%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL311-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n003.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 02:59:47 PM UTC 2026
% Result : Unsatisfiable 23.79s 24.07s
% Output : Proof 23.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 62
% Syntax : Number of formulae : 197 ( 104 unt; 0 typ; 0 def)
% Number of atoms : 489 ( 86 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 514 ( 232 ~; 224 |; 0 &)
% ( 58 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 10 ( 3 avg)
% Number of FOOLs : 10 ( 10 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 : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 247 ( 228 !; 0 ?; 247 :)
% Comments :
%------------------------------------------------------------------------------
tff(theorem_type,type,
theorem: $i > $o ).
tff(implies_type,type,
implies: ( $i * $i ) > $i ).
tff(and_type,type,
and: ( $i * $i ) > $i ).
tff(not_type,type,
not: $i > $i ).
tff(p_type,type,
p: $i ).
tff(or_type,type,
or: ( $i * $i ) > $i ).
tff(axiom_type,type,
axiom: $i > $o ).
tff(equivalent_type,type,
equivalent: ( $i * $i ) > $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( implies(X,Y) = or(not(X),Y) )
<=> ( implies(X,Y) = or(not(X),Y) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
<=> ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
<=> ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',implies_definition) ).
tff(5,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(p,not(p)) = or(not(p),not(p)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
implies(p,not(p)) = or(not(p),not(p)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
implies(implies(p,not(p)),not(p)) = implies(or(not(p),not(p)),not(p)),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
implies(or(not(p),not(p)),not(p)) = implies(implies(p,not(p)),not(p)),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(not(p),not(p)),not(p)) = or(not(or(not(p),not(p))),not(p)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
implies(or(not(p),not(p)),not(p)) = or(not(or(not(p),not(p))),not(p)),
inference(unit_resolution,[status(thm)],[12,7]) ).
tff(14,plain,
or(not(or(not(p),not(p))),not(p)) = implies(or(not(p),not(p)),not(p)),
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
or(not(or(not(p),not(p))),not(p)) = implies(implies(p,not(p)),not(p)),
inference(transitivity,[status(thm)],[14,11]) ).
tff(16,plain,
not(or(not(or(not(p),not(p))),not(p))) = not(implies(implies(p,not(p)),not(p))),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
not(implies(implies(p,not(p)),not(p))) = not(or(not(or(not(p),not(p))),not(p))),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))) = or(not(or(not(or(not(p),not(p))),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
or(not(or(not(or(not(p),not(p))),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))) = or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(not(or(not(p),not(p))),not(p)),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))) = or(not(or(not(or(not(p),not(p))),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
implies(or(not(or(not(p),not(p))),not(p)),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))) = or(not(or(not(or(not(p),not(p))),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))),
inference(unit_resolution,[status(thm)],[20,7]) ).
tff(22,plain,
implies(or(not(or(not(p),not(p))),not(p)),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))) = or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))),
inference(transitivity,[status(thm)],[21,19]) ).
tff(23,plain,
( theorem(implies(or(not(or(not(p),not(p))),not(p)),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))))
<=> theorem(or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))))) ),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
( theorem(or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))))
<=> theorem(implies(or(not(or(not(p),not(p))),not(p)),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))))) ),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
or(not(implies(implies(p,not(p)),not(p))),not(implies(not(p),implies(p,not(p))))) = or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p))))),
inference(monotonicity,[status(thm)],[17]) ).
tff(26,plain,
or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p))))) = or(not(implies(implies(p,not(p)),not(p))),not(implies(not(p),implies(p,not(p))))),
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))) = not(or(not(implies(implies(p,not(p)),not(p))),not(implies(not(p),implies(p,not(p)))))),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
not(or(not(implies(implies(p,not(p)),not(p))),not(implies(not(p),implies(p,not(p)))))) = not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),
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/sandbox/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(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))) = not(or(not(implies(implies(p,not(p)),not(p))),not(implies(not(p),implies(p,not(p)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))) = not(or(not(implies(implies(p,not(p)),not(p))),not(implies(not(p),implies(p,not(p)))))),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))) = not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),
inference(transitivity,[status(thm)],[37,28]) ).
tff(39,plain,
or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))) = or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
implies(or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))),or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))))) = implies(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))),or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))))),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( theorem(implies(or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))),or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))))))
<=> theorem(implies(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))),or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))))) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,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(43,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)],[42]) ).
tff(44,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(45,axiom,
! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_4) ).
tff(46,plain,
! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
( ~ ! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A)))
| axiom(implies(or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))),or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
axiom(implies(or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))),or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))))),
inference(unit_resolution,[status(thm)],[49,48]) ).
tff(51,plain,
^ [X: $i] :
refl(( ( theorem(X)
| ~ axiom(X) )
<=> ( theorem(X)
| ~ axiom(X) ) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,axiom,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',rule_1) ).
tff(55,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))),or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))))))
| ~ axiom(implies(or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))),or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))),or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))))))
| ~ axiom(implies(or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))),or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))),or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))))))
| ~ axiom(implies(or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))),or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))),or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))))))
| ~ axiom(implies(or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))),or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))))) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
theorem(implies(or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))),or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))))),
inference(unit_resolution,[status(thm)],[60,57,50]) ).
tff(62,plain,
theorem(implies(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))),or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))))),
inference(modus_ponens,[status(thm)],[61,41]) ).
tff(63,plain,
implies(not(p),implies(p,not(p))) = implies(not(p),or(not(p),not(p))),
inference(monotonicity,[status(thm)],[9]) ).
tff(64,plain,
implies(not(p),or(not(p),not(p))) = implies(not(p),implies(p,not(p))),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(not(p),or(not(p),not(p))) = or(not(not(p)),or(not(p),not(p))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
implies(not(p),or(not(p),not(p))) = or(not(not(p)),or(not(p),not(p))),
inference(unit_resolution,[status(thm)],[65,7]) ).
tff(67,plain,
or(not(not(p)),or(not(p),not(p))) = implies(not(p),or(not(p),not(p))),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
or(not(not(p)),or(not(p),not(p))) = implies(not(p),implies(p,not(p))),
inference(transitivity,[status(thm)],[67,64]) ).
tff(69,plain,
not(or(not(not(p)),or(not(p),not(p)))) = not(implies(not(p),implies(p,not(p)))),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
not(implies(not(p),implies(p,not(p)))) = not(or(not(not(p)),or(not(p),not(p)))),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))) = or(not(or(not(not(p)),or(not(p),not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
or(not(or(not(not(p)),or(not(p),not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))) = or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(not(not(p)),or(not(p),not(p))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))) = or(not(or(not(not(p)),or(not(p),not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
implies(or(not(not(p)),or(not(p),not(p))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))) = or(not(or(not(not(p)),or(not(p),not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),
inference(unit_resolution,[status(thm)],[73,7]) ).
tff(75,plain,
or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))) = or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))),
inference(symmetry,[status(thm)],[39]) ).
tff(76,plain,
implies(or(not(not(p)),or(not(p),not(p))),or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p))))) = implies(or(not(not(p)),or(not(p),not(p))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
implies(or(not(not(p)),or(not(p),not(p))),or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p))))) = or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),
inference(transitivity,[status(thm)],[76,74,72]) ).
tff(78,plain,
( theorem(implies(or(not(not(p)),or(not(p),not(p))),or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p))))))
<=> theorem(or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))))) ),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
( theorem(or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))
<=> theorem(implies(or(not(not(p)),or(not(p),not(p))),or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))) ),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))) = or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),
inference(monotonicity,[status(thm)],[38]) ).
tff(81,plain,
implies(or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))))) = implies(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))))),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
( theorem(implies(or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))))))
<=> theorem(implies(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))) ),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,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(84,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)],[83]) ).
tff(85,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(86,axiom,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_5) ).
tff(87,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(skolemize,[status(sab)],[87]) ).
tff(89,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
( ~ ! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C))))
| axiom(implies(or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
axiom(implies(or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))),
inference(unit_resolution,[status(thm)],[90,89]) ).
tff(92,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))))))
| ~ axiom(implies(or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))))))
| ~ axiom(implies(or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))))))
| ~ axiom(implies(or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(94,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))))))
| ~ axiom(implies(or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
theorem(implies(or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))),
inference(unit_resolution,[status(thm)],[94,57,91]) ).
tff(96,plain,
theorem(implies(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))),
inference(modus_ponens,[status(thm)],[95,82]) ).
tff(97,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))) = or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
implies(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))) = or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),
inference(unit_resolution,[status(thm)],[97,7]) ).
tff(99,plain,
or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))) = implies(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
( theorem(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))
<=> theorem(implies(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))))) ),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
( theorem(implies(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))
<=> theorem(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))))) ),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
implies(or(not(implies(implies(p,not(p)),not(p))),not(implies(not(p),implies(p,not(p))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))) = implies(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),
inference(monotonicity,[status(thm)],[25]) ).
tff(103,plain,
( theorem(implies(or(not(implies(implies(p,not(p)),not(p))),not(implies(not(p),implies(p,not(p))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))
<=> theorem(implies(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))))) ),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
( ~ ! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A)))
| axiom(implies(or(not(implies(implies(p,not(p)),not(p))),not(implies(not(p),implies(p,not(p))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
axiom(implies(or(not(implies(implies(p,not(p)),not(p))),not(implies(not(p),implies(p,not(p))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))))),
inference(unit_resolution,[status(thm)],[104,48]) ).
tff(106,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(implies(p,not(p)),not(p))),not(implies(not(p),implies(p,not(p))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))
| ~ axiom(implies(or(not(implies(implies(p,not(p)),not(p))),not(implies(not(p),implies(p,not(p))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(implies(p,not(p)),not(p))),not(implies(not(p),implies(p,not(p))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))
| ~ axiom(implies(or(not(implies(implies(p,not(p)),not(p))),not(implies(not(p),implies(p,not(p))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(implies(p,not(p)),not(p))),not(implies(not(p),implies(p,not(p))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))
| ~ axiom(implies(or(not(implies(implies(p,not(p)),not(p))),not(implies(not(p),implies(p,not(p))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(108,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(implies(p,not(p)),not(p))),not(implies(not(p),implies(p,not(p))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))
| ~ axiom(implies(or(not(implies(implies(p,not(p)),not(p))),not(implies(not(p),implies(p,not(p))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))))) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
theorem(implies(or(not(implies(implies(p,not(p)),not(p))),not(implies(not(p),implies(p,not(p))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))))),
inference(unit_resolution,[status(thm)],[108,57,105]) ).
tff(110,plain,
theorem(implies(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))))),
inference(modus_ponens,[status(thm)],[109,103]) ).
tff(111,plain,
theorem(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))))),
inference(modus_ponens,[status(thm)],[110,101]) ).
tff(112,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(113,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)],[112]) ).
tff(114,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(115,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(116,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)],[115]) ).
tff(117,axiom,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(implies(Y,X))
| ~ theorem(Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',rule_2) ).
tff(118,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[118,114]) ).
tff(120,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(skolemize,[status(sab)],[119]) ).
tff(121,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[120,113]) ).
tff(122,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))
| ~ theorem(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))
| ~ theorem(implies(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))
| ~ theorem(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))
| ~ theorem(implies(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(123,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))
| ~ theorem(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))
| ~ theorem(implies(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(124,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))
| ~ theorem(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))
| ~ theorem(implies(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
( theorem(or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))
| ~ theorem(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))
| ~ theorem(implies(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),or(not(implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))),or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p))))))) ),
inference(unit_resolution,[status(thm)],[124,121]) ).
tff(126,plain,
theorem(or(not(implies(not(p),implies(p,not(p)))),or(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),not(implies(implies(p,not(p)),not(p)))))),
inference(unit_resolution,[status(thm)],[125,111,96]) ).
tff(127,plain,
theorem(implies(or(not(not(p)),or(not(p),not(p))),or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))),
inference(modus_ponens,[status(thm)],[126,79]) ).
tff(128,plain,
( axiom(or(not(not(p)),or(not(p),not(p))))
<=> axiom(implies(not(p),or(not(p),not(p)))) ),
inference(monotonicity,[status(thm)],[67]) ).
tff(129,plain,
( axiom(implies(not(p),or(not(p),not(p))))
<=> axiom(or(not(not(p)),or(not(p),not(p)))) ),
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
^ [B: $i,A: $i] :
refl(( axiom(implies(A,or(B,A)))
<=> axiom(implies(A,or(B,A))) )),
inference(bind,[status(th)],[]) ).
tff(131,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)],[130]) ).
tff(132,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(133,axiom,
! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_3) ).
tff(134,plain,
! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
inference(skolemize,[status(sab)],[134]) ).
tff(136,plain,
! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
inference(modus_ponens,[status(thm)],[135,131]) ).
tff(137,plain,
( ~ ! [B: $i,A: $i] : axiom(implies(A,or(B,A)))
| axiom(implies(not(p),or(not(p),not(p)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(138,plain,
axiom(implies(not(p),or(not(p),not(p)))),
inference(unit_resolution,[status(thm)],[137,136]) ).
tff(139,plain,
axiom(or(not(not(p)),or(not(p),not(p)))),
inference(modus_ponens,[status(thm)],[138,129]) ).
tff(140,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(not(p)),or(not(p),not(p))))
| ~ axiom(or(not(not(p)),or(not(p),not(p)))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(not(p)),or(not(p),not(p))))
| ~ axiom(or(not(not(p)),or(not(p),not(p)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(not(p)),or(not(p),not(p))))
| ~ axiom(or(not(not(p)),or(not(p),not(p)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(142,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(not(p)),or(not(p),not(p))))
| ~ axiom(or(not(not(p)),or(not(p),not(p)))) ),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
( theorem(or(not(not(p)),or(not(p),not(p))))
| ~ axiom(or(not(not(p)),or(not(p),not(p)))) ),
inference(unit_resolution,[status(thm)],[142,57]) ).
tff(144,plain,
theorem(or(not(not(p)),or(not(p),not(p)))),
inference(unit_resolution,[status(thm)],[143,139]) ).
tff(145,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(not(p)),or(not(p),not(p))))
| theorem(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))
| ~ theorem(implies(or(not(not(p)),or(not(p),not(p))),or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(not(p)),or(not(p),not(p))))
| theorem(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))
| ~ theorem(implies(or(not(not(p)),or(not(p),not(p))),or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(146,plain,
( ( theorem(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))
| ~ theorem(or(not(not(p)),or(not(p),not(p))))
| ~ theorem(implies(or(not(not(p)),or(not(p),not(p))),or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))) )
<=> ( ~ theorem(or(not(not(p)),or(not(p),not(p))))
| theorem(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))
| ~ theorem(implies(or(not(not(p)),or(not(p),not(p))),or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(147,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))
| ~ theorem(or(not(not(p)),or(not(p),not(p))))
| ~ theorem(implies(or(not(not(p)),or(not(p),not(p))),or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(not(p)),or(not(p),not(p))))
| theorem(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))
| ~ theorem(implies(or(not(not(p)),or(not(p),not(p))),or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))) ) ),
inference(monotonicity,[status(thm)],[146]) ).
tff(148,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))
| ~ theorem(or(not(not(p)),or(not(p),not(p))))
| ~ theorem(implies(or(not(not(p)),or(not(p),not(p))),or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(not(p)),or(not(p),not(p))))
| theorem(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))
| ~ theorem(implies(or(not(not(p)),or(not(p),not(p))),or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))) ) ),
inference(transitivity,[status(thm)],[147,145]) ).
tff(149,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))
| ~ theorem(or(not(not(p)),or(not(p),not(p))))
| ~ theorem(implies(or(not(not(p)),or(not(p),not(p))),or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(150,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| ~ theorem(or(not(not(p)),or(not(p),not(p))))
| theorem(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))
| ~ theorem(implies(or(not(not(p)),or(not(p),not(p))),or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))) ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
( theorem(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))
| ~ theorem(implies(or(not(not(p)),or(not(p),not(p))),or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))) ),
inference(unit_resolution,[status(thm)],[150,121,144]) ).
tff(152,plain,
theorem(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p))))),
inference(unit_resolution,[status(thm)],[151,127]) ).
tff(153,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))))
| ~ theorem(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))
| ~ theorem(implies(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))),or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))))
| ~ theorem(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))
| ~ theorem(implies(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))),or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(154,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))))
| ~ theorem(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))
| ~ theorem(implies(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))),or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(155,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))))
| ~ theorem(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))
| ~ theorem(implies(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))),or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))))) ),
inference(modus_ponens,[status(thm)],[154,153]) ).
tff(156,plain,
( theorem(or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))))
| ~ theorem(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))))
| ~ theorem(implies(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(implies(not(p),implies(p,not(p)))))),not(implies(implies(p,not(p)),not(p)))),or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))))) ),
inference(unit_resolution,[status(thm)],[155,121]) ).
tff(157,plain,
theorem(or(not(implies(implies(p,not(p)),not(p))),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))))),
inference(unit_resolution,[status(thm)],[156,152,62]) ).
tff(158,plain,
theorem(implies(or(not(or(not(p),not(p))),not(p)),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))))),
inference(modus_ponens,[status(thm)],[157,24]) ).
tff(159,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(160,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)],[159]) ).
tff(161,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(162,axiom,
! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-2.ax',equivalent_defn) ).
tff(163,plain,
! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ),
inference(modus_ponens,[status(thm)],[162,161]) ).
tff(164,plain,
! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ),
inference(skolemize,[status(sab)],[163]) ).
tff(165,plain,
! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ),
inference(modus_ponens,[status(thm)],[164,160]) ).
tff(166,plain,
( ~ ! [Q: $i,P: $i] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) )
| ( equivalent(implies(p,not(p)),not(p)) = and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(167,plain,
equivalent(implies(p,not(p)),not(p)) = and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))),
inference(unit_resolution,[status(thm)],[166,165]) ).
tff(168,plain,
and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))) = equivalent(implies(p,not(p)),not(p)),
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
( theorem(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))))
<=> theorem(equivalent(implies(p,not(p)),not(p))) ),
inference(monotonicity,[status(thm)],[168]) ).
tff(170,plain,
( theorem(equivalent(implies(p,not(p)),not(p)))
<=> theorem(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))) ),
inference(symmetry,[status(thm)],[169]) ).
tff(171,plain,
( ~ theorem(equivalent(implies(p,not(p)),not(p)))
<=> ~ theorem(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))) ),
inference(monotonicity,[status(thm)],[170]) ).
tff(172,plain,
( ~ theorem(equivalent(implies(p,not(p)),not(p)))
<=> ~ theorem(equivalent(implies(p,not(p)),not(p))) ),
inference(rewrite,[status(thm)],[]) ).
tff(173,axiom,
~ theorem(equivalent(implies(p,not(p)),not(p))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(174,plain,
~ theorem(equivalent(implies(p,not(p)),not(p))),
inference(modus_ponens,[status(thm)],[173,172]) ).
tff(175,plain,
~ theorem(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p))))),
inference(modus_ponens,[status(thm)],[174,171]) ).
tff(176,plain,
( axiom(or(not(or(not(p),not(p))),not(p)))
<=> axiom(implies(or(not(p),not(p)),not(p))) ),
inference(monotonicity,[status(thm)],[14]) ).
tff(177,plain,
( axiom(implies(or(not(p),not(p)),not(p)))
<=> axiom(or(not(or(not(p),not(p))),not(p))) ),
inference(symmetry,[status(thm)],[176]) ).
tff(178,plain,
^ [A: $i] :
refl(( axiom(implies(or(A,A),A))
<=> axiom(implies(or(A,A),A)) )),
inference(bind,[status(th)],[]) ).
tff(179,plain,
( ! [A: $i] : axiom(implies(or(A,A),A))
<=> ! [A: $i] : axiom(implies(or(A,A),A)) ),
inference(quant_intro,[status(thm)],[178]) ).
tff(180,plain,
( ! [A: $i] : axiom(implies(or(A,A),A))
<=> ! [A: $i] : axiom(implies(or(A,A),A)) ),
inference(rewrite,[status(thm)],[]) ).
tff(181,axiom,
! [A: $i] : axiom(implies(or(A,A),A)),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_2) ).
tff(182,plain,
! [A: $i] : axiom(implies(or(A,A),A)),
inference(modus_ponens,[status(thm)],[181,180]) ).
tff(183,plain,
! [A: $i] : axiom(implies(or(A,A),A)),
inference(skolemize,[status(sab)],[182]) ).
tff(184,plain,
! [A: $i] : axiom(implies(or(A,A),A)),
inference(modus_ponens,[status(thm)],[183,179]) ).
tff(185,plain,
( ~ ! [A: $i] : axiom(implies(or(A,A),A))
| axiom(implies(or(not(p),not(p)),not(p))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(186,plain,
axiom(implies(or(not(p),not(p)),not(p))),
inference(unit_resolution,[status(thm)],[185,184]) ).
tff(187,plain,
axiom(or(not(or(not(p),not(p))),not(p))),
inference(modus_ponens,[status(thm)],[186,177]) ).
tff(188,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(or(not(p),not(p))),not(p)))
| ~ axiom(or(not(or(not(p),not(p))),not(p))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(or(not(p),not(p))),not(p)))
| ~ axiom(or(not(or(not(p),not(p))),not(p))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(189,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(or(not(p),not(p))),not(p)))
| ~ axiom(or(not(or(not(p),not(p))),not(p))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(190,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(or(not(p),not(p))),not(p)))
| ~ axiom(or(not(or(not(p),not(p))),not(p))) ),
inference(modus_ponens,[status(thm)],[189,188]) ).
tff(191,plain,
( theorem(or(not(or(not(p),not(p))),not(p)))
| ~ axiom(or(not(or(not(p),not(p))),not(p))) ),
inference(unit_resolution,[status(thm)],[190,57]) ).
tff(192,plain,
theorem(or(not(or(not(p),not(p))),not(p))),
inference(unit_resolution,[status(thm)],[191,187]) ).
tff(193,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))))
| ~ theorem(or(not(or(not(p),not(p))),not(p)))
| ~ theorem(implies(or(not(or(not(p),not(p))),not(p)),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))))
| ~ theorem(or(not(or(not(p),not(p))),not(p)))
| ~ theorem(implies(or(not(or(not(p),not(p))),not(p)),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(194,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))))
| ~ theorem(or(not(or(not(p),not(p))),not(p)))
| ~ theorem(implies(or(not(or(not(p),not(p))),not(p)),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(195,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))))
| ~ theorem(or(not(or(not(p),not(p))),not(p)))
| ~ theorem(implies(or(not(or(not(p),not(p))),not(p)),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))))) ),
inference(modus_ponens,[status(thm)],[194,193]) ).
tff(196,plain,
~ theorem(implies(or(not(or(not(p),not(p))),not(p)),and(implies(implies(p,not(p)),not(p)),implies(not(p),implies(p,not(p)))))),
inference(unit_resolution,[status(thm)],[195,121,192,175]) ).
tff(197,plain,
$false,
inference(unit_resolution,[status(thm)],[196,158]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL311-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.06/0.34 % Computer : n003.cluster.edu
% 0.06/0.34 % Model : x86_64 x86_64
% 0.06/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.34 % Memory : 8046.5625MB
% 0.06/0.34 % OS : Linux 6.8.0-71-generic
% 0.06/0.34 % CPULimit : 300
% 0.06/0.34 % WCLimit : 300
% 0.06/0.34 % DateTime : Sat Sep 5 20:39:38 UTC 2026
% 0.06/0.34 % CPUTime :
% 23.79/24.07 % SZS status Unsatisfiable
% 23.79/24.07 % SZS output start Proof
% See solution above
% 0.13/24.39 % E exiting
%------------------------------------------------------------------------------