : axiom(implies(or(A,A),A)),
inference(modus_ponens,[status(thm)],[140,136]) ).
tff(142,plain,
( ~ ! [A: $i] : axiom(implies(or(A,A),A))
| axiom(implies(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q)))),not(implies(not(implies(p,not(q))),and(p,q))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(143,plain,
axiom(implies(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q)))),not(implies(not(implies(p,not(q))),and(p,q))))),
inference(unit_resolution,[status(thm)],[142,141]) ).
tff(144,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q)))),not(implies(not(implies(p,not(q))),and(p,q)))))
| ~ axiom(implies(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q)))),not(implies(not(implies(p,not(q))),and(p,q))))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q)))),not(implies(not(implies(p,not(q))),and(p,q)))))
| ~ axiom(implies(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q)))),not(implies(not(implies(p,not(q))),and(p,q))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(145,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q)))),not(implies(not(implies(p,not(q))),and(p,q)))))
| ~ axiom(implies(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q)))),not(implies(not(implies(p,not(q))),and(p,q))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(146,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q)))),not(implies(not(implies(p,not(q))),and(p,q)))))
| ~ axiom(implies(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q)))),not(implies(not(implies(p,not(q))),and(p,q))))) ),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
theorem(implies(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q)))),not(implies(not(implies(p,not(q))),and(p,q))))),
inference(unit_resolution,[status(thm)],[146,60,143]) ).
tff(148,plain,
theorem(implies(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q)))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))))),
inference(modus_ponens,[status(thm)],[147,134]) ).
tff(149,plain,
theorem(or(not(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))))),
inference(modus_ponens,[status(thm)],[148,132]) ).
tff(150,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(151,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)],[150]) ).
tff(152,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(153,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(154,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)],[153]) ).
tff(155,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(156,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[155,154]) ).
tff(157,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[156,152]) ).
tff(158,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(skolemize,[status(sab)],[157]) ).
tff(159,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[158,151]) ).
tff(160,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))))
| ~ theorem(or(not(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))))
| ~ theorem(implies(or(not(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))),or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))))
| ~ theorem(or(not(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))))
| ~ theorem(implies(or(not(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))),or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(161,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))))
| ~ theorem(or(not(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))))
| ~ theorem(implies(or(not(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))),or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(162,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))))
| ~ theorem(or(not(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))))
| ~ theorem(implies(or(not(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))),or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))))) ),
inference(modus_ponens,[status(thm)],[161,160]) ).
tff(163,plain,
( theorem(or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))))
| ~ theorem(or(not(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))))
| ~ theorem(implies(or(not(or(not(implies(not(implies(p,not(q))),and(p,q))),not(implies(not(implies(p,not(q))),and(p,q))))),not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q)))))),or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))))) ),
inference(unit_resolution,[status(thm)],[162,159]) ).
tff(164,plain,
theorem(or(not(or(not(not(or(not(p),not(q)))),not(or(not(p),not(q))))),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))),
inference(unit_resolution,[status(thm)],[163,149,127]) ).
tff(165,plain,
theorem(implies(implies(not(implies(p,not(q))),and(p,q)),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))),
inference(modus_ponens,[status(thm)],[164,101]) ).
tff(166,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(167,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)],[166]) ).
tff(168,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(169,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(170,plain,
! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ),
inference(modus_ponens,[status(thm)],[169,168]) ).
tff(171,plain,
! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ),
inference(skolemize,[status(sab)],[170]) ).
tff(172,plain,
! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ),
inference(modus_ponens,[status(thm)],[171,167]) ).
tff(173,plain,
( ~ ! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) )
| ( equivalent(not(implies(p,not(q))),and(p,q)) = and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(174,plain,
equivalent(not(implies(p,not(q))),and(p,q)) = and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))),
inference(unit_resolution,[status(thm)],[173,172]) ).
tff(175,plain,
and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))) = equivalent(not(implies(p,not(q))),and(p,q)),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
( theorem(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))
<=> theorem(equivalent(not(implies(p,not(q))),and(p,q))) ),
inference(monotonicity,[status(thm)],[175]) ).
tff(177,plain,
( theorem(equivalent(not(implies(p,not(q))),and(p,q)))
<=> theorem(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))) ),
inference(symmetry,[status(thm)],[176]) ).
tff(178,plain,
( ~ theorem(equivalent(not(implies(p,not(q))),and(p,q)))
<=> ~ theorem(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))) ),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
( ~ theorem(equivalent(not(implies(p,not(q))),and(p,q)))
<=> ~ theorem(equivalent(not(implies(p,not(q))),and(p,q))) ),
inference(rewrite,[status(thm)],]) ).
tff(180,axiom,
~ theorem(equivalent(not(implies(p,not(q))),and(p,q))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(181,plain,
~ theorem(equivalent(not(implies(p,not(q))),and(p,q))),
inference(modus_ponens,[status(thm)],[180,179]) ).
tff(182,plain,
~ theorem(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q)))))),
inference(modus_ponens,[status(thm)],[181,178]) ).
tff(183,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(implies(not(implies(p,not(q))),and(p,q)))
| theorem(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))
| ~ theorem(implies(implies(not(implies(p,not(q))),and(p,q)),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(implies(not(implies(p,not(q))),and(p,q)))
| theorem(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))
| ~ theorem(implies(implies(not(implies(p,not(q))),and(p,q)),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(184,plain,
( ( theorem(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))
| ~ theorem(implies(not(implies(p,not(q))),and(p,q)))
| ~ theorem(implies(implies(not(implies(p,not(q))),and(p,q)),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))) )
<=> ( ~ theorem(implies(not(implies(p,not(q))),and(p,q)))
| theorem(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))
| ~ theorem(implies(implies(not(implies(p,not(q))),and(p,q)),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(185,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))
| ~ theorem(implies(not(implies(p,not(q))),and(p,q)))
| ~ theorem(implies(implies(not(implies(p,not(q))),and(p,q)),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(implies(not(implies(p,not(q))),and(p,q)))
| theorem(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))
| ~ theorem(implies(implies(not(implies(p,not(q))),and(p,q)),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))) ) ),
inference(monotonicity,[status(thm)],[184]) ).
tff(186,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))
| ~ theorem(implies(not(implies(p,not(q))),and(p,q)))
| ~ theorem(implies(implies(not(implies(p,not(q))),and(p,q)),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(implies(not(implies(p,not(q))),and(p,q)))
| theorem(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))
| ~ theorem(implies(implies(not(implies(p,not(q))),and(p,q)),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))) ) ),
inference(transitivity,[status(thm)],[185,183]) ).
tff(187,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))
| ~ theorem(implies(not(implies(p,not(q))),and(p,q)))
| ~ theorem(implies(implies(not(implies(p,not(q))),and(p,q)),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(188,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(implies(not(implies(p,not(q))),and(p,q)))
| theorem(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))
| ~ theorem(implies(implies(not(implies(p,not(q))),and(p,q)),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))) ),
inference(modus_ponens,[status(thm)],[187,186]) ).
tff(189,plain,
( ~ theorem(implies(not(implies(p,not(q))),and(p,q)))
| theorem(and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))
| ~ theorem(implies(implies(not(implies(p,not(q))),and(p,q)),and(implies(not(implies(p,not(q))),and(p,q)),implies(and(p,q),not(implies(p,not(q))))))) ),
inference(unit_resolution,[status(thm)],[188,159]) ).
tff(190,plain,
~ theorem(implies(not(implies(p,not(q))),and(p,q))),
inference(unit_resolution,[status(thm)],[189,182,165]) ).
tff(191,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(not(implies(p,not(q))),and(p,q)))
| ~ theorem(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q))))))
| ~ theorem(implies(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q))))),implies(not(implies(p,not(q))),and(p,q)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(not(implies(p,not(q))),and(p,q)))
| ~ theorem(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q))))))
| ~ theorem(implies(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q))))),implies(not(implies(p,not(q))),and(p,q)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(192,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(not(implies(p,not(q))),and(p,q)))
| ~ theorem(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q))))))
| ~ theorem(implies(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q))))),implies(not(implies(p,not(q))),and(p,q)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(193,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(not(implies(p,not(q))),and(p,q)))
| ~ theorem(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q))))))
| ~ theorem(implies(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q))))),implies(not(implies(p,not(q))),and(p,q)))) ),
inference(modus_ponens,[status(thm)],[192,191]) ).
tff(194,plain,
~ theorem(implies(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q))))),implies(not(implies(p,not(q))),and(p,q)))),
inference(unit_resolution,[status(thm)],[193,159,190,90]) ).
tff(195,plain,
~ theorem(or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),implies(not(implies(p,not(q))),and(p,q)))),
inference(modus_ponens,[status(thm)],[194,69]) ).
tff(196,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),implies(not(implies(p,not(q))),and(p,q))))
| ~ theorem(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))))
| ~ theorem(implies(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),implies(not(implies(p,not(q))),and(p,q))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),implies(not(implies(p,not(q))),and(p,q))))
| ~ theorem(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))))
| ~ theorem(implies(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),implies(not(implies(p,not(q))),and(p,q))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(197,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),implies(not(implies(p,not(q))),and(p,q))))
| ~ theorem(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))))
| ~ theorem(implies(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),implies(not(implies(p,not(q))),and(p,q))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(198,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),implies(not(implies(p,not(q))),and(p,q))))
| ~ theorem(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))))
| ~ theorem(implies(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),implies(not(implies(p,not(q))),and(p,q))))) ),
inference(modus_ponens,[status(thm)],[197,196]) ).
tff(199,plain,
( theorem(or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),implies(not(implies(p,not(q))),and(p,q))))
| ~ theorem(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))))
| ~ theorem(implies(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),implies(not(implies(p,not(q))),and(p,q))))) ),
inference(unit_resolution,[status(thm)],[198,159]) ).
tff(200,plain,
~ theorem(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q)))))),
inference(unit_resolution,[status(thm)],[199,195,65]) ).
tff(201,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))))
| ~ axiom(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q)))))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))))
| ~ axiom(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q)))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(202,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))))
| ~ axiom(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q)))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(203,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))))
| ~ axiom(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q)))))) ),
inference(modus_ponens,[status(thm)],[202,201]) ).
tff(204,plain,
( theorem(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q))))))
| ~ axiom(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q)))))) ),
inference(unit_resolution,[status(thm)],[203,60]) ).
tff(205,plain,
~ axiom(or(not(not(or(not(p),not(q)))),or(not(or(not(not(or(not(p),not(q)))),or(not(or(not(not(q)),p)),not(or(not(p),not(q)))))),not(or(not(p),not(q)))))),
inference(unit_resolution,[status(thm)],[204,200]) ).
tff(206,plain,
$false,
inference(unit_resolution,[status(thm)],[205,22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : LCL297-3 : TPTP v8.1.0. Released v2.3.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 20:16:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 2.54/1.88 % SZS status Unsatisfiable
% 2.54/1.88 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------