%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV065+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 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 05:31:26 AM UTC 2025
% Result : Theorem 0.18s 0.40s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of formulae : 34 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 136 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 150 ( 49 ~; 27 |; 59 &)
% ( 13 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 10 ( 9 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(n0_type,type,
n0: $i ).
tff(minus_type,type,
minus: ( $i * $i ) > $i ).
tff(n1_type,type,
n1: $i ).
tff(n5_type,type,
n5: $i ).
tff(pv53_type,type,
pv53: $i ).
tff(n135300_type,type,
n135300: $i ).
tff(pv10_type,type,
pv10: $i ).
tff(1,plain,
( leq(pv53,minus(n5,n1))
<=> leq(pv53,minus(n5,n1)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,plain,
( ~ ( ( leq(n0,pv10)
& leq(n0,pv53)
& leq(pv10,minus(n135300,n1))
& leq(pv53,minus(n5,n1)) )
=> ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,pv53)
& leq(pv10,minus(n135300,n1))
& leq(pv53,minus(n5,n1)) ) )
<=> ~ ( ~ ( leq(n0,pv10)
& leq(n0,pv53)
& leq(pv10,minus(n135300,n1))
& leq(pv53,minus(n5,n1)) )
| ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,pv53)
& leq(pv10,minus(n135300,n1))
& leq(pv53,minus(n5,n1)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
~ ( ( leq(n0,pv10)
& leq(n0,pv53)
& leq(pv10,minus(n135300,n1))
& leq(pv53,minus(n5,n1)) )
=> ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,pv53)
& leq(pv10,minus(n135300,n1))
& leq(pv53,minus(n5,n1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_array_0006) ).
tff(4,plain,
~ ( ~ ( leq(n0,pv10)
& leq(n0,pv53)
& leq(pv10,minus(n135300,n1))
& leq(pv53,minus(n5,n1)) )
| ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,pv53)
& leq(pv10,minus(n135300,n1))
& leq(pv53,minus(n5,n1)) ) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
( leq(n0,pv10)
& leq(n0,pv53)
& leq(pv10,minus(n135300,n1))
& leq(pv53,minus(n5,n1)) ),
inference(or_elim,[status(thm)],[4]) ).
tff(6,plain,
leq(pv53,minus(n5,n1)),
inference(and_elim,[status(thm)],[5]) ).
tff(7,plain,
leq(pv53,minus(n5,n1)),
inference(modus_ponens,[status(thm)],[6,1]) ).
tff(8,plain,
( leq(pv10,minus(n135300,n1))
<=> leq(pv10,minus(n135300,n1)) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,plain,
leq(pv10,minus(n135300,n1)),
inference(and_elim,[status(thm)],[5]) ).
tff(10,plain,
leq(pv10,minus(n135300,n1)),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( leq(n0,pv53)
<=> leq(n0,pv53) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
leq(n0,pv53),
inference(and_elim,[status(thm)],[5]) ).
tff(13,plain,
leq(n0,pv53),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( leq(n0,pv10)
<=> leq(n0,pv10) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
leq(n0,pv10),
inference(and_elim,[status(thm)],[5]) ).
tff(16,plain,
leq(n0,pv10),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ~ ~ ( ~ leq(n0,n0)
| ~ leq(n0,pv10)
| ~ leq(n0,pv53)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(pv53,minus(n5,n1)) )
<=> ( ~ leq(n0,n0)
| ~ leq(n0,pv10)
| ~ leq(n0,pv53)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(pv53,minus(n5,n1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,pv53)
& leq(pv10,minus(n135300,n1))
& leq(pv53,minus(n5,n1)) )
<=> ~ ( ~ leq(n0,n0)
| ~ leq(n0,pv10)
| ~ leq(n0,pv53)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(pv53,minus(n5,n1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ~ ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,pv53)
& leq(pv10,minus(n135300,n1))
& leq(pv53,minus(n5,n1)) )
<=> ~ ~ ( ~ leq(n0,n0)
| ~ leq(n0,pv10)
| ~ leq(n0,pv53)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(pv53,minus(n5,n1)) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ~ ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,pv53)
& leq(pv10,minus(n135300,n1))
& leq(pv53,minus(n5,n1)) )
<=> ( ~ leq(n0,n0)
| ~ leq(n0,pv10)
| ~ leq(n0,pv53)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(pv53,minus(n5,n1)) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,pv53)
& leq(pv10,minus(n135300,n1))
& leq(pv53,minus(n5,n1)) )
<=> ~ ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,pv53)
& leq(pv10,minus(n135300,n1))
& leq(pv53,minus(n5,n1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
~ ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,pv53)
& leq(pv10,minus(n135300,n1))
& leq(pv53,minus(n5,n1)) ),
inference(or_elim,[status(thm)],[4]) ).
tff(23,plain,
~ ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,pv53)
& leq(pv10,minus(n135300,n1))
& leq(pv53,minus(n5,n1)) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
( ~ leq(n0,n0)
| ~ leq(n0,pv10)
| ~ leq(n0,pv53)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(pv53,minus(n5,n1)) ),
inference(modus_ponens,[status(thm)],[23,20]) ).
tff(25,plain,
~ leq(n0,n0),
inference(unit_resolution,[status(thm)],[24,16,13,10,7]) ).
tff(26,plain,
^ [X: $i] :
refl(( leq(X,X)
<=> leq(X,X) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [X: $i] : leq(X,X)
<=> ! [X: $i] : leq(X,X) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [X: $i] : leq(X,X)
<=> ! [X: $i] : leq(X,X) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
! [X: $i] : leq(X,X),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',reflexivity_leq) ).
tff(30,plain,
! [X: $i] : leq(X,X),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [X: $i] : leq(X,X),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [X: $i] : leq(X,X),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ~ ! [X: $i] : leq(X,X)
| leq(n0,n0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
$false,
inference(unit_resolution,[status(thm)],[33,32,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWV065+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n003.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 09:27:09 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.40 % SZS status Theorem
% 0.18/0.40 % SZS output start Proof
% See solution above
% 0.18/0.40 % E exiting
%------------------------------------------------------------------------------