TSTP Solution File: LCL189-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL189-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 04:55:18 EDT 2022
% Result : Unsatisfiable 1.03s 0.92s
% Output : Proof 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 58
% Syntax : Number of formulae : 153 ( 66 unt; 7 typ; 0 def)
% Number of atoms : 393 ( 43 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 456 ( 216 ~; 196 |; 0 &)
% ( 44 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 7 ( 7 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 5 >; 2 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 204 ( 189 !; 0 ?; 204 :)
% Comments :
%------------------------------------------------------------------------------
tff(axiom_type,type,
axiom: $i > $o ).
tff(or_type,type,
or: ( $i * $i ) > $i ).
tff(q_type,type,
q: $i ).
tff(not_type,type,
not: $i > $i ).
tff(p_type,type,
p: $i ).
tff(implies_type,type,
implies: ( $i * $i ) > $i ).
tff(theorem_type,type,
theorem: $i > $o ).
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/sandbox2/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(q,or(not(or(not(q),or(not(p),q))),q)) = or(not(q),or(not(or(not(q),or(not(p),q))),q)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
implies(q,or(not(or(not(q),or(not(p),q))),q)) = or(not(q),or(not(or(not(q),or(not(p),q))),q)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
or(not(q),or(not(or(not(q),or(not(p),q))),q)) = implies(q,or(not(or(not(q),or(not(p),q))),q)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( axiom(or(not(q),or(not(or(not(q),or(not(p),q))),q)))
<=> axiom(implies(q,or(not(or(not(q),or(not(p),q))),q))) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( axiom(implies(q,or(not(or(not(q),or(not(p),q))),q)))
<=> axiom(or(not(q),or(not(or(not(q),or(not(p),q))),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/sandbox2/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(q,or(not(or(not(q),or(not(p),q))),q))) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
axiom(implies(q,or(not(or(not(q),or(not(p),q))),q))),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
axiom(or(not(q),or(not(or(not(q),or(not(p),q))),q))),
inference(modus_ponens,[status(thm)],[21,12]) ).
tff(23,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(not(q),or(not(p),q)),or(not(q),q)) = or(not(or(not(q),or(not(p),q))),or(not(q),q)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
implies(or(not(q),or(not(p),q)),or(not(q),q)) = or(not(or(not(q),or(not(p),q))),or(not(q),q)),
inference(unit_resolution,[status(thm)],[23,7]) ).
tff(25,plain,
( theorem(implies(or(not(q),or(not(p),q)),or(not(q),q)))
<=> theorem(or(not(or(not(q),or(not(p),q))),or(not(q),q))) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ~ theorem(implies(or(not(q),or(not(p),q)),or(not(q),q)))
<=> ~ theorem(or(not(or(not(q),or(not(p),q))),or(not(q),q))) ),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(q,q) = or(not(q),q) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
implies(q,q) = or(not(q),q),
inference(unit_resolution,[status(thm)],[27,7]) ).
tff(29,plain,
or(not(q),q) = implies(q,q),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
( theorem(or(not(q),q))
<=> theorem(implies(q,q)) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( theorem(implies(q,q))
<=> theorem(or(not(q),q)) ),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
( ~ theorem(implies(q,q))
<=> ~ theorem(or(not(q),q)) ),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(not(p),q),or(not(p),q)) = or(not(or(not(p),q)),or(not(p),q)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
implies(or(not(p),q),or(not(p),q)) = or(not(or(not(p),q)),or(not(p),q)),
inference(unit_resolution,[status(thm)],[33,7]) ).
tff(35,plain,
implies(implies(q,q),implies(or(not(p),q),or(not(p),q))) = implies(implies(q,q),or(not(or(not(p),q)),or(not(p),q))),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( theorem(implies(implies(q,q),implies(or(not(p),q),or(not(p),q))))
<=> theorem(implies(implies(q,q),or(not(or(not(p),q)),or(not(p),q)))) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( axiom(implies(implies(A,B),implies(or(C,A),or(C,B))))
<=> axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B))))
<=> ! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B))))
<=> ! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) ),
inference(rewrite,[status(thm)],]) ).
tff(40,axiom,
! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',axiom_1_6) ).
tff(41,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
( ~ ! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B))))
| axiom(implies(implies(q,q),implies(or(not(p),q),or(not(p),q)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
axiom(implies(implies(q,q),implies(or(not(p),q),or(not(p),q)))),
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/sandbox2/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(implies(q,q),implies(or(not(p),q),or(not(p),q))))
| ~ axiom(implies(implies(q,q),implies(or(not(p),q),or(not(p),q)))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(q,q),implies(or(not(p),q),or(not(p),q))))
| ~ axiom(implies(implies(q,q),implies(or(not(p),q),or(not(p),q)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(q,q),implies(or(not(p),q),or(not(p),q))))
| ~ axiom(implies(implies(q,q),implies(or(not(p),q),or(not(p),q)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(q,q),implies(or(not(p),q),or(not(p),q))))
| ~ axiom(implies(implies(q,q),implies(or(not(p),q),or(not(p),q)))) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
theorem(implies(implies(q,q),implies(or(not(p),q),or(not(p),q)))),
inference(unit_resolution,[status(thm)],[55,52,45]) ).
tff(57,plain,
theorem(implies(implies(q,q),or(not(or(not(p),q)),or(not(p),q)))),
inference(modus_ponens,[status(thm)],[56,36]) ).
tff(58,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(p,q) = or(not(p),q) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
implies(p,q) = or(not(p),q),
inference(unit_resolution,[status(thm)],[58,7]) ).
tff(60,plain,
or(not(p),q) = implies(p,q),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
not(or(not(p),q)) = not(implies(p,q)),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
not(implies(p,q)) = not(or(not(p),q)),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
or(not(implies(p,q)),or(not(p),q)) = or(not(or(not(p),q)),or(not(p),q)),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
or(not(or(not(p),q)),or(not(p),q)) = or(not(implies(p,q)),or(not(p),q)),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
( theorem(or(not(or(not(p),q)),or(not(p),q)))
<=> theorem(or(not(implies(p,q)),or(not(p),q))) ),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( theorem(or(not(implies(p,q)),or(not(p),q)))
<=> theorem(or(not(or(not(p),q)),or(not(p),q))) ),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
( ~ theorem(or(not(implies(p,q)),or(not(p),q)))
<=> ~ theorem(or(not(or(not(p),q)),or(not(p),q))) ),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(implies(p,q),q) = or(not(implies(p,q)),q) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
implies(implies(p,q),q) = or(not(implies(p,q)),q),
inference(unit_resolution,[status(thm)],[68,7]) ).
tff(70,plain,
or(not(implies(p,q)),q) = implies(implies(p,q),q),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
or(not(p),or(not(implies(p,q)),q)) = or(not(p),implies(implies(p,q),q)),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
implies(or(not(implies(p,q)),or(not(p),q)),or(not(p),or(not(implies(p,q)),q))) = implies(or(not(implies(p,q)),or(not(p),q)),or(not(p),implies(implies(p,q),q))),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
( theorem(implies(or(not(implies(p,q)),or(not(p),q)),or(not(p),or(not(implies(p,q)),q))))
<=> theorem(implies(or(not(implies(p,q)),or(not(p),q)),or(not(p),implies(implies(p,q),q)))) ),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,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(75,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)],[74]) ).
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(rewrite,[status(thm)],]) ).
tff(77,axiom,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',axiom_1_5) ).
tff(78,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(modus_ponens,[status(thm)],[79,75]) ).
tff(81,plain,
( ~ ! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C))))
| axiom(implies(or(not(implies(p,q)),or(not(p),q)),or(not(p),or(not(implies(p,q)),q)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
axiom(implies(or(not(implies(p,q)),or(not(p),q)),or(not(p),or(not(implies(p,q)),q)))),
inference(unit_resolution,[status(thm)],[81,80]) ).
tff(83,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(p,q)),or(not(p),q)),or(not(p),or(not(implies(p,q)),q))))
| ~ axiom(implies(or(not(implies(p,q)),or(not(p),q)),or(not(p),or(not(implies(p,q)),q)))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(p,q)),or(not(p),q)),or(not(p),or(not(implies(p,q)),q))))
| ~ axiom(implies(or(not(implies(p,q)),or(not(p),q)),or(not(p),or(not(implies(p,q)),q)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(p,q)),or(not(p),q)),or(not(p),or(not(implies(p,q)),q))))
| ~ axiom(implies(or(not(implies(p,q)),or(not(p),q)),or(not(p),or(not(implies(p,q)),q)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(p,q)),or(not(p),q)),or(not(p),or(not(implies(p,q)),q))))
| ~ axiom(implies(or(not(implies(p,q)),or(not(p),q)),or(not(p),or(not(implies(p,q)),q)))) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
theorem(implies(or(not(implies(p,q)),or(not(p),q)),or(not(p),or(not(implies(p,q)),q)))),
inference(unit_resolution,[status(thm)],[85,52,82]) ).
tff(87,plain,
theorem(implies(or(not(implies(p,q)),or(not(p),q)),or(not(p),implies(implies(p,q),q)))),
inference(modus_ponens,[status(thm)],[86,73]) ).
tff(88,plain,
( ~ theorem(or(not(p),implies(implies(p,q),q)))
<=> ~ theorem(or(not(p),implies(implies(p,q),q))) ),
inference(rewrite,[status(thm)],]) ).
tff(89,axiom,
~ theorem(or(not(p),implies(implies(p,q),q))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(90,plain,
~ theorem(or(not(p),implies(implies(p,q),q))),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,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(92,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)],[91]) ).
tff(93,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(94,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(95,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)],[94]) ).
tff(96,axiom,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(implies(Y,X))
| ~ theorem(Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',rule_2) ).
tff(97,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[97,93]) ).
tff(99,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(skolemize,[status(sab)],[98]) ).
tff(100,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[99,92]) ).
tff(101,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(p),implies(implies(p,q),q)))
| ~ theorem(or(not(implies(p,q)),or(not(p),q)))
| ~ theorem(implies(or(not(implies(p,q)),or(not(p),q)),or(not(p),implies(implies(p,q),q)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(p),implies(implies(p,q),q)))
| ~ theorem(or(not(implies(p,q)),or(not(p),q)))
| ~ theorem(implies(or(not(implies(p,q)),or(not(p),q)),or(not(p),implies(implies(p,q),q)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(p),implies(implies(p,q),q)))
| ~ theorem(or(not(implies(p,q)),or(not(p),q)))
| ~ theorem(implies(or(not(implies(p,q)),or(not(p),q)),or(not(p),implies(implies(p,q),q)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(103,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(p),implies(implies(p,q),q)))
| ~ theorem(or(not(implies(p,q)),or(not(p),q)))
| ~ theorem(implies(or(not(implies(p,q)),or(not(p),q)),or(not(p),implies(implies(p,q),q)))) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
( ~ theorem(or(not(implies(p,q)),or(not(p),q)))
| ~ theorem(implies(or(not(implies(p,q)),or(not(p),q)),or(not(p),implies(implies(p,q),q)))) ),
inference(unit_resolution,[status(thm)],[103,100,90]) ).
tff(105,plain,
~ theorem(or(not(implies(p,q)),or(not(p),q))),
inference(unit_resolution,[status(thm)],[104,87]) ).
tff(106,plain,
~ theorem(or(not(or(not(p),q)),or(not(p),q))),
inference(modus_ponens,[status(thm)],[105,67]) ).
tff(107,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(p),q)),or(not(p),q)))
| ~ theorem(implies(q,q))
| ~ theorem(implies(implies(q,q),or(not(or(not(p),q)),or(not(p),q)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(p),q)),or(not(p),q)))
| ~ theorem(implies(q,q))
| ~ theorem(implies(implies(q,q),or(not(or(not(p),q)),or(not(p),q)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(p),q)),or(not(p),q)))
| ~ theorem(implies(q,q))
| ~ theorem(implies(implies(q,q),or(not(or(not(p),q)),or(not(p),q)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(109,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(p),q)),or(not(p),q)))
| ~ theorem(implies(q,q))
| ~ theorem(implies(implies(q,q),or(not(or(not(p),q)),or(not(p),q)))) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
( ~ theorem(implies(q,q))
| ~ theorem(implies(implies(q,q),or(not(or(not(p),q)),or(not(p),q)))) ),
inference(unit_resolution,[status(thm)],[109,100,106]) ).
tff(111,plain,
~ theorem(implies(q,q)),
inference(unit_resolution,[status(thm)],[110,57]) ).
tff(112,plain,
~ theorem(or(not(q),q)),
inference(modus_ponens,[status(thm)],[111,32]) ).
tff(113,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(q,or(not(p),q)) = or(not(q),or(not(p),q)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,plain,
implies(q,or(not(p),q)) = or(not(q),or(not(p),q)),
inference(unit_resolution,[status(thm)],[113,7]) ).
tff(115,plain,
or(not(q),or(not(p),q)) = implies(q,or(not(p),q)),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
( theorem(or(not(q),or(not(p),q)))
<=> theorem(implies(q,or(not(p),q))) ),
inference(monotonicity,[status(thm)],[115]) ).
tff(117,plain,
( theorem(implies(q,or(not(p),q)))
<=> theorem(or(not(q),or(not(p),q))) ),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
( ~ ! [B: $i,A: $i] : axiom(implies(A,or(B,A)))
| axiom(implies(q,or(not(p),q))) ),
inference(quant_inst,[status(thm)],]) ).
tff(119,plain,
axiom(implies(q,or(not(p),q))),
inference(unit_resolution,[status(thm)],[118,19]) ).
tff(120,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(q,or(not(p),q)))
| ~ axiom(implies(q,or(not(p),q))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(q,or(not(p),q)))
| ~ axiom(implies(q,or(not(p),q))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(121,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(q,or(not(p),q)))
| ~ axiom(implies(q,or(not(p),q))) ),
inference(quant_inst,[status(thm)],]) ).
tff(122,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(q,or(not(p),q)))
| ~ axiom(implies(q,or(not(p),q))) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
theorem(implies(q,or(not(p),q))),
inference(unit_resolution,[status(thm)],[122,52,119]) ).
tff(124,plain,
theorem(or(not(q),or(not(p),q))),
inference(modus_ponens,[status(thm)],[123,117]) ).
tff(125,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(q),q))
| ~ theorem(or(not(q),or(not(p),q)))
| ~ theorem(implies(or(not(q),or(not(p),q)),or(not(q),q))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(q),q))
| ~ theorem(or(not(q),or(not(p),q)))
| ~ theorem(implies(or(not(q),or(not(p),q)),or(not(q),q))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(126,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(q),q))
| ~ theorem(or(not(q),or(not(p),q)))
| ~ theorem(implies(or(not(q),or(not(p),q)),or(not(q),q))) ),
inference(quant_inst,[status(thm)],]) ).
tff(127,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(q),q))
| ~ theorem(or(not(q),or(not(p),q)))
| ~ theorem(implies(or(not(q),or(not(p),q)),or(not(q),q))) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
~ theorem(implies(or(not(q),or(not(p),q)),or(not(q),q))),
inference(unit_resolution,[status(thm)],[127,100,124,112]) ).
tff(129,plain,
~ theorem(or(not(or(not(q),or(not(p),q))),or(not(q),q))),
inference(modus_ponens,[status(thm)],[128,26]) ).
tff(130,plain,
( ~ ! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C))))
| axiom(implies(or(not(q),or(not(or(not(q),or(not(p),q))),q)),or(not(or(not(q),or(not(p),q))),or(not(q),q)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(131,plain,
axiom(implies(or(not(q),or(not(or(not(q),or(not(p),q))),q)),or(not(or(not(q),or(not(p),q))),or(not(q),q)))),
inference(unit_resolution,[status(thm)],[130,80]) ).
tff(132,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(q),or(not(or(not(q),or(not(p),q))),q)),or(not(or(not(q),or(not(p),q))),or(not(q),q))))
| ~ axiom(implies(or(not(q),or(not(or(not(q),or(not(p),q))),q)),or(not(or(not(q),or(not(p),q))),or(not(q),q)))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(q),or(not(or(not(q),or(not(p),q))),q)),or(not(or(not(q),or(not(p),q))),or(not(q),q))))
| ~ axiom(implies(or(not(q),or(not(or(not(q),or(not(p),q))),q)),or(not(or(not(q),or(not(p),q))),or(not(q),q)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(133,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(q),or(not(or(not(q),or(not(p),q))),q)),or(not(or(not(q),or(not(p),q))),or(not(q),q))))
| ~ axiom(implies(or(not(q),or(not(or(not(q),or(not(p),q))),q)),or(not(or(not(q),or(not(p),q))),or(not(q),q)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(134,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(q),or(not(or(not(q),or(not(p),q))),q)),or(not(or(not(q),or(not(p),q))),or(not(q),q))))
| ~ axiom(implies(or(not(q),or(not(or(not(q),or(not(p),q))),q)),or(not(or(not(q),or(not(p),q))),or(not(q),q)))) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
theorem(implies(or(not(q),or(not(or(not(q),or(not(p),q))),q)),or(not(or(not(q),or(not(p),q))),or(not(q),q)))),
inference(unit_resolution,[status(thm)],[134,52,131]) ).
tff(136,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(q),or(not(p),q))),or(not(q),q)))
| ~ theorem(or(not(q),or(not(or(not(q),or(not(p),q))),q)))
| ~ theorem(implies(or(not(q),or(not(or(not(q),or(not(p),q))),q)),or(not(or(not(q),or(not(p),q))),or(not(q),q)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(q),or(not(p),q))),or(not(q),q)))
| ~ theorem(or(not(q),or(not(or(not(q),or(not(p),q))),q)))
| ~ theorem(implies(or(not(q),or(not(or(not(q),or(not(p),q))),q)),or(not(or(not(q),or(not(p),q))),or(not(q),q)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(137,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(q),or(not(p),q))),or(not(q),q)))
| ~ theorem(or(not(q),or(not(or(not(q),or(not(p),q))),q)))
| ~ theorem(implies(or(not(q),or(not(or(not(q),or(not(p),q))),q)),or(not(or(not(q),or(not(p),q))),or(not(q),q)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(q),or(not(p),q))),or(not(q),q)))
| ~ theorem(or(not(q),or(not(or(not(q),or(not(p),q))),q)))
| ~ theorem(implies(or(not(q),or(not(or(not(q),or(not(p),q))),q)),or(not(or(not(q),or(not(p),q))),or(not(q),q)))) ),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
( theorem(or(not(or(not(q),or(not(p),q))),or(not(q),q)))
| ~ theorem(or(not(q),or(not(or(not(q),or(not(p),q))),q))) ),
inference(unit_resolution,[status(thm)],[138,100,135]) ).
tff(140,plain,
~ theorem(or(not(q),or(not(or(not(q),or(not(p),q))),q))),
inference(unit_resolution,[status(thm)],[139,129]) ).
tff(141,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(q),or(not(or(not(q),or(not(p),q))),q)))
| ~ axiom(or(not(q),or(not(or(not(q),or(not(p),q))),q))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(q),or(not(or(not(q),or(not(p),q))),q)))
| ~ axiom(or(not(q),or(not(or(not(q),or(not(p),q))),q))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(142,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(q),or(not(or(not(q),or(not(p),q))),q)))
| ~ axiom(or(not(q),or(not(or(not(q),or(not(p),q))),q))) ),
inference(quant_inst,[status(thm)],]) ).
tff(143,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(q),or(not(or(not(q),or(not(p),q))),q)))
| ~ axiom(or(not(q),or(not(or(not(q),or(not(p),q))),q))) ),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
( theorem(or(not(q),or(not(or(not(q),or(not(p),q))),q)))
| ~ axiom(or(not(q),or(not(or(not(q),or(not(p),q))),q))) ),
inference(unit_resolution,[status(thm)],[143,52]) ).
tff(145,plain,
~ axiom(or(not(q),or(not(or(not(q),or(not(p),q))),q))),
inference(unit_resolution,[status(thm)],[144,140]) ).
tff(146,plain,
$false,
inference(unit_resolution,[status(thm)],[145,22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL189-3 : TPTP v8.1.0. Released v2.3.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.31 % Computer : n028.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Thu Sep 1 18:47:21 EDT 2022
% 0.13/0.31 % CPUTime :
% 0.13/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.32 Usage: tptp [options] [-file:]file
% 0.13/0.32 -h, -? prints this message.
% 0.13/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.32 -m, -model generate model.
% 0.13/0.32 -p, -proof generate proof.
% 0.13/0.32 -c, -core generate unsat core of named formulas.
% 0.13/0.32 -st, -statistics display statistics.
% 0.13/0.32 -t:timeout set timeout (in second).
% 0.13/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.32 -<param>:<value> configuration parameter and value.
% 0.13/0.32 -o:<output-file> file to place output in.
% 1.03/0.92 % SZS status Unsatisfiable
% 1.03/0.92 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------