%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT106+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n004.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 0.43s
% Output : Proof 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 36
% Syntax : Number of formulae : 79 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 434 ( 37 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 569 ( 256 ~; 183 |; 44 &)
% ( 77 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 42 ( 42 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; 4 con; 0-0 aty)
% Number of variables : 188 ( 168 !; 0 ?; 188 :)
% Comments :
%------------------------------------------------------------------------------
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(v600_type,type,
v600: $i ).
tff(v800_type,type,
v800: $i ).
tff(w_type,type,
w: $i ).
tff(less_type,type,
less: ( $i * $i ) > $o ).
tff(v0_type,type,
v0: $i ).
tff(in_lopen_type,type,
in_lopen: ( $i * $i * $i ) > $o ).
tff(1,plain,
^ [X: $i,A: $i,B: $i] :
refl(( ~ ( ( ~ leq(X,B)
| ~ less(A,X) )
<=> in_lopen(X,A,B) )
<=> ~ ( ( ~ leq(X,B)
| ~ less(A,X) )
<=> in_lopen(X,A,B) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i,A: $i,B: $i] :
~ ( ( ~ leq(X,B)
| ~ less(A,X) )
<=> in_lopen(X,A,B) )
<=> ! [X: $i,A: $i,B: $i] :
~ ( ( ~ leq(X,B)
| ~ less(A,X) )
<=> in_lopen(X,A,B) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i,A: $i,B: $i] :
trans(trans(monotonicity(rewrite(( ( less(A,X)
& leq(X,B) )
<=> ~ ( ~ leq(X,B)
| ~ less(A,X) ) )),
( ( in_lopen(X,A,B)
<=> ( less(A,X)
& leq(X,B) ) )
<=> ( in_lopen(X,A,B)
<=> ~ ( ~ leq(X,B)
| ~ less(A,X) ) ) )),
rewrite(( ( in_lopen(X,A,B)
<=> ~ ( ~ leq(X,B)
| ~ less(A,X) ) )
<=> ~ ( ( ~ leq(X,B)
| ~ less(A,X) )
<=> in_lopen(X,A,B) ) )),
( ( in_lopen(X,A,B)
<=> ( less(A,X)
& leq(X,B) ) )
<=> ~ ( ( ~ leq(X,B)
| ~ less(A,X) )
<=> in_lopen(X,A,B) ) )),
rewrite(( ~ ( ( ~ leq(X,B)
| ~ less(A,X) )
<=> in_lopen(X,A,B) )
<=> ~ ( ( ~ leq(X,B)
| ~ less(A,X) )
<=> in_lopen(X,A,B) ) )),
( ( in_lopen(X,A,B)
<=> ( less(A,X)
& leq(X,B) ) )
<=> ~ ( ( ~ leq(X,B)
| ~ less(A,X) )
<=> in_lopen(X,A,B) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [X: $i,A: $i,B: $i] :
( in_lopen(X,A,B)
<=> ( less(A,X)
& leq(X,B) ) )
<=> ! [X: $i,A: $i,B: $i] :
~ ( ( ~ leq(X,B)
| ~ less(A,X) )
<=> in_lopen(X,A,B) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i,A: $i,B: $i] :
( in_lopen(X,A,B)
<=> ( less(A,X)
& leq(X,B) ) )
<=> ! [X: $i,A: $i,B: $i] :
( in_lopen(X,A,B)
<=> ( less(A,X)
& leq(X,B) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
! [X: $i,A: $i,B: $i] :
( in_lopen(X,A,B)
<=> ( less(A,X)
& leq(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MGT002+2.ax',in_lopen) ).
tff(7,plain,
! [X: $i,A: $i,B: $i] :
( in_lopen(X,A,B)
<=> ( less(A,X)
& leq(X,B) ) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X: $i,A: $i,B: $i] :
( in_lopen(X,A,B)
<=> ( less(A,X)
& leq(X,B) ) ),
inference(skolemize,[status(sab)],[7]) ).
tff(9,plain,
! [X: $i,A: $i,B: $i] :
~ ( ( ~ leq(X,B)
| ~ less(A,X) )
<=> in_lopen(X,A,B) ),
inference(modus_ponens,[status(thm)],[8,4]) ).
tff(10,plain,
! [X: $i,A: $i,B: $i] :
~ ( ( ~ leq(X,B)
| ~ less(A,X) )
<=> in_lopen(X,A,B) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ ! [X: $i,A: $i,B: $i] :
~ ( ( ~ leq(X,B)
| ~ less(A,X) )
<=> in_lopen(X,A,B) )
| ~ ( ( ~ leq(w,v600)
| ~ less(v0,w) )
<=> in_lopen(w,v0,v600) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
~ ( ( ~ leq(w,v600)
| ~ less(v0,w) )
<=> in_lopen(w,v0,v600) ),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
( in_lopen(w,v0,v600)
<=> in_lopen(w,v0,v600) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
in_lopen(w,v0,v600),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wit_in_lopen) ).
tff(15,plain,
in_lopen(w,v0,v600),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
( ( ( ~ leq(w,v600)
| ~ less(v0,w) )
<=> in_lopen(w,v0,v600) )
| ~ ( ~ leq(w,v600)
| ~ less(v0,w) )
| ~ in_lopen(w,v0,v600) ),
inference(tautology,[status(thm)],[]) ).
tff(17,plain,
( ( ( ~ leq(w,v600)
| ~ less(v0,w) )
<=> in_lopen(w,v0,v600) )
| ~ ( ~ leq(w,v600)
| ~ less(v0,w) ) ),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
~ ( ~ leq(w,v600)
| ~ less(v0,w) ),
inference(unit_resolution,[status(thm)],[17,12]) ).
tff(19,plain,
( ~ leq(w,v600)
| ~ less(v0,w)
| leq(w,v600) ),
inference(tautology,[status(thm)],[]) ).
tff(20,plain,
leq(w,v600),
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
( leq(v800,w)
<=> leq(v800,w) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
leq(v800,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wit_leq) ).
tff(23,plain,
leq(v800,w),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,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(25,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(26,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)],[25]) ).
tff(27,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(28,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(29,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)],[28]) ).
tff(30,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( leq(X,Y)
& leq(Y,Z) )
=> leq(X,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MGT002+0.ax',leq_trans) ).
tff(31,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ),
inference(modus_ponens,[status(thm)],[33,26]) ).
tff(35,plain,
! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ),
inference(modus_ponens,[status(thm)],[34,24]) ).
tff(36,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| ~ leq(w,v600)
| ~ leq(v800,w)
| leq(v800,v600) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| ~ leq(w,v600)
| ~ leq(v800,w)
| leq(v800,v600) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,plain,
( ( leq(v800,v600)
| ~ leq(w,v600)
| ~ leq(v800,w) )
<=> ( ~ leq(w,v600)
| ~ leq(v800,w)
| leq(v800,v600) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| leq(v800,v600)
| ~ leq(w,v600)
| ~ leq(v800,w) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| ~ leq(w,v600)
| ~ leq(v800,w)
| leq(v800,v600) ) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| leq(v800,v600)
| ~ leq(w,v600)
| ~ leq(v800,w) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| ~ leq(w,v600)
| ~ leq(v800,w)
| leq(v800,v600) ) ),
inference(transitivity,[status(thm)],[38,36]) ).
tff(40,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| leq(v800,v600)
| ~ leq(w,v600)
| ~ leq(v800,w) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| ~ leq(w,v600)
| ~ leq(v800,w)
| leq(v800,v600) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
leq(v800,v600),
inference(unit_resolution,[status(thm)],[41,35,23,20]) ).
tff(43,plain,
( less(v600,v800)
<=> less(v600,v800) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
less(v600,v800),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v600_v800) ).
tff(45,plain,
less(v600,v800),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ less(X,Y)
| leq(X,Y) )
<=> ( ~ less(X,Y)
| leq(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(47,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)],[46]) ).
tff(48,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(49,plain,
^ [X: $i,Y: $i] :
rewrite(( ( less(X,Y)
=> leq(X,Y) )
<=> ( ~ less(X,Y)
| leq(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(50,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)],[49]) ).
tff(51,axiom,
! [X: $i,Y: $i] :
( less(X,Y)
=> leq(X,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MGT002+0.ax',less_implies_leq) ).
tff(52,plain,
! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[54,47]) ).
tff(56,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v600,v800)
| leq(v600,v800) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v600,v800)
| leq(v600,v800) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v600,v800)
| leq(v600,v800) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [X: $i,Y: $i] :
( ~ less(X,Y)
| leq(X,Y) )
| ~ less(v600,v800)
| leq(v600,v800) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
leq(v600,v800),
inference(unit_resolution,[status(thm)],[58,55,45]) ).
tff(60,plain,
( ( v600 != v800 )
<=> ( v600 != v800 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,axiom,
( ( v0 != v600 )
& ( v0 != v800 )
& ( v600 != v800 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distinct) ).
tff(62,plain,
v600 != v800,
inference(and_elim,[status(thm)],[61]) ).
tff(63,plain,
v600 != v800,
inference(modus_ponens,[status(thm)],[62,60]) ).
tff(64,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(65,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(66,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)],[65]) ).
tff(67,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(68,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(69,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)],[68]) ).
tff(70,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(71,plain,
! [X: $i,Y: $i] :
( ~ ( leq(X,Y)
& leq(Y,X) )
| ( X = Y ) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
! [X: $i,Y: $i] :
( ~ ( leq(X,Y)
& leq(Y,X) )
| ( X = Y ) ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
! [X: $i,Y: $i] :
( ~ ( leq(X,Y)
& leq(Y,X) )
| ( X = Y ) ),
inference(skolemize,[status(sab)],[72]) ).
tff(74,plain,
! [X: $i,Y: $i] :
( ( X = Y )
| ~ leq(X,Y)
| ~ leq(Y,X) ),
inference(modus_ponens,[status(thm)],[73,66]) ).
tff(75,plain,
! [X: $i,Y: $i] :
( ( X = Y )
| ~ leq(X,Y)
| ~ leq(Y,X) ),
inference(modus_ponens,[status(thm)],[74,64]) ).
tff(76,plain,
( ( ~ ! [X: $i,Y: $i] :
( ( X = Y )
| ~ leq(X,Y)
| ~ leq(Y,X) )
| ( v600 = v800 )
| ~ leq(v600,v800)
| ~ leq(v800,v600) )
<=> ( ~ ! [X: $i,Y: $i] :
( ( X = Y )
| ~ leq(X,Y)
| ~ leq(Y,X) )
| ( v600 = v800 )
| ~ leq(v600,v800)
| ~ leq(v800,v600) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
( ~ ! [X: $i,Y: $i] :
( ( X = Y )
| ~ leq(X,Y)
| ~ leq(Y,X) )
| ( v600 = v800 )
| ~ leq(v600,v800)
| ~ leq(v800,v600) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
( ~ ! [X: $i,Y: $i] :
( ( X = Y )
| ~ leq(X,Y)
| ~ leq(Y,X) )
| ( v600 = v800 )
| ~ leq(v600,v800)
| ~ leq(v800,v600) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
$false,
inference(unit_resolution,[status(thm)],[78,75,63,59,42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT106+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 7 14:42:17 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.43 % SZS status Unsatisfiable
% 0.10/0.43 % SZS output start Proof
% See solution above
% 0.10/0.44 % E exiting
%------------------------------------------------------------------------------