%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP166-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% 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(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(least_upper_bound_type,type,
least_upper_bound: ( $i * $i ) > $i ).
tff(identity_type,type,
identity: $i ).
tff(1,plain,
( ( least_upper_bound(b,identity) = b )
<=> ( least_upper_bound(b,identity) = b ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
least_upper_bound(b,identity) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lat3a_2) ).
tff(3,plain,
least_upper_bound(b,identity) = b,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
b = least_upper_bound(b,identity),
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
multiply(b,a) = multiply(least_upper_bound(b,identity),a),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
multiply(least_upper_bound(b,identity),a) = multiply(b,a),
inference(symmetry,[status(thm)],[5]) ).
tff(7,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(8,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)],[7]) ).
tff(9,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(10,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(11,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)],[10,9]) ).
tff(12,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)],[11]) ).
tff(13,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)],[12,8]) ).
tff(14,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(b,identity),a) = least_upper_bound(multiply(b,a),multiply(identity,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(15,plain,
multiply(least_upper_bound(b,identity),a) = least_upper_bound(multiply(b,a),multiply(identity,a)),
inference(unit_resolution,[status(thm)],[14,13]) ).
tff(16,plain,
least_upper_bound(multiply(b,a),multiply(identity,a)) = multiply(least_upper_bound(b,identity),a),
inference(symmetry,[status(thm)],[15]) ).
tff(17,plain,
^ [X: $i] :
refl(( ( multiply(identity,X) = X )
<=> ( multiply(identity,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
! [X: $i] : ( multiply(identity,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
tff(21,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
multiply(identity,a) = a,
inference(unit_resolution,[status(thm)],[24,23]) ).
tff(26,plain,
least_upper_bound(multiply(b,a),multiply(identity,a)) = least_upper_bound(multiply(b,a),a),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
least_upper_bound(multiply(b,a),a) = least_upper_bound(multiply(b,a),multiply(identity,a)),
inference(symmetry,[status(thm)],[26]) ).
tff(28,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(29,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)],[28]) ).
tff(30,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(31,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(32,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ~ ! [Y: $i,X: $i] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) )
| ( least_upper_bound(a,multiply(b,a)) = least_upper_bound(multiply(b,a),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
least_upper_bound(a,multiply(b,a)) = least_upper_bound(multiply(b,a),a),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
least_upper_bound(a,multiply(b,a)) = multiply(b,a),
inference(transitivity,[status(thm)],[36,27,16,6]) ).
tff(38,plain,
( ( least_upper_bound(a,multiply(b,a)) != multiply(b,a) )
<=> ( least_upper_bound(a,multiply(b,a)) != multiply(b,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
least_upper_bound(a,multiply(b,a)) != multiply(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lat3a) ).
tff(40,plain,
least_upper_bound(a,multiply(b,a)) != multiply(b,a),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
$false,
inference(unit_resolution,[status(thm)],[40,37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP166-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n003.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Jun 19 15:44:54 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.12/0.36 % SZS status Unsatisfiable
% 0.12/0.36 % SZS output start Proof
% See solution above
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------