%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL296-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n017.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 02:59:45 PM UTC 2026
% Result : Unsatisfiable 108.66s 108.92s
% Output : Proof 109.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 59
% Syntax : Number of formulae : 169 ( 81 unt; 0 typ; 0 def)
% Number of atoms : 455 ( 70 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 508 ( 231 ~; 224 |; 0 &)
% ( 53 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 9 ( 9 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 : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 229 ( 212 !; 0 ?; 229 :)
% Comments :
%------------------------------------------------------------------------------
tff(theorem_type,type,
theorem: $i > $o ).
tff(and_type,type,
and: ( $i * $i ) > $i ).
tff(implies_type,type,
implies: ( $i * $i ) > $i ).
tff(not_type,type,
not: $i > $i ).
tff(q_type,type,
q: $i ).
tff(p_type,type,
p: $i ).
tff(or_type,type,
or: ( $i * $i ) > $i ).
tff(equivalent_type,type,
equivalent: ( $i * $i ) > $i ).
tff(axiom_type,type,
axiom: $i > $o ).
tff(1,plain,
^ [Q: $i,P: $i] :
refl(( ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) )
<=> ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) )
<=> ! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) )
<=> ! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-2.ax',equivalent_defn) ).
tff(5,plain,
! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) )
| ( equivalent(implies(p,not(q)),or(not(p),not(q))) = and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
equivalent(implies(p,not(q)),or(not(p),not(q))) = and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))) = equivalent(implies(p,not(q)),or(not(p),not(q))),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( theorem(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))
<=> theorem(equivalent(implies(p,not(q)),or(not(p),not(q)))) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( theorem(equivalent(implies(p,not(q)),or(not(p),not(q))))
<=> theorem(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))) ),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( ~ theorem(equivalent(implies(p,not(q)),or(not(p),not(q))))
<=> ~ theorem(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ~ theorem(equivalent(implies(p,not(q)),or(not(p),not(q))))
<=> ~ theorem(equivalent(implies(p,not(q)),or(not(p),not(q)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
~ theorem(equivalent(implies(p,not(q)),or(not(p),not(q)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(16,plain,
~ theorem(equivalent(implies(p,not(q)),or(not(p),not(q)))),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
~ theorem(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))),
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,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(19,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)],[18]) ).
tff(20,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(21,axiom,
! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',implies_definition) ).
tff(22,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(implies(or(not(p),not(q)),or(not(p),not(q))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))) = or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
implies(implies(or(not(p),not(q)),or(not(p),not(q))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))) = or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
( theorem(implies(implies(or(not(p),not(q)),or(not(p),not(q))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))))
<=> theorem(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( theorem(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))))
<=> theorem(implies(implies(or(not(p),not(q)),or(not(p),not(q))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))) ),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
^ [Q: $i,P: $i] :
refl(( ( and(P,Q) = not(or(not(P),not(Q))) )
<=> ( and(P,Q) = not(or(not(P),not(Q))) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) )
<=> ! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) )
<=> ! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-1.ax',and_defn) ).
tff(33,plain,
! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ~ ! [Q: $i,P: $i] : ( and(P,Q) = not(or(not(P),not(Q))) )
| ( and(implies(or(not(p),not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),or(not(p),not(q)))) = not(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
and(implies(or(not(p),not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),or(not(p),not(q)))) = not(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(p,not(q)) = or(not(p),not(q)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
implies(p,not(q)) = or(not(p),not(q)),
inference(unit_resolution,[status(thm)],[38,24]) ).
tff(40,plain,
implies(or(not(p),not(q)),implies(p,not(q))) = implies(or(not(p),not(q)),or(not(p),not(q))),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
implies(or(not(p),not(q)),or(not(p),not(q))) = implies(or(not(p),not(q)),implies(p,not(q))),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
implies(implies(p,not(q)),or(not(p),not(q))) = implies(or(not(p),not(q)),or(not(p),not(q))),
inference(monotonicity,[status(thm)],[39]) ).
tff(43,plain,
implies(or(not(p),not(q)),or(not(p),not(q))) = implies(implies(p,not(q)),or(not(p),not(q))),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
and(implies(or(not(p),not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),or(not(p),not(q)))) = and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))),
inference(monotonicity,[status(thm)],[43,41]) ).
tff(45,plain,
and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))) = and(implies(or(not(p),not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),or(not(p),not(q)))),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))) = not(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))),
inference(transitivity,[status(thm)],[45,37]) ).
tff(47,plain,
or(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))) = or(not(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
implies(or(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))) = implies(or(not(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( theorem(implies(or(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))))
<=> theorem(implies(or(not(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))))) ),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,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(51,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)],[50]) ).
tff(52,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(53,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(54,plain,
! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
( ~ ! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A)))
| axiom(implies(or(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
axiom(implies(or(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))))),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
^ [X: $i] :
refl(( ( theorem(X)
| ~ axiom(X) )
<=> ( theorem(X)
| ~ axiom(X) ) )),
inference(bind,[status(th)],[]) ).
tff(60,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,axiom,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',rule_1) ).
tff(63,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))))
| ~ axiom(implies(or(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))))
| ~ axiom(implies(or(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))))
| ~ axiom(implies(or(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))))
| ~ axiom(implies(or(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))))) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
theorem(implies(or(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))))),
inference(unit_resolution,[status(thm)],[68,65,58]) ).
tff(70,plain,
theorem(implies(or(not(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))))),
inference(modus_ponens,[status(thm)],[69,49]) ).
tff(71,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),not(implies(or(not(p),not(q)),or(not(p),not(q))))) = or(not(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))),not(implies(or(not(p),not(q)),or(not(p),not(q))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
implies(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),not(implies(or(not(p),not(q)),or(not(p),not(q))))) = or(not(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),
inference(unit_resolution,[status(thm)],[71,24]) ).
tff(73,plain,
or(not(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))),not(implies(or(not(p),not(q)),or(not(p),not(q))))) = implies(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
( theorem(or(not(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))),not(implies(or(not(p),not(q)),or(not(p),not(q))))))
<=> theorem(implies(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))) ),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( theorem(implies(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),not(implies(or(not(p),not(q)),or(not(p),not(q))))))
<=> theorem(or(not(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))) ),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
^ [A: $i] :
refl(( axiom(implies(or(A,A),A))
<=> axiom(implies(or(A,A),A)) )),
inference(bind,[status(th)],[]) ).
tff(77,plain,
( ! [A: $i] : axiom(implies(or(A,A),A))
<=> ! [A: $i] : axiom(implies(or(A,A),A)) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,plain,
( ! [A: $i] : axiom(implies(or(A,A),A))
<=> ! [A: $i] : axiom(implies(or(A,A),A)) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,axiom,
! [A: $i] : axiom(implies(or(A,A),A)),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',axiom_1_2) ).
tff(80,plain,
! [A: $i] : axiom(implies(or(A,A),A)),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [A: $i] : axiom(implies(or(A,A),A)),
inference(skolemize,[status(sab)],[80]) ).
tff(82,plain,
! [A: $i] : axiom(implies(or(A,A),A)),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
( ~ ! [A: $i] : axiom(implies(or(A,A),A))
| axiom(implies(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
axiom(implies(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))),
inference(unit_resolution,[status(thm)],[83,82]) ).
tff(85,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),not(implies(or(not(p),not(q)),or(not(p),not(q))))))
| ~ axiom(implies(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),not(implies(or(not(p),not(q)),or(not(p),not(q))))))
| ~ axiom(implies(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),not(implies(or(not(p),not(q)),or(not(p),not(q))))))
| ~ axiom(implies(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),not(implies(or(not(p),not(q)),or(not(p),not(q))))))
| ~ axiom(implies(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
theorem(implies(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))),
inference(unit_resolution,[status(thm)],[87,65,84]) ).
tff(89,plain,
theorem(or(not(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))),
inference(modus_ponens,[status(thm)],[88,75]) ).
tff(90,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(91,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)],[90]) ).
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(rewrite,[status(thm)],[]) ).
tff(93,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(94,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)],[93]) ).
tff(95,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(96,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[96,92]) ).
tff(98,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(skolemize,[status(sab)],[97]) ).
tff(99,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[98,91]) ).
tff(100,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))))
| ~ theorem(or(not(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))),not(implies(or(not(p),not(q)),or(not(p),not(q))))))
| ~ theorem(implies(or(not(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))))
| ~ theorem(or(not(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))),not(implies(or(not(p),not(q)),or(not(p),not(q))))))
| ~ theorem(implies(or(not(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))))
| ~ theorem(or(not(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))),not(implies(or(not(p),not(q)),or(not(p),not(q))))))
| ~ theorem(implies(or(not(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))))
| ~ theorem(or(not(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))),not(implies(or(not(p),not(q)),or(not(p),not(q))))))
| ~ theorem(implies(or(not(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))))) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
( theorem(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))))
| ~ theorem(or(not(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))),not(implies(or(not(p),not(q)),or(not(p),not(q))))))
| ~ theorem(implies(or(not(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),not(implies(or(not(p),not(q)),or(not(p),not(q)))))),not(implies(or(not(p),not(q)),or(not(p),not(q))))),or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q))))))) ),
inference(unit_resolution,[status(thm)],[102,99]) ).
tff(104,plain,
theorem(or(not(implies(or(not(p),not(q)),or(not(p),not(q)))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))),
inference(unit_resolution,[status(thm)],[103,89,70]) ).
tff(105,plain,
theorem(implies(implies(or(not(p),not(q)),or(not(p),not(q))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))),
inference(modus_ponens,[status(thm)],[104,28]) ).
tff(106,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(not(p),not(q)),or(not(q),not(p))) = or(not(or(not(p),not(q))),or(not(q),not(p))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(107,plain,
implies(or(not(p),not(q)),or(not(q),not(p))) = or(not(or(not(p),not(q))),or(not(q),not(p))),
inference(unit_resolution,[status(thm)],[106,24]) ).
tff(108,plain,
or(not(or(not(p),not(q))),or(not(q),not(p))) = implies(or(not(p),not(q)),or(not(q),not(p))),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
( theorem(or(not(or(not(p),not(q))),or(not(q),not(p))))
<=> theorem(implies(or(not(p),not(q)),or(not(q),not(p)))) ),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
( theorem(implies(or(not(p),not(q)),or(not(q),not(p))))
<=> theorem(or(not(or(not(p),not(q))),or(not(q),not(p)))) ),
inference(symmetry,[status(thm)],[109]) ).
tff(111,plain,
( ~ ! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A)))
| axiom(implies(or(not(p),not(q)),or(not(q),not(p)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
axiom(implies(or(not(p),not(q)),or(not(q),not(p)))),
inference(unit_resolution,[status(thm)],[111,56]) ).
tff(113,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(p),not(q)),or(not(q),not(p))))
| ~ axiom(implies(or(not(p),not(q)),or(not(q),not(p)))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(p),not(q)),or(not(q),not(p))))
| ~ axiom(implies(or(not(p),not(q)),or(not(q),not(p)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(p),not(q)),or(not(q),not(p))))
| ~ axiom(implies(or(not(p),not(q)),or(not(q),not(p)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(p),not(q)),or(not(q),not(p))))
| ~ axiom(implies(or(not(p),not(q)),or(not(q),not(p)))) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
theorem(implies(or(not(p),not(q)),or(not(q),not(p)))),
inference(unit_resolution,[status(thm)],[115,65,112]) ).
tff(117,plain,
theorem(or(not(or(not(p),not(q))),or(not(q),not(p)))),
inference(modus_ponens,[status(thm)],[116,110]) ).
tff(118,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(not(p),not(q)),or(not(p),not(q))) = or(not(or(not(p),not(q))),or(not(p),not(q))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(119,plain,
implies(or(not(p),not(q)),or(not(p),not(q))) = or(not(or(not(p),not(q))),or(not(p),not(q))),
inference(unit_resolution,[status(thm)],[118,24]) ).
tff(120,plain,
or(not(or(not(p),not(q))),or(not(p),not(q))) = implies(or(not(p),not(q)),or(not(p),not(q))),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q)))) = implies(or(not(or(not(p),not(q))),or(not(q),not(p))),implies(or(not(p),not(q)),or(not(p),not(q)))),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
( theorem(implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q)))))
<=> theorem(implies(or(not(or(not(p),not(q))),or(not(q),not(p))),implies(or(not(p),not(q)),or(not(p),not(q))))) ),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(not(q),not(p)),or(not(p),not(q))) = or(not(or(not(q),not(p))),or(not(p),not(q))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(124,plain,
implies(or(not(q),not(p)),or(not(p),not(q))) = or(not(or(not(q),not(p))),or(not(p),not(q))),
inference(unit_resolution,[status(thm)],[123,24]) ).
tff(125,plain,
implies(implies(or(not(q),not(p)),or(not(p),not(q))),implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q))))) = implies(or(not(or(not(q),not(p))),or(not(p),not(q))),implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q))))),
inference(monotonicity,[status(thm)],[124]) ).
tff(126,plain,
( theorem(implies(implies(or(not(q),not(p)),or(not(p),not(q))),implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q))))))
<=> theorem(implies(or(not(or(not(q),not(p))),or(not(p),not(q))),implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q)))))) ),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,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(128,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)],[127]) ).
tff(129,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(130,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(131,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(skolemize,[status(sab)],[131]) ).
tff(133,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(modus_ponens,[status(thm)],[132,128]) ).
tff(134,plain,
( ~ ! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B))))
| axiom(implies(implies(or(not(q),not(p)),or(not(p),not(q))),implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(135,plain,
axiom(implies(implies(or(not(q),not(p)),or(not(p),not(q))),implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q)))))),
inference(unit_resolution,[status(thm)],[134,133]) ).
tff(136,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(or(not(q),not(p)),or(not(p),not(q))),implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q))))))
| ~ axiom(implies(implies(or(not(q),not(p)),or(not(p),not(q))),implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q)))))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(or(not(q),not(p)),or(not(p),not(q))),implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q))))))
| ~ axiom(implies(implies(or(not(q),not(p)),or(not(p),not(q))),implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(137,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(or(not(q),not(p)),or(not(p),not(q))),implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q))))))
| ~ axiom(implies(implies(or(not(q),not(p)),or(not(p),not(q))),implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(138,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(or(not(q),not(p)),or(not(p),not(q))),implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q))))))
| ~ axiom(implies(implies(or(not(q),not(p)),or(not(p),not(q))),implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q)))))) ),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
theorem(implies(implies(or(not(q),not(p)),or(not(p),not(q))),implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q)))))),
inference(unit_resolution,[status(thm)],[138,65,135]) ).
tff(140,plain,
theorem(implies(or(not(or(not(q),not(p))),or(not(p),not(q))),implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q)))))),
inference(modus_ponens,[status(thm)],[139,126]) ).
tff(141,plain,
or(not(or(not(q),not(p))),or(not(p),not(q))) = implies(or(not(q),not(p)),or(not(p),not(q))),
inference(symmetry,[status(thm)],[124]) ).
tff(142,plain,
( theorem(or(not(or(not(q),not(p))),or(not(p),not(q))))
<=> theorem(implies(or(not(q),not(p)),or(not(p),not(q)))) ),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,plain,
( theorem(implies(or(not(q),not(p)),or(not(p),not(q))))
<=> theorem(or(not(or(not(q),not(p))),or(not(p),not(q)))) ),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
( ~ ! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A)))
| axiom(implies(or(not(q),not(p)),or(not(p),not(q)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
axiom(implies(or(not(q),not(p)),or(not(p),not(q)))),
inference(unit_resolution,[status(thm)],[144,56]) ).
tff(146,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(q),not(p)),or(not(p),not(q))))
| ~ axiom(implies(or(not(q),not(p)),or(not(p),not(q)))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(q),not(p)),or(not(p),not(q))))
| ~ axiom(implies(or(not(q),not(p)),or(not(p),not(q)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(147,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(q),not(p)),or(not(p),not(q))))
| ~ axiom(implies(or(not(q),not(p)),or(not(p),not(q)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(148,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(q),not(p)),or(not(p),not(q))))
| ~ axiom(implies(or(not(q),not(p)),or(not(p),not(q)))) ),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
theorem(implies(or(not(q),not(p)),or(not(p),not(q)))),
inference(unit_resolution,[status(thm)],[148,65,145]) ).
tff(150,plain,
theorem(or(not(or(not(q),not(p))),or(not(p),not(q)))),
inference(modus_ponens,[status(thm)],[149,143]) ).
tff(151,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q)))))
| ~ theorem(or(not(or(not(q),not(p))),or(not(p),not(q))))
| ~ theorem(implies(or(not(or(not(q),not(p))),or(not(p),not(q))),implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q)))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q)))))
| ~ theorem(or(not(or(not(q),not(p))),or(not(p),not(q))))
| ~ theorem(implies(or(not(or(not(q),not(p))),or(not(p),not(q))),implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(152,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q)))))
| ~ theorem(or(not(or(not(q),not(p))),or(not(p),not(q))))
| ~ theorem(implies(or(not(or(not(q),not(p))),or(not(p),not(q))),implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(153,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q)))))
| ~ theorem(or(not(or(not(q),not(p))),or(not(p),not(q))))
| ~ theorem(implies(or(not(or(not(q),not(p))),or(not(p),not(q))),implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q)))))) ),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
( theorem(implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q)))))
| ~ theorem(or(not(or(not(q),not(p))),or(not(p),not(q))))
| ~ theorem(implies(or(not(or(not(q),not(p))),or(not(p),not(q))),implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q)))))) ),
inference(unit_resolution,[status(thm)],[153,99]) ).
tff(155,plain,
theorem(implies(or(not(or(not(p),not(q))),or(not(q),not(p))),or(not(or(not(p),not(q))),or(not(p),not(q))))),
inference(unit_resolution,[status(thm)],[154,150,140]) ).
tff(156,plain,
theorem(implies(or(not(or(not(p),not(q))),or(not(q),not(p))),implies(or(not(p),not(q)),or(not(p),not(q))))),
inference(modus_ponens,[status(thm)],[155,122]) ).
tff(157,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(not(p),not(q)),or(not(p),not(q))))
| ~ theorem(or(not(or(not(p),not(q))),or(not(q),not(p))))
| ~ theorem(implies(or(not(or(not(p),not(q))),or(not(q),not(p))),implies(or(not(p),not(q)),or(not(p),not(q))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(not(p),not(q)),or(not(p),not(q))))
| ~ theorem(or(not(or(not(p),not(q))),or(not(q),not(p))))
| ~ theorem(implies(or(not(or(not(p),not(q))),or(not(q),not(p))),implies(or(not(p),not(q)),or(not(p),not(q))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(158,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(not(p),not(q)),or(not(p),not(q))))
| ~ theorem(or(not(or(not(p),not(q))),or(not(q),not(p))))
| ~ theorem(implies(or(not(or(not(p),not(q))),or(not(q),not(p))),implies(or(not(p),not(q)),or(not(p),not(q))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(159,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(not(p),not(q)),or(not(p),not(q))))
| ~ theorem(or(not(or(not(p),not(q))),or(not(q),not(p))))
| ~ theorem(implies(or(not(or(not(p),not(q))),or(not(q),not(p))),implies(or(not(p),not(q)),or(not(p),not(q))))) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
( theorem(implies(or(not(p),not(q)),or(not(p),not(q))))
| ~ theorem(or(not(or(not(p),not(q))),or(not(q),not(p))))
| ~ theorem(implies(or(not(or(not(p),not(q))),or(not(q),not(p))),implies(or(not(p),not(q)),or(not(p),not(q))))) ),
inference(unit_resolution,[status(thm)],[159,99]) ).
tff(161,plain,
theorem(implies(or(not(p),not(q)),or(not(p),not(q)))),
inference(unit_resolution,[status(thm)],[160,156,117]) ).
tff(162,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(implies(or(not(p),not(q)),or(not(p),not(q))))
| theorem(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))
| ~ theorem(implies(implies(or(not(p),not(q)),or(not(p),not(q))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(implies(or(not(p),not(q)),or(not(p),not(q))))
| theorem(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))
| ~ theorem(implies(implies(or(not(p),not(q)),or(not(p),not(q))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(163,plain,
( ( theorem(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))
| ~ theorem(implies(or(not(p),not(q)),or(not(p),not(q))))
| ~ theorem(implies(implies(or(not(p),not(q)),or(not(p),not(q))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))) )
<=> ( ~ theorem(implies(or(not(p),not(q)),or(not(p),not(q))))
| theorem(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))
| ~ theorem(implies(implies(or(not(p),not(q)),or(not(p),not(q))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(164,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))
| ~ theorem(implies(or(not(p),not(q)),or(not(p),not(q))))
| ~ theorem(implies(implies(or(not(p),not(q)),or(not(p),not(q))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(implies(or(not(p),not(q)),or(not(p),not(q))))
| theorem(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))
| ~ theorem(implies(implies(or(not(p),not(q)),or(not(p),not(q))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))) ) ),
inference(monotonicity,[status(thm)],[163]) ).
tff(165,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))
| ~ theorem(implies(or(not(p),not(q)),or(not(p),not(q))))
| ~ theorem(implies(implies(or(not(p),not(q)),or(not(p),not(q))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(implies(or(not(p),not(q)),or(not(p),not(q))))
| theorem(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))
| ~ theorem(implies(implies(or(not(p),not(q)),or(not(p),not(q))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))) ) ),
inference(transitivity,[status(thm)],[164,162]) ).
tff(166,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))
| ~ theorem(implies(or(not(p),not(q)),or(not(p),not(q))))
| ~ theorem(implies(implies(or(not(p),not(q)),or(not(p),not(q))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(167,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(implies(or(not(p),not(q)),or(not(p),not(q))))
| theorem(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))
| ~ theorem(implies(implies(or(not(p),not(q)),or(not(p),not(q))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))) ),
inference(modus_ponens,[status(thm)],[166,165]) ).
tff(168,plain,
( theorem(and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))
| ~ theorem(implies(implies(or(not(p),not(q)),or(not(p),not(q))),and(implies(implies(p,not(q)),or(not(p),not(q))),implies(or(not(p),not(q)),implies(p,not(q)))))) ),
inference(unit_resolution,[status(thm)],[167,99,161]) ).
tff(169,plain,
$false,
inference(unit_resolution,[status(thm)],[168,105,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL296-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.09/0.34 % Computer : n017.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 11:35:53 UTC 2026
% 0.09/0.35 % CPUTime :
% 108.66/108.92 % SZS status Unsatisfiable
% 108.66/108.92 % SZS output start Proof
% See solution above
% 0.14/109.98 % E exiting
%------------------------------------------------------------------------------