%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP181-4 : 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 05:07:22 AM UTC 2025
% Result : Unsatisfiable 3.02s 3.22s
% Output : Proof 3.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 81
% Syntax : Number of formulae : 268 ( 204 unt; 0 typ; 0 def)
% Number of atoms : 356 ( 343 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 114 ( 38 ~; 34 |; 0 &)
% ( 42 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 12 ( 12 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 319 ( 292 !; 0 ?; 319 :)
% Comments :
%------------------------------------------------------------------------------
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(identity_type,type,
identity: $i ).
tff(greatest_lower_bound_type,type,
greatest_lower_bound: ( $i * $i ) > $i ).
tff(least_upper_bound_type,type,
least_upper_bound: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(1,plain,
( ! [X: $i] : ( inverse(inverse(X)) = X )
<=> ! [X: $i] : ( inverse(inverse(X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,plain,
( ! [X: $i] : ( inverse(inverse(X)) = X )
<=> ! [X: $i] : ( inverse(inverse(X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
! [X: $i] : ( inverse(inverse(X)) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12x_2) ).
tff(4,plain,
! [X: $i] : ( inverse(inverse(X)) = X ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
! [X: $i] : ( inverse(inverse(X)) = X ),
inference(skolemize,[status(sab)],[4]) ).
tff(6,plain,
! [X: $i] : ( inverse(inverse(X)) = X ),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
( ~ ! [X: $i] : ( inverse(inverse(X)) = X )
| ( inverse(inverse(b)) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(8,plain,
inverse(inverse(b)) = b,
inference(unit_resolution,[status(thm)],[7,6]) ).
tff(9,plain,
^ [X: $i] :
refl(( ( multiply(identity,X) = X )
<=> ( multiply(identity,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(10,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
! [X: $i] : ( multiply(identity,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
tff(13,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,inverse(b)) = inverse(b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(17,plain,
multiply(identity,inverse(b)) = inverse(b),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
inverse(b) = multiply(identity,inverse(b)),
inference(symmetry,[status(thm)],[17]) ).
tff(19,plain,
inverse(inverse(b)) = inverse(multiply(identity,inverse(b))),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
inverse(multiply(identity,inverse(b))) = inverse(inverse(b)),
inference(symmetry,[status(thm)],[19]) ).
tff(21,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(22,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)],[21]) ).
tff(23,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(24,axiom,
! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12x_3) ).
tff(25,plain,
! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [Y: $i,X: $i] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) )
| ( inverse(multiply(identity,inverse(b))) = multiply(inverse(inverse(b)),inverse(identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
inverse(multiply(identity,inverse(b))) = multiply(inverse(inverse(b)),inverse(identity)),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
multiply(inverse(inverse(b)),inverse(identity)) = inverse(multiply(identity,inverse(b))),
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',p12x_1) ).
tff(33,plain,
inverse(identity) = identity,
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
multiply(inverse(inverse(b)),inverse(identity)) = multiply(b,identity),
inference(monotonicity,[status(thm)],[8,33]) ).
tff(35,plain,
multiply(b,identity) = multiply(inverse(inverse(b)),inverse(identity)),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
^ [X: $i] :
refl(( ( multiply(inverse(X),X) = identity )
<=> ( multiply(inverse(X),X) = identity ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
tff(40,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(identity),identity) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
multiply(inverse(identity),identity) = identity,
inference(unit_resolution,[status(thm)],[43,42]) ).
tff(45,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[33]) ).
tff(46,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(b),b) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
multiply(inverse(b),b) = identity,
inference(unit_resolution,[status(thm)],[46,42]) ).
tff(48,plain,
multiply(inverse(b),b) = inverse(identity),
inference(transitivity,[status(thm)],[47,45]) ).
tff(49,plain,
multiply(multiply(inverse(b),b),identity) = multiply(inverse(identity),identity),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,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(51,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)],[50]) ).
tff(52,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(53,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(54,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(b),b),identity) = multiply(inverse(b),multiply(b,identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
multiply(multiply(inverse(b),b),identity) = multiply(inverse(b),multiply(b,identity)),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
multiply(inverse(b),multiply(b,identity)) = multiply(multiply(inverse(b),b),identity),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
multiply(inverse(b),multiply(b,identity)) = identity,
inference(transitivity,[status(thm)],[59,49,44]) ).
tff(61,plain,
multiply(b,multiply(inverse(b),multiply(b,identity))) = multiply(b,identity),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,inverse(b)),multiply(b,identity)) = multiply(b,multiply(inverse(b),multiply(b,identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
multiply(multiply(b,inverse(b)),multiply(b,identity)) = multiply(b,multiply(inverse(b),multiply(b,identity))),
inference(unit_resolution,[status(thm)],[62,56]) ).
tff(64,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(65,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)],[64]) ).
tff(66,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(67,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(68,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)],[67,66]) ).
tff(69,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)],[68]) ).
tff(70,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)],[69,65]) ).
tff(71,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(inverse(c),inverse(a)),least_upper_bound(b,c)) = greatest_lower_bound(multiply(inverse(c),least_upper_bound(b,c)),multiply(inverse(a),least_upper_bound(b,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
multiply(greatest_lower_bound(inverse(c),inverse(a)),least_upper_bound(b,c)) = greatest_lower_bound(multiply(inverse(c),least_upper_bound(b,c)),multiply(inverse(a),least_upper_bound(b,c))),
inference(unit_resolution,[status(thm)],[71,70]) ).
tff(73,plain,
( ( least_upper_bound(a,c) = least_upper_bound(b,c) )
<=> ( least_upper_bound(a,c) = least_upper_bound(b,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,axiom,
least_upper_bound(a,c) = least_upper_bound(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12x_5) ).
tff(75,plain,
least_upper_bound(a,c) = least_upper_bound(b,c),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
least_upper_bound(b,c) = least_upper_bound(a,c),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
inverse(least_upper_bound(b,c)) = inverse(least_upper_bound(a,c)),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
inverse(least_upper_bound(a,c)) = inverse(least_upper_bound(b,c)),
inference(symmetry,[status(thm)],[77]) ).
tff(79,plain,
^ [Y: $i,X: $i] :
refl(( ( inverse(least_upper_bound(X,Y)) = greatest_lower_bound(inverse(X),inverse(Y)) )
<=> ( inverse(least_upper_bound(X,Y)) = greatest_lower_bound(inverse(X),inverse(Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(80,plain,
( ! [Y: $i,X: $i] : ( inverse(least_upper_bound(X,Y)) = greatest_lower_bound(inverse(X),inverse(Y)) )
<=> ! [Y: $i,X: $i] : ( inverse(least_upper_bound(X,Y)) = greatest_lower_bound(inverse(X),inverse(Y)) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,plain,
( ! [Y: $i,X: $i] : ( inverse(least_upper_bound(X,Y)) = greatest_lower_bound(inverse(X),inverse(Y)) )
<=> ! [Y: $i,X: $i] : ( inverse(least_upper_bound(X,Y)) = greatest_lower_bound(inverse(X),inverse(Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,axiom,
! [Y: $i,X: $i] : ( inverse(least_upper_bound(X,Y)) = greatest_lower_bound(inverse(X),inverse(Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12x_7) ).
tff(83,plain,
! [Y: $i,X: $i] : ( inverse(least_upper_bound(X,Y)) = greatest_lower_bound(inverse(X),inverse(Y)) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
! [Y: $i,X: $i] : ( inverse(least_upper_bound(X,Y)) = greatest_lower_bound(inverse(X),inverse(Y)) ),
inference(skolemize,[status(sab)],[83]) ).
tff(85,plain,
! [Y: $i,X: $i] : ( inverse(least_upper_bound(X,Y)) = greatest_lower_bound(inverse(X),inverse(Y)) ),
inference(modus_ponens,[status(thm)],[84,80]) ).
tff(86,plain,
( ~ ! [Y: $i,X: $i] : ( inverse(least_upper_bound(X,Y)) = greatest_lower_bound(inverse(X),inverse(Y)) )
| ( inverse(least_upper_bound(a,c)) = greatest_lower_bound(inverse(a),inverse(c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
inverse(least_upper_bound(a,c)) = greatest_lower_bound(inverse(a),inverse(c)),
inference(unit_resolution,[status(thm)],[86,85]) ).
tff(88,plain,
greatest_lower_bound(inverse(a),inverse(c)) = inverse(least_upper_bound(a,c)),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
^ [Y: $i,X: $i] :
refl(( ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
<=> ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(90,plain,
( ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
<=> ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
<=> ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,axiom,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
tff(93,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(skolemize,[status(sab)],[93]) ).
tff(95,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[94,90]) ).
tff(96,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
| ( greatest_lower_bound(inverse(a),inverse(c)) = greatest_lower_bound(inverse(c),inverse(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(97,plain,
greatest_lower_bound(inverse(a),inverse(c)) = greatest_lower_bound(inverse(c),inverse(a)),
inference(unit_resolution,[status(thm)],[96,95]) ).
tff(98,plain,
greatest_lower_bound(inverse(c),inverse(a)) = greatest_lower_bound(inverse(a),inverse(c)),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
greatest_lower_bound(inverse(c),inverse(a)) = inverse(least_upper_bound(b,c)),
inference(transitivity,[status(thm)],[98,88,78]) ).
tff(100,plain,
multiply(greatest_lower_bound(inverse(c),inverse(a)),least_upper_bound(b,c)) = multiply(inverse(least_upper_bound(b,c)),least_upper_bound(b,c)),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
multiply(inverse(least_upper_bound(b,c)),least_upper_bound(b,c)) = multiply(greatest_lower_bound(inverse(c),inverse(a)),least_upper_bound(b,c)),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(least_upper_bound(b,c)),least_upper_bound(b,c)) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,plain,
multiply(inverse(least_upper_bound(b,c)),least_upper_bound(b,c)) = identity,
inference(unit_resolution,[status(thm)],[102,42]) ).
tff(104,plain,
identity = multiply(inverse(least_upper_bound(b,c)),least_upper_bound(b,c)),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
identity = greatest_lower_bound(multiply(inverse(c),least_upper_bound(b,c)),multiply(inverse(a),least_upper_bound(b,c))),
inference(transitivity,[status(thm)],[104,101,72]) ).
tff(106,plain,
multiply(b,identity) = multiply(b,greatest_lower_bound(multiply(inverse(c),least_upper_bound(b,c)),multiply(inverse(a),least_upper_bound(b,c)))),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
multiply(b,greatest_lower_bound(multiply(inverse(c),least_upper_bound(b,c)),multiply(inverse(a),least_upper_bound(b,c)))) = multiply(b,identity),
inference(symmetry,[status(thm)],[106]) ).
tff(108,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(109,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)],[108]) ).
tff(110,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(111,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(112,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)],[111,110]) ).
tff(113,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)],[112]) ).
tff(114,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)],[113,109]) ).
tff(115,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) )
| ( multiply(b,greatest_lower_bound(multiply(inverse(c),least_upper_bound(b,c)),multiply(inverse(a),least_upper_bound(b,c)))) = greatest_lower_bound(multiply(b,multiply(inverse(c),least_upper_bound(b,c))),multiply(b,multiply(inverse(a),least_upper_bound(b,c)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(116,plain,
multiply(b,greatest_lower_bound(multiply(inverse(c),least_upper_bound(b,c)),multiply(inverse(a),least_upper_bound(b,c)))) = greatest_lower_bound(multiply(b,multiply(inverse(c),least_upper_bound(b,c))),multiply(b,multiply(inverse(a),least_upper_bound(b,c)))),
inference(unit_resolution,[status(thm)],[115,114]) ).
tff(117,plain,
greatest_lower_bound(multiply(b,multiply(inverse(c),least_upper_bound(b,c))),multiply(b,multiply(inverse(a),least_upper_bound(b,c)))) = multiply(b,greatest_lower_bound(multiply(inverse(c),least_upper_bound(b,c)),multiply(inverse(a),least_upper_bound(b,c)))),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
greatest_lower_bound(multiply(b,multiply(inverse(c),least_upper_bound(b,c))),multiply(b,multiply(inverse(a),least_upper_bound(b,c)))) = multiply(b,identity),
inference(transitivity,[status(thm)],[117,107]) ).
tff(119,plain,
b = inverse(inverse(b)),
inference(symmetry,[status(thm)],[8]) ).
tff(120,plain,
multiply(b,inverse(b)) = multiply(inverse(inverse(b)),inverse(b)),
inference(monotonicity,[status(thm)],[119]) ).
tff(121,plain,
multiply(inverse(inverse(b)),inverse(b)) = multiply(b,inverse(b)),
inference(symmetry,[status(thm)],[120]) ).
tff(122,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(inverse(b)),inverse(b)) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(123,plain,
multiply(inverse(inverse(b)),inverse(b)) = identity,
inference(unit_resolution,[status(thm)],[122,42]) ).
tff(124,plain,
identity = multiply(inverse(inverse(b)),inverse(b)),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(least_upper_bound(inverse(a),inverse(c))),least_upper_bound(inverse(a),inverse(c))) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(126,plain,
multiply(inverse(least_upper_bound(inverse(a),inverse(c))),least_upper_bound(inverse(a),inverse(c))) = identity,
inference(unit_resolution,[status(thm)],[125,42]) ).
tff(127,plain,
( ( greatest_lower_bound(a,c) = greatest_lower_bound(b,c) )
<=> ( greatest_lower_bound(a,c) = greatest_lower_bound(b,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,axiom,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12x_4) ).
tff(129,plain,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
greatest_lower_bound(b,c) = greatest_lower_bound(a,c),
inference(symmetry,[status(thm)],[129]) ).
tff(131,plain,
inverse(greatest_lower_bound(b,c)) = inverse(greatest_lower_bound(a,c)),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
inverse(greatest_lower_bound(a,c)) = inverse(greatest_lower_bound(b,c)),
inference(symmetry,[status(thm)],[131]) ).
tff(133,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(134,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)],[133]) ).
tff(135,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(136,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',p12x_6) ).
tff(137,plain,
! [Y: $i,X: $i] : ( inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
! [Y: $i,X: $i] : ( inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)) ),
inference(skolemize,[status(sab)],[137]) ).
tff(139,plain,
! [Y: $i,X: $i] : ( inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)) ),
inference(modus_ponens,[status(thm)],[138,134]) ).
tff(140,plain,
( ~ ! [Y: $i,X: $i] : ( inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)) )
| ( inverse(greatest_lower_bound(a,c)) = least_upper_bound(inverse(a),inverse(c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(141,plain,
inverse(greatest_lower_bound(a,c)) = least_upper_bound(inverse(a),inverse(c)),
inference(unit_resolution,[status(thm)],[140,139]) ).
tff(142,plain,
least_upper_bound(inverse(a),inverse(c)) = inverse(greatest_lower_bound(a,c)),
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
least_upper_bound(inverse(a),inverse(c)) = inverse(greatest_lower_bound(b,c)),
inference(transitivity,[status(thm)],[142,132]) ).
tff(144,plain,
inverse(least_upper_bound(inverse(a),inverse(c))) = inverse(inverse(greatest_lower_bound(b,c))),
inference(monotonicity,[status(thm)],[143]) ).
tff(145,plain,
inverse(inverse(greatest_lower_bound(b,c))) = inverse(least_upper_bound(inverse(a),inverse(c))),
inference(symmetry,[status(thm)],[144]) ).
tff(146,plain,
( ~ ! [X: $i] : ( inverse(inverse(X)) = X )
| ( inverse(inverse(greatest_lower_bound(b,c))) = greatest_lower_bound(b,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(147,plain,
inverse(inverse(greatest_lower_bound(b,c))) = greatest_lower_bound(b,c),
inference(unit_resolution,[status(thm)],[146,6]) ).
tff(148,plain,
greatest_lower_bound(b,c) = inverse(inverse(greatest_lower_bound(b,c))),
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
greatest_lower_bound(b,c) = inverse(least_upper_bound(inverse(a),inverse(c))),
inference(transitivity,[status(thm)],[148,145]) ).
tff(150,plain,
multiply(greatest_lower_bound(b,c),least_upper_bound(inverse(a),inverse(c))) = multiply(inverse(least_upper_bound(inverse(a),inverse(c))),least_upper_bound(inverse(a),inverse(c))),
inference(monotonicity,[status(thm)],[149]) ).
tff(151,plain,
multiply(greatest_lower_bound(b,c),least_upper_bound(inverse(a),inverse(c))) = multiply(b,inverse(b)),
inference(transitivity,[status(thm)],[150,126,124,121]) ).
tff(152,plain,
multiply(multiply(greatest_lower_bound(b,c),least_upper_bound(inverse(a),inverse(c))),greatest_lower_bound(multiply(b,multiply(inverse(c),least_upper_bound(b,c))),multiply(b,multiply(inverse(a),least_upper_bound(b,c))))) = multiply(multiply(b,inverse(b)),multiply(b,identity)),
inference(monotonicity,[status(thm)],[151,118]) ).
tff(153,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(greatest_lower_bound(b,c),least_upper_bound(inverse(a),inverse(c))),greatest_lower_bound(multiply(b,multiply(inverse(c),least_upper_bound(b,c))),multiply(b,multiply(inverse(a),least_upper_bound(b,c))))) = multiply(greatest_lower_bound(b,c),multiply(least_upper_bound(inverse(a),inverse(c)),greatest_lower_bound(multiply(b,multiply(inverse(c),least_upper_bound(b,c))),multiply(b,multiply(inverse(a),least_upper_bound(b,c)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(154,plain,
multiply(multiply(greatest_lower_bound(b,c),least_upper_bound(inverse(a),inverse(c))),greatest_lower_bound(multiply(b,multiply(inverse(c),least_upper_bound(b,c))),multiply(b,multiply(inverse(a),least_upper_bound(b,c))))) = multiply(greatest_lower_bound(b,c),multiply(least_upper_bound(inverse(a),inverse(c)),greatest_lower_bound(multiply(b,multiply(inverse(c),least_upper_bound(b,c))),multiply(b,multiply(inverse(a),least_upper_bound(b,c)))))),
inference(unit_resolution,[status(thm)],[153,56]) ).
tff(155,plain,
multiply(greatest_lower_bound(b,c),multiply(least_upper_bound(inverse(a),inverse(c)),greatest_lower_bound(multiply(b,multiply(inverse(c),least_upper_bound(b,c))),multiply(b,multiply(inverse(a),least_upper_bound(b,c)))))) = multiply(multiply(greatest_lower_bound(b,c),least_upper_bound(inverse(a),inverse(c))),greatest_lower_bound(multiply(b,multiply(inverse(c),least_upper_bound(b,c))),multiply(b,multiply(inverse(a),least_upper_bound(b,c))))),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
multiply(least_upper_bound(inverse(a),inverse(c)),greatest_lower_bound(multiply(b,multiply(inverse(c),least_upper_bound(b,c))),multiply(b,multiply(inverse(a),least_upper_bound(b,c))))) = multiply(least_upper_bound(inverse(a),inverse(c)),multiply(b,identity)),
inference(monotonicity,[status(thm)],[118]) ).
tff(157,plain,
multiply(least_upper_bound(inverse(a),inverse(c)),multiply(b,identity)) = multiply(least_upper_bound(inverse(a),inverse(c)),greatest_lower_bound(multiply(b,multiply(inverse(c),least_upper_bound(b,c))),multiply(b,multiply(inverse(a),least_upper_bound(b,c))))),
inference(symmetry,[status(thm)],[156]) ).
tff(158,plain,
multiply(b,identity) = b,
inference(transitivity,[status(thm)],[35,30,20,8]) ).
tff(159,plain,
multiply(least_upper_bound(inverse(a),inverse(c)),multiply(b,identity)) = multiply(least_upper_bound(inverse(a),inverse(c)),b),
inference(monotonicity,[status(thm)],[158]) ).
tff(160,plain,
multiply(least_upper_bound(inverse(a),inverse(c)),b) = multiply(least_upper_bound(inverse(a),inverse(c)),multiply(b,identity)),
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
multiply(least_upper_bound(inverse(a),inverse(c)),b) = multiply(least_upper_bound(inverse(a),inverse(c)),greatest_lower_bound(multiply(b,multiply(inverse(c),least_upper_bound(b,c))),multiply(b,multiply(inverse(a),least_upper_bound(b,c))))),
inference(transitivity,[status(thm)],[160,157]) ).
tff(162,plain,
multiply(greatest_lower_bound(b,c),multiply(least_upper_bound(inverse(a),inverse(c)),b)) = multiply(greatest_lower_bound(b,c),multiply(least_upper_bound(inverse(a),inverse(c)),greatest_lower_bound(multiply(b,multiply(inverse(c),least_upper_bound(b,c))),multiply(b,multiply(inverse(a),least_upper_bound(b,c)))))),
inference(monotonicity,[status(thm)],[161]) ).
tff(163,plain,
( ~ ! [Y: $i,X: $i] : ( inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)) )
| ( inverse(greatest_lower_bound(b,c)) = least_upper_bound(inverse(b),inverse(c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(164,plain,
inverse(greatest_lower_bound(b,c)) = least_upper_bound(inverse(b),inverse(c)),
inference(unit_resolution,[status(thm)],[163,139]) ).
tff(165,plain,
least_upper_bound(inverse(b),inverse(c)) = inverse(greatest_lower_bound(b,c)),
inference(symmetry,[status(thm)],[164]) ).
tff(166,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(167,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)],[166]) ).
tff(168,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(169,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(170,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[169,168]) ).
tff(171,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(skolemize,[status(sab)],[170]) ).
tff(172,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[171,167]) ).
tff(173,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
| ( least_upper_bound(inverse(b),inverse(c)) = least_upper_bound(inverse(c),inverse(b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(174,plain,
least_upper_bound(inverse(b),inverse(c)) = least_upper_bound(inverse(c),inverse(b)),
inference(unit_resolution,[status(thm)],[173,172]) ).
tff(175,plain,
least_upper_bound(inverse(c),inverse(b)) = least_upper_bound(inverse(b),inverse(c)),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
least_upper_bound(inverse(c),inverse(b)) = least_upper_bound(inverse(a),inverse(c)),
inference(transitivity,[status(thm)],[175,165,131,141]) ).
tff(177,plain,
multiply(least_upper_bound(inverse(c),inverse(b)),b) = multiply(least_upper_bound(inverse(a),inverse(c)),b),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,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(179,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)],[178]) ).
tff(180,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(181,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(182,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)],[181,180]) ).
tff(183,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)],[182]) ).
tff(184,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)],[183,179]) ).
tff(185,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(c),inverse(b)),b) = least_upper_bound(multiply(inverse(c),b),multiply(inverse(b),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(186,plain,
multiply(least_upper_bound(inverse(c),inverse(b)),b) = least_upper_bound(multiply(inverse(c),b),multiply(inverse(b),b)),
inference(unit_resolution,[status(thm)],[185,184]) ).
tff(187,plain,
least_upper_bound(multiply(inverse(c),b),multiply(inverse(b),b)) = multiply(least_upper_bound(inverse(c),inverse(b)),b),
inference(symmetry,[status(thm)],[186]) ).
tff(188,plain,
identity = multiply(inverse(b),b),
inference(symmetry,[status(thm)],[47]) ).
tff(189,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(c),c) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(190,plain,
multiply(inverse(c),c) = identity,
inference(unit_resolution,[status(thm)],[189,42]) ).
tff(191,plain,
multiply(inverse(c),c) = multiply(inverse(b),b),
inference(transitivity,[status(thm)],[190,188]) ).
tff(192,plain,
least_upper_bound(multiply(inverse(c),b),multiply(inverse(c),c)) = least_upper_bound(multiply(inverse(c),b),multiply(inverse(b),b)),
inference(monotonicity,[status(thm)],[191]) ).
tff(193,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(194,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)],[193]) ).
tff(195,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(196,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(197,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)],[196,195]) ).
tff(198,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)],[197]) ).
tff(199,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)],[198,194]) ).
tff(200,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(c),least_upper_bound(b,c)) = least_upper_bound(multiply(inverse(c),b),multiply(inverse(c),c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(201,plain,
multiply(inverse(c),least_upper_bound(b,c)) = least_upper_bound(multiply(inverse(c),b),multiply(inverse(c),c)),
inference(unit_resolution,[status(thm)],[200,199]) ).
tff(202,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
| ( least_upper_bound(a,c) = least_upper_bound(c,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(203,plain,
least_upper_bound(a,c) = least_upper_bound(c,a),
inference(unit_resolution,[status(thm)],[202,172]) ).
tff(204,plain,
least_upper_bound(c,a) = least_upper_bound(a,c),
inference(symmetry,[status(thm)],[203]) ).
tff(205,plain,
least_upper_bound(c,a) = least_upper_bound(b,c),
inference(transitivity,[status(thm)],[204,75]) ).
tff(206,plain,
multiply(inverse(c),least_upper_bound(c,a)) = multiply(inverse(c),least_upper_bound(b,c)),
inference(monotonicity,[status(thm)],[205]) ).
tff(207,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(c),least_upper_bound(c,a)) = least_upper_bound(multiply(inverse(c),c),multiply(inverse(c),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(208,plain,
multiply(inverse(c),least_upper_bound(c,a)) = least_upper_bound(multiply(inverse(c),c),multiply(inverse(c),a)),
inference(unit_resolution,[status(thm)],[207,199]) ).
tff(209,plain,
least_upper_bound(multiply(inverse(c),c),multiply(inverse(c),a)) = multiply(inverse(c),least_upper_bound(c,a)),
inference(symmetry,[status(thm)],[208]) ).
tff(210,plain,
identity = multiply(inverse(c),c),
inference(symmetry,[status(thm)],[190]) ).
tff(211,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(a),a) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(212,plain,
multiply(inverse(a),a) = identity,
inference(unit_resolution,[status(thm)],[211,42]) ).
tff(213,plain,
multiply(inverse(a),a) = multiply(inverse(c),c),
inference(transitivity,[status(thm)],[212,210]) ).
tff(214,plain,
least_upper_bound(multiply(inverse(a),a),multiply(inverse(c),a)) = least_upper_bound(multiply(inverse(c),c),multiply(inverse(c),a)),
inference(monotonicity,[status(thm)],[213]) ).
tff(215,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),inverse(c)),a) = least_upper_bound(multiply(inverse(a),a),multiply(inverse(c),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(216,plain,
multiply(least_upper_bound(inverse(a),inverse(c)),a) = least_upper_bound(multiply(inverse(a),a),multiply(inverse(c),a)),
inference(unit_resolution,[status(thm)],[215,184]) ).
tff(217,plain,
( ~ ! [X: $i] : ( inverse(inverse(X)) = X )
| ( inverse(inverse(a)) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(218,plain,
inverse(inverse(a)) = a,
inference(unit_resolution,[status(thm)],[217,6]) ).
tff(219,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,inverse(a)) = inverse(a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(220,plain,
multiply(identity,inverse(a)) = inverse(a),
inference(unit_resolution,[status(thm)],[219,15]) ).
tff(221,plain,
inverse(a) = multiply(identity,inverse(a)),
inference(symmetry,[status(thm)],[220]) ).
tff(222,plain,
inverse(inverse(a)) = inverse(multiply(identity,inverse(a))),
inference(monotonicity,[status(thm)],[221]) ).
tff(223,plain,
inverse(multiply(identity,inverse(a))) = inverse(inverse(a)),
inference(symmetry,[status(thm)],[222]) ).
tff(224,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(225,plain,
inverse(multiply(identity,inverse(a))) = multiply(inverse(inverse(a)),inverse(identity)),
inference(unit_resolution,[status(thm)],[224,27]) ).
tff(226,plain,
multiply(inverse(inverse(a)),inverse(identity)) = inverse(multiply(identity,inverse(a))),
inference(symmetry,[status(thm)],[225]) ).
tff(227,plain,
multiply(inverse(inverse(a)),inverse(identity)) = multiply(a,identity),
inference(monotonicity,[status(thm)],[218,33]) ).
tff(228,plain,
multiply(a,identity) = multiply(inverse(inverse(a)),inverse(identity)),
inference(symmetry,[status(thm)],[227]) ).
tff(229,plain,
multiply(a,identity) = a,
inference(transitivity,[status(thm)],[228,226,223,218]) ).
tff(230,plain,
multiply(least_upper_bound(inverse(a),inverse(c)),multiply(a,identity)) = multiply(least_upper_bound(inverse(a),inverse(c)),a),
inference(monotonicity,[status(thm)],[229]) ).
tff(231,plain,
greatest_lower_bound(multiply(inverse(c),least_upper_bound(b,c)),multiply(inverse(a),least_upper_bound(b,c))) = multiply(greatest_lower_bound(inverse(c),inverse(a)),least_upper_bound(b,c)),
inference(symmetry,[status(thm)],[72]) ).
tff(232,plain,
greatest_lower_bound(multiply(inverse(c),least_upper_bound(b,c)),multiply(inverse(a),least_upper_bound(b,c))) = identity,
inference(transitivity,[status(thm)],[231,100,103]) ).
tff(233,plain,
multiply(a,greatest_lower_bound(multiply(inverse(c),least_upper_bound(b,c)),multiply(inverse(a),least_upper_bound(b,c)))) = multiply(a,identity),
inference(monotonicity,[status(thm)],[232]) ).
tff(234,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) )
| ( multiply(a,greatest_lower_bound(multiply(inverse(c),least_upper_bound(b,c)),multiply(inverse(a),least_upper_bound(b,c)))) = greatest_lower_bound(multiply(a,multiply(inverse(c),least_upper_bound(b,c))),multiply(a,multiply(inverse(a),least_upper_bound(b,c)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(235,plain,
multiply(a,greatest_lower_bound(multiply(inverse(c),least_upper_bound(b,c)),multiply(inverse(a),least_upper_bound(b,c)))) = greatest_lower_bound(multiply(a,multiply(inverse(c),least_upper_bound(b,c))),multiply(a,multiply(inverse(a),least_upper_bound(b,c)))),
inference(unit_resolution,[status(thm)],[234,114]) ).
tff(236,plain,
greatest_lower_bound(multiply(a,multiply(inverse(c),least_upper_bound(b,c))),multiply(a,multiply(inverse(a),least_upper_bound(b,c)))) = multiply(a,greatest_lower_bound(multiply(inverse(c),least_upper_bound(b,c)),multiply(inverse(a),least_upper_bound(b,c)))),
inference(symmetry,[status(thm)],[235]) ).
tff(237,plain,
greatest_lower_bound(multiply(a,multiply(inverse(c),least_upper_bound(b,c))),multiply(a,multiply(inverse(a),least_upper_bound(b,c)))) = multiply(a,identity),
inference(transitivity,[status(thm)],[236,233]) ).
tff(238,plain,
multiply(least_upper_bound(inverse(a),inverse(c)),greatest_lower_bound(multiply(a,multiply(inverse(c),least_upper_bound(b,c))),multiply(a,multiply(inverse(a),least_upper_bound(b,c))))) = multiply(least_upper_bound(inverse(a),inverse(c)),multiply(a,identity)),
inference(monotonicity,[status(thm)],[237]) ).
tff(239,plain,
multiply(least_upper_bound(inverse(a),inverse(c)),greatest_lower_bound(multiply(a,multiply(inverse(c),least_upper_bound(b,c))),multiply(a,multiply(inverse(a),least_upper_bound(b,c))))) = multiply(least_upper_bound(inverse(a),inverse(c)),b),
inference(transitivity,[status(thm)],[238,230,216,214,209,206,201,192,187,177]) ).
tff(240,plain,
multiply(greatest_lower_bound(b,c),multiply(least_upper_bound(inverse(a),inverse(c)),greatest_lower_bound(multiply(a,multiply(inverse(c),least_upper_bound(b,c))),multiply(a,multiply(inverse(a),least_upper_bound(b,c)))))) = multiply(greatest_lower_bound(b,c),multiply(least_upper_bound(inverse(a),inverse(c)),b)),
inference(monotonicity,[status(thm)],[239]) ).
tff(241,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(greatest_lower_bound(b,c),least_upper_bound(inverse(a),inverse(c))),greatest_lower_bound(multiply(a,multiply(inverse(c),least_upper_bound(b,c))),multiply(a,multiply(inverse(a),least_upper_bound(b,c))))) = multiply(greatest_lower_bound(b,c),multiply(least_upper_bound(inverse(a),inverse(c)),greatest_lower_bound(multiply(a,multiply(inverse(c),least_upper_bound(b,c))),multiply(a,multiply(inverse(a),least_upper_bound(b,c)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(242,plain,
multiply(multiply(greatest_lower_bound(b,c),least_upper_bound(inverse(a),inverse(c))),greatest_lower_bound(multiply(a,multiply(inverse(c),least_upper_bound(b,c))),multiply(a,multiply(inverse(a),least_upper_bound(b,c))))) = multiply(greatest_lower_bound(b,c),multiply(least_upper_bound(inverse(a),inverse(c)),greatest_lower_bound(multiply(a,multiply(inverse(c),least_upper_bound(b,c))),multiply(a,multiply(inverse(a),least_upper_bound(b,c)))))),
inference(unit_resolution,[status(thm)],[241,56]) ).
tff(243,plain,
multiply(a,identity) = multiply(a,greatest_lower_bound(multiply(inverse(c),least_upper_bound(b,c)),multiply(inverse(a),least_upper_bound(b,c)))),
inference(symmetry,[status(thm)],[233]) ).
tff(244,plain,
multiply(a,identity) = greatest_lower_bound(multiply(a,multiply(inverse(c),least_upper_bound(b,c))),multiply(a,multiply(inverse(a),least_upper_bound(b,c)))),
inference(transitivity,[status(thm)],[243,235]) ).
tff(245,plain,
multiply(inverse(least_upper_bound(inverse(a),inverse(c))),least_upper_bound(inverse(a),inverse(c))) = multiply(greatest_lower_bound(b,c),least_upper_bound(inverse(a),inverse(c))),
inference(symmetry,[status(thm)],[150]) ).
tff(246,plain,
identity = multiply(inverse(least_upper_bound(inverse(a),inverse(c))),least_upper_bound(inverse(a),inverse(c))),
inference(symmetry,[status(thm)],[126]) ).
tff(247,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(inverse(a)),inverse(a)) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(248,plain,
multiply(inverse(inverse(a)),inverse(a)) = identity,
inference(unit_resolution,[status(thm)],[247,42]) ).
tff(249,plain,
a = inverse(inverse(a)),
inference(symmetry,[status(thm)],[218]) ).
tff(250,plain,
multiply(a,inverse(a)) = multiply(inverse(inverse(a)),inverse(a)),
inference(monotonicity,[status(thm)],[249]) ).
tff(251,plain,
multiply(a,inverse(a)) = multiply(greatest_lower_bound(b,c),least_upper_bound(inverse(a),inverse(c))),
inference(transitivity,[status(thm)],[250,248,246,245]) ).
tff(252,plain,
multiply(multiply(a,inverse(a)),multiply(a,identity)) = multiply(multiply(greatest_lower_bound(b,c),least_upper_bound(inverse(a),inverse(c))),greatest_lower_bound(multiply(a,multiply(inverse(c),least_upper_bound(b,c))),multiply(a,multiply(inverse(a),least_upper_bound(b,c))))),
inference(monotonicity,[status(thm)],[251,244]) ).
tff(253,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,inverse(a)),multiply(a,identity)) = multiply(a,multiply(inverse(a),multiply(a,identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(254,plain,
multiply(multiply(a,inverse(a)),multiply(a,identity)) = multiply(a,multiply(inverse(a),multiply(a,identity))),
inference(unit_resolution,[status(thm)],[253,56]) ).
tff(255,plain,
multiply(a,multiply(inverse(a),multiply(a,identity))) = multiply(multiply(a,inverse(a)),multiply(a,identity)),
inference(symmetry,[status(thm)],[254]) ).
tff(256,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(a),a),identity) = multiply(inverse(a),multiply(a,identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(257,plain,
multiply(multiply(inverse(a),a),identity) = multiply(inverse(a),multiply(a,identity)),
inference(unit_resolution,[status(thm)],[256,56]) ).
tff(258,plain,
multiply(inverse(a),a) = inverse(identity),
inference(transitivity,[status(thm)],[212,45]) ).
tff(259,plain,
multiply(multiply(inverse(a),a),identity) = multiply(inverse(identity),identity),
inference(monotonicity,[status(thm)],[258]) ).
tff(260,plain,
multiply(inverse(identity),identity) = multiply(multiply(inverse(a),a),identity),
inference(symmetry,[status(thm)],[259]) ).
tff(261,plain,
identity = multiply(inverse(identity),identity),
inference(symmetry,[status(thm)],[44]) ).
tff(262,plain,
identity = multiply(inverse(a),multiply(a,identity)),
inference(transitivity,[status(thm)],[261,260,257]) ).
tff(263,plain,
multiply(a,identity) = multiply(a,multiply(inverse(a),multiply(a,identity))),
inference(monotonicity,[status(thm)],[262]) ).
tff(264,plain,
a = b,
inference(transitivity,[status(thm)],[249,222,225,227,263,255,252,242,240,162,155,152,63,61,35,30,20,8]) ).
tff(265,plain,
( ( a != b )
<=> ( a != b ) ),
inference(rewrite,[status(thm)],[]) ).
tff(266,axiom,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p12x) ).
tff(267,plain,
a != b,
inference(modus_ponens,[status(thm)],[266,265]) ).
tff(268,plain,
$false,
inference(unit_resolution,[status(thm)],[267,264]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP181-4 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.07/0.13 % 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 15:44:11 EDT 2025
% 0.13/0.35 % CPUTime :
% 3.02/3.22 % SZS status Unsatisfiable
% 3.02/3.22 % SZS output start Proof
% See solution above
% 3.02/3.24 % E exiting
%------------------------------------------------------------------------------