%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ARI764-2 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% 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 : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:16:56 PM UTC 2026
% Result : Unsatisfiable 2.23s 2.46s
% Output : Proof 2.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 166
% Syntax : Number of formulae : 667 ( 513 unt; 0 typ; 0 def)
% Number of atoms : 841 ( 830 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 300 ( 136 ~; 132 |; 0 &)
% ( 32 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 376 ( 361 !; 0 ?; 376 :)
% Comments :
%------------------------------------------------------------------------------
tff(s_type,type,
s: $i > $i ).
tff(zero_type,type,
zero: $i ).
tff(quot_type,type,
quot: ( $i * $i ) > $i ).
tff(d_type,type,
d: $i > $i ).
tff(minus_type,type,
minus: ( $i * $i ) > $i ).
tff(ifMinus_type,type,
ifMinus: ( $i * $i * $i ) > $i ).
tff(le_type,type,
le: ( $i * $i ) > $i ).
tff(false_type,type,
false: $i ).
tff(true_type,type,
true: $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( d(s(X)) = s(s(d(X))) )
<=> ( d(s(X)) = s(s(d(X))) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( d(s(X)) = s(s(d(X))) )
<=> ! [X: $i] : ( d(s(X)) = s(s(d(X))) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( d(s(X)) = s(s(d(X))) )
<=> ! [X: $i] : ( d(s(X)) = s(s(d(X))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( d(s(X)) = s(s(d(X))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',double2) ).
tff(5,plain,
! [X: $i] : ( d(s(X)) = s(s(d(X))) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( d(s(X)) = s(s(d(X))) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( d(s(X)) = s(s(d(X))) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( d(s(X)) = s(s(d(X))) )
| ( d(s(zero)) = s(s(d(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
d(s(zero)) = s(s(d(zero))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
s(s(d(zero))) = d(s(zero)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( ( d(zero) = zero )
<=> ( d(zero) = zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
d(zero) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',double1) ).
tff(13,plain,
d(zero) = zero,
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
s(d(zero)) = s(zero),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
s(s(d(zero))) = s(s(zero)),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
s(s(zero)) = s(s(d(zero))),
inference(symmetry,[status(thm)],[15]) ).
tff(17,plain,
s(s(zero)) = d(s(zero)),
inference(transitivity,[status(thm)],[16,10]) ).
tff(18,plain,
s(s(s(zero))) = s(d(s(zero))),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
s(s(s(s(zero)))) = s(s(d(s(zero)))),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
s(s(d(s(zero)))) = s(s(s(s(zero)))),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
^ [Y: $i,X: $i] :
refl(( ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
<=> ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
<=> ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
<=> ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule5) ).
tff(25,plain,
! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(d(s(zero)))),s(zero)) = ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
minus(s(s(d(s(zero)))),s(zero)) = ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)) = minus(s(s(d(s(zero)))),s(zero)),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
le(s(s(d(s(zero)))),s(zero)) = le(s(s(s(s(zero)))),s(zero)),
inference(monotonicity,[status(thm)],[20]) ).
tff(32,plain,
le(s(s(s(s(zero)))),s(zero)) = le(s(s(d(s(zero)))),s(zero)),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
^ [Y: $i,X: $i] :
refl(( ( le(s(X),s(Y)) = le(X,Y) )
<=> ( le(s(X),s(Y)) = le(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
<=> ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
<=> ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule3) ).
tff(37,plain,
! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(s(zero)))),s(zero)) = le(s(s(s(zero))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
le(s(s(s(s(zero)))),s(zero)) = le(s(s(s(zero))),zero),
inference(unit_resolution,[status(thm)],[40,39]) ).
tff(42,plain,
le(s(s(s(zero))),zero) = le(s(s(s(s(zero)))),s(zero)),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
^ [X: $i] :
refl(( ( le(s(X),zero) = false )
<=> ( le(s(X),zero) = false ) )),
inference(bind,[status(th)],[]) ).
tff(44,plain,
( ! [X: $i] : ( le(s(X),zero) = false )
<=> ! [X: $i] : ( le(s(X),zero) = false ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [X: $i] : ( le(s(X),zero) = false )
<=> ! [X: $i] : ( le(s(X),zero) = false ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,axiom,
! [X: $i] : ( le(s(X),zero) = false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule2) ).
tff(47,plain,
! [X: $i] : ( le(s(X),zero) = false ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [X: $i] : ( le(s(X),zero) = false ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [X: $i] : ( le(s(X),zero) = false ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(s(zero))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
le(s(s(s(zero))),zero) = false,
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
false = le(s(s(s(zero))),zero),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
false = le(s(s(d(s(zero)))),s(zero)),
inference(transitivity,[status(thm)],[52,42,32]) ).
tff(54,plain,
ifMinus(false,s(s(d(s(zero)))),s(zero)) = ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
^ [Y: $i,X: $i] :
refl(( ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
<=> ( ifMinus(false,s(X),Y) = s(minus(X,Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
<=> ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
<=> ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,axiom,
! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule7) ).
tff(59,plain,
! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(d(s(zero)))),s(zero)) = s(minus(s(d(s(zero))),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
ifMinus(false,s(s(d(s(zero)))),s(zero)) = s(minus(s(d(s(zero))),s(zero))),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
s(minus(s(d(s(zero))),s(zero))) = ifMinus(false,s(s(d(s(zero)))),s(zero)),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
s(s(s(d(zero)))) = s(d(s(zero))),
inference(monotonicity,[status(thm)],[10]) ).
tff(66,plain,
s(d(s(zero))) = s(s(s(d(zero)))),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
minus(s(d(s(zero))),s(zero)) = minus(s(s(s(d(zero)))),s(zero)),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
minus(s(s(s(d(zero)))),s(zero)) = minus(s(d(s(zero))),s(zero)),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(s(d(zero)))),s(zero)) = ifMinus(le(s(s(s(d(zero)))),s(zero)),s(s(s(d(zero)))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
minus(s(s(s(d(zero)))),s(zero)) = ifMinus(le(s(s(s(d(zero)))),s(zero)),s(s(s(d(zero)))),s(zero)),
inference(unit_resolution,[status(thm)],[69,27]) ).
tff(71,plain,
ifMinus(le(s(s(s(d(zero)))),s(zero)),s(s(s(d(zero)))),s(zero)) = minus(s(s(s(d(zero)))),s(zero)),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
s(d(s(zero))) = s(s(s(zero))),
inference(symmetry,[status(thm)],[18]) ).
tff(73,plain,
s(s(s(d(zero)))) = s(s(s(zero))),
inference(transitivity,[status(thm)],[65,72]) ).
tff(74,plain,
le(s(s(s(d(zero)))),s(zero)) = le(s(s(s(zero))),s(zero)),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
le(s(s(s(zero))),s(zero)) = le(s(s(s(d(zero)))),s(zero)),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(zero))),s(zero)) = le(s(s(zero)),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
le(s(s(s(zero))),s(zero)) = le(s(s(zero)),zero),
inference(unit_resolution,[status(thm)],[76,39]) ).
tff(78,plain,
le(s(s(zero)),zero) = le(s(s(s(zero))),s(zero)),
inference(symmetry,[status(thm)],[77]) ).
tff(79,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(zero)),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
le(s(s(zero)),zero) = false,
inference(unit_resolution,[status(thm)],[79,49]) ).
tff(81,plain,
false = le(s(s(zero)),zero),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
false = le(s(s(s(d(zero)))),s(zero)),
inference(transitivity,[status(thm)],[81,78,75]) ).
tff(83,plain,
ifMinus(false,s(s(s(d(zero)))),s(zero)) = ifMinus(le(s(s(s(d(zero)))),s(zero)),s(s(s(d(zero)))),s(zero)),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(s(d(zero)))),s(zero)) = s(minus(s(s(d(zero))),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(85,plain,
ifMinus(false,s(s(s(d(zero)))),s(zero)) = s(minus(s(s(d(zero))),s(zero))),
inference(unit_resolution,[status(thm)],[84,61]) ).
tff(86,plain,
s(minus(s(s(d(zero))),s(zero))) = ifMinus(false,s(s(s(d(zero)))),s(zero)),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
minus(s(s(d(zero))),s(zero)) = minus(s(s(zero)),s(zero)),
inference(monotonicity,[status(thm)],[15]) ).
tff(88,plain,
minus(s(s(zero)),s(zero)) = minus(s(s(d(zero))),s(zero)),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(zero)),s(zero)) = ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(90,plain,
minus(s(s(zero)),s(zero)) = ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)),
inference(unit_resolution,[status(thm)],[89,27]) ).
tff(91,plain,
ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)) = minus(s(s(zero)),s(zero)),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(zero)),s(zero)) = le(s(zero),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(93,plain,
le(s(s(zero)),s(zero)) = le(s(zero),zero),
inference(unit_resolution,[status(thm)],[92,39]) ).
tff(94,plain,
le(s(zero),zero) = le(s(s(zero)),s(zero)),
inference(symmetry,[status(thm)],[93]) ).
tff(95,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(zero),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
le(s(zero),zero) = false,
inference(unit_resolution,[status(thm)],[95,49]) ).
tff(97,plain,
false = le(s(zero),zero),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
false = le(s(s(zero)),s(zero)),
inference(transitivity,[status(thm)],[97,94]) ).
tff(99,plain,
ifMinus(false,s(s(zero)),s(zero)) = ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(zero)),s(zero)) = s(minus(s(zero),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
ifMinus(false,s(s(zero)),s(zero)) = s(minus(s(zero),s(zero))),
inference(unit_resolution,[status(thm)],[100,61]) ).
tff(102,plain,
s(minus(s(zero),s(zero))) = ifMinus(false,s(s(zero)),s(zero)),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(zero),s(zero)) = ifMinus(le(s(zero),s(zero)),s(zero),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(104,plain,
minus(s(zero),s(zero)) = ifMinus(le(s(zero),s(zero)),s(zero),s(zero)),
inference(unit_resolution,[status(thm)],[103,27]) ).
tff(105,plain,
ifMinus(le(s(zero),s(zero)),s(zero),s(zero)) = minus(s(zero),s(zero)),
inference(symmetry,[status(thm)],[104]) ).
tff(106,plain,
^ [Y: $i] :
refl(( ( le(zero,Y) = true )
<=> ( le(zero,Y) = true ) )),
inference(bind,[status(th)],[]) ).
tff(107,plain,
( ! [Y: $i] : ( le(zero,Y) = true )
<=> ! [Y: $i] : ( le(zero,Y) = true ) ),
inference(quant_intro,[status(thm)],[106]) ).
tff(108,plain,
( ! [Y: $i] : ( le(zero,Y) = true )
<=> ! [Y: $i] : ( le(zero,Y) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,axiom,
! [Y: $i] : ( le(zero,Y) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule1) ).
tff(110,plain,
! [Y: $i] : ( le(zero,Y) = true ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
! [Y: $i] : ( le(zero,Y) = true ),
inference(skolemize,[status(sab)],[110]) ).
tff(112,plain,
! [Y: $i] : ( le(zero,Y) = true ),
inference(modus_ponens,[status(thm)],[111,107]) ).
tff(113,plain,
( ~ ! [Y: $i] : ( le(zero,Y) = true )
| ( le(zero,zero) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(114,plain,
le(zero,zero) = true,
inference(unit_resolution,[status(thm)],[113,112]) ).
tff(115,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(zero),s(zero)) = le(zero,zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(116,plain,
le(s(zero),s(zero)) = le(zero,zero),
inference(unit_resolution,[status(thm)],[115,39]) ).
tff(117,plain,
le(s(zero),s(zero)) = true,
inference(transitivity,[status(thm)],[116,114]) ).
tff(118,plain,
ifMinus(le(s(zero),s(zero)),s(zero),s(zero)) = ifMinus(true,s(zero),s(zero)),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
ifMinus(true,s(zero),s(zero)) = ifMinus(le(s(zero),s(zero)),s(zero),s(zero)),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
^ [Y: $i,X: $i] :
refl(( ( ifMinus(true,s(X),Y) = zero )
<=> ( ifMinus(true,s(X),Y) = zero ) )),
inference(bind,[status(th)],[]) ).
tff(121,plain,
( ! [Y: $i,X: $i] : ( ifMinus(true,s(X),Y) = zero )
<=> ! [Y: $i,X: $i] : ( ifMinus(true,s(X),Y) = zero ) ),
inference(quant_intro,[status(thm)],[120]) ).
tff(122,plain,
( ! [Y: $i,X: $i] : ( ifMinus(true,s(X),Y) = zero )
<=> ! [Y: $i,X: $i] : ( ifMinus(true,s(X),Y) = zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(123,axiom,
! [Y: $i,X: $i] : ( ifMinus(true,s(X),Y) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule6) ).
tff(124,plain,
! [Y: $i,X: $i] : ( ifMinus(true,s(X),Y) = zero ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
! [Y: $i,X: $i] : ( ifMinus(true,s(X),Y) = zero ),
inference(skolemize,[status(sab)],[124]) ).
tff(126,plain,
! [Y: $i,X: $i] : ( ifMinus(true,s(X),Y) = zero ),
inference(modus_ponens,[status(thm)],[125,121]) ).
tff(127,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(true,s(X),Y) = zero )
| ( ifMinus(true,s(zero),s(zero)) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(128,plain,
ifMinus(true,s(zero),s(zero)) = zero,
inference(unit_resolution,[status(thm)],[127,126]) ).
tff(129,plain,
zero = ifMinus(true,s(zero),s(zero)),
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
zero = minus(s(zero),s(zero)),
inference(transitivity,[status(thm)],[129,119,105]) ).
tff(131,plain,
s(zero) = s(minus(s(zero),s(zero))),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
s(zero) = minus(s(s(d(zero))),s(zero)),
inference(transitivity,[status(thm)],[131,102,99,91,88]) ).
tff(133,plain,
s(s(zero)) = s(minus(s(s(d(zero))),s(zero))),
inference(monotonicity,[status(thm)],[132]) ).
tff(134,plain,
d(s(zero)) = minus(s(d(s(zero))),s(zero)),
inference(transitivity,[status(thm)],[9,15,133,86,83,71,68]) ).
tff(135,plain,
s(d(s(zero))) = s(minus(s(d(s(zero))),s(zero))),
inference(monotonicity,[status(thm)],[134]) ).
tff(136,plain,
s(d(s(zero))) = minus(s(s(d(s(zero)))),s(zero)),
inference(transitivity,[status(thm)],[135,64,54,30]) ).
tff(137,plain,
s(s(d(s(zero)))) = s(minus(s(s(d(s(zero)))),s(zero))),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
s(minus(s(s(d(s(zero)))),s(zero))) = s(s(d(s(zero)))),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
^ [Y: $i] :
refl(( ( quot(zero,s(Y)) = zero )
<=> ( quot(zero,s(Y)) = zero ) )),
inference(bind,[status(th)],[]) ).
tff(140,plain,
( ! [Y: $i] : ( quot(zero,s(Y)) = zero )
<=> ! [Y: $i] : ( quot(zero,s(Y)) = zero ) ),
inference(quant_intro,[status(thm)],[139]) ).
tff(141,plain,
( ! [Y: $i] : ( quot(zero,s(Y)) = zero )
<=> ! [Y: $i] : ( quot(zero,s(Y)) = zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(142,axiom,
! [Y: $i] : ( quot(zero,s(Y)) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule8) ).
tff(143,plain,
! [Y: $i] : ( quot(zero,s(Y)) = zero ),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
! [Y: $i] : ( quot(zero,s(Y)) = zero ),
inference(skolemize,[status(sab)],[143]) ).
tff(145,plain,
! [Y: $i] : ( quot(zero,s(Y)) = zero ),
inference(modus_ponens,[status(thm)],[144,140]) ).
tff(146,plain,
( ~ ! [Y: $i] : ( quot(zero,s(Y)) = zero )
| ( quot(zero,s(s(s(s(zero))))) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(147,plain,
quot(zero,s(s(s(s(zero))))) = zero,
inference(unit_resolution,[status(thm)],[146,145]) ).
tff(148,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(true,s(X),Y) = zero )
| ( ifMinus(true,s(s(s(d(zero)))),s(d(s(zero)))) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(149,plain,
ifMinus(true,s(s(s(d(zero)))),s(d(s(zero)))) = zero,
inference(unit_resolution,[status(thm)],[148,126]) ).
tff(150,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(zero)),s(s(zero))) = le(s(zero),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(151,plain,
le(s(s(zero)),s(s(zero))) = le(s(zero),s(zero)),
inference(unit_resolution,[status(thm)],[150,39]) ).
tff(152,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(zero))),s(s(s(zero)))) = le(s(s(zero)),s(s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(153,plain,
le(s(s(s(zero))),s(s(s(zero)))) = le(s(s(zero)),s(s(zero))),
inference(unit_resolution,[status(thm)],[152,39]) ).
tff(154,plain,
le(s(s(s(d(zero)))),s(d(s(zero)))) = le(s(s(s(zero))),s(s(s(zero)))),
inference(monotonicity,[status(thm)],[73,72]) ).
tff(155,plain,
le(s(s(s(d(zero)))),s(d(s(zero)))) = true,
inference(transitivity,[status(thm)],[154,153,151,116,114]) ).
tff(156,plain,
ifMinus(le(s(s(s(d(zero)))),s(d(s(zero)))),s(s(s(d(zero)))),s(d(s(zero)))) = ifMinus(true,s(s(s(d(zero)))),s(d(s(zero)))),
inference(monotonicity,[status(thm)],[155]) ).
tff(157,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(s(d(zero)))),s(d(s(zero)))) = ifMinus(le(s(s(s(d(zero)))),s(d(s(zero)))),s(s(s(d(zero)))),s(d(s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(158,plain,
minus(s(s(s(d(zero)))),s(d(s(zero)))) = ifMinus(le(s(s(s(d(zero)))),s(d(s(zero)))),s(s(s(d(zero)))),s(d(s(zero)))),
inference(unit_resolution,[status(thm)],[157,27]) ).
tff(159,plain,
minus(s(d(s(zero))),s(d(s(zero)))) = minus(s(s(s(d(zero)))),s(d(s(zero)))),
inference(monotonicity,[status(thm)],[66]) ).
tff(160,plain,
minus(s(d(s(zero))),s(d(s(zero)))) = zero,
inference(transitivity,[status(thm)],[159,158,156,149]) ).
tff(161,plain,
quot(minus(s(d(s(zero))),s(d(s(zero)))),s(s(d(s(zero))))) = quot(zero,s(s(s(s(zero))))),
inference(monotonicity,[status(thm)],[160,20]) ).
tff(162,plain,
quot(minus(s(d(s(zero))),s(d(s(zero)))),s(s(d(s(zero))))) = zero,
inference(transitivity,[status(thm)],[161,147]) ).
tff(163,plain,
s(quot(minus(s(d(s(zero))),s(d(s(zero)))),s(s(d(s(zero)))))) = s(zero),
inference(monotonicity,[status(thm)],[162]) ).
tff(164,plain,
^ [Y: $i,X: $i] :
refl(( ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) )
<=> ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) ) )),
inference(bind,[status(th)],[]) ).
tff(165,plain,
( ! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) )
<=> ! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) ) ),
inference(quant_intro,[status(thm)],[164]) ).
tff(166,plain,
( ! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) )
<=> ! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(167,axiom,
! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule9) ).
tff(168,plain,
! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) ),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) ),
inference(skolemize,[status(sab)],[168]) ).
tff(170,plain,
! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) ),
inference(modus_ponens,[status(thm)],[169,165]) ).
tff(171,plain,
( ~ ! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) )
| ( quot(s(s(d(s(zero)))),s(s(d(s(zero))))) = s(quot(minus(s(d(s(zero))),s(d(s(zero)))),s(s(d(s(zero)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(172,plain,
quot(s(s(d(s(zero)))),s(s(d(s(zero))))) = s(quot(minus(s(d(s(zero))),s(d(s(zero)))),s(s(d(s(zero)))))),
inference(unit_resolution,[status(thm)],[171,170]) ).
tff(173,plain,
s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = s(minus(s(s(d(s(zero)))),s(zero))),
inference(monotonicity,[status(thm)],[30]) ).
tff(174,plain,
s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = s(s(d(s(zero)))),
inference(transitivity,[status(thm)],[173,138]) ).
tff(175,plain,
s(minus(s(d(s(zero))),s(d(s(zero))))) = s(zero),
inference(monotonicity,[status(thm)],[160]) ).
tff(176,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(d(s(zero)))),s(d(s(zero)))) = s(minus(s(d(s(zero))),s(d(s(zero))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(177,plain,
ifMinus(false,s(s(d(s(zero)))),s(d(s(zero)))) = s(minus(s(d(s(zero))),s(d(s(zero))))),
inference(unit_resolution,[status(thm)],[176,61]) ).
tff(178,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(zero))),s(s(zero))) = le(s(s(zero)),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(179,plain,
le(s(s(s(zero))),s(s(zero))) = le(s(s(zero)),s(zero)),
inference(unit_resolution,[status(thm)],[178,39]) ).
tff(180,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(s(zero)))),s(s(s(zero)))) = le(s(s(s(zero))),s(s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(181,plain,
le(s(s(s(s(zero)))),s(s(s(zero)))) = le(s(s(s(zero))),s(s(zero))),
inference(unit_resolution,[status(thm)],[180,39]) ).
tff(182,plain,
le(s(s(d(s(zero)))),s(d(s(zero)))) = le(s(s(s(s(zero)))),s(s(s(zero)))),
inference(monotonicity,[status(thm)],[20,72]) ).
tff(183,plain,
le(s(s(d(s(zero)))),s(d(s(zero)))) = false,
inference(transitivity,[status(thm)],[182,181,179,93,96]) ).
tff(184,plain,
ifMinus(le(s(s(d(s(zero)))),s(d(s(zero)))),s(s(d(s(zero)))),s(d(s(zero)))) = ifMinus(false,s(s(d(s(zero)))),s(d(s(zero)))),
inference(monotonicity,[status(thm)],[183]) ).
tff(185,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(d(s(zero)))),s(d(s(zero)))) = ifMinus(le(s(s(d(s(zero)))),s(d(s(zero)))),s(s(d(s(zero)))),s(d(s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(186,plain,
minus(s(s(d(s(zero)))),s(d(s(zero)))) = ifMinus(le(s(s(d(s(zero)))),s(d(s(zero)))),s(s(d(s(zero)))),s(d(s(zero)))),
inference(unit_resolution,[status(thm)],[185,27]) ).
tff(187,plain,
minus(s(s(d(s(zero)))),s(d(s(zero)))) = minus(s(s(d(zero))),s(zero)),
inference(transitivity,[status(thm)],[186,184,177,175,131,102,99,91,88]) ).
tff(188,plain,
s(minus(s(s(d(s(zero)))),s(d(s(zero))))) = s(minus(s(s(d(zero))),s(zero))),
inference(monotonicity,[status(thm)],[187]) ).
tff(189,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(s(d(s(zero))))),s(d(s(zero)))) = s(minus(s(s(d(s(zero)))),s(d(s(zero))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(190,plain,
ifMinus(false,s(s(s(d(s(zero))))),s(d(s(zero)))) = s(minus(s(s(d(s(zero)))),s(d(s(zero))))),
inference(unit_resolution,[status(thm)],[189,61]) ).
tff(191,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(s(zero)))),s(s(zero))) = le(s(s(s(zero))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(192,plain,
le(s(s(s(s(zero)))),s(s(zero))) = le(s(s(s(zero))),s(zero)),
inference(unit_resolution,[status(thm)],[191,39]) ).
tff(193,plain,
le(s(s(d(s(zero)))),s(s(d(zero)))) = le(s(s(s(s(zero)))),s(s(zero))),
inference(monotonicity,[status(thm)],[20,15]) ).
tff(194,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(d(s(zero))))),s(s(s(d(zero))))) = le(s(s(d(s(zero)))),s(s(d(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(195,plain,
le(s(s(s(d(s(zero))))),s(s(s(d(zero))))) = le(s(s(d(s(zero)))),s(s(d(zero)))),
inference(unit_resolution,[status(thm)],[194,39]) ).
tff(196,plain,
( ~ ! [X: $i] : ( d(s(X)) = s(s(d(X))) )
| ( d(s(s(zero))) = s(s(d(s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(197,plain,
d(s(s(zero))) = s(s(d(s(zero)))),
inference(unit_resolution,[status(thm)],[196,7]) ).
tff(198,plain,
s(s(d(s(zero)))) = d(s(s(zero))),
inference(symmetry,[status(thm)],[197]) ).
tff(199,plain,
s(s(s(d(s(zero))))) = s(d(s(s(zero)))),
inference(monotonicity,[status(thm)],[198]) ).
tff(200,plain,
s(d(s(s(zero)))) = s(s(s(d(s(zero))))),
inference(symmetry,[status(thm)],[199]) ).
tff(201,plain,
le(s(d(s(s(zero)))),s(d(s(zero)))) = le(s(s(s(d(s(zero))))),s(s(s(d(zero))))),
inference(monotonicity,[status(thm)],[200,66]) ).
tff(202,plain,
le(s(s(s(d(s(zero))))),s(d(s(zero)))) = le(s(d(s(s(zero)))),s(d(s(zero)))),
inference(monotonicity,[status(thm)],[199]) ).
tff(203,plain,
le(s(s(s(d(s(zero))))),s(d(s(zero)))) = false,
inference(transitivity,[status(thm)],[202,201,195,193,192,77,80]) ).
tff(204,plain,
ifMinus(le(s(s(s(d(s(zero))))),s(d(s(zero)))),s(s(s(d(s(zero))))),s(d(s(zero)))) = ifMinus(false,s(s(s(d(s(zero))))),s(d(s(zero)))),
inference(monotonicity,[status(thm)],[203]) ).
tff(205,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(s(d(s(zero))))),s(d(s(zero)))) = ifMinus(le(s(s(s(d(s(zero))))),s(d(s(zero)))),s(s(s(d(s(zero))))),s(d(s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(206,plain,
minus(s(s(s(d(s(zero))))),s(d(s(zero)))) = ifMinus(le(s(s(s(d(s(zero))))),s(d(s(zero)))),s(s(s(d(s(zero))))),s(d(s(zero)))),
inference(unit_resolution,[status(thm)],[205,27]) ).
tff(207,plain,
s(minus(s(d(s(zero))),s(zero))) = s(d(s(zero))),
inference(symmetry,[status(thm)],[135]) ).
tff(208,plain,
ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)) = ifMinus(false,s(s(d(s(zero)))),s(zero)),
inference(symmetry,[status(thm)],[54]) ).
tff(209,plain,
ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)) = s(d(s(zero))),
inference(transitivity,[status(thm)],[208,63,207]) ).
tff(210,plain,
minus(s(d(s(s(zero)))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = minus(s(s(s(d(s(zero))))),s(d(s(zero)))),
inference(monotonicity,[status(thm)],[200,209]) ).
tff(211,plain,
minus(s(d(s(s(zero)))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = minus(s(d(s(zero))),s(zero)),
inference(transitivity,[status(thm)],[210,206,204,190,188,86,83,71,68]) ).
tff(212,plain,
s(minus(s(d(s(s(zero)))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) = s(minus(s(d(s(zero))),s(zero))),
inference(monotonicity,[status(thm)],[211]) ).
tff(213,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(d(s(s(zero))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = s(minus(s(d(s(s(zero)))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(214,plain,
ifMinus(false,s(s(d(s(s(zero))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = s(minus(s(d(s(s(zero)))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))),
inference(unit_resolution,[status(thm)],[213,61]) ).
tff(215,plain,
s(d(s(zero))) = ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)),
inference(transitivity,[status(thm)],[135,64,54]) ).
tff(216,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(d(s(zero))))),s(s(zero))) = le(s(s(d(s(zero)))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(217,plain,
le(s(s(s(d(s(zero))))),s(s(zero))) = le(s(s(d(s(zero)))),s(zero)),
inference(unit_resolution,[status(thm)],[216,39]) ).
tff(218,plain,
le(s(d(s(s(zero)))),s(s(d(zero)))) = le(s(s(s(d(s(zero))))),s(s(zero))),
inference(monotonicity,[status(thm)],[200,15]) ).
tff(219,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(d(s(s(zero))))),s(s(s(d(zero))))) = le(s(d(s(s(zero)))),s(s(d(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(220,plain,
le(s(s(d(s(s(zero))))),s(s(s(d(zero))))) = le(s(d(s(s(zero)))),s(s(d(zero)))),
inference(unit_resolution,[status(thm)],[219,39]) ).
tff(221,plain,
le(s(s(d(s(s(zero))))),s(d(s(zero)))) = le(s(s(d(s(s(zero))))),s(s(s(d(zero))))),
inference(monotonicity,[status(thm)],[66]) ).
tff(222,plain,
le(s(s(d(s(s(zero))))),s(d(s(zero)))) = false,
inference(transitivity,[status(thm)],[221,220,218,217,31,41,51]) ).
tff(223,plain,
ifMinus(le(s(s(d(s(s(zero))))),s(d(s(zero)))),s(s(d(s(s(zero))))),s(d(s(zero)))) = ifMinus(false,s(s(d(s(s(zero))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),
inference(monotonicity,[status(thm)],[222,215]) ).
tff(224,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(d(s(s(zero))))),s(d(s(zero)))) = ifMinus(le(s(s(d(s(s(zero))))),s(d(s(zero)))),s(s(d(s(s(zero))))),s(d(s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(225,plain,
minus(s(s(d(s(s(zero))))),s(d(s(zero)))) = ifMinus(le(s(s(d(s(s(zero))))),s(d(s(zero)))),s(s(d(s(s(zero))))),s(d(s(zero)))),
inference(unit_resolution,[status(thm)],[224,27]) ).
tff(226,plain,
minus(s(s(d(s(s(zero))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = minus(s(s(d(s(s(zero))))),s(d(s(zero)))),
inference(monotonicity,[status(thm)],[209]) ).
tff(227,plain,
minus(s(s(d(s(s(zero))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = minus(s(s(d(s(zero)))),s(zero)),
inference(transitivity,[status(thm)],[226,225,223,214,212,64,54,30]) ).
tff(228,plain,
s(minus(s(s(d(s(s(zero))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) = s(minus(s(s(d(s(zero)))),s(zero))),
inference(monotonicity,[status(thm)],[227]) ).
tff(229,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(s(d(s(s(zero)))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = s(minus(s(s(d(s(s(zero))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(230,plain,
ifMinus(false,s(s(s(d(s(s(zero)))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = s(minus(s(s(d(s(s(zero))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))),
inference(unit_resolution,[status(thm)],[229,61]) ).
tff(231,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(s(s(zero)))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(232,plain,
le(s(s(s(s(zero)))),zero) = false,
inference(unit_resolution,[status(thm)],[231,49]) ).
tff(233,plain,
le(s(s(d(s(zero)))),zero) = le(s(s(s(s(zero)))),zero),
inference(monotonicity,[status(thm)],[20]) ).
tff(234,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(d(s(zero))))),s(zero)) = le(s(s(d(s(zero)))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(235,plain,
le(s(s(s(d(s(zero))))),s(zero)) = le(s(s(d(s(zero)))),zero),
inference(unit_resolution,[status(thm)],[234,39]) ).
tff(236,plain,
le(s(d(s(s(zero)))),s(zero)) = le(s(s(s(d(s(zero))))),s(zero)),
inference(monotonicity,[status(thm)],[200]) ).
tff(237,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(d(s(s(zero))))),s(s(zero))) = le(s(d(s(s(zero)))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(238,plain,
le(s(s(d(s(s(zero))))),s(s(zero))) = le(s(d(s(s(zero)))),s(zero)),
inference(unit_resolution,[status(thm)],[237,39]) ).
tff(239,plain,
le(s(s(d(s(s(zero))))),s(s(d(zero)))) = le(s(s(d(s(s(zero))))),s(s(zero))),
inference(monotonicity,[status(thm)],[15]) ).
tff(240,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(d(s(s(zero)))))),s(s(s(d(zero))))) = le(s(s(d(s(s(zero))))),s(s(d(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(241,plain,
le(s(s(s(d(s(s(zero)))))),s(s(s(d(zero))))) = le(s(s(d(s(s(zero))))),s(s(d(zero)))),
inference(unit_resolution,[status(thm)],[240,39]) ).
tff(242,plain,
( ~ ! [X: $i] : ( d(s(X)) = s(s(d(X))) )
| ( d(s(s(s(zero)))) = s(s(d(s(s(zero))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(243,plain,
d(s(s(s(zero)))) = s(s(d(s(s(zero))))),
inference(unit_resolution,[status(thm)],[242,7]) ).
tff(244,plain,
s(s(d(s(s(zero))))) = d(s(s(s(zero)))),
inference(symmetry,[status(thm)],[243]) ).
tff(245,plain,
s(s(s(d(s(s(zero)))))) = s(d(s(s(s(zero))))),
inference(monotonicity,[status(thm)],[244]) ).
tff(246,plain,
s(d(s(s(s(zero))))) = s(s(s(d(s(s(zero)))))),
inference(symmetry,[status(thm)],[245]) ).
tff(247,plain,
le(s(d(s(s(s(zero))))),s(d(s(zero)))) = le(s(s(s(d(s(s(zero)))))),s(s(s(d(zero))))),
inference(monotonicity,[status(thm)],[246,66]) ).
tff(248,plain,
le(s(s(s(d(s(s(zero)))))),s(d(s(zero)))) = le(s(d(s(s(s(zero))))),s(d(s(zero)))),
inference(monotonicity,[status(thm)],[245]) ).
tff(249,plain,
le(s(s(s(d(s(s(zero)))))),s(d(s(zero)))) = false,
inference(transitivity,[status(thm)],[248,247,241,239,238,236,235,233,232]) ).
tff(250,plain,
ifMinus(le(s(s(s(d(s(s(zero)))))),s(d(s(zero)))),s(s(s(d(s(s(zero)))))),s(d(s(zero)))) = ifMinus(false,s(s(s(d(s(s(zero)))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),
inference(monotonicity,[status(thm)],[249,215]) ).
tff(251,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(s(d(s(s(zero)))))),s(d(s(zero)))) = ifMinus(le(s(s(s(d(s(s(zero)))))),s(d(s(zero)))),s(s(s(d(s(s(zero)))))),s(d(s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(252,plain,
minus(s(s(s(d(s(s(zero)))))),s(d(s(zero)))) = ifMinus(le(s(s(s(d(s(s(zero)))))),s(d(s(zero)))),s(s(s(d(s(s(zero)))))),s(d(s(zero)))),
inference(unit_resolution,[status(thm)],[251,27]) ).
tff(253,plain,
minus(s(d(s(s(s(zero))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = minus(s(s(s(d(s(s(zero)))))),s(d(s(zero)))),
inference(monotonicity,[status(thm)],[246,209]) ).
tff(254,plain,
minus(s(d(s(s(s(zero))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = s(s(d(s(zero)))),
inference(transitivity,[status(thm)],[253,252,250,230,228,138]) ).
tff(255,plain,
quot(minus(s(d(s(s(s(zero))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) = quot(s(s(d(s(zero)))),s(s(d(s(zero))))),
inference(monotonicity,[status(thm)],[254,174]) ).
tff(256,plain,
quot(minus(s(d(s(s(s(zero))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) = minus(s(s(d(zero))),s(zero)),
inference(transitivity,[status(thm)],[255,172,163,131,102,99,91,88]) ).
tff(257,plain,
s(quot(minus(s(d(s(s(s(zero))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))))) = s(minus(s(s(d(zero))),s(zero))),
inference(monotonicity,[status(thm)],[256]) ).
tff(258,plain,
( ~ ! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) )
| ( quot(s(s(d(s(s(s(zero)))))),s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) = s(quot(minus(s(d(s(s(s(zero))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(259,plain,
quot(s(s(d(s(s(s(zero)))))),s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) = s(quot(minus(s(d(s(s(s(zero))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))))),
inference(unit_resolution,[status(thm)],[258,170]) ).
tff(260,plain,
s(minus(s(zero),s(zero))) = s(zero),
inference(symmetry,[status(thm)],[131]) ).
tff(261,plain,
ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)) = ifMinus(false,s(s(zero)),s(zero)),
inference(symmetry,[status(thm)],[99]) ).
tff(262,plain,
ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)) = s(zero),
inference(transitivity,[status(thm)],[261,101,260]) ).
tff(263,plain,
minus(s(s(d(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))) = minus(s(s(d(s(s(s(zero)))))),s(zero)),
inference(monotonicity,[status(thm)],[262]) ).
tff(264,plain,
minus(s(s(d(s(s(s(zero)))))),s(zero)) = minus(s(s(d(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(symmetry,[status(thm)],[263]) ).
tff(265,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(d(s(s(s(zero)))))),s(zero)) = ifMinus(le(s(s(d(s(s(s(zero)))))),s(zero)),s(s(d(s(s(s(zero)))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(266,plain,
minus(s(s(d(s(s(s(zero)))))),s(zero)) = ifMinus(le(s(s(d(s(s(s(zero)))))),s(zero)),s(s(d(s(s(s(zero)))))),s(zero)),
inference(unit_resolution,[status(thm)],[265,27]) ).
tff(267,plain,
ifMinus(le(s(s(d(s(s(s(zero)))))),s(zero)),s(s(d(s(s(s(zero)))))),s(zero)) = minus(s(s(d(s(s(s(zero)))))),s(zero)),
inference(symmetry,[status(thm)],[266]) ).
tff(268,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(d(s(s(s(zero)))))),s(zero)) = le(s(d(s(s(s(zero))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(269,plain,
le(s(s(d(s(s(s(zero)))))),s(zero)) = le(s(d(s(s(s(zero))))),zero),
inference(unit_resolution,[status(thm)],[268,39]) ).
tff(270,plain,
le(s(d(s(s(s(zero))))),zero) = le(s(s(d(s(s(s(zero)))))),s(zero)),
inference(symmetry,[status(thm)],[269]) ).
tff(271,plain,
le(s(d(s(s(s(zero))))),zero) = le(s(s(s(d(s(s(zero)))))),zero),
inference(monotonicity,[status(thm)],[246]) ).
tff(272,plain,
le(s(s(s(d(s(s(zero)))))),zero) = le(s(d(s(s(s(zero))))),zero),
inference(symmetry,[status(thm)],[271]) ).
tff(273,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(s(d(s(s(zero)))))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(274,plain,
le(s(s(s(d(s(s(zero)))))),zero) = false,
inference(unit_resolution,[status(thm)],[273,49]) ).
tff(275,plain,
false = le(s(s(s(d(s(s(zero)))))),zero),
inference(symmetry,[status(thm)],[274]) ).
tff(276,plain,
false = le(s(s(d(s(s(s(zero)))))),s(zero)),
inference(transitivity,[status(thm)],[275,272,270]) ).
tff(277,plain,
ifMinus(false,s(s(d(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))) = ifMinus(le(s(s(d(s(s(s(zero)))))),s(zero)),s(s(d(s(s(s(zero)))))),s(zero)),
inference(monotonicity,[status(thm)],[276,262]) ).
tff(278,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(d(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))) = s(minus(s(d(s(s(s(zero))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(279,plain,
ifMinus(false,s(s(d(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))) = s(minus(s(d(s(s(s(zero))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))),
inference(unit_resolution,[status(thm)],[278,61]) ).
tff(280,plain,
s(minus(s(d(s(s(s(zero))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))) = ifMinus(false,s(s(d(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(symmetry,[status(thm)],[279]) ).
tff(281,plain,
minus(s(d(s(s(s(zero))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))) = minus(s(s(s(d(s(s(zero)))))),s(zero)),
inference(monotonicity,[status(thm)],[246,262]) ).
tff(282,plain,
minus(s(s(s(d(s(s(zero)))))),s(zero)) = minus(s(d(s(s(s(zero))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(symmetry,[status(thm)],[281]) ).
tff(283,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(s(d(s(s(zero)))))),s(zero)) = ifMinus(le(s(s(s(d(s(s(zero)))))),s(zero)),s(s(s(d(s(s(zero)))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(284,plain,
minus(s(s(s(d(s(s(zero)))))),s(zero)) = ifMinus(le(s(s(s(d(s(s(zero)))))),s(zero)),s(s(s(d(s(s(zero)))))),s(zero)),
inference(unit_resolution,[status(thm)],[283,27]) ).
tff(285,plain,
ifMinus(le(s(s(s(d(s(s(zero)))))),s(zero)),s(s(s(d(s(s(zero)))))),s(zero)) = minus(s(s(s(d(s(s(zero)))))),s(zero)),
inference(symmetry,[status(thm)],[284]) ).
tff(286,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(d(s(s(zero)))))),s(zero)) = le(s(s(d(s(s(zero))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(287,plain,
le(s(s(s(d(s(s(zero)))))),s(zero)) = le(s(s(d(s(s(zero))))),zero),
inference(unit_resolution,[status(thm)],[286,39]) ).
tff(288,plain,
le(s(s(d(s(s(zero))))),zero) = le(s(s(s(d(s(s(zero)))))),s(zero)),
inference(symmetry,[status(thm)],[287]) ).
tff(289,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(d(s(s(zero))))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(290,plain,
le(s(s(d(s(s(zero))))),zero) = false,
inference(unit_resolution,[status(thm)],[289,49]) ).
tff(291,plain,
false = le(s(s(d(s(s(zero))))),zero),
inference(symmetry,[status(thm)],[290]) ).
tff(292,plain,
false = le(s(s(s(d(s(s(zero)))))),s(zero)),
inference(transitivity,[status(thm)],[291,288]) ).
tff(293,plain,
ifMinus(false,s(s(s(d(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))) = ifMinus(le(s(s(s(d(s(s(zero)))))),s(zero)),s(s(s(d(s(s(zero)))))),s(zero)),
inference(monotonicity,[status(thm)],[292,262]) ).
tff(294,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(s(d(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))) = s(minus(s(s(d(s(s(zero))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(295,plain,
ifMinus(false,s(s(s(d(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))) = s(minus(s(s(d(s(s(zero))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))),
inference(unit_resolution,[status(thm)],[294,61]) ).
tff(296,plain,
s(minus(s(s(d(s(s(zero))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))) = ifMinus(false,s(s(s(d(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(symmetry,[status(thm)],[295]) ).
tff(297,plain,
minus(s(s(d(s(s(zero))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))) = minus(s(s(d(s(s(zero))))),s(zero)),
inference(monotonicity,[status(thm)],[262]) ).
tff(298,plain,
minus(s(s(d(s(s(zero))))),s(zero)) = minus(s(s(d(s(s(zero))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(symmetry,[status(thm)],[297]) ).
tff(299,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(d(s(s(zero))))),s(zero)) = ifMinus(le(s(s(d(s(s(zero))))),s(zero)),s(s(d(s(s(zero))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(300,plain,
minus(s(s(d(s(s(zero))))),s(zero)) = ifMinus(le(s(s(d(s(s(zero))))),s(zero)),s(s(d(s(s(zero))))),s(zero)),
inference(unit_resolution,[status(thm)],[299,27]) ).
tff(301,plain,
ifMinus(le(s(s(d(s(s(zero))))),s(zero)),s(s(d(s(s(zero))))),s(zero)) = minus(s(s(d(s(s(zero))))),s(zero)),
inference(symmetry,[status(thm)],[300]) ).
tff(302,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(d(s(s(zero))))),s(zero)) = le(s(d(s(s(zero)))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(303,plain,
le(s(s(d(s(s(zero))))),s(zero)) = le(s(d(s(s(zero)))),zero),
inference(unit_resolution,[status(thm)],[302,39]) ).
tff(304,plain,
le(s(d(s(s(zero)))),zero) = le(s(s(d(s(s(zero))))),s(zero)),
inference(symmetry,[status(thm)],[303]) ).
tff(305,plain,
le(s(d(s(s(zero)))),zero) = le(s(s(s(d(s(zero))))),zero),
inference(monotonicity,[status(thm)],[200]) ).
tff(306,plain,
le(s(s(s(d(s(zero))))),zero) = le(s(d(s(s(zero)))),zero),
inference(symmetry,[status(thm)],[305]) ).
tff(307,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(s(d(s(zero))))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(308,plain,
le(s(s(s(d(s(zero))))),zero) = false,
inference(unit_resolution,[status(thm)],[307,49]) ).
tff(309,plain,
false = le(s(s(s(d(s(zero))))),zero),
inference(symmetry,[status(thm)],[308]) ).
tff(310,plain,
false = le(s(s(d(s(s(zero))))),s(zero)),
inference(transitivity,[status(thm)],[309,306,304]) ).
tff(311,plain,
ifMinus(false,s(s(d(s(s(zero))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))) = ifMinus(le(s(s(d(s(s(zero))))),s(zero)),s(s(d(s(s(zero))))),s(zero)),
inference(monotonicity,[status(thm)],[310,262]) ).
tff(312,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(d(s(s(zero))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))) = s(minus(s(d(s(s(zero)))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(313,plain,
ifMinus(false,s(s(d(s(s(zero))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))) = s(minus(s(d(s(s(zero)))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))),
inference(unit_resolution,[status(thm)],[312,61]) ).
tff(314,plain,
s(minus(s(d(s(s(zero)))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))) = ifMinus(false,s(s(d(s(s(zero))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(symmetry,[status(thm)],[313]) ).
tff(315,plain,
minus(s(d(s(s(zero)))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))) = minus(s(s(s(d(s(zero))))),s(zero)),
inference(monotonicity,[status(thm)],[200,262]) ).
tff(316,plain,
minus(s(s(s(d(s(zero))))),s(zero)) = minus(s(d(s(s(zero)))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(symmetry,[status(thm)],[315]) ).
tff(317,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(s(d(s(zero))))),s(zero)) = ifMinus(le(s(s(s(d(s(zero))))),s(zero)),s(s(s(d(s(zero))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(318,plain,
minus(s(s(s(d(s(zero))))),s(zero)) = ifMinus(le(s(s(s(d(s(zero))))),s(zero)),s(s(s(d(s(zero))))),s(zero)),
inference(unit_resolution,[status(thm)],[317,27]) ).
tff(319,plain,
ifMinus(le(s(s(s(d(s(zero))))),s(zero)),s(s(s(d(s(zero))))),s(zero)) = minus(s(s(s(d(s(zero))))),s(zero)),
inference(symmetry,[status(thm)],[318]) ).
tff(320,plain,
le(s(s(d(s(zero)))),zero) = le(s(s(s(d(s(zero))))),s(zero)),
inference(symmetry,[status(thm)],[235]) ).
tff(321,plain,
le(s(s(s(s(zero)))),zero) = le(s(s(d(s(zero)))),zero),
inference(symmetry,[status(thm)],[233]) ).
tff(322,plain,
false = le(s(s(s(s(zero)))),zero),
inference(symmetry,[status(thm)],[232]) ).
tff(323,plain,
false = le(s(s(s(d(s(zero))))),s(zero)),
inference(transitivity,[status(thm)],[322,321,320]) ).
tff(324,plain,
ifMinus(false,s(s(s(d(s(zero))))),s(zero)) = ifMinus(le(s(s(s(d(s(zero))))),s(zero)),s(s(s(d(s(zero))))),s(zero)),
inference(monotonicity,[status(thm)],[323]) ).
tff(325,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(s(d(s(zero))))),s(zero)) = s(minus(s(s(d(s(zero)))),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(326,plain,
ifMinus(false,s(s(s(d(s(zero))))),s(zero)) = s(minus(s(s(d(s(zero)))),s(zero))),
inference(unit_resolution,[status(thm)],[325,61]) ).
tff(327,plain,
s(minus(s(s(d(s(zero)))),s(zero))) = ifMinus(false,s(s(s(d(s(zero))))),s(zero)),
inference(symmetry,[status(thm)],[326]) ).
tff(328,plain,
d(s(s(zero))) = minus(s(d(s(s(zero)))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(transitivity,[status(thm)],[197,137,327,324,319,316]) ).
tff(329,plain,
s(d(s(s(zero)))) = s(minus(s(d(s(s(zero)))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))),
inference(monotonicity,[status(thm)],[328]) ).
tff(330,plain,
s(d(s(s(zero)))) = minus(s(s(d(s(s(zero))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(transitivity,[status(thm)],[329,314,311,301,298]) ).
tff(331,plain,
s(s(d(s(s(zero))))) = s(minus(s(s(d(s(s(zero))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))),
inference(monotonicity,[status(thm)],[330]) ).
tff(332,plain,
d(s(s(s(zero)))) = minus(s(d(s(s(s(zero))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(transitivity,[status(thm)],[243,331,296,293,285,282]) ).
tff(333,plain,
s(d(s(s(s(zero))))) = s(minus(s(d(s(s(s(zero))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))),
inference(monotonicity,[status(thm)],[332]) ).
tff(334,plain,
s(d(s(s(s(zero))))) = minus(s(s(d(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(transitivity,[status(thm)],[333,280,277,267,264]) ).
tff(335,plain,
s(s(d(s(s(s(zero)))))) = s(minus(s(s(d(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))),
inference(monotonicity,[status(thm)],[334]) ).
tff(336,plain,
s(minus(s(s(d(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))) = s(s(d(s(s(s(zero)))))),
inference(symmetry,[status(thm)],[335]) ).
tff(337,plain,
minus(s(d(s(s(s(zero))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = d(s(s(zero))),
inference(transitivity,[status(thm)],[253,252,250,230,228,138,198]) ).
tff(338,plain,
s(minus(s(d(s(s(s(zero))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) = s(d(s(s(zero)))),
inference(monotonicity,[status(thm)],[337]) ).
tff(339,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(d(s(s(s(zero)))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = s(minus(s(d(s(s(s(zero))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(340,plain,
ifMinus(false,s(s(d(s(s(s(zero)))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = s(minus(s(d(s(s(s(zero))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))),
inference(unit_resolution,[status(thm)],[339,61]) ).
tff(341,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(d(s(s(zero)))))),s(s(zero))) = le(s(s(d(s(s(zero))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(342,plain,
le(s(s(s(d(s(s(zero)))))),s(s(zero))) = le(s(s(d(s(s(zero))))),s(zero)),
inference(unit_resolution,[status(thm)],[341,39]) ).
tff(343,plain,
le(s(d(s(s(s(zero))))),s(s(d(zero)))) = le(s(s(s(d(s(s(zero)))))),s(s(zero))),
inference(monotonicity,[status(thm)],[246,15]) ).
tff(344,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(d(s(s(s(zero)))))),s(s(s(d(zero))))) = le(s(d(s(s(s(zero))))),s(s(d(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(345,plain,
le(s(s(d(s(s(s(zero)))))),s(s(s(d(zero))))) = le(s(d(s(s(s(zero))))),s(s(d(zero)))),
inference(unit_resolution,[status(thm)],[344,39]) ).
tff(346,plain,
le(s(s(d(s(s(s(zero)))))),s(d(s(zero)))) = le(s(s(d(s(s(s(zero)))))),s(s(s(d(zero))))),
inference(monotonicity,[status(thm)],[66]) ).
tff(347,plain,
le(s(s(d(s(s(s(zero)))))),s(d(s(zero)))) = false,
inference(transitivity,[status(thm)],[346,345,343,342,303,305,308]) ).
tff(348,plain,
ifMinus(le(s(s(d(s(s(s(zero)))))),s(d(s(zero)))),s(s(d(s(s(s(zero)))))),s(d(s(zero)))) = ifMinus(false,s(s(d(s(s(s(zero)))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),
inference(monotonicity,[status(thm)],[347,215]) ).
tff(349,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(d(s(s(s(zero)))))),s(d(s(zero)))) = ifMinus(le(s(s(d(s(s(s(zero)))))),s(d(s(zero)))),s(s(d(s(s(s(zero)))))),s(d(s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(350,plain,
minus(s(s(d(s(s(s(zero)))))),s(d(s(zero)))) = ifMinus(le(s(s(d(s(s(s(zero)))))),s(d(s(zero)))),s(s(d(s(s(s(zero)))))),s(d(s(zero)))),
inference(unit_resolution,[status(thm)],[349,27]) ).
tff(351,plain,
minus(s(s(d(s(s(s(zero)))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = minus(s(s(d(s(s(s(zero)))))),s(d(s(zero)))),
inference(monotonicity,[status(thm)],[209]) ).
tff(352,plain,
minus(s(s(d(s(s(s(zero)))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = minus(s(s(d(s(s(zero))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(transitivity,[status(thm)],[351,350,348,340,338,329,314,311,301,298]) ).
tff(353,plain,
s(minus(s(s(d(s(s(s(zero)))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) = s(minus(s(s(d(s(s(zero))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))),
inference(monotonicity,[status(thm)],[352]) ).
tff(354,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(s(d(s(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = s(minus(s(s(d(s(s(s(zero)))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(355,plain,
ifMinus(false,s(s(s(d(s(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = s(minus(s(s(d(s(s(s(zero)))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))),
inference(unit_resolution,[status(thm)],[354,61]) ).
tff(356,plain,
le(s(d(s(s(s(zero))))),s(zero)) = le(s(s(s(d(s(s(zero)))))),s(zero)),
inference(monotonicity,[status(thm)],[246]) ).
tff(357,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(d(s(s(s(zero)))))),s(s(zero))) = le(s(d(s(s(s(zero))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(358,plain,
le(s(s(d(s(s(s(zero)))))),s(s(zero))) = le(s(d(s(s(s(zero))))),s(zero)),
inference(unit_resolution,[status(thm)],[357,39]) ).
tff(359,plain,
le(s(s(d(s(s(s(zero)))))),s(s(d(zero)))) = le(s(s(d(s(s(s(zero)))))),s(s(zero))),
inference(monotonicity,[status(thm)],[15]) ).
tff(360,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(d(s(s(s(zero))))))),s(s(s(d(zero))))) = le(s(s(d(s(s(s(zero)))))),s(s(d(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(361,plain,
le(s(s(s(d(s(s(s(zero))))))),s(s(s(d(zero))))) = le(s(s(d(s(s(s(zero)))))),s(s(d(zero)))),
inference(unit_resolution,[status(thm)],[360,39]) ).
tff(362,plain,
( ~ ! [X: $i] : ( d(s(X)) = s(s(d(X))) )
| ( d(s(s(s(s(zero))))) = s(s(d(s(s(s(zero)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(363,plain,
d(s(s(s(s(zero))))) = s(s(d(s(s(s(zero)))))),
inference(unit_resolution,[status(thm)],[362,7]) ).
tff(364,plain,
s(s(d(s(s(s(zero)))))) = d(s(s(s(s(zero))))),
inference(symmetry,[status(thm)],[363]) ).
tff(365,plain,
s(s(s(d(s(s(s(zero))))))) = s(d(s(s(s(s(zero)))))),
inference(monotonicity,[status(thm)],[364]) ).
tff(366,plain,
s(d(s(s(s(s(zero)))))) = s(s(s(d(s(s(s(zero))))))),
inference(symmetry,[status(thm)],[365]) ).
tff(367,plain,
le(s(d(s(s(s(s(zero)))))),s(d(s(zero)))) = le(s(s(s(d(s(s(s(zero))))))),s(s(s(d(zero))))),
inference(monotonicity,[status(thm)],[366,66]) ).
tff(368,plain,
le(s(s(s(d(s(s(s(zero))))))),s(d(s(zero)))) = le(s(d(s(s(s(s(zero)))))),s(d(s(zero)))),
inference(monotonicity,[status(thm)],[365]) ).
tff(369,plain,
le(s(s(s(d(s(s(s(zero))))))),s(d(s(zero)))) = false,
inference(transitivity,[status(thm)],[368,367,361,359,358,356,287,290]) ).
tff(370,plain,
ifMinus(le(s(s(s(d(s(s(s(zero))))))),s(d(s(zero)))),s(s(s(d(s(s(s(zero))))))),s(d(s(zero)))) = ifMinus(false,s(s(s(d(s(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),
inference(monotonicity,[status(thm)],[369,215]) ).
tff(371,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(s(d(s(s(s(zero))))))),s(d(s(zero)))) = ifMinus(le(s(s(s(d(s(s(s(zero))))))),s(d(s(zero)))),s(s(s(d(s(s(s(zero))))))),s(d(s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(372,plain,
minus(s(s(s(d(s(s(s(zero))))))),s(d(s(zero)))) = ifMinus(le(s(s(s(d(s(s(s(zero))))))),s(d(s(zero)))),s(s(s(d(s(s(s(zero))))))),s(d(s(zero)))),
inference(unit_resolution,[status(thm)],[371,27]) ).
tff(373,plain,
minus(s(d(s(s(s(s(zero)))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = minus(s(s(s(d(s(s(s(zero))))))),s(d(s(zero)))),
inference(monotonicity,[status(thm)],[366,209]) ).
tff(374,plain,
minus(s(d(s(s(s(s(zero)))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = minus(s(d(s(s(s(zero))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(transitivity,[status(thm)],[373,372,370,355,353,296,293,285,282]) ).
tff(375,plain,
s(minus(s(d(s(s(s(s(zero)))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) = s(minus(s(d(s(s(s(zero))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))),
inference(monotonicity,[status(thm)],[374]) ).
tff(376,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(d(s(s(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = s(minus(s(d(s(s(s(s(zero)))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(377,plain,
ifMinus(false,s(s(d(s(s(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = s(minus(s(d(s(s(s(s(zero)))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))),
inference(unit_resolution,[status(thm)],[376,61]) ).
tff(378,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(d(s(s(s(zero))))))),s(s(zero))) = le(s(s(d(s(s(s(zero)))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(379,plain,
le(s(s(s(d(s(s(s(zero))))))),s(s(zero))) = le(s(s(d(s(s(s(zero)))))),s(zero)),
inference(unit_resolution,[status(thm)],[378,39]) ).
tff(380,plain,
le(s(d(s(s(s(s(zero)))))),s(s(d(zero)))) = le(s(s(s(d(s(s(s(zero))))))),s(s(zero))),
inference(monotonicity,[status(thm)],[366,15]) ).
tff(381,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(d(s(s(s(s(zero))))))),s(s(s(d(zero))))) = le(s(d(s(s(s(s(zero)))))),s(s(d(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(382,plain,
le(s(s(d(s(s(s(s(zero))))))),s(s(s(d(zero))))) = le(s(d(s(s(s(s(zero)))))),s(s(d(zero)))),
inference(unit_resolution,[status(thm)],[381,39]) ).
tff(383,plain,
le(s(s(d(s(s(s(s(zero))))))),s(d(s(zero)))) = le(s(s(d(s(s(s(s(zero))))))),s(s(s(d(zero))))),
inference(monotonicity,[status(thm)],[66]) ).
tff(384,plain,
le(s(s(d(s(s(s(s(zero))))))),s(d(s(zero)))) = false,
inference(transitivity,[status(thm)],[383,382,380,379,269,271,274]) ).
tff(385,plain,
ifMinus(le(s(s(d(s(s(s(s(zero))))))),s(d(s(zero)))),s(s(d(s(s(s(s(zero))))))),s(d(s(zero)))) = ifMinus(false,s(s(d(s(s(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),
inference(monotonicity,[status(thm)],[384,215]) ).
tff(386,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(d(s(s(s(s(zero))))))),s(d(s(zero)))) = ifMinus(le(s(s(d(s(s(s(s(zero))))))),s(d(s(zero)))),s(s(d(s(s(s(s(zero))))))),s(d(s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(387,plain,
minus(s(s(d(s(s(s(s(zero))))))),s(d(s(zero)))) = ifMinus(le(s(s(d(s(s(s(s(zero))))))),s(d(s(zero)))),s(s(d(s(s(s(s(zero))))))),s(d(s(zero)))),
inference(unit_resolution,[status(thm)],[386,27]) ).
tff(388,plain,
minus(s(s(d(s(s(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = minus(s(s(d(s(s(s(s(zero))))))),s(d(s(zero)))),
inference(monotonicity,[status(thm)],[209]) ).
tff(389,plain,
minus(s(s(d(s(s(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = minus(s(s(d(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(transitivity,[status(thm)],[388,387,385,377,375,280,277,267,264]) ).
tff(390,plain,
s(minus(s(s(d(s(s(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) = s(minus(s(s(d(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))),
inference(monotonicity,[status(thm)],[389]) ).
tff(391,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(s(d(s(s(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = s(minus(s(s(d(s(s(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(392,plain,
ifMinus(false,s(s(s(d(s(s(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = s(minus(s(s(d(s(s(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))),
inference(unit_resolution,[status(thm)],[391,61]) ).
tff(393,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(d(s(s(s(zero)))))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(394,plain,
le(s(s(d(s(s(s(zero)))))),zero) = false,
inference(unit_resolution,[status(thm)],[393,49]) ).
tff(395,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(d(s(s(s(zero))))))),s(zero)) = le(s(s(d(s(s(s(zero)))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(396,plain,
le(s(s(s(d(s(s(s(zero))))))),s(zero)) = le(s(s(d(s(s(s(zero)))))),zero),
inference(unit_resolution,[status(thm)],[395,39]) ).
tff(397,plain,
le(s(d(s(s(s(s(zero)))))),s(zero)) = le(s(s(s(d(s(s(s(zero))))))),s(zero)),
inference(monotonicity,[status(thm)],[366]) ).
tff(398,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(d(s(s(s(s(zero))))))),s(s(zero))) = le(s(d(s(s(s(s(zero)))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(399,plain,
le(s(s(d(s(s(s(s(zero))))))),s(s(zero))) = le(s(d(s(s(s(s(zero)))))),s(zero)),
inference(unit_resolution,[status(thm)],[398,39]) ).
tff(400,plain,
le(s(s(d(s(s(s(s(zero))))))),s(s(d(zero)))) = le(s(s(d(s(s(s(s(zero))))))),s(s(zero))),
inference(monotonicity,[status(thm)],[15]) ).
tff(401,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(d(s(s(s(s(zero)))))))),s(s(s(d(zero))))) = le(s(s(d(s(s(s(s(zero))))))),s(s(d(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(402,plain,
le(s(s(s(d(s(s(s(s(zero)))))))),s(s(s(d(zero))))) = le(s(s(d(s(s(s(s(zero))))))),s(s(d(zero)))),
inference(unit_resolution,[status(thm)],[401,39]) ).
tff(403,plain,
s(s(s(s(zero)))) = d(s(s(zero))),
inference(transitivity,[status(thm)],[19,198]) ).
tff(404,plain,
s(s(s(s(s(zero))))) = s(d(s(s(zero)))),
inference(monotonicity,[status(thm)],[403]) ).
tff(405,plain,
s(d(s(s(zero)))) = s(s(s(s(s(zero))))),
inference(symmetry,[status(thm)],[404]) ).
tff(406,plain,
d(s(d(s(s(zero))))) = d(s(s(s(s(s(zero)))))),
inference(monotonicity,[status(thm)],[405]) ).
tff(407,plain,
d(s(s(s(s(s(zero)))))) = d(s(d(s(s(zero))))),
inference(symmetry,[status(thm)],[406]) ).
tff(408,plain,
( ~ ! [X: $i] : ( d(s(X)) = s(s(d(X))) )
| ( d(s(s(s(s(s(zero)))))) = s(s(d(s(s(s(s(zero))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(409,plain,
d(s(s(s(s(s(zero)))))) = s(s(d(s(s(s(s(zero))))))),
inference(unit_resolution,[status(thm)],[408,7]) ).
tff(410,plain,
s(s(d(s(s(s(s(zero))))))) = d(s(s(s(s(s(zero)))))),
inference(symmetry,[status(thm)],[409]) ).
tff(411,plain,
s(s(d(s(s(s(s(zero))))))) = d(s(d(s(s(zero))))),
inference(transitivity,[status(thm)],[410,407]) ).
tff(412,plain,
s(s(s(d(s(s(s(s(zero)))))))) = s(d(s(d(s(s(zero)))))),
inference(monotonicity,[status(thm)],[411]) ).
tff(413,plain,
s(d(s(d(s(s(zero)))))) = s(s(s(d(s(s(s(s(zero)))))))),
inference(symmetry,[status(thm)],[412]) ).
tff(414,plain,
le(s(d(s(d(s(s(zero)))))),s(d(s(zero)))) = le(s(s(s(d(s(s(s(s(zero)))))))),s(s(s(d(zero))))),
inference(monotonicity,[status(thm)],[413,66]) ).
tff(415,plain,
le(s(s(s(d(s(s(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = le(s(d(s(d(s(s(zero)))))),s(d(s(zero)))),
inference(monotonicity,[status(thm)],[412,209]) ).
tff(416,plain,
le(s(s(s(d(s(s(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = false,
inference(transitivity,[status(thm)],[415,414,402,400,399,397,396,394]) ).
tff(417,plain,
ifMinus(le(s(s(s(d(s(s(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(s(s(d(s(s(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = ifMinus(false,s(s(s(d(s(s(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),
inference(monotonicity,[status(thm)],[416]) ).
tff(418,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(s(d(s(s(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = ifMinus(le(s(s(s(d(s(s(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(s(s(d(s(s(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(419,plain,
minus(s(s(s(d(s(s(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = ifMinus(le(s(s(s(d(s(s(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(s(s(d(s(s(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),
inference(unit_resolution,[status(thm)],[418,27]) ).
tff(420,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(d(s(s(s(s(zero))))))),zero) = ifMinus(le(s(s(d(s(s(s(s(zero))))))),zero),s(s(d(s(s(s(s(zero))))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(421,plain,
minus(s(s(d(s(s(s(s(zero))))))),zero) = ifMinus(le(s(s(d(s(s(s(s(zero))))))),zero),s(s(d(s(s(s(s(zero))))))),zero),
inference(unit_resolution,[status(thm)],[420,27]) ).
tff(422,plain,
ifMinus(le(s(s(d(s(s(s(s(zero))))))),zero),s(s(d(s(s(s(s(zero))))))),zero) = minus(s(s(d(s(s(s(s(zero))))))),zero),
inference(symmetry,[status(thm)],[421]) ).
tff(423,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(d(s(s(s(s(zero))))))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(424,plain,
le(s(s(d(s(s(s(s(zero))))))),zero) = false,
inference(unit_resolution,[status(thm)],[423,49]) ).
tff(425,plain,
ifMinus(le(s(s(d(s(s(s(s(zero))))))),zero),s(s(d(s(s(s(s(zero))))))),zero) = ifMinus(false,s(s(d(s(s(s(s(zero))))))),zero),
inference(monotonicity,[status(thm)],[424]) ).
tff(426,plain,
ifMinus(false,s(s(d(s(s(s(s(zero))))))),zero) = ifMinus(le(s(s(d(s(s(s(s(zero))))))),zero),s(s(d(s(s(s(s(zero))))))),zero),
inference(symmetry,[status(thm)],[425]) ).
tff(427,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(d(s(s(s(s(zero))))))),zero) = s(minus(s(d(s(s(s(s(zero)))))),zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(428,plain,
ifMinus(false,s(s(d(s(s(s(s(zero))))))),zero) = s(minus(s(d(s(s(s(s(zero)))))),zero)),
inference(unit_resolution,[status(thm)],[427,61]) ).
tff(429,plain,
s(minus(s(d(s(s(s(s(zero)))))),zero)) = ifMinus(false,s(s(d(s(s(s(s(zero))))))),zero),
inference(symmetry,[status(thm)],[428]) ).
tff(430,plain,
minus(s(s(d(s(s(s(s(zero))))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))) = minus(s(s(d(s(s(s(s(zero))))))),s(zero)),
inference(monotonicity,[status(thm)],[262]) ).
tff(431,plain,
minus(s(s(d(s(s(s(s(zero))))))),s(zero)) = minus(s(s(d(s(s(s(s(zero))))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(symmetry,[status(thm)],[430]) ).
tff(432,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(d(s(s(s(s(zero))))))),s(zero)) = ifMinus(le(s(s(d(s(s(s(s(zero))))))),s(zero)),s(s(d(s(s(s(s(zero))))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(433,plain,
minus(s(s(d(s(s(s(s(zero))))))),s(zero)) = ifMinus(le(s(s(d(s(s(s(s(zero))))))),s(zero)),s(s(d(s(s(s(s(zero))))))),s(zero)),
inference(unit_resolution,[status(thm)],[432,27]) ).
tff(434,plain,
ifMinus(le(s(s(d(s(s(s(s(zero))))))),s(zero)),s(s(d(s(s(s(s(zero))))))),s(zero)) = minus(s(s(d(s(s(s(s(zero))))))),s(zero)),
inference(symmetry,[status(thm)],[433]) ).
tff(435,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(d(s(s(s(s(zero))))))),s(zero)) = le(s(d(s(s(s(s(zero)))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(436,plain,
le(s(s(d(s(s(s(s(zero))))))),s(zero)) = le(s(d(s(s(s(s(zero)))))),zero),
inference(unit_resolution,[status(thm)],[435,39]) ).
tff(437,plain,
le(s(d(s(s(s(s(zero)))))),zero) = le(s(s(d(s(s(s(s(zero))))))),s(zero)),
inference(symmetry,[status(thm)],[436]) ).
tff(438,plain,
le(s(d(s(s(s(s(zero)))))),zero) = le(s(s(s(d(s(s(s(zero))))))),zero),
inference(monotonicity,[status(thm)],[366]) ).
tff(439,plain,
le(s(s(s(d(s(s(s(zero))))))),zero) = le(s(d(s(s(s(s(zero)))))),zero),
inference(symmetry,[status(thm)],[438]) ).
tff(440,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(s(d(s(s(s(zero))))))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(441,plain,
le(s(s(s(d(s(s(s(zero))))))),zero) = false,
inference(unit_resolution,[status(thm)],[440,49]) ).
tff(442,plain,
false = le(s(s(s(d(s(s(s(zero))))))),zero),
inference(symmetry,[status(thm)],[441]) ).
tff(443,plain,
false = le(s(s(d(s(s(s(s(zero))))))),s(zero)),
inference(transitivity,[status(thm)],[442,439,437]) ).
tff(444,plain,
ifMinus(false,s(s(d(s(s(s(s(zero))))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))) = ifMinus(le(s(s(d(s(s(s(s(zero))))))),s(zero)),s(s(d(s(s(s(s(zero))))))),s(zero)),
inference(monotonicity,[status(thm)],[443,262]) ).
tff(445,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(d(s(s(s(s(zero))))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))) = s(minus(s(d(s(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(446,plain,
ifMinus(false,s(s(d(s(s(s(s(zero))))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))) = s(minus(s(d(s(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))),
inference(unit_resolution,[status(thm)],[445,61]) ).
tff(447,plain,
s(minus(s(d(s(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))) = ifMinus(false,s(s(d(s(s(s(s(zero))))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(symmetry,[status(thm)],[446]) ).
tff(448,plain,
minus(s(d(s(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))) = minus(s(s(s(d(s(s(s(zero))))))),s(zero)),
inference(monotonicity,[status(thm)],[366,262]) ).
tff(449,plain,
minus(s(s(s(d(s(s(s(zero))))))),s(zero)) = minus(s(d(s(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(symmetry,[status(thm)],[448]) ).
tff(450,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(s(d(s(s(s(zero))))))),s(zero)) = ifMinus(le(s(s(s(d(s(s(s(zero))))))),s(zero)),s(s(s(d(s(s(s(zero))))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(451,plain,
minus(s(s(s(d(s(s(s(zero))))))),s(zero)) = ifMinus(le(s(s(s(d(s(s(s(zero))))))),s(zero)),s(s(s(d(s(s(s(zero))))))),s(zero)),
inference(unit_resolution,[status(thm)],[450,27]) ).
tff(452,plain,
ifMinus(le(s(s(s(d(s(s(s(zero))))))),s(zero)),s(s(s(d(s(s(s(zero))))))),s(zero)) = minus(s(s(s(d(s(s(s(zero))))))),s(zero)),
inference(symmetry,[status(thm)],[451]) ).
tff(453,plain,
le(s(s(d(s(s(s(zero)))))),zero) = le(s(s(s(d(s(s(s(zero))))))),s(zero)),
inference(symmetry,[status(thm)],[396]) ).
tff(454,plain,
false = le(s(s(d(s(s(s(zero)))))),zero),
inference(symmetry,[status(thm)],[394]) ).
tff(455,plain,
false = le(s(s(s(d(s(s(s(zero))))))),s(zero)),
inference(transitivity,[status(thm)],[454,453]) ).
tff(456,plain,
ifMinus(false,s(s(s(d(s(s(s(zero))))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))) = ifMinus(le(s(s(s(d(s(s(s(zero))))))),s(zero)),s(s(s(d(s(s(s(zero))))))),s(zero)),
inference(monotonicity,[status(thm)],[455,262]) ).
tff(457,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(s(d(s(s(s(zero))))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))) = s(minus(s(s(d(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(458,plain,
ifMinus(false,s(s(s(d(s(s(s(zero))))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))) = s(minus(s(s(d(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))),
inference(unit_resolution,[status(thm)],[457,61]) ).
tff(459,plain,
s(minus(s(s(d(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))) = ifMinus(false,s(s(s(d(s(s(s(zero))))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(symmetry,[status(thm)],[458]) ).
tff(460,plain,
^ [Y: $i] :
refl(( ( minus(zero,Y) = zero )
<=> ( minus(zero,Y) = zero ) )),
inference(bind,[status(th)],[]) ).
tff(461,plain,
( ! [Y: $i] : ( minus(zero,Y) = zero )
<=> ! [Y: $i] : ( minus(zero,Y) = zero ) ),
inference(quant_intro,[status(thm)],[460]) ).
tff(462,plain,
( ! [Y: $i] : ( minus(zero,Y) = zero )
<=> ! [Y: $i] : ( minus(zero,Y) = zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(463,axiom,
! [Y: $i] : ( minus(zero,Y) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule4) ).
tff(464,plain,
! [Y: $i] : ( minus(zero,Y) = zero ),
inference(modus_ponens,[status(thm)],[463,462]) ).
tff(465,plain,
! [Y: $i] : ( minus(zero,Y) = zero ),
inference(skolemize,[status(sab)],[464]) ).
tff(466,plain,
! [Y: $i] : ( minus(zero,Y) = zero ),
inference(modus_ponens,[status(thm)],[465,461]) ).
tff(467,plain,
( ~ ! [Y: $i] : ( minus(zero,Y) = zero )
| ( minus(zero,zero) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(468,plain,
minus(zero,zero) = zero,
inference(unit_resolution,[status(thm)],[467,466]) ).
tff(469,plain,
s(minus(zero,zero)) = s(zero),
inference(monotonicity,[status(thm)],[468]) ).
tff(470,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(zero),zero) = s(minus(zero,zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(471,plain,
ifMinus(false,s(zero),zero) = s(minus(zero,zero)),
inference(unit_resolution,[status(thm)],[470,61]) ).
tff(472,plain,
ifMinus(le(s(zero),zero),s(zero),zero) = ifMinus(false,s(zero),zero),
inference(monotonicity,[status(thm)],[96]) ).
tff(473,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(zero),zero) = ifMinus(le(s(zero),zero),s(zero),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(474,plain,
minus(s(zero),zero) = ifMinus(le(s(zero),zero),s(zero),zero),
inference(unit_resolution,[status(thm)],[473,27]) ).
tff(475,plain,
minus(s(zero),zero) = minus(s(s(d(zero))),s(zero)),
inference(transitivity,[status(thm)],[474,472,471,469,131,102,99,91,88]) ).
tff(476,plain,
s(minus(s(zero),zero)) = s(minus(s(s(d(zero))),s(zero))),
inference(monotonicity,[status(thm)],[475]) ).
tff(477,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(zero)),zero) = s(minus(s(zero),zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(478,plain,
ifMinus(false,s(s(zero)),zero) = s(minus(s(zero),zero)),
inference(unit_resolution,[status(thm)],[477,61]) ).
tff(479,plain,
ifMinus(le(s(s(zero)),zero),s(s(zero)),zero) = ifMinus(false,s(s(zero)),zero),
inference(monotonicity,[status(thm)],[80]) ).
tff(480,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(zero)),zero) = ifMinus(le(s(s(zero)),zero),s(s(zero)),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(481,plain,
minus(s(s(zero)),zero) = ifMinus(le(s(s(zero)),zero),s(s(zero)),zero),
inference(unit_resolution,[status(thm)],[480,27]) ).
tff(482,plain,
minus(s(s(d(zero))),zero) = minus(s(s(zero)),zero),
inference(monotonicity,[status(thm)],[15]) ).
tff(483,plain,
minus(s(s(d(zero))),zero) = minus(s(d(s(zero))),s(zero)),
inference(transitivity,[status(thm)],[482,481,479,478,476,86,83,71,68]) ).
tff(484,plain,
s(minus(s(s(d(zero))),zero)) = s(minus(s(d(s(zero))),s(zero))),
inference(monotonicity,[status(thm)],[483]) ).
tff(485,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(s(d(zero)))),zero) = s(minus(s(s(d(zero))),zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(486,plain,
ifMinus(false,s(s(s(d(zero)))),zero) = s(minus(s(s(d(zero))),zero)),
inference(unit_resolution,[status(thm)],[485,61]) ).
tff(487,plain,
le(s(s(s(d(zero)))),zero) = le(s(s(s(zero))),zero),
inference(monotonicity,[status(thm)],[73]) ).
tff(488,plain,
le(s(s(s(d(zero)))),zero) = false,
inference(transitivity,[status(thm)],[487,51]) ).
tff(489,plain,
ifMinus(le(s(s(s(d(zero)))),zero),s(s(s(d(zero)))),zero) = ifMinus(false,s(s(s(d(zero)))),zero),
inference(monotonicity,[status(thm)],[488]) ).
tff(490,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(s(d(zero)))),zero) = ifMinus(le(s(s(s(d(zero)))),zero),s(s(s(d(zero)))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(491,plain,
minus(s(s(s(d(zero)))),zero) = ifMinus(le(s(s(s(d(zero)))),zero),s(s(s(d(zero)))),zero),
inference(unit_resolution,[status(thm)],[490,27]) ).
tff(492,plain,
minus(s(d(s(zero))),zero) = minus(s(s(s(d(zero)))),zero),
inference(monotonicity,[status(thm)],[66]) ).
tff(493,plain,
minus(s(d(s(zero))),zero) = minus(s(s(d(s(zero)))),s(zero)),
inference(transitivity,[status(thm)],[492,491,489,486,484,64,54,30]) ).
tff(494,plain,
s(minus(s(d(s(zero))),zero)) = s(minus(s(s(d(s(zero)))),s(zero))),
inference(monotonicity,[status(thm)],[493]) ).
tff(495,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(d(s(zero)))),zero) = s(minus(s(d(s(zero))),zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(496,plain,
ifMinus(false,s(s(d(s(zero)))),zero) = s(minus(s(d(s(zero))),zero)),
inference(unit_resolution,[status(thm)],[495,61]) ).
tff(497,plain,
le(s(s(d(s(zero)))),zero) = false,
inference(transitivity,[status(thm)],[233,232]) ).
tff(498,plain,
ifMinus(le(s(s(d(s(zero)))),zero),s(s(d(s(zero)))),zero) = ifMinus(false,s(s(d(s(zero)))),zero),
inference(monotonicity,[status(thm)],[497]) ).
tff(499,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(d(s(zero)))),zero) = ifMinus(le(s(s(d(s(zero)))),zero),s(s(d(s(zero)))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(500,plain,
minus(s(s(d(s(zero)))),zero) = ifMinus(le(s(s(d(s(zero)))),zero),s(s(d(s(zero)))),zero),
inference(unit_resolution,[status(thm)],[499,27]) ).
tff(501,plain,
minus(s(s(d(s(zero)))),zero) = d(s(s(zero))),
inference(transitivity,[status(thm)],[500,498,496,494,138,198]) ).
tff(502,plain,
s(minus(s(s(d(s(zero)))),zero)) = s(d(s(s(zero)))),
inference(monotonicity,[status(thm)],[501]) ).
tff(503,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(s(d(s(zero))))),zero) = s(minus(s(s(d(s(zero)))),zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(504,plain,
ifMinus(false,s(s(s(d(s(zero))))),zero) = s(minus(s(s(d(s(zero)))),zero)),
inference(unit_resolution,[status(thm)],[503,61]) ).
tff(505,plain,
ifMinus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero) = ifMinus(false,s(s(s(d(s(zero))))),zero),
inference(monotonicity,[status(thm)],[308]) ).
tff(506,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(s(d(s(zero))))),zero) = ifMinus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(507,plain,
minus(s(s(s(d(s(zero))))),zero) = ifMinus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero),
inference(unit_resolution,[status(thm)],[506,27]) ).
tff(508,plain,
minus(s(d(s(s(zero)))),zero) = minus(s(s(s(d(s(zero))))),zero),
inference(monotonicity,[status(thm)],[200]) ).
tff(509,plain,
minus(s(d(s(s(zero)))),zero) = minus(s(s(d(s(s(zero))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(transitivity,[status(thm)],[508,507,505,504,502,329,314,311,301,298]) ).
tff(510,plain,
s(minus(s(d(s(s(zero)))),zero)) = s(minus(s(s(d(s(s(zero))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))),
inference(monotonicity,[status(thm)],[509]) ).
tff(511,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(d(s(s(zero))))),zero) = s(minus(s(d(s(s(zero)))),zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(512,plain,
ifMinus(false,s(s(d(s(s(zero))))),zero) = s(minus(s(d(s(s(zero)))),zero)),
inference(unit_resolution,[status(thm)],[511,61]) ).
tff(513,plain,
ifMinus(le(s(s(d(s(s(zero))))),zero),s(s(d(s(s(zero))))),zero) = ifMinus(false,s(s(d(s(s(zero))))),zero),
inference(monotonicity,[status(thm)],[290]) ).
tff(514,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(d(s(s(zero))))),zero) = ifMinus(le(s(s(d(s(s(zero))))),zero),s(s(d(s(s(zero))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(515,plain,
minus(s(s(d(s(s(zero))))),zero) = ifMinus(le(s(s(d(s(s(zero))))),zero),s(s(d(s(s(zero))))),zero),
inference(unit_resolution,[status(thm)],[514,27]) ).
tff(516,plain,
minus(s(s(d(s(s(zero))))),zero) = minus(s(d(s(s(s(zero))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(transitivity,[status(thm)],[515,513,512,510,296,293,285,282]) ).
tff(517,plain,
s(minus(s(s(d(s(s(zero))))),zero)) = s(minus(s(d(s(s(s(zero))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))),
inference(monotonicity,[status(thm)],[516]) ).
tff(518,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(s(d(s(s(zero)))))),zero) = s(minus(s(s(d(s(s(zero))))),zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(519,plain,
ifMinus(false,s(s(s(d(s(s(zero)))))),zero) = s(minus(s(s(d(s(s(zero))))),zero)),
inference(unit_resolution,[status(thm)],[518,61]) ).
tff(520,plain,
ifMinus(le(s(s(s(d(s(s(zero)))))),zero),s(s(s(d(s(s(zero)))))),zero) = ifMinus(false,s(s(s(d(s(s(zero)))))),zero),
inference(monotonicity,[status(thm)],[274]) ).
tff(521,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(s(d(s(s(zero)))))),zero) = ifMinus(le(s(s(s(d(s(s(zero)))))),zero),s(s(s(d(s(s(zero)))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(522,plain,
minus(s(s(s(d(s(s(zero)))))),zero) = ifMinus(le(s(s(s(d(s(s(zero)))))),zero),s(s(s(d(s(s(zero)))))),zero),
inference(unit_resolution,[status(thm)],[521,27]) ).
tff(523,plain,
minus(s(d(s(s(s(zero))))),zero) = minus(s(s(s(d(s(s(zero)))))),zero),
inference(monotonicity,[status(thm)],[246]) ).
tff(524,plain,
minus(s(d(s(s(s(zero))))),zero) = minus(s(s(d(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(transitivity,[status(thm)],[523,522,520,519,517,280,277,267,264]) ).
tff(525,plain,
s(minus(s(d(s(s(s(zero))))),zero)) = s(minus(s(s(d(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))),
inference(monotonicity,[status(thm)],[524]) ).
tff(526,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(d(s(s(s(zero)))))),zero) = s(minus(s(d(s(s(s(zero))))),zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(527,plain,
ifMinus(false,s(s(d(s(s(s(zero)))))),zero) = s(minus(s(d(s(s(s(zero))))),zero)),
inference(unit_resolution,[status(thm)],[526,61]) ).
tff(528,plain,
ifMinus(le(s(s(d(s(s(s(zero)))))),zero),s(s(d(s(s(s(zero)))))),zero) = ifMinus(false,s(s(d(s(s(s(zero)))))),zero),
inference(monotonicity,[status(thm)],[394]) ).
tff(529,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(d(s(s(s(zero)))))),zero) = ifMinus(le(s(s(d(s(s(s(zero)))))),zero),s(s(d(s(s(s(zero)))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(530,plain,
minus(s(s(d(s(s(s(zero)))))),zero) = ifMinus(le(s(s(d(s(s(s(zero)))))),zero),s(s(d(s(s(s(zero)))))),zero),
inference(unit_resolution,[status(thm)],[529,27]) ).
tff(531,plain,
minus(s(s(d(s(s(s(zero)))))),zero) = minus(s(d(s(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(transitivity,[status(thm)],[530,528,527,525,459,456,452,449]) ).
tff(532,plain,
s(minus(s(s(d(s(s(s(zero)))))),zero)) = s(minus(s(d(s(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))),
inference(monotonicity,[status(thm)],[531]) ).
tff(533,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(s(d(s(s(s(zero))))))),zero) = s(minus(s(s(d(s(s(s(zero)))))),zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(534,plain,
ifMinus(false,s(s(s(d(s(s(s(zero))))))),zero) = s(minus(s(s(d(s(s(s(zero)))))),zero)),
inference(unit_resolution,[status(thm)],[533,61]) ).
tff(535,plain,
ifMinus(le(s(s(s(d(s(s(s(zero))))))),zero),s(s(s(d(s(s(s(zero))))))),zero) = ifMinus(false,s(s(s(d(s(s(s(zero))))))),zero),
inference(monotonicity,[status(thm)],[441]) ).
tff(536,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(s(d(s(s(s(zero))))))),zero) = ifMinus(le(s(s(s(d(s(s(s(zero))))))),zero),s(s(s(d(s(s(s(zero))))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(537,plain,
minus(s(s(s(d(s(s(s(zero))))))),zero) = ifMinus(le(s(s(s(d(s(s(s(zero))))))),zero),s(s(s(d(s(s(s(zero))))))),zero),
inference(unit_resolution,[status(thm)],[536,27]) ).
tff(538,plain,
minus(s(d(s(s(s(s(zero)))))),zero) = minus(s(s(s(d(s(s(s(zero))))))),zero),
inference(monotonicity,[status(thm)],[366]) ).
tff(539,plain,
minus(s(d(s(s(s(s(zero)))))),zero) = minus(s(s(d(s(s(s(s(zero))))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(transitivity,[status(thm)],[538,537,535,534,532,447,444,434,431]) ).
tff(540,plain,
s(minus(s(d(s(s(s(s(zero)))))),zero)) = s(minus(s(s(d(s(s(s(s(zero))))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))),
inference(monotonicity,[status(thm)],[539]) ).
tff(541,plain,
s(minus(s(s(d(s(s(s(s(zero))))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))) = s(minus(s(d(s(s(s(s(zero)))))),zero)),
inference(symmetry,[status(thm)],[540]) ).
tff(542,plain,
d(s(s(s(s(zero))))) = minus(s(d(s(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(transitivity,[status(thm)],[363,335,459,456,452,449]) ).
tff(543,plain,
s(d(s(s(s(s(zero)))))) = s(minus(s(d(s(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))),
inference(monotonicity,[status(thm)],[542]) ).
tff(544,plain,
s(minus(s(d(s(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))) = s(d(s(s(s(s(zero)))))),
inference(symmetry,[status(thm)],[543]) ).
tff(545,plain,
ifMinus(le(s(s(d(s(s(s(s(zero))))))),s(zero)),s(s(d(s(s(s(s(zero))))))),s(zero)) = ifMinus(false,s(s(d(s(s(s(s(zero))))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(symmetry,[status(thm)],[444]) ).
tff(546,plain,
minus(s(s(d(s(s(s(s(zero))))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))) = s(d(s(s(s(s(zero)))))),
inference(transitivity,[status(thm)],[430,433,545,446,544]) ).
tff(547,plain,
s(minus(s(s(d(s(s(s(s(zero))))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))) = s(s(d(s(s(s(s(zero))))))),
inference(monotonicity,[status(thm)],[546]) ).
tff(548,plain,
s(s(d(s(s(s(s(zero))))))) = s(minus(s(s(d(s(s(s(s(zero))))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))),
inference(symmetry,[status(thm)],[547]) ).
tff(549,plain,
d(s(d(s(s(zero))))) = minus(s(s(d(s(s(s(s(zero))))))),zero),
inference(transitivity,[status(thm)],[406,409,548,541,429,426,422]) ).
tff(550,plain,
s(d(s(d(s(s(zero)))))) = s(minus(s(s(d(s(s(s(s(zero))))))),zero)),
inference(monotonicity,[status(thm)],[549]) ).
tff(551,plain,
s(minus(s(s(d(s(s(s(s(zero))))))),zero)) = s(d(s(d(s(s(zero)))))),
inference(symmetry,[status(thm)],[550]) ).
tff(552,plain,
s(minus(s(s(d(s(s(s(s(zero))))))),zero)) = s(s(s(d(s(s(s(s(zero)))))))),
inference(transitivity,[status(thm)],[551,413]) ).
tff(553,plain,
minus(s(minus(s(s(d(s(s(s(s(zero))))))),zero)),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = minus(s(s(s(d(s(s(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),
inference(monotonicity,[status(thm)],[552]) ).
tff(554,plain,
minus(s(minus(s(s(d(s(s(s(s(zero))))))),zero)),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = s(s(d(s(s(s(zero)))))),
inference(transitivity,[status(thm)],[553,419,417,392,390,336]) ).
tff(555,plain,
quot(minus(s(minus(s(s(d(s(s(s(s(zero))))))),zero)),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) = quot(s(s(d(s(s(s(zero)))))),s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))),
inference(monotonicity,[status(thm)],[554]) ).
tff(556,plain,
quot(minus(s(minus(s(s(d(s(s(s(s(zero))))))),zero)),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) = minus(s(d(s(zero))),s(zero)),
inference(transitivity,[status(thm)],[555,259,257,86,83,71,68]) ).
tff(557,plain,
s(quot(minus(s(minus(s(s(d(s(s(s(s(zero))))))),zero)),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))))) = s(minus(s(d(s(zero))),s(zero))),
inference(monotonicity,[status(thm)],[556]) ).
tff(558,plain,
( ~ ! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) )
| ( quot(s(s(minus(s(s(d(s(s(s(s(zero))))))),zero))),s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) = s(quot(minus(s(minus(s(s(d(s(s(s(s(zero))))))),zero)),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(559,plain,
quot(s(s(minus(s(s(d(s(s(s(s(zero))))))),zero))),s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) = s(quot(minus(s(minus(s(s(d(s(s(s(s(zero))))))),zero)),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))))),
inference(unit_resolution,[status(thm)],[558,170]) ).
tff(560,plain,
s(s(minus(s(s(d(s(s(s(s(zero))))))),zero))) = s(s(d(s(d(s(s(zero))))))),
inference(monotonicity,[status(thm)],[551]) ).
tff(561,plain,
s(s(d(s(d(s(s(zero))))))) = s(s(minus(s(s(d(s(s(s(s(zero))))))),zero))),
inference(symmetry,[status(thm)],[560]) ).
tff(562,plain,
minus(s(minus(s(s(d(s(s(s(s(zero))))))),zero)),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = minus(s(d(s(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(transitivity,[status(thm)],[553,419,417,392,390,459,456,452,449]) ).
tff(563,plain,
s(minus(s(minus(s(s(d(s(s(s(s(zero))))))),zero)),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) = s(minus(s(d(s(s(s(s(zero)))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))),
inference(monotonicity,[status(thm)],[562]) ).
tff(564,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(minus(s(s(d(s(s(s(s(zero))))))),zero))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = s(minus(s(minus(s(s(d(s(s(s(s(zero))))))),zero)),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(565,plain,
ifMinus(false,s(s(minus(s(s(d(s(s(s(s(zero))))))),zero))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = s(minus(s(minus(s(s(d(s(s(s(s(zero))))))),zero)),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))),
inference(unit_resolution,[status(thm)],[564,61]) ).
tff(566,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(d(s(s(s(s(zero)))))))),s(s(zero))) = le(s(s(d(s(s(s(s(zero))))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(567,plain,
le(s(s(s(d(s(s(s(s(zero)))))))),s(s(zero))) = le(s(s(d(s(s(s(s(zero))))))),s(zero)),
inference(unit_resolution,[status(thm)],[566,39]) ).
tff(568,plain,
le(s(d(s(d(s(s(zero)))))),s(s(d(zero)))) = le(s(s(s(d(s(s(s(s(zero)))))))),s(s(zero))),
inference(monotonicity,[status(thm)],[413,15]) ).
tff(569,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(d(s(d(s(s(zero))))))),s(s(s(d(zero))))) = le(s(d(s(d(s(s(zero)))))),s(s(d(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(570,plain,
le(s(s(d(s(d(s(s(zero))))))),s(s(s(d(zero))))) = le(s(d(s(d(s(s(zero)))))),s(s(d(zero)))),
inference(unit_resolution,[status(thm)],[569,39]) ).
tff(571,plain,
ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)) = s(s(s(d(zero)))),
inference(transitivity,[status(thm)],[208,63,207,66]) ).
tff(572,plain,
le(s(s(d(s(d(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = le(s(s(d(s(d(s(s(zero))))))),s(s(s(d(zero))))),
inference(monotonicity,[status(thm)],[571]) ).
tff(573,plain,
le(s(s(d(s(d(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = false,
inference(transitivity,[status(thm)],[572,570,568,567,436,438,441]) ).
tff(574,plain,
ifMinus(le(s(s(d(s(d(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(s(d(s(d(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = ifMinus(false,s(s(minus(s(s(d(s(s(s(s(zero))))))),zero))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),
inference(monotonicity,[status(thm)],[573,561]) ).
tff(575,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(d(s(d(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = ifMinus(le(s(s(d(s(d(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(s(d(s(d(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(576,plain,
minus(s(s(d(s(d(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = ifMinus(le(s(s(d(s(d(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(s(d(s(d(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),
inference(unit_resolution,[status(thm)],[575,27]) ).
tff(577,plain,
minus(s(s(d(s(d(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = minus(s(s(d(s(s(s(s(zero))))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero))),
inference(transitivity,[status(thm)],[576,574,565,563,447,444,434,431]) ).
tff(578,plain,
s(minus(s(s(d(s(d(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) = s(minus(s(s(d(s(s(s(s(zero))))))),ifMinus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)))),
inference(monotonicity,[status(thm)],[577]) ).
tff(579,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(s(d(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = s(minus(s(s(d(s(d(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(580,plain,
ifMinus(false,s(s(s(d(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = s(minus(s(s(d(s(d(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))),
inference(unit_resolution,[status(thm)],[579,61]) ).
tff(581,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(d(s(s(s(s(zero)))))))),s(zero)) = le(s(s(d(s(s(s(s(zero))))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(582,plain,
le(s(s(s(d(s(s(s(s(zero)))))))),s(zero)) = le(s(s(d(s(s(s(s(zero))))))),zero),
inference(unit_resolution,[status(thm)],[581,39]) ).
tff(583,plain,
le(s(d(s(d(s(s(zero)))))),s(zero)) = le(s(s(s(d(s(s(s(s(zero)))))))),s(zero)),
inference(monotonicity,[status(thm)],[413]) ).
tff(584,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(d(s(d(s(s(zero))))))),s(s(zero))) = le(s(d(s(d(s(s(zero)))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(585,plain,
le(s(s(d(s(d(s(s(zero))))))),s(s(zero))) = le(s(d(s(d(s(s(zero)))))),s(zero)),
inference(unit_resolution,[status(thm)],[584,39]) ).
tff(586,plain,
le(s(s(d(s(d(s(s(zero))))))),s(s(d(zero)))) = le(s(s(d(s(d(s(s(zero))))))),s(s(zero))),
inference(monotonicity,[status(thm)],[15]) ).
tff(587,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(d(s(d(s(s(zero)))))))),s(s(s(d(zero))))) = le(s(s(d(s(d(s(s(zero))))))),s(s(d(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(588,plain,
le(s(s(s(d(s(d(s(s(zero)))))))),s(s(s(d(zero))))) = le(s(s(d(s(d(s(s(zero))))))),s(s(d(zero)))),
inference(unit_resolution,[status(thm)],[587,39]) ).
tff(589,plain,
( ~ ! [X: $i] : ( d(s(X)) = s(s(d(X))) )
| ( d(s(s(d(s(s(zero)))))) = s(s(d(s(d(s(s(zero))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(590,plain,
d(s(s(d(s(s(zero)))))) = s(s(d(s(d(s(s(zero))))))),
inference(unit_resolution,[status(thm)],[589,7]) ).
tff(591,plain,
s(s(d(s(d(s(s(zero))))))) = d(s(s(d(s(s(zero)))))),
inference(symmetry,[status(thm)],[590]) ).
tff(592,plain,
s(s(s(d(s(d(s(s(zero)))))))) = s(d(s(s(d(s(s(zero))))))),
inference(monotonicity,[status(thm)],[591]) ).
tff(593,plain,
s(d(s(s(d(s(s(zero))))))) = s(s(s(d(s(d(s(s(zero)))))))),
inference(symmetry,[status(thm)],[592]) ).
tff(594,plain,
le(s(d(s(s(d(s(s(zero))))))),s(d(s(zero)))) = le(s(s(s(d(s(d(s(s(zero)))))))),s(s(s(d(zero))))),
inference(monotonicity,[status(thm)],[593,66]) ).
tff(595,plain,
le(s(s(s(d(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = le(s(d(s(s(d(s(s(zero))))))),s(d(s(zero)))),
inference(monotonicity,[status(thm)],[592,209]) ).
tff(596,plain,
le(s(s(s(d(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = false,
inference(transitivity,[status(thm)],[595,594,588,586,585,583,582,424]) ).
tff(597,plain,
ifMinus(le(s(s(s(d(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(s(s(d(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = ifMinus(false,s(s(s(d(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),
inference(monotonicity,[status(thm)],[596]) ).
tff(598,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(s(d(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = ifMinus(le(s(s(s(d(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(s(s(d(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(599,plain,
minus(s(s(s(d(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = ifMinus(le(s(s(s(d(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(s(s(d(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),
inference(unit_resolution,[status(thm)],[598,27]) ).
tff(600,plain,
minus(s(d(s(s(d(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = minus(s(s(s(d(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),
inference(monotonicity,[status(thm)],[593]) ).
tff(601,plain,
minus(s(d(s(s(d(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = d(s(d(s(s(zero))))),
inference(transitivity,[status(thm)],[600,599,597,580,578,547,410,407]) ).
tff(602,plain,
s(minus(s(d(s(s(d(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) = s(d(s(d(s(s(zero)))))),
inference(monotonicity,[status(thm)],[601]) ).
tff(603,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(d(s(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = s(minus(s(d(s(s(d(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(604,plain,
ifMinus(false,s(s(d(s(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = s(minus(s(d(s(s(d(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))),
inference(unit_resolution,[status(thm)],[603,61]) ).
tff(605,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(s(d(s(s(s(s(zero)))))))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(606,plain,
le(s(s(s(d(s(s(s(s(zero)))))))),zero) = false,
inference(unit_resolution,[status(thm)],[605,49]) ).
tff(607,plain,
le(s(d(s(d(s(s(zero)))))),zero) = le(s(s(s(d(s(s(s(s(zero)))))))),zero),
inference(monotonicity,[status(thm)],[413]) ).
tff(608,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(d(s(d(s(s(zero))))))),s(zero)) = le(s(d(s(d(s(s(zero)))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(609,plain,
le(s(s(d(s(d(s(s(zero))))))),s(zero)) = le(s(d(s(d(s(s(zero)))))),zero),
inference(unit_resolution,[status(thm)],[608,39]) ).
tff(610,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(d(s(d(s(s(zero)))))))),s(s(zero))) = le(s(s(d(s(d(s(s(zero))))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(611,plain,
le(s(s(s(d(s(d(s(s(zero)))))))),s(s(zero))) = le(s(s(d(s(d(s(s(zero))))))),s(zero)),
inference(unit_resolution,[status(thm)],[610,39]) ).
tff(612,plain,
le(s(d(s(s(d(s(s(zero))))))),s(s(d(zero)))) = le(s(s(s(d(s(d(s(s(zero)))))))),s(s(zero))),
inference(monotonicity,[status(thm)],[593,15]) ).
tff(613,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(d(s(s(d(s(s(zero)))))))),s(s(s(d(zero))))) = le(s(d(s(s(d(s(s(zero))))))),s(s(d(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(614,plain,
le(s(s(d(s(s(d(s(s(zero)))))))),s(s(s(d(zero))))) = le(s(d(s(s(d(s(s(zero))))))),s(s(d(zero)))),
inference(unit_resolution,[status(thm)],[613,39]) ).
tff(615,plain,
le(s(s(d(s(s(d(s(s(zero)))))))),s(d(s(zero)))) = le(s(s(d(s(s(d(s(s(zero)))))))),s(s(s(d(zero))))),
inference(monotonicity,[status(thm)],[66]) ).
tff(616,plain,
le(s(s(d(s(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = le(s(s(d(s(s(d(s(s(zero)))))))),s(d(s(zero)))),
inference(monotonicity,[status(thm)],[209]) ).
tff(617,plain,
le(s(s(d(s(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = false,
inference(transitivity,[status(thm)],[616,615,614,612,611,609,607,606]) ).
tff(618,plain,
ifMinus(le(s(s(d(s(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(s(d(s(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = ifMinus(false,s(s(d(s(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),
inference(monotonicity,[status(thm)],[617]) ).
tff(619,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(d(s(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = ifMinus(le(s(s(d(s(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(s(d(s(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(620,plain,
minus(s(s(d(s(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = ifMinus(le(s(s(d(s(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(s(d(s(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),
inference(unit_resolution,[status(thm)],[619,27]) ).
tff(621,plain,
minus(s(s(d(s(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = s(d(s(d(s(s(zero)))))),
inference(transitivity,[status(thm)],[620,618,604,602]) ).
tff(622,plain,
s(minus(s(s(d(s(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) = s(s(d(s(d(s(s(zero))))))),
inference(monotonicity,[status(thm)],[621]) ).
tff(623,plain,
( ~ ! [Y: $i,X: $i] : ( ifMinus(false,s(X),Y) = s(minus(X,Y)) )
| ( ifMinus(false,s(s(s(d(s(s(d(s(s(zero))))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = s(minus(s(s(d(s(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(624,plain,
ifMinus(false,s(s(s(d(s(s(d(s(s(zero))))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = s(minus(s(s(d(s(s(d(s(s(zero)))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))),
inference(unit_resolution,[status(thm)],[623,61]) ).
tff(625,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(d(s(d(s(s(zero))))))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(626,plain,
le(s(s(d(s(d(s(s(zero))))))),zero) = false,
inference(unit_resolution,[status(thm)],[625,49]) ).
tff(627,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(d(s(d(s(s(zero)))))))),s(zero)) = le(s(s(d(s(d(s(s(zero))))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(628,plain,
le(s(s(s(d(s(d(s(s(zero)))))))),s(zero)) = le(s(s(d(s(d(s(s(zero))))))),zero),
inference(unit_resolution,[status(thm)],[627,39]) ).
tff(629,plain,
le(s(d(s(s(d(s(s(zero))))))),s(zero)) = le(s(s(s(d(s(d(s(s(zero)))))))),s(zero)),
inference(monotonicity,[status(thm)],[593]) ).
tff(630,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(d(s(s(d(s(s(zero)))))))),s(s(zero))) = le(s(d(s(s(d(s(s(zero))))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(631,plain,
le(s(s(d(s(s(d(s(s(zero)))))))),s(s(zero))) = le(s(d(s(s(d(s(s(zero))))))),s(zero)),
inference(unit_resolution,[status(thm)],[630,39]) ).
tff(632,plain,
le(s(s(d(s(s(d(s(s(zero)))))))),s(s(d(zero)))) = le(s(s(d(s(s(d(s(s(zero)))))))),s(s(zero))),
inference(monotonicity,[status(thm)],[15]) ).
tff(633,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(d(s(s(d(s(s(zero))))))))),s(s(s(d(zero))))) = le(s(s(d(s(s(d(s(s(zero)))))))),s(s(d(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(634,plain,
le(s(s(s(d(s(s(d(s(s(zero))))))))),s(s(s(d(zero))))) = le(s(s(d(s(s(d(s(s(zero)))))))),s(s(d(zero)))),
inference(unit_resolution,[status(thm)],[633,39]) ).
tff(635,plain,
d(s(d(s(s(s(zero)))))) = d(s(s(s(d(s(s(zero))))))),
inference(monotonicity,[status(thm)],[246]) ).
tff(636,plain,
d(s(s(s(d(s(s(zero))))))) = d(s(d(s(s(s(zero)))))),
inference(symmetry,[status(thm)],[635]) ).
tff(637,plain,
( ~ ! [X: $i] : ( d(s(X)) = s(s(d(X))) )
| ( d(s(s(s(d(s(s(zero))))))) = s(s(d(s(s(d(s(s(zero)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(638,plain,
d(s(s(s(d(s(s(zero))))))) = s(s(d(s(s(d(s(s(zero)))))))),
inference(unit_resolution,[status(thm)],[637,7]) ).
tff(639,plain,
s(s(d(s(s(d(s(s(zero)))))))) = d(s(s(s(d(s(s(zero))))))),
inference(symmetry,[status(thm)],[638]) ).
tff(640,plain,
s(s(d(s(s(d(s(s(zero)))))))) = d(s(d(s(s(s(zero)))))),
inference(transitivity,[status(thm)],[639,636]) ).
tff(641,plain,
s(s(s(d(s(s(d(s(s(zero))))))))) = s(d(s(d(s(s(s(zero))))))),
inference(monotonicity,[status(thm)],[640]) ).
tff(642,plain,
s(d(s(d(s(s(s(zero))))))) = s(s(s(d(s(s(d(s(s(zero))))))))),
inference(symmetry,[status(thm)],[641]) ).
tff(643,plain,
le(s(d(s(d(s(s(s(zero))))))),s(d(s(zero)))) = le(s(s(s(d(s(s(d(s(s(zero))))))))),s(s(s(d(zero))))),
inference(monotonicity,[status(thm)],[642,66]) ).
tff(644,plain,
le(s(s(s(d(s(s(d(s(s(zero))))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = le(s(d(s(d(s(s(s(zero))))))),s(d(s(zero)))),
inference(monotonicity,[status(thm)],[641,209]) ).
tff(645,plain,
le(s(s(s(d(s(s(d(s(s(zero))))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = false,
inference(transitivity,[status(thm)],[644,643,634,632,631,629,628,626]) ).
tff(646,plain,
ifMinus(le(s(s(s(d(s(s(d(s(s(zero))))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(s(s(d(s(s(d(s(s(zero))))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = ifMinus(false,s(s(s(d(s(s(d(s(s(zero))))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),
inference(monotonicity,[status(thm)],[645]) ).
tff(647,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = ifMinus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(s(d(s(s(d(s(s(zero))))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = ifMinus(le(s(s(s(d(s(s(d(s(s(zero))))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(s(s(d(s(s(d(s(s(zero))))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(648,plain,
minus(s(s(s(d(s(s(d(s(s(zero))))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = ifMinus(le(s(s(s(d(s(s(d(s(s(zero))))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(s(s(d(s(s(d(s(s(zero))))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),
inference(unit_resolution,[status(thm)],[647,27]) ).
tff(649,plain,
minus(s(d(s(d(s(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = minus(s(s(s(d(s(s(d(s(s(zero))))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),
inference(monotonicity,[status(thm)],[642]) ).
tff(650,plain,
minus(s(d(s(d(s(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))) = s(s(minus(s(s(d(s(s(s(s(zero))))))),zero))),
inference(transitivity,[status(thm)],[649,648,646,624,622,561]) ).
tff(651,plain,
quot(minus(s(d(s(d(s(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) = quot(s(s(minus(s(s(d(s(s(s(s(zero))))))),zero))),s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))),
inference(monotonicity,[status(thm)],[650]) ).
tff(652,plain,
quot(minus(s(d(s(d(s(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) = minus(s(s(d(s(zero)))),s(zero)),
inference(transitivity,[status(thm)],[651,559,557,64,54,30]) ).
tff(653,plain,
s(quot(minus(s(d(s(d(s(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))))) = s(minus(s(s(d(s(zero)))),s(zero))),
inference(monotonicity,[status(thm)],[652]) ).
tff(654,plain,
( ~ ! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) )
| ( quot(s(s(d(s(d(s(s(s(zero)))))))),s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) = s(quot(minus(s(d(s(d(s(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(655,plain,
quot(s(s(d(s(d(s(s(s(zero)))))))),s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))) = s(quot(minus(s(d(s(d(s(s(s(zero))))))),ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))))),
inference(unit_resolution,[status(thm)],[654,170]) ).
tff(656,plain,
s(minus(s(s(d(s(zero)))),s(zero))) = s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),
inference(symmetry,[status(thm)],[173]) ).
tff(657,plain,
s(s(s(s(zero)))) = s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero))),
inference(transitivity,[status(thm)],[19,137,656]) ).
tff(658,plain,
( ~ ! [X: $i] : ( d(s(X)) = s(s(d(X))) )
| ( d(s(s(d(s(s(s(zero))))))) = s(s(d(s(d(s(s(s(zero)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(659,plain,
d(s(s(d(s(s(s(zero))))))) = s(s(d(s(d(s(s(s(zero)))))))),
inference(unit_resolution,[status(thm)],[658,7]) ).
tff(660,plain,
d(d(s(s(s(s(zero)))))) = d(s(s(d(s(s(s(zero))))))),
inference(monotonicity,[status(thm)],[363]) ).
tff(661,plain,
d(d(s(s(s(s(zero)))))) = s(s(d(s(d(s(s(s(zero)))))))),
inference(transitivity,[status(thm)],[660,659]) ).
tff(662,plain,
quot(d(d(s(s(s(s(zero)))))),s(s(s(s(zero))))) = quot(s(s(d(s(d(s(s(s(zero)))))))),s(ifMinus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)))),
inference(monotonicity,[status(thm)],[661,657]) ).
tff(663,plain,
quot(d(d(s(s(s(s(zero)))))),s(s(s(s(zero))))) = s(s(s(s(zero)))),
inference(transitivity,[status(thm)],[662,655,653,138,20]) ).
tff(664,plain,
( ( quot(d(d(s(s(s(s(zero)))))),s(s(s(s(zero))))) != s(s(s(s(zero)))) )
<=> ( quot(d(d(s(s(s(s(zero)))))),s(s(s(s(zero))))) != s(s(s(s(zero)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(665,axiom,
quot(d(d(s(s(s(s(zero)))))),s(s(s(s(zero))))) != s(s(s(s(zero)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
tff(666,plain,
quot(d(d(s(s(s(s(zero)))))),s(s(s(s(zero))))) != s(s(s(s(zero)))),
inference(modus_ponens,[status(thm)],[665,664]) ).
tff(667,plain,
$false,
inference(unit_resolution,[status(thm)],[666,663]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ARI764-2 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.10 % Command : run_E %s %d THM
% 0.12/0.30 % Computer : n006.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Mon May 4 18:36:47 EDT 2026
% 0.12/0.30 % CPUTime :
% 2.23/2.46 % SZS status Unsatisfiable
% 2.23/2.46 % SZS output start Proof
% See solution above
% 2.32/2.57 % E exiting
%------------------------------------------------------------------------------