%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT087+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 8 06:24:12 AM UTC 2026
% Result : Theorem 0.12s 0.44s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 22
% Syntax : Number of formulae : 50 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 184 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 227 ( 111 ~; 54 |; 10 &)
% ( 49 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 18 ( 18 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 90 ( 71 !; 7 ?; 90 :)
% Comments :
%------------------------------------------------------------------------------
tff(in_lopen_type,type,
in_lopen: ( $i * $i * $i ) > $o ).
tff(v600_type,type,
v600: $i ).
tff(v0_type,type,
v0: $i ).
tff(v200_type,type,
v200: $i ).
tff(less_type,type,
less: ( $i * $i ) > $o ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(1,plain,
^ [X: $i,A: $i,B: $i] :
refl(( ~ ( ( ~ leq(X,B)
| ~ less(A,X) )
<=> in_lopen(X,A,B) )
<=> ~ ( ( ~ leq(X,B)
| ~ less(A,X) )
<=> in_lopen(X,A,B) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i,A: $i,B: $i] :
~ ( ( ~ leq(X,B)
| ~ less(A,X) )
<=> in_lopen(X,A,B) )
<=> ! [X: $i,A: $i,B: $i] :
~ ( ( ~ leq(X,B)
| ~ less(A,X) )
<=> in_lopen(X,A,B) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i,A: $i,B: $i] :
trans(trans(monotonicity(rewrite(( ( less(A,X)
& leq(X,B) )
<=> ~ ( ~ leq(X,B)
| ~ less(A,X) ) )),
( ( in_lopen(X,A,B)
<=> ( less(A,X)
& leq(X,B) ) )
<=> ( in_lopen(X,A,B)
<=> ~ ( ~ leq(X,B)
| ~ less(A,X) ) ) )),
rewrite(( ( in_lopen(X,A,B)
<=> ~ ( ~ leq(X,B)
| ~ less(A,X) ) )
<=> ~ ( ( ~ leq(X,B)
| ~ less(A,X) )
<=> in_lopen(X,A,B) ) )),
( ( in_lopen(X,A,B)
<=> ( less(A,X)
& leq(X,B) ) )
<=> ~ ( ( ~ leq(X,B)
| ~ less(A,X) )
<=> in_lopen(X,A,B) ) )),
rewrite(( ~ ( ( ~ leq(X,B)
| ~ less(A,X) )
<=> in_lopen(X,A,B) )
<=> ~ ( ( ~ leq(X,B)
| ~ less(A,X) )
<=> in_lopen(X,A,B) ) )),
( ( in_lopen(X,A,B)
<=> ( less(A,X)
& leq(X,B) ) )
<=> ~ ( ( ~ leq(X,B)
| ~ less(A,X) )
<=> in_lopen(X,A,B) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [X: $i,A: $i,B: $i] :
( in_lopen(X,A,B)
<=> ( less(A,X)
& leq(X,B) ) )
<=> ! [X: $i,A: $i,B: $i] :
~ ( ( ~ leq(X,B)
| ~ less(A,X) )
<=> in_lopen(X,A,B) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i,A: $i,B: $i] :
( in_lopen(X,A,B)
<=> ( less(A,X)
& leq(X,B) ) )
<=> ! [X: $i,A: $i,B: $i] :
( in_lopen(X,A,B)
<=> ( less(A,X)
& leq(X,B) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
! [X: $i,A: $i,B: $i] :
( in_lopen(X,A,B)
<=> ( less(A,X)
& leq(X,B) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/MGT002+2.ax',in_lopen) ).
tff(7,plain,
! [X: $i,A: $i,B: $i] :
( in_lopen(X,A,B)
<=> ( less(A,X)
& leq(X,B) ) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X: $i,A: $i,B: $i] :
( in_lopen(X,A,B)
<=> ( less(A,X)
& leq(X,B) ) ),
inference(skolemize,[status(sab)],[7]) ).
tff(9,plain,
! [X: $i,A: $i,B: $i] :
~ ( ( ~ leq(X,B)
| ~ less(A,X) )
<=> in_lopen(X,A,B) ),
inference(modus_ponens,[status(thm)],[8,4]) ).
tff(10,plain,
! [X: $i,A: $i,B: $i] :
~ ( ( ~ leq(X,B)
| ~ less(A,X) )
<=> in_lopen(X,A,B) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ ! [X: $i,A: $i,B: $i] :
~ ( ( ~ leq(X,B)
| ~ less(A,X) )
<=> in_lopen(X,A,B) )
| ~ ( ( ~ leq(v200,v600)
| ~ less(v0,v200) )
<=> in_lopen(v200,v0,v600) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
~ ( ( ~ leq(v200,v600)
| ~ less(v0,v200) )
<=> in_lopen(v200,v0,v600) ),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
( less(v200,v600)
<=> less(v200,v600) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
less(v200,v600),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ord_v200_v600) ).
tff(15,plain,
less(v200,v600),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ less(X,Y)
| leq(X,Y) )
<=> ( ~ less(X,Y)
| leq(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
^ [X: $i,Y: $i] :
rewrite(( ( less(X,Y)
=> leq(X,Y) )
<=> ( ~ less(X,Y)
| leq(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [X: $i,Y: $i] :
( less(X,Y)
=> leq(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,axiom,
! [X: $i,Y: $i] :
( less(X,Y)
=> leq(X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/MGT002+0.ax',less_implies_leq) ).
tff(22,plain,
! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[24,17]) ).
tff(26,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v200,v600)
| leq(v200,v600) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v200,v600)
| leq(v200,v600) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v200,v600)
| leq(v200,v600) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v200,v600)
| leq(v200,v600) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
leq(v200,v600),
inference(unit_resolution,[status(thm)],[28,25,15]) ).
tff(30,plain,
( less(v0,v200)
<=> less(v0,v200) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
less(v0,v200),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ord_v0_v200) ).
tff(32,plain,
less(v0,v200),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
( ~ ( ~ leq(v200,v600)
| ~ less(v0,v200) )
| ~ leq(v200,v600)
| ~ less(v0,v200) ),
inference(tautology,[status(thm)],[]) ).
tff(34,plain,
~ ( ~ leq(v200,v600)
| ~ less(v0,v200) ),
inference(unit_resolution,[status(thm)],[33,32,29]) ).
tff(35,plain,
( ( ( ~ leq(v200,v600)
| ~ less(v0,v200) )
<=> in_lopen(v200,v0,v600) )
| ~ leq(v200,v600)
| ~ less(v0,v200)
| in_lopen(v200,v0,v600) ),
inference(tautology,[status(thm)],[]) ).
tff(36,plain,
( ( ( ~ leq(v200,v600)
| ~ less(v0,v200) )
<=> in_lopen(v200,v0,v600) )
| in_lopen(v200,v0,v600) ),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
in_lopen(v200,v0,v600),
inference(unit_resolution,[status(thm)],[36,12]) ).
tff(38,plain,
^ [X: $i] :
refl(( ~ in_lopen(X,v0,v600)
<=> ~ in_lopen(X,v0,v600) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [X: $i] : ~ in_lopen(X,v0,v600)
<=> ! [X: $i] : ~ in_lopen(X,v0,v600) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ~ ? [X: $i] : in_lopen(X,v0,v600)
<=> ~ ? [X: $i] : in_lopen(X,v0,v600) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,axiom,
~ ? [X: $i] : in_lopen(X,v0,v600),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',odrl500) ).
tff(42,plain,
~ ? [X: $i] : in_lopen(X,v0,v600),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
~ ? [X: $i] : in_lopen(X,v0,v600),
inference(modus_ponens,[status(thm)],[42,40]) ).
tff(44,plain,
~ ? [X: $i] : in_lopen(X,v0,v600),
inference(modus_ponens,[status(thm)],[43,40]) ).
tff(45,plain,
~ ? [X: $i] : in_lopen(X,v0,v600),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
^ [X: $i] : refl($oeq(~ in_lopen(X,v0,v600),~ in_lopen(X,v0,v600))),
inference(bind,[status(th)],[]) ).
tff(47,plain,
! [X: $i] : ~ in_lopen(X,v0,v600),
inference(nnf-neg,[status(sab)],[45,46]) ).
tff(48,plain,
! [X: $i] : ~ in_lopen(X,v0,v600),
inference(modus_ponens,[status(thm)],[47,39]) ).
tff(49,plain,
( ~ ! [X: $i] : ~ in_lopen(X,v0,v600)
| ~ in_lopen(v200,v0,v600) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
$false,
inference(unit_resolution,[status(thm)],[49,48,37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT087+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.34 % Computer : n028.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 7 14:23:19 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.44 % SZS status Theorem
% 0.12/0.44 % SZS output start Proof
% See solution above
% 0.12/0.44 % E exiting
%------------------------------------------------------------------------------