%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP184-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 0.55s 0.75s
% Output : Proof 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 49
% Syntax : Number of formulae : 135 ( 97 unt; 0 typ; 0 def)
% Number of atoms : 189 ( 180 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 68 ( 22 ~; 18 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 210 ( 191 !; 0 ?; 210 :)
% 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/sandbox/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,
( ! [X: $i] : ( inverse(inverse(X)) = X )
<=> ! [X: $i] : ( inverse(inverse(X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ! [X: $i] : ( inverse(inverse(X)) = X )
<=> ! [X: $i] : ( inverse(inverse(X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [X: $i] : ( inverse(inverse(X)) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21_2) ).
tff(14,plain,
! [X: $i] : ( inverse(inverse(X)) = X ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : ( inverse(inverse(X)) = X ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : ( inverse(inverse(X)) = X ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,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(18,plain,
inverse(inverse(greatest_lower_bound(a,identity))) = greatest_lower_bound(a,identity),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
greatest_lower_bound(a,identity) = inverse(inverse(greatest_lower_bound(a,identity))),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
multiply(greatest_lower_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = multiply(inverse(inverse(greatest_lower_bound(a,identity))),inverse(greatest_lower_bound(a,identity))),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
multiply(inverse(inverse(greatest_lower_bound(a,identity))),inverse(greatest_lower_bound(a,identity))) = multiply(greatest_lower_bound(a,identity),inverse(greatest_lower_bound(a,identity))),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
^ [X: $i] :
refl(( ( multiply(inverse(X),X) = identity )
<=> ( multiply(inverse(X),X) = identity ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
tff(26,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(inverse(greatest_lower_bound(a,identity))),inverse(greatest_lower_bound(a,identity))) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
multiply(inverse(inverse(greatest_lower_bound(a,identity))),inverse(greatest_lower_bound(a,identity))) = identity,
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,plain,
identity = multiply(inverse(inverse(greatest_lower_bound(a,identity))),inverse(greatest_lower_bound(a,identity))),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
identity = multiply(greatest_lower_bound(a,identity),inverse(greatest_lower_bound(a,identity))),
inference(transitivity,[status(thm)],[31,21]) ).
tff(33,plain,
multiply(inverse(greatest_lower_bound(a,identity)),identity) = multiply(inverse(greatest_lower_bound(a,identity)),multiply(greatest_lower_bound(a,identity),inverse(greatest_lower_bound(a,identity)))),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
multiply(inverse(greatest_lower_bound(a,identity)),multiply(greatest_lower_bound(a,identity),inverse(greatest_lower_bound(a,identity)))) = multiply(inverse(greatest_lower_bound(a,identity)),identity),
inference(symmetry,[status(thm)],[33]) ).
tff(35,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(36,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)],[35]) ).
tff(37,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(38,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
tff(39,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(greatest_lower_bound(a,identity)),greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(a,identity))) = multiply(inverse(greatest_lower_bound(a,identity)),multiply(greatest_lower_bound(a,identity),inverse(greatest_lower_bound(a,identity)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
multiply(multiply(inverse(greatest_lower_bound(a,identity)),greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(a,identity))) = multiply(inverse(greatest_lower_bound(a,identity)),multiply(greatest_lower_bound(a,identity),inverse(greatest_lower_bound(a,identity)))),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,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(45,plain,
multiply(inverse(greatest_lower_bound(a,identity)),greatest_lower_bound(a,identity)) = identity,
inference(unit_resolution,[status(thm)],[44,28]) ).
tff(46,plain,
multiply(multiply(inverse(greatest_lower_bound(a,identity)),greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(a,identity))) = multiply(identity,inverse(greatest_lower_bound(a,identity))),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
multiply(identity,inverse(greatest_lower_bound(a,identity))) = multiply(multiply(inverse(greatest_lower_bound(a,identity)),greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(a,identity))),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
multiply(identity,inverse(greatest_lower_bound(a,identity))) = multiply(inverse(greatest_lower_bound(a,identity)),identity),
inference(transitivity,[status(thm)],[47,43,34]) ).
tff(49,plain,
( ~ ! [X: $i] : ( inverse(inverse(X)) = X )
| ( inverse(inverse(multiply(inverse(greatest_lower_bound(a,identity)),a))) = multiply(inverse(greatest_lower_bound(a,identity)),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
inverse(inverse(multiply(inverse(greatest_lower_bound(a,identity)),a))) = multiply(inverse(greatest_lower_bound(a,identity)),a),
inference(unit_resolution,[status(thm)],[49,16]) ).
tff(51,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(52,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)],[51]) ).
tff(53,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(54,axiom,
! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21_3) ).
tff(55,plain,
! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
( ~ ! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) )
| ( inverse(multiply(inverse(greatest_lower_bound(a,identity)),a)) = multiply(inverse(a),inverse(inverse(greatest_lower_bound(a,identity)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
inverse(multiply(inverse(greatest_lower_bound(a,identity)),a)) = multiply(inverse(a),inverse(inverse(greatest_lower_bound(a,identity)))),
inference(unit_resolution,[status(thm)],[58,57]) ).
tff(60,plain,
multiply(inverse(a),inverse(inverse(greatest_lower_bound(a,identity)))) = inverse(multiply(inverse(greatest_lower_bound(a,identity)),a)),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
multiply(inverse(a),greatest_lower_bound(a,identity)) = multiply(inverse(a),inverse(inverse(greatest_lower_bound(a,identity)))),
inference(monotonicity,[status(thm)],[19]) ).
tff(62,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) )
<=> ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(63,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).
tff(66,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) )
| ( multiply(inverse(a),greatest_lower_bound(a,identity)) = greatest_lower_bound(multiply(inverse(a),a),multiply(inverse(a),identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
multiply(inverse(a),greatest_lower_bound(a,identity)) = greatest_lower_bound(multiply(inverse(a),a),multiply(inverse(a),identity)),
inference(unit_resolution,[status(thm)],[69,68]) ).
tff(71,plain,
greatest_lower_bound(multiply(inverse(a),a),multiply(inverse(a),identity)) = multiply(inverse(a),greatest_lower_bound(a,identity)),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
( ( inverse(identity) = identity )
<=> ( inverse(identity) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21_1) ).
tff(74,plain,
inverse(identity) = identity,
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
multiply(inverse(a),inverse(identity)) = multiply(inverse(a),identity),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
( ~ ! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) )
| ( inverse(multiply(identity,a)) = multiply(inverse(a),inverse(identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
inverse(multiply(identity,a)) = multiply(inverse(a),inverse(identity)),
inference(unit_resolution,[status(thm)],[76,57]) ).
tff(78,plain,
^ [X: $i] :
refl(( ( multiply(identity,X) = X )
<=> ( multiply(identity,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(79,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,axiom,
! [X: $i] : ( multiply(identity,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
tff(82,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[83,79]) ).
tff(85,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
multiply(identity,a) = a,
inference(unit_resolution,[status(thm)],[85,84]) ).
tff(87,plain,
a = multiply(identity,a),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
inverse(a) = inverse(multiply(identity,a)),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,inverse(a)) = inverse(a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(90,plain,
multiply(identity,inverse(a)) = inverse(a),
inference(unit_resolution,[status(thm)],[89,84]) ).
tff(91,plain,
multiply(identity,inverse(a)) = multiply(inverse(a),identity),
inference(transitivity,[status(thm)],[90,88,77,75]) ).
tff(92,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(a),a) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(93,plain,
multiply(inverse(a),a) = identity,
inference(unit_resolution,[status(thm)],[92,28]) ).
tff(94,plain,
identity = multiply(inverse(a),a),
inference(symmetry,[status(thm)],[93]) ).
tff(95,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(inverse(a)),inverse(a)) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
multiply(inverse(inverse(a)),inverse(a)) = identity,
inference(unit_resolution,[status(thm)],[95,28]) ).
tff(97,plain,
( ~ ! [X: $i] : ( inverse(inverse(X)) = X )
| ( inverse(inverse(a)) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
inverse(inverse(a)) = a,
inference(unit_resolution,[status(thm)],[97,16]) ).
tff(99,plain,
a = inverse(inverse(a)),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
multiply(a,inverse(a)) = multiply(inverse(inverse(a)),inverse(a)),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
multiply(a,inverse(a)) = multiply(inverse(a),a),
inference(transitivity,[status(thm)],[100,96,94]) ).
tff(102,plain,
greatest_lower_bound(multiply(a,inverse(a)),multiply(identity,inverse(a))) = greatest_lower_bound(multiply(inverse(a),a),multiply(inverse(a),identity)),
inference(monotonicity,[status(thm)],[101,91]) ).
tff(103,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(104,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)],[103]) ).
tff(105,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(106,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/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
tff(107,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)],[106,105]) ).
tff(108,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)],[107]) ).
tff(109,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)],[108,104]) ).
tff(110,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,identity),inverse(a)) = greatest_lower_bound(multiply(a,inverse(a)),multiply(identity,inverse(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(111,plain,
multiply(greatest_lower_bound(a,identity),inverse(a)) = greatest_lower_bound(multiply(a,inverse(a)),multiply(identity,inverse(a))),
inference(unit_resolution,[status(thm)],[110,109]) ).
tff(112,plain,
multiply(inverse(inverse(greatest_lower_bound(a,identity))),inverse(a)) = multiply(greatest_lower_bound(a,identity),inverse(a)),
inference(monotonicity,[status(thm)],[18]) ).
tff(113,plain,
( ~ ! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) )
| ( inverse(multiply(a,inverse(greatest_lower_bound(a,identity)))) = multiply(inverse(inverse(greatest_lower_bound(a,identity))),inverse(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(114,plain,
inverse(multiply(a,inverse(greatest_lower_bound(a,identity)))) = multiply(inverse(inverse(greatest_lower_bound(a,identity))),inverse(a)),
inference(unit_resolution,[status(thm)],[113,57]) ).
tff(115,plain,
inverse(multiply(a,inverse(greatest_lower_bound(a,identity)))) = inverse(multiply(inverse(greatest_lower_bound(a,identity)),a)),
inference(transitivity,[status(thm)],[114,112,111,102,71,61,60]) ).
tff(116,plain,
inverse(inverse(multiply(a,inverse(greatest_lower_bound(a,identity))))) = inverse(inverse(multiply(inverse(greatest_lower_bound(a,identity)),a))),
inference(monotonicity,[status(thm)],[115]) ).
tff(117,plain,
( ~ ! [X: $i] : ( inverse(inverse(X)) = X )
| ( inverse(inverse(multiply(a,inverse(greatest_lower_bound(a,identity))))) = multiply(a,inverse(greatest_lower_bound(a,identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(118,plain,
inverse(inverse(multiply(a,inverse(greatest_lower_bound(a,identity))))) = multiply(a,inverse(greatest_lower_bound(a,identity))),
inference(unit_resolution,[status(thm)],[117,16]) ).
tff(119,plain,
multiply(a,inverse(greatest_lower_bound(a,identity))) = inverse(inverse(multiply(a,inverse(greatest_lower_bound(a,identity))))),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
multiply(a,inverse(greatest_lower_bound(a,identity))) = multiply(inverse(greatest_lower_bound(a,identity)),a),
inference(transitivity,[status(thm)],[119,116,50]) ).
tff(121,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(monotonicity,[status(thm)],[120,48]) ).
tff(122,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(123,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)],[122]) ).
tff(124,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(125,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/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).
tff(126,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)],[125,124]) ).
tff(127,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)],[126]) ).
tff(128,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)],[127,123]) ).
tff(129,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(130,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)],[129,128]) ).
tff(131,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)],[130,121,10]) ).
tff(132,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(133,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/sandbox/benchmark/theBenchmark.p',prove_p21) ).
tff(134,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)],[133,132]) ).
tff(135,plain,
$false,
inference(unit_resolution,[status(thm)],[134,131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : GRP184-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.13/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Jun 19 15:44:26 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.55/0.75 % SZS status Unsatisfiable
% 0.55/0.75 % SZS output start Proof
% See solution above
% 0.55/0.77 % E exiting
%------------------------------------------------------------------------------