TSTP Solution File: LCL272-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL272-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 04:55:44 EDT 2022
% Result : Unsatisfiable 0.19s 0.55s
% Output : Proof 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 70
% Syntax : Number of formulae : 198 ( 97 unt; 8 typ; 0 def)
% Number of atoms : 506 ( 77 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 559 ( 253 ~; 245 |; 0 &)
% ( 61 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 8 ( 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 : 253 ( 234 !; 0 ?; 253 :)
% Comments :
%------------------------------------------------------------------------------
tff(theorem_type,type,
theorem: $i > $o ).
tff(implies_type,type,
implies: ( $i * $i ) > $i ).
tff(and_type,type,
and: ( $i * $i ) > $i ).
tff(p_type,type,
p: $i ).
tff(or_type,type,
or: ( $i * $i ) > $i ).
tff(not_type,type,
not: $i > $i ).
tff(axiom_type,type,
axiom: $i > $o ).
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(p,p)) = or(not(p),or(p,p)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
implies(p,or(p,p)) = or(not(p),or(p,p)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
or(not(p),or(p,p)) = implies(p,or(p,p)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
not(or(not(p),or(p,p))) = not(implies(p,or(p,p))),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
not(implies(p,or(p,p))) = not(or(not(p),or(p,p))),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))) = or(not(or(not(p),or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
or(not(or(not(p),or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))) = or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))),
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(not(p),or(p,p)),and(implies(p,or(p,p)),implies(or(p,p),p))) = or(not(or(not(p),or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
implies(or(not(p),or(p,p)),and(implies(p,or(p,p)),implies(or(p,p),p))) = or(not(or(not(p),or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))),
inference(unit_resolution,[status(thm)],[15,7]) ).
tff(17,plain,
implies(or(not(p),or(p,p)),and(implies(p,or(p,p)),implies(or(p,p),p))) = or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))),
inference(transitivity,[status(thm)],[16,14]) ).
tff(18,plain,
( theorem(implies(or(not(p),or(p,p)),and(implies(p,or(p,p)),implies(or(p,p),p))))
<=> theorem(or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p)))) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
( theorem(or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))))
<=> theorem(implies(or(not(p),or(p,p)),and(implies(p,or(p,p)),implies(or(p,p),p)))) ),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
or(not(implies(p,or(p,p))),not(implies(or(p,p),p))) = or(not(or(not(p),or(p,p))),not(implies(or(p,p),p))),
inference(monotonicity,[status(thm)],[12]) ).
tff(21,plain,
or(not(or(not(p),or(p,p))),not(implies(or(p,p),p))) = or(not(implies(p,or(p,p))),not(implies(or(p,p),p))),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))) = not(or(not(implies(p,or(p,p))),not(implies(or(p,p),p)))),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
not(or(not(implies(p,or(p,p))),not(implies(or(p,p),p)))) = not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),
inference(symmetry,[status(thm)],[22]) ).
tff(24,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(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(quant_intro,[status(thm)],[24]) ).
tff(26,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(27,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(28,plain,
! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ~ ! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) )
| ( and(implies(p,or(p,p)),implies(or(p,p),p)) = not(or(not(implies(p,or(p,p))),not(implies(or(p,p),p)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
and(implies(p,or(p,p)),implies(or(p,p),p)) = not(or(not(implies(p,or(p,p))),not(implies(or(p,p),p)))),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
and(implies(p,or(p,p)),implies(or(p,p),p)) = not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),
inference(transitivity,[status(thm)],[32,23]) ).
tff(34,plain,
or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p)))) = or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
implies(or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p)))),or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p)))) = implies(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))),or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p)))),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( theorem(implies(or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p)))),or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p)))))
<=> theorem(implies(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))),or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))))) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,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(38,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)],[37]) ).
tff(39,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(40,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(41,plain,
! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
( ~ ! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A)))
| axiom(implies(or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p)))),or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
axiom(implies(or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p)))),or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))))),
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
^ [X: $i] :
refl(
( ( theorem(X)
| ~ axiom(X) )
<=> ( theorem(X)
| ~ axiom(X) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,axiom,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',rule_1) ).
tff(50,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p)))),or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p)))))
| ~ axiom(implies(or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p)))),or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p)))),or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p)))))
| ~ axiom(implies(or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p)))),or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p)))),or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p)))))
| ~ axiom(implies(or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p)))),or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p)))),or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p)))))
| ~ axiom(implies(or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p)))),or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))))) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
theorem(implies(or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p)))),or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))))),
inference(unit_resolution,[status(thm)],[55,52,45]) ).
tff(57,plain,
theorem(implies(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))),or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))))),
inference(modus_ponens,[status(thm)],[56,36]) ).
tff(58,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(p,p),p) = or(not(or(p,p)),p) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
implies(or(p,p),p) = or(not(or(p,p)),p),
inference(unit_resolution,[status(thm)],[58,7]) ).
tff(60,plain,
or(not(or(p,p)),p) = implies(or(p,p),p),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
not(or(not(or(p,p)),p)) = not(implies(or(p,p),p)),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
not(implies(or(p,p),p)) = not(or(not(or(p,p)),p)),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))) = or(not(or(not(or(p,p)),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
or(not(or(not(or(p,p)),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))) = or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(not(or(p,p)),p),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))) = or(not(or(not(or(p,p)),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
implies(or(not(or(p,p)),p),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))) = or(not(or(not(or(p,p)),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))),
inference(unit_resolution,[status(thm)],[65,7]) ).
tff(67,plain,
or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))) = or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p)))),
inference(symmetry,[status(thm)],[34]) ).
tff(68,plain,
implies(or(not(or(p,p)),p),or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p))))) = implies(or(not(or(p,p)),p),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
implies(or(not(or(p,p)),p),or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p))))) = or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))),
inference(transitivity,[status(thm)],[68,66,64]) ).
tff(70,plain,
( theorem(implies(or(not(or(p,p)),p),or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p))))))
<=> theorem(or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p)))))) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( theorem(or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))))
<=> theorem(implies(or(not(or(p,p)),p),or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))) ),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
or(and(implies(p,or(p,p)),implies(or(p,p),p)),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))) = or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))),
inference(monotonicity,[status(thm)],[33]) ).
tff(73,plain,
implies(or(and(implies(p,or(p,p)),implies(or(p,p),p)),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))),or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p)))))) = implies(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))),or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p)))))),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
( theorem(implies(or(and(implies(p,or(p,p)),implies(or(p,p),p)),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))),or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p)))))))
<=> theorem(implies(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))),or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))))) ),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,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(76,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)],[75]) ).
tff(77,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(78,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(79,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
( ~ ! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C))))
| axiom(implies(or(and(implies(p,or(p,p)),implies(or(p,p),p)),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))),or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(83,plain,
axiom(implies(or(and(implies(p,or(p,p)),implies(or(p,p),p)),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))),or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))))),
inference(unit_resolution,[status(thm)],[82,81]) ).
tff(84,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(p,or(p,p)),implies(or(p,p),p)),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))),or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p)))))))
| ~ axiom(implies(or(and(implies(p,or(p,p)),implies(or(p,p),p)),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))),or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(p,or(p,p)),implies(or(p,p),p)),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))),or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p)))))))
| ~ axiom(implies(or(and(implies(p,or(p,p)),implies(or(p,p),p)),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))),or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(p,or(p,p)),implies(or(p,p),p)),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))),or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p)))))))
| ~ axiom(implies(or(and(implies(p,or(p,p)),implies(or(p,p),p)),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))),or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(p,or(p,p)),implies(or(p,p),p)),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))),or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p)))))))
| ~ axiom(implies(or(and(implies(p,or(p,p)),implies(or(p,p),p)),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))),or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))))) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
theorem(implies(or(and(implies(p,or(p,p)),implies(or(p,p),p)),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))),or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))))),
inference(unit_resolution,[status(thm)],[86,52,83]) ).
tff(88,plain,
theorem(implies(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))),or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))))),
inference(modus_ponens,[status(thm)],[87,74]) ).
tff(89,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))) = or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
implies(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))) = or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))),
inference(unit_resolution,[status(thm)],[89,7]) ).
tff(91,plain,
or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))) = implies(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
( theorem(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))))
<=> theorem(implies(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p)))))) ),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
( theorem(implies(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))))
<=> theorem(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p)))))) ),
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
implies(or(not(implies(p,or(p,p))),not(implies(or(p,p),p))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))) = implies(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))),
inference(monotonicity,[status(thm)],[20]) ).
tff(95,plain,
( theorem(implies(or(not(implies(p,or(p,p))),not(implies(or(p,p),p))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))))
<=> theorem(implies(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p)))))) ),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
( ~ ! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A)))
| axiom(implies(or(not(implies(p,or(p,p))),not(implies(or(p,p),p))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p)))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
axiom(implies(or(not(implies(p,or(p,p))),not(implies(or(p,p),p))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p)))))),
inference(unit_resolution,[status(thm)],[96,43]) ).
tff(98,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(p,or(p,p))),not(implies(or(p,p),p))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))))
| ~ axiom(implies(or(not(implies(p,or(p,p))),not(implies(or(p,p),p))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p)))))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(p,or(p,p))),not(implies(or(p,p),p))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))))
| ~ axiom(implies(or(not(implies(p,or(p,p))),not(implies(or(p,p),p))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p)))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(99,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(p,or(p,p))),not(implies(or(p,p),p))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))))
| ~ axiom(implies(or(not(implies(p,or(p,p))),not(implies(or(p,p),p))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p)))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(100,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(p,or(p,p))),not(implies(or(p,p),p))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))))
| ~ axiom(implies(or(not(implies(p,or(p,p))),not(implies(or(p,p),p))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p)))))) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
theorem(implies(or(not(implies(p,or(p,p))),not(implies(or(p,p),p))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p)))))),
inference(unit_resolution,[status(thm)],[100,52,97]) ).
tff(102,plain,
theorem(implies(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p)))))),
inference(modus_ponens,[status(thm)],[101,95]) ).
tff(103,plain,
theorem(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p)))))),
inference(modus_ponens,[status(thm)],[102,93]) ).
tff(104,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(105,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)],[104]) ).
tff(106,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(107,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(108,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)],[107]) ).
tff(109,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(110,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[110,106]) ).
tff(112,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(skolemize,[status(sab)],[111]) ).
tff(113,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[112,105]) ).
tff(114,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))))
| ~ theorem(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))))
| ~ theorem(implies(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))),or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))))
| ~ theorem(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))))
| ~ theorem(implies(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))),or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(115,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))))
| ~ theorem(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))))
| ~ theorem(implies(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))),or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(116,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))))
| ~ theorem(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))))
| ~ theorem(implies(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))),or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))))) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
( theorem(or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))))
| ~ theorem(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))))
| ~ theorem(implies(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),or(not(implies(or(p,p),p)),not(implies(p,or(p,p))))),or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p))))))) ),
inference(unit_resolution,[status(thm)],[116,113]) ).
tff(118,plain,
theorem(or(not(implies(or(p,p),p)),or(and(implies(p,or(p,p)),implies(or(p,p),p)),not(implies(p,or(p,p)))))),
inference(unit_resolution,[status(thm)],[117,103,88]) ).
tff(119,plain,
theorem(implies(or(not(or(p,p)),p),or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))),
inference(modus_ponens,[status(thm)],[118,71]) ).
tff(120,plain,
( theorem(or(not(or(p,p)),p))
<=> theorem(implies(or(p,p),p)) ),
inference(monotonicity,[status(thm)],[60]) ).
tff(121,plain,
( theorem(implies(or(p,p),p))
<=> theorem(or(not(or(p,p)),p)) ),
inference(symmetry,[status(thm)],[120]) ).
tff(122,plain,
^ [A: $i] :
refl(
( axiom(implies(or(A,A),A))
<=> axiom(implies(or(A,A),A)) )),
inference(bind,[status(th)],]) ).
tff(123,plain,
( ! [A: $i] : axiom(implies(or(A,A),A))
<=> ! [A: $i] : axiom(implies(or(A,A),A)) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,plain,
( ! [A: $i] : axiom(implies(or(A,A),A))
<=> ! [A: $i] : axiom(implies(or(A,A),A)) ),
inference(rewrite,[status(thm)],]) ).
tff(125,axiom,
! [A: $i] : axiom(implies(or(A,A),A)),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_2) ).
tff(126,plain,
! [A: $i] : axiom(implies(or(A,A),A)),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
! [A: $i] : axiom(implies(or(A,A),A)),
inference(skolemize,[status(sab)],[126]) ).
tff(128,plain,
! [A: $i] : axiom(implies(or(A,A),A)),
inference(modus_ponens,[status(thm)],[127,123]) ).
tff(129,plain,
( ~ ! [A: $i] : axiom(implies(or(A,A),A))
| axiom(implies(or(p,p),p)) ),
inference(quant_inst,[status(thm)],]) ).
tff(130,plain,
axiom(implies(or(p,p),p)),
inference(unit_resolution,[status(thm)],[129,128]) ).
tff(131,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(p,p),p))
| ~ axiom(implies(or(p,p),p)) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(p,p),p))
| ~ axiom(implies(or(p,p),p)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(132,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(p,p),p))
| ~ axiom(implies(or(p,p),p)) ),
inference(quant_inst,[status(thm)],]) ).
tff(133,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(p,p),p))
| ~ axiom(implies(or(p,p),p)) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
theorem(implies(or(p,p),p)),
inference(unit_resolution,[status(thm)],[133,52,130]) ).
tff(135,plain,
theorem(or(not(or(p,p)),p)),
inference(modus_ponens,[status(thm)],[134,121]) ).
tff(136,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(or(p,p)),p))
| theorem(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))
| ~ theorem(implies(or(not(or(p,p)),p),or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(or(p,p)),p))
| theorem(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))
| ~ theorem(implies(or(not(or(p,p)),p),or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(137,plain,
( ( theorem(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))
| ~ theorem(or(not(or(p,p)),p))
| ~ theorem(implies(or(not(or(p,p)),p),or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))) )
<=> ( ~ theorem(or(not(or(p,p)),p))
| theorem(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))
| ~ theorem(implies(or(not(or(p,p)),p),or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(138,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))
| ~ theorem(or(not(or(p,p)),p))
| ~ theorem(implies(or(not(or(p,p)),p),or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(or(p,p)),p))
| theorem(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))
| ~ theorem(implies(or(not(or(p,p)),p),or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))) ) ),
inference(monotonicity,[status(thm)],[137]) ).
tff(139,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))
| ~ theorem(or(not(or(p,p)),p))
| ~ theorem(implies(or(not(or(p,p)),p),or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(or(p,p)),p))
| theorem(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))
| ~ theorem(implies(or(not(or(p,p)),p),or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))) ) ),
inference(transitivity,[status(thm)],[138,136]) ).
tff(140,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))
| ~ theorem(or(not(or(p,p)),p))
| ~ theorem(implies(or(not(or(p,p)),p),or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(141,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(or(p,p)),p))
| theorem(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))
| ~ theorem(implies(or(not(or(p,p)),p),or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))) ),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
( theorem(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))
| ~ theorem(implies(or(not(or(p,p)),p),or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))) ),
inference(unit_resolution,[status(thm)],[141,113,135]) ).
tff(143,plain,
theorem(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p))))),
inference(unit_resolution,[status(thm)],[142,119]) ).
tff(144,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))))
| ~ theorem(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))
| ~ theorem(implies(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))),or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))))
| ~ theorem(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))
| ~ theorem(implies(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))),or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(145,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))))
| ~ theorem(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))
| ~ theorem(implies(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))),or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(146,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))))
| ~ theorem(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))
| ~ theorem(implies(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))),or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))))) ),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
( theorem(or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))))
| ~ theorem(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))))
| ~ theorem(implies(or(not(or(not(or(not(p),or(p,p))),not(implies(or(p,p),p)))),not(implies(p,or(p,p)))),or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p))))) ),
inference(unit_resolution,[status(thm)],[146,113]) ).
tff(148,plain,
theorem(or(not(implies(p,or(p,p))),and(implies(p,or(p,p)),implies(or(p,p),p)))),
inference(unit_resolution,[status(thm)],[147,143,57]) ).
tff(149,plain,
theorem(implies(or(not(p),or(p,p)),and(implies(p,or(p,p)),implies(or(p,p),p)))),
inference(modus_ponens,[status(thm)],[148,19]) ).
tff(150,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(151,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)],[150]) ).
tff(152,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(153,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(154,plain,
! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ),
inference(modus_ponens,[status(thm)],[153,152]) ).
tff(155,plain,
! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ),
inference(skolemize,[status(sab)],[154]) ).
tff(156,plain,
! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ),
inference(modus_ponens,[status(thm)],[155,151]) ).
tff(157,plain,
( ~ ! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) )
| ( equivalent(p,or(p,p)) = and(implies(p,or(p,p)),implies(or(p,p),p)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(158,plain,
equivalent(p,or(p,p)) = and(implies(p,or(p,p)),implies(or(p,p),p)),
inference(unit_resolution,[status(thm)],[157,156]) ).
tff(159,plain,
and(implies(p,or(p,p)),implies(or(p,p),p)) = equivalent(p,or(p,p)),
inference(symmetry,[status(thm)],[158]) ).
tff(160,plain,
( theorem(and(implies(p,or(p,p)),implies(or(p,p),p)))
<=> theorem(equivalent(p,or(p,p))) ),
inference(monotonicity,[status(thm)],[159]) ).
tff(161,plain,
( theorem(equivalent(p,or(p,p)))
<=> theorem(and(implies(p,or(p,p)),implies(or(p,p),p))) ),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
( ~ theorem(equivalent(p,or(p,p)))
<=> ~ theorem(and(implies(p,or(p,p)),implies(or(p,p),p))) ),
inference(monotonicity,[status(thm)],[161]) ).
tff(163,plain,
( ~ theorem(equivalent(p,or(p,p)))
<=> ~ theorem(equivalent(p,or(p,p))) ),
inference(rewrite,[status(thm)],]) ).
tff(164,axiom,
~ theorem(equivalent(p,or(p,p))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(165,plain,
~ theorem(equivalent(p,or(p,p))),
inference(modus_ponens,[status(thm)],[164,163]) ).
tff(166,plain,
~ theorem(and(implies(p,or(p,p)),implies(or(p,p),p))),
inference(modus_ponens,[status(thm)],[165,162]) ).
tff(167,plain,
( theorem(or(not(p),or(p,p)))
<=> theorem(implies(p,or(p,p))) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(168,plain,
( theorem(implies(p,or(p,p)))
<=> theorem(or(not(p),or(p,p))) ),
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
^ [B: $i,A: $i] :
refl(
( axiom(implies(A,or(B,A)))
<=> axiom(implies(A,or(B,A))) )),
inference(bind,[status(th)],]) ).
tff(170,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)],[169]) ).
tff(171,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(172,axiom,
! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_3) ).
tff(173,plain,
! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
inference(modus_ponens,[status(thm)],[172,171]) ).
tff(174,plain,
! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
inference(skolemize,[status(sab)],[173]) ).
tff(175,plain,
! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
inference(modus_ponens,[status(thm)],[174,170]) ).
tff(176,plain,
( ~ ! [B: $i,A: $i] : axiom(implies(A,or(B,A)))
| axiom(implies(p,or(p,p))) ),
inference(quant_inst,[status(thm)],]) ).
tff(177,plain,
axiom(implies(p,or(p,p))),
inference(unit_resolution,[status(thm)],[176,175]) ).
tff(178,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(p,or(p,p)))
| ~ axiom(implies(p,or(p,p))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(p,or(p,p)))
| ~ axiom(implies(p,or(p,p))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(179,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(p,or(p,p)))
| ~ axiom(implies(p,or(p,p))) ),
inference(quant_inst,[status(thm)],]) ).
tff(180,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(p,or(p,p)))
| ~ axiom(implies(p,or(p,p))) ),
inference(modus_ponens,[status(thm)],[179,178]) ).
tff(181,plain,
theorem(implies(p,or(p,p))),
inference(unit_resolution,[status(thm)],[180,52,177]) ).
tff(182,plain,
theorem(or(not(p),or(p,p))),
inference(modus_ponens,[status(thm)],[181,168]) ).
tff(183,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(p),or(p,p)))
| theorem(and(implies(p,or(p,p)),implies(or(p,p),p)))
| ~ theorem(implies(or(not(p),or(p,p)),and(implies(p,or(p,p)),implies(or(p,p),p)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(p),or(p,p)))
| theorem(and(implies(p,or(p,p)),implies(or(p,p),p)))
| ~ theorem(implies(or(not(p),or(p,p)),and(implies(p,or(p,p)),implies(or(p,p),p)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(184,plain,
( ( theorem(and(implies(p,or(p,p)),implies(or(p,p),p)))
| ~ theorem(or(not(p),or(p,p)))
| ~ theorem(implies(or(not(p),or(p,p)),and(implies(p,or(p,p)),implies(or(p,p),p)))) )
<=> ( ~ theorem(or(not(p),or(p,p)))
| theorem(and(implies(p,or(p,p)),implies(or(p,p),p)))
| ~ theorem(implies(or(not(p),or(p,p)),and(implies(p,or(p,p)),implies(or(p,p),p)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(185,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(and(implies(p,or(p,p)),implies(or(p,p),p)))
| ~ theorem(or(not(p),or(p,p)))
| ~ theorem(implies(or(not(p),or(p,p)),and(implies(p,or(p,p)),implies(or(p,p),p)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(p),or(p,p)))
| theorem(and(implies(p,or(p,p)),implies(or(p,p),p)))
| ~ theorem(implies(or(not(p),or(p,p)),and(implies(p,or(p,p)),implies(or(p,p),p)))) ) ),
inference(monotonicity,[status(thm)],[184]) ).
tff(186,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(and(implies(p,or(p,p)),implies(or(p,p),p)))
| ~ theorem(or(not(p),or(p,p)))
| ~ theorem(implies(or(not(p),or(p,p)),and(implies(p,or(p,p)),implies(or(p,p),p)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(p),or(p,p)))
| theorem(and(implies(p,or(p,p)),implies(or(p,p),p)))
| ~ theorem(implies(or(not(p),or(p,p)),and(implies(p,or(p,p)),implies(or(p,p),p)))) ) ),
inference(transitivity,[status(thm)],[185,183]) ).
tff(187,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(and(implies(p,or(p,p)),implies(or(p,p),p)))
| ~ theorem(or(not(p),or(p,p)))
| ~ theorem(implies(or(not(p),or(p,p)),and(implies(p,or(p,p)),implies(or(p,p),p)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(188,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(p),or(p,p)))
| theorem(and(implies(p,or(p,p)),implies(or(p,p),p)))
| ~ theorem(implies(or(not(p),or(p,p)),and(implies(p,or(p,p)),implies(or(p,p),p)))) ),
inference(modus_ponens,[status(thm)],[187,186]) ).
tff(189,plain,
~ theorem(implies(or(not(p),or(p,p)),and(implies(p,or(p,p)),implies(or(p,p),p)))),
inference(unit_resolution,[status(thm)],[188,113,182,166]) ).
tff(190,plain,
$false,
inference(unit_resolution,[status(thm)],[189,149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL272-3 : TPTP v8.1.0. Released v2.3.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n002.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 20:03:15 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.
% 0.19/0.55 % SZS status Unsatisfiable
% 0.19/0.55 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------