%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP137-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:07:14 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 12 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 15 ( 14 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 0 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(greatest_lower_bound_type,type,
greatest_lower_bound: ( $i * $i ) > $i ).
tff(1,plain,
( ( greatest_lower_bound(a,b) = b )
<=> ( greatest_lower_bound(a,b) = b ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
greatest_lower_bound(a,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_antisymb_2) ).
tff(3,plain,
greatest_lower_bound(a,b) = b,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ( greatest_lower_bound(a,b) = a )
<=> ( greatest_lower_bound(a,b) = a ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
greatest_lower_bound(a,b) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_antisymb_1) ).
tff(6,plain,
greatest_lower_bound(a,b) = a,
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
a = greatest_lower_bound(a,b),
inference(symmetry,[status(thm)],[6]) ).
tff(8,plain,
a = b,
inference(transitivity,[status(thm)],[7,3]) ).
tff(9,plain,
( ( a != b )
<=> ( a != b ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ax_antisymb) ).
tff(11,plain,
a != b,
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
$false,
inference(unit_resolution,[status(thm)],[11,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP137-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.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 15:44:23 EDT 2025
% 0.12/0.33 % 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
%------------------------------------------------------------------------------