%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : FLD056-3 : TPTP v9.0.0. Bugfixed v2.1.0.
% 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 05:05:05 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of formulae : 23 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 156 ( 0 equ)
% Maximal formula atoms : 14 ( 6 avg)
% Number of connectives : 207 ( 82 ~; 111 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 42 ( 38 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
tff(less_or_equal_type,type,
less_or_equal: ( $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
tff(defined_type,type,
defined: $i > $o ).
tff(1,plain,
( ~ less_or_equal(a,a)
<=> ~ less_or_equal(a,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ less_or_equal(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_2) ).
tff(3,plain,
~ less_or_equal(a,a),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( defined(a)
<=> defined(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
tff(6,plain,
defined(a),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ defined(X)
| ~ defined(Y)
| less_or_equal(Y,X)
| less_or_equal(X,Y) )
<=> ( ~ defined(X)
| ~ defined(Y)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| less_or_equal(Y,X)
| less_or_equal(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| less_or_equal(Y,X)
| less_or_equal(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
trans(monotonicity(rewrite(( ( less_or_equal(X,Y)
| less_or_equal(Y,X)
| ~ defined(X) )
<=> ( ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ) )),
( ( less_or_equal(X,Y)
| less_or_equal(Y,X)
| ~ defined(X)
| ~ defined(Y) )
<=> ( ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y)
| ~ defined(Y) ) )),
rewrite(( ( ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y)
| ~ defined(Y) )
<=> ( ~ defined(X)
| ~ defined(Y)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ) )),
( ( less_or_equal(X,Y)
| less_or_equal(Y,X)
| ~ defined(X)
| ~ defined(Y) )
<=> ( ~ defined(X)
| ~ defined(Y)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Y: $i,X: $i] :
( less_or_equal(X,Y)
| less_or_equal(Y,X)
| ~ defined(X)
| ~ defined(Y) )
<=> ! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [Y: $i,X: $i] :
( less_or_equal(X,Y)
| less_or_equal(Y,X)
| ~ defined(X)
| ~ defined(Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_order_relation) ).
tff(13,plain,
! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| less_or_equal(Y,X)
| less_or_equal(X,Y) )
| less_or_equal(a,a)
| ~ defined(a) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| less_or_equal(Y,X)
| less_or_equal(X,Y) )
| less_or_equal(a,a)
| ~ defined(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( ~ defined(a)
| ~ defined(a)
| less_or_equal(a,a)
| less_or_equal(a,a) )
<=> ( less_or_equal(a,a)
| ~ defined(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| less_or_equal(Y,X)
| less_or_equal(X,Y) )
| ~ defined(a)
| ~ defined(a)
| less_or_equal(a,a)
| less_or_equal(a,a) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| less_or_equal(Y,X)
| less_or_equal(X,Y) )
| less_or_equal(a,a)
| ~ defined(a) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| less_or_equal(Y,X)
| less_or_equal(X,Y) )
| ~ defined(a)
| ~ defined(a)
| less_or_equal(a,a)
| less_or_equal(a,a) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| less_or_equal(Y,X)
| less_or_equal(X,Y) )
| less_or_equal(a,a)
| ~ defined(a) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| less_or_equal(Y,X)
| less_or_equal(X,Y) )
| ~ defined(a)
| ~ defined(a)
| less_or_equal(a,a)
| less_or_equal(a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X)
| ~ defined(Y)
| less_or_equal(Y,X)
| less_or_equal(X,Y) )
| less_or_equal(a,a)
| ~ defined(a) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
$false,
inference(unit_resolution,[status(thm)],[22,16,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : FLD056-3 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.13/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n013.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 13:44:23 EDT 2025
% 0.20/0.35 % CPUTime :
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39 % SZS output start Proof
% See solution above
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------