%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP162-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:07:17 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 23 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 29 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 5 ~; 1 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 1 ( 1 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 27 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_type,type,
c: $i ).
tff(least_upper_bound_type,type,
least_upper_bound: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(1,plain,
( ( least_upper_bound(b,c) = c )
<=> ( least_upper_bound(b,c) = c ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
least_upper_bound(b,c) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_transa_2) ).
tff(3,plain,
least_upper_bound(b,c) = c,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ( least_upper_bound(a,b) = b )
<=> ( least_upper_bound(a,b) = b ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
least_upper_bound(a,b) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_transa_1) ).
tff(6,plain,
least_upper_bound(a,b) = b,
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
least_upper_bound(least_upper_bound(a,b),c) = least_upper_bound(b,c),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) )
<=> ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',associativity_of_lub) ).
tff(12,plain,
! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) )
| ( least_upper_bound(a,least_upper_bound(b,c)) = least_upper_bound(least_upper_bound(a,b),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
least_upper_bound(a,least_upper_bound(b,c)) = least_upper_bound(least_upper_bound(a,b),c),
inference(unit_resolution,[status(thm)],[15,14]) ).
tff(17,plain,
c = least_upper_bound(b,c),
inference(symmetry,[status(thm)],[3]) ).
tff(18,plain,
least_upper_bound(a,c) = least_upper_bound(a,least_upper_bound(b,c)),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
least_upper_bound(a,c) = c,
inference(transitivity,[status(thm)],[18,16,7,3]) ).
tff(20,plain,
( ( least_upper_bound(a,c) != c )
<=> ( least_upper_bound(a,c) != c ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
least_upper_bound(a,c) != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ax_transa) ).
tff(22,plain,
least_upper_bound(a,c) != c,
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
$false,
inference(unit_resolution,[status(thm)],[22,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP162-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 15:44:47 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% See solution above
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------