TSTP Solution File: LCL188-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL188-3 : 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 0.64s 0.63s
% Output : Proof 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 57
% Syntax : Number of formulae : 137 ( 57 unt; 7 typ; 0 def)
% Number of atoms : 370 ( 34 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 442 ( 209 ~; 195 |; 0 &)
% ( 38 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 7 ( 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 : 202 ( 187 !; 0 ?; 202 :)
% 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(p,q))),q)) = or(not(q),or(not(or(not(q),or(p,q))),q)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
implies(q,or(not(or(not(q),or(p,q))),q)) = or(not(q),or(not(or(not(q),or(p,q))),q)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
or(not(q),or(not(or(not(q),or(p,q))),q)) = implies(q,or(not(or(not(q),or(p,q))),q)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( axiom(or(not(q),or(not(or(not(q),or(p,q))),q)))
<=> axiom(implies(q,or(not(or(not(q),or(p,q))),q))) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( axiom(implies(q,or(not(or(not(q),or(p,q))),q)))
<=> axiom(or(not(q),or(not(or(not(q),or(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(p,q))),q))) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
axiom(implies(q,or(not(or(not(q),or(p,q))),q))),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
axiom(or(not(q),or(not(or(not(q),or(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(p,q)),or(not(q),q)) = or(not(or(not(q),or(p,q))),or(not(q),q)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
implies(or(not(q),or(p,q)),or(not(q),q)) = or(not(or(not(q),or(p,q))),or(not(q),q)),
inference(unit_resolution,[status(thm)],[23,7]) ).
tff(25,plain,
( theorem(implies(or(not(q),or(p,q)),or(not(q),q)))
<=> theorem(or(not(or(not(q),or(p,q))),or(not(q),q))) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ~ theorem(implies(or(not(q),or(p,q)),or(not(q),q)))
<=> ~ theorem(or(not(or(not(q),or(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(or(p,q),or(p,q)) = or(not(or(p,q)),or(p,q)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
implies(or(p,q),or(p,q)) = or(not(or(p,q)),or(p,q)),
inference(unit_resolution,[status(thm)],[27,7]) ).
tff(29,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(30,plain,
implies(q,q) = or(not(q),q),
inference(unit_resolution,[status(thm)],[29,7]) ).
tff(31,plain,
implies(implies(q,q),implies(or(p,q),or(p,q))) = implies(or(not(q),q),or(not(or(p,q)),or(p,q))),
inference(monotonicity,[status(thm)],[30,28]) ).
tff(32,plain,
( theorem(implies(implies(q,q),implies(or(p,q),or(p,q))))
<=> theorem(implies(or(not(q),q),or(not(or(p,q)),or(p,q)))) ),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,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(34,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)],[33]) ).
tff(35,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(36,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(37,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,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(p,q),or(p,q)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
axiom(implies(implies(q,q),implies(or(p,q),or(p,q)))),
inference(unit_resolution,[status(thm)],[40,39]) ).
tff(42,plain,
^ [X: $i] :
refl(
( ( theorem(X)
| ~ axiom(X) )
<=> ( theorem(X)
| ~ axiom(X) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,axiom,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',rule_1) ).
tff(46,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(q,q),implies(or(p,q),or(p,q))))
| ~ axiom(implies(implies(q,q),implies(or(p,q),or(p,q)))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(q,q),implies(or(p,q),or(p,q))))
| ~ axiom(implies(implies(q,q),implies(or(p,q),or(p,q)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(q,q),implies(or(p,q),or(p,q))))
| ~ axiom(implies(implies(q,q),implies(or(p,q),or(p,q)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(q,q),implies(or(p,q),or(p,q))))
| ~ axiom(implies(implies(q,q),implies(or(p,q),or(p,q)))) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
theorem(implies(implies(q,q),implies(or(p,q),or(p,q)))),
inference(unit_resolution,[status(thm)],[51,48,41]) ).
tff(53,plain,
theorem(implies(or(not(q),q),or(not(or(p,q)),or(p,q)))),
inference(modus_ponens,[status(thm)],[52,32]) ).
tff(54,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(p,q),q) = or(not(or(p,q)),q) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
implies(or(p,q),q) = or(not(or(p,q)),q),
inference(unit_resolution,[status(thm)],[54,7]) ).
tff(56,plain,
or(not(or(p,q)),q) = implies(or(p,q),q),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
or(p,or(not(or(p,q)),q)) = or(p,implies(or(p,q),q)),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
implies(or(not(or(p,q)),or(p,q)),or(p,or(not(or(p,q)),q))) = implies(or(not(or(p,q)),or(p,q)),or(p,implies(or(p,q),q))),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
( theorem(implies(or(not(or(p,q)),or(p,q)),or(p,or(not(or(p,q)),q))))
<=> theorem(implies(or(not(or(p,q)),or(p,q)),or(p,implies(or(p,q),q)))) ),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,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(61,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)],[60]) ).
tff(62,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(63,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(64,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
( ~ ! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C))))
| axiom(implies(or(not(or(p,q)),or(p,q)),or(p,or(not(or(p,q)),q)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
axiom(implies(or(not(or(p,q)),or(p,q)),or(p,or(not(or(p,q)),q)))),
inference(unit_resolution,[status(thm)],[67,66]) ).
tff(69,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(or(p,q)),or(p,q)),or(p,or(not(or(p,q)),q))))
| ~ axiom(implies(or(not(or(p,q)),or(p,q)),or(p,or(not(or(p,q)),q)))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(or(p,q)),or(p,q)),or(p,or(not(or(p,q)),q))))
| ~ axiom(implies(or(not(or(p,q)),or(p,q)),or(p,or(not(or(p,q)),q)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(or(p,q)),or(p,q)),or(p,or(not(or(p,q)),q))))
| ~ axiom(implies(or(not(or(p,q)),or(p,q)),or(p,or(not(or(p,q)),q)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(or(p,q)),or(p,q)),or(p,or(not(or(p,q)),q))))
| ~ axiom(implies(or(not(or(p,q)),or(p,q)),or(p,or(not(or(p,q)),q)))) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
theorem(implies(or(not(or(p,q)),or(p,q)),or(p,or(not(or(p,q)),q)))),
inference(unit_resolution,[status(thm)],[71,48,68]) ).
tff(73,plain,
theorem(implies(or(not(or(p,q)),or(p,q)),or(p,implies(or(p,q),q)))),
inference(modus_ponens,[status(thm)],[72,59]) ).
tff(74,plain,
( ~ theorem(or(p,implies(or(p,q),q)))
<=> ~ theorem(or(p,implies(or(p,q),q))) ),
inference(rewrite,[status(thm)],]) ).
tff(75,axiom,
~ theorem(or(p,implies(or(p,q),q))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(76,plain,
~ theorem(or(p,implies(or(p,q),q))),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,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(78,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)],[77]) ).
tff(79,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(80,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(81,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)],[80]) ).
tff(82,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(83,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[83,79]) ).
tff(85,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(skolemize,[status(sab)],[84]) ).
tff(86,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[85,78]) ).
tff(87,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(p,implies(or(p,q),q)))
| ~ theorem(or(not(or(p,q)),or(p,q)))
| ~ theorem(implies(or(not(or(p,q)),or(p,q)),or(p,implies(or(p,q),q)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(p,implies(or(p,q),q)))
| ~ theorem(or(not(or(p,q)),or(p,q)))
| ~ theorem(implies(or(not(or(p,q)),or(p,q)),or(p,implies(or(p,q),q)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(p,implies(or(p,q),q)))
| ~ theorem(or(not(or(p,q)),or(p,q)))
| ~ theorem(implies(or(not(or(p,q)),or(p,q)),or(p,implies(or(p,q),q)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(89,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(p,implies(or(p,q),q)))
| ~ theorem(or(not(or(p,q)),or(p,q)))
| ~ theorem(implies(or(not(or(p,q)),or(p,q)),or(p,implies(or(p,q),q)))) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
( ~ theorem(or(not(or(p,q)),or(p,q)))
| ~ theorem(implies(or(not(or(p,q)),or(p,q)),or(p,implies(or(p,q),q)))) ),
inference(unit_resolution,[status(thm)],[89,86,76]) ).
tff(91,plain,
~ theorem(or(not(or(p,q)),or(p,q))),
inference(unit_resolution,[status(thm)],[90,73]) ).
tff(92,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(p,q)),or(p,q)))
| ~ theorem(or(not(q),q))
| ~ theorem(implies(or(not(q),q),or(not(or(p,q)),or(p,q)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(p,q)),or(p,q)))
| ~ theorem(or(not(q),q))
| ~ theorem(implies(or(not(q),q),or(not(or(p,q)),or(p,q)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(p,q)),or(p,q)))
| ~ theorem(or(not(q),q))
| ~ theorem(implies(or(not(q),q),or(not(or(p,q)),or(p,q)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(p,q)),or(p,q)))
| ~ theorem(or(not(q),q))
| ~ theorem(implies(or(not(q),q),or(not(or(p,q)),or(p,q)))) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
( ~ theorem(or(not(q),q))
| ~ theorem(implies(or(not(q),q),or(not(or(p,q)),or(p,q)))) ),
inference(unit_resolution,[status(thm)],[94,86,91]) ).
tff(96,plain,
~ theorem(or(not(q),q)),
inference(unit_resolution,[status(thm)],[95,53]) ).
tff(97,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(q,or(p,q)) = or(not(q),or(p,q)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(98,plain,
implies(q,or(p,q)) = or(not(q),or(p,q)),
inference(unit_resolution,[status(thm)],[97,7]) ).
tff(99,plain,
or(not(q),or(p,q)) = implies(q,or(p,q)),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
( theorem(or(not(q),or(p,q)))
<=> theorem(implies(q,or(p,q))) ),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
( theorem(implies(q,or(p,q)))
<=> theorem(or(not(q),or(p,q))) ),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
( ~ ! [B: $i,A: $i] : axiom(implies(A,or(B,A)))
| axiom(implies(q,or(p,q))) ),
inference(quant_inst,[status(thm)],]) ).
tff(103,plain,
axiom(implies(q,or(p,q))),
inference(unit_resolution,[status(thm)],[102,19]) ).
tff(104,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(q,or(p,q)))
| ~ axiom(implies(q,or(p,q))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(q,or(p,q)))
| ~ axiom(implies(q,or(p,q))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(q,or(p,q)))
| ~ axiom(implies(q,or(p,q))) ),
inference(quant_inst,[status(thm)],]) ).
tff(106,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(q,or(p,q)))
| ~ axiom(implies(q,or(p,q))) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
theorem(implies(q,or(p,q))),
inference(unit_resolution,[status(thm)],[106,48,103]) ).
tff(108,plain,
theorem(or(not(q),or(p,q))),
inference(modus_ponens,[status(thm)],[107,101]) ).
tff(109,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(q),q))
| ~ theorem(or(not(q),or(p,q)))
| ~ theorem(implies(or(not(q),or(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(p,q)))
| ~ theorem(implies(or(not(q),or(p,q)),or(not(q),q))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(110,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(q),q))
| ~ theorem(or(not(q),or(p,q)))
| ~ theorem(implies(or(not(q),or(p,q)),or(not(q),q))) ),
inference(quant_inst,[status(thm)],]) ).
tff(111,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(q),q))
| ~ theorem(or(not(q),or(p,q)))
| ~ theorem(implies(or(not(q),or(p,q)),or(not(q),q))) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
~ theorem(implies(or(not(q),or(p,q)),or(not(q),q))),
inference(unit_resolution,[status(thm)],[111,86,108,96]) ).
tff(113,plain,
~ theorem(or(not(or(not(q),or(p,q))),or(not(q),q))),
inference(modus_ponens,[status(thm)],[112,26]) ).
tff(114,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(p,q))),q)),or(not(or(not(q),or(p,q))),or(not(q),q)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(115,plain,
axiom(implies(or(not(q),or(not(or(not(q),or(p,q))),q)),or(not(or(not(q),or(p,q))),or(not(q),q)))),
inference(unit_resolution,[status(thm)],[114,66]) ).
tff(116,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(q),or(not(or(not(q),or(p,q))),q)),or(not(or(not(q),or(p,q))),or(not(q),q))))
| ~ axiom(implies(or(not(q),or(not(or(not(q),or(p,q))),q)),or(not(or(not(q),or(p,q))),or(not(q),q)))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(q),or(not(or(not(q),or(p,q))),q)),or(not(or(not(q),or(p,q))),or(not(q),q))))
| ~ axiom(implies(or(not(q),or(not(or(not(q),or(p,q))),q)),or(not(or(not(q),or(p,q))),or(not(q),q)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(q),or(not(or(not(q),or(p,q))),q)),or(not(or(not(q),or(p,q))),or(not(q),q))))
| ~ axiom(implies(or(not(q),or(not(or(not(q),or(p,q))),q)),or(not(or(not(q),or(p,q))),or(not(q),q)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(118,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(q),or(not(or(not(q),or(p,q))),q)),or(not(or(not(q),or(p,q))),or(not(q),q))))
| ~ axiom(implies(or(not(q),or(not(or(not(q),or(p,q))),q)),or(not(or(not(q),or(p,q))),or(not(q),q)))) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
theorem(implies(or(not(q),or(not(or(not(q),or(p,q))),q)),or(not(or(not(q),or(p,q))),or(not(q),q)))),
inference(unit_resolution,[status(thm)],[118,48,115]) ).
tff(120,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(q),or(p,q))),or(not(q),q)))
| ~ theorem(or(not(q),or(not(or(not(q),or(p,q))),q)))
| ~ theorem(implies(or(not(q),or(not(or(not(q),or(p,q))),q)),or(not(or(not(q),or(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(p,q))),or(not(q),q)))
| ~ theorem(or(not(q),or(not(or(not(q),or(p,q))),q)))
| ~ theorem(implies(or(not(q),or(not(or(not(q),or(p,q))),q)),or(not(or(not(q),or(p,q))),or(not(q),q)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(121,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(q),or(p,q))),or(not(q),q)))
| ~ theorem(or(not(q),or(not(or(not(q),or(p,q))),q)))
| ~ theorem(implies(or(not(q),or(not(or(not(q),or(p,q))),q)),or(not(or(not(q),or(p,q))),or(not(q),q)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(122,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(q),or(p,q))),or(not(q),q)))
| ~ theorem(or(not(q),or(not(or(not(q),or(p,q))),q)))
| ~ theorem(implies(or(not(q),or(not(or(not(q),or(p,q))),q)),or(not(or(not(q),or(p,q))),or(not(q),q)))) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
( theorem(or(not(or(not(q),or(p,q))),or(not(q),q)))
| ~ theorem(or(not(q),or(not(or(not(q),or(p,q))),q))) ),
inference(unit_resolution,[status(thm)],[122,86,119]) ).
tff(124,plain,
~ theorem(or(not(q),or(not(or(not(q),or(p,q))),q))),
inference(unit_resolution,[status(thm)],[123,113]) ).
tff(125,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(q),or(not(or(not(q),or(p,q))),q)))
| ~ axiom(or(not(q),or(not(or(not(q),or(p,q))),q))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(q),or(not(or(not(q),or(p,q))),q)))
| ~ axiom(or(not(q),or(not(or(not(q),or(p,q))),q))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(126,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(q),or(not(or(not(q),or(p,q))),q)))
| ~ axiom(or(not(q),or(not(or(not(q),or(p,q))),q))) ),
inference(quant_inst,[status(thm)],]) ).
tff(127,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(q),or(not(or(not(q),or(p,q))),q)))
| ~ axiom(or(not(q),or(not(or(not(q),or(p,q))),q))) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
( theorem(or(not(q),or(not(or(not(q),or(p,q))),q)))
| ~ axiom(or(not(q),or(not(or(not(q),or(p,q))),q))) ),
inference(unit_resolution,[status(thm)],[127,48]) ).
tff(129,plain,
~ axiom(or(not(q),or(not(or(not(q),or(p,q))),q))),
inference(unit_resolution,[status(thm)],[128,124]) ).
tff(130,plain,
$false,
inference(unit_resolution,[status(thm)],[129,22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL188-3 : TPTP v8.1.0. Released v2.3.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n028.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 18:47:06 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.
% 0.64/0.63 % SZS status Unsatisfiable
% 0.64/0.63 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------