%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT070+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n006.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 06:24:11 AM UTC 2026
% Result : Theorem 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 39
% Syntax : Number of formulae : 88 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 612 ( 0 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 860 ( 379 ~; 292 |; 126 &)
% ( 51 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 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 : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 224 ( 181 !; 18 ?; 224 :)
% Comments :
%------------------------------------------------------------------------------
tff(completion_compatible_type,type,
completion_compatible: ( $i * $i * $i ) > $o ).
tff(nsup_type,type,
nsup: $i ).
tff(ninf_type,type,
ninf: $i ).
tff(n0_type,type,
n0: $i ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(less_type,type,
less: ( $i * $i ) > $o ).
tff(tptp_fun_Z_0_type,type,
tptp_fun_Z_0: ( $i * $i ) > $i ).
tff(1,plain,
( less(n0,nsup)
<=> less(n0,nsup) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
less(n0,nsup),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_0_sup) ).
tff(3,plain,
less(n0,nsup),
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/sandbox2/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(n0,nsup)
| leq(n0,nsup) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(n0,nsup)
| leq(n0,nsup) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(n0,nsup)
| leq(n0,nsup) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(n0,nsup)
| leq(n0,nsup) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
leq(n0,nsup),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
( less(ninf,n0)
<=> less(ninf,n0) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
less(ninf,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_inf_0) ).
tff(20,plain,
less(ninf,n0),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(ninf,n0)
| leq(ninf,n0) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(ninf,n0)
| leq(ninf,n0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(ninf,n0)
| leq(ninf,n0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(ninf,n0)
| leq(ninf,n0) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
leq(ninf,n0),
inference(unit_resolution,[status(thm)],[23,13,20]) ).
tff(25,plain,
^ [V: $i] :
refl(( ( ~ leq(ninf,V)
| ~ leq(V,nsup)
| ~ completion_compatible(V,ninf,nsup) )
<=> ( ~ leq(ninf,V)
| ~ leq(V,nsup)
| ~ completion_compatible(V,ninf,nsup) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [V: $i] :
( ~ leq(ninf,V)
| ~ leq(V,nsup)
| ~ completion_compatible(V,ninf,nsup) )
<=> ! [V: $i] :
( ~ leq(ninf,V)
| ~ leq(V,nsup)
| ~ completion_compatible(V,ninf,nsup) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
^ [V: $i] :
trans(monotonicity(rewrite(( ( leq(ninf,V)
& leq(V,nsup)
& completion_compatible(V,ninf,nsup) )
<=> ~ ( ~ leq(ninf,V)
| ~ leq(V,nsup)
| ~ completion_compatible(V,ninf,nsup) ) )),
( ~ ( leq(ninf,V)
& leq(V,nsup)
& completion_compatible(V,ninf,nsup) )
<=> ~ ~ ( ~ leq(ninf,V)
| ~ leq(V,nsup)
| ~ completion_compatible(V,ninf,nsup) ) )),
rewrite(( ~ ~ ( ~ leq(ninf,V)
| ~ leq(V,nsup)
| ~ completion_compatible(V,ninf,nsup) )
<=> ( ~ leq(ninf,V)
| ~ leq(V,nsup)
| ~ completion_compatible(V,ninf,nsup) ) )),
( ~ ( leq(ninf,V)
& leq(V,nsup)
& completion_compatible(V,ninf,nsup) )
<=> ( ~ leq(ninf,V)
| ~ leq(V,nsup)
| ~ completion_compatible(V,ninf,nsup) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [V: $i] :
~ ( leq(ninf,V)
& leq(V,nsup)
& completion_compatible(V,ninf,nsup) )
<=> ! [V: $i] :
( ~ leq(ninf,V)
| ~ leq(V,nsup)
| ~ completion_compatible(V,ninf,nsup) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ~ ? [V: $i] :
( leq(ninf,V)
& leq(V,nsup)
& completion_compatible(V,ninf,nsup) )
<=> ~ ? [V: $i] :
( leq(ninf,V)
& leq(V,nsup)
& completion_compatible(V,ninf,nsup) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ~ ? [V: $i] :
( leq(ninf,V)
& leq(V,nsup)
& completion_compatible(V,ninf,nsup) )
<=> ~ ? [V: $i] :
( leq(ninf,V)
& leq(V,nsup)
& completion_compatible(V,ninf,nsup) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
~ ? [V: $i] :
( leq(ninf,V)
& leq(V,nsup)
& completion_compatible(V,ninf,nsup) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown_sound_compatible) ).
tff(32,plain,
~ ? [V: $i] :
( leq(ninf,V)
& leq(V,nsup)
& completion_compatible(V,ninf,nsup) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
~ ? [V: $i] :
( leq(ninf,V)
& leq(V,nsup)
& completion_compatible(V,ninf,nsup) ),
inference(modus_ponens,[status(thm)],[32,29]) ).
tff(34,plain,
~ ? [V: $i] :
( leq(ninf,V)
& leq(V,nsup)
& completion_compatible(V,ninf,nsup) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
~ ? [V: $i] :
( leq(ninf,V)
& leq(V,nsup)
& completion_compatible(V,ninf,nsup) ),
inference(modus_ponens,[status(thm)],[34,29]) ).
tff(36,plain,
^ [V: $i] :
refl($oeq(~ ( leq(ninf,V)
& leq(V,nsup)
& completion_compatible(V,ninf,nsup) ),
~ ( leq(ninf,V)
& leq(V,nsup)
& completion_compatible(V,ninf,nsup) ))),
inference(bind,[status(th)],[]) ).
tff(37,plain,
! [V: $i] :
~ ( leq(ninf,V)
& leq(V,nsup)
& completion_compatible(V,ninf,nsup) ),
inference(nnf-neg,[status(sab)],[35,36]) ).
tff(38,plain,
! [V: $i] :
( ~ leq(ninf,V)
| ~ leq(V,nsup)
| ~ completion_compatible(V,ninf,nsup) ),
inference(modus_ponens,[status(thm)],[37,28]) ).
tff(39,plain,
! [V: $i] :
( ~ leq(ninf,V)
| ~ leq(V,nsup)
| ~ completion_compatible(V,ninf,nsup) ),
inference(modus_ponens,[status(thm)],[38,26]) ).
tff(40,plain,
( ( ~ ! [V: $i] :
( ~ leq(ninf,V)
| ~ leq(V,nsup)
| ~ completion_compatible(V,ninf,nsup) )
| ~ leq(ninf,n0)
| ~ leq(n0,nsup)
| ~ completion_compatible(n0,ninf,nsup) )
<=> ( ~ ! [V: $i] :
( ~ leq(ninf,V)
| ~ leq(V,nsup)
| ~ completion_compatible(V,ninf,nsup) )
| ~ leq(ninf,n0)
| ~ leq(n0,nsup)
| ~ completion_compatible(n0,ninf,nsup) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ~ ! [V: $i] :
( ~ leq(ninf,V)
| ~ leq(V,nsup)
| ~ completion_compatible(V,ninf,nsup) )
| ~ leq(ninf,n0)
| ~ leq(n0,nsup)
| ~ completion_compatible(n0,ninf,nsup) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [V: $i] :
( ~ leq(ninf,V)
| ~ leq(V,nsup)
| ~ completion_compatible(V,ninf,nsup) )
| ~ leq(ninf,n0)
| ~ leq(n0,nsup)
| ~ completion_compatible(n0,ninf,nsup) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
~ completion_compatible(n0,ninf,nsup),
inference(unit_resolution,[status(thm)],[42,39,24,17]) ).
tff(44,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ less(X,Y)
| ~ ( ~ less(X,tptp_fun_Z_0(Y,X))
| ~ less(tptp_fun_Z_0(Y,X),Y) ) )
<=> ( ~ less(X,Y)
| ~ ( ~ less(X,tptp_fun_Z_0(Y,X))
| ~ less(tptp_fun_Z_0(Y,X),Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [X: $i,Y: $i] :
( ~ less(X,Y)
| ~ ( ~ less(X,tptp_fun_Z_0(Y,X))
| ~ less(tptp_fun_Z_0(Y,X),Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ less(X,Y)
| ~ ( ~ less(X,tptp_fun_Z_0(Y,X))
| ~ less(tptp_fun_Z_0(Y,X),Y) ) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
^ [X: $i,Y: $i] :
rewrite(( ( ~ less(X,Y)
| ( less(X,tptp_fun_Z_0(Y,X))
& less(tptp_fun_Z_0(Y,X),Y) ) )
<=> ( ~ less(X,Y)
| ~ ( ~ less(X,tptp_fun_Z_0(Y,X))
| ~ less(tptp_fun_Z_0(Y,X),Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [X: $i,Y: $i] :
( ~ less(X,Y)
| ( less(X,tptp_fun_Z_0(Y,X))
& less(tptp_fun_Z_0(Y,X),Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ less(X,Y)
| ~ ( ~ less(X,tptp_fun_Z_0(Y,X))
| ~ less(tptp_fun_Z_0(Y,X),Y) ) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [X: $i,Y: $i] :
( ~ less(X,Y)
| ? [Z: $i] :
( less(X,Z)
& less(Z,Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ less(X,Y)
| ? [Z: $i] :
( less(X,Z)
& less(Z,Y) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
^ [X: $i,Y: $i] :
rewrite(( ( less(X,Y)
=> ? [Z: $i] :
( less(X,Z)
& less(Z,Y) ) )
<=> ( ~ less(X,Y)
| ? [Z: $i] :
( less(X,Z)
& less(Z,Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [X: $i,Y: $i] :
( less(X,Y)
=> ? [Z: $i] :
( less(X,Z)
& less(Z,Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ less(X,Y)
| ? [Z: $i] :
( less(X,Z)
& less(Z,Y) ) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,axiom,
! [X: $i,Y: $i] :
( less(X,Y)
=> ? [Z: $i] :
( less(X,Z)
& less(Z,Y) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MGT002+1.ax',dense) ).
tff(52,plain,
! [X: $i,Y: $i] :
( ~ less(X,Y)
| ? [Z: $i] :
( less(X,Z)
& less(Z,Y) ) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [X: $i,Y: $i] :
( ~ less(X,Y)
| ? [Z: $i] :
( less(X,Z)
& less(Z,Y) ) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
! [X: $i,Y: $i] :
( ~ less(X,Y)
| ( less(X,tptp_fun_Z_0(Y,X))
& less(tptp_fun_Z_0(Y,X),Y) ) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [X: $i,Y: $i] :
( ~ less(X,Y)
| ~ ( ~ less(X,tptp_fun_Z_0(Y,X))
| ~ less(tptp_fun_Z_0(Y,X),Y) ) ),
inference(modus_ponens,[status(thm)],[54,47]) ).
tff(56,plain,
! [X: $i,Y: $i] :
( ~ less(X,Y)
| ~ ( ~ less(X,tptp_fun_Z_0(Y,X))
| ~ less(tptp_fun_Z_0(Y,X),Y) ) ),
inference(modus_ponens,[status(thm)],[55,45]) ).
tff(57,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| ~ ( ~ less(X,tptp_fun_Z_0(Y,X))
| ~ less(tptp_fun_Z_0(Y,X),Y) ) )
| ~ less(n0,nsup)
| ~ ( ~ less(n0,tptp_fun_Z_0(nsup,n0))
| ~ less(tptp_fun_Z_0(nsup,n0),nsup) ) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| ~ ( ~ less(X,tptp_fun_Z_0(Y,X))
| ~ less(tptp_fun_Z_0(Y,X),Y) ) )
| ~ less(n0,nsup)
| ~ ( ~ less(n0,tptp_fun_Z_0(nsup,n0))
| ~ less(tptp_fun_Z_0(nsup,n0),nsup) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| ~ ( ~ less(X,tptp_fun_Z_0(Y,X))
| ~ less(tptp_fun_Z_0(Y,X),Y) ) )
| ~ less(n0,nsup)
| ~ ( ~ less(n0,tptp_fun_Z_0(nsup,n0))
| ~ less(tptp_fun_Z_0(nsup,n0),nsup) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| ~ ( ~ less(X,tptp_fun_Z_0(Y,X))
| ~ less(tptp_fun_Z_0(Y,X),Y) ) )
| ~ less(n0,nsup)
| ~ ( ~ less(n0,tptp_fun_Z_0(nsup,n0))
| ~ less(tptp_fun_Z_0(nsup,n0),nsup) ) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
~ ( ~ less(n0,tptp_fun_Z_0(nsup,n0))
| ~ less(tptp_fun_Z_0(nsup,n0),nsup) ),
inference(unit_resolution,[status(thm)],[59,56,3]) ).
tff(61,plain,
( ~ less(n0,tptp_fun_Z_0(nsup,n0))
| ~ less(tptp_fun_Z_0(nsup,n0),nsup)
| less(tptp_fun_Z_0(nsup,n0),nsup) ),
inference(tautology,[status(thm)],[]) ).
tff(62,plain,
less(tptp_fun_Z_0(nsup,n0),nsup),
inference(unit_resolution,[status(thm)],[61,60]) ).
tff(63,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(tptp_fun_Z_0(nsup,n0),nsup)
| leq(tptp_fun_Z_0(nsup,n0),nsup) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(tptp_fun_Z_0(nsup,n0),nsup)
| leq(tptp_fun_Z_0(nsup,n0),nsup) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(tptp_fun_Z_0(nsup,n0),nsup)
| leq(tptp_fun_Z_0(nsup,n0),nsup) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(tptp_fun_Z_0(nsup,n0),nsup)
| leq(tptp_fun_Z_0(nsup,n0),nsup) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
leq(tptp_fun_Z_0(nsup,n0),nsup),
inference(unit_resolution,[status(thm)],[65,13,62]) ).
tff(67,plain,
( ~ less(n0,tptp_fun_Z_0(nsup,n0))
| ~ less(tptp_fun_Z_0(nsup,n0),nsup)
| less(n0,tptp_fun_Z_0(nsup,n0)) ),
inference(tautology,[status(thm)],[]) ).
tff(68,plain,
less(n0,tptp_fun_Z_0(nsup,n0)),
inference(unit_resolution,[status(thm)],[67,60]) ).
tff(69,plain,
^ [U: $i,V: $i,InfD: $i,SupD: $i] :
refl(( ( completion_compatible(U,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) )
<=> ( completion_compatible(U,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(70,plain,
( ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( completion_compatible(U,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) )
<=> ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( completion_compatible(U,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,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_compatible(U,InfD,SupD) )
<=> ( ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V)
| completion_compatible(U,InfD,SupD) ) )),
rewrite(( ( ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V)
| completion_compatible(U,InfD,SupD) )
<=> ( completion_compatible(U,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_compatible(U,InfD,SupD) )
<=> ( completion_compatible(U,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(72,plain,
( ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( ~ ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
| completion_compatible(U,InfD,SupD) )
<=> ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( completion_compatible(U,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( ~ ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
| completion_compatible(U,InfD,SupD) )
<=> ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( ~ ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
| completion_compatible(U,InfD,SupD) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,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_compatible(U,InfD,SupD) )
<=> ( ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
=> completion_compatible(U,InfD,SupD) ) )),
rewrite(( ( ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
=> completion_compatible(U,InfD,SupD) )
<=> ( ~ ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
| completion_compatible(U,InfD,SupD) ) )),
( ( ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
=> completion_compatible(U,InfD,SupD) )
<=> ( ~ ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
| completion_compatible(U,InfD,SupD) ) )),
inference(bind,[status(th)],[]) ).
tff(75,plain,
( ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
=> completion_compatible(U,InfD,SupD) )
<=> ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( ~ ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
| completion_compatible(U,InfD,SupD) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,axiom,
! [U: $i,V: $i,InfD: $i,SupD: $i] :
( ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
=> completion_compatible(U,InfD,SupD) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MGT002+4.ax',sharpness_compat) ).
tff(77,plain,
! [U: $i,V: $i,InfD: $i,SupD: $i] :
( ~ ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
| completion_compatible(U,InfD,SupD) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [U: $i,V: $i,InfD: $i,SupD: $i] :
( ~ ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
| completion_compatible(U,InfD,SupD) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
! [U: $i,V: $i,InfD: $i,SupD: $i] :
( ~ ( leq(InfD,U)
& leq(U,SupD)
& less(U,V)
& leq(V,SupD) )
| completion_compatible(U,InfD,SupD) ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [U: $i,V: $i,InfD: $i,SupD: $i] :
( completion_compatible(U,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) ),
inference(modus_ponens,[status(thm)],[79,72]) ).
tff(81,plain,
! [U: $i,V: $i,InfD: $i,SupD: $i] :
( completion_compatible(U,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) ),
inference(modus_ponens,[status(thm)],[80,70]) ).
tff(82,plain,
( ( ~ ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( completion_compatible(U,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) )
| ~ less(n0,tptp_fun_Z_0(nsup,n0))
| ~ leq(ninf,n0)
| ~ leq(n0,nsup)
| completion_compatible(n0,ninf,nsup)
| ~ leq(tptp_fun_Z_0(nsup,n0),nsup) )
<=> ( ~ ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( completion_compatible(U,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) )
| ~ less(n0,tptp_fun_Z_0(nsup,n0))
| ~ leq(ninf,n0)
| ~ leq(n0,nsup)
| completion_compatible(n0,ninf,nsup)
| ~ leq(tptp_fun_Z_0(nsup,n0),nsup) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
( ( completion_compatible(n0,ninf,nsup)
| ~ leq(tptp_fun_Z_0(nsup,n0),nsup)
| ~ leq(ninf,n0)
| ~ leq(n0,nsup)
| ~ less(n0,tptp_fun_Z_0(nsup,n0)) )
<=> ( ~ less(n0,tptp_fun_Z_0(nsup,n0))
| ~ leq(ninf,n0)
| ~ leq(n0,nsup)
| completion_compatible(n0,ninf,nsup)
| ~ leq(tptp_fun_Z_0(nsup,n0),nsup) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
( ( ~ ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( completion_compatible(U,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) )
| completion_compatible(n0,ninf,nsup)
| ~ leq(tptp_fun_Z_0(nsup,n0),nsup)
| ~ leq(ninf,n0)
| ~ leq(n0,nsup)
| ~ less(n0,tptp_fun_Z_0(nsup,n0)) )
<=> ( ~ ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( completion_compatible(U,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) )
| ~ less(n0,tptp_fun_Z_0(nsup,n0))
| ~ leq(ninf,n0)
| ~ leq(n0,nsup)
| completion_compatible(n0,ninf,nsup)
| ~ leq(tptp_fun_Z_0(nsup,n0),nsup) ) ),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
( ( ~ ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( completion_compatible(U,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) )
| completion_compatible(n0,ninf,nsup)
| ~ leq(tptp_fun_Z_0(nsup,n0),nsup)
| ~ leq(ninf,n0)
| ~ leq(n0,nsup)
| ~ less(n0,tptp_fun_Z_0(nsup,n0)) )
<=> ( ~ ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( completion_compatible(U,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) )
| ~ less(n0,tptp_fun_Z_0(nsup,n0))
| ~ leq(ninf,n0)
| ~ leq(n0,nsup)
| completion_compatible(n0,ninf,nsup)
| ~ leq(tptp_fun_Z_0(nsup,n0),nsup) ) ),
inference(transitivity,[status(thm)],[84,82]) ).
tff(86,plain,
( ~ ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( completion_compatible(U,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) )
| completion_compatible(n0,ninf,nsup)
| ~ leq(tptp_fun_Z_0(nsup,n0),nsup)
| ~ leq(ninf,n0)
| ~ leq(n0,nsup)
| ~ less(n0,tptp_fun_Z_0(nsup,n0)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
( ~ ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( completion_compatible(U,InfD,SupD)
| ~ leq(V,SupD)
| ~ leq(InfD,U)
| ~ leq(U,SupD)
| ~ less(U,V) )
| ~ less(n0,tptp_fun_Z_0(nsup,n0))
| ~ leq(ninf,n0)
| ~ leq(n0,nsup)
| completion_compatible(n0,ninf,nsup)
| ~ leq(tptp_fun_Z_0(nsup,n0),nsup) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
$false,
inference(unit_resolution,[status(thm)],[87,81,24,68,17,66,43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT070+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.32 % Computer : n006.cluster.edu
% 0.08/0.32 % Model : x86_64 x86_64
% 0.08/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.32 % Memory : 8046.5625MB
% 0.08/0.32 % OS : Linux 6.8.0-71-generic
% 0.08/0.33 % CPULimit : 300
% 0.08/0.33 % WCLimit : 300
% 0.08/0.33 % DateTime : Mon Sep 7 13:54:18 UTC 2026
% 0.08/0.33 % CPUTime :
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 % SZS output start Proof
% See solution above
% 0.13/0.38 % E exiting
%------------------------------------------------------------------------------