%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT090+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n008.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 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 24
% Syntax : Number of formulae : 55 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 256 ( 53 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 323 ( 137 ~; 94 |; 33 &)
% ( 56 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 15 ( 15 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; 0-4 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 96 ( 83 !; 0 ?; 96 :)
% Comments :
%------------------------------------------------------------------------------
tff(v600_type,type,
v600: $i ).
tff(v0_type,type,
v0: $i ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(v1200_type,type,
v1200: $i ).
tff(wf_type,type,
wf: ( $i * $i * $i * $i ) > $o ).
tff(lt_type,type,
lt: $i ).
tff(less_type,type,
less: ( $i * $i ) > $o ).
tff(1,plain,
^ [V: $i,InfD: $i,SupD: $i] :
refl(( ~ ( ( ~ leq(InfD,V)
| ~ leq(V,SupD)
| ( V = InfD ) )
<=> wf(lt,V,InfD,SupD) )
<=> ~ ( ( ~ leq(InfD,V)
| ~ leq(V,SupD)
| ( V = InfD ) )
<=> wf(lt,V,InfD,SupD) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V: $i,InfD: $i,SupD: $i] :
~ ( ( ~ leq(InfD,V)
| ~ leq(V,SupD)
| ( V = InfD ) )
<=> wf(lt,V,InfD,SupD) )
<=> ! [V: $i,InfD: $i,SupD: $i] :
~ ( ( ~ leq(InfD,V)
| ~ leq(V,SupD)
| ( V = InfD ) )
<=> wf(lt,V,InfD,SupD) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [V: $i,InfD: $i,SupD: $i] :
trans(trans(monotonicity(rewrite(( ( leq(InfD,V)
& leq(V,SupD)
& ( V != InfD ) )
<=> ~ ( ~ leq(InfD,V)
| ~ leq(V,SupD)
| ( V = InfD ) ) )),
( ( wf(lt,V,InfD,SupD)
<=> ( leq(InfD,V)
& leq(V,SupD)
& ( V != InfD ) ) )
<=> ( wf(lt,V,InfD,SupD)
<=> ~ ( ~ leq(InfD,V)
| ~ leq(V,SupD)
| ( V = InfD ) ) ) )),
rewrite(( ( wf(lt,V,InfD,SupD)
<=> ~ ( ~ leq(InfD,V)
| ~ leq(V,SupD)
| ( V = InfD ) ) )
<=> ~ ( ( ~ leq(InfD,V)
| ~ leq(V,SupD)
| ( V = InfD ) )
<=> wf(lt,V,InfD,SupD) ) )),
( ( wf(lt,V,InfD,SupD)
<=> ( leq(InfD,V)
& leq(V,SupD)
& ( V != InfD ) ) )
<=> ~ ( ( ~ leq(InfD,V)
| ~ leq(V,SupD)
| ( V = InfD ) )
<=> wf(lt,V,InfD,SupD) ) )),
rewrite(( ~ ( ( ~ leq(InfD,V)
| ~ leq(V,SupD)
| ( V = InfD ) )
<=> wf(lt,V,InfD,SupD) )
<=> ~ ( ( ~ leq(InfD,V)
| ~ leq(V,SupD)
| ( V = InfD ) )
<=> wf(lt,V,InfD,SupD) ) )),
( ( wf(lt,V,InfD,SupD)
<=> ( leq(InfD,V)
& leq(V,SupD)
& ( V != InfD ) ) )
<=> ~ ( ( ~ leq(InfD,V)
| ~ leq(V,SupD)
| ( V = InfD ) )
<=> wf(lt,V,InfD,SupD) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [V: $i,InfD: $i,SupD: $i] :
( wf(lt,V,InfD,SupD)
<=> ( leq(InfD,V)
& leq(V,SupD)
& ( V != InfD ) ) )
<=> ! [V: $i,InfD: $i,SupD: $i] :
~ ( ( ~ leq(InfD,V)
| ~ leq(V,SupD)
| ( V = InfD ) )
<=> wf(lt,V,InfD,SupD) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [V: $i,InfD: $i,SupD: $i] :
( wf(lt,V,InfD,SupD)
<=> ( leq(InfD,V)
& leq(V,SupD)
& ( V != InfD ) ) )
<=> ! [V: $i,InfD: $i,SupD: $i] :
( wf(lt,V,InfD,SupD)
<=> ( leq(InfD,V)
& leq(V,SupD)
& ( V != InfD ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,plain,
^ [V: $i,InfD: $i,SupD: $i] :
rewrite(( ( wf(lt,V,InfD,SupD)
<=> ( leq(InfD,V)
& leq(V,SupD)
& ( V != InfD ) ) )
<=> ( wf(lt,V,InfD,SupD)
<=> ( leq(InfD,V)
& leq(V,SupD)
& ( V != InfD ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [V: $i,InfD: $i,SupD: $i] :
( wf(lt,V,InfD,SupD)
<=> ( leq(InfD,V)
& leq(V,SupD)
& ( V != InfD ) ) )
<=> ! [V: $i,InfD: $i,SupD: $i] :
( wf(lt,V,InfD,SupD)
<=> ( leq(InfD,V)
& leq(V,SupD)
& ( V != InfD ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,axiom,
! [V: $i,InfD: $i,SupD: $i] :
( wf(lt,V,InfD,SupD)
<=> ( leq(InfD,V)
& leq(V,SupD)
& ( V != InfD ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/MGT002+8.ax',wf_lt) ).
tff(9,plain,
! [V: $i,InfD: $i,SupD: $i] :
( wf(lt,V,InfD,SupD)
<=> ( leq(InfD,V)
& leq(V,SupD)
& ( V != InfD ) ) ),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
! [V: $i,InfD: $i,SupD: $i] :
( wf(lt,V,InfD,SupD)
<=> ( leq(InfD,V)
& leq(V,SupD)
& ( V != InfD ) ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
! [V: $i,InfD: $i,SupD: $i] :
( wf(lt,V,InfD,SupD)
<=> ( leq(InfD,V)
& leq(V,SupD)
& ( V != InfD ) ) ),
inference(skolemize,[status(sab)],[10]) ).
tff(12,plain,
! [V: $i,InfD: $i,SupD: $i] :
~ ( ( ~ leq(InfD,V)
| ~ leq(V,SupD)
| ( V = InfD ) )
<=> wf(lt,V,InfD,SupD) ),
inference(modus_ponens,[status(thm)],[11,4]) ).
tff(13,plain,
! [V: $i,InfD: $i,SupD: $i] :
~ ( ( ~ leq(InfD,V)
| ~ leq(V,SupD)
| ( V = InfD ) )
<=> wf(lt,V,InfD,SupD) ),
inference(modus_ponens,[status(thm)],[12,2]) ).
tff(14,plain,
( ~ ! [V: $i,InfD: $i,SupD: $i] :
~ ( ( ~ leq(InfD,V)
| ~ leq(V,SupD)
| ( V = InfD ) )
<=> wf(lt,V,InfD,SupD) )
| ~ ( ( ~ leq(v0,v600)
| ~ leq(v600,v1200)
| ( v600 = v0 ) )
<=> wf(lt,v600,v0,v1200) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(15,plain,
~ ( ( ~ leq(v0,v600)
| ~ leq(v600,v1200)
| ( v600 = v0 ) )
<=> wf(lt,v600,v0,v1200) ),
inference(unit_resolution,[status(thm)],[14,13]) ).
tff(16,plain,
( ~ wf(lt,v600,v0,v1200)
<=> ~ wf(lt,v600,v0,v1200) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
~ wf(lt,v600,v0,v1200),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',odrl613) ).
tff(18,plain,
~ wf(lt,v600,v0,v1200),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
( ( ( ~ leq(v0,v600)
| ~ leq(v600,v1200)
| ( v600 = v0 ) )
<=> wf(lt,v600,v0,v1200) )
| ~ leq(v0,v600)
| ~ leq(v600,v1200)
| ( v600 = v0 )
| wf(lt,v600,v0,v1200) ),
inference(tautology,[status(thm)],[]) ).
tff(20,plain,
( ( ( ~ leq(v0,v600)
| ~ leq(v600,v1200)
| ( v600 = v0 ) )
<=> wf(lt,v600,v0,v1200) )
| ~ leq(v0,v600)
| ~ leq(v600,v1200)
| ( v600 = v0 ) ),
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
( ~ leq(v0,v600)
| ~ leq(v600,v1200)
| ( v600 = v0 ) ),
inference(unit_resolution,[status(thm)],[20,15]) ).
tff(22,plain,
( less(v600,v1200)
<=> less(v600,v1200) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
less(v600,v1200),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ord_v600_v1200) ).
tff(24,plain,
less(v600,v1200),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ less(X,Y)
| leq(X,Y) )
<=> ( ~ less(X,Y)
| leq(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(26,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)],[25]) ).
tff(27,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(28,plain,
^ [X: $i,Y: $i] :
rewrite(( ( less(X,Y)
=> leq(X,Y) )
<=> ( ~ less(X,Y)
| leq(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(29,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)],[28]) ).
tff(30,axiom,
! [X: $i,Y: $i] :
( less(X,Y)
=> leq(X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/MGT002+0.ax',less_implies_leq) ).
tff(31,plain,
! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[33,26]) ).
tff(35,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v600,v1200)
| leq(v600,v1200) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v600,v1200)
| leq(v600,v1200) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v600,v1200)
| leq(v600,v1200) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v600,v1200)
| leq(v600,v1200) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
leq(v600,v1200),
inference(unit_resolution,[status(thm)],[37,34,24]) ).
tff(39,plain,
( less(v0,v600)
<=> less(v0,v600) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,axiom,
less(v0,v600),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ord_v0_v600) ).
tff(41,plain,
less(v0,v600),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v0,v600)
| leq(v0,v600) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v0,v600)
| leq(v0,v600) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v0,v600)
| leq(v0,v600) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v0,v600)
| leq(v0,v600) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
leq(v0,v600),
inference(unit_resolution,[status(thm)],[44,34,41]) ).
tff(46,plain,
( ~ ( ~ leq(v0,v600)
| ~ leq(v600,v1200)
| ( v600 = v0 ) )
| ~ leq(v0,v600)
| ~ leq(v600,v1200)
| ( v600 = v0 ) ),
inference(tautology,[status(thm)],[]) ).
tff(47,plain,
( ~ ( ~ leq(v0,v600)
| ~ leq(v600,v1200)
| ( v600 = v0 ) )
| ( v600 = v0 ) ),
inference(unit_resolution,[status(thm)],[46,45,38]) ).
tff(48,plain,
v600 = v0,
inference(unit_resolution,[status(thm)],[47,21]) ).
tff(49,plain,
v0 = v600,
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
( ( v0 != v600 )
<=> ( v0 != v600 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,axiom,
( ( v0 != v600 )
& ( v0 != v1200 )
& ( v600 != v1200 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distinct) ).
tff(52,plain,
( ( v0 != v600 )
& ( v0 != v1200 ) ),
inference(and_elim,[status(thm)],[51]) ).
tff(53,plain,
v0 != v600,
inference(and_elim,[status(thm)],[52]) ).
tff(54,plain,
v0 != v600,
inference(modus_ponens,[status(thm)],[53,50]) ).
tff(55,plain,
$false,
inference(unit_resolution,[status(thm)],[54,49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT090+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.07/0.34 % Computer : n008.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
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 7 14:23:57 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% See solution above
% 0.13/0.39 % E exiting
%------------------------------------------------------------------------------