%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT102+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n011.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 06:24:14 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.41s
% Output : Proof 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 21
% Syntax : Number of formulae : 45 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 198 ( 37 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 245 ( 108 ~; 89 |; 19 &)
% ( 23 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 16 ( 16 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 82 ( 74 !; 0 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(v600_type,type,
v600: $i ).
tff(v700_type,type,
v700: $i ).
tff(less_type,type,
less: ( $i * $i ) > $o ).
tff(v0_type,type,
v0: $i ).
tff(1,plain,
( less(v700,v600)
<=> less(v700,v600) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( less(v700,v600)
& less(v600,v700) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contradiction) ).
tff(3,plain,
less(v700,v600),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
less(v700,v600),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ less(X,Y)
| leq(X,Y) )
<=> ( ~ less(X,Y)
| leq(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(6,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)],[5]) ).
tff(7,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(8,plain,
^ [X: $i,Y: $i] :
rewrite(( ( less(X,Y)
=> leq(X,Y) )
<=> ( ~ less(X,Y)
| leq(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(9,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)],[8]) ).
tff(10,axiom,
! [X: $i,Y: $i] :
( less(X,Y)
=> leq(X,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MGT002+0.ax',less_implies_leq) ).
tff(11,plain,
! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[13,6]) ).
tff(15,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v700,v600)
| leq(v700,v600) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v700,v600)
| leq(v700,v600) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v700,v600)
| leq(v700,v600) ),
inference(quant_inst,[status(thm)],[]) ).
tff(17,plain,
( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v700,v600)
| leq(v700,v600) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
leq(v700,v600),
inference(unit_resolution,[status(thm)],[17,14,4]) ).
tff(19,plain,
( less(v600,v700)
<=> less(v600,v700) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
less(v600,v700),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v600_v700) ).
tff(21,plain,
less(v600,v700),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v600,v700)
| leq(v600,v700) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v600,v700)
| leq(v600,v700) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v600,v700)
| leq(v600,v700) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v600,v700)
| leq(v600,v700) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
leq(v600,v700),
inference(unit_resolution,[status(thm)],[24,14,21]) ).
tff(26,plain,
( ( v600 != v700 )
<=> ( v600 != v700 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
( ( v0 != v600 )
& ( v0 != v700 )
& ( v600 != v700 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distinct) ).
tff(28,plain,
v600 != v700,
inference(and_elim,[status(thm)],[27]) ).
tff(29,plain,
v600 != v700,
inference(modus_ponens,[status(thm)],[28,26]) ).
tff(30,plain,
( ! [X: $i,Y: $i] :
( ( X = Y )
| ~ leq(X,Y)
| ~ leq(Y,X) )
<=> ! [X: $i,Y: $i] :
( ( X = Y )
| ~ leq(X,Y)
| ~ leq(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
^ [X: $i,Y: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( leq(X,Y)
& leq(Y,X) )
<=> ~ ( ~ leq(X,Y)
| ~ leq(Y,X) ) )),
( ~ ( leq(X,Y)
& leq(Y,X) )
<=> ~ ~ ( ~ leq(X,Y)
| ~ leq(Y,X) ) )),
rewrite(( ~ ~ ( ~ leq(X,Y)
| ~ leq(Y,X) )
<=> ( ~ leq(X,Y)
| ~ leq(Y,X) ) )),
( ~ ( leq(X,Y)
& leq(Y,X) )
<=> ( ~ leq(X,Y)
| ~ leq(Y,X) ) )),
( ( ~ ( leq(X,Y)
& leq(Y,X) )
| ( X = Y ) )
<=> ( ~ leq(X,Y)
| ~ leq(Y,X)
| ( X = Y ) ) )),
rewrite(( ( ~ leq(X,Y)
| ~ leq(Y,X)
| ( X = Y ) )
<=> ( ( X = Y )
| ~ leq(X,Y)
| ~ leq(Y,X) ) )),
( ( ~ ( leq(X,Y)
& leq(Y,X) )
| ( X = Y ) )
<=> ( ( X = Y )
| ~ leq(X,Y)
| ~ leq(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [X: $i,Y: $i] :
( ~ ( leq(X,Y)
& leq(Y,X) )
| ( X = Y ) )
<=> ! [X: $i,Y: $i] :
( ( X = Y )
| ~ leq(X,Y)
| ~ leq(Y,X) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [X: $i,Y: $i] :
( ~ ( leq(X,Y)
& leq(Y,X) )
| ( X = Y ) )
<=> ! [X: $i,Y: $i] :
( ~ ( leq(X,Y)
& leq(Y,X) )
| ( X = Y ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
^ [X: $i,Y: $i] :
rewrite(( ( ( leq(X,Y)
& leq(Y,X) )
=> ( X = Y ) )
<=> ( ~ ( leq(X,Y)
& leq(Y,X) )
| ( X = Y ) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [X: $i,Y: $i] :
( ( leq(X,Y)
& leq(Y,X) )
=> ( X = Y ) )
<=> ! [X: $i,Y: $i] :
( ~ ( leq(X,Y)
& leq(Y,X) )
| ( X = Y ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,axiom,
! [X: $i,Y: $i] :
( ( leq(X,Y)
& leq(Y,X) )
=> ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MGT002+0.ax',leq_antisym) ).
tff(37,plain,
! [X: $i,Y: $i] :
( ~ ( leq(X,Y)
& leq(Y,X) )
| ( X = Y ) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [X: $i,Y: $i] :
( ~ ( leq(X,Y)
& leq(Y,X) )
| ( X = Y ) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
! [X: $i,Y: $i] :
( ~ ( leq(X,Y)
& leq(Y,X) )
| ( X = Y ) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [X: $i,Y: $i] :
( ( X = Y )
| ~ leq(X,Y)
| ~ leq(Y,X) ),
inference(modus_ponens,[status(thm)],[39,32]) ).
tff(41,plain,
! [X: $i,Y: $i] :
( ( X = Y )
| ~ leq(X,Y)
| ~ leq(Y,X) ),
inference(modus_ponens,[status(thm)],[40,30]) ).
tff(42,plain,
( ( ~ ! [X: $i,Y: $i] :
( ( X = Y )
| ~ leq(X,Y)
| ~ leq(Y,X) )
| ( v600 = v700 )
| ~ leq(v600,v700)
| ~ leq(v700,v600) )
<=> ( ~ ! [X: $i,Y: $i] :
( ( X = Y )
| ~ leq(X,Y)
| ~ leq(Y,X) )
| ( v600 = v700 )
| ~ leq(v600,v700)
| ~ leq(v700,v600) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [X: $i,Y: $i] :
( ( X = Y )
| ~ leq(X,Y)
| ~ leq(Y,X) )
| ( v600 = v700 )
| ~ leq(v600,v700)
| ~ leq(v700,v600) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [X: $i,Y: $i] :
( ( X = Y )
| ~ leq(X,Y)
| ~ leq(Y,X) )
| ( v600 = v700 )
| ~ leq(v600,v700)
| ~ leq(v700,v600) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
$false,
inference(unit_resolution,[status(thm)],[44,41,29,25,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT102+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 7 14:38:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.41 % SZS status Unsatisfiable
% 0.10/0.41 % SZS output start Proof
% See solution above
% 0.10/0.41 % E exiting
%------------------------------------------------------------------------------