%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT088+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n031.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 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 26
% Syntax : Number of formulae : 62 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 288 ( 26 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 348 ( 146 ~; 91 |; 24 &)
% ( 87 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 24 ( 24 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 7 usr; 2 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 97 ( 79 !; 7 ?; 97 :)
% Comments :
%------------------------------------------------------------------------------
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(v400_type,type,
v400: $i ).
tff(less_type,type,
less: ( $i * $i ) > $o ).
tff(v0_type,type,
v0: $i ).
tff(in_lopen_type,type,
in_lopen: ( $i * $i * $i ) > $o ).
tff(v200_type,type,
v200: $i ).
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/sandbox2/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(v400,v400)
| ~ less(v0,v400) )
<=> in_lopen(v400,v0,v400) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
~ ( ( ~ leq(v400,v400)
| ~ less(v0,v400) )
<=> in_lopen(v400,v0,v400) ),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
^ [X: $i] :
refl(( ( ~ less(v200,X)
| ~ in_lopen(X,v0,v400) )
<=> ( ~ less(v200,X)
| ~ in_lopen(X,v0,v400) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [X: $i] :
( ~ less(v200,X)
| ~ in_lopen(X,v0,v400) )
<=> ! [X: $i] :
( ~ less(v200,X)
| ~ in_lopen(X,v0,v400) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( less(v200,X)
& in_lopen(X,v0,v400) )
<=> ~ ( ~ less(v200,X)
| ~ in_lopen(X,v0,v400) ) )),
( ~ ( less(v200,X)
& in_lopen(X,v0,v400) )
<=> ~ ~ ( ~ less(v200,X)
| ~ in_lopen(X,v0,v400) ) )),
rewrite(( ~ ~ ( ~ less(v200,X)
| ~ in_lopen(X,v0,v400) )
<=> ( ~ less(v200,X)
| ~ in_lopen(X,v0,v400) ) )),
( ~ ( less(v200,X)
& in_lopen(X,v0,v400) )
<=> ( ~ less(v200,X)
| ~ in_lopen(X,v0,v400) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [X: $i] :
~ ( less(v200,X)
& in_lopen(X,v0,v400) )
<=> ! [X: $i] :
( ~ less(v200,X)
| ~ in_lopen(X,v0,v400) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ~ ? [X: $i] :
( less(v200,X)
& in_lopen(X,v0,v400) )
<=> ~ ? [X: $i] :
( less(v200,X)
& in_lopen(X,v0,v400) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
~ ? [X: $i] :
( less(v200,X)
& in_lopen(X,v0,v400) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',odrl509) ).
tff(19,plain,
~ ? [X: $i] :
( less(v200,X)
& in_lopen(X,v0,v400) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
~ ? [X: $i] :
( less(v200,X)
& in_lopen(X,v0,v400) ),
inference(modus_ponens,[status(thm)],[19,17]) ).
tff(21,plain,
~ ? [X: $i] :
( less(v200,X)
& in_lopen(X,v0,v400) ),
inference(modus_ponens,[status(thm)],[20,17]) ).
tff(22,plain,
~ ? [X: $i] :
( less(v200,X)
& in_lopen(X,v0,v400) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
^ [X: $i] :
refl($oeq(~ ( less(v200,X)
& in_lopen(X,v0,v400) ),
~ ( less(v200,X)
& in_lopen(X,v0,v400) ))),
inference(bind,[status(th)],[]) ).
tff(24,plain,
! [X: $i] :
~ ( less(v200,X)
& in_lopen(X,v0,v400) ),
inference(nnf-neg,[status(sab)],[22,23]) ).
tff(25,plain,
! [X: $i] :
( ~ less(v200,X)
| ~ in_lopen(X,v0,v400) ),
inference(modus_ponens,[status(thm)],[24,16]) ).
tff(26,plain,
! [X: $i] :
( ~ less(v200,X)
| ~ in_lopen(X,v0,v400) ),
inference(modus_ponens,[status(thm)],[25,14]) ).
tff(27,plain,
( less(v200,v400)
<=> less(v200,v400) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
less(v200,v400),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v200_v400) ).
tff(29,plain,
less(v200,v400),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
( ( ~ ! [X: $i] :
( ~ less(v200,X)
| ~ in_lopen(X,v0,v400) )
| ~ less(v200,v400)
| ~ in_lopen(v400,v0,v400) )
<=> ( ~ ! [X: $i] :
( ~ less(v200,X)
| ~ in_lopen(X,v0,v400) )
| ~ less(v200,v400)
| ~ in_lopen(v400,v0,v400) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
( ~ ! [X: $i] :
( ~ less(v200,X)
| ~ in_lopen(X,v0,v400) )
| ~ less(v200,v400)
| ~ in_lopen(v400,v0,v400) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [X: $i] :
( ~ less(v200,X)
| ~ in_lopen(X,v0,v400) )
| ~ less(v200,v400)
| ~ in_lopen(v400,v0,v400) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
~ in_lopen(v400,v0,v400),
inference(unit_resolution,[status(thm)],[32,29,26]) ).
tff(34,plain,
( ( ( ~ leq(v400,v400)
| ~ less(v0,v400) )
<=> in_lopen(v400,v0,v400) )
| ~ leq(v400,v400)
| ~ less(v0,v400)
| in_lopen(v400,v0,v400) ),
inference(tautology,[status(thm)],[]) ).
tff(35,plain,
( ( ( ~ leq(v400,v400)
| ~ less(v0,v400) )
<=> in_lopen(v400,v0,v400) )
| ~ leq(v400,v400)
| ~ less(v0,v400) ),
inference(unit_resolution,[status(thm)],[34,33]) ).
tff(36,plain,
( ~ leq(v400,v400)
| ~ less(v0,v400) ),
inference(unit_resolution,[status(thm)],[35,12]) ).
tff(37,plain,
( less(v0,v400)
<=> less(v0,v400) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
less(v0,v400),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v0_v400) ).
tff(39,plain,
less(v0,v400),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ~ ( ~ leq(v400,v400)
| ~ less(v0,v400) )
| ~ leq(v400,v400)
| ~ less(v0,v400) ),
inference(tautology,[status(thm)],[]) ).
tff(41,plain,
( ~ ( ~ leq(v400,v400)
| ~ less(v0,v400) )
| ~ leq(v400,v400) ),
inference(unit_resolution,[status(thm)],[40,39]) ).
tff(42,plain,
~ leq(v400,v400),
inference(unit_resolution,[status(thm)],[41,36]) ).
tff(43,plain,
^ [X: $i,Y: $i] :
refl(( ( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) )
<=> ( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(44,plain,
( ! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) )
<=> ! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) )
<=> ! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,axiom,
! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MGT002+0.ax',leq_def) ).
tff(47,plain,
! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ( ~ ! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) )
| leq(v400,v400) )
<=> ( ~ ! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) )
| leq(v400,v400) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ( leq(v400,v400)
<=> $true )
<=> leq(v400,v400) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ( less(v400,v400)
| $true )
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ( v400 = v400 )
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ( less(v400,v400)
| ( v400 = v400 ) )
<=> ( less(v400,v400)
| $true ) ),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
( ( less(v400,v400)
| ( v400 = v400 ) )
<=> $true ),
inference(transitivity,[status(thm)],[54,52]) ).
tff(56,plain,
( ( leq(v400,v400)
<=> ( less(v400,v400)
| ( v400 = v400 ) ) )
<=> ( leq(v400,v400)
<=> $true ) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( ( leq(v400,v400)
<=> ( less(v400,v400)
| ( v400 = v400 ) ) )
<=> leq(v400,v400) ),
inference(transitivity,[status(thm)],[56,51]) ).
tff(58,plain,
( ( ~ ! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) )
| ( leq(v400,v400)
<=> ( less(v400,v400)
| ( v400 = v400 ) ) ) )
<=> ( ~ ! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) )
| leq(v400,v400) ) ),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
( ( ~ ! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) )
| ( leq(v400,v400)
<=> ( less(v400,v400)
| ( v400 = v400 ) ) ) )
<=> ( ~ ! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) )
| leq(v400,v400) ) ),
inference(transitivity,[status(thm)],[58,50]) ).
tff(60,plain,
( ~ ! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) )
| ( leq(v400,v400)
<=> ( less(v400,v400)
| ( v400 = v400 ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) )
| leq(v400,v400) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
$false,
inference(unit_resolution,[status(thm)],[61,49,42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT088+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.09/0.34 % Computer : n031.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 7 14:25:28 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% See solution above
% 0.12/0.40 % E exiting
%------------------------------------------------------------------------------