%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP175-4 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:07:21 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 40
% Syntax : Number of formulae : 111 ( 82 unt; 0 typ; 0 def)
% Number of atoms : 158 ( 148 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 51 ( 13 ~; 9 |; 0 &)
% ( 29 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 9 ( 9 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 : 180 ( 162 !; 0 ?; 180 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(least_upper_bound_type,type,
least_upper_bound: ( $i * $i ) > $i ).
tff(identity_type,type,
identity: $i ).
tff(greatest_lower_bound_type,type,
greatest_lower_bound: ( $i * $i ) > $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( greatest_lower_bound(X,X) = X )
<=> ( greatest_lower_bound(X,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( greatest_lower_bound(X,X) = X )
<=> ! [X: $i] : ( greatest_lower_bound(X,X) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( greatest_lower_bound(X,X) = X )
<=> ! [X: $i] : ( greatest_lower_bound(X,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( greatest_lower_bound(X,X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',idempotence_of_gld) ).
tff(5,plain,
! [X: $i] : ( greatest_lower_bound(X,X) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( greatest_lower_bound(X,X) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( greatest_lower_bound(X,X) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( greatest_lower_bound(X,X) = X )
| ( greatest_lower_bound(b,b) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
greatest_lower_bound(b,b) = b,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
b = greatest_lower_bound(b,b),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
multiply(b,a) = multiply(greatest_lower_bound(b,b),a),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
multiply(greatest_lower_bound(b,b),a) = multiply(b,a),
inference(symmetry,[status(thm)],[11]) ).
tff(13,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(14,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)],[13]) ).
tff(15,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(16,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(17,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)],[16,15]) ).
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)) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,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)],[18,14]) ).
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)) )
| ( multiply(greatest_lower_bound(b,b),a) = greatest_lower_bound(multiply(b,a),multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
multiply(greatest_lower_bound(b,b),a) = greatest_lower_bound(multiply(b,a),multiply(b,a)),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
greatest_lower_bound(multiply(b,a),multiply(b,a)) = multiply(greatest_lower_bound(b,b),a),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
greatest_lower_bound(multiply(b,a),multiply(b,a)) = multiply(b,a),
inference(transitivity,[status(thm)],[22,12]) ).
tff(24,plain,
least_upper_bound(greatest_lower_bound(multiply(b,a),multiply(b,a)),multiply(identity,a)) = least_upper_bound(multiply(b,a),multiply(identity,a)),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
least_upper_bound(multiply(b,a),multiply(identity,a)) = least_upper_bound(greatest_lower_bound(multiply(b,a),multiply(b,a)),multiply(identity,a)),
inference(symmetry,[status(thm)],[24]) ).
tff(26,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(27,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)],[26]) ).
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)) )
<=> ! [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(29,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(30,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)],[29,28]) ).
tff(31,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)],[30]) ).
tff(32,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)],[31,27]) ).
tff(33,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(b,identity),a) = least_upper_bound(multiply(b,a),multiply(identity,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
multiply(least_upper_bound(b,identity),a) = least_upper_bound(multiply(b,a),multiply(identity,a)),
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,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(36,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)],[35]) ).
tff(37,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(38,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(39,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X )
| ( least_upper_bound(b,greatest_lower_bound(b,identity)) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
least_upper_bound(b,greatest_lower_bound(b,identity)) = b,
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,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(45,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)],[44]) ).
tff(46,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(47,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(48,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,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(52,plain,
greatest_lower_bound(identity,b) = greatest_lower_bound(b,identity),
inference(unit_resolution,[status(thm)],[51,50]) ).
tff(53,plain,
( ( greatest_lower_bound(identity,b) = identity )
<=> ( greatest_lower_bound(identity,b) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,axiom,
greatest_lower_bound(identity,b) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p06d_1) ).
tff(55,plain,
greatest_lower_bound(identity,b) = identity,
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
identity = greatest_lower_bound(identity,b),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
identity = greatest_lower_bound(b,identity),
inference(transitivity,[status(thm)],[56,52]) ).
tff(58,plain,
least_upper_bound(b,identity) = least_upper_bound(b,greatest_lower_bound(b,identity)),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
least_upper_bound(b,identity) = b,
inference(transitivity,[status(thm)],[58,43]) ).
tff(60,plain,
multiply(least_upper_bound(b,identity),a) = multiply(b,a),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
multiply(b,a) = multiply(least_upper_bound(b,identity),a),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
multiply(b,a) = least_upper_bound(greatest_lower_bound(multiply(b,a),multiply(b,a)),multiply(identity,a)),
inference(transitivity,[status(thm)],[61,34,25]) ).
tff(63,plain,
multiply(inverse(a),multiply(b,a)) = multiply(inverse(a),least_upper_bound(greatest_lower_bound(multiply(b,a),multiply(b,a)),multiply(identity,a))),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
multiply(inverse(a),least_upper_bound(greatest_lower_bound(multiply(b,a),multiply(b,a)),multiply(identity,a))) = multiply(inverse(a),multiply(b,a)),
inference(symmetry,[status(thm)],[63]) ).
tff(65,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(66,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)],[65]) ).
tff(67,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(68,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(69,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)],[68,67]) ).
tff(70,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)],[69]) ).
tff(71,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)],[70,66]) ).
tff(72,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) )
| ( multiply(inverse(a),least_upper_bound(greatest_lower_bound(multiply(b,a),multiply(b,a)),multiply(identity,a))) = least_upper_bound(multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(b,a))),multiply(inverse(a),multiply(identity,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
multiply(inverse(a),least_upper_bound(greatest_lower_bound(multiply(b,a),multiply(b,a)),multiply(identity,a))) = least_upper_bound(multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(b,a))),multiply(inverse(a),multiply(identity,a))),
inference(unit_resolution,[status(thm)],[72,71]) ).
tff(74,plain,
least_upper_bound(multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(b,a))),multiply(inverse(a),multiply(identity,a))) = multiply(inverse(a),least_upper_bound(greatest_lower_bound(multiply(b,a),multiply(b,a)),multiply(identity,a))),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
^ [X: $i] :
refl(( ( multiply(inverse(X),X) = identity )
<=> ( multiply(inverse(X),X) = identity ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,axiom,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
tff(79,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(a),a) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
multiply(inverse(a),a) = identity,
inference(unit_resolution,[status(thm)],[82,81]) ).
tff(84,plain,
^ [X: $i] :
refl(( ( multiply(identity,X) = X )
<=> ( multiply(identity,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(85,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,axiom,
! [X: $i] : ( multiply(identity,X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
tff(88,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(skolemize,[status(sab)],[88]) ).
tff(90,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
multiply(identity,a) = a,
inference(unit_resolution,[status(thm)],[91,90]) ).
tff(93,plain,
multiply(inverse(a),multiply(identity,a)) = multiply(inverse(a),a),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
multiply(inverse(a),multiply(identity,a)) = identity,
inference(transitivity,[status(thm)],[93,83]) ).
tff(95,plain,
multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(b,a))) = multiply(inverse(a),multiply(b,a)),
inference(monotonicity,[status(thm)],[23]) ).
tff(96,plain,
least_upper_bound(multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(b,a))),multiply(inverse(a),multiply(identity,a))) = least_upper_bound(multiply(inverse(a),multiply(b,a)),identity),
inference(monotonicity,[status(thm)],[95,94]) ).
tff(97,plain,
least_upper_bound(multiply(inverse(a),multiply(b,a)),identity) = least_upper_bound(multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(b,a))),multiply(inverse(a),multiply(identity,a))),
inference(symmetry,[status(thm)],[96]) ).
tff(98,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(99,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)],[98]) ).
tff(100,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(101,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(102,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(skolemize,[status(sab)],[102]) ).
tff(104,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[103,99]) ).
tff(105,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
| ( least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) = least_upper_bound(multiply(inverse(a),multiply(b,a)),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) = least_upper_bound(multiply(inverse(a),multiply(b,a)),identity),
inference(unit_resolution,[status(thm)],[105,104]) ).
tff(107,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) = multiply(inverse(a),multiply(b,a)),
inference(transitivity,[status(thm)],[106,97,74,64]) ).
tff(108,plain,
( ( least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),multiply(b,a)) )
<=> ( least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),multiply(b,a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,axiom,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),multiply(b,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p06d) ).
tff(110,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),multiply(b,a)),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
$false,
inference(unit_resolution,[status(thm)],[110,107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP175-4 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.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 15:45:02 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% See solution above
% 0.12/0.40 % E exiting
%------------------------------------------------------------------------------