%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP143-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:07:15 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of formulae : 51 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 73 ( 68 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 27 ( 9 ~; 5 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 4 ( 4 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; 2 con; 0-2 aty)
% Number of variables : 92 ( 83 !; 0 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
tff(greatest_lower_bound_type,type,
greatest_lower_bound: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(least_upper_bound_type,type,
least_upper_bound: ( $i * $i ) > $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X )
<=> ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
tff(5,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X )
| ( greatest_lower_bound(a,least_upper_bound(a,greatest_lower_bound(b,a))) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
greatest_lower_bound(a,least_upper_bound(a,greatest_lower_bound(b,a))) = a,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(( ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
<=> ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
<=> ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
<=> ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
tff(14,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
| ( greatest_lower_bound(a,b) = greatest_lower_bound(b,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
greatest_lower_bound(a,b) = greatest_lower_bound(b,a),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
greatest_lower_bound(b,a) = greatest_lower_bound(a,b),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
least_upper_bound(a,greatest_lower_bound(b,a)) = least_upper_bound(a,greatest_lower_bound(a,b)),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
least_upper_bound(a,greatest_lower_bound(a,b)) = least_upper_bound(a,greatest_lower_bound(b,a)),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
^ [Y: $i,X: $i] :
refl(( ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X )
<=> ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).
tff(26,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X )
| ( least_upper_bound(a,greatest_lower_bound(a,b)) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
least_upper_bound(a,greatest_lower_bound(a,b)) = a,
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,plain,
a = least_upper_bound(a,greatest_lower_bound(a,b)),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
a = least_upper_bound(a,greatest_lower_bound(b,a)),
inference(transitivity,[status(thm)],[31,21]) ).
tff(33,plain,
greatest_lower_bound(a,a) = greatest_lower_bound(a,least_upper_bound(a,greatest_lower_bound(b,a))),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
greatest_lower_bound(a,a) = a,
inference(transitivity,[status(thm)],[33,9]) ).
tff(35,plain,
greatest_lower_bound(greatest_lower_bound(a,a),b) = greatest_lower_bound(a,b),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) )
<=> ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [Z: $i,Y: $i,X: $i] : ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [Z: $i,Y: $i,X: $i] : ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
! [Z: $i,Y: $i,X: $i] : ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).
tff(40,plain,
! [Z: $i,Y: $i,X: $i] : ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [Z: $i,Y: $i,X: $i] : ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [Z: $i,Y: $i,X: $i] : ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) )
| ( greatest_lower_bound(a,greatest_lower_bound(a,b)) = greatest_lower_bound(greatest_lower_bound(a,a),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
greatest_lower_bound(a,greatest_lower_bound(a,b)) = greatest_lower_bound(greatest_lower_bound(a,a),b),
inference(unit_resolution,[status(thm)],[43,42]) ).
tff(45,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
| ( greatest_lower_bound(greatest_lower_bound(a,b),a) = greatest_lower_bound(a,greatest_lower_bound(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
greatest_lower_bound(greatest_lower_bound(a,b),a) = greatest_lower_bound(a,greatest_lower_bound(a,b)),
inference(unit_resolution,[status(thm)],[45,16]) ).
tff(47,plain,
greatest_lower_bound(greatest_lower_bound(a,b),a) = greatest_lower_bound(a,b),
inference(transitivity,[status(thm)],[46,44,35]) ).
tff(48,plain,
( ( greatest_lower_bound(greatest_lower_bound(a,b),a) != greatest_lower_bound(a,b) )
<=> ( greatest_lower_bound(greatest_lower_bound(a,b),a) != greatest_lower_bound(a,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
greatest_lower_bound(greatest_lower_bound(a,b),a) != greatest_lower_bound(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ax_glb2b) ).
tff(50,plain,
greatest_lower_bound(greatest_lower_bound(a,b),a) != greatest_lower_bound(a,b),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
$false,
inference(unit_resolution,[status(thm)],[50,47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP143-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 15:45:46 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.37 % SZS status Unsatisfiable
% 0.20/0.37 % SZS output start Proof
% See solution above
% 0.20/0.38 % E exiting
%------------------------------------------------------------------------------