TSTP Solution File: LCL268-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL268-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 04:55:43 EDT 2022
% Result : Unsatisfiable 0.82s 0.76s
% Output : Proof 0.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 69
% Syntax : Number of formulae : 188 ( 90 unt; 8 typ; 0 def)
% Number of atoms : 446 ( 73 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 471 ( 215 ~; 201 |; 0 &)
% ( 55 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 9 ( 2 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 : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 239 ( 220 !; 0 ?; 239 :)
% Comments :
%------------------------------------------------------------------------------
tff(axiom_type,type,
axiom: $i > $o ).
tff(or_type,type,
or: ( $i * $i ) > $i ).
tff(p_type,type,
p: $i ).
tff(not_type,type,
not: $i > $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(p,or(not(or(not(or(p,not(p))),or(not(p),p))),p)) = or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
implies(p,or(not(or(not(or(p,not(p))),or(not(p),p))),p)) = or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)) = implies(p,or(not(or(not(or(p,not(p))),or(not(p),p))),p)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( axiom(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)))
<=> axiom(implies(p,or(not(or(not(or(p,not(p))),or(not(p),p))),p))) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( axiom(implies(p,or(not(or(not(or(p,not(p))),or(not(p),p))),p)))
<=> axiom(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p))) ),
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(p,or(not(or(not(or(p,not(p))),or(not(p),p))),p))) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
axiom(implies(p,or(not(or(not(or(p,not(p))),or(not(p),p))),p))),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
axiom(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p))),
inference(modus_ponens,[status(thm)],[21,12]) ).
tff(23,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(24,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)],[23]) ).
tff(25,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(26,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(27,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
( ~ ! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C))))
| axiom(implies(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)),or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
axiom(implies(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)),or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p)))),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
^ [X: $i] :
refl(
( ( theorem(X)
| ~ axiom(X) )
<=> ( theorem(X)
| ~ axiom(X) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',rule_1) ).
tff(36,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)),or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p))))
| ~ axiom(implies(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)),or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p)))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)),or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p))))
| ~ axiom(implies(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)),or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)),or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p))))
| ~ axiom(implies(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)),or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)),or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p))))
| ~ axiom(implies(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)),or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p)))) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
theorem(implies(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)),or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p)))),
inference(unit_resolution,[status(thm)],[41,38,31]) ).
tff(43,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(not(or(p,not(p))),or(not(p),p)),or(not(p),p)) = or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
implies(or(not(or(p,not(p))),or(not(p),p)),or(not(p),p)) = or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p)),
inference(unit_resolution,[status(thm)],[43,7]) ).
tff(45,plain,
or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p)) = implies(or(not(or(p,not(p))),or(not(p),p)),or(not(p),p)),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
( theorem(or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p)))
<=> theorem(implies(or(not(or(p,not(p))),or(not(p),p)),or(not(p),p))) ),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( theorem(implies(or(not(or(p,not(p))),or(not(p),p)),or(not(p),p)))
<=> theorem(or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p))) ),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
( ~ theorem(implies(or(not(or(p,not(p))),or(not(p),p)),or(not(p),p)))
<=> ~ theorem(or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p))) ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(p,p) = or(not(p),p) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
implies(p,p) = or(not(p),p),
inference(unit_resolution,[status(thm)],[49,7]) ).
tff(51,plain,
or(not(p),p) = implies(p,p),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
not(or(not(p),p)) = not(implies(p,p)),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
not(implies(p,p)) = not(or(not(p),p)),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
or(not(implies(p,p)),and(implies(p,p),implies(p,p))) = or(not(or(not(p),p)),and(implies(p,p),implies(p,p))),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
or(not(or(not(p),p)),and(implies(p,p),implies(p,p))) = or(not(implies(p,p)),and(implies(p,p),implies(p,p))),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(not(p),p),and(implies(p,p),implies(p,p))) = or(not(or(not(p),p)),and(implies(p,p),implies(p,p))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
implies(or(not(p),p),and(implies(p,p),implies(p,p))) = or(not(or(not(p),p)),and(implies(p,p),implies(p,p))),
inference(unit_resolution,[status(thm)],[56,7]) ).
tff(58,plain,
implies(or(not(p),p),and(implies(p,p),implies(p,p))) = or(not(implies(p,p)),and(implies(p,p),implies(p,p))),
inference(transitivity,[status(thm)],[57,55]) ).
tff(59,plain,
( theorem(implies(or(not(p),p),and(implies(p,p),implies(p,p))))
<=> theorem(or(not(implies(p,p)),and(implies(p,p),implies(p,p)))) ),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( theorem(or(not(implies(p,p)),and(implies(p,p),implies(p,p))))
<=> theorem(implies(or(not(p),p),and(implies(p,p),implies(p,p)))) ),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
or(not(implies(p,p)),not(implies(p,p))) = or(not(or(not(p),p)),not(implies(p,p))),
inference(monotonicity,[status(thm)],[53]) ).
tff(62,plain,
or(not(or(not(p),p)),not(implies(p,p))) = or(not(implies(p,p)),not(implies(p,p))),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
not(or(not(or(not(p),p)),not(implies(p,p)))) = not(or(not(implies(p,p)),not(implies(p,p)))),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
not(or(not(implies(p,p)),not(implies(p,p)))) = not(or(not(or(not(p),p)),not(implies(p,p)))),
inference(symmetry,[status(thm)],[63]) ).
tff(65,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(66,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)],[65]) ).
tff(67,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(68,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(69,plain,
! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) ),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
( ~ ! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) )
| ( and(implies(p,p),implies(p,p)) = not(or(not(implies(p,p)),not(implies(p,p)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
and(implies(p,p),implies(p,p)) = not(or(not(implies(p,p)),not(implies(p,p)))),
inference(unit_resolution,[status(thm)],[72,71]) ).
tff(74,plain,
and(implies(p,p),implies(p,p)) = not(or(not(or(not(p),p)),not(implies(p,p)))),
inference(transitivity,[status(thm)],[73,64]) ).
tff(75,plain,
or(and(implies(p,p),implies(p,p)),not(implies(p,p))) = or(not(or(not(or(not(p),p)),not(implies(p,p)))),not(implies(p,p))),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
implies(or(and(implies(p,p),implies(p,p)),not(implies(p,p))),or(not(implies(p,p)),and(implies(p,p),implies(p,p)))) = implies(or(not(or(not(or(not(p),p)),not(implies(p,p)))),not(implies(p,p))),or(not(implies(p,p)),and(implies(p,p),implies(p,p)))),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
( theorem(implies(or(and(implies(p,p),implies(p,p)),not(implies(p,p))),or(not(implies(p,p)),and(implies(p,p),implies(p,p)))))
<=> theorem(implies(or(not(or(not(or(not(p),p)),not(implies(p,p)))),not(implies(p,p))),or(not(implies(p,p)),and(implies(p,p),implies(p,p))))) ),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,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(79,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)],[78]) ).
tff(80,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(81,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(82,plain,
! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
inference(modus_ponens,[status(thm)],[83,79]) ).
tff(85,plain,
( ~ ! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A)))
| axiom(implies(or(and(implies(p,p),implies(p,p)),not(implies(p,p))),or(not(implies(p,p)),and(implies(p,p),implies(p,p))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
axiom(implies(or(and(implies(p,p),implies(p,p)),not(implies(p,p))),or(not(implies(p,p)),and(implies(p,p),implies(p,p))))),
inference(unit_resolution,[status(thm)],[85,84]) ).
tff(87,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(p,p),implies(p,p)),not(implies(p,p))),or(not(implies(p,p)),and(implies(p,p),implies(p,p)))))
| ~ axiom(implies(or(and(implies(p,p),implies(p,p)),not(implies(p,p))),or(not(implies(p,p)),and(implies(p,p),implies(p,p))))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(p,p),implies(p,p)),not(implies(p,p))),or(not(implies(p,p)),and(implies(p,p),implies(p,p)))))
| ~ axiom(implies(or(and(implies(p,p),implies(p,p)),not(implies(p,p))),or(not(implies(p,p)),and(implies(p,p),implies(p,p))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(p,p),implies(p,p)),not(implies(p,p))),or(not(implies(p,p)),and(implies(p,p),implies(p,p)))))
| ~ axiom(implies(or(and(implies(p,p),implies(p,p)),not(implies(p,p))),or(not(implies(p,p)),and(implies(p,p),implies(p,p))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(89,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(p,p),implies(p,p)),not(implies(p,p))),or(not(implies(p,p)),and(implies(p,p),implies(p,p)))))
| ~ axiom(implies(or(and(implies(p,p),implies(p,p)),not(implies(p,p))),or(not(implies(p,p)),and(implies(p,p),implies(p,p))))) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
theorem(implies(or(and(implies(p,p),implies(p,p)),not(implies(p,p))),or(not(implies(p,p)),and(implies(p,p),implies(p,p))))),
inference(unit_resolution,[status(thm)],[89,38,86]) ).
tff(91,plain,
theorem(implies(or(not(or(not(or(not(p),p)),not(implies(p,p)))),not(implies(p,p))),or(not(implies(p,p)),and(implies(p,p),implies(p,p))))),
inference(modus_ponens,[status(thm)],[90,77]) ).
tff(92,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(not(or(not(p),p)),not(implies(p,p))),not(implies(p,p))) = or(not(or(not(or(not(p),p)),not(implies(p,p)))),not(implies(p,p))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
implies(or(not(or(not(p),p)),not(implies(p,p))),not(implies(p,p))) = or(not(or(not(or(not(p),p)),not(implies(p,p)))),not(implies(p,p))),
inference(unit_resolution,[status(thm)],[92,7]) ).
tff(94,plain,
or(not(or(not(or(not(p),p)),not(implies(p,p)))),not(implies(p,p))) = implies(or(not(or(not(p),p)),not(implies(p,p))),not(implies(p,p))),
inference(symmetry,[status(thm)],[93]) ).
tff(95,plain,
( theorem(or(not(or(not(or(not(p),p)),not(implies(p,p)))),not(implies(p,p))))
<=> theorem(implies(or(not(or(not(p),p)),not(implies(p,p))),not(implies(p,p)))) ),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
( theorem(implies(or(not(or(not(p),p)),not(implies(p,p))),not(implies(p,p))))
<=> theorem(or(not(or(not(or(not(p),p)),not(implies(p,p)))),not(implies(p,p)))) ),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
implies(or(not(implies(p,p)),not(implies(p,p))),not(implies(p,p))) = implies(or(not(or(not(p),p)),not(implies(p,p))),not(implies(p,p))),
inference(monotonicity,[status(thm)],[61]) ).
tff(98,plain,
( theorem(implies(or(not(implies(p,p)),not(implies(p,p))),not(implies(p,p))))
<=> theorem(implies(or(not(or(not(p),p)),not(implies(p,p))),not(implies(p,p)))) ),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
^ [A: $i] :
refl(
( axiom(implies(or(A,A),A))
<=> axiom(implies(or(A,A),A)) )),
inference(bind,[status(th)],]) ).
tff(100,plain,
( ! [A: $i] : axiom(implies(or(A,A),A))
<=> ! [A: $i] : axiom(implies(or(A,A),A)) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,plain,
( ! [A: $i] : axiom(implies(or(A,A),A))
<=> ! [A: $i] : axiom(implies(or(A,A),A)) ),
inference(rewrite,[status(thm)],]) ).
tff(102,axiom,
! [A: $i] : axiom(implies(or(A,A),A)),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_2) ).
tff(103,plain,
! [A: $i] : axiom(implies(or(A,A),A)),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
! [A: $i] : axiom(implies(or(A,A),A)),
inference(skolemize,[status(sab)],[103]) ).
tff(105,plain,
! [A: $i] : axiom(implies(or(A,A),A)),
inference(modus_ponens,[status(thm)],[104,100]) ).
tff(106,plain,
( ~ ! [A: $i] : axiom(implies(or(A,A),A))
| axiom(implies(or(not(implies(p,p)),not(implies(p,p))),not(implies(p,p)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(107,plain,
axiom(implies(or(not(implies(p,p)),not(implies(p,p))),not(implies(p,p)))),
inference(unit_resolution,[status(thm)],[106,105]) ).
tff(108,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(p,p)),not(implies(p,p))),not(implies(p,p))))
| ~ axiom(implies(or(not(implies(p,p)),not(implies(p,p))),not(implies(p,p)))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(p,p)),not(implies(p,p))),not(implies(p,p))))
| ~ axiom(implies(or(not(implies(p,p)),not(implies(p,p))),not(implies(p,p)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(109,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(p,p)),not(implies(p,p))),not(implies(p,p))))
| ~ axiom(implies(or(not(implies(p,p)),not(implies(p,p))),not(implies(p,p)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(110,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(p,p)),not(implies(p,p))),not(implies(p,p))))
| ~ axiom(implies(or(not(implies(p,p)),not(implies(p,p))),not(implies(p,p)))) ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
theorem(implies(or(not(implies(p,p)),not(implies(p,p))),not(implies(p,p)))),
inference(unit_resolution,[status(thm)],[110,38,107]) ).
tff(112,plain,
theorem(implies(or(not(or(not(p),p)),not(implies(p,p))),not(implies(p,p)))),
inference(modus_ponens,[status(thm)],[111,98]) ).
tff(113,plain,
theorem(or(not(or(not(or(not(p),p)),not(implies(p,p)))),not(implies(p,p)))),
inference(modus_ponens,[status(thm)],[112,96]) ).
tff(114,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(115,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)],[114]) ).
tff(116,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(117,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(118,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)],[117]) ).
tff(119,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(120,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[120,116]) ).
tff(122,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(skolemize,[status(sab)],[121]) ).
tff(123,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[122,115]) ).
tff(124,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(p,p)),and(implies(p,p),implies(p,p))))
| ~ theorem(or(not(or(not(or(not(p),p)),not(implies(p,p)))),not(implies(p,p))))
| ~ theorem(implies(or(not(or(not(or(not(p),p)),not(implies(p,p)))),not(implies(p,p))),or(not(implies(p,p)),and(implies(p,p),implies(p,p))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(p,p)),and(implies(p,p),implies(p,p))))
| ~ theorem(or(not(or(not(or(not(p),p)),not(implies(p,p)))),not(implies(p,p))))
| ~ theorem(implies(or(not(or(not(or(not(p),p)),not(implies(p,p)))),not(implies(p,p))),or(not(implies(p,p)),and(implies(p,p),implies(p,p))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(125,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(p,p)),and(implies(p,p),implies(p,p))))
| ~ theorem(or(not(or(not(or(not(p),p)),not(implies(p,p)))),not(implies(p,p))))
| ~ theorem(implies(or(not(or(not(or(not(p),p)),not(implies(p,p)))),not(implies(p,p))),or(not(implies(p,p)),and(implies(p,p),implies(p,p))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(126,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(p,p)),and(implies(p,p),implies(p,p))))
| ~ theorem(or(not(or(not(or(not(p),p)),not(implies(p,p)))),not(implies(p,p))))
| ~ theorem(implies(or(not(or(not(or(not(p),p)),not(implies(p,p)))),not(implies(p,p))),or(not(implies(p,p)),and(implies(p,p),implies(p,p))))) ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
( theorem(or(not(implies(p,p)),and(implies(p,p),implies(p,p))))
| ~ theorem(or(not(or(not(or(not(p),p)),not(implies(p,p)))),not(implies(p,p))))
| ~ theorem(implies(or(not(or(not(or(not(p),p)),not(implies(p,p)))),not(implies(p,p))),or(not(implies(p,p)),and(implies(p,p),implies(p,p))))) ),
inference(unit_resolution,[status(thm)],[126,123]) ).
tff(128,plain,
theorem(or(not(implies(p,p)),and(implies(p,p),implies(p,p)))),
inference(unit_resolution,[status(thm)],[127,113,91]) ).
tff(129,plain,
theorem(implies(or(not(p),p),and(implies(p,p),implies(p,p)))),
inference(modus_ponens,[status(thm)],[128,60]) ).
tff(130,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(131,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)],[130]) ).
tff(132,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(133,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(134,plain,
! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ),
inference(skolemize,[status(sab)],[134]) ).
tff(136,plain,
! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ),
inference(modus_ponens,[status(thm)],[135,131]) ).
tff(137,plain,
( ~ ! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) )
| ( equivalent(p,p) = and(implies(p,p),implies(p,p)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
equivalent(p,p) = and(implies(p,p),implies(p,p)),
inference(unit_resolution,[status(thm)],[137,136]) ).
tff(139,plain,
and(implies(p,p),implies(p,p)) = equivalent(p,p),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
( theorem(and(implies(p,p),implies(p,p)))
<=> theorem(equivalent(p,p)) ),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
( theorem(equivalent(p,p))
<=> theorem(and(implies(p,p),implies(p,p))) ),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
( ~ theorem(equivalent(p,p))
<=> ~ theorem(and(implies(p,p),implies(p,p))) ),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,plain,
( ~ theorem(equivalent(p,p))
<=> ~ theorem(equivalent(p,p)) ),
inference(rewrite,[status(thm)],]) ).
tff(144,axiom,
~ theorem(equivalent(p,p)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(145,plain,
~ theorem(equivalent(p,p)),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
~ theorem(and(implies(p,p),implies(p,p))),
inference(modus_ponens,[status(thm)],[145,142]) ).
tff(147,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(and(implies(p,p),implies(p,p)))
| ~ theorem(or(not(p),p))
| ~ theorem(implies(or(not(p),p),and(implies(p,p),implies(p,p)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(and(implies(p,p),implies(p,p)))
| ~ theorem(or(not(p),p))
| ~ theorem(implies(or(not(p),p),and(implies(p,p),implies(p,p)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(148,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(and(implies(p,p),implies(p,p)))
| ~ theorem(or(not(p),p))
| ~ theorem(implies(or(not(p),p),and(implies(p,p),implies(p,p)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(149,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(and(implies(p,p),implies(p,p)))
| ~ theorem(or(not(p),p))
| ~ theorem(implies(or(not(p),p),and(implies(p,p),implies(p,p)))) ),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
( theorem(and(implies(p,p),implies(p,p)))
| ~ theorem(or(not(p),p))
| ~ theorem(implies(or(not(p),p),and(implies(p,p),implies(p,p)))) ),
inference(unit_resolution,[status(thm)],[149,123]) ).
tff(151,plain,
~ theorem(or(not(p),p)),
inference(unit_resolution,[status(thm)],[150,146,129]) ).
tff(152,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(p,not(p)),or(not(p),p)) = or(not(or(p,not(p))),or(not(p),p)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(153,plain,
implies(or(p,not(p)),or(not(p),p)) = or(not(or(p,not(p))),or(not(p),p)),
inference(unit_resolution,[status(thm)],[152,7]) ).
tff(154,plain,
or(not(or(p,not(p))),or(not(p),p)) = implies(or(p,not(p)),or(not(p),p)),
inference(symmetry,[status(thm)],[153]) ).
tff(155,plain,
( theorem(or(not(or(p,not(p))),or(not(p),p)))
<=> theorem(implies(or(p,not(p)),or(not(p),p))) ),
inference(monotonicity,[status(thm)],[154]) ).
tff(156,plain,
( theorem(implies(or(p,not(p)),or(not(p),p)))
<=> theorem(or(not(or(p,not(p))),or(not(p),p))) ),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
( ~ ! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A)))
| axiom(implies(or(p,not(p)),or(not(p),p))) ),
inference(quant_inst,[status(thm)],]) ).
tff(158,plain,
axiom(implies(or(p,not(p)),or(not(p),p))),
inference(unit_resolution,[status(thm)],[157,84]) ).
tff(159,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(p,not(p)),or(not(p),p)))
| ~ axiom(implies(or(p,not(p)),or(not(p),p))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(p,not(p)),or(not(p),p)))
| ~ axiom(implies(or(p,not(p)),or(not(p),p))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(160,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(p,not(p)),or(not(p),p)))
| ~ axiom(implies(or(p,not(p)),or(not(p),p))) ),
inference(quant_inst,[status(thm)],]) ).
tff(161,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(p,not(p)),or(not(p),p)))
| ~ axiom(implies(or(p,not(p)),or(not(p),p))) ),
inference(modus_ponens,[status(thm)],[160,159]) ).
tff(162,plain,
theorem(implies(or(p,not(p)),or(not(p),p))),
inference(unit_resolution,[status(thm)],[161,38,158]) ).
tff(163,plain,
theorem(or(not(or(p,not(p))),or(not(p),p))),
inference(modus_ponens,[status(thm)],[162,156]) ).
tff(164,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(p),p))
| ~ theorem(or(not(or(p,not(p))),or(not(p),p)))
| ~ theorem(implies(or(not(or(p,not(p))),or(not(p),p)),or(not(p),p))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(p),p))
| ~ theorem(or(not(or(p,not(p))),or(not(p),p)))
| ~ theorem(implies(or(not(or(p,not(p))),or(not(p),p)),or(not(p),p))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(165,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(p),p))
| ~ theorem(or(not(or(p,not(p))),or(not(p),p)))
| ~ theorem(implies(or(not(or(p,not(p))),or(not(p),p)),or(not(p),p))) ),
inference(quant_inst,[status(thm)],]) ).
tff(166,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(p),p))
| ~ theorem(or(not(or(p,not(p))),or(not(p),p)))
| ~ theorem(implies(or(not(or(p,not(p))),or(not(p),p)),or(not(p),p))) ),
inference(modus_ponens,[status(thm)],[165,164]) ).
tff(167,plain,
( theorem(or(not(p),p))
| ~ theorem(implies(or(not(or(p,not(p))),or(not(p),p)),or(not(p),p))) ),
inference(unit_resolution,[status(thm)],[166,123,163]) ).
tff(168,plain,
~ theorem(implies(or(not(or(p,not(p))),or(not(p),p)),or(not(p),p))),
inference(unit_resolution,[status(thm)],[167,151]) ).
tff(169,plain,
~ theorem(or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p))),
inference(modus_ponens,[status(thm)],[168,48]) ).
tff(170,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p)))
| ~ theorem(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)))
| ~ theorem(implies(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)),or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p)))
| ~ theorem(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)))
| ~ theorem(implies(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)),or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(171,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p)))
| ~ theorem(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)))
| ~ theorem(implies(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)),or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(172,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p)))
| ~ theorem(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)))
| ~ theorem(implies(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)),or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p)))) ),
inference(modus_ponens,[status(thm)],[171,170]) ).
tff(173,plain,
( theorem(or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p)))
| ~ theorem(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)))
| ~ theorem(implies(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)),or(not(or(not(or(p,not(p))),or(not(p),p))),or(not(p),p)))) ),
inference(unit_resolution,[status(thm)],[172,123]) ).
tff(174,plain,
~ theorem(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p))),
inference(unit_resolution,[status(thm)],[173,169,42]) ).
tff(175,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)))
| ~ axiom(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)))
| ~ axiom(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(176,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)))
| ~ axiom(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p))) ),
inference(quant_inst,[status(thm)],]) ).
tff(177,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)))
| ~ axiom(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p))) ),
inference(modus_ponens,[status(thm)],[176,175]) ).
tff(178,plain,
( theorem(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p)))
| ~ axiom(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p))) ),
inference(unit_resolution,[status(thm)],[177,38]) ).
tff(179,plain,
~ axiom(or(not(p),or(not(or(not(or(p,not(p))),or(not(p),p))),p))),
inference(unit_resolution,[status(thm)],[178,174]) ).
tff(180,plain,
$false,
inference(unit_resolution,[status(thm)],[179,22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL268-3 : TPTP v8.1.0. Released v2.3.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Sep 1 19:34:17 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.18/0.34 Usage: tptp [options] [-file:]file
% 0.18/0.34 -h, -? prints this message.
% 0.18/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.18/0.34 -m, -model generate model.
% 0.18/0.34 -p, -proof generate proof.
% 0.18/0.34 -c, -core generate unsat core of named formulas.
% 0.18/0.34 -st, -statistics display statistics.
% 0.18/0.34 -t:timeout set timeout (in second).
% 0.18/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.18/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.18/0.34 -<param>:<value> configuration parameter and value.
% 0.18/0.34 -o:<output-file> file to place output in.
% 0.82/0.76 % SZS status Unsatisfiable
% 0.82/0.76 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------