%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP147-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 29
% Syntax : Number of formulae : 76 ( 55 unt; 0 typ; 0 def)
% Number of atoms : 107 ( 101 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 38 ( 12 ~; 8 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 5 ( 5 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 116 ( 105 !; 0 ?; 116 :)
% 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(greatest_lower_bound_type,type,
greatest_lower_bound: ( $i * $i ) > $i ).
tff(c_type,type,
c: $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/sandbox2/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(least_upper_bound(a,b),least_upper_bound(least_upper_bound(a,b),c)) = least_upper_bound(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(least_upper_bound(a,b),c)) = least_upper_bound(a,b),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(( ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
<=> ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
<=> ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
<=> ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
tff(14,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
| ( least_upper_bound(c,least_upper_bound(a,b)) = least_upper_bound(least_upper_bound(a,b),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
least_upper_bound(c,least_upper_bound(a,b)) = least_upper_bound(least_upper_bound(a,b),c),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
| ( least_upper_bound(a,b) = least_upper_bound(b,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
least_upper_bound(a,b) = least_upper_bound(b,a),
inference(unit_resolution,[status(thm)],[19,16]) ).
tff(21,plain,
least_upper_bound(c,least_upper_bound(a,b)) = least_upper_bound(c,least_upper_bound(b,a)),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
least_upper_bound(c,least_upper_bound(b,a)) = least_upper_bound(c,least_upper_bound(a,b)),
inference(symmetry,[status(thm)],[21]) ).
tff(23,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(24,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)],[23]) ).
tff(25,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(26,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(27,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)],[26,25]) ).
tff(28,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)],[27]) ).
tff(29,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)],[28,24]) ).
tff(30,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(c,least_upper_bound(b,a)) = least_upper_bound(least_upper_bound(c,b),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
least_upper_bound(c,least_upper_bound(b,a)) = least_upper_bound(least_upper_bound(c,b),a),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
least_upper_bound(least_upper_bound(c,b),a) = least_upper_bound(c,least_upper_bound(b,a)),
inference(symmetry,[status(thm)],[31]) ).
tff(33,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(34,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)],[33]) ).
tff(35,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(36,axiom,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
tff(37,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
| ( greatest_lower_bound(a,c) = greatest_lower_bound(c,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
greatest_lower_bound(a,c) = greatest_lower_bound(c,a),
inference(unit_resolution,[status(thm)],[40,39]) ).
tff(42,plain,
( ( greatest_lower_bound(a,c) = a )
<=> ( greatest_lower_bound(a,c) = a ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
greatest_lower_bound(a,c) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_lub1b_1) ).
tff(44,plain,
greatest_lower_bound(a,c) = a,
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
a = greatest_lower_bound(a,c),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
a = greatest_lower_bound(c,a),
inference(transitivity,[status(thm)],[45,41]) ).
tff(47,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(48,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)],[47]) ).
tff(49,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(50,axiom,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).
tff(51,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X )
| ( least_upper_bound(c,greatest_lower_bound(c,b)) = c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
least_upper_bound(c,greatest_lower_bound(c,b)) = c,
inference(unit_resolution,[status(thm)],[54,53]) ).
tff(56,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
| ( greatest_lower_bound(b,c) = greatest_lower_bound(c,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
greatest_lower_bound(b,c) = greatest_lower_bound(c,b),
inference(unit_resolution,[status(thm)],[56,39]) ).
tff(58,plain,
( ( greatest_lower_bound(b,c) = b )
<=> ( greatest_lower_bound(b,c) = b ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,axiom,
greatest_lower_bound(b,c) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_lub1b_2) ).
tff(60,plain,
greatest_lower_bound(b,c) = b,
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
b = greatest_lower_bound(b,c),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
b = greatest_lower_bound(c,b),
inference(transitivity,[status(thm)],[61,57]) ).
tff(63,plain,
least_upper_bound(c,b) = least_upper_bound(c,greatest_lower_bound(c,b)),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
least_upper_bound(c,b) = c,
inference(transitivity,[status(thm)],[63,55]) ).
tff(65,plain,
least_upper_bound(least_upper_bound(c,b),a) = least_upper_bound(c,greatest_lower_bound(c,a)),
inference(monotonicity,[status(thm)],[64,46]) ).
tff(66,plain,
least_upper_bound(c,greatest_lower_bound(c,a)) = least_upper_bound(least_upper_bound(c,b),a),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X )
| ( least_upper_bound(c,greatest_lower_bound(c,a)) = c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
least_upper_bound(c,greatest_lower_bound(c,a)) = c,
inference(unit_resolution,[status(thm)],[67,53]) ).
tff(69,plain,
c = least_upper_bound(c,greatest_lower_bound(c,a)),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
c = least_upper_bound(least_upper_bound(a,b),c),
inference(transitivity,[status(thm)],[69,66,32,22,18]) ).
tff(71,plain,
greatest_lower_bound(least_upper_bound(a,b),c) = greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(least_upper_bound(a,b),c)),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
greatest_lower_bound(least_upper_bound(a,b),c) = least_upper_bound(a,b),
inference(transitivity,[status(thm)],[71,9]) ).
tff(73,plain,
( ( greatest_lower_bound(least_upper_bound(a,b),c) != least_upper_bound(a,b) )
<=> ( greatest_lower_bound(least_upper_bound(a,b),c) != least_upper_bound(a,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,axiom,
greatest_lower_bound(least_upper_bound(a,b),c) != least_upper_bound(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ax_lub1b) ).
tff(75,plain,
greatest_lower_bound(least_upper_bound(a,b),c) != least_upper_bound(a,b),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
$false,
inference(unit_resolution,[status(thm)],[75,72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP147-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.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 15:45:56 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% See solution above
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------