%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP150-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:07:16 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 26 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 34 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 6 ~; 2 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 40 ( 36 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
tff(least_upper_bound_type,type,
least_upper_bound: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( least_upper_bound(X,X) = X )
<=> ( least_upper_bound(X,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( least_upper_bound(X,X) = X )
<=> ! [X: $i] : ( least_upper_bound(X,X) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( least_upper_bound(X,X) = X )
<=> ! [X: $i] : ( least_upper_bound(X,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( least_upper_bound(X,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',idempotence_of_lub) ).
tff(5,plain,
! [X: $i] : ( least_upper_bound(X,X) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( least_upper_bound(X,X) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( least_upper_bound(X,X) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( least_upper_bound(X,X) = X )
| ( least_upper_bound(a,a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
least_upper_bound(a,a) = a,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
a = least_upper_bound(a,a),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
least_upper_bound(a,b) = least_upper_bound(least_upper_bound(a,a),b),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
least_upper_bound(least_upper_bound(a,a),b) = least_upper_bound(a,b),
inference(symmetry,[status(thm)],[11]) ).
tff(13,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(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) )
<=> ! [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)],[13]) ).
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) )
<=> ! [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(16,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/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_lub) ).
tff(17,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)],[16,15]) ).
tff(18,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)],[17]) ).
tff(19,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)],[18,14]) ).
tff(20,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(a,b)) = least_upper_bound(least_upper_bound(a,a),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
least_upper_bound(a,least_upper_bound(a,b)) = least_upper_bound(least_upper_bound(a,a),b),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
least_upper_bound(a,least_upper_bound(a,b)) = least_upper_bound(a,b),
inference(transitivity,[status(thm)],[21,12]) ).
tff(23,plain,
( ( least_upper_bound(a,least_upper_bound(a,b)) != least_upper_bound(a,b) )
<=> ( least_upper_bound(a,least_upper_bound(a,b)) != least_upper_bound(a,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
least_upper_bound(a,least_upper_bound(a,b)) != least_upper_bound(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ax_lub2a) ).
tff(25,plain,
least_upper_bound(a,least_upper_bound(a,b)) != least_upper_bound(a,b),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
$false,
inference(unit_resolution,[status(thm)],[25,22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP150-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 15:44:18 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.36 % SZS status Unsatisfiable
% 0.11/0.36 % SZS output start Proof
% See solution above
% 0.11/0.36 % E exiting
%------------------------------------------------------------------------------