%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT035-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:13:46 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of formulae : 37 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 58 ( 55 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 38 ( 19 ~; 10 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 36 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(f_type,type,
f: $i > $i ).
tff(k_type,type,
k: $i > $i ).
tff(bb_type,type,
bb: $i ).
tff(aa_type,type,
aa: $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(n0_type,type,
n0: $i ).
tff(n1_type,type,
n1: $i ).
tff(1,plain,
^ [V: $i,U: $i] :
refl(( ( f(meet(U,V)) = join(f(U),f(V)) )
<=> ( f(meet(U,V)) = join(f(U),f(V)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V: $i,U: $i] : ( f(meet(U,V)) = join(f(U),f(V)) )
<=> ! [V: $i,U: $i] : ( f(meet(U,V)) = join(f(U),f(V)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V: $i,U: $i] : ( f(meet(U,V)) = join(f(U),f(V)) )
<=> ! [V: $i,U: $i] : ( f(meet(U,V)) = join(f(U),f(V)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V: $i,U: $i] : ( f(meet(U,V)) = join(f(U),f(V)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_on_meet) ).
tff(5,plain,
! [V: $i,U: $i] : ( f(meet(U,V)) = join(f(U),f(V)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V: $i,U: $i] : ( f(meet(U,V)) = join(f(U),f(V)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V: $i,U: $i] : ( f(meet(U,V)) = join(f(U),f(V)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V: $i,U: $i] : ( f(meet(U,V)) = join(f(U),f(V)) )
| ( f(meet(k(aa),k(bb))) = join(f(k(aa)),f(k(bb))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
f(meet(k(aa),k(bb))) = join(f(k(aa)),f(k(bb))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [V: $i,U: $i] :
refl(( ( k(join(U,V)) = meet(k(U),k(V)) )
<=> ( k(join(U,V)) = meet(k(U),k(V)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) )
<=> ! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) )
<=> ! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_on_join) ).
tff(14,plain,
! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) )
| ( k(join(aa,bb)) = meet(k(aa),k(bb)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
k(join(aa,bb)) = meet(k(aa),k(bb)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
f(k(join(aa,bb))) = f(meet(k(aa),k(bb))),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
f(k(join(aa,bb))) = join(f(k(aa)),f(k(bb))),
inference(transitivity,[status(thm)],[19,9]) ).
tff(21,plain,
( ( f(n1) = n0 )
<=> ( f(n1) = n0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
f(n1) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_on_top) ).
tff(23,plain,
f(n1) = n0,
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
( ( k(n0) = n1 )
<=> ( k(n0) = n1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
k(n0) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_on_bottom) ).
tff(26,plain,
k(n0) = n1,
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
f(k(n0)) = f(n1),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
f(k(n0)) = n0,
inference(transitivity,[status(thm)],[27,23]) ).
tff(29,plain,
( ( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(k(n0)) != n0 ) )
<=> ( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(k(n0)) != n0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(k(n0)) != n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',comp_join_hemimorphism) ).
tff(31,plain,
( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(k(n0)) != n0 ) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(k(n0)) != n0 ) ),
inference(modus_ponens,[status(thm)],[31,29]) ).
tff(33,plain,
( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(k(n0)) != n0 ) ),
inference(modus_ponens,[status(thm)],[32,29]) ).
tff(34,plain,
( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(k(n0)) != n0 ) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) )
| ( f(k(n0)) != n0 ) ),
inference(modus_ponens,[status(thm)],[34,29]) ).
tff(36,plain,
f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))),
inference(unit_resolution,[status(thm)],[35,28]) ).
tff(37,plain,
$false,
inference(unit_resolution,[status(thm)],[36,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT035-1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 19:27:26 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------