%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP166-4 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:07:18 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 41 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 58 ( 54 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 7 ~; 3 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 3 ( 3 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 60 ( 54 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
tff(a_type,type,
a: $i ).
tff(greatest_lower_bound_type,type,
greatest_lower_bound: ( $i * $i ) > $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(identity_type,type,
identity: $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( multiply(identity,X) = X )
<=> ( multiply(identity,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( multiply(identity,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
tff(5,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
multiply(identity,a) = a,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ( greatest_lower_bound(b,identity) = identity )
<=> ( greatest_lower_bound(b,identity) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
greatest_lower_bound(b,identity) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lat3b_2) ).
tff(12,plain,
greatest_lower_bound(b,identity) = identity,
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,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(14,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)],[13]) ).
tff(15,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(16,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(17,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
( ~ ! [Y: $i,X: $i] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )
| ( greatest_lower_bound(b,identity) = greatest_lower_bound(identity,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
greatest_lower_bound(b,identity) = greatest_lower_bound(identity,b),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
greatest_lower_bound(identity,b) = greatest_lower_bound(b,identity),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
greatest_lower_bound(identity,b) = identity,
inference(transitivity,[status(thm)],[22,12]) ).
tff(24,plain,
multiply(greatest_lower_bound(identity,b),a) = multiply(identity,a),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,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(26,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)],[25]) ).
tff(27,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(28,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(29,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)],[28,27]) ).
tff(30,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)],[29]) ).
tff(31,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)],[30,26]) ).
tff(32,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(identity,b),a) = greatest_lower_bound(multiply(identity,a),multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
multiply(greatest_lower_bound(identity,b),a) = greatest_lower_bound(multiply(identity,a),multiply(b,a)),
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,plain,
greatest_lower_bound(multiply(identity,a),multiply(b,a)) = multiply(greatest_lower_bound(identity,b),a),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
a = multiply(identity,a),
inference(symmetry,[status(thm)],[9]) ).
tff(36,plain,
greatest_lower_bound(a,multiply(b,a)) = greatest_lower_bound(multiply(identity,a),multiply(b,a)),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
greatest_lower_bound(a,multiply(b,a)) = a,
inference(transitivity,[status(thm)],[36,34,24,9]) ).
tff(38,plain,
( ( greatest_lower_bound(a,multiply(b,a)) != a )
<=> ( greatest_lower_bound(a,multiply(b,a)) != a ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
greatest_lower_bound(a,multiply(b,a)) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lat3b) ).
tff(40,plain,
greatest_lower_bound(a,multiply(b,a)) != a,
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
$false,
inference(unit_resolution,[status(thm)],[40,37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP166-4 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 15:45:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------