%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP184-4 : 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 0.14s 0.43s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 51
% Syntax : Number of formulae : 161 ( 121 unt; 0 typ; 0 def)
% Number of atoms : 217 ( 208 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 72 ( 24 ~; 20 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 199 ( 182 !; 0 ?; 199 :)
% 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(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(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) = least_upper_bound(multiply(inverse(greatest_lower_bound(a,identity)),a),multiply(inverse(greatest_lower_bound(a,identity)),identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) = least_upper_bound(multiply(inverse(greatest_lower_bound(a,identity)),a),multiply(inverse(greatest_lower_bound(a,identity)),identity)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
least_upper_bound(multiply(inverse(greatest_lower_bound(a,identity)),a),multiply(inverse(greatest_lower_bound(a,identity)),identity)) = multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [Y: $i,X: $i] :
refl(( ( inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)) )
<=> ( inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)) )
<=> ! [Y: $i,X: $i] : ( inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [Y: $i,X: $i] : ( inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)) )
<=> ! [Y: $i,X: $i] : ( inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
! [Y: $i,X: $i] : ( inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21x_4) ).
tff(15,plain,
! [Y: $i,X: $i] : ( inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [Y: $i,X: $i] : ( inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [Y: $i,X: $i] : ( inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)) )
| ( inverse(greatest_lower_bound(a,identity)) = least_upper_bound(inverse(a),inverse(identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
inverse(greatest_lower_bound(a,identity)) = least_upper_bound(inverse(a),inverse(identity)),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
least_upper_bound(inverse(a),inverse(identity)) = inverse(greatest_lower_bound(a,identity)),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
^ [X: $i] :
refl(( ( multiply(inverse(X),X) = identity )
<=> ( multiply(inverse(X),X) = identity ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
tff(25,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(greatest_lower_bound(a,identity)),greatest_lower_bound(a,identity)) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
multiply(inverse(greatest_lower_bound(a,identity)),greatest_lower_bound(a,identity)) = identity,
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
multiply(least_upper_bound(inverse(a),inverse(identity)),greatest_lower_bound(a,identity)) = multiply(inverse(greatest_lower_bound(a,identity)),greatest_lower_bound(a,identity)),
inference(monotonicity,[status(thm)],[20]) ).
tff(31,plain,
multiply(least_upper_bound(inverse(a),inverse(identity)),greatest_lower_bound(a,identity)) = identity,
inference(transitivity,[status(thm)],[30,29]) ).
tff(32,plain,
multiply(multiply(least_upper_bound(inverse(a),inverse(identity)),greatest_lower_bound(a,identity)),least_upper_bound(inverse(a),inverse(identity))) = multiply(identity,inverse(greatest_lower_bound(a,identity))),
inference(monotonicity,[status(thm)],[31,20]) ).
tff(33,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
tff(37,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(least_upper_bound(inverse(a),inverse(identity)),greatest_lower_bound(a,identity)),least_upper_bound(inverse(a),inverse(identity))) = multiply(least_upper_bound(inverse(a),inverse(identity)),multiply(greatest_lower_bound(a,identity),least_upper_bound(inverse(a),inverse(identity)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
multiply(multiply(least_upper_bound(inverse(a),inverse(identity)),greatest_lower_bound(a,identity)),least_upper_bound(inverse(a),inverse(identity))) = multiply(least_upper_bound(inverse(a),inverse(identity)),multiply(greatest_lower_bound(a,identity),least_upper_bound(inverse(a),inverse(identity)))),
inference(unit_resolution,[status(thm)],[40,39]) ).
tff(42,plain,
multiply(least_upper_bound(inverse(a),inverse(identity)),multiply(greatest_lower_bound(a,identity),least_upper_bound(inverse(a),inverse(identity)))) = multiply(multiply(least_upper_bound(inverse(a),inverse(identity)),greatest_lower_bound(a,identity)),least_upper_bound(inverse(a),inverse(identity))),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
inverse(least_upper_bound(inverse(a),inverse(identity))) = inverse(inverse(greatest_lower_bound(a,identity))),
inference(monotonicity,[status(thm)],[20]) ).
tff(44,plain,
inverse(inverse(greatest_lower_bound(a,identity))) = inverse(least_upper_bound(inverse(a),inverse(identity))),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
( ! [X: $i] : ( inverse(inverse(X)) = X )
<=> ! [X: $i] : ( inverse(inverse(X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ! [X: $i] : ( inverse(inverse(X)) = X )
<=> ! [X: $i] : ( inverse(inverse(X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
! [X: $i] : ( inverse(inverse(X)) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21x_2) ).
tff(48,plain,
! [X: $i] : ( inverse(inverse(X)) = X ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [X: $i] : ( inverse(inverse(X)) = X ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [X: $i] : ( inverse(inverse(X)) = X ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
( ~ ! [X: $i] : ( inverse(inverse(X)) = X )
| ( inverse(inverse(greatest_lower_bound(a,identity))) = greatest_lower_bound(a,identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
inverse(inverse(greatest_lower_bound(a,identity))) = greatest_lower_bound(a,identity),
inference(unit_resolution,[status(thm)],[51,50]) ).
tff(53,plain,
greatest_lower_bound(a,identity) = inverse(inverse(greatest_lower_bound(a,identity))),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
greatest_lower_bound(a,identity) = inverse(least_upper_bound(inverse(a),inverse(identity))),
inference(transitivity,[status(thm)],[53,44]) ).
tff(55,plain,
multiply(greatest_lower_bound(a,identity),least_upper_bound(inverse(a),inverse(identity))) = multiply(inverse(least_upper_bound(inverse(a),inverse(identity))),least_upper_bound(inverse(a),inverse(identity))),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
multiply(inverse(least_upper_bound(inverse(a),inverse(identity))),least_upper_bound(inverse(a),inverse(identity))) = multiply(greatest_lower_bound(a,identity),least_upper_bound(inverse(a),inverse(identity))),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(least_upper_bound(inverse(a),inverse(identity))),least_upper_bound(inverse(a),inverse(identity))) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
multiply(inverse(least_upper_bound(inverse(a),inverse(identity))),least_upper_bound(inverse(a),inverse(identity))) = identity,
inference(unit_resolution,[status(thm)],[57,27]) ).
tff(59,plain,
identity = multiply(inverse(least_upper_bound(inverse(a),inverse(identity))),least_upper_bound(inverse(a),inverse(identity))),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
identity = multiply(greatest_lower_bound(a,identity),least_upper_bound(inverse(a),inverse(identity))),
inference(transitivity,[status(thm)],[59,56]) ).
tff(61,plain,
multiply(inverse(greatest_lower_bound(a,identity)),identity) = multiply(least_upper_bound(inverse(a),inverse(identity)),multiply(greatest_lower_bound(a,identity),least_upper_bound(inverse(a),inverse(identity)))),
inference(monotonicity,[status(thm)],[19,60]) ).
tff(62,plain,
multiply(inverse(greatest_lower_bound(a,identity)),identity) = multiply(identity,inverse(greatest_lower_bound(a,identity))),
inference(transitivity,[status(thm)],[61,42,32]) ).
tff(63,plain,
( ( inverse(identity) = identity )
<=> ( inverse(identity) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21x_1) ).
tff(65,plain,
inverse(identity) = identity,
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
least_upper_bound(inverse(a),identity) = least_upper_bound(inverse(a),inverse(identity)),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
least_upper_bound(inverse(a),inverse(identity)) = least_upper_bound(inverse(a),identity),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
inverse(greatest_lower_bound(a,identity)) = least_upper_bound(inverse(a),identity),
inference(transitivity,[status(thm)],[19,68]) ).
tff(70,plain,
multiply(a,inverse(greatest_lower_bound(a,identity))) = multiply(a,least_upper_bound(inverse(a),identity)),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
multiply(a,least_upper_bound(inverse(a),identity)) = multiply(a,inverse(greatest_lower_bound(a,identity))),
inference(symmetry,[status(thm)],[70]) ).
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(a,least_upper_bound(inverse(a),identity)) = least_upper_bound(multiply(a,inverse(a)),multiply(a,identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
multiply(a,least_upper_bound(inverse(a),identity)) = least_upper_bound(multiply(a,inverse(a)),multiply(a,identity)),
inference(unit_resolution,[status(thm)],[72,7]) ).
tff(74,plain,
least_upper_bound(multiply(a,inverse(a)),multiply(a,identity)) = multiply(a,least_upper_bound(inverse(a),identity)),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
multiply(identity,identity) = multiply(inverse(identity),identity),
inference(monotonicity,[status(thm)],[66]) ).
tff(76,plain,
multiply(inverse(identity),identity) = multiply(identity,identity),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(identity),identity) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
multiply(inverse(identity),identity) = identity,
inference(unit_resolution,[status(thm)],[77,27]) ).
tff(79,plain,
identity = multiply(inverse(identity),identity),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(inverse(a)),inverse(a)) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(81,plain,
multiply(inverse(inverse(a)),inverse(a)) = identity,
inference(unit_resolution,[status(thm)],[80,27]) ).
tff(82,plain,
( ~ ! [X: $i] : ( inverse(inverse(X)) = X )
| ( inverse(inverse(a)) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
inverse(inverse(a)) = a,
inference(unit_resolution,[status(thm)],[82,50]) ).
tff(84,plain,
a = inverse(inverse(a)),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
multiply(a,inverse(a)) = multiply(inverse(inverse(a)),inverse(a)),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
multiply(a,inverse(a)) = multiply(identity,identity),
inference(transitivity,[status(thm)],[85,81,79,76]) ).
tff(87,plain,
least_upper_bound(multiply(a,inverse(a)),multiply(a,identity)) = least_upper_bound(multiply(identity,identity),multiply(a,identity)),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
least_upper_bound(multiply(identity,identity),multiply(a,identity)) = least_upper_bound(multiply(a,inverse(a)),multiply(a,identity)),
inference(symmetry,[status(thm)],[87]) ).
tff(89,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(90,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)],[89]) ).
tff(91,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(92,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(93,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)],[92,91]) ).
tff(94,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)],[93]) ).
tff(95,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)],[94,90]) ).
tff(96,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(identity,a),identity) = least_upper_bound(multiply(identity,identity),multiply(a,identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(97,plain,
multiply(least_upper_bound(identity,a),identity) = least_upper_bound(multiply(identity,identity),multiply(a,identity)),
inference(unit_resolution,[status(thm)],[96,95]) ).
tff(98,plain,
greatest_lower_bound(inverse(a),identity) = greatest_lower_bound(inverse(a),inverse(identity)),
inference(monotonicity,[status(thm)],[66]) ).
tff(99,plain,
greatest_lower_bound(inverse(a),inverse(identity)) = greatest_lower_bound(inverse(a),identity),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
inverse(greatest_lower_bound(inverse(a),inverse(identity))) = inverse(greatest_lower_bound(inverse(a),identity)),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
inverse(greatest_lower_bound(inverse(a),identity)) = inverse(greatest_lower_bound(inverse(a),inverse(identity))),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
( ~ ! [Y: $i,X: $i] : ( inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)) )
| ( inverse(greatest_lower_bound(inverse(a),identity)) = least_upper_bound(inverse(inverse(a)),inverse(identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,plain,
inverse(greatest_lower_bound(inverse(a),identity)) = least_upper_bound(inverse(inverse(a)),inverse(identity)),
inference(unit_resolution,[status(thm)],[102,17]) ).
tff(104,plain,
least_upper_bound(inverse(inverse(a)),inverse(identity)) = inverse(greatest_lower_bound(inverse(a),identity)),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
least_upper_bound(inverse(inverse(a)),inverse(identity)) = least_upper_bound(a,identity),
inference(monotonicity,[status(thm)],[83,65]) ).
tff(106,plain,
least_upper_bound(a,identity) = least_upper_bound(inverse(inverse(a)),inverse(identity)),
inference(symmetry,[status(thm)],[105]) ).
tff(107,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(108,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)],[107]) ).
tff(109,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(110,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(111,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(skolemize,[status(sab)],[111]) ).
tff(113,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[112,108]) ).
tff(114,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
| ( least_upper_bound(a,identity) = least_upper_bound(identity,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
least_upper_bound(a,identity) = least_upper_bound(identity,a),
inference(unit_resolution,[status(thm)],[114,113]) ).
tff(116,plain,
least_upper_bound(identity,a) = least_upper_bound(a,identity),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
least_upper_bound(identity,a) = inverse(greatest_lower_bound(inverse(a),inverse(identity))),
inference(transitivity,[status(thm)],[116,106,104,101]) ).
tff(118,plain,
multiply(least_upper_bound(identity,a),identity) = multiply(inverse(greatest_lower_bound(inverse(a),inverse(identity))),inverse(identity)),
inference(monotonicity,[status(thm)],[117,66]) ).
tff(119,plain,
multiply(inverse(greatest_lower_bound(inverse(a),inverse(identity))),inverse(identity)) = multiply(least_upper_bound(identity,a),identity),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
^ [Y: $i,X: $i] :
refl(( ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) )
<=> ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(121,plain,
( ! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) )
<=> ! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ) ),
inference(quant_intro,[status(thm)],[120]) ).
tff(122,plain,
( ! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) )
<=> ! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(123,axiom,
! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21x_3) ).
tff(124,plain,
! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ),
inference(skolemize,[status(sab)],[124]) ).
tff(126,plain,
! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ),
inference(modus_ponens,[status(thm)],[125,121]) ).
tff(127,plain,
( ~ ! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) )
| ( inverse(multiply(identity,greatest_lower_bound(inverse(a),inverse(identity)))) = multiply(inverse(greatest_lower_bound(inverse(a),inverse(identity))),inverse(identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(128,plain,
inverse(multiply(identity,greatest_lower_bound(inverse(a),inverse(identity)))) = multiply(inverse(greatest_lower_bound(inverse(a),inverse(identity))),inverse(identity)),
inference(unit_resolution,[status(thm)],[127,126]) ).
tff(129,plain,
^ [X: $i] :
refl(( ( multiply(identity,X) = X )
<=> ( multiply(identity,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(130,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(quant_intro,[status(thm)],[129]) ).
tff(131,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(132,axiom,
! [X: $i] : ( multiply(identity,X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
tff(133,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(skolemize,[status(sab)],[133]) ).
tff(135,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[134,130]) ).
tff(136,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,greatest_lower_bound(inverse(a),inverse(identity))) = greatest_lower_bound(inverse(a),inverse(identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
multiply(identity,greatest_lower_bound(inverse(a),inverse(identity))) = greatest_lower_bound(inverse(a),inverse(identity)),
inference(unit_resolution,[status(thm)],[136,135]) ).
tff(138,plain,
inverse(multiply(identity,greatest_lower_bound(inverse(a),inverse(identity)))) = inverse(greatest_lower_bound(inverse(a),inverse(identity))),
inference(monotonicity,[status(thm)],[137]) ).
tff(139,plain,
inverse(greatest_lower_bound(inverse(a),inverse(identity))) = inverse(multiply(identity,greatest_lower_bound(inverse(a),inverse(identity)))),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,least_upper_bound(identity,a)) = least_upper_bound(identity,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(141,plain,
multiply(identity,least_upper_bound(identity,a)) = least_upper_bound(identity,a),
inference(unit_resolution,[status(thm)],[140,135]) ).
tff(142,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) )
| ( multiply(identity,least_upper_bound(identity,a)) = least_upper_bound(multiply(identity,identity),multiply(identity,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(143,plain,
multiply(identity,least_upper_bound(identity,a)) = least_upper_bound(multiply(identity,identity),multiply(identity,a)),
inference(unit_resolution,[status(thm)],[142,7]) ).
tff(144,plain,
least_upper_bound(multiply(identity,identity),multiply(identity,a)) = multiply(identity,least_upper_bound(identity,a)),
inference(symmetry,[status(thm)],[143]) ).
tff(145,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(a),a) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(146,plain,
multiply(inverse(a),a) = identity,
inference(unit_resolution,[status(thm)],[145,27]) ).
tff(147,plain,
multiply(inverse(a),a) = multiply(identity,identity),
inference(transitivity,[status(thm)],[146,79,76]) ).
tff(148,plain,
least_upper_bound(multiply(inverse(a),a),multiply(identity,a)) = least_upper_bound(multiply(identity,identity),multiply(identity,a)),
inference(monotonicity,[status(thm)],[147]) ).
tff(149,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(inverse(a),identity),a) = least_upper_bound(multiply(inverse(a),a),multiply(identity,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(150,plain,
multiply(least_upper_bound(inverse(a),identity),a) = least_upper_bound(multiply(inverse(a),a),multiply(identity,a)),
inference(unit_resolution,[status(thm)],[149,95]) ).
tff(151,plain,
multiply(inverse(greatest_lower_bound(a,identity)),a) = multiply(least_upper_bound(inverse(a),identity),a),
inference(monotonicity,[status(thm)],[69]) ).
tff(152,plain,
multiply(inverse(greatest_lower_bound(a,identity)),a) = multiply(a,inverse(greatest_lower_bound(a,identity))),
inference(transitivity,[status(thm)],[151,150,148,144,141,116,106,104,101,139,128,119,97,88,74,71]) ).
tff(153,plain,
least_upper_bound(multiply(inverse(greatest_lower_bound(a,identity)),a),multiply(inverse(greatest_lower_bound(a,identity)),identity)) = least_upper_bound(multiply(a,inverse(greatest_lower_bound(a,identity))),multiply(identity,inverse(greatest_lower_bound(a,identity)))),
inference(monotonicity,[status(thm)],[152,62]) ).
tff(154,plain,
least_upper_bound(multiply(a,inverse(greatest_lower_bound(a,identity))),multiply(identity,inverse(greatest_lower_bound(a,identity)))) = least_upper_bound(multiply(inverse(greatest_lower_bound(a,identity)),a),multiply(inverse(greatest_lower_bound(a,identity)),identity)),
inference(symmetry,[status(thm)],[153]) ).
tff(155,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),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(multiply(a,inverse(greatest_lower_bound(a,identity))),multiply(identity,inverse(greatest_lower_bound(a,identity)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(156,plain,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(multiply(a,inverse(greatest_lower_bound(a,identity))),multiply(identity,inverse(greatest_lower_bound(a,identity)))),
inference(unit_resolution,[status(thm)],[155,95]) ).
tff(157,plain,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
inference(transitivity,[status(thm)],[156,154,10]) ).
tff(158,plain,
( ( multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) )
<=> ( multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(159,axiom,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p21x) ).
tff(160,plain,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
$false,
inference(unit_resolution,[status(thm)],[160,157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : GRP184-4 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.14/0.14 % 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 15:46:12 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.14/0.43 % SZS status Unsatisfiable
% 0.14/0.43 % SZS output start Proof
% See solution above
% 0.23/0.45 % E exiting
%------------------------------------------------------------------------------