%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP172-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:07:20 AM UTC 2025
% Result : Unsatisfiable 0.38s 0.61s
% Output : Proof 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 32
% Syntax : Number of formulae : 90 ( 67 unt; 0 typ; 0 def)
% Number of atoms : 125 ( 118 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 41 ( 12 ~; 8 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 6 ( 6 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; 3 con; 0-2 aty)
% Number of variables : 134 ( 121 !; 0 ?; 134 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(least_upper_bound_type,type,
least_upper_bound: ( $i * $i ) > $i ).
tff(identity_type,type,
identity: $i ).
tff(greatest_lower_bound_type,type,
greatest_lower_bound: ( $i * $i ) > $i ).
tff(1,plain,
^ [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(2,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)],[1]) ).
tff(3,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(4,axiom,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
tff(5,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
| ( greatest_lower_bound(identity,a) = greatest_lower_bound(a,identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
greatest_lower_bound(identity,a) = greatest_lower_bound(a,identity),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ( greatest_lower_bound(identity,a) = identity )
<=> ( greatest_lower_bound(identity,a) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
greatest_lower_bound(identity,a) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p04d_1) ).
tff(12,plain,
greatest_lower_bound(identity,a) = identity,
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
identity = greatest_lower_bound(identity,a),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
identity = greatest_lower_bound(a,identity),
inference(transitivity,[status(thm)],[13,9]) ).
tff(15,plain,
least_upper_bound(a,identity) = least_upper_bound(a,greatest_lower_bound(a,identity)),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
least_upper_bound(a,greatest_lower_bound(a,identity)) = least_upper_bound(a,identity),
inference(symmetry,[status(thm)],[15]) ).
tff(17,plain,
^ [Y: $i,X: $i] :
refl(( ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X )
<=> ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).
tff(21,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X )
| ( least_upper_bound(a,greatest_lower_bound(a,identity)) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
least_upper_bound(a,greatest_lower_bound(a,identity)) = a,
inference(unit_resolution,[status(thm)],[24,23]) ).
tff(26,plain,
a = least_upper_bound(a,greatest_lower_bound(a,identity)),
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
a = least_upper_bound(a,identity),
inference(transitivity,[status(thm)],[26,16]) ).
tff(28,plain,
multiply(a,b) = multiply(least_upper_bound(a,identity),b),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
multiply(least_upper_bound(a,identity),b) = multiply(a,b),
inference(symmetry,[status(thm)],[28]) ).
tff(30,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(31,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)],[30]) ).
tff(32,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) )
<=> ! [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(33,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).
tff(34,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)],[33,32]) ).
tff(35,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)],[34]) ).
tff(36,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)],[35,31]) ).
tff(37,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),b) = least_upper_bound(multiply(a,b),multiply(identity,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
multiply(least_upper_bound(a,identity),b) = least_upper_bound(multiply(a,b),multiply(identity,b)),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
least_upper_bound(multiply(a,b),multiply(identity,b)) = multiply(least_upper_bound(a,identity),b),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
| ( greatest_lower_bound(identity,b) = greatest_lower_bound(b,identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
greatest_lower_bound(identity,b) = greatest_lower_bound(b,identity),
inference(unit_resolution,[status(thm)],[40,7]) ).
tff(42,plain,
( ( greatest_lower_bound(identity,b) = identity )
<=> ( greatest_lower_bound(identity,b) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
greatest_lower_bound(identity,b) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p04d_2) ).
tff(44,plain,
greatest_lower_bound(identity,b) = identity,
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
identity = greatest_lower_bound(identity,b),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
identity = greatest_lower_bound(b,identity),
inference(transitivity,[status(thm)],[45,41]) ).
tff(47,plain,
^ [X: $i] :
refl(( ( multiply(identity,X) = X )
<=> ( multiply(identity,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
! [X: $i] : ( multiply(identity,X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
tff(51,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,b) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
multiply(identity,b) = b,
inference(unit_resolution,[status(thm)],[54,53]) ).
tff(56,plain,
least_upper_bound(multiply(identity,b),identity) = least_upper_bound(b,greatest_lower_bound(b,identity)),
inference(monotonicity,[status(thm)],[55,46]) ).
tff(57,plain,
least_upper_bound(b,greatest_lower_bound(b,identity)) = least_upper_bound(multiply(identity,b),identity),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X )
| ( least_upper_bound(b,greatest_lower_bound(b,identity)) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
least_upper_bound(b,greatest_lower_bound(b,identity)) = b,
inference(unit_resolution,[status(thm)],[58,23]) ).
tff(60,plain,
b = least_upper_bound(b,greatest_lower_bound(b,identity)),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
multiply(identity,b) = least_upper_bound(multiply(identity,b),identity),
inference(transitivity,[status(thm)],[55,60,57]) ).
tff(62,plain,
least_upper_bound(multiply(a,b),multiply(identity,b)) = least_upper_bound(multiply(a,b),least_upper_bound(multiply(identity,b),identity)),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
least_upper_bound(multiply(a,b),least_upper_bound(multiply(identity,b),identity)) = least_upper_bound(multiply(a,b),multiply(identity,b)),
inference(symmetry,[status(thm)],[62]) ).
tff(64,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(65,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)],[64]) ).
tff(66,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(67,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/sandbox2/benchmark/Axioms/GRP004-2.ax',associativity_of_lub) ).
tff(68,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)],[67,66]) ).
tff(69,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)],[68]) ).
tff(70,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)],[69,65]) ).
tff(71,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(multiply(a,b),least_upper_bound(multiply(identity,b),identity)) = least_upper_bound(least_upper_bound(multiply(a,b),multiply(identity,b)),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
least_upper_bound(multiply(a,b),least_upper_bound(multiply(identity,b),identity)) = least_upper_bound(least_upper_bound(multiply(a,b),multiply(identity,b)),identity),
inference(unit_resolution,[status(thm)],[71,70]) ).
tff(73,plain,
least_upper_bound(least_upper_bound(multiply(a,b),multiply(identity,b)),identity) = least_upper_bound(multiply(a,b),least_upper_bound(multiply(identity,b),identity)),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
least_upper_bound(multiply(a,b),multiply(identity,b)) = multiply(a,b),
inference(transitivity,[status(thm)],[39,29]) ).
tff(75,plain,
least_upper_bound(least_upper_bound(multiply(a,b),multiply(identity,b)),identity) = least_upper_bound(multiply(a,b),identity),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
least_upper_bound(multiply(a,b),identity) = least_upper_bound(least_upper_bound(multiply(a,b),multiply(identity,b)),identity),
inference(symmetry,[status(thm)],[75]) ).
tff(77,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(78,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)],[77]) ).
tff(79,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(80,axiom,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
tff(81,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[82,78]) ).
tff(84,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
| ( least_upper_bound(identity,multiply(a,b)) = least_upper_bound(multiply(a,b),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(85,plain,
least_upper_bound(identity,multiply(a,b)) = least_upper_bound(multiply(a,b),identity),
inference(unit_resolution,[status(thm)],[84,83]) ).
tff(86,plain,
least_upper_bound(identity,multiply(a,b)) = multiply(a,b),
inference(transitivity,[status(thm)],[85,76,73,63,39,29]) ).
tff(87,plain,
( ( least_upper_bound(identity,multiply(a,b)) != multiply(a,b) )
<=> ( least_upper_bound(identity,multiply(a,b)) != multiply(a,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,axiom,
least_upper_bound(identity,multiply(a,b)) != multiply(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p04d) ).
tff(89,plain,
least_upper_bound(identity,multiply(a,b)) != multiply(a,b),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
$false,
inference(unit_resolution,[status(thm)],[89,86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP172-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 15:44:21 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.38/0.61 % SZS status Unsatisfiable
% 0.38/0.61 % SZS output start Proof
% See solution above
% 0.38/0.61 % E exiting
%------------------------------------------------------------------------------