%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT089+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n020.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 0.00s 0.43s
% Output : Proof 0.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 35 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 133 ( 26 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 114 ( 18 ~; 39 |; 0 &)
% ( 57 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 4 usr; 2 prp; 0-4 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 54 ( 50 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(v5_type,type,
v5: $i ).
tff(prec_type,type,
prec: ( $i * $i * $i * $i ) > $o ).
tff(o_type,type,
o: $i ).
tff(less_type,type,
less: ( $i * $i ) > $o ).
tff(1,plain,
^ [U: $i,L: $i] :
refl(( ( prec(U,L,o,o)
<=> leq(U,L) )
<=> ( prec(U,L,o,o)
<=> leq(U,L) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [U: $i,L: $i] :
( prec(U,L,o,o)
<=> leq(U,L) )
<=> ! [U: $i,L: $i] :
( prec(U,L,o,o)
<=> leq(U,L) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [U: $i,L: $i] :
( prec(U,L,o,o)
<=> leq(U,L) )
<=> ! [U: $i,L: $i] :
( prec(U,L,o,o)
<=> leq(U,L) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [U: $i,L: $i] :
( prec(U,L,o,o)
<=> leq(U,L) ),
file('/export/starexec/sandbox/benchmark/Axioms/MGT002+5.ax',prec_oo) ).
tff(5,plain,
! [U: $i,L: $i] :
( prec(U,L,o,o)
<=> leq(U,L) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [U: $i,L: $i] :
( prec(U,L,o,o)
<=> leq(U,L) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [U: $i,L: $i] :
( prec(U,L,o,o)
<=> leq(U,L) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [U: $i,L: $i] :
( prec(U,L,o,o)
<=> leq(U,L) )
| ( prec(v5,v5,o,o)
<=> leq(v5,v5) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
( prec(v5,v5,o,o)
<=> leq(v5,v5) ),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ prec(v5,v5,o,o)
<=> ~ prec(v5,v5,o,o) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
~ prec(v5,v5,o,o),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',odrl604) ).
tff(12,plain,
~ prec(v5,v5,o,o),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
( ~ ( prec(v5,v5,o,o)
<=> leq(v5,v5) )
| prec(v5,v5,o,o)
| ~ leq(v5,v5) ),
inference(tautology,[status(thm)],[]) ).
tff(14,plain,
( ~ ( prec(v5,v5,o,o)
<=> leq(v5,v5) )
| ~ leq(v5,v5) ),
inference(unit_resolution,[status(thm)],[13,12]) ).
tff(15,plain,
~ leq(v5,v5),
inference(unit_resolution,[status(thm)],[14,9]) ).
tff(16,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(17,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)],[16]) ).
tff(18,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(19,axiom,
! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/MGT002+0.ax',leq_def) ).
tff(20,plain,
! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
( ( ~ ! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) )
| leq(v5,v5) )
<=> ( ~ ! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) )
| leq(v5,v5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ( leq(v5,v5)
<=> $true )
<=> leq(v5,v5) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( less(v5,v5)
| $true )
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ( v5 = v5 )
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ( less(v5,v5)
| ( v5 = v5 ) )
<=> ( less(v5,v5)
| $true ) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( ( less(v5,v5)
| ( v5 = v5 ) )
<=> $true ),
inference(transitivity,[status(thm)],[27,25]) ).
tff(29,plain,
( ( leq(v5,v5)
<=> ( less(v5,v5)
| ( v5 = v5 ) ) )
<=> ( leq(v5,v5)
<=> $true ) ),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
( ( leq(v5,v5)
<=> ( less(v5,v5)
| ( v5 = v5 ) ) )
<=> leq(v5,v5) ),
inference(transitivity,[status(thm)],[29,24]) ).
tff(31,plain,
( ( ~ ! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) )
| ( leq(v5,v5)
<=> ( less(v5,v5)
| ( v5 = v5 ) ) ) )
<=> ( ~ ! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) )
| leq(v5,v5) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( ~ ! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) )
| ( leq(v5,v5)
<=> ( less(v5,v5)
| ( v5 = v5 ) ) ) )
<=> ( ~ ! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) )
| leq(v5,v5) ) ),
inference(transitivity,[status(thm)],[31,23]) ).
tff(33,plain,
( ~ ! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) )
| ( leq(v5,v5)
<=> ( less(v5,v5)
| ( v5 = v5 ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [X: $i,Y: $i] :
( leq(X,Y)
<=> ( less(X,Y)
| ( X = Y ) ) )
| leq(v5,v5) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
$false,
inference(unit_resolution,[status(thm)],[34,22,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT089+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.07/0.36 % Computer : n020.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.00/0.36 % CPULimit : 300
% 0.00/0.36 % WCLimit : 300
% 0.00/0.36 % DateTime : Mon Sep 7 14:01:45 UTC 2026
% 0.00/0.36 % CPUTime :
% 0.00/0.43 % SZS status Theorem
% 0.00/0.43 % SZS output start Proof
% See solution above
% 0.00/0.44 % E exiting
%------------------------------------------------------------------------------