%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP193-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:07:26 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.50s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 43
% Syntax : Number of formulae : 119 ( 87 unt; 0 typ; 0 def)
% Number of atoms : 165 ( 157 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 57 ( 18 ~; 14 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 7 ( 7 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; 4 con; 0-2 aty)
% Number of variables : 165 ( 150 !; 0 ?; 165 :)
% Comments :
%------------------------------------------------------------------------------
tff(greatest_lower_bound_type,type,
greatest_lower_bound: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(a_type,type,
a: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(identity_type,type,
identity: $i ).
tff(least_upper_bound_type,type,
least_upper_bound: ( $i * $i ) > $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( multiply(identity,X) = X )
<=> ( multiply(identity,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( multiply(identity,X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
tff(5,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,greatest_lower_bound(a,c)) = greatest_lower_bound(a,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
multiply(identity,greatest_lower_bound(a,c)) = greatest_lower_bound(a,c),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ( greatest_lower_bound(a,b) = identity )
<=> ( greatest_lower_bound(a,b) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
greatest_lower_bound(a,b) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8_9b_4) ).
tff(12,plain,
greatest_lower_bound(a,b) = identity,
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
identity = greatest_lower_bound(a,b),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
multiply(identity,greatest_lower_bound(a,c)) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) = multiply(identity,greatest_lower_bound(a,c)),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) )
<=> ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
tff(20,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) )
| ( multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) = greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) = greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))),
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(symmetry,[status(thm)],[24]) ).
tff(26,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(27,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)],[26]) ).
tff(28,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(29,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(30,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X )
| ( greatest_lower_bound(greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))),least_upper_bound(greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))),a)) = greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
greatest_lower_bound(greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))),least_upper_bound(greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))),a)) = greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))),
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,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(36,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)],[35]) ).
tff(37,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(38,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(39,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
| ( least_upper_bound(a,greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c)))) = least_upper_bound(greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
least_upper_bound(a,greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c)))) = least_upper_bound(greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))),a),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))) = greatest_lower_bound(a,c),
inference(transitivity,[status(thm)],[25,15,9]) ).
tff(45,plain,
least_upper_bound(a,greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c)))) = least_upper_bound(a,greatest_lower_bound(a,c)),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
least_upper_bound(a,greatest_lower_bound(a,c)) = least_upper_bound(a,greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c)))),
inference(symmetry,[status(thm)],[45]) ).
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(a,greatest_lower_bound(a,c)) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
least_upper_bound(a,greatest_lower_bound(a,c)) = a,
inference(unit_resolution,[status(thm)],[54,53]) ).
tff(56,plain,
a = least_upper_bound(a,greatest_lower_bound(a,c)),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
a = least_upper_bound(greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))),a),
inference(transitivity,[status(thm)],[56,46,43]) ).
tff(58,plain,
greatest_lower_bound(greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))),a) = greatest_lower_bound(greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))),least_upper_bound(greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))),a)),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
greatest_lower_bound(a,c) = multiply(identity,greatest_lower_bound(a,c)),
inference(symmetry,[status(thm)],[9]) ).
tff(60,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(61,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)],[60]) ).
tff(62,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(63,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(64,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,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(68,plain,
greatest_lower_bound(a,c) = greatest_lower_bound(c,a),
inference(unit_resolution,[status(thm)],[67,66]) ).
tff(69,plain,
greatest_lower_bound(c,a) = greatest_lower_bound(a,c),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,c) = c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
multiply(identity,c) = c,
inference(unit_resolution,[status(thm)],[70,7]) ).
tff(72,plain,
( ( greatest_lower_bound(identity,b) = identity )
<=> ( greatest_lower_bound(identity,b) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,axiom,
greatest_lower_bound(identity,b) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8_9b_2) ).
tff(74,plain,
greatest_lower_bound(identity,b) = identity,
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
| ( greatest_lower_bound(identity,b) = greatest_lower_bound(b,identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
greatest_lower_bound(identity,b) = greatest_lower_bound(b,identity),
inference(unit_resolution,[status(thm)],[75,66]) ).
tff(77,plain,
greatest_lower_bound(b,identity) = greatest_lower_bound(identity,b),
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
greatest_lower_bound(b,identity) = identity,
inference(transitivity,[status(thm)],[77,74]) ).
tff(79,plain,
multiply(greatest_lower_bound(b,identity),c) = multiply(identity,c),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) )
| ( multiply(greatest_lower_bound(b,identity),c) = greatest_lower_bound(multiply(b,c),multiply(identity,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(81,plain,
multiply(greatest_lower_bound(b,identity),c) = greatest_lower_bound(multiply(b,c),multiply(identity,c)),
inference(unit_resolution,[status(thm)],[80,22]) ).
tff(82,plain,
greatest_lower_bound(multiply(b,c),multiply(identity,c)) = multiply(greatest_lower_bound(b,identity),c),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
c = multiply(identity,c),
inference(symmetry,[status(thm)],[71]) ).
tff(84,plain,
greatest_lower_bound(multiply(b,c),c) = greatest_lower_bound(multiply(b,c),multiply(identity,c)),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
greatest_lower_bound(multiply(b,c),c) = c,
inference(transitivity,[status(thm)],[84,82,79,71]) ).
tff(86,plain,
greatest_lower_bound(greatest_lower_bound(multiply(b,c),c),a) = greatest_lower_bound(c,a),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,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(88,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)],[87]) ).
tff(89,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(90,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/sandbox2/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).
tff(91,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)],[90,89]) ).
tff(92,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)],[91]) ).
tff(93,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)],[92,88]) ).
tff(94,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(multiply(b,c),greatest_lower_bound(c,a)) = greatest_lower_bound(greatest_lower_bound(multiply(b,c),c),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(95,plain,
greatest_lower_bound(multiply(b,c),greatest_lower_bound(c,a)) = greatest_lower_bound(greatest_lower_bound(multiply(b,c),c),a),
inference(unit_resolution,[status(thm)],[94,93]) ).
tff(96,plain,
multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) = greatest_lower_bound(c,a),
inference(transitivity,[status(thm)],[15,9,68]) ).
tff(97,plain,
greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(c,a)),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
greatest_lower_bound(multiply(b,c),greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c)))) = greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
inference(monotonicity,[status(thm)],[25]) ).
tff(99,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
| ( greatest_lower_bound(multiply(b,c),greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c)))) = greatest_lower_bound(greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))),multiply(b,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(100,plain,
greatest_lower_bound(multiply(b,c),greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c)))) = greatest_lower_bound(greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))),multiply(b,c)),
inference(unit_resolution,[status(thm)],[99,66]) ).
tff(101,plain,
greatest_lower_bound(greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))),multiply(b,c)) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c)))),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
greatest_lower_bound(greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))),multiply(b,c)) = greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))),
inference(transitivity,[status(thm)],[101,98,97,95,86,69,59,14,24]) ).
tff(103,plain,
greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))),multiply(b,c)),a) = greatest_lower_bound(greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))),a),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,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(greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))),greatest_lower_bound(multiply(b,c),a)) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))),multiply(b,c)),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
greatest_lower_bound(greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))),greatest_lower_bound(multiply(b,c),a)) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))),multiply(b,c)),a),
inference(unit_resolution,[status(thm)],[104,93]) ).
tff(106,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
| ( greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(multiply(b,c),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(107,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(multiply(b,c),a),
inference(unit_resolution,[status(thm)],[106,66]) ).
tff(108,plain,
greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),greatest_lower_bound(a,multiply(b,c))) = greatest_lower_bound(greatest_lower_bound(multiply(a,greatest_lower_bound(a,c)),multiply(b,greatest_lower_bound(a,c))),greatest_lower_bound(multiply(b,c),a)),
inference(monotonicity,[status(thm)],[24,107]) ).
tff(109,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
| ( greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),greatest_lower_bound(a,multiply(b,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),greatest_lower_bound(a,multiply(b,c))),
inference(unit_resolution,[status(thm)],[109,66]) ).
tff(111,plain,
( ( greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)) )
<=> ( greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(112,axiom,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8_9b_5) ).
tff(113,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c),
inference(transitivity,[status(thm)],[114,110,108,105,103,58,34,25,15,9]) ).
tff(116,plain,
( ( greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c) )
<=> ( greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,axiom,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p8_9b) ).
tff(118,plain,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
$false,
inference(unit_resolution,[status(thm)],[118,115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP193-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n004.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 15:47:08 EDT 2025
% 0.20/0.34 % CPUTime :
% 0.21/0.50 % SZS status Unsatisfiable
% 0.21/0.50 % SZS output start Proof
% See solution above
% 0.21/0.52 % E exiting
%------------------------------------------------------------------------------