TSTP Solution File: GRP184-4 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP184-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 : Fri Sep 16 22:26:39 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 60
% Syntax : Number of formulae : 170 ( 122 unt; 6 typ; 0 def)
% Number of atoms : 224 ( 214 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 75 ( 24 ~; 20 |; 0 &)
% ( 31 <=>; 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 : 7 ( 4 >; 3 *; 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 : 226 ( 206 !; 0 ?; 226 :)
% 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,
^ [Y: $i,X: $i] :
refl(
( ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
<=> ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
<=> ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
<=> ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
tff(15,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
| ( least_upper_bound(multiply(inverse(greatest_lower_bound(a,identity)),a),multiply(inverse(greatest_lower_bound(a,identity)),identity)) = least_upper_bound(multiply(inverse(greatest_lower_bound(a,identity)),identity),multiply(inverse(greatest_lower_bound(a,identity)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
least_upper_bound(multiply(inverse(greatest_lower_bound(a,identity)),a),multiply(inverse(greatest_lower_bound(a,identity)),identity)) = least_upper_bound(multiply(inverse(greatest_lower_bound(a,identity)),identity),multiply(inverse(greatest_lower_bound(a,identity)),a)),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
least_upper_bound(multiply(inverse(greatest_lower_bound(a,identity)),identity),multiply(inverse(greatest_lower_bound(a,identity)),a)) = least_upper_bound(multiply(inverse(greatest_lower_bound(a,identity)),a),multiply(inverse(greatest_lower_bound(a,identity)),identity)),
inference(symmetry,[status(thm)],[19]) ).
tff(21,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(22,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)],[21]) ).
tff(23,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(24,axiom,
! [Y: $i,X: $i] : ( inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21x_4) ).
tff(25,plain,
! [Y: $i,X: $i] : ( inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [Y: $i,X: $i] : ( inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Y: $i,X: $i] : ( inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,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(29,plain,
inverse(greatest_lower_bound(a,identity)) = least_upper_bound(inverse(a),inverse(identity)),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
least_upper_bound(inverse(a),inverse(identity)) = inverse(greatest_lower_bound(a,identity)),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
( ( inverse(identity) = identity )
<=> ( inverse(identity) = identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21x_1) ).
tff(33,plain,
inverse(identity) = identity,
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
least_upper_bound(inverse(a),identity) = least_upper_bound(inverse(a),inverse(identity)),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
least_upper_bound(inverse(a),identity) = inverse(greatest_lower_bound(a,identity)),
inference(transitivity,[status(thm)],[35,30]) ).
tff(37,plain,
multiply(least_upper_bound(inverse(a),identity),a) = multiply(inverse(greatest_lower_bound(a,identity)),a),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,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(39,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)],[38]) ).
tff(40,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(41,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(42,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)],[41,40]) ).
tff(43,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)],[42]) ).
tff(44,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)],[43,39]) ).
tff(45,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(46,plain,
multiply(least_upper_bound(inverse(a),identity),a) = least_upper_bound(multiply(inverse(a),a),multiply(identity,a)),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
least_upper_bound(multiply(inverse(a),a),multiply(identity,a)) = multiply(least_upper_bound(inverse(a),identity),a),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
^ [X: $i] :
refl(
( ( multiply(inverse(X),X) = identity )
<=> ( multiply(inverse(X),X) = identity ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,axiom,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
tff(52,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(a),a) = identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
multiply(inverse(a),a) = identity,
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
identity = multiply(inverse(a),a),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
least_upper_bound(identity,multiply(identity,a)) = least_upper_bound(multiply(inverse(a),a),multiply(identity,a)),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
least_upper_bound(identity,multiply(identity,a)) = multiply(inverse(greatest_lower_bound(a,identity)),a),
inference(transitivity,[status(thm)],[58,47,37]) ).
tff(60,plain,
inverse(least_upper_bound(inverse(a),inverse(identity))) = inverse(inverse(greatest_lower_bound(a,identity))),
inference(monotonicity,[status(thm)],[30]) ).
tff(61,plain,
inverse(inverse(greatest_lower_bound(a,identity))) = inverse(least_upper_bound(inverse(a),inverse(identity))),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
( ! [X: $i] : ( inverse(inverse(X)) = X )
<=> ! [X: $i] : ( inverse(inverse(X)) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
( ! [X: $i] : ( inverse(inverse(X)) = X )
<=> ! [X: $i] : ( inverse(inverse(X)) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,axiom,
! [X: $i] : ( inverse(inverse(X)) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21x_2) ).
tff(65,plain,
! [X: $i] : ( inverse(inverse(X)) = X ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [X: $i] : ( inverse(inverse(X)) = X ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [X: $i] : ( inverse(inverse(X)) = X ),
inference(modus_ponens,[status(thm)],[66,62]) ).
tff(68,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(69,plain,
inverse(inverse(greatest_lower_bound(a,identity))) = greatest_lower_bound(a,identity),
inference(unit_resolution,[status(thm)],[68,67]) ).
tff(70,plain,
greatest_lower_bound(a,identity) = inverse(inverse(greatest_lower_bound(a,identity))),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
greatest_lower_bound(a,identity) = inverse(least_upper_bound(inverse(a),inverse(identity))),
inference(transitivity,[status(thm)],[70,61]) ).
tff(72,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)],[71]) ).
tff(73,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)],[72]) ).
tff(74,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(75,plain,
multiply(inverse(least_upper_bound(inverse(a),inverse(identity))),least_upper_bound(inverse(a),inverse(identity))) = identity,
inference(unit_resolution,[status(thm)],[74,54]) ).
tff(76,plain,
identity = multiply(inverse(least_upper_bound(inverse(a),inverse(identity))),least_upper_bound(inverse(a),inverse(identity))),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
identity = multiply(greatest_lower_bound(a,identity),least_upper_bound(inverse(a),inverse(identity))),
inference(transitivity,[status(thm)],[76,73]) ).
tff(78,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)],[29,77]) ).
tff(79,plain,
multiply(least_upper_bound(inverse(a),inverse(identity)),multiply(greatest_lower_bound(a,identity),least_upper_bound(inverse(a),inverse(identity)))) = multiply(inverse(greatest_lower_bound(a,identity)),identity),
inference(symmetry,[status(thm)],[78]) ).
tff(80,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(81,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)],[80]) ).
tff(82,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(83,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(84,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[84]) ).
tff(86,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[85,81]) ).
tff(87,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(88,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)],[87,86]) ).
tff(89,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(90,plain,
multiply(inverse(greatest_lower_bound(a,identity)),greatest_lower_bound(a,identity)) = identity,
inference(unit_resolution,[status(thm)],[89,54]) ).
tff(91,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)],[30]) ).
tff(92,plain,
multiply(least_upper_bound(inverse(a),inverse(identity)),greatest_lower_bound(a,identity)) = identity,
inference(transitivity,[status(thm)],[91,90]) ).
tff(93,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)],[92,30]) ).
tff(94,plain,
multiply(identity,inverse(greatest_lower_bound(a,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)],[93]) ).
tff(95,plain,
multiply(identity,inverse(greatest_lower_bound(a,identity))) = multiply(identity,least_upper_bound(inverse(a),inverse(identity))),
inference(monotonicity,[status(thm)],[29]) ).
tff(96,plain,
multiply(identity,least_upper_bound(inverse(a),inverse(identity))) = multiply(identity,inverse(greatest_lower_bound(a,identity))),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
^ [X: $i] :
refl(
( ( multiply(identity,X) = X )
<=> ( multiply(identity,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(98,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,axiom,
! [X: $i] : ( multiply(identity,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
tff(101,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(skolemize,[status(sab)],[101]) ).
tff(103,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[102,98]) ).
tff(104,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,least_upper_bound(inverse(a),inverse(identity))) = least_upper_bound(inverse(a),inverse(identity)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(105,plain,
multiply(identity,least_upper_bound(inverse(a),inverse(identity))) = least_upper_bound(inverse(a),inverse(identity)),
inference(unit_resolution,[status(thm)],[104,103]) ).
tff(106,plain,
least_upper_bound(inverse(a),inverse(identity)) = multiply(identity,least_upper_bound(inverse(a),inverse(identity))),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
least_upper_bound(inverse(a),inverse(identity)) = multiply(inverse(greatest_lower_bound(a,identity)),identity),
inference(transitivity,[status(thm)],[106,96,94,88,79]) ).
tff(108,plain,
least_upper_bound(least_upper_bound(inverse(a),inverse(identity)),least_upper_bound(identity,multiply(identity,a))) = least_upper_bound(multiply(inverse(greatest_lower_bound(a,identity)),identity),multiply(inverse(greatest_lower_bound(a,identity)),a)),
inference(monotonicity,[status(thm)],[107,59]) ).
tff(109,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) )
<=> ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ) )),
inference(bind,[status(th)],]) ).
tff(110,plain,
( ! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ) ),
inference(quant_intro,[status(thm)],[109]) ).
tff(111,plain,
( ! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(112,axiom,
! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_lub) ).
tff(113,plain,
! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ),
inference(skolemize,[status(sab)],[113]) ).
tff(115,plain,
! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[114,110]) ).
tff(116,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) )
| ( least_upper_bound(least_upper_bound(inverse(a),inverse(identity)),least_upper_bound(identity,multiply(identity,a))) = least_upper_bound(least_upper_bound(least_upper_bound(inverse(a),inverse(identity)),identity),multiply(identity,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(117,plain,
least_upper_bound(least_upper_bound(inverse(a),inverse(identity)),least_upper_bound(identity,multiply(identity,a))) = least_upper_bound(least_upper_bound(least_upper_bound(inverse(a),inverse(identity)),identity),multiply(identity,a)),
inference(unit_resolution,[status(thm)],[116,115]) ).
tff(118,plain,
least_upper_bound(least_upper_bound(least_upper_bound(inverse(a),inverse(identity)),identity),multiply(identity,a)) = least_upper_bound(least_upper_bound(inverse(a),inverse(identity)),least_upper_bound(identity,multiply(identity,a))),
inference(symmetry,[status(thm)],[117]) ).
tff(119,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(120,plain,
multiply(identity,a) = a,
inference(unit_resolution,[status(thm)],[119,103]) ).
tff(121,plain,
a = multiply(identity,a),
inference(symmetry,[status(thm)],[120]) ).
tff(122,plain,
( ~ ! [X: $i] : ( inverse(inverse(X)) = X )
| ( inverse(inverse(a)) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(123,plain,
inverse(inverse(a)) = a,
inference(unit_resolution,[status(thm)],[122,67]) ).
tff(124,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,inverse(a)) = inverse(a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(125,plain,
multiply(identity,inverse(a)) = inverse(a),
inference(unit_resolution,[status(thm)],[124,103]) ).
tff(126,plain,
inverse(multiply(identity,inverse(a))) = inverse(inverse(a)),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,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(128,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)],[127]) ).
tff(129,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(130,axiom,
! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21x_3) ).
tff(131,plain,
! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ),
inference(skolemize,[status(sab)],[131]) ).
tff(133,plain,
! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ),
inference(modus_ponens,[status(thm)],[132,128]) ).
tff(134,plain,
( ~ ! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) )
| ( inverse(multiply(identity,inverse(a))) = multiply(inverse(inverse(a)),inverse(identity)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(135,plain,
inverse(multiply(identity,inverse(a))) = multiply(inverse(inverse(a)),inverse(identity)),
inference(unit_resolution,[status(thm)],[134,133]) ).
tff(136,plain,
multiply(inverse(inverse(a)),inverse(identity)) = inverse(multiply(identity,inverse(a))),
inference(symmetry,[status(thm)],[135]) ).
tff(137,plain,
a = inverse(inverse(a)),
inference(symmetry,[status(thm)],[123]) ).
tff(138,plain,
multiply(a,identity) = multiply(inverse(inverse(a)),inverse(identity)),
inference(monotonicity,[status(thm)],[137,34]) ).
tff(139,plain,
multiply(a,identity) = multiply(identity,a),
inference(transitivity,[status(thm)],[138,136,126,123,121]) ).
tff(140,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(inverse(a)),inverse(a)) = identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(141,plain,
multiply(inverse(inverse(a)),inverse(a)) = identity,
inference(unit_resolution,[status(thm)],[140,54]) ).
tff(142,plain,
multiply(a,inverse(a)) = multiply(inverse(inverse(a)),inverse(a)),
inference(monotonicity,[status(thm)],[137]) ).
tff(143,plain,
multiply(a,inverse(a)) = identity,
inference(transitivity,[status(thm)],[142,141]) ).
tff(144,plain,
least_upper_bound(least_upper_bound(inverse(a),inverse(identity)),multiply(a,inverse(a))) = least_upper_bound(least_upper_bound(inverse(a),inverse(identity)),identity),
inference(monotonicity,[status(thm)],[143]) ).
tff(145,plain,
least_upper_bound(least_upper_bound(least_upper_bound(inverse(a),inverse(identity)),multiply(a,inverse(a))),multiply(a,identity)) = least_upper_bound(least_upper_bound(least_upper_bound(inverse(a),inverse(identity)),identity),multiply(identity,a)),
inference(monotonicity,[status(thm)],[144,139]) ).
tff(146,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) )
| ( least_upper_bound(least_upper_bound(inverse(a),inverse(identity)),least_upper_bound(multiply(a,inverse(a)),multiply(a,identity))) = least_upper_bound(least_upper_bound(least_upper_bound(inverse(a),inverse(identity)),multiply(a,inverse(a))),multiply(a,identity)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(147,plain,
least_upper_bound(least_upper_bound(inverse(a),inverse(identity)),least_upper_bound(multiply(a,inverse(a)),multiply(a,identity))) = least_upper_bound(least_upper_bound(least_upper_bound(inverse(a),inverse(identity)),multiply(a,inverse(a))),multiply(a,identity)),
inference(unit_resolution,[status(thm)],[146,115]) ).
tff(148,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(149,plain,
multiply(a,least_upper_bound(inverse(a),identity)) = least_upper_bound(multiply(a,inverse(a)),multiply(a,identity)),
inference(unit_resolution,[status(thm)],[148,7]) ).
tff(150,plain,
least_upper_bound(inverse(a),inverse(identity)) = least_upper_bound(inverse(a),identity),
inference(symmetry,[status(thm)],[35]) ).
tff(151,plain,
inverse(greatest_lower_bound(a,identity)) = least_upper_bound(inverse(a),identity),
inference(transitivity,[status(thm)],[29,150]) ).
tff(152,plain,
multiply(a,inverse(greatest_lower_bound(a,identity))) = multiply(a,least_upper_bound(inverse(a),identity)),
inference(monotonicity,[status(thm)],[151]) ).
tff(153,plain,
multiply(a,inverse(greatest_lower_bound(a,identity))) = least_upper_bound(multiply(a,inverse(a)),multiply(a,identity)),
inference(transitivity,[status(thm)],[152,149]) ).
tff(154,plain,
multiply(identity,inverse(greatest_lower_bound(a,identity))) = least_upper_bound(inverse(a),inverse(identity)),
inference(transitivity,[status(thm)],[95,105]) ).
tff(155,plain,
least_upper_bound(multiply(identity,inverse(greatest_lower_bound(a,identity))),multiply(a,inverse(greatest_lower_bound(a,identity)))) = least_upper_bound(least_upper_bound(inverse(a),inverse(identity)),least_upper_bound(multiply(a,inverse(a)),multiply(a,identity))),
inference(monotonicity,[status(thm)],[154,153]) ).
tff(156,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
| ( least_upper_bound(multiply(a,inverse(greatest_lower_bound(a,identity))),multiply(identity,inverse(greatest_lower_bound(a,identity)))) = least_upper_bound(multiply(identity,inverse(greatest_lower_bound(a,identity))),multiply(a,inverse(greatest_lower_bound(a,identity)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(157,plain,
least_upper_bound(multiply(a,inverse(greatest_lower_bound(a,identity))),multiply(identity,inverse(greatest_lower_bound(a,identity)))) = least_upper_bound(multiply(identity,inverse(greatest_lower_bound(a,identity))),multiply(a,inverse(greatest_lower_bound(a,identity)))),
inference(unit_resolution,[status(thm)],[156,17]) ).
tff(158,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(159,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)],[158,44]) ).
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(transitivity,[status(thm)],[159,157,155,147,145,118,108,20,10]) ).
tff(161,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(162,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_p21x) ).
tff(163,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)],[162,161]) ).
tff(164,plain,
$false,
inference(unit_resolution,[status(thm)],[163,160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP184-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n008.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 : Wed Aug 31 15:38:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.43 % SZS status Unsatisfiable
% 0.19/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------