%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL173-3 : 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 02:59:26 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.41s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 43 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 85 ( 20 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 72 ( 33 ~; 25 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 59 !; 0 ?; 65 :)
% 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(r_type,type,
r: $i ).
tff(not_type,type,
not: $i > $i ).
tff(p_type,type,
p: $i ).
tff(q_type,type,
q: $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,r) = or(not(p),r) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
implies(p,r) = or(not(p),r),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
or(not(p),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,q) = or(not(p),q) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
implies(p,q) = or(not(p),q),
inference(unit_resolution,[status(thm)],[11,7]) ).
tff(13,plain,
or(not(p),q) = implies(p,q),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
implies(or(not(p),q),or(not(p),r)) = implies(implies(p,q),implies(p,r)),
inference(monotonicity,[status(thm)],[13,10]) ).
tff(15,plain,
implies(implies(q,r),implies(or(not(p),q),or(not(p),r))) = implies(implies(q,r),implies(implies(p,q),implies(p,r))),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( axiom(implies(implies(q,r),implies(or(not(p),q),or(not(p),r))))
<=> axiom(implies(implies(q,r),implies(implies(p,q),implies(p,r)))) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( axiom(implies(implies(q,r),implies(implies(p,q),implies(p,r))))
<=> axiom(implies(implies(q,r),implies(or(not(p),q),or(not(p),r)))) ),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
( ~ axiom(implies(implies(q,r),implies(implies(p,q),implies(p,r))))
<=> ~ axiom(implies(implies(q,r),implies(or(not(p),q),or(not(p),r)))) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
( ~ theorem(implies(implies(q,r),implies(implies(p,q),implies(p,r))))
<=> ~ theorem(implies(implies(q,r),implies(implies(p,q),implies(p,r)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
~ theorem(implies(implies(q,r),implies(implies(p,q),implies(p,r)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(21,plain,
~ theorem(implies(implies(q,r),implies(implies(p,q),implies(p,r)))),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
^ [X: $i] :
refl(( ( theorem(X)
| ~ axiom(X) )
<=> ( theorem(X)
| ~ axiom(X) ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax',rule_1) ).
tff(26,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(q,r),implies(implies(p,q),implies(p,r))))
| ~ axiom(implies(implies(q,r),implies(implies(p,q),implies(p,r)))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(q,r),implies(implies(p,q),implies(p,r))))
| ~ axiom(implies(implies(q,r),implies(implies(p,q),implies(p,r)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(q,r),implies(implies(p,q),implies(p,r))))
| ~ axiom(implies(implies(q,r),implies(implies(p,q),implies(p,r)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(implies(implies(q,r),implies(implies(p,q),implies(p,r))))
| ~ axiom(implies(implies(q,r),implies(implies(p,q),implies(p,r)))) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
~ axiom(implies(implies(q,r),implies(implies(p,q),implies(p,r)))),
inference(unit_resolution,[status(thm)],[31,28,21]) ).
tff(33,plain,
~ axiom(implies(implies(q,r),implies(or(not(p),q),or(not(p),r)))),
inference(modus_ponens,[status(thm)],[32,18]) ).
tff(34,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(35,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)],[34]) ).
tff(36,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(37,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(38,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [B: $i,A: $i,C: $i] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,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(42,plain,
axiom(implies(implies(q,r),implies(or(not(p),q),or(not(p),r)))),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
$false,
inference(unit_resolution,[status(thm)],[42,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL173-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 5 03:35:52 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.14/0.41 % SZS status Unsatisfiable
% 0.14/0.41 % SZS output start Proof
% See solution above
% 0.14/0.42 % E exiting
%------------------------------------------------------------------------------