%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL187-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n026.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 02:59:29 PM UTC 2026
% Result : Unsatisfiable 25.79s 26.08s
% Output : Proof 25.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 46
% Syntax : Number of formulae : 123 ( 57 unt; 0 typ; 0 def)
% Number of atoms : 331 ( 29 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 370 ( 170 ~; 160 |; 0 &)
% ( 40 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 201 ( 184 !; 0 ?; 201 :)
% Comments :
%------------------------------------------------------------------------------
tff(theorem_type,type,
theorem: $i > $o ).
tff(implies_type,type,
implies: ( $i * $i ) > $i ).
tff(or_type,type,
or: ( $i * $i ) > $i ).
tff(q_type,type,
q: $i ).
tff(not_type,type,
not: $i > $i ).
tff(p_type,type,
p: $i ).
tff(axiom_type,type,
axiom: $i > $o ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( implies(X,Y) = or(not(X),Y) )
<=> ( implies(X,Y) = or(not(X),Y) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
<=> ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
<=> ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',implies_definition) ).
tff(5,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(q,not(p)),or(not(p),q)) = or(not(or(q,not(p))),or(not(p),q)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
implies(or(q,not(p)),or(not(p),q)) = or(not(or(q,not(p))),or(not(p),q)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
implies(implies(or(q,not(p)),or(not(p),q)),implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q)))) = implies(or(not(or(q,not(p))),or(not(p),q)),implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q)))),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( theorem(implies(implies(or(q,not(p)),or(not(p),q)),implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q)))))
<=> theorem(implies(or(not(or(q,not(p))),or(not(p),q)),implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q))))) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,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(13,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)],[12]) ).
tff(14,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(15,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(16,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
( ~ ! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B))))
| axiom(implies(implies(or(q,not(p)),or(not(p),q)),implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
axiom(implies(implies(or(q,not(p)),or(not(p),q)),implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q))))),
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
^ [X: $i] :
refl(( ( theorem(X)
| ~ axiom(X) )
<=> ( theorem(X)
| ~ axiom(X) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',rule_1) ).
tff(25,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(or(q,not(p)),or(not(p),q)),implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q)))))
| ~ axiom(implies(implies(or(q,not(p)),or(not(p),q)),implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q))))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(or(q,not(p)),or(not(p),q)),implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q)))))
| ~ axiom(implies(implies(or(q,not(p)),or(not(p),q)),implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(or(q,not(p)),or(not(p),q)),implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q)))))
| ~ axiom(implies(implies(or(q,not(p)),or(not(p),q)),implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(or(q,not(p)),or(not(p),q)),implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q)))))
| ~ axiom(implies(implies(or(q,not(p)),or(not(p),q)),implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q))))) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
theorem(implies(implies(or(q,not(p)),or(not(p),q)),implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q))))),
inference(unit_resolution,[status(thm)],[30,27,20]) ).
tff(32,plain,
theorem(implies(or(not(or(q,not(p))),or(not(p),q)),implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q))))),
inference(modus_ponens,[status(thm)],[31,11]) ).
tff(33,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(not(p),or(q,not(p))) = or(not(not(p)),or(q,not(p))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
implies(not(p),or(q,not(p))) = or(not(not(p)),or(q,not(p))),
inference(unit_resolution,[status(thm)],[33,7]) ).
tff(35,plain,
or(not(not(p)),or(q,not(p))) = implies(not(p),or(q,not(p))),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
( theorem(or(not(not(p)),or(q,not(p))))
<=> theorem(implies(not(p),or(q,not(p)))) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( theorem(implies(not(p),or(q,not(p))))
<=> theorem(or(not(not(p)),or(q,not(p)))) ),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
^ [B: $i,A: $i] :
refl(( axiom(implies(A,or(B,A)))
<=> axiom(implies(A,or(B,A))) )),
inference(bind,[status(th)],[]) ).
tff(39,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)],[38]) ).
tff(40,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(41,axiom,
! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',axiom_1_3) ).
tff(42,plain,
! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
( ~ ! [B: $i,A: $i] : axiom(implies(A,or(B,A)))
| axiom(implies(not(p),or(q,not(p)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
axiom(implies(not(p),or(q,not(p)))),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(not(p),or(q,not(p))))
| ~ axiom(implies(not(p),or(q,not(p)))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(not(p),or(q,not(p))))
| ~ axiom(implies(not(p),or(q,not(p)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(not(p),or(q,not(p))))
| ~ axiom(implies(not(p),or(q,not(p)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(not(p),or(q,not(p))))
| ~ axiom(implies(not(p),or(q,not(p)))) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
theorem(implies(not(p),or(q,not(p)))),
inference(unit_resolution,[status(thm)],[49,27,46]) ).
tff(51,plain,
theorem(or(not(not(p)),or(q,not(p)))),
inference(modus_ponens,[status(thm)],[50,37]) ).
tff(52,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(not(p),q) = or(not(not(p)),q) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
implies(not(p),q) = or(not(not(p)),q),
inference(unit_resolution,[status(thm)],[52,7]) ).
tff(54,plain,
or(not(not(p)),q) = implies(not(p),q),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
or(not(p),or(not(not(p)),q)) = or(not(p),implies(not(p),q)),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
implies(or(not(not(p)),or(not(p),q)),or(not(p),or(not(not(p)),q))) = implies(or(not(not(p)),or(not(p),q)),or(not(p),implies(not(p),q))),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( theorem(implies(or(not(not(p)),or(not(p),q)),or(not(p),or(not(not(p)),q))))
<=> theorem(implies(or(not(not(p)),or(not(p),q)),or(not(p),implies(not(p),q)))) ),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,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(59,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)],[58]) ).
tff(60,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(61,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(62,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
( ~ ! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C))))
| axiom(implies(or(not(not(p)),or(not(p),q)),or(not(p),or(not(not(p)),q)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
axiom(implies(or(not(not(p)),or(not(p),q)),or(not(p),or(not(not(p)),q)))),
inference(unit_resolution,[status(thm)],[65,64]) ).
tff(67,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(not(p)),or(not(p),q)),or(not(p),or(not(not(p)),q))))
| ~ axiom(implies(or(not(not(p)),or(not(p),q)),or(not(p),or(not(not(p)),q)))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(not(p)),or(not(p),q)),or(not(p),or(not(not(p)),q))))
| ~ axiom(implies(or(not(not(p)),or(not(p),q)),or(not(p),or(not(not(p)),q)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(not(p)),or(not(p),q)),or(not(p),or(not(not(p)),q))))
| ~ axiom(implies(or(not(not(p)),or(not(p),q)),or(not(p),or(not(not(p)),q)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(69,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(not(p)),or(not(p),q)),or(not(p),or(not(not(p)),q))))
| ~ axiom(implies(or(not(not(p)),or(not(p),q)),or(not(p),or(not(not(p)),q)))) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
theorem(implies(or(not(not(p)),or(not(p),q)),or(not(p),or(not(not(p)),q)))),
inference(unit_resolution,[status(thm)],[69,27,66]) ).
tff(71,plain,
theorem(implies(or(not(not(p)),or(not(p),q)),or(not(p),implies(not(p),q)))),
inference(modus_ponens,[status(thm)],[70,57]) ).
tff(72,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(p,implies(not(p),q)) = or(not(p),implies(not(p),q)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
implies(p,implies(not(p),q)) = or(not(p),implies(not(p),q)),
inference(unit_resolution,[status(thm)],[72,7]) ).
tff(74,plain,
or(not(p),implies(not(p),q)) = implies(p,implies(not(p),q)),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
( theorem(or(not(p),implies(not(p),q)))
<=> theorem(implies(p,implies(not(p),q))) ),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
( theorem(implies(p,implies(not(p),q)))
<=> theorem(or(not(p),implies(not(p),q))) ),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
( ~ theorem(implies(p,implies(not(p),q)))
<=> ~ theorem(or(not(p),implies(not(p),q))) ),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
( ~ theorem(implies(p,implies(not(p),q)))
<=> ~ theorem(implies(p,implies(not(p),q))) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,axiom,
~ theorem(implies(p,implies(not(p),q))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(80,plain,
~ theorem(implies(p,implies(not(p),q))),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
~ theorem(or(not(p),implies(not(p),q))),
inference(modus_ponens,[status(thm)],[80,77]) ).
tff(82,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(83,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)],[82]) ).
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(rewrite,[status(thm)],[]) ).
tff(85,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(86,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)],[85]) ).
tff(87,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(88,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[90,83]) ).
tff(92,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(p),implies(not(p),q)))
| ~ theorem(or(not(not(p)),or(not(p),q)))
| ~ theorem(implies(or(not(not(p)),or(not(p),q)),or(not(p),implies(not(p),q)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(p),implies(not(p),q)))
| ~ theorem(or(not(not(p)),or(not(p),q)))
| ~ theorem(implies(or(not(not(p)),or(not(p),q)),or(not(p),implies(not(p),q)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(p),implies(not(p),q)))
| ~ theorem(or(not(not(p)),or(not(p),q)))
| ~ theorem(implies(or(not(not(p)),or(not(p),q)),or(not(p),implies(not(p),q)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(94,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(p),implies(not(p),q)))
| ~ theorem(or(not(not(p)),or(not(p),q)))
| ~ theorem(implies(or(not(not(p)),or(not(p),q)),or(not(p),implies(not(p),q)))) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
( theorem(or(not(p),implies(not(p),q)))
| ~ theorem(or(not(not(p)),or(not(p),q)))
| ~ theorem(implies(or(not(not(p)),or(not(p),q)),or(not(p),implies(not(p),q)))) ),
inference(unit_resolution,[status(thm)],[94,91]) ).
tff(96,plain,
~ theorem(or(not(not(p)),or(not(p),q))),
inference(unit_resolution,[status(thm)],[95,81,71]) ).
tff(97,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(not(p)),or(not(p),q)))
| ~ theorem(or(not(not(p)),or(q,not(p))))
| ~ theorem(implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(not(p)),or(not(p),q)))
| ~ theorem(or(not(not(p)),or(q,not(p))))
| ~ theorem(implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(98,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(not(p)),or(not(p),q)))
| ~ theorem(or(not(not(p)),or(q,not(p))))
| ~ theorem(implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(99,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(not(p)),or(not(p),q)))
| ~ theorem(or(not(not(p)),or(q,not(p))))
| ~ theorem(implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q)))) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
( ~ theorem(or(not(not(p)),or(q,not(p))))
| ~ theorem(implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q)))) ),
inference(unit_resolution,[status(thm)],[99,91,96]) ).
tff(101,plain,
~ theorem(implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q)))),
inference(unit_resolution,[status(thm)],[100,51]) ).
tff(102,plain,
or(not(or(q,not(p))),or(not(p),q)) = implies(or(q,not(p)),or(not(p),q)),
inference(symmetry,[status(thm)],[9]) ).
tff(103,plain,
( theorem(or(not(or(q,not(p))),or(not(p),q)))
<=> theorem(implies(or(q,not(p)),or(not(p),q))) ),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
( theorem(implies(or(q,not(p)),or(not(p),q)))
<=> theorem(or(not(or(q,not(p))),or(not(p),q))) ),
inference(symmetry,[status(thm)],[103]) ).
tff(105,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(106,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)],[105]) ).
tff(107,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(108,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(109,plain,
! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
inference(skolemize,[status(sab)],[109]) ).
tff(111,plain,
! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A))),
inference(modus_ponens,[status(thm)],[110,106]) ).
tff(112,plain,
( ~ ! [B: $i,A: $i] : axiom(implies(or(A,B),or(B,A)))
| axiom(implies(or(q,not(p)),or(not(p),q))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(113,plain,
axiom(implies(or(q,not(p)),or(not(p),q))),
inference(unit_resolution,[status(thm)],[112,111]) ).
tff(114,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(q,not(p)),or(not(p),q)))
| ~ axiom(implies(or(q,not(p)),or(not(p),q))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(q,not(p)),or(not(p),q)))
| ~ axiom(implies(or(q,not(p)),or(not(p),q))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(115,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(q,not(p)),or(not(p),q)))
| ~ axiom(implies(or(q,not(p)),or(not(p),q))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(116,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(q,not(p)),or(not(p),q)))
| ~ axiom(implies(or(q,not(p)),or(not(p),q))) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
theorem(implies(or(q,not(p)),or(not(p),q))),
inference(unit_resolution,[status(thm)],[116,27,113]) ).
tff(118,plain,
theorem(or(not(or(q,not(p))),or(not(p),q))),
inference(modus_ponens,[status(thm)],[117,104]) ).
tff(119,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q))))
| ~ theorem(or(not(or(q,not(p))),or(not(p),q)))
| ~ theorem(implies(or(not(or(q,not(p))),or(not(p),q)),implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q))))
| ~ theorem(or(not(or(q,not(p))),or(not(p),q)))
| ~ theorem(implies(or(not(or(q,not(p))),or(not(p),q)),implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(120,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q))))
| ~ theorem(or(not(or(q,not(p))),or(not(p),q)))
| ~ theorem(implies(or(not(or(q,not(p))),or(not(p),q)),implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(121,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q))))
| ~ theorem(or(not(or(q,not(p))),or(not(p),q)))
| ~ theorem(implies(or(not(or(q,not(p))),or(not(p),q)),implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q))))) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
( theorem(implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q))))
| ~ theorem(implies(or(not(or(q,not(p))),or(not(p),q)),implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q))))) ),
inference(unit_resolution,[status(thm)],[121,91,118]) ).
tff(123,plain,
$false,
inference(unit_resolution,[status(thm)],[122,101,32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL187-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.05 % Command : run_E %s %d THM
% 0.14/0.41 % Computer : n026.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Fri Sep 4 13:34:42 UTC 2026
% 0.14/0.41 % CPUTime :
% 25.79/26.08 % SZS status Unsatisfiable
% 25.79/26.08 % SZS output start Proof
% See solution above
% 0.21/26.39 % E exiting
%------------------------------------------------------------------------------