%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT092+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n019.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 06:24:13 AM UTC 2026
% Result : Theorem 0.12s 0.41s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 34
% Syntax : Number of formulae : 73 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 552 ( 0 equ)
% Maximal formula atoms : 20 ( 7 avg)
% Number of connectives : 740 ( 304 ~; 275 |; 98 &)
% ( 51 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 43 ( 43 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 222 ( 200 !; 0 ?; 222 :)
% Comments :
%------------------------------------------------------------------------------
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(v1200_type,type,
v1200: $i ).
tff(v400_type,type,
v400: $i ).
tff(v800_type,type,
v800: $i ).
tff(less_type,type,
less: ( $i * $i ) > $o ).
tff(v0_type,type,
v0: $i ).
tff(completion_conflict_type,type,
completion_conflict: ( $i * $i * $i * $i ) > $o ).
tff(1,plain,
( less(v800,v1200)
<=> less(v800,v1200) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
less(v800,v1200),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ord_v800_v1200) ).
tff(3,plain,
less(v800,v1200),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ less(X,Y)
| leq(X,Y) )
<=> ( ~ less(X,Y)
| leq(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(5,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)],[4]) ).
tff(6,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(7,plain,
^ [X: $i,Y: $i] :
rewrite(( ( less(X,Y)
=> leq(X,Y) )
<=> ( ~ less(X,Y)
| leq(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(8,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)],[7]) ).
tff(9,axiom,
! [X: $i,Y: $i] :
( less(X,Y)
=> leq(X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/MGT002+0.ax',less_implies_leq) ).
tff(10,plain,
! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v800,v1200)
| leq(v800,v1200) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v800,v1200)
| leq(v800,v1200) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v800,v1200)
| leq(v800,v1200) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v800,v1200)
| leq(v800,v1200) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
leq(v800,v1200),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
( less(v0,v400)
<=> less(v0,v400) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
less(v0,v400),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ord_v0_v400) ).
tff(20,plain,
less(v0,v400),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v0,v400)
| leq(v0,v400) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v0,v400)
| leq(v0,v400) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v0,v400)
| leq(v0,v400) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v0,v400)
| leq(v0,v400) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
leq(v0,v400),
inference(unit_resolution,[status(thm)],[23,13,20]) ).
tff(25,plain,
( ~ completion_conflict(v400,v800,v0,v1200)
<=> ~ completion_conflict(v400,v800,v0,v1200) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
~ completion_conflict(v400,v800,v0,v1200),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',odrl633) ).
tff(27,plain,
~ completion_conflict(v400,v800,v0,v1200),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( less(v400,v800)
<=> less(v400,v800) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
less(v400,v800),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ord_v400_v800) ).
tff(30,plain,
less(v400,v800),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
^ [U: $i,V: $i,InfD: $i,SupD: $i] :
refl(( ( completion_conflict(U,V,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) )
<=> ( completion_conflict(U,V,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( completion_conflict(U,V,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) )
<=> ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( completion_conflict(U,V,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
^ [U: $i,V: $i,InfD: $i,SupD: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
<=> ~ ( ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) ) )),
( ~ ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
<=> ~ ~ ( ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) ) )),
rewrite(( ~ ~ ( ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) )
<=> ( ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) ) )),
( ~ ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
<=> ( ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) ) )),
( ( ~ ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
| completion_conflict(U,V,InfD,SupD) )
<=> ( ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V)
| completion_conflict(U,V,InfD,SupD) ) )),
rewrite(( ( ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V)
| completion_conflict(U,V,InfD,SupD) )
<=> ( completion_conflict(U,V,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) ) )),
( ( ~ ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
| completion_conflict(U,V,InfD,SupD) )
<=> ( completion_conflict(U,V,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( ~ ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
| completion_conflict(U,V,InfD,SupD) )
<=> ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( completion_conflict(U,V,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( ~ ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
| completion_conflict(U,V,InfD,SupD) )
<=> ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( ~ ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
| completion_conflict(U,V,InfD,SupD) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
^ [U: $i,V: $i,InfD: $i,SupD: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( leq(InfD,U)
& leq(U,SupD)
& less(U,V) )
<=> ( leq(InfD,U)
& leq(U,SupD)
& less(U,V) ) )),
( ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
<=> ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) ) )),
rewrite(( ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
<=> ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) ) )),
( ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
<=> ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) ) )),
( ( ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
=> completion_conflict(U,V,InfD,SupD) )
<=> ( ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
=> completion_conflict(U,V,InfD,SupD) ) )),
rewrite(( ( ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
=> completion_conflict(U,V,InfD,SupD) )
<=> ( ~ ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
| completion_conflict(U,V,InfD,SupD) ) )),
( ( ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
=> completion_conflict(U,V,InfD,SupD) )
<=> ( ~ ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
| completion_conflict(U,V,InfD,SupD) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
=> completion_conflict(U,V,InfD,SupD) )
<=> ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( ~ ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
| completion_conflict(U,V,InfD,SupD) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,axiom,
! [U: $i,V: $i,InfD: $i,SupD: $i] :
( ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
=> completion_conflict(U,V,InfD,SupD) ),
file('/export/starexec/sandbox/benchmark/Axioms/MGT002+4.ax',sharpness_conflict) ).
tff(39,plain,
! [U: $i,V: $i,InfD: $i,SupD: $i] :
( ~ ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
| completion_conflict(U,V,InfD,SupD) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [U: $i,V: $i,InfD: $i,SupD: $i] :
( ~ ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
| completion_conflict(U,V,InfD,SupD) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
! [U: $i,V: $i,InfD: $i,SupD: $i] :
( ~ ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
| completion_conflict(U,V,InfD,SupD) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [U: $i,V: $i,InfD: $i,SupD: $i] :
( completion_conflict(U,V,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,plain,
! [U: $i,V: $i,InfD: $i,SupD: $i] :
( completion_conflict(U,V,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) ),
inference(modus_ponens,[status(thm)],[42,32]) ).
tff(44,plain,
( ( ~ ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( completion_conflict(U,V,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) )
| completion_conflict(v400,v800,v0,v1200)
| ~ less(v400,v800)
| ~ leq(v800,v1200)
| ~ leq(v0,v400)
| ~ leq(v400,v1200) )
<=> ( ~ ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( completion_conflict(U,V,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) )
| completion_conflict(v400,v800,v0,v1200)
| ~ less(v400,v800)
| ~ leq(v800,v1200)
| ~ leq(v0,v400)
| ~ leq(v400,v1200) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,plain,
( ( completion_conflict(v400,v800,v0,v1200)
| ~ leq(v800,v1200)
| ~ leq(v0,v400)
| ~ leq(v400,v1200)
| ~ less(v400,v800) )
<=> ( completion_conflict(v400,v800,v0,v1200)
| ~ less(v400,v800)
| ~ leq(v800,v1200)
| ~ leq(v0,v400)
| ~ leq(v400,v1200) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ( ~ ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( completion_conflict(U,V,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) )
| completion_conflict(v400,v800,v0,v1200)
| ~ leq(v800,v1200)
| ~ leq(v0,v400)
| ~ leq(v400,v1200)
| ~ less(v400,v800) )
<=> ( ~ ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( completion_conflict(U,V,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) )
| completion_conflict(v400,v800,v0,v1200)
| ~ less(v400,v800)
| ~ leq(v800,v1200)
| ~ leq(v0,v400)
| ~ leq(v400,v1200) ) ),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( ( ~ ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( completion_conflict(U,V,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) )
| completion_conflict(v400,v800,v0,v1200)
| ~ leq(v800,v1200)
| ~ leq(v0,v400)
| ~ leq(v400,v1200)
| ~ less(v400,v800) )
<=> ( ~ ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( completion_conflict(U,V,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) )
| completion_conflict(v400,v800,v0,v1200)
| ~ less(v400,v800)
| ~ leq(v800,v1200)
| ~ leq(v0,v400)
| ~ leq(v400,v1200) ) ),
inference(transitivity,[status(thm)],[46,44]) ).
tff(48,plain,
( ~ ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( completion_conflict(U,V,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) )
| completion_conflict(v400,v800,v0,v1200)
| ~ leq(v800,v1200)
| ~ leq(v0,v400)
| ~ leq(v400,v1200)
| ~ less(v400,v800) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( completion_conflict(U,V,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) )
| completion_conflict(v400,v800,v0,v1200)
| ~ less(v400,v800)
| ~ leq(v800,v1200)
| ~ leq(v0,v400)
| ~ leq(v400,v1200) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
~ leq(v400,v1200),
inference(unit_resolution,[status(thm)],[49,43,30,27,24,17]) ).
tff(51,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v400,v800)
| leq(v400,v800) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v400,v800)
| leq(v400,v800) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v400,v800)
| leq(v400,v800) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v400,v800)
| leq(v400,v800) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
leq(v400,v800),
inference(unit_resolution,[status(thm)],[53,13,30]) ).
tff(55,plain,
( ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
<=> ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,plain,
^ [X: $i,Y: $i,Z: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( leq(X,Y)
& leq(Y,Z) )
<=> ~ ( ~ leq(Y,Z)
| ~ leq(X,Y) ) )),
( ~ ( leq(X,Y)
& leq(Y,Z) )
<=> ~ ~ ( ~ leq(Y,Z)
| ~ leq(X,Y) ) )),
rewrite(( ~ ~ ( ~ leq(Y,Z)
| ~ leq(X,Y) )
<=> ( ~ leq(Y,Z)
| ~ leq(X,Y) ) )),
( ~ ( leq(X,Y)
& leq(Y,Z) )
<=> ( ~ leq(Y,Z)
| ~ leq(X,Y) ) )),
( ( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) )
<=> ( ~ leq(Y,Z)
| ~ leq(X,Y)
| leq(X,Z) ) )),
rewrite(( ( ~ leq(Y,Z)
| ~ leq(X,Y)
| leq(X,Z) )
<=> ( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ) )),
( ( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) )
<=> ( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
^ [X: $i,Y: $i,Z: $i] :
rewrite(( ( ( leq(X,Y)
& leq(Y,Z) )
=> leq(X,Z) )
<=> ( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(60,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( leq(X,Y)
& leq(Y,Z) )
=> leq(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( leq(X,Y)
& leq(Y,Z) )
=> leq(X,Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/MGT002+0.ax',leq_trans) ).
tff(62,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ),
inference(modus_ponens,[status(thm)],[64,57]) ).
tff(66,plain,
! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ),
inference(modus_ponens,[status(thm)],[65,55]) ).
tff(67,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| ~ leq(v800,v1200)
| leq(v400,v1200)
| ~ leq(v400,v800) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| ~ leq(v800,v1200)
| leq(v400,v1200)
| ~ leq(v400,v800) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
( ( leq(v400,v1200)
| ~ leq(v800,v1200)
| ~ leq(v400,v800) )
<=> ( ~ leq(v800,v1200)
| leq(v400,v1200)
| ~ leq(v400,v800) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| leq(v400,v1200)
| ~ leq(v800,v1200)
| ~ leq(v400,v800) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| ~ leq(v800,v1200)
| leq(v400,v1200)
| ~ leq(v400,v800) ) ),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| leq(v400,v1200)
| ~ leq(v800,v1200)
| ~ leq(v400,v800) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| ~ leq(v800,v1200)
| leq(v400,v1200)
| ~ leq(v400,v800) ) ),
inference(transitivity,[status(thm)],[69,67]) ).
tff(71,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| leq(v400,v1200)
| ~ leq(v800,v1200)
| ~ leq(v400,v800) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| ~ leq(v800,v1200)
| leq(v400,v1200)
| ~ leq(v400,v800) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
$false,
inference(unit_resolution,[status(thm)],[72,66,54,17,50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT092+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.07/0.34 % Computer : n019.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 7 14:25:24 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.12/0.41 % SZS status Theorem
% 0.12/0.41 % SZS output start Proof
% See solution above
% 0.12/0.43 % E exiting
%------------------------------------------------------------------------------