%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL176-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n016.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 02:59:27 PM UTC 2026
% Result : Unsatisfiable 1.88s 2.19s
% Output : Proof 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 52
% Syntax : Number of formulae : 142 ( 62 unt; 0 typ; 0 def)
% Number of atoms : 393 ( 31 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 454 ( 211 ~; 197 |; 0 &)
% ( 46 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 217 ( 200 !; 0 ?; 217 :)
% Comments :
%------------------------------------------------------------------------------
tff(axiom_type,type,
axiom: $i > $o ).
tff(or_type,type,
or: ( $i * $i ) > $i ).
tff(p_type,type,
p: $i ).
tff(not_type,type,
not: $i > $i ).
tff(implies_type,type,
implies: ( $i * $i ) > $i ).
tff(theorem_type,type,
theorem: $i > $o ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( implies(X,Y) = or(not(X),Y) )
<=> ( implies(X,Y) = or(not(X),Y) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
<=> ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
<=> ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',implies_definition) ).
tff(5,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(p,or(not(or(not(or(not(p),p)),or(not(p),p))),p)) = or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
implies(p,or(not(or(not(or(not(p),p)),or(not(p),p))),p)) = or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)) = implies(p,or(not(or(not(or(not(p),p)),or(not(p),p))),p)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( axiom(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)))
<=> axiom(implies(p,or(not(or(not(or(not(p),p)),or(not(p),p))),p))) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( axiom(implies(p,or(not(or(not(or(not(p),p)),or(not(p),p))),p)))
<=> axiom(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p))) ),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
^ [B: $i,A: $i] :
refl(( axiom(implies(A,or(B,A)))
<=> axiom(implies(A,or(B,A))) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [B: $i,A: $i] : axiom(implies(A,or(B,A)))
<=> ! [B: $i,A: $i] : axiom(implies(A,or(B,A))) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [B: $i,A: $i] : axiom(implies(A,or(B,A)))
<=> ! [B: $i,A: $i] : axiom(implies(A,or(B,A))) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',axiom_1_3) ).
tff(17,plain,
! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
( ~ ! [B: $i,A: $i] : axiom(implies(A,or(B,A)))
| axiom(implies(p,or(not(or(not(or(not(p),p)),or(not(p),p))),p))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
axiom(implies(p,or(not(or(not(or(not(p),p)),or(not(p),p))),p))),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
axiom(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p))),
inference(modus_ponens,[status(thm)],[21,12]) ).
tff(23,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(not(or(not(p),p)),or(not(p),p)),or(not(p),p)) = or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
implies(or(not(or(not(p),p)),or(not(p),p)),or(not(p),p)) = or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p)),
inference(unit_resolution,[status(thm)],[23,7]) ).
tff(25,plain,
or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p)) = implies(or(not(or(not(p),p)),or(not(p),p)),or(not(p),p)),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
( theorem(or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p)))
<=> theorem(implies(or(not(or(not(p),p)),or(not(p),p)),or(not(p),p))) ),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
( theorem(implies(or(not(or(not(p),p)),or(not(p),p)),or(not(p),p)))
<=> theorem(or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p))) ),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
( ~ theorem(implies(or(not(or(not(p),p)),or(not(p),p)),or(not(p),p)))
<=> ~ theorem(or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p))) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(not(p),p),or(p,not(p))) = or(not(or(not(p),p)),or(p,not(p))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
implies(or(not(p),p),or(p,not(p))) = or(not(or(not(p),p)),or(p,not(p))),
inference(unit_resolution,[status(thm)],[29,7]) ).
tff(31,plain,
or(not(or(not(p),p)),or(p,not(p))) = implies(or(not(p),p),or(p,not(p))),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
( theorem(or(not(or(not(p),p)),or(p,not(p))))
<=> theorem(implies(or(not(p),p),or(p,not(p)))) ),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
( theorem(implies(or(not(p),p),or(p,not(p))))
<=> theorem(or(not(or(not(p),p)),or(p,not(p)))) ),
inference(symmetry,[status(thm)],[32]) ).
tff(34,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(35,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)],[34]) ).
tff(36,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(37,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(38,plain,
! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ~ ! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A)))
| axiom(implies(or(not(p),p),or(p,not(p)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
axiom(implies(or(not(p),p),or(p,not(p)))),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
^ [X: $i] :
refl(( ( theorem(X)
| ~ axiom(X) )
<=> ( theorem(X)
| ~ axiom(X) ) )),
inference(bind,[status(th)],[]) ).
tff(44,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,axiom,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',rule_1) ).
tff(47,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(p),p),or(p,not(p))))
| ~ axiom(implies(or(not(p),p),or(p,not(p)))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(p),p),or(p,not(p))))
| ~ axiom(implies(or(not(p),p),or(p,not(p)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(p),p),or(p,not(p))))
| ~ axiom(implies(or(not(p),p),or(p,not(p)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(p),p),or(p,not(p))))
| ~ axiom(implies(or(not(p),p),or(p,not(p)))) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
theorem(implies(or(not(p),p),or(p,not(p)))),
inference(unit_resolution,[status(thm)],[52,49,42]) ).
tff(54,plain,
theorem(or(not(or(not(p),p)),or(p,not(p)))),
inference(modus_ponens,[status(thm)],[53,33]) ).
tff(55,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(p,not(p)),or(not(p),p)) = or(not(or(p,not(p))),or(not(p),p)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
implies(or(p,not(p)),or(not(p),p)) = or(not(or(p,not(p))),or(not(p),p)),
inference(unit_resolution,[status(thm)],[55,7]) ).
tff(57,plain,
implies(implies(or(p,not(p)),or(not(p),p)),implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p)))) = implies(or(not(or(p,not(p))),or(not(p),p)),implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p)))),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
( theorem(implies(implies(or(p,not(p)),or(not(p),p)),implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p)))))
<=> theorem(implies(or(not(or(p,not(p))),or(not(p),p)),implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p))))) ),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,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(60,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)],[59]) ).
tff(61,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(62,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(63,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
( ~ ! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B))))
| axiom(implies(implies(or(p,not(p)),or(not(p),p)),implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
axiom(implies(implies(or(p,not(p)),or(not(p),p)),implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p))))),
inference(unit_resolution,[status(thm)],[66,65]) ).
tff(68,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(or(p,not(p)),or(not(p),p)),implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p)))))
| ~ axiom(implies(implies(or(p,not(p)),or(not(p),p)),implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p))))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(or(p,not(p)),or(not(p),p)),implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p)))))
| ~ axiom(implies(implies(or(p,not(p)),or(not(p),p)),implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(or(p,not(p)),or(not(p),p)),implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p)))))
| ~ axiom(implies(implies(or(p,not(p)),or(not(p),p)),implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(or(p,not(p)),or(not(p),p)),implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p)))))
| ~ axiom(implies(implies(or(p,not(p)),or(not(p),p)),implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p))))) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
theorem(implies(implies(or(p,not(p)),or(not(p),p)),implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p))))),
inference(unit_resolution,[status(thm)],[70,49,67]) ).
tff(72,plain,
theorem(implies(or(not(or(p,not(p))),or(not(p),p)),implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p))))),
inference(modus_ponens,[status(thm)],[71,58]) ).
tff(73,plain,
or(not(or(p,not(p))),or(not(p),p)) = implies(or(p,not(p)),or(not(p),p)),
inference(symmetry,[status(thm)],[56]) ).
tff(74,plain,
( theorem(or(not(or(p,not(p))),or(not(p),p)))
<=> theorem(implies(or(p,not(p)),or(not(p),p))) ),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( theorem(implies(or(p,not(p)),or(not(p),p)))
<=> theorem(or(not(or(p,not(p))),or(not(p),p))) ),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
( ~ ! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A)))
| axiom(implies(or(p,not(p)),or(not(p),p))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
axiom(implies(or(p,not(p)),or(not(p),p))),
inference(unit_resolution,[status(thm)],[76,40]) ).
tff(78,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(p,not(p)),or(not(p),p)))
| ~ axiom(implies(or(p,not(p)),or(not(p),p))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(p,not(p)),or(not(p),p)))
| ~ axiom(implies(or(p,not(p)),or(not(p),p))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(p,not(p)),or(not(p),p)))
| ~ axiom(implies(or(p,not(p)),or(not(p),p))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(p,not(p)),or(not(p),p)))
| ~ axiom(implies(or(p,not(p)),or(not(p),p))) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
theorem(implies(or(p,not(p)),or(not(p),p))),
inference(unit_resolution,[status(thm)],[80,49,77]) ).
tff(82,plain,
theorem(or(not(or(p,not(p))),or(not(p),p))),
inference(modus_ponens,[status(thm)],[81,75]) ).
tff(83,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(84,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)],[83]) ).
tff(85,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(86,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(87,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)],[86]) ).
tff(88,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(89,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(skolemize,[status(sab)],[90]) ).
tff(92,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[91,84]) ).
tff(93,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p))))
| ~ theorem(or(not(or(p,not(p))),or(not(p),p)))
| ~ theorem(implies(or(not(or(p,not(p))),or(not(p),p)),implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p))))
| ~ theorem(or(not(or(p,not(p))),or(not(p),p)))
| ~ theorem(implies(or(not(or(p,not(p))),or(not(p),p)),implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p))))
| ~ theorem(or(not(or(p,not(p))),or(not(p),p)))
| ~ theorem(implies(or(not(or(p,not(p))),or(not(p),p)),implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(95,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p))))
| ~ theorem(or(not(or(p,not(p))),or(not(p),p)))
| ~ theorem(implies(or(not(or(p,not(p))),or(not(p),p)),implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p))))) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
( theorem(implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p))))
| ~ theorem(or(not(or(p,not(p))),or(not(p),p)))
| ~ theorem(implies(or(not(or(p,not(p))),or(not(p),p)),implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p))))) ),
inference(unit_resolution,[status(thm)],[95,92]) ).
tff(97,plain,
theorem(implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p)))),
inference(unit_resolution,[status(thm)],[96,82,72]) ).
tff(98,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(p),p)),or(not(p),p)))
| ~ theorem(or(not(or(not(p),p)),or(p,not(p))))
| ~ theorem(implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(p),p)),or(not(p),p)))
| ~ theorem(or(not(or(not(p),p)),or(p,not(p))))
| ~ theorem(implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(p),p)),or(not(p),p)))
| ~ theorem(or(not(or(not(p),p)),or(p,not(p))))
| ~ theorem(implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(100,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(p),p)),or(not(p),p)))
| ~ theorem(or(not(or(not(p),p)),or(p,not(p))))
| ~ theorem(implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p)))) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
( theorem(or(not(or(not(p),p)),or(not(p),p)))
| ~ theorem(or(not(or(not(p),p)),or(p,not(p))))
| ~ theorem(implies(or(not(or(not(p),p)),or(p,not(p))),or(not(or(not(p),p)),or(not(p),p)))) ),
inference(unit_resolution,[status(thm)],[100,92]) ).
tff(102,plain,
theorem(or(not(or(not(p),p)),or(not(p),p))),
inference(unit_resolution,[status(thm)],[101,97,54]) ).
tff(103,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(p,p) = or(not(p),p) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(104,plain,
implies(p,p) = or(not(p),p),
inference(unit_resolution,[status(thm)],[103,7]) ).
tff(105,plain,
or(not(p),p) = implies(p,p),
inference(symmetry,[status(thm)],[104]) ).
tff(106,plain,
( theorem(or(not(p),p))
<=> theorem(implies(p,p)) ),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
( theorem(implies(p,p))
<=> theorem(or(not(p),p)) ),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
( ~ theorem(implies(p,p))
<=> ~ theorem(or(not(p),p)) ),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
( ~ theorem(implies(p,p))
<=> ~ theorem(implies(p,p)) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,axiom,
~ theorem(implies(p,p)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(111,plain,
~ theorem(implies(p,p)),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
~ theorem(or(not(p),p)),
inference(modus_ponens,[status(thm)],[111,108]) ).
tff(113,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(p),p))
| ~ theorem(or(not(or(not(p),p)),or(not(p),p)))
| ~ theorem(implies(or(not(or(not(p),p)),or(not(p),p)),or(not(p),p))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(p),p))
| ~ theorem(or(not(or(not(p),p)),or(not(p),p)))
| ~ theorem(implies(or(not(or(not(p),p)),or(not(p),p)),or(not(p),p))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(p),p))
| ~ theorem(or(not(or(not(p),p)),or(not(p),p)))
| ~ theorem(implies(or(not(or(not(p),p)),or(not(p),p)),or(not(p),p))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(p),p))
| ~ theorem(or(not(or(not(p),p)),or(not(p),p)))
| ~ theorem(implies(or(not(or(not(p),p)),or(not(p),p)),or(not(p),p))) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
( ~ theorem(or(not(or(not(p),p)),or(not(p),p)))
| ~ theorem(implies(or(not(or(not(p),p)),or(not(p),p)),or(not(p),p))) ),
inference(unit_resolution,[status(thm)],[115,92,112]) ).
tff(117,plain,
~ theorem(implies(or(not(or(not(p),p)),or(not(p),p)),or(not(p),p))),
inference(unit_resolution,[status(thm)],[116,102]) ).
tff(118,plain,
~ theorem(or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p))),
inference(modus_ponens,[status(thm)],[117,28]) ).
tff(119,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(120,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)],[119]) ).
tff(121,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(122,axiom,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',axiom_1_5) ).
tff(123,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(skolemize,[status(sab)],[123]) ).
tff(125,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(modus_ponens,[status(thm)],[124,120]) ).
tff(126,plain,
( ~ ! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C))))
| axiom(implies(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)),or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(127,plain,
axiom(implies(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)),or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p)))),
inference(unit_resolution,[status(thm)],[126,125]) ).
tff(128,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)),or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p))))
| ~ axiom(implies(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)),or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p)))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)),or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p))))
| ~ axiom(implies(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)),or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)),or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p))))
| ~ axiom(implies(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)),or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(130,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)),or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p))))
| ~ axiom(implies(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)),or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p)))) ),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
theorem(implies(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)),or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p)))),
inference(unit_resolution,[status(thm)],[130,49,127]) ).
tff(132,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p)))
| ~ theorem(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)))
| ~ theorem(implies(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)),or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p)))
| ~ theorem(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)))
| ~ theorem(implies(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)),or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(133,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p)))
| ~ theorem(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)))
| ~ theorem(implies(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)),or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(134,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p)))
| ~ theorem(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)))
| ~ theorem(implies(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)),or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p)))) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
( theorem(or(not(or(not(or(not(p),p)),or(not(p),p))),or(not(p),p)))
| ~ theorem(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p))) ),
inference(unit_resolution,[status(thm)],[134,92,131]) ).
tff(136,plain,
~ theorem(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p))),
inference(unit_resolution,[status(thm)],[135,118]) ).
tff(137,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)))
| ~ axiom(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)))
| ~ axiom(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(138,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)))
| ~ axiom(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(139,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)))
| ~ axiom(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p))) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
( theorem(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p)))
| ~ axiom(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p))) ),
inference(unit_resolution,[status(thm)],[139,49]) ).
tff(141,plain,
~ axiom(or(not(p),or(not(or(not(or(not(p),p)),or(not(p),p))),p))),
inference(unit_resolution,[status(thm)],[140,136]) ).
tff(142,plain,
$false,
inference(unit_resolution,[status(thm)],[141,22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL176-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % 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 09:27:31 UTC 2026
% 0.09/0.35 % CPUTime :
% 1.88/2.19 % SZS status Unsatisfiable
% 1.88/2.19 % SZS output start Proof
% See solution above
% 1.96/2.24 % E exiting
%------------------------------------------------------------------------------