%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP185-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:07:24 AM UTC 2025
% Result : Unsatisfiable 0.60s 0.79s
% Output : Proof 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 49
% Syntax : Number of formulae : 164 ( 125 unt; 0 typ; 0 def)
% Number of atoms : 219 ( 210 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 72 ( 25 ~; 21 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 8 ( 8 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 214 ( 196 !; 0 ?; 214 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(least_upper_bound_type,type,
least_upper_bound: ( $i * $i ) > $i ).
tff(identity_type,type,
identity: $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(greatest_lower_bound_type,type,
greatest_lower_bound: ( $i * $i ) > $i ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) )
<=> ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) )
| ( multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) = least_upper_bound(multiply(least_upper_bound(a,identity),b),multiply(least_upper_bound(a,identity),identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) = least_upper_bound(multiply(least_upper_bound(a,identity),b),multiply(least_upper_bound(a,identity),identity)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
least_upper_bound(multiply(least_upper_bound(a,identity),b),multiply(least_upper_bound(a,identity),identity)) = multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,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(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(quant_intro,[status(thm)],[11]) ).
tff(13,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(14,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(15,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
| ( least_upper_bound(multiply(least_upper_bound(a,identity),b),multiply(least_upper_bound(a,identity),identity)) = least_upper_bound(multiply(least_upper_bound(a,identity),identity),multiply(least_upper_bound(a,identity),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
least_upper_bound(multiply(least_upper_bound(a,identity),b),multiply(least_upper_bound(a,identity),identity)) = least_upper_bound(multiply(least_upper_bound(a,identity),identity),multiply(least_upper_bound(a,identity),b)),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
least_upper_bound(multiply(least_upper_bound(a,identity),identity),multiply(least_upper_bound(a,identity),b)) = least_upper_bound(multiply(least_upper_bound(a,identity),b),multiply(least_upper_bound(a,identity),identity)),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) )
<=> ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).
tff(25,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) )
| ( multiply(least_upper_bound(a,identity),b) = least_upper_bound(multiply(a,b),multiply(identity,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
multiply(least_upper_bound(a,identity),b) = least_upper_bound(multiply(a,b),multiply(identity,b)),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
( ( inverse(identity) = identity )
<=> ( inverse(identity) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22a_1) ).
tff(32,plain,
inverse(identity) = identity,
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
multiply(identity,identity) = multiply(inverse(identity),identity),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
multiply(inverse(identity),identity) = multiply(identity,identity),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
^ [X: $i] :
refl(( ( multiply(inverse(X),X) = identity )
<=> ( multiply(inverse(X),X) = identity ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
tff(40,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(identity),identity) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
multiply(inverse(identity),identity) = identity,
inference(unit_resolution,[status(thm)],[43,42]) ).
tff(45,plain,
identity = multiply(inverse(identity),identity),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
identity = multiply(identity,identity),
inference(transitivity,[status(thm)],[45,35]) ).
tff(47,plain,
least_upper_bound(multiply(a,identity),identity) = least_upper_bound(multiply(a,identity),multiply(identity,identity)),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
least_upper_bound(multiply(a,identity),multiply(identity,identity)) = least_upper_bound(multiply(a,identity),identity),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) )
| ( multiply(least_upper_bound(a,identity),identity) = least_upper_bound(multiply(a,identity),multiply(identity,identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
multiply(least_upper_bound(a,identity),identity) = least_upper_bound(multiply(a,identity),multiply(identity,identity)),
inference(unit_resolution,[status(thm)],[49,27]) ).
tff(51,plain,
multiply(least_upper_bound(a,identity),identity) = least_upper_bound(multiply(a,identity),identity),
inference(transitivity,[status(thm)],[50,48]) ).
tff(52,plain,
least_upper_bound(multiply(least_upper_bound(a,identity),identity),multiply(least_upper_bound(a,identity),b)) = least_upper_bound(least_upper_bound(multiply(a,identity),identity),least_upper_bound(multiply(a,b),multiply(identity,b))),
inference(monotonicity,[status(thm)],[51,29]) ).
tff(53,plain,
least_upper_bound(least_upper_bound(multiply(a,identity),identity),least_upper_bound(multiply(a,b),multiply(identity,b))) = least_upper_bound(multiply(least_upper_bound(a,identity),identity),multiply(least_upper_bound(a,identity),b)),
inference(symmetry,[status(thm)],[52]) ).
tff(54,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(55,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)],[54]) ).
tff(56,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(57,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(58,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)],[57,56]) ).
tff(59,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)],[58]) ).
tff(60,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)],[59,55]) ).
tff(61,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(multiply(a,identity),least_upper_bound(identity,least_upper_bound(multiply(a,b),multiply(identity,b)))) = least_upper_bound(least_upper_bound(multiply(a,identity),identity),least_upper_bound(multiply(a,b),multiply(identity,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
least_upper_bound(multiply(a,identity),least_upper_bound(identity,least_upper_bound(multiply(a,b),multiply(identity,b)))) = least_upper_bound(least_upper_bound(multiply(a,identity),identity),least_upper_bound(multiply(a,b),multiply(identity,b))),
inference(unit_resolution,[status(thm)],[61,60]) ).
tff(63,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(least_upper_bound(identity,multiply(a,b)),least_upper_bound(multiply(a,b),multiply(identity,b))) = least_upper_bound(least_upper_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,b)),multiply(identity,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
least_upper_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(multiply(a,b),multiply(identity,b))) = least_upper_bound(least_upper_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,b)),multiply(identity,b)),
inference(unit_resolution,[status(thm)],[63,60]) ).
tff(65,plain,
least_upper_bound(least_upper_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,b)),multiply(identity,b)) = least_upper_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(multiply(a,b),multiply(identity,b))),
inference(symmetry,[status(thm)],[64]) ).
tff(66,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(67,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)],[66]) ).
tff(68,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(69,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(70,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
| ( greatest_lower_bound(multiply(a,b),least_upper_bound(identity,multiply(a,b))) = greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
greatest_lower_bound(multiply(a,b),least_upper_bound(identity,multiply(a,b))) = greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,b)),
inference(unit_resolution,[status(thm)],[73,72]) ).
tff(75,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
| ( least_upper_bound(multiply(a,b),identity) = least_upper_bound(identity,multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
least_upper_bound(multiply(a,b),identity) = least_upper_bound(identity,multiply(a,b)),
inference(unit_resolution,[status(thm)],[75,17]) ).
tff(77,plain,
least_upper_bound(identity,multiply(a,b)) = least_upper_bound(multiply(a,b),identity),
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
greatest_lower_bound(multiply(a,b),least_upper_bound(identity,multiply(a,b))) = greatest_lower_bound(multiply(a,b),least_upper_bound(multiply(a,b),identity)),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
greatest_lower_bound(multiply(a,b),least_upper_bound(multiply(a,b),identity)) = greatest_lower_bound(multiply(a,b),least_upper_bound(identity,multiply(a,b))),
inference(symmetry,[status(thm)],[78]) ).
tff(80,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(81,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)],[80]) ).
tff(82,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(83,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(84,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(skolemize,[status(sab)],[84]) ).
tff(86,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[85,81]) ).
tff(87,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X )
| ( greatest_lower_bound(multiply(a,b),least_upper_bound(multiply(a,b),identity)) = multiply(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(88,plain,
greatest_lower_bound(multiply(a,b),least_upper_bound(multiply(a,b),identity)) = multiply(a,b),
inference(unit_resolution,[status(thm)],[87,86]) ).
tff(89,plain,
multiply(a,b) = greatest_lower_bound(multiply(a,b),least_upper_bound(multiply(a,b),identity)),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
multiply(a,b) = greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,b)),
inference(transitivity,[status(thm)],[89,79,74]) ).
tff(91,plain,
least_upper_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,b)) = least_upper_bound(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,b))),
inference(monotonicity,[status(thm)],[90]) ).
tff(92,plain,
least_upper_bound(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,b))) = least_upper_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,b)),
inference(symmetry,[status(thm)],[91]) ).
tff(93,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(94,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)],[93]) ).
tff(95,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(96,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(97,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
inference(skolemize,[status(sab)],[97]) ).
tff(99,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[98,94]) ).
tff(100,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X )
| ( least_upper_bound(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,b))) = least_upper_bound(identity,multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
least_upper_bound(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,b))) = least_upper_bound(identity,multiply(a,b)),
inference(unit_resolution,[status(thm)],[100,99]) ).
tff(102,plain,
least_upper_bound(identity,multiply(a,b)) = least_upper_bound(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,b))),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
least_upper_bound(identity,multiply(a,b)) = least_upper_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,b)),
inference(transitivity,[status(thm)],[102,92]) ).
tff(104,plain,
least_upper_bound(least_upper_bound(identity,multiply(a,b)),multiply(identity,b)) = least_upper_bound(least_upper_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,b)),multiply(identity,b)),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,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(identity,least_upper_bound(multiply(a,b),multiply(identity,b))) = least_upper_bound(least_upper_bound(identity,multiply(a,b)),multiply(identity,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
least_upper_bound(identity,least_upper_bound(multiply(a,b),multiply(identity,b))) = least_upper_bound(least_upper_bound(identity,multiply(a,b)),multiply(identity,b)),
inference(unit_resolution,[status(thm)],[105,60]) ).
tff(107,plain,
least_upper_bound(identity,least_upper_bound(multiply(a,b),multiply(identity,b))) = least_upper_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(multiply(a,b),multiply(identity,b))),
inference(transitivity,[status(thm)],[106,104,65]) ).
tff(108,plain,
least_upper_bound(multiply(a,identity),least_upper_bound(identity,least_upper_bound(multiply(a,b),multiply(identity,b)))) = least_upper_bound(multiply(a,identity),least_upper_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(multiply(a,b),multiply(identity,b)))),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
least_upper_bound(multiply(a,identity),least_upper_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(multiply(a,b),multiply(identity,b)))) = least_upper_bound(multiply(a,identity),least_upper_bound(identity,least_upper_bound(multiply(a,b),multiply(identity,b)))),
inference(symmetry,[status(thm)],[108]) ).
tff(110,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(multiply(a,identity),least_upper_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(multiply(a,b),multiply(identity,b)))) = least_upper_bound(least_upper_bound(multiply(a,identity),least_upper_bound(identity,multiply(a,b))),least_upper_bound(multiply(a,b),multiply(identity,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(111,plain,
least_upper_bound(multiply(a,identity),least_upper_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(multiply(a,b),multiply(identity,b)))) = least_upper_bound(least_upper_bound(multiply(a,identity),least_upper_bound(identity,multiply(a,b))),least_upper_bound(multiply(a,b),multiply(identity,b))),
inference(unit_resolution,[status(thm)],[110,60]) ).
tff(112,plain,
least_upper_bound(least_upper_bound(multiply(a,identity),least_upper_bound(identity,multiply(a,b))),least_upper_bound(multiply(a,b),multiply(identity,b))) = least_upper_bound(multiply(a,identity),least_upper_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(multiply(a,b),multiply(identity,b)))),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
| ( least_upper_bound(least_upper_bound(multiply(a,identity),multiply(identity,identity)),least_upper_bound(identity,multiply(a,b))) = least_upper_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(multiply(a,identity),multiply(identity,identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(114,plain,
least_upper_bound(least_upper_bound(multiply(a,identity),multiply(identity,identity)),least_upper_bound(identity,multiply(a,b))) = least_upper_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(multiply(a,identity),multiply(identity,identity))),
inference(unit_resolution,[status(thm)],[113,17]) ).
tff(115,plain,
least_upper_bound(multiply(a,identity),multiply(identity,identity)) = multiply(least_upper_bound(a,identity),identity),
inference(symmetry,[status(thm)],[50]) ).
tff(116,plain,
least_upper_bound(least_upper_bound(multiply(a,identity),multiply(identity,identity)),least_upper_bound(identity,multiply(a,b))) = least_upper_bound(multiply(least_upper_bound(a,identity),identity),least_upper_bound(identity,multiply(a,b))),
inference(monotonicity,[status(thm)],[115]) ).
tff(117,plain,
least_upper_bound(multiply(least_upper_bound(a,identity),identity),least_upper_bound(identity,multiply(a,b))) = least_upper_bound(least_upper_bound(multiply(a,identity),multiply(identity,identity)),least_upper_bound(identity,multiply(a,b))),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
least_upper_bound(multiply(least_upper_bound(a,identity),identity),least_upper_bound(identity,multiply(a,b))) = least_upper_bound(least_upper_bound(multiply(a,identity),identity),least_upper_bound(identity,multiply(a,b))),
inference(monotonicity,[status(thm)],[51]) ).
tff(119,plain,
least_upper_bound(least_upper_bound(multiply(a,identity),identity),least_upper_bound(identity,multiply(a,b))) = least_upper_bound(multiply(least_upper_bound(a,identity),identity),least_upper_bound(identity,multiply(a,b))),
inference(symmetry,[status(thm)],[118]) ).
tff(120,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(multiply(a,identity),least_upper_bound(identity,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(least_upper_bound(multiply(a,identity),identity),least_upper_bound(identity,multiply(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(121,plain,
least_upper_bound(multiply(a,identity),least_upper_bound(identity,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(least_upper_bound(multiply(a,identity),identity),least_upper_bound(identity,multiply(a,b))),
inference(unit_resolution,[status(thm)],[120,60]) ).
tff(122,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X )
| ( least_upper_bound(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))))) = least_upper_bound(identity,multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(123,plain,
least_upper_bound(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))))) = least_upper_bound(identity,multiply(a,b)),
inference(unit_resolution,[status(thm)],[122,99]) ).
tff(124,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)))) = greatest_lower_bound(least_upper_bound(multiply(a,b),identity),least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)))),
inference(monotonicity,[status(thm)],[77]) ).
tff(125,plain,
greatest_lower_bound(least_upper_bound(multiply(a,b),identity),least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)))) = greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)))),
inference(symmetry,[status(thm)],[124]) ).
tff(126,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X )
| ( greatest_lower_bound(least_upper_bound(multiply(a,b),identity),least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)))) = least_upper_bound(multiply(a,b),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(127,plain,
greatest_lower_bound(least_upper_bound(multiply(a,b),identity),least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)))) = least_upper_bound(multiply(a,b),identity),
inference(unit_resolution,[status(thm)],[126,86]) ).
tff(128,plain,
least_upper_bound(multiply(a,b),identity) = greatest_lower_bound(least_upper_bound(multiply(a,b),identity),least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)))),
inference(symmetry,[status(thm)],[127]) ).
tff(129,plain,
least_upper_bound(identity,multiply(a,b)) = greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)))),
inference(transitivity,[status(thm)],[77,128,125]) ).
tff(130,plain,
least_upper_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(identity,multiply(a,b))) = least_upper_bound(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))))),
inference(monotonicity,[status(thm)],[129]) ).
tff(131,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(identity,least_upper_bound(multiply(a,b),least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(identity,multiply(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(132,plain,
least_upper_bound(identity,least_upper_bound(multiply(a,b),least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(identity,multiply(a,b))),
inference(unit_resolution,[status(thm)],[131,60]) ).
tff(133,plain,
least_upper_bound(multiply(a,b),least_upper_bound(identity,multiply(a,b))) = least_upper_bound(multiply(a,b),least_upper_bound(multiply(a,b),identity)),
inference(monotonicity,[status(thm)],[77]) ).
tff(134,plain,
least_upper_bound(multiply(a,b),least_upper_bound(multiply(a,b),identity)) = least_upper_bound(multiply(a,b),least_upper_bound(identity,multiply(a,b))),
inference(symmetry,[status(thm)],[133]) ).
tff(135,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(multiply(a,b),least_upper_bound(multiply(a,b),identity)) = least_upper_bound(least_upper_bound(multiply(a,b),multiply(a,b)),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(136,plain,
least_upper_bound(multiply(a,b),least_upper_bound(multiply(a,b),identity)) = least_upper_bound(least_upper_bound(multiply(a,b),multiply(a,b)),identity),
inference(unit_resolution,[status(thm)],[135,60]) ).
tff(137,plain,
least_upper_bound(least_upper_bound(multiply(a,b),multiply(a,b)),identity) = least_upper_bound(multiply(a,b),least_upper_bound(multiply(a,b),identity)),
inference(symmetry,[status(thm)],[136]) ).
tff(138,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X )
| ( least_upper_bound(multiply(a,b),greatest_lower_bound(multiply(a,b),least_upper_bound(identity,multiply(a,b)))) = multiply(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(139,plain,
least_upper_bound(multiply(a,b),greatest_lower_bound(multiply(a,b),least_upper_bound(identity,multiply(a,b)))) = multiply(a,b),
inference(unit_resolution,[status(thm)],[138,99]) ).
tff(140,plain,
multiply(a,b) = greatest_lower_bound(multiply(a,b),least_upper_bound(identity,multiply(a,b))),
inference(transitivity,[status(thm)],[89,79]) ).
tff(141,plain,
least_upper_bound(multiply(a,b),multiply(a,b)) = least_upper_bound(multiply(a,b),greatest_lower_bound(multiply(a,b),least_upper_bound(identity,multiply(a,b)))),
inference(monotonicity,[status(thm)],[140]) ).
tff(142,plain,
least_upper_bound(multiply(a,b),multiply(a,b)) = multiply(a,b),
inference(transitivity,[status(thm)],[141,139]) ).
tff(143,plain,
least_upper_bound(least_upper_bound(multiply(a,b),multiply(a,b)),identity) = least_upper_bound(multiply(a,b),identity),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
least_upper_bound(multiply(a,b),identity) = least_upper_bound(least_upper_bound(multiply(a,b),multiply(a,b)),identity),
inference(symmetry,[status(thm)],[143]) ).
tff(145,plain,
least_upper_bound(identity,multiply(a,b)) = least_upper_bound(multiply(a,b),least_upper_bound(identity,multiply(a,b))),
inference(transitivity,[status(thm)],[77,144,137,134]) ).
tff(146,plain,
least_upper_bound(identity,least_upper_bound(identity,multiply(a,b))) = least_upper_bound(identity,least_upper_bound(multiply(a,b),least_upper_bound(identity,multiply(a,b)))),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
least_upper_bound(identity,least_upper_bound(identity,multiply(a,b))) = least_upper_bound(identity,multiply(a,b)),
inference(transitivity,[status(thm)],[146,132,130,123]) ).
tff(148,plain,
least_upper_bound(multiply(a,identity),least_upper_bound(identity,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(multiply(a,identity),least_upper_bound(identity,multiply(a,b))),
inference(monotonicity,[status(thm)],[147]) ).
tff(149,plain,
least_upper_bound(multiply(a,identity),least_upper_bound(identity,multiply(a,b))) = least_upper_bound(multiply(a,identity),least_upper_bound(identity,least_upper_bound(identity,multiply(a,b)))),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
least_upper_bound(multiply(a,identity),least_upper_bound(identity,multiply(a,b))) = least_upper_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(multiply(a,identity),multiply(identity,identity))),
inference(transitivity,[status(thm)],[149,121,119,117,114]) ).
tff(151,plain,
least_upper_bound(least_upper_bound(multiply(a,identity),least_upper_bound(identity,multiply(a,b))),least_upper_bound(multiply(a,b),multiply(identity,b))) = least_upper_bound(least_upper_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(multiply(a,identity),multiply(identity,identity))),least_upper_bound(multiply(a,b),multiply(identity,b))),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
least_upper_bound(least_upper_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(multiply(a,identity),multiply(identity,identity))),least_upper_bound(multiply(a,b),multiply(identity,b))) = least_upper_bound(least_upper_bound(multiply(a,identity),least_upper_bound(identity,multiply(a,b))),least_upper_bound(multiply(a,b),multiply(identity,b))),
inference(symmetry,[status(thm)],[151]) ).
tff(153,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(least_upper_bound(identity,multiply(a,b)),least_upper_bound(least_upper_bound(multiply(a,identity),multiply(identity,identity)),least_upper_bound(multiply(a,b),multiply(identity,b)))) = least_upper_bound(least_upper_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(multiply(a,identity),multiply(identity,identity))),least_upper_bound(multiply(a,b),multiply(identity,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(154,plain,
least_upper_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(least_upper_bound(multiply(a,identity),multiply(identity,identity)),least_upper_bound(multiply(a,b),multiply(identity,b)))) = least_upper_bound(least_upper_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(multiply(a,identity),multiply(identity,identity))),least_upper_bound(multiply(a,b),multiply(identity,b))),
inference(unit_resolution,[status(thm)],[153,60]) ).
tff(155,plain,
least_upper_bound(multiply(a,b),multiply(identity,b)) = multiply(least_upper_bound(a,identity),b),
inference(symmetry,[status(thm)],[29]) ).
tff(156,plain,
least_upper_bound(least_upper_bound(multiply(a,identity),multiply(identity,identity)),least_upper_bound(multiply(a,b),multiply(identity,b))) = least_upper_bound(multiply(least_upper_bound(a,identity),identity),multiply(least_upper_bound(a,identity),b)),
inference(monotonicity,[status(thm)],[115,155]) ).
tff(157,plain,
least_upper_bound(least_upper_bound(multiply(a,identity),multiply(identity,identity)),least_upper_bound(multiply(a,b),multiply(identity,b))) = multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
inference(transitivity,[status(thm)],[156,20,10]) ).
tff(158,plain,
least_upper_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(least_upper_bound(multiply(a,identity),multiply(identity,identity)),least_upper_bound(multiply(a,b),multiply(identity,b)))) = least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))),
inference(monotonicity,[status(thm)],[77,157]) ).
tff(159,plain,
least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) = least_upper_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(least_upper_bound(multiply(a,identity),multiply(identity,identity)),least_upper_bound(multiply(a,b),multiply(identity,b)))),
inference(symmetry,[status(thm)],[158]) ).
tff(160,plain,
least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) = multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
inference(transitivity,[status(thm)],[159,154,152,112,109,62,53,20,10]) ).
tff(161,plain,
( ( least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) )
<=> ( least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(162,axiom,
least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p22a) ).
tff(163,plain,
least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
inference(modus_ponens,[status(thm)],[162,161]) ).
tff(164,plain,
$false,
inference(unit_resolution,[status(thm)],[163,160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GRP185-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 15:45:56 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.60/0.79 % SZS status Unsatisfiable
% 0.60/0.79 % SZS output start Proof
% See solution above
% 0.60/0.81 % E exiting
%------------------------------------------------------------------------------