%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL170-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 02:59:25 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 39 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 80 ( 15 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 70 ( 32 ~; 24 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 48 !; 0 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
tff(axiom_type,type,
axiom: $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(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/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,q) = or(not(p),q) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
implies(p,q) = or(not(p),q),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
or(not(p),q) = implies(p,q),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
implies(q,or(not(p),q)) = implies(q,implies(p,q)),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( axiom(implies(q,or(not(p),q)))
<=> axiom(implies(q,implies(p,q))) ),
inference(monotonicity,[status(thm)],[11]) ).
tff(13,plain,
( axiom(implies(q,implies(p,q)))
<=> axiom(implies(q,or(not(p),q))) ),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
( ~ axiom(implies(q,implies(p,q)))
<=> ~ axiom(implies(q,or(not(p),q))) ),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
( ~ theorem(implies(q,implies(p,q)))
<=> ~ theorem(implies(q,implies(p,q))) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
~ theorem(implies(q,implies(p,q))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(17,plain,
~ theorem(implies(q,implies(p,q))),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
^ [X: $i] :
refl(( ( theorem(X)
| ~ axiom(X) )
<=> ( theorem(X)
| ~ axiom(X) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',rule_1) ).
tff(22,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(q,implies(p,q)))
| ~ axiom(implies(q,implies(p,q))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(q,implies(p,q)))
| ~ axiom(implies(q,implies(p,q))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(q,implies(p,q)))
| ~ axiom(implies(q,implies(p,q))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(q,implies(p,q)))
| ~ axiom(implies(q,implies(p,q))) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
~ axiom(implies(q,implies(p,q))),
inference(unit_resolution,[status(thm)],[27,24,17]) ).
tff(29,plain,
~ axiom(implies(q,or(not(p),q))),
inference(modus_ponens,[status(thm)],[28,14]) ).
tff(30,plain,
^ [B: $i,A: $i] :
refl(( axiom(implies(A,or(B,A)))
<=> axiom(implies(A,or(B,A))) )),
inference(bind,[status(th)],[]) ).
tff(31,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)],[30]) ).
tff(32,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(33,axiom,
! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',axiom_1_3) ).
tff(34,plain,
! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [B: $i,A: $i] : axiom(implies(A,or(B,A))),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ~ ! [B: $i,A: $i] : axiom(implies(A,or(B,A)))
| axiom(implies(q,or(not(p),q))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
axiom(implies(q,or(not(p),q))),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
$false,
inference(unit_resolution,[status(thm)],[38,29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL170-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.09/0.34 % Computer : n017.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 5 22:51:24 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.13/0.38 % SZS status Unsatisfiable
% 0.13/0.38 % SZS output start Proof
% See solution above
% 0.13/0.39 % E exiting
%------------------------------------------------------------------------------