%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL219-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 02:59:36 PM UTC 2026
% Result : Unsatisfiable 165.96s 166.25s
% Output : Proof 167.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 85
% Syntax : Number of formulae : 242 ( 97 unt; 0 typ; 0 def)
% Number of atoms : 797 ( 55 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1038 ( 491 ~; 469 |; 0 &)
% ( 78 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 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 : 331 ( 314 !; 0 ?; 331 :)
% Comments :
%------------------------------------------------------------------------------
tff(theorem_type,type,
theorem: $i > $o ).
tff(implies_type,type,
implies: ( $i * $i ) > $i ).
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(axiom_type,type,
axiom: $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(or(not(p),q),or(not(or(q,not(implies(p,q)))),q)) = or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
implies(or(not(p),q),or(not(or(q,not(implies(p,q)))),q)) = or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
implies(implies(or(not(p),q),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q)))) = implies(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q)))),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( theorem(implies(implies(or(not(p),q),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q)))))
<=> theorem(implies(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( theorem(implies(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q)))))
<=> theorem(implies(implies(or(not(p),q),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))) ),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( ~ theorem(implies(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q)))))
<=> ~ theorem(implies(implies(or(not(p),q),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,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(15,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)],[14]) ).
tff(16,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(17,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(18,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
( ~ ! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C))))
| axiom(implies(or(p,or(not(or(q,not(implies(p,q)))),q)),or(not(or(q,not(implies(p,q)))),or(p,q)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
axiom(implies(or(p,or(not(or(q,not(implies(p,q)))),q)),or(not(or(q,not(implies(p,q)))),or(p,q)))),
inference(unit_resolution,[status(thm)],[21,20]) ).
tff(23,plain,
^ [X: $i] :
refl(( ( theorem(X)
| ~ axiom(X) )
<=> ( theorem(X)
| ~ axiom(X) ) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',rule_1) ).
tff(27,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(p,or(not(or(q,not(implies(p,q)))),q)),or(not(or(q,not(implies(p,q)))),or(p,q))))
| ~ axiom(implies(or(p,or(not(or(q,not(implies(p,q)))),q)),or(not(or(q,not(implies(p,q)))),or(p,q)))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(p,or(not(or(q,not(implies(p,q)))),q)),or(not(or(q,not(implies(p,q)))),or(p,q))))
| ~ axiom(implies(or(p,or(not(or(q,not(implies(p,q)))),q)),or(not(or(q,not(implies(p,q)))),or(p,q)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(p,or(not(or(q,not(implies(p,q)))),q)),or(not(or(q,not(implies(p,q)))),or(p,q))))
| ~ axiom(implies(or(p,or(not(or(q,not(implies(p,q)))),q)),or(not(or(q,not(implies(p,q)))),or(p,q)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(p,or(not(or(q,not(implies(p,q)))),q)),or(not(or(q,not(implies(p,q)))),or(p,q))))
| ~ axiom(implies(or(p,or(not(or(q,not(implies(p,q)))),q)),or(not(or(q,not(implies(p,q)))),or(p,q)))) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
theorem(implies(or(p,or(not(or(q,not(implies(p,q)))),q)),or(not(or(q,not(implies(p,q)))),or(p,q)))),
inference(unit_resolution,[status(thm)],[32,29,22]) ).
tff(34,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(q,not(implies(p,q))),or(p,q)) = or(not(or(q,not(implies(p,q)))),or(p,q)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
implies(or(q,not(implies(p,q))),or(p,q)) = or(not(or(q,not(implies(p,q)))),or(p,q)),
inference(unit_resolution,[status(thm)],[34,7]) ).
tff(36,plain,
or(not(or(q,not(implies(p,q)))),or(p,q)) = implies(or(q,not(implies(p,q))),or(p,q)),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
( theorem(or(not(or(q,not(implies(p,q)))),or(p,q)))
<=> theorem(implies(or(q,not(implies(p,q))),or(p,q))) ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( theorem(implies(or(q,not(implies(p,q))),or(p,q)))
<=> theorem(or(not(or(q,not(implies(p,q)))),or(p,q))) ),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
( ~ theorem(implies(or(q,not(implies(p,q))),or(p,q)))
<=> ~ theorem(or(not(or(q,not(implies(p,q)))),or(p,q))) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,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(41,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)],[40]) ).
tff(42,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(43,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(44,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
( ~ ! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B))))
| axiom(implies(implies(or(q,not(implies(p,q))),or(p,q)),implies(or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
axiom(implies(implies(or(q,not(implies(p,q))),or(p,q)),implies(or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q))))),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(or(q,not(implies(p,q))),or(p,q)),implies(or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q)))))
| ~ axiom(implies(implies(or(q,not(implies(p,q))),or(p,q)),implies(or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q))))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(or(q,not(implies(p,q))),or(p,q)),implies(or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q)))))
| ~ axiom(implies(implies(or(q,not(implies(p,q))),or(p,q)),implies(or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(or(q,not(implies(p,q))),or(p,q)),implies(or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q)))))
| ~ axiom(implies(implies(or(q,not(implies(p,q))),or(p,q)),implies(or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(or(q,not(implies(p,q))),or(p,q)),implies(or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q)))))
| ~ axiom(implies(implies(or(q,not(implies(p,q))),or(p,q)),implies(or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q))))) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
theorem(implies(implies(or(q,not(implies(p,q))),or(p,q)),implies(or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q))))),
inference(unit_resolution,[status(thm)],[51,29,48]) ).
tff(53,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(54,plain,
implies(implies(p,q),q) = or(not(implies(p,q)),q),
inference(unit_resolution,[status(thm)],[53,7]) ).
tff(55,plain,
or(not(implies(p,q)),q) = implies(implies(p,q),q),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
not(or(not(implies(p,q)),q)) = not(implies(implies(p,q),q)),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
not(implies(implies(p,q),q)) = not(or(not(implies(p,q)),q)),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))) = or(not(or(not(implies(p,q)),q)),or(q,not(implies(p,q)))),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
implies(or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q))) = implies(or(not(or(not(implies(p,q)),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q))),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( theorem(implies(or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q))))
<=> theorem(implies(or(not(or(not(implies(p,q)),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q)))) ),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
( theorem(implies(or(not(or(not(implies(p,q)),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q))))
<=> theorem(implies(or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q)))) ),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
( ~ theorem(implies(or(not(or(not(implies(p,q)),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q))))
<=> ~ theorem(implies(or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q)))) ),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(not(implies(p,q)),q),or(q,not(implies(p,q)))) = or(not(or(not(implies(p,q)),q)),or(q,not(implies(p,q)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
implies(or(not(implies(p,q)),q),or(q,not(implies(p,q)))) = or(not(or(not(implies(p,q)),q)),or(q,not(implies(p,q)))),
inference(unit_resolution,[status(thm)],[63,7]) ).
tff(65,plain,
or(not(or(not(implies(p,q)),q)),or(q,not(implies(p,q)))) = implies(or(not(implies(p,q)),q),or(q,not(implies(p,q)))),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
( theorem(or(not(or(not(implies(p,q)),q)),or(q,not(implies(p,q)))))
<=> theorem(implies(or(not(implies(p,q)),q),or(q,not(implies(p,q))))) ),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
( theorem(implies(or(not(implies(p,q)),q),or(q,not(implies(p,q)))))
<=> theorem(or(not(or(not(implies(p,q)),q)),or(q,not(implies(p,q))))) ),
inference(symmetry,[status(thm)],[66]) ).
tff(68,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(69,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)],[68]) ).
tff(70,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(71,axiom,
! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',axiom_1_4) ).
tff(72,plain,
! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
inference(skolemize,[status(sab)],[72]) ).
tff(74,plain,
! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
inference(modus_ponens,[status(thm)],[73,69]) ).
tff(75,plain,
( ~ ! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A)))
| axiom(implies(or(not(implies(p,q)),q),or(q,not(implies(p,q))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
axiom(implies(or(not(implies(p,q)),q),or(q,not(implies(p,q))))),
inference(unit_resolution,[status(thm)],[75,74]) ).
tff(77,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(p,q)),q),or(q,not(implies(p,q)))))
| ~ axiom(implies(or(not(implies(p,q)),q),or(q,not(implies(p,q))))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(p,q)),q),or(q,not(implies(p,q)))))
| ~ axiom(implies(or(not(implies(p,q)),q),or(q,not(implies(p,q))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(p,q)),q),or(q,not(implies(p,q)))))
| ~ axiom(implies(or(not(implies(p,q)),q),or(q,not(implies(p,q))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(p,q)),q),or(q,not(implies(p,q)))))
| ~ axiom(implies(or(not(implies(p,q)),q),or(q,not(implies(p,q))))) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
theorem(implies(or(not(implies(p,q)),q),or(q,not(implies(p,q))))),
inference(unit_resolution,[status(thm)],[79,29,76]) ).
tff(81,plain,
theorem(or(not(or(not(implies(p,q)),q)),or(q,not(implies(p,q))))),
inference(modus_ponens,[status(thm)],[80,67]) ).
tff(82,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(implies(implies(p,q),q),or(p,q)) = or(not(implies(implies(p,q),q)),or(p,q)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
implies(implies(implies(p,q),q),or(p,q)) = or(not(implies(implies(p,q),q)),or(p,q)),
inference(unit_resolution,[status(thm)],[82,7]) ).
tff(84,plain,
or(not(implies(implies(p,q),q)),or(p,q)) = implies(implies(implies(p,q),q),or(p,q)),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
( theorem(or(not(implies(implies(p,q),q)),or(p,q)))
<=> theorem(implies(implies(implies(p,q),q),or(p,q))) ),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
( theorem(implies(implies(implies(p,q),q),or(p,q)))
<=> theorem(or(not(implies(implies(p,q),q)),or(p,q))) ),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
( ~ theorem(implies(implies(implies(p,q),q),or(p,q)))
<=> ~ theorem(or(not(implies(implies(p,q),q)),or(p,q))) ),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
( ~ theorem(implies(implies(implies(p,q),q),or(p,q)))
<=> ~ theorem(implies(implies(implies(p,q),q),or(p,q))) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,axiom,
~ theorem(implies(implies(implies(p,q),q),or(p,q))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(90,plain,
~ theorem(implies(implies(implies(p,q),q),or(p,q))),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
~ theorem(or(not(implies(implies(p,q),q)),or(p,q))),
inference(modus_ponens,[status(thm)],[90,87]) ).
tff(92,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(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(quant_intro,[status(thm)],[92]) ).
tff(94,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(95,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(96,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)],[95]) ).
tff(97,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(98,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[98,94]) ).
tff(100,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(skolemize,[status(sab)],[99]) ).
tff(101,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[100,93]) ).
tff(102,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(implies(p,q),q)),or(p,q)))
| ~ theorem(or(not(or(not(implies(p,q)),q)),or(q,not(implies(p,q)))))
| ~ theorem(implies(or(not(or(not(implies(p,q)),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(implies(p,q),q)),or(p,q)))
| ~ theorem(or(not(or(not(implies(p,q)),q)),or(q,not(implies(p,q)))))
| ~ theorem(implies(or(not(or(not(implies(p,q)),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(103,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(implies(p,q),q)),or(p,q)))
| ~ theorem(or(not(or(not(implies(p,q)),q)),or(q,not(implies(p,q)))))
| ~ theorem(implies(or(not(or(not(implies(p,q)),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(104,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(implies(p,q),q)),or(p,q)))
| ~ theorem(or(not(or(not(implies(p,q)),q)),or(q,not(implies(p,q)))))
| ~ theorem(implies(or(not(or(not(implies(p,q)),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q)))) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
( ~ theorem(or(not(or(not(implies(p,q)),q)),or(q,not(implies(p,q)))))
| ~ theorem(implies(or(not(or(not(implies(p,q)),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q)))) ),
inference(unit_resolution,[status(thm)],[104,101,91]) ).
tff(106,plain,
~ theorem(implies(or(not(or(not(implies(p,q)),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q)))),
inference(unit_resolution,[status(thm)],[105,81]) ).
tff(107,plain,
~ theorem(implies(or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q)))),
inference(modus_ponens,[status(thm)],[106,62]) ).
tff(108,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q))))
| ~ theorem(implies(or(q,not(implies(p,q))),or(p,q)))
| ~ theorem(implies(implies(or(q,not(implies(p,q))),or(p,q)),implies(or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q))))
| ~ theorem(implies(or(q,not(implies(p,q))),or(p,q)))
| ~ theorem(implies(implies(or(q,not(implies(p,q))),or(p,q)),implies(or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q))))
| ~ theorem(implies(or(q,not(implies(p,q))),or(p,q)))
| ~ theorem(implies(implies(or(q,not(implies(p,q))),or(p,q)),implies(or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q))))
| ~ theorem(implies(or(q,not(implies(p,q))),or(p,q)))
| ~ theorem(implies(implies(or(q,not(implies(p,q))),or(p,q)),implies(or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q))))) ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
( theorem(implies(or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q))))
| ~ theorem(implies(or(q,not(implies(p,q))),or(p,q)))
| ~ theorem(implies(implies(or(q,not(implies(p,q))),or(p,q)),implies(or(not(implies(implies(p,q),q)),or(q,not(implies(p,q)))),or(not(implies(implies(p,q),q)),or(p,q))))) ),
inference(unit_resolution,[status(thm)],[110,101]) ).
tff(112,plain,
~ theorem(implies(or(q,not(implies(p,q))),or(p,q))),
inference(unit_resolution,[status(thm)],[111,107,52]) ).
tff(113,plain,
~ theorem(or(not(or(q,not(implies(p,q)))),or(p,q))),
inference(modus_ponens,[status(thm)],[112,39]) ).
tff(114,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(q,not(implies(p,q)))),or(p,q)))
| ~ theorem(or(p,or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(implies(or(p,or(not(or(q,not(implies(p,q)))),q)),or(not(or(q,not(implies(p,q)))),or(p,q)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(q,not(implies(p,q)))),or(p,q)))
| ~ theorem(or(p,or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(implies(or(p,or(not(or(q,not(implies(p,q)))),q)),or(not(or(q,not(implies(p,q)))),or(p,q)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(115,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(q,not(implies(p,q)))),or(p,q)))
| ~ theorem(or(p,or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(implies(or(p,or(not(or(q,not(implies(p,q)))),q)),or(not(or(q,not(implies(p,q)))),or(p,q)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(116,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(q,not(implies(p,q)))),or(p,q)))
| ~ theorem(or(p,or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(implies(or(p,or(not(or(q,not(implies(p,q)))),q)),or(not(or(q,not(implies(p,q)))),or(p,q)))) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
( theorem(or(not(or(q,not(implies(p,q)))),or(p,q)))
| ~ theorem(or(p,or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(implies(or(p,or(not(or(q,not(implies(p,q)))),q)),or(not(or(q,not(implies(p,q)))),or(p,q)))) ),
inference(unit_resolution,[status(thm)],[116,101]) ).
tff(118,plain,
~ theorem(or(p,or(not(or(q,not(implies(p,q)))),q))),
inference(unit_resolution,[status(thm)],[117,113,33]) ).
tff(119,plain,
( ~ ! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C))))
| axiom(implies(or(not(p),or(p,q)),or(p,or(not(p),q)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(120,plain,
axiom(implies(or(not(p),or(p,q)),or(p,or(not(p),q)))),
inference(unit_resolution,[status(thm)],[119,20]) ).
tff(121,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(p),or(p,q)),or(p,or(not(p),q))))
| ~ axiom(implies(or(not(p),or(p,q)),or(p,or(not(p),q)))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(p),or(p,q)),or(p,or(not(p),q))))
| ~ axiom(implies(or(not(p),or(p,q)),or(p,or(not(p),q)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(p),or(p,q)),or(p,or(not(p),q))))
| ~ axiom(implies(or(not(p),or(p,q)),or(p,or(not(p),q)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(123,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(p),or(p,q)),or(p,or(not(p),q))))
| ~ axiom(implies(or(not(p),or(p,q)),or(p,or(not(p),q)))) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
theorem(implies(or(not(p),or(p,q)),or(p,or(not(p),q)))),
inference(unit_resolution,[status(thm)],[123,29,120]) ).
tff(125,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(q,p),or(p,q)) = or(not(or(q,p)),or(p,q)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(126,plain,
implies(or(q,p),or(p,q)) = or(not(or(q,p)),or(p,q)),
inference(unit_resolution,[status(thm)],[125,7]) ).
tff(127,plain,
implies(implies(or(q,p),or(p,q)),implies(or(not(p),or(q,p)),or(not(p),or(p,q)))) = implies(or(not(or(q,p)),or(p,q)),implies(or(not(p),or(q,p)),or(not(p),or(p,q)))),
inference(monotonicity,[status(thm)],[126]) ).
tff(128,plain,
( theorem(implies(implies(or(q,p),or(p,q)),implies(or(not(p),or(q,p)),or(not(p),or(p,q)))))
<=> theorem(implies(or(not(or(q,p)),or(p,q)),implies(or(not(p),or(q,p)),or(not(p),or(p,q))))) ),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
( ~ ! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B))))
| axiom(implies(implies(or(q,p),or(p,q)),implies(or(not(p),or(q,p)),or(not(p),or(p,q))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(130,plain,
axiom(implies(implies(or(q,p),or(p,q)),implies(or(not(p),or(q,p)),or(not(p),or(p,q))))),
inference(unit_resolution,[status(thm)],[129,46]) ).
tff(131,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(or(q,p),or(p,q)),implies(or(not(p),or(q,p)),or(not(p),or(p,q)))))
| ~ axiom(implies(implies(or(q,p),or(p,q)),implies(or(not(p),or(q,p)),or(not(p),or(p,q))))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(or(q,p),or(p,q)),implies(or(not(p),or(q,p)),or(not(p),or(p,q)))))
| ~ axiom(implies(implies(or(q,p),or(p,q)),implies(or(not(p),or(q,p)),or(not(p),or(p,q))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(132,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(or(q,p),or(p,q)),implies(or(not(p),or(q,p)),or(not(p),or(p,q)))))
| ~ axiom(implies(implies(or(q,p),or(p,q)),implies(or(not(p),or(q,p)),or(not(p),or(p,q))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(133,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(or(q,p),or(p,q)),implies(or(not(p),or(q,p)),or(not(p),or(p,q)))))
| ~ axiom(implies(implies(or(q,p),or(p,q)),implies(or(not(p),or(q,p)),or(not(p),or(p,q))))) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
theorem(implies(implies(or(q,p),or(p,q)),implies(or(not(p),or(q,p)),or(not(p),or(p,q))))),
inference(unit_resolution,[status(thm)],[133,29,130]) ).
tff(135,plain,
theorem(implies(or(not(or(q,p)),or(p,q)),implies(or(not(p),or(q,p)),or(not(p),or(p,q))))),
inference(modus_ponens,[status(thm)],[134,128]) ).
tff(136,plain,
or(not(or(q,p)),or(p,q)) = implies(or(q,p),or(p,q)),
inference(symmetry,[status(thm)],[126]) ).
tff(137,plain,
( theorem(or(not(or(q,p)),or(p,q)))
<=> theorem(implies(or(q,p),or(p,q))) ),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
( theorem(implies(or(q,p),or(p,q)))
<=> theorem(or(not(or(q,p)),or(p,q))) ),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
( ~ ! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A)))
| axiom(implies(or(q,p),or(p,q))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(140,plain,
axiom(implies(or(q,p),or(p,q))),
inference(unit_resolution,[status(thm)],[139,74]) ).
tff(141,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(q,p),or(p,q)))
| ~ axiom(implies(or(q,p),or(p,q))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(q,p),or(p,q)))
| ~ axiom(implies(or(q,p),or(p,q))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(142,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(q,p),or(p,q)))
| ~ axiom(implies(or(q,p),or(p,q))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(143,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(q,p),or(p,q)))
| ~ axiom(implies(or(q,p),or(p,q))) ),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
theorem(implies(or(q,p),or(p,q))),
inference(unit_resolution,[status(thm)],[143,29,140]) ).
tff(145,plain,
theorem(or(not(or(q,p)),or(p,q))),
inference(modus_ponens,[status(thm)],[144,138]) ).
tff(146,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(not(p),or(q,p)),or(not(p),or(p,q))))
| ~ theorem(or(not(or(q,p)),or(p,q)))
| ~ theorem(implies(or(not(or(q,p)),or(p,q)),implies(or(not(p),or(q,p)),or(not(p),or(p,q))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(not(p),or(q,p)),or(not(p),or(p,q))))
| ~ theorem(or(not(or(q,p)),or(p,q)))
| ~ theorem(implies(or(not(or(q,p)),or(p,q)),implies(or(not(p),or(q,p)),or(not(p),or(p,q))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(147,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(not(p),or(q,p)),or(not(p),or(p,q))))
| ~ theorem(or(not(or(q,p)),or(p,q)))
| ~ theorem(implies(or(not(or(q,p)),or(p,q)),implies(or(not(p),or(q,p)),or(not(p),or(p,q))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(148,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(not(p),or(q,p)),or(not(p),or(p,q))))
| ~ theorem(or(not(or(q,p)),or(p,q)))
| ~ theorem(implies(or(not(or(q,p)),or(p,q)),implies(or(not(p),or(q,p)),or(not(p),or(p,q))))) ),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
( theorem(implies(or(not(p),or(q,p)),or(not(p),or(p,q))))
| ~ theorem(implies(or(not(or(q,p)),or(p,q)),implies(or(not(p),or(q,p)),or(not(p),or(p,q))))) ),
inference(unit_resolution,[status(thm)],[148,101,145]) ).
tff(150,plain,
theorem(implies(or(not(p),or(q,p)),or(not(p),or(p,q)))),
inference(unit_resolution,[status(thm)],[149,135]) ).
tff(151,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(p,or(q,p)) = or(not(p),or(q,p)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(152,plain,
implies(p,or(q,p)) = or(not(p),or(q,p)),
inference(unit_resolution,[status(thm)],[151,7]) ).
tff(153,plain,
or(not(p),or(q,p)) = implies(p,or(q,p)),
inference(symmetry,[status(thm)],[152]) ).
tff(154,plain,
( theorem(or(not(p),or(q,p)))
<=> theorem(implies(p,or(q,p))) ),
inference(monotonicity,[status(thm)],[153]) ).
tff(155,plain,
( theorem(implies(p,or(q,p)))
<=> theorem(or(not(p),or(q,p))) ),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
^ [B: $i,A: $i] :
refl(( axiom(implies(A,or(B,A)))
<=> axiom(implies(A,or(B,A))) )),
inference(bind,[status(th)],[]) ).
tff(157,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)],[156]) ).
tff(158,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(159,axiom,
! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',axiom_1_3) ).
tff(160,plain,
! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
inference(skolemize,[status(sab)],[160]) ).
tff(162,plain,
! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
inference(modus_ponens,[status(thm)],[161,157]) ).
tff(163,plain,
( ~ ! [B: $i,A: $i] : axiom(implies(A,or(B,A)))
| axiom(implies(p,or(q,p))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(164,plain,
axiom(implies(p,or(q,p))),
inference(unit_resolution,[status(thm)],[163,162]) ).
tff(165,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(p,or(q,p)))
| ~ axiom(implies(p,or(q,p))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(p,or(q,p)))
| ~ axiom(implies(p,or(q,p))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(166,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(p,or(q,p)))
| ~ axiom(implies(p,or(q,p))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(167,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(p,or(q,p)))
| ~ axiom(implies(p,or(q,p))) ),
inference(modus_ponens,[status(thm)],[166,165]) ).
tff(168,plain,
theorem(implies(p,or(q,p))),
inference(unit_resolution,[status(thm)],[167,29,164]) ).
tff(169,plain,
theorem(or(not(p),or(q,p))),
inference(modus_ponens,[status(thm)],[168,155]) ).
tff(170,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(p),or(p,q)))
| ~ theorem(or(not(p),or(q,p)))
| ~ theorem(implies(or(not(p),or(q,p)),or(not(p),or(p,q)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(p),or(p,q)))
| ~ theorem(or(not(p),or(q,p)))
| ~ theorem(implies(or(not(p),or(q,p)),or(not(p),or(p,q)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(171,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(p),or(p,q)))
| ~ theorem(or(not(p),or(q,p)))
| ~ theorem(implies(or(not(p),or(q,p)),or(not(p),or(p,q)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(172,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(p),or(p,q)))
| ~ theorem(or(not(p),or(q,p)))
| ~ theorem(implies(or(not(p),or(q,p)),or(not(p),or(p,q)))) ),
inference(modus_ponens,[status(thm)],[171,170]) ).
tff(173,plain,
( theorem(or(not(p),or(p,q)))
| ~ theorem(implies(or(not(p),or(q,p)),or(not(p),or(p,q)))) ),
inference(unit_resolution,[status(thm)],[172,101,169]) ).
tff(174,plain,
theorem(or(not(p),or(p,q))),
inference(unit_resolution,[status(thm)],[173,150]) ).
tff(175,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(p),or(p,q)))
| theorem(or(p,or(not(p),q)))
| ~ theorem(implies(or(not(p),or(p,q)),or(p,or(not(p),q)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(p),or(p,q)))
| theorem(or(p,or(not(p),q)))
| ~ theorem(implies(or(not(p),or(p,q)),or(p,or(not(p),q)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(176,plain,
( ( theorem(or(p,or(not(p),q)))
| ~ theorem(or(not(p),or(p,q)))
| ~ theorem(implies(or(not(p),or(p,q)),or(p,or(not(p),q)))) )
<=> ( ~ theorem(or(not(p),or(p,q)))
| theorem(or(p,or(not(p),q)))
| ~ theorem(implies(or(not(p),or(p,q)),or(p,or(not(p),q)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(177,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(p,or(not(p),q)))
| ~ theorem(or(not(p),or(p,q)))
| ~ theorem(implies(or(not(p),or(p,q)),or(p,or(not(p),q)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(p),or(p,q)))
| theorem(or(p,or(not(p),q)))
| ~ theorem(implies(or(not(p),or(p,q)),or(p,or(not(p),q)))) ) ),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(p,or(not(p),q)))
| ~ theorem(or(not(p),or(p,q)))
| ~ theorem(implies(or(not(p),or(p,q)),or(p,or(not(p),q)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(p),or(p,q)))
| theorem(or(p,or(not(p),q)))
| ~ theorem(implies(or(not(p),or(p,q)),or(p,or(not(p),q)))) ) ),
inference(transitivity,[status(thm)],[177,175]) ).
tff(179,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(p,or(not(p),q)))
| ~ theorem(or(not(p),or(p,q)))
| ~ theorem(implies(or(not(p),or(p,q)),or(p,or(not(p),q)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(180,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(p),or(p,q)))
| theorem(or(p,or(not(p),q)))
| ~ theorem(implies(or(not(p),or(p,q)),or(p,or(not(p),q)))) ),
inference(modus_ponens,[status(thm)],[179,178]) ).
tff(181,plain,
( ~ theorem(or(not(p),or(p,q)))
| theorem(or(p,or(not(p),q)))
| ~ theorem(implies(or(not(p),or(p,q)),or(p,or(not(p),q)))) ),
inference(unit_resolution,[status(thm)],[180,101]) ).
tff(182,plain,
theorem(or(p,or(not(p),q))),
inference(unit_resolution,[status(thm)],[181,174,124]) ).
tff(183,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(p,or(not(p),q)))
| theorem(or(p,or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(p,or(not(p),q)))
| theorem(or(p,or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(184,plain,
( ( theorem(or(p,or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(or(p,or(not(p),q)))
| ~ theorem(implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q)))) )
<=> ( ~ theorem(or(p,or(not(p),q)))
| theorem(or(p,or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(185,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(p,or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(or(p,or(not(p),q)))
| ~ theorem(implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(p,or(not(p),q)))
| theorem(or(p,or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q)))) ) ),
inference(monotonicity,[status(thm)],[184]) ).
tff(186,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(p,or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(or(p,or(not(p),q)))
| ~ theorem(implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(p,or(not(p),q)))
| theorem(or(p,or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q)))) ) ),
inference(transitivity,[status(thm)],[185,183]) ).
tff(187,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(p,or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(or(p,or(not(p),q)))
| ~ theorem(implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(188,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(p,or(not(p),q)))
| theorem(or(p,or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q)))) ),
inference(modus_ponens,[status(thm)],[187,186]) ).
tff(189,plain,
( ~ theorem(or(p,or(not(p),q)))
| theorem(or(p,or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q)))) ),
inference(unit_resolution,[status(thm)],[188,101]) ).
tff(190,plain,
~ theorem(implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q)))),
inference(unit_resolution,[status(thm)],[189,182,118]) ).
tff(191,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(192,plain,
implies(p,q) = or(not(p),q),
inference(unit_resolution,[status(thm)],[191,7]) ).
tff(193,plain,
or(not(p),q) = implies(p,q),
inference(symmetry,[status(thm)],[192]) ).
tff(194,plain,
not(or(not(p),q)) = not(implies(p,q)),
inference(monotonicity,[status(thm)],[193]) ).
tff(195,plain,
not(implies(p,q)) = not(or(not(p),q)),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)) = or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)),
inference(monotonicity,[status(thm)],[195]) ).
tff(197,plain,
or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)) = or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)),
inference(symmetry,[status(thm)],[196]) ).
tff(198,plain,
( theorem(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)))
<=> theorem(or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q))) ),
inference(monotonicity,[status(thm)],[197]) ).
tff(199,plain,
( theorem(or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))
<=> theorem(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q))) ),
inference(symmetry,[status(thm)],[198]) ).
tff(200,plain,
( ~ ! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C))))
| axiom(implies(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)),or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(201,plain,
axiom(implies(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)),or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))),
inference(unit_resolution,[status(thm)],[200,20]) ).
tff(202,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)),or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q))))
| ~ axiom(implies(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)),or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)),or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q))))
| ~ axiom(implies(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)),or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(203,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)),or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q))))
| ~ axiom(implies(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)),or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(204,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)),or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q))))
| ~ axiom(implies(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)),or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))) ),
inference(modus_ponens,[status(thm)],[203,202]) ).
tff(205,plain,
theorem(implies(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)),or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))),
inference(unit_resolution,[status(thm)],[204,29,201]) ).
tff(206,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(q,not(implies(p,q))),or(not(implies(p,q)),q)) = or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(207,plain,
implies(or(q,not(implies(p,q))),or(not(implies(p,q)),q)) = or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)),
inference(unit_resolution,[status(thm)],[206,7]) ).
tff(208,plain,
or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)) = implies(or(q,not(implies(p,q))),or(not(implies(p,q)),q)),
inference(symmetry,[status(thm)],[207]) ).
tff(209,plain,
( theorem(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)))
<=> theorem(implies(or(q,not(implies(p,q))),or(not(implies(p,q)),q))) ),
inference(monotonicity,[status(thm)],[208]) ).
tff(210,plain,
( theorem(implies(or(q,not(implies(p,q))),or(not(implies(p,q)),q)))
<=> theorem(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q))) ),
inference(symmetry,[status(thm)],[209]) ).
tff(211,plain,
( ~ ! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A)))
| axiom(implies(or(q,not(implies(p,q))),or(not(implies(p,q)),q))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(212,plain,
axiom(implies(or(q,not(implies(p,q))),or(not(implies(p,q)),q))),
inference(unit_resolution,[status(thm)],[211,74]) ).
tff(213,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(q,not(implies(p,q))),or(not(implies(p,q)),q)))
| ~ axiom(implies(or(q,not(implies(p,q))),or(not(implies(p,q)),q))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(q,not(implies(p,q))),or(not(implies(p,q)),q)))
| ~ axiom(implies(or(q,not(implies(p,q))),or(not(implies(p,q)),q))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(214,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(q,not(implies(p,q))),or(not(implies(p,q)),q)))
| ~ axiom(implies(or(q,not(implies(p,q))),or(not(implies(p,q)),q))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(215,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(q,not(implies(p,q))),or(not(implies(p,q)),q)))
| ~ axiom(implies(or(q,not(implies(p,q))),or(not(implies(p,q)),q))) ),
inference(modus_ponens,[status(thm)],[214,213]) ).
tff(216,plain,
theorem(implies(or(q,not(implies(p,q))),or(not(implies(p,q)),q))),
inference(unit_resolution,[status(thm)],[215,29,212]) ).
tff(217,plain,
theorem(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q))),
inference(modus_ponens,[status(thm)],[216,210]) ).
tff(218,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)))
| theorem(or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(implies(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)),or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)))
| theorem(or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(implies(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)),or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(219,plain,
( ( theorem(or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)))
| ~ theorem(implies(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)),or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))) )
<=> ( ~ theorem(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)))
| theorem(or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(implies(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)),or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(220,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)))
| ~ theorem(implies(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)),or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)))
| theorem(or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(implies(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)),or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))) ) ),
inference(monotonicity,[status(thm)],[219]) ).
tff(221,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)))
| ~ theorem(implies(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)),or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)))
| theorem(or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(implies(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)),or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))) ) ),
inference(transitivity,[status(thm)],[220,218]) ).
tff(222,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)))
| ~ theorem(implies(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)),or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(223,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)))
| theorem(or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(implies(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)),or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))) ),
inference(modus_ponens,[status(thm)],[222,221]) ).
tff(224,plain,
( ~ theorem(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)))
| theorem(or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(implies(or(not(or(q,not(implies(p,q)))),or(not(implies(p,q)),q)),or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q)))) ),
inference(unit_resolution,[status(thm)],[223,101]) ).
tff(225,plain,
theorem(or(not(implies(p,q)),or(not(or(q,not(implies(p,q)))),q))),
inference(unit_resolution,[status(thm)],[224,217,205]) ).
tff(226,plain,
theorem(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q))),
inference(modus_ponens,[status(thm)],[225,199]) ).
tff(227,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)))
| theorem(implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))
| ~ theorem(implies(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)))
| theorem(implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))
| ~ theorem(implies(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(228,plain,
( ( theorem(implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))
| ~ theorem(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(implies(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))) )
<=> ( ~ theorem(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)))
| theorem(implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))
| ~ theorem(implies(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(229,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))
| ~ theorem(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(implies(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)))
| theorem(implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))
| ~ theorem(implies(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))) ) ),
inference(monotonicity,[status(thm)],[228]) ).
tff(230,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))
| ~ theorem(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(implies(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)))
| theorem(implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))
| ~ theorem(implies(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))) ) ),
inference(transitivity,[status(thm)],[229,227]) ).
tff(231,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))
| ~ theorem(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)))
| ~ theorem(implies(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(232,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)))
| theorem(implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))
| ~ theorem(implies(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))) ),
inference(modus_ponens,[status(thm)],[231,230]) ).
tff(233,plain,
( theorem(implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))
| ~ theorem(implies(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))) ),
inference(unit_resolution,[status(thm)],[232,101,226]) ).
tff(234,plain,
~ theorem(implies(or(not(or(not(p),q)),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))),
inference(unit_resolution,[status(thm)],[233,190]) ).
tff(235,plain,
~ theorem(implies(implies(or(not(p),q),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))),
inference(modus_ponens,[status(thm)],[234,13]) ).
tff(236,plain,
( ~ ! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B))))
| axiom(implies(implies(or(not(p),q),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(237,plain,
axiom(implies(implies(or(not(p),q),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))),
inference(unit_resolution,[status(thm)],[236,46]) ).
tff(238,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(or(not(p),q),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q)))))
| ~ axiom(implies(implies(or(not(p),q),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(or(not(p),q),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q)))))
| ~ axiom(implies(implies(or(not(p),q),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(239,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(or(not(p),q),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q)))))
| ~ axiom(implies(implies(or(not(p),q),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(240,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(or(not(p),q),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q)))))
| ~ axiom(implies(implies(or(not(p),q),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))) ),
inference(modus_ponens,[status(thm)],[239,238]) ).
tff(241,plain,
theorem(implies(implies(or(not(p),q),or(not(or(q,not(implies(p,q)))),q)),implies(or(p,or(not(p),q)),or(p,or(not(or(q,not(implies(p,q)))),q))))),
inference(unit_resolution,[status(thm)],[240,29,237]) ).
tff(242,plain,
$false,
inference(unit_resolution,[status(thm)],[241,235]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL219-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.07/0.34 % Computer : n007.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 4 20:22:25 UTC 2026
% 0.07/0.35 % CPUTime :
% 165.96/166.25 % SZS status Unsatisfiable
% 165.96/166.25 % SZS output start Proof
% See solution above
% 0.15/168.04 % E exiting
%------------------------------------------------------------------------------