%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL174-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n002.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 02:59:26 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.41s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 33
% Syntax : Number of formulae : 103 ( 56 unt; 0 typ; 0 def)
% Number of atoms : 232 ( 51 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 225 ( 102 ~; 95 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 6 ( 6 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; 3 con; 0-2 aty)
% Number of variables : 143 ( 130 !; 0 ?; 143 :)
% 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(r_type,type,
r: $i ).
tff(p_type,type,
p: $i ).
tff(q_type,type,
q: $i ).
tff(not_type,type,
not: $i > $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/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(implies(q,r),implies(p,r)) = or(not(implies(q,r)),implies(p,r)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
implies(implies(q,r),implies(p,r)) = or(not(implies(q,r)),implies(p,r)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
or(not(implies(q,r)),implies(p,r)) = implies(implies(q,r),implies(p,r)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(p,r) = or(not(p),r) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
implies(p,r) = or(not(p),r),
inference(unit_resolution,[status(thm)],[11,7]) ).
tff(13,plain,
or(not(p),r) = implies(p,r),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
or(not(implies(q,r)),or(not(p),r)) = or(not(implies(q,r)),implies(p,r)),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
or(not(implies(q,r)),or(not(p),r)) = implies(implies(q,r),implies(p,r)),
inference(transitivity,[status(thm)],[14,10]) ).
tff(16,plain,
or(not(implies(p,q)),or(not(implies(q,r)),or(not(p),r))) = or(not(implies(p,q)),implies(implies(q,r),implies(p,r))),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
implies(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))),or(not(implies(p,q)),or(not(implies(q,r)),or(not(p),r)))) = implies(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))),or(not(implies(p,q)),implies(implies(q,r),implies(p,r)))),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
( theorem(implies(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))),or(not(implies(p,q)),or(not(implies(q,r)),or(not(p),r)))))
<=> theorem(implies(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))),or(not(implies(p,q)),implies(implies(q,r),implies(p,r))))) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,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(20,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)],[19]) ).
tff(21,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(22,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(23,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [B: $i,A: $i,C: $i] : axiom(implies(or(A,or(B,C)),or(B,or(A,C))))
| axiom(implies(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))),or(not(implies(p,q)),or(not(implies(q,r)),or(not(p),r))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
axiom(implies(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))),or(not(implies(p,q)),or(not(implies(q,r)),or(not(p),r))))),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
^ [X: $i] :
refl(( ( theorem(X)
| ~ axiom(X) )
<=> ( theorem(X)
| ~ axiom(X) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',rule_1) ).
tff(32,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))),or(not(implies(p,q)),or(not(implies(q,r)),or(not(p),r)))))
| ~ axiom(implies(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))),or(not(implies(p,q)),or(not(implies(q,r)),or(not(p),r))))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))),or(not(implies(p,q)),or(not(implies(q,r)),or(not(p),r)))))
| ~ axiom(implies(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))),or(not(implies(p,q)),or(not(implies(q,r)),or(not(p),r))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))),or(not(implies(p,q)),or(not(implies(q,r)),or(not(p),r)))))
| ~ axiom(implies(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))),or(not(implies(p,q)),or(not(implies(q,r)),or(not(p),r))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))),or(not(implies(p,q)),or(not(implies(q,r)),or(not(p),r)))))
| ~ axiom(implies(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))),or(not(implies(p,q)),or(not(implies(q,r)),or(not(p),r))))) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
theorem(implies(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))),or(not(implies(p,q)),or(not(implies(q,r)),or(not(p),r))))),
inference(unit_resolution,[status(thm)],[37,34,27]) ).
tff(39,plain,
theorem(implies(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))),or(not(implies(p,q)),implies(implies(q,r),implies(p,r))))),
inference(modus_ponens,[status(thm)],[38,18]) ).
tff(40,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(implies(p,q),implies(implies(q,r),implies(p,r))) = or(not(implies(p,q)),implies(implies(q,r),implies(p,r))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
implies(implies(p,q),implies(implies(q,r),implies(p,r))) = or(not(implies(p,q)),implies(implies(q,r),implies(p,r))),
inference(unit_resolution,[status(thm)],[40,7]) ).
tff(42,plain,
or(not(implies(p,q)),implies(implies(q,r),implies(p,r))) = implies(implies(p,q),implies(implies(q,r),implies(p,r))),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
( theorem(or(not(implies(p,q)),implies(implies(q,r),implies(p,r))))
<=> theorem(implies(implies(p,q),implies(implies(q,r),implies(p,r)))) ),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( theorem(implies(implies(p,q),implies(implies(q,r),implies(p,r))))
<=> theorem(or(not(implies(p,q)),implies(implies(q,r),implies(p,r)))) ),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
( ~ theorem(implies(implies(p,q),implies(implies(q,r),implies(p,r))))
<=> ~ theorem(or(not(implies(p,q)),implies(implies(q,r),implies(p,r)))) ),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
( ~ theorem(implies(implies(p,q),implies(implies(q,r),implies(p,r))))
<=> ~ theorem(implies(implies(p,q),implies(implies(q,r),implies(p,r)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
~ theorem(implies(implies(p,q),implies(implies(q,r),implies(p,r)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(48,plain,
~ theorem(implies(implies(p,q),implies(implies(q,r),implies(p,r)))),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
~ theorem(or(not(implies(p,q)),implies(implies(q,r),implies(p,r)))),
inference(modus_ponens,[status(thm)],[48,45]) ).
tff(50,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(not(q),r),implies(or(not(p),q),or(not(p),r))) = or(not(or(not(q),r)),implies(or(not(p),q),or(not(p),r))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
implies(or(not(q),r),implies(or(not(p),q),or(not(p),r))) = or(not(or(not(q),r)),implies(or(not(p),q),or(not(p),r))),
inference(unit_resolution,[status(thm)],[50,7]) ).
tff(52,plain,
or(not(or(not(q),r)),implies(or(not(p),q),or(not(p),r))) = implies(or(not(q),r),implies(or(not(p),q),or(not(p),r))),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(not(p),q),or(not(p),r)) = or(not(or(not(p),q)),or(not(p),r)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
implies(or(not(p),q),or(not(p),r)) = or(not(or(not(p),q)),or(not(p),r)),
inference(unit_resolution,[status(thm)],[53,7]) ).
tff(55,plain,
or(not(or(not(p),q)),or(not(p),r)) = implies(or(not(p),q),or(not(p),r)),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(p,q) = or(not(p),q) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
implies(p,q) = or(not(p),q),
inference(unit_resolution,[status(thm)],[56,7]) ).
tff(58,plain,
or(not(p),q) = implies(p,q),
inference(symmetry,[status(thm)],[57]) ).
tff(59,plain,
not(or(not(p),q)) = not(implies(p,q)),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
not(implies(p,q)) = not(or(not(p),q)),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
or(not(implies(p,q)),or(not(p),r)) = or(not(or(not(p),q)),or(not(p),r)),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
or(not(implies(p,q)),or(not(p),r)) = implies(or(not(p),q),or(not(p),r)),
inference(transitivity,[status(thm)],[61,55]) ).
tff(63,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(q,r) = or(not(q),r) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
implies(q,r) = or(not(q),r),
inference(unit_resolution,[status(thm)],[63,7]) ).
tff(65,plain,
or(not(q),r) = implies(q,r),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
not(or(not(q),r)) = not(implies(q,r)),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
not(implies(q,r)) = not(or(not(q),r)),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))) = or(not(or(not(q),r)),implies(or(not(p),q),or(not(p),r))),
inference(monotonicity,[status(thm)],[67,62]) ).
tff(69,plain,
or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))) = implies(or(not(q),r),implies(or(not(p),q),or(not(p),r))),
inference(transitivity,[status(thm)],[68,52]) ).
tff(70,plain,
( theorem(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))))
<=> theorem(implies(or(not(q),r),implies(or(not(p),q),or(not(p),r)))) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( theorem(implies(or(not(q),r),implies(or(not(p),q),or(not(p),r))))
<=> theorem(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r)))) ),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
implies(implies(q,r),implies(or(not(p),q),or(not(p),r))) = implies(or(not(q),r),implies(or(not(p),q),or(not(p),r))),
inference(monotonicity,[status(thm)],[64]) ).
tff(73,plain,
( theorem(implies(implies(q,r),implies(or(not(p),q),or(not(p),r))))
<=> theorem(implies(or(not(q),r),implies(or(not(p),q),or(not(p),r)))) ),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,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(75,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)],[74]) ).
tff(76,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(77,axiom,
! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_6) ).
tff(78,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(modus_ponens,[status(thm)],[79,75]) ).
tff(81,plain,
( ~ ! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B))))
| axiom(implies(implies(q,r),implies(or(not(p),q),or(not(p),r)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
axiom(implies(implies(q,r),implies(or(not(p),q),or(not(p),r)))),
inference(unit_resolution,[status(thm)],[81,80]) ).
tff(83,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(q,r),implies(or(not(p),q),or(not(p),r))))
| ~ axiom(implies(implies(q,r),implies(or(not(p),q),or(not(p),r)))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(q,r),implies(or(not(p),q),or(not(p),r))))
| ~ axiom(implies(implies(q,r),implies(or(not(p),q),or(not(p),r)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(q,r),implies(or(not(p),q),or(not(p),r))))
| ~ axiom(implies(implies(q,r),implies(or(not(p),q),or(not(p),r)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(85,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(q,r),implies(or(not(p),q),or(not(p),r))))
| ~ axiom(implies(implies(q,r),implies(or(not(p),q),or(not(p),r)))) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
theorem(implies(implies(q,r),implies(or(not(p),q),or(not(p),r)))),
inference(unit_resolution,[status(thm)],[85,34,82]) ).
tff(87,plain,
theorem(implies(or(not(q),r),implies(or(not(p),q),or(not(p),r)))),
inference(modus_ponens,[status(thm)],[86,73]) ).
tff(88,plain,
theorem(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r)))),
inference(modus_ponens,[status(thm)],[87,71]) ).
tff(89,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(90,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)],[89]) ).
tff(91,plain,
( ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
<=> ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,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(93,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)],[92]) ).
tff(94,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(95,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(p,q)),implies(implies(q,r),implies(p,r))))
| ~ theorem(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))))
| ~ theorem(implies(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))),or(not(implies(p,q)),implies(implies(q,r),implies(p,r))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(p,q)),implies(implies(q,r),implies(p,r))))
| ~ theorem(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))))
| ~ theorem(implies(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))),or(not(implies(p,q)),implies(implies(q,r),implies(p,r))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(p,q)),implies(implies(q,r),implies(p,r))))
| ~ theorem(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))))
| ~ theorem(implies(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))),or(not(implies(p,q)),implies(implies(q,r),implies(p,r))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ theorem(implies(Y,X)) )
| theorem(or(not(implies(p,q)),implies(implies(q,r),implies(p,r))))
| ~ theorem(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))))
| ~ theorem(implies(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))),or(not(implies(p,q)),implies(implies(q,r),implies(p,r))))) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
( theorem(or(not(implies(p,q)),implies(implies(q,r),implies(p,r))))
| ~ theorem(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))))
| ~ theorem(implies(or(not(implies(q,r)),or(not(implies(p,q)),or(not(p),r))),or(not(implies(p,q)),implies(implies(q,r),implies(p,r))))) ),
inference(unit_resolution,[status(thm)],[101,98]) ).
tff(103,plain,
$false,
inference(unit_resolution,[status(thm)],[102,88,49,39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL174-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.34 % Computer : n002.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 5 11:37:07 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.12/0.41 % SZS status Unsatisfiable
% 0.12/0.41 % SZS output start Proof
% See solution above
% 0.12/0.43 % E exiting
%------------------------------------------------------------------------------