%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ARI765-2 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n025.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 06:16:57 PM UTC 2026
% Result : Unsatisfiable 23.86s 24.10s
% Output : Proof 24.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 145
% Syntax : Number of formulae : 597 ( 468 unt; 0 typ; 0 def)
% Number of atoms : 752 ( 738 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 255 ( 113 ~; 100 |; 0 &)
% ( 42 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of FOOLs : 13 ( 13 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 : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 330 ( 312 !; 0 ?; 330 :)
% Comments :
%------------------------------------------------------------------------------
tff(s_type,type,
s: $i > $i ).
tff(zero_type,type,
zero: $i ).
tff(log_type,type,
log: $i > $i ).
tff(e_type,type,
e: $i > $i ).
tff(d_type,type,
d: $i > $i ).
tff(quot_type,type,
quot: ( $i * $i ) > $i ).
tff(minus_type,type,
minus: ( $i * $i ) > $i ).
tff(if_minus_type,type,
if_minus: ( $i * $i * $i ) > $i ).
tff(true_type,type,
true: $i ).
tff(le_type,type,
le: ( $i * $i ) > $i ).
tff(false_type,type,
false: $i ).
tff(1,plain,
( ( log(s(zero)) = zero )
<=> ( log(s(zero)) = zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
log(s(zero)) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule10) ).
tff(3,plain,
log(s(zero)) = zero,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Y: $i] :
refl(( ( quot(zero,s(Y)) = zero )
<=> ( quot(zero,s(Y)) = zero ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [Y: $i] : ( quot(zero,s(Y)) = zero )
<=> ! [Y: $i] : ( quot(zero,s(Y)) = zero ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Y: $i] : ( quot(zero,s(Y)) = zero )
<=> ! [Y: $i] : ( quot(zero,s(Y)) = zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [Y: $i] : ( quot(zero,s(Y)) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule8) ).
tff(8,plain,
! [Y: $i] : ( quot(zero,s(Y)) = zero ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Y: $i] : ( quot(zero,s(Y)) = zero ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Y: $i] : ( quot(zero,s(Y)) = zero ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ~ ! [Y: $i] : ( quot(zero,s(Y)) = zero )
| ( quot(zero,s(s(zero))) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
quot(zero,s(s(zero))) = zero,
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
s(quot(zero,s(s(zero)))) = s(zero),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
log(s(quot(zero,s(s(zero))))) = log(s(zero)),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
log(s(quot(zero,s(s(zero))))) = zero,
inference(transitivity,[status(thm)],[14,3]) ).
tff(16,plain,
s(log(s(quot(zero,s(s(zero)))))) = s(zero),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
^ [X: $i] :
refl(( ( log(s(s(X))) = s(log(s(quot(X,s(s(zero)))))) )
<=> ( log(s(s(X))) = s(log(s(quot(X,s(s(zero)))))) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [X: $i] : ( log(s(s(X))) = s(log(s(quot(X,s(s(zero)))))) )
<=> ! [X: $i] : ( log(s(s(X))) = s(log(s(quot(X,s(s(zero)))))) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [X: $i] : ( log(s(s(X))) = s(log(s(quot(X,s(s(zero)))))) )
<=> ! [X: $i] : ( log(s(s(X))) = s(log(s(quot(X,s(s(zero)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
! [X: $i] : ( log(s(s(X))) = s(log(s(quot(X,s(s(zero)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule11) ).
tff(21,plain,
! [X: $i] : ( log(s(s(X))) = s(log(s(quot(X,s(s(zero)))))) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [X: $i] : ( log(s(s(X))) = s(log(s(quot(X,s(s(zero)))))) ),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [X: $i] : ( log(s(s(X))) = s(log(s(quot(X,s(s(zero)))))) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
( ~ ! [X: $i] : ( log(s(s(X))) = s(log(s(quot(X,s(s(zero)))))) )
| ( log(s(s(zero))) = s(log(s(quot(zero,s(s(zero)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
log(s(s(zero))) = s(log(s(quot(zero,s(s(zero)))))),
inference(unit_resolution,[status(thm)],[24,23]) ).
tff(26,plain,
^ [Y: $i,X: $i] :
refl(( ( if_minus(true,s(X),Y) = zero )
<=> ( if_minus(true,s(X),Y) = zero ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [Y: $i,X: $i] : ( if_minus(true,s(X),Y) = zero )
<=> ! [Y: $i,X: $i] : ( if_minus(true,s(X),Y) = zero ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [Y: $i,X: $i] : ( if_minus(true,s(X),Y) = zero )
<=> ! [Y: $i,X: $i] : ( if_minus(true,s(X),Y) = zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
! [Y: $i,X: $i] : ( if_minus(true,s(X),Y) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule6) ).
tff(30,plain,
! [Y: $i,X: $i] : ( if_minus(true,s(X),Y) = zero ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [Y: $i,X: $i] : ( if_minus(true,s(X),Y) = zero ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [Y: $i,X: $i] : ( if_minus(true,s(X),Y) = zero ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(true,s(X),Y) = zero )
| ( if_minus(true,s(zero),s(zero)) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
if_minus(true,s(zero),s(zero)) = zero,
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
^ [Y: $i] :
refl(( ( le(zero,Y) = true )
<=> ( le(zero,Y) = true ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [Y: $i] : ( le(zero,Y) = true )
<=> ! [Y: $i] : ( le(zero,Y) = true ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [Y: $i] : ( le(zero,Y) = true )
<=> ! [Y: $i] : ( le(zero,Y) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
! [Y: $i] : ( le(zero,Y) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule1) ).
tff(39,plain,
! [Y: $i] : ( le(zero,Y) = true ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [Y: $i] : ( le(zero,Y) = true ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [Y: $i] : ( le(zero,Y) = true ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ~ ! [Y: $i] : ( le(zero,Y) = true )
| ( le(zero,zero) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
le(zero,zero) = true,
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,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(45,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)],[44]) ).
tff(46,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(47,axiom,
! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule3) ).
tff(48,plain,
! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,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(52,plain,
le(s(zero),s(zero)) = le(zero,zero),
inference(unit_resolution,[status(thm)],[51,50]) ).
tff(53,plain,
le(s(zero),s(zero)) = true,
inference(transitivity,[status(thm)],[52,43]) ).
tff(54,plain,
if_minus(le(s(zero),s(zero)),s(zero),s(zero)) = if_minus(true,s(zero),s(zero)),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
^ [Y: $i,X: $i] :
refl(( ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
<=> ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
<=> ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
<=> ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,axiom,
! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule5) ).
tff(59,plain,
! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(zero),s(zero)) = if_minus(le(s(zero),s(zero)),s(zero),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
minus(s(zero),s(zero)) = if_minus(le(s(zero),s(zero)),s(zero),s(zero)),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
minus(s(zero),s(zero)) = zero,
inference(transitivity,[status(thm)],[63,54,34]) ).
tff(65,plain,
quot(minus(s(zero),s(zero)),s(s(zero))) = quot(zero,s(s(zero))),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
quot(minus(s(zero),s(zero)),s(s(zero))) = zero,
inference(transitivity,[status(thm)],[65,12]) ).
tff(67,plain,
s(quot(minus(s(zero),s(zero)),s(s(zero)))) = s(zero),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,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(69,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)],[68]) ).
tff(70,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(71,axiom,
! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule9) ).
tff(72,plain,
! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) ),
inference(skolemize,[status(sab)],[72]) ).
tff(74,plain,
! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) ),
inference(modus_ponens,[status(thm)],[73,69]) ).
tff(75,plain,
( ~ ! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) )
| ( quot(s(s(zero)),s(s(zero))) = s(quot(minus(s(zero),s(zero)),s(s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
quot(s(s(zero)),s(s(zero))) = s(quot(minus(s(zero),s(zero)),s(s(zero)))),
inference(unit_resolution,[status(thm)],[75,74]) ).
tff(77,plain,
( ( d(zero) = zero )
<=> ( d(zero) = zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,axiom,
d(zero) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',double1) ).
tff(79,plain,
d(zero) = zero,
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
s(d(zero)) = s(zero),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
s(zero) = s(d(zero)),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
s(s(zero)) = s(s(d(zero))),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
s(s(d(zero))) = s(s(zero)),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
^ [X: $i] :
refl(( ( d(s(X)) = s(s(d(X))) )
<=> ( d(s(X)) = s(s(d(X))) ) )),
inference(bind,[status(th)],[]) ).
tff(85,plain,
( ! [X: $i] : ( d(s(X)) = s(s(d(X))) )
<=> ! [X: $i] : ( d(s(X)) = s(s(d(X))) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,plain,
( ! [X: $i] : ( d(s(X)) = s(s(d(X))) )
<=> ! [X: $i] : ( d(s(X)) = s(s(d(X))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,axiom,
! [X: $i] : ( d(s(X)) = s(s(d(X))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',double2) ).
tff(88,plain,
! [X: $i] : ( d(s(X)) = s(s(d(X))) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [X: $i] : ( d(s(X)) = s(s(d(X))) ),
inference(skolemize,[status(sab)],[88]) ).
tff(90,plain,
! [X: $i] : ( d(s(X)) = s(s(d(X))) ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
( ~ ! [X: $i] : ( d(s(X)) = s(s(d(X))) )
| ( d(s(zero)) = s(s(d(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
d(s(zero)) = s(s(d(zero))),
inference(unit_resolution,[status(thm)],[91,90]) ).
tff(93,plain,
( ( e(zero) = s(zero) )
<=> ( e(zero) = s(zero) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,axiom,
e(zero) = s(zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exp1) ).
tff(95,plain,
e(zero) = s(zero),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
s(zero) = e(zero),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
d(s(zero)) = d(e(zero)),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
d(e(zero)) = d(s(zero)),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
d(e(zero)) = s(s(zero)),
inference(transitivity,[status(thm)],[98,92,83]) ).
tff(100,plain,
quot(d(e(zero)),s(s(zero))) = quot(s(s(zero)),s(s(zero))),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
quot(d(e(zero)),s(s(zero))) = s(zero),
inference(transitivity,[status(thm)],[100,76,67]) ).
tff(102,plain,
s(quot(d(e(zero)),s(s(zero)))) = s(s(zero)),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
log(s(quot(d(e(zero)),s(s(zero))))) = log(s(s(zero))),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
log(s(quot(d(e(zero)),s(s(zero))))) = s(zero),
inference(transitivity,[status(thm)],[103,25,16]) ).
tff(105,plain,
s(log(s(quot(d(e(zero)),s(s(zero)))))) = s(s(zero)),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
( ~ ! [X: $i] : ( log(s(s(X))) = s(log(s(quot(X,s(s(zero)))))) )
| ( log(s(s(d(e(zero))))) = s(log(s(quot(d(e(zero)),s(s(zero)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(107,plain,
log(s(s(d(e(zero))))) = s(log(s(quot(d(e(zero)),s(s(zero)))))),
inference(unit_resolution,[status(thm)],[106,23]) ).
tff(108,plain,
s(d(e(zero))) = s(s(s(zero))),
inference(monotonicity,[status(thm)],[99]) ).
tff(109,plain,
s(s(d(e(zero)))) = s(s(s(s(zero)))),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
s(s(s(s(zero)))) = s(s(d(e(zero)))),
inference(symmetry,[status(thm)],[109]) ).
tff(111,plain,
s(s(d(zero))) = d(s(zero)),
inference(symmetry,[status(thm)],[92]) ).
tff(112,plain,
s(minus(s(zero),s(zero))) = s(zero),
inference(monotonicity,[status(thm)],[64]) ).
tff(113,plain,
^ [Y: $i,X: $i] :
refl(( ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
<=> ( if_minus(false,s(X),Y) = s(minus(X,Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(114,plain,
( ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
<=> ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,plain,
( ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
<=> ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,axiom,
! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule7) ).
tff(117,plain,
! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) ),
inference(skolemize,[status(sab)],[117]) ).
tff(119,plain,
! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) ),
inference(modus_ponens,[status(thm)],[118,114]) ).
tff(120,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(s(zero)),s(zero)) = s(minus(s(zero),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(121,plain,
if_minus(false,s(s(zero)),s(zero)) = s(minus(s(zero),s(zero))),
inference(unit_resolution,[status(thm)],[120,119]) ).
tff(122,plain,
^ [X: $i] :
refl(( ( le(s(X),zero) = false )
<=> ( le(s(X),zero) = false ) )),
inference(bind,[status(th)],[]) ).
tff(123,plain,
( ! [X: $i] : ( le(s(X),zero) = false )
<=> ! [X: $i] : ( le(s(X),zero) = false ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,plain,
( ! [X: $i] : ( le(s(X),zero) = false )
<=> ! [X: $i] : ( le(s(X),zero) = false ) ),
inference(rewrite,[status(thm)],[]) ).
tff(125,axiom,
! [X: $i] : ( le(s(X),zero) = false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule2) ).
tff(126,plain,
! [X: $i] : ( le(s(X),zero) = false ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
! [X: $i] : ( le(s(X),zero) = false ),
inference(skolemize,[status(sab)],[126]) ).
tff(128,plain,
! [X: $i] : ( le(s(X),zero) = false ),
inference(modus_ponens,[status(thm)],[127,123]) ).
tff(129,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(zero),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(130,plain,
le(s(zero),zero) = false,
inference(unit_resolution,[status(thm)],[129,128]) ).
tff(131,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(132,plain,
le(s(s(zero)),s(zero)) = le(s(zero),zero),
inference(unit_resolution,[status(thm)],[131,50]) ).
tff(133,plain,
le(s(s(zero)),s(zero)) = false,
inference(transitivity,[status(thm)],[132,130]) ).
tff(134,plain,
if_minus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)) = if_minus(false,s(s(zero)),s(zero)),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(zero)),s(zero)) = if_minus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(136,plain,
minus(s(s(zero)),s(zero)) = if_minus(le(s(s(zero)),s(zero)),s(s(zero)),s(zero)),
inference(unit_resolution,[status(thm)],[135,61]) ).
tff(137,plain,
minus(d(e(zero)),s(zero)) = minus(s(s(zero)),s(zero)),
inference(monotonicity,[status(thm)],[99]) ).
tff(138,plain,
minus(d(e(zero)),s(zero)) = s(zero),
inference(transitivity,[status(thm)],[137,136,134,121,112]) ).
tff(139,plain,
s(minus(d(e(zero)),s(zero))) = s(s(zero)),
inference(monotonicity,[status(thm)],[138]) ).
tff(140,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(d(e(zero))),s(zero)) = s(minus(d(e(zero)),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(141,plain,
if_minus(false,s(d(e(zero))),s(zero)) = s(minus(d(e(zero)),s(zero))),
inference(unit_resolution,[status(thm)],[140,119]) ).
tff(142,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(zero)),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(143,plain,
le(s(s(zero)),zero) = false,
inference(unit_resolution,[status(thm)],[142,128]) ).
tff(144,plain,
le(d(e(zero)),zero) = le(s(s(zero)),zero),
inference(monotonicity,[status(thm)],[99]) ).
tff(145,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(d(e(zero))),s(zero)) = le(d(e(zero)),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(146,plain,
le(s(d(e(zero))),s(zero)) = le(d(e(zero)),zero),
inference(unit_resolution,[status(thm)],[145,50]) ).
tff(147,plain,
le(s(d(e(zero))),s(zero)) = false,
inference(transitivity,[status(thm)],[146,144,143]) ).
tff(148,plain,
if_minus(le(s(d(e(zero))),s(zero)),s(d(e(zero))),s(zero)) = if_minus(false,s(d(e(zero))),s(zero)),
inference(monotonicity,[status(thm)],[147]) ).
tff(149,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(d(e(zero))),s(zero)) = if_minus(le(s(d(e(zero))),s(zero)),s(d(e(zero))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(150,plain,
minus(s(d(e(zero))),s(zero)) = if_minus(le(s(d(e(zero))),s(zero)),s(d(e(zero))),s(zero)),
inference(unit_resolution,[status(thm)],[149,61]) ).
tff(151,plain,
s(s(s(zero))) = s(d(e(zero))),
inference(symmetry,[status(thm)],[108]) ).
tff(152,plain,
minus(s(s(s(zero))),s(zero)) = minus(s(d(e(zero))),s(zero)),
inference(monotonicity,[status(thm)],[151]) ).
tff(153,plain,
minus(s(s(s(zero))),s(zero)) = d(e(zero)),
inference(transitivity,[status(thm)],[152,150,148,141,139,82,111,97]) ).
tff(154,plain,
quot(minus(s(s(s(zero))),s(zero)),s(s(zero))) = quot(d(e(zero)),s(s(zero))),
inference(monotonicity,[status(thm)],[153]) ).
tff(155,plain,
quot(minus(s(s(s(zero))),s(zero)),s(s(zero))) = s(zero),
inference(transitivity,[status(thm)],[154,100,76,67]) ).
tff(156,plain,
s(quot(minus(s(s(s(zero))),s(zero)),s(s(zero)))) = s(s(zero)),
inference(monotonicity,[status(thm)],[155]) ).
tff(157,plain,
( ~ ! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) )
| ( quot(s(s(s(s(zero)))),s(s(zero))) = s(quot(minus(s(s(s(zero))),s(zero)),s(s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(158,plain,
quot(s(s(s(s(zero)))),s(s(zero))) = s(quot(minus(s(s(s(zero))),s(zero)),s(s(zero)))),
inference(unit_resolution,[status(thm)],[157,74]) ).
tff(159,plain,
d(s(zero)) = s(s(zero)),
inference(transitivity,[status(thm)],[92,83]) ).
tff(160,plain,
s(d(s(zero))) = s(s(s(zero))),
inference(monotonicity,[status(thm)],[159]) ).
tff(161,plain,
s(s(s(zero))) = s(d(s(zero))),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
s(s(s(s(zero)))) = s(s(d(s(zero)))),
inference(monotonicity,[status(thm)],[161]) ).
tff(163,plain,
s(s(d(s(zero)))) = s(s(s(s(zero)))),
inference(symmetry,[status(thm)],[162]) ).
tff(164,plain,
quot(s(s(d(s(zero)))),s(s(zero))) = quot(s(s(s(s(zero)))),s(s(zero))),
inference(monotonicity,[status(thm)],[163]) ).
tff(165,plain,
minus(s(s(s(zero))),s(zero)) = s(s(zero)),
inference(transitivity,[status(thm)],[152,150,148,141,139]) ).
tff(166,plain,
s(minus(s(s(s(zero))),s(zero))) = s(s(s(zero))),
inference(monotonicity,[status(thm)],[165]) ).
tff(167,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(s(s(s(zero)))),s(zero)) = s(minus(s(s(s(zero))),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(168,plain,
if_minus(false,s(s(s(s(zero)))),s(zero)) = s(minus(s(s(s(zero))),s(zero))),
inference(unit_resolution,[status(thm)],[167,119]) ).
tff(169,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(d(e(zero))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(170,plain,
le(s(d(e(zero))),zero) = false,
inference(unit_resolution,[status(thm)],[169,128]) ).
tff(171,plain,
le(s(s(s(zero))),zero) = le(s(d(e(zero))),zero),
inference(monotonicity,[status(thm)],[151]) ).
tff(172,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(173,plain,
le(s(s(s(s(zero)))),s(zero)) = le(s(s(s(zero))),zero),
inference(unit_resolution,[status(thm)],[172,50]) ).
tff(174,plain,
le(s(s(s(s(zero)))),s(zero)) = false,
inference(transitivity,[status(thm)],[173,171,170]) ).
tff(175,plain,
if_minus(le(s(s(s(s(zero)))),s(zero)),s(s(s(s(zero)))),s(zero)) = if_minus(false,s(s(s(s(zero)))),s(zero)),
inference(monotonicity,[status(thm)],[174]) ).
tff(176,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(s(s(zero)))),s(zero)) = if_minus(le(s(s(s(s(zero)))),s(zero)),s(s(s(s(zero)))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(177,plain,
minus(s(s(s(s(zero)))),s(zero)) = if_minus(le(s(s(s(s(zero)))),s(zero)),s(s(s(s(zero)))),s(zero)),
inference(unit_resolution,[status(thm)],[176,61]) ).
tff(178,plain,
minus(s(s(d(s(zero)))),s(zero)) = minus(s(s(s(s(zero)))),s(zero)),
inference(monotonicity,[status(thm)],[163]) ).
tff(179,plain,
minus(s(s(d(s(zero)))),s(zero)) = s(s(s(zero))),
inference(transitivity,[status(thm)],[178,177,175,168,166]) ).
tff(180,plain,
s(minus(s(s(d(s(zero)))),s(zero))) = s(s(s(s(zero)))),
inference(monotonicity,[status(thm)],[179]) ).
tff(181,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(s(s(d(s(zero))))),s(zero)) = s(minus(s(s(d(s(zero)))),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(182,plain,
if_minus(false,s(s(s(d(s(zero))))),s(zero)) = s(minus(s(s(d(s(zero)))),s(zero))),
inference(unit_resolution,[status(thm)],[181,119]) ).
tff(183,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(s(s(zero)))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(184,plain,
le(s(s(s(s(zero)))),zero) = false,
inference(unit_resolution,[status(thm)],[183,128]) ).
tff(185,plain,
le(s(s(d(s(zero)))),zero) = le(s(s(s(s(zero)))),zero),
inference(monotonicity,[status(thm)],[163]) ).
tff(186,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(187,plain,
le(s(s(s(d(s(zero))))),s(zero)) = le(s(s(d(s(zero)))),zero),
inference(unit_resolution,[status(thm)],[186,50]) ).
tff(188,plain,
le(s(s(s(d(s(zero))))),s(zero)) = false,
inference(transitivity,[status(thm)],[187,185,184]) ).
tff(189,plain,
if_minus(le(s(s(s(d(s(zero))))),s(zero)),s(s(s(d(s(zero))))),s(zero)) = if_minus(false,s(s(s(d(s(zero))))),s(zero)),
inference(monotonicity,[status(thm)],[188]) ).
tff(190,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(s(d(s(zero))))),s(zero)) = if_minus(le(s(s(s(d(s(zero))))),s(zero)),s(s(s(d(s(zero))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(191,plain,
minus(s(s(s(d(s(zero))))),s(zero)) = if_minus(le(s(s(s(d(s(zero))))),s(zero)),s(s(s(d(s(zero))))),s(zero)),
inference(unit_resolution,[status(thm)],[190,61]) ).
tff(192,plain,
d(d(e(zero))) = d(s(s(zero))),
inference(monotonicity,[status(thm)],[99]) ).
tff(193,plain,
d(s(s(zero))) = d(d(e(zero))),
inference(symmetry,[status(thm)],[192]) ).
tff(194,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(195,plain,
d(s(s(zero))) = s(s(d(s(zero)))),
inference(unit_resolution,[status(thm)],[194,90]) ).
tff(196,plain,
s(s(d(s(zero)))) = d(s(s(zero))),
inference(symmetry,[status(thm)],[195]) ).
tff(197,plain,
s(s(d(s(zero)))) = d(d(e(zero))),
inference(transitivity,[status(thm)],[196,193]) ).
tff(198,plain,
s(s(s(d(s(zero))))) = s(d(d(e(zero)))),
inference(monotonicity,[status(thm)],[197]) ).
tff(199,plain,
s(d(d(e(zero)))) = s(s(s(d(s(zero))))),
inference(symmetry,[status(thm)],[198]) ).
tff(200,plain,
minus(s(s(d(s(zero)))),zero) = minus(s(s(s(s(zero)))),zero),
inference(monotonicity,[status(thm)],[163]) ).
tff(201,plain,
minus(s(s(s(s(zero)))),zero) = minus(s(s(d(s(zero)))),zero),
inference(symmetry,[status(thm)],[200]) ).
tff(202,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(s(s(zero)))),zero) = if_minus(le(s(s(s(s(zero)))),zero),s(s(s(s(zero)))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(203,plain,
minus(s(s(s(s(zero)))),zero) = if_minus(le(s(s(s(s(zero)))),zero),s(s(s(s(zero)))),zero),
inference(unit_resolution,[status(thm)],[202,61]) ).
tff(204,plain,
if_minus(le(s(s(s(s(zero)))),zero),s(s(s(s(zero)))),zero) = minus(s(s(s(s(zero)))),zero),
inference(symmetry,[status(thm)],[203]) ).
tff(205,plain,
if_minus(le(s(s(s(s(zero)))),zero),s(s(s(s(zero)))),zero) = if_minus(false,s(s(s(s(zero)))),zero),
inference(monotonicity,[status(thm)],[184]) ).
tff(206,plain,
if_minus(false,s(s(s(s(zero)))),zero) = if_minus(le(s(s(s(s(zero)))),zero),s(s(s(s(zero)))),zero),
inference(symmetry,[status(thm)],[205]) ).
tff(207,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(s(s(s(zero)))),zero) = s(minus(s(s(s(zero))),zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(208,plain,
if_minus(false,s(s(s(s(zero)))),zero) = s(minus(s(s(s(zero))),zero)),
inference(unit_resolution,[status(thm)],[207,119]) ).
tff(209,plain,
s(minus(s(s(s(zero))),zero)) = if_minus(false,s(s(s(s(zero)))),zero),
inference(symmetry,[status(thm)],[208]) ).
tff(210,plain,
^ [Y: $i] :
refl(( ( minus(zero,Y) = zero )
<=> ( minus(zero,Y) = zero ) )),
inference(bind,[status(th)],[]) ).
tff(211,plain,
( ! [Y: $i] : ( minus(zero,Y) = zero )
<=> ! [Y: $i] : ( minus(zero,Y) = zero ) ),
inference(quant_intro,[status(thm)],[210]) ).
tff(212,plain,
( ! [Y: $i] : ( minus(zero,Y) = zero )
<=> ! [Y: $i] : ( minus(zero,Y) = zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(213,axiom,
! [Y: $i] : ( minus(zero,Y) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule4) ).
tff(214,plain,
! [Y: $i] : ( minus(zero,Y) = zero ),
inference(modus_ponens,[status(thm)],[213,212]) ).
tff(215,plain,
! [Y: $i] : ( minus(zero,Y) = zero ),
inference(skolemize,[status(sab)],[214]) ).
tff(216,plain,
! [Y: $i] : ( minus(zero,Y) = zero ),
inference(modus_ponens,[status(thm)],[215,211]) ).
tff(217,plain,
( ~ ! [Y: $i] : ( minus(zero,Y) = zero )
| ( minus(zero,zero) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(218,plain,
minus(zero,zero) = zero,
inference(unit_resolution,[status(thm)],[217,216]) ).
tff(219,plain,
s(minus(zero,zero)) = s(zero),
inference(monotonicity,[status(thm)],[218]) ).
tff(220,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(zero),zero) = s(minus(zero,zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(221,plain,
if_minus(false,s(zero),zero) = s(minus(zero,zero)),
inference(unit_resolution,[status(thm)],[220,119]) ).
tff(222,plain,
if_minus(le(s(zero),zero),s(zero),zero) = if_minus(false,s(zero),zero),
inference(monotonicity,[status(thm)],[130]) ).
tff(223,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(zero),zero) = if_minus(le(s(zero),zero),s(zero),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(224,plain,
minus(s(zero),zero) = if_minus(le(s(zero),zero),s(zero),zero),
inference(unit_resolution,[status(thm)],[223,61]) ).
tff(225,plain,
minus(s(zero),zero) = s(zero),
inference(transitivity,[status(thm)],[224,222,221,219]) ).
tff(226,plain,
s(minus(s(zero),zero)) = s(s(zero)),
inference(monotonicity,[status(thm)],[225]) ).
tff(227,plain,
if_minus(le(s(zero),zero),s(zero),zero) = minus(s(zero),zero),
inference(symmetry,[status(thm)],[224]) ).
tff(228,plain,
s(if_minus(le(s(zero),zero),s(zero),zero)) = s(minus(s(zero),zero)),
inference(monotonicity,[status(thm)],[227]) ).
tff(229,plain,
s(if_minus(le(s(zero),zero),s(zero),zero)) = s(s(zero)),
inference(transitivity,[status(thm)],[228,226]) ).
tff(230,plain,
s(s(if_minus(le(s(zero),zero),s(zero),zero))) = s(s(s(zero))),
inference(monotonicity,[status(thm)],[229]) ).
tff(231,plain,
s(minus(s(zero),zero)) = s(if_minus(le(s(zero),zero),s(zero),zero)),
inference(symmetry,[status(thm)],[228]) ).
tff(232,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(s(zero)),zero) = s(minus(s(zero),zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(233,plain,
if_minus(false,s(s(zero)),zero) = s(minus(s(zero),zero)),
inference(unit_resolution,[status(thm)],[232,119]) ).
tff(234,plain,
if_minus(le(s(s(zero)),zero),s(s(zero)),zero) = if_minus(false,s(s(zero)),zero),
inference(monotonicity,[status(thm)],[143]) ).
tff(235,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(zero)),zero) = if_minus(le(s(s(zero)),zero),s(s(zero)),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(236,plain,
minus(s(s(zero)),zero) = if_minus(le(s(s(zero)),zero),s(s(zero)),zero),
inference(unit_resolution,[status(thm)],[235,61]) ).
tff(237,plain,
minus(d(e(zero)),zero) = minus(s(s(zero)),zero),
inference(monotonicity,[status(thm)],[99]) ).
tff(238,plain,
minus(d(e(zero)),zero) = s(if_minus(le(s(zero),zero),s(zero),zero)),
inference(transitivity,[status(thm)],[237,236,234,233,231]) ).
tff(239,plain,
s(minus(d(e(zero)),zero)) = s(s(if_minus(le(s(zero),zero),s(zero),zero))),
inference(monotonicity,[status(thm)],[238]) ).
tff(240,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(d(e(zero))),zero) = s(minus(d(e(zero)),zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(241,plain,
if_minus(false,s(d(e(zero))),zero) = s(minus(d(e(zero)),zero)),
inference(unit_resolution,[status(thm)],[240,119]) ).
tff(242,plain,
if_minus(le(s(d(e(zero))),zero),s(d(e(zero))),zero) = if_minus(false,s(d(e(zero))),zero),
inference(monotonicity,[status(thm)],[170]) ).
tff(243,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(d(e(zero))),zero) = if_minus(le(s(d(e(zero))),zero),s(d(e(zero))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(244,plain,
minus(s(d(e(zero))),zero) = if_minus(le(s(d(e(zero))),zero),s(d(e(zero))),zero),
inference(unit_resolution,[status(thm)],[243,61]) ).
tff(245,plain,
minus(s(s(s(zero))),zero) = minus(s(d(e(zero))),zero),
inference(monotonicity,[status(thm)],[151]) ).
tff(246,plain,
minus(s(s(s(zero))),zero) = s(s(s(zero))),
inference(transitivity,[status(thm)],[245,244,242,241,239,230]) ).
tff(247,plain,
s(minus(s(s(s(zero))),zero)) = s(s(s(s(zero)))),
inference(monotonicity,[status(thm)],[246]) ).
tff(248,plain,
s(s(s(s(zero)))) = s(minus(s(s(s(zero))),zero)),
inference(symmetry,[status(thm)],[247]) ).
tff(249,plain,
d(d(e(zero))) = minus(s(s(d(s(zero)))),zero),
inference(transitivity,[status(thm)],[192,195,163,248,209,206,204,201]) ).
tff(250,plain,
s(d(d(e(zero)))) = s(minus(s(s(d(s(zero)))),zero)),
inference(monotonicity,[status(thm)],[249]) ).
tff(251,plain,
s(minus(s(s(d(s(zero)))),zero)) = s(d(d(e(zero)))),
inference(symmetry,[status(thm)],[250]) ).
tff(252,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(s(s(d(s(zero))))),zero) = s(minus(s(s(d(s(zero)))),zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(253,plain,
if_minus(false,s(s(s(d(s(zero))))),zero) = s(minus(s(s(d(s(zero)))),zero)),
inference(unit_resolution,[status(thm)],[252,119]) ).
tff(254,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(s(d(s(zero))))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(255,plain,
le(s(s(s(d(s(zero))))),zero) = false,
inference(unit_resolution,[status(thm)],[254,128]) ).
tff(256,plain,
false = le(s(s(s(d(s(zero))))),zero),
inference(symmetry,[status(thm)],[255]) ).
tff(257,plain,
if_minus(false,s(s(s(d(s(zero))))),zero) = if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero),
inference(monotonicity,[status(thm)],[256]) ).
tff(258,plain,
if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero) = if_minus(false,s(s(s(d(s(zero))))),zero),
inference(symmetry,[status(thm)],[257]) ).
tff(259,plain,
if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero) = s(s(s(d(s(zero))))),
inference(transitivity,[status(thm)],[258,253,251,199]) ).
tff(260,plain,
minus(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero),s(zero)) = minus(s(s(s(d(s(zero))))),s(zero)),
inference(monotonicity,[status(thm)],[259]) ).
tff(261,plain,
minus(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero),s(zero)) = s(s(d(s(zero)))),
inference(transitivity,[status(thm)],[260,191,189,182,180,162]) ).
tff(262,plain,
quot(minus(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero),s(zero)),s(s(zero))) = quot(s(s(d(s(zero)))),s(s(zero))),
inference(monotonicity,[status(thm)],[261]) ).
tff(263,plain,
quot(minus(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero),s(zero)),s(s(zero))) = s(s(zero)),
inference(transitivity,[status(thm)],[262,164,158,156]) ).
tff(264,plain,
s(quot(minus(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero),s(zero)),s(s(zero)))) = s(s(s(zero))),
inference(monotonicity,[status(thm)],[263]) ).
tff(265,plain,
( ~ ! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) )
| ( quot(s(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero)),s(s(zero))) = s(quot(minus(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero),s(zero)),s(s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(266,plain,
quot(s(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero)),s(s(zero))) = s(quot(minus(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero),s(zero)),s(s(zero)))),
inference(unit_resolution,[status(thm)],[265,74]) ).
tff(267,plain,
if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero) = s(d(d(e(zero)))),
inference(transitivity,[status(thm)],[258,253,251]) ).
tff(268,plain,
s(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero)) = s(s(d(d(e(zero))))),
inference(monotonicity,[status(thm)],[267]) ).
tff(269,plain,
s(s(d(d(e(zero))))) = s(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero)),
inference(symmetry,[status(thm)],[268]) ).
tff(270,plain,
quot(s(s(d(d(e(zero))))),s(s(zero))) = quot(s(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero)),s(s(zero))),
inference(monotonicity,[status(thm)],[269]) ).
tff(271,plain,
quot(s(s(d(d(e(zero))))),s(s(zero))) = s(s(s(zero))),
inference(transitivity,[status(thm)],[270,266,264]) ).
tff(272,plain,
s(quot(s(s(d(d(e(zero))))),s(s(zero)))) = s(s(s(s(zero)))),
inference(monotonicity,[status(thm)],[271]) ).
tff(273,plain,
s(quot(s(s(d(d(e(zero))))),s(s(zero)))) = s(s(d(e(zero)))),
inference(transitivity,[status(thm)],[272,110]) ).
tff(274,plain,
log(s(quot(s(s(d(d(e(zero))))),s(s(zero))))) = log(s(s(d(e(zero))))),
inference(monotonicity,[status(thm)],[273]) ).
tff(275,plain,
log(s(quot(s(s(d(d(e(zero))))),s(s(zero))))) = s(s(zero)),
inference(transitivity,[status(thm)],[274,107,105]) ).
tff(276,plain,
s(log(s(quot(s(s(d(d(e(zero))))),s(s(zero)))))) = s(s(s(zero))),
inference(monotonicity,[status(thm)],[275]) ).
tff(277,plain,
( ~ ! [X: $i] : ( log(s(s(X))) = s(log(s(quot(X,s(s(zero)))))) )
| ( log(s(s(s(s(d(d(e(zero)))))))) = s(log(s(quot(s(s(d(d(e(zero))))),s(s(zero)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(278,plain,
log(s(s(s(s(d(d(e(zero)))))))) = s(log(s(quot(s(s(d(d(e(zero))))),s(s(zero)))))),
inference(unit_resolution,[status(thm)],[277,23]) ).
tff(279,plain,
d(s(s(s(zero)))) = d(s(d(e(zero)))),
inference(monotonicity,[status(thm)],[151]) ).
tff(280,plain,
d(s(d(e(zero)))) = d(s(s(s(zero)))),
inference(symmetry,[status(thm)],[279]) ).
tff(281,plain,
( ~ ! [X: $i] : ( d(s(X)) = s(s(d(X))) )
| ( d(s(d(e(zero)))) = s(s(d(d(e(zero))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(282,plain,
d(s(d(e(zero)))) = s(s(d(d(e(zero))))),
inference(unit_resolution,[status(thm)],[281,90]) ).
tff(283,plain,
s(s(d(d(e(zero))))) = d(s(d(e(zero)))),
inference(symmetry,[status(thm)],[282]) ).
tff(284,plain,
s(s(d(d(e(zero))))) = d(s(s(s(zero)))),
inference(transitivity,[status(thm)],[283,280]) ).
tff(285,plain,
s(s(s(d(d(e(zero)))))) = s(d(s(s(s(zero))))),
inference(monotonicity,[status(thm)],[284]) ).
tff(286,plain,
s(s(s(s(d(d(e(zero))))))) = s(s(d(s(s(s(zero)))))),
inference(monotonicity,[status(thm)],[285]) ).
tff(287,plain,
s(s(d(s(s(s(zero)))))) = s(s(s(s(d(d(e(zero))))))),
inference(symmetry,[status(thm)],[286]) ).
tff(288,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(289,plain,
d(s(s(s(s(zero))))) = s(s(d(s(s(s(zero)))))),
inference(unit_resolution,[status(thm)],[288,90]) ).
tff(290,plain,
e(d(e(zero))) = e(s(s(zero))),
inference(monotonicity,[status(thm)],[99]) ).
tff(291,plain,
e(s(s(zero))) = e(d(e(zero))),
inference(symmetry,[status(thm)],[290]) ).
tff(292,plain,
^ [X: $i] :
refl(( ( e(s(X)) = d(e(X)) )
<=> ( e(s(X)) = d(e(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(293,plain,
( ! [X: $i] : ( e(s(X)) = d(e(X)) )
<=> ! [X: $i] : ( e(s(X)) = d(e(X)) ) ),
inference(quant_intro,[status(thm)],[292]) ).
tff(294,plain,
( ! [X: $i] : ( e(s(X)) = d(e(X)) )
<=> ! [X: $i] : ( e(s(X)) = d(e(X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(295,axiom,
! [X: $i] : ( e(s(X)) = d(e(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exp2) ).
tff(296,plain,
! [X: $i] : ( e(s(X)) = d(e(X)) ),
inference(modus_ponens,[status(thm)],[295,294]) ).
tff(297,plain,
! [X: $i] : ( e(s(X)) = d(e(X)) ),
inference(skolemize,[status(sab)],[296]) ).
tff(298,plain,
! [X: $i] : ( e(s(X)) = d(e(X)) ),
inference(modus_ponens,[status(thm)],[297,293]) ).
tff(299,plain,
( ~ ! [X: $i] : ( e(s(X)) = d(e(X)) )
| ( e(s(s(zero))) = d(e(s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(300,plain,
e(s(s(zero))) = d(e(s(zero))),
inference(unit_resolution,[status(thm)],[299,298]) ).
tff(301,plain,
d(e(s(zero))) = e(s(s(zero))),
inference(symmetry,[status(thm)],[300]) ).
tff(302,plain,
( ~ ! [X: $i] : ( e(s(X)) = d(e(X)) )
| ( e(s(zero)) = d(e(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(303,plain,
e(s(zero)) = d(e(zero)),
inference(unit_resolution,[status(thm)],[302,298]) ).
tff(304,plain,
e(s(zero)) = s(s(zero)),
inference(transitivity,[status(thm)],[303,98,92,83]) ).
tff(305,plain,
d(e(s(zero))) = d(s(s(zero))),
inference(monotonicity,[status(thm)],[304]) ).
tff(306,plain,
d(s(s(zero))) = d(e(s(zero))),
inference(symmetry,[status(thm)],[305]) ).
tff(307,plain,
s(s(s(s(zero)))) = e(d(e(zero))),
inference(transitivity,[status(thm)],[162,196,306,301,291]) ).
tff(308,plain,
d(s(s(s(s(zero))))) = d(e(d(e(zero)))),
inference(monotonicity,[status(thm)],[307]) ).
tff(309,plain,
d(e(d(e(zero)))) = d(s(s(s(s(zero))))),
inference(symmetry,[status(thm)],[308]) ).
tff(310,plain,
( ~ ! [X: $i] : ( e(s(X)) = d(e(X)) )
| ( e(s(d(e(zero)))) = d(e(d(e(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(311,plain,
e(s(d(e(zero)))) = d(e(d(e(zero)))),
inference(unit_resolution,[status(thm)],[310,298]) ).
tff(312,plain,
e(s(s(s(zero)))) = e(s(d(e(zero)))),
inference(monotonicity,[status(thm)],[151]) ).
tff(313,plain,
e(s(s(s(zero)))) = s(s(s(s(d(d(e(zero))))))),
inference(transitivity,[status(thm)],[312,311,309,289,287]) ).
tff(314,plain,
log(e(s(s(s(zero))))) = log(s(s(s(s(d(d(e(zero)))))))),
inference(monotonicity,[status(thm)],[313]) ).
tff(315,plain,
e(s(d(e(zero)))) = e(s(s(s(zero)))),
inference(symmetry,[status(thm)],[312]) ).
tff(316,plain,
d(e(d(e(zero)))) = e(s(d(e(zero)))),
inference(symmetry,[status(thm)],[311]) ).
tff(317,plain,
s(s(d(s(s(s(zero)))))) = d(s(s(s(s(zero))))),
inference(symmetry,[status(thm)],[289]) ).
tff(318,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(d(d(e(zero))))),zero) = if_minus(le(s(s(d(d(e(zero))))),zero),s(s(d(d(e(zero))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(319,plain,
minus(s(s(d(d(e(zero))))),zero) = if_minus(le(s(s(d(d(e(zero))))),zero),s(s(d(d(e(zero))))),zero),
inference(unit_resolution,[status(thm)],[318,61]) ).
tff(320,plain,
if_minus(le(s(s(d(d(e(zero))))),zero),s(s(d(d(e(zero))))),zero) = minus(s(s(d(d(e(zero))))),zero),
inference(symmetry,[status(thm)],[319]) ).
tff(321,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(d(d(e(zero))))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(322,plain,
le(s(s(d(d(e(zero))))),zero) = false,
inference(unit_resolution,[status(thm)],[321,128]) ).
tff(323,plain,
if_minus(le(s(s(d(d(e(zero))))),zero),s(s(d(d(e(zero))))),zero) = if_minus(false,s(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero)),zero),
inference(monotonicity,[status(thm)],[322,269]) ).
tff(324,plain,
if_minus(false,s(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero)),zero) = if_minus(le(s(s(d(d(e(zero))))),zero),s(s(d(d(e(zero))))),zero),
inference(symmetry,[status(thm)],[323]) ).
tff(325,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero)),zero) = s(minus(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero),zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(326,plain,
if_minus(false,s(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero)),zero) = s(minus(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero),zero)),
inference(unit_resolution,[status(thm)],[325,119]) ).
tff(327,plain,
s(minus(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero),zero)) = if_minus(false,s(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero)),zero),
inference(symmetry,[status(thm)],[326]) ).
tff(328,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(s(d(s(zero))))),zero) = if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(329,plain,
minus(s(s(s(d(s(zero))))),zero) = if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero),
inference(unit_resolution,[status(thm)],[328,61]) ).
tff(330,plain,
minus(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero),zero) = minus(s(s(s(d(s(zero))))),zero),
inference(monotonicity,[status(thm)],[259]) ).
tff(331,plain,
minus(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero),zero) = s(d(d(e(zero)))),
inference(transitivity,[status(thm)],[330,329,258,253,251]) ).
tff(332,plain,
s(minus(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero),zero)) = s(s(d(d(e(zero))))),
inference(monotonicity,[status(thm)],[331]) ).
tff(333,plain,
s(s(d(d(e(zero))))) = s(minus(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero),zero)),
inference(symmetry,[status(thm)],[332]) ).
tff(334,plain,
d(s(s(s(zero)))) = minus(s(s(d(d(e(zero))))),zero),
inference(transitivity,[status(thm)],[279,282,333,327,324,320]) ).
tff(335,plain,
s(d(s(s(s(zero))))) = s(minus(s(s(d(d(e(zero))))),zero)),
inference(monotonicity,[status(thm)],[334]) ).
tff(336,plain,
s(minus(s(s(d(d(e(zero))))),zero)) = s(d(s(s(s(zero))))),
inference(symmetry,[status(thm)],[335]) ).
tff(337,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(s(s(d(d(e(zero)))))),zero) = s(minus(s(s(d(d(e(zero))))),zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(338,plain,
if_minus(false,s(s(s(d(d(e(zero)))))),zero) = s(minus(s(s(d(d(e(zero))))),zero)),
inference(unit_resolution,[status(thm)],[337,119]) ).
tff(339,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(s(d(d(e(zero)))))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(340,plain,
le(s(s(s(d(d(e(zero)))))),zero) = false,
inference(unit_resolution,[status(thm)],[339,128]) ).
tff(341,plain,
false = le(s(s(s(d(d(e(zero)))))),zero),
inference(symmetry,[status(thm)],[340]) ).
tff(342,plain,
if_minus(false,s(s(s(d(d(e(zero)))))),zero) = if_minus(le(s(s(s(d(d(e(zero)))))),zero),s(s(s(d(d(e(zero)))))),zero),
inference(monotonicity,[status(thm)],[341]) ).
tff(343,plain,
if_minus(le(s(s(s(d(d(e(zero)))))),zero),s(s(s(d(d(e(zero)))))),zero) = if_minus(false,s(s(s(d(d(e(zero)))))),zero),
inference(symmetry,[status(thm)],[342]) ).
tff(344,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(s(d(d(e(zero)))))),zero) = if_minus(le(s(s(s(d(d(e(zero)))))),zero),s(s(s(d(d(e(zero)))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(345,plain,
minus(s(s(s(d(d(e(zero)))))),zero) = if_minus(le(s(s(s(d(d(e(zero)))))),zero),s(s(s(d(d(e(zero)))))),zero),
inference(unit_resolution,[status(thm)],[344,61]) ).
tff(346,plain,
s(d(s(s(s(zero))))) = s(s(s(d(d(e(zero)))))),
inference(symmetry,[status(thm)],[285]) ).
tff(347,plain,
minus(s(d(s(s(s(zero))))),zero) = minus(s(s(s(d(d(e(zero)))))),zero),
inference(monotonicity,[status(thm)],[346]) ).
tff(348,plain,
minus(s(d(s(s(s(zero))))),zero) = s(d(s(s(s(zero))))),
inference(transitivity,[status(thm)],[347,345,343,338,336]) ).
tff(349,plain,
s(minus(s(d(s(s(s(zero))))),zero)) = s(s(d(s(s(s(zero)))))),
inference(monotonicity,[status(thm)],[348]) ).
tff(350,plain,
minus(s(s(s(d(d(e(zero)))))),zero) = minus(s(d(s(s(s(zero))))),zero),
inference(symmetry,[status(thm)],[347]) ).
tff(351,plain,
if_minus(le(s(s(s(d(d(e(zero)))))),zero),s(s(s(d(d(e(zero)))))),zero) = minus(s(s(s(d(d(e(zero)))))),zero),
inference(symmetry,[status(thm)],[345]) ).
tff(352,plain,
s(minus(s(s(d(d(e(zero))))),zero)) = if_minus(false,s(s(s(d(d(e(zero)))))),zero),
inference(symmetry,[status(thm)],[338]) ).
tff(353,plain,
minus(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero),s(zero)) = d(d(e(zero))),
inference(transitivity,[status(thm)],[260,191,189,182,180,162,196,193]) ).
tff(354,plain,
s(minus(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero),s(zero))) = s(d(d(e(zero)))),
inference(monotonicity,[status(thm)],[353]) ).
tff(355,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero)),s(zero)) = s(minus(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(356,plain,
if_minus(false,s(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero)),s(zero)) = s(minus(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero),s(zero))),
inference(unit_resolution,[status(thm)],[355,119]) ).
tff(357,plain,
le(s(d(d(e(zero)))),zero) = le(s(s(s(d(s(zero))))),zero),
inference(monotonicity,[status(thm)],[199]) ).
tff(358,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(d(d(e(zero))))),s(zero)) = le(s(d(d(e(zero)))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(359,plain,
le(s(s(d(d(e(zero))))),s(zero)) = le(s(d(d(e(zero)))),zero),
inference(unit_resolution,[status(thm)],[358,50]) ).
tff(360,plain,
le(s(s(d(d(e(zero))))),s(zero)) = false,
inference(transitivity,[status(thm)],[359,357,255]) ).
tff(361,plain,
if_minus(le(s(s(d(d(e(zero))))),s(zero)),s(s(d(d(e(zero))))),s(zero)) = if_minus(false,s(if_minus(le(s(s(s(d(s(zero))))),zero),s(s(s(d(s(zero))))),zero)),s(zero)),
inference(monotonicity,[status(thm)],[360,269]) ).
tff(362,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(d(d(e(zero))))),s(zero)) = if_minus(le(s(s(d(d(e(zero))))),s(zero)),s(s(d(d(e(zero))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(363,plain,
minus(s(s(d(d(e(zero))))),s(zero)) = if_minus(le(s(s(d(d(e(zero))))),s(zero)),s(s(d(d(e(zero))))),s(zero)),
inference(unit_resolution,[status(thm)],[362,61]) ).
tff(364,plain,
minus(s(s(d(d(e(zero))))),s(zero)) = s(d(d(e(zero)))),
inference(transitivity,[status(thm)],[363,361,356,354]) ).
tff(365,plain,
s(minus(s(s(d(d(e(zero))))),s(zero))) = s(s(d(d(e(zero))))),
inference(monotonicity,[status(thm)],[364]) ).
tff(366,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(s(s(d(d(e(zero)))))),s(zero)) = s(minus(s(s(d(d(e(zero))))),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(367,plain,
if_minus(false,s(s(s(d(d(e(zero)))))),s(zero)) = s(minus(s(s(d(d(e(zero))))),s(zero))),
inference(unit_resolution,[status(thm)],[366,119]) ).
tff(368,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(d(d(e(zero)))))),s(zero)) = le(s(s(d(d(e(zero))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(369,plain,
le(s(s(s(d(d(e(zero)))))),s(zero)) = le(s(s(d(d(e(zero))))),zero),
inference(unit_resolution,[status(thm)],[368,50]) ).
tff(370,plain,
le(s(s(s(d(d(e(zero)))))),s(zero)) = false,
inference(transitivity,[status(thm)],[369,322]) ).
tff(371,plain,
if_minus(le(s(s(s(d(d(e(zero)))))),s(zero)),s(s(s(d(d(e(zero)))))),s(zero)) = if_minus(false,s(s(s(d(d(e(zero)))))),s(zero)),
inference(monotonicity,[status(thm)],[370]) ).
tff(372,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(s(d(d(e(zero)))))),s(zero)) = if_minus(le(s(s(s(d(d(e(zero)))))),s(zero)),s(s(s(d(d(e(zero)))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(373,plain,
minus(s(s(s(d(d(e(zero)))))),s(zero)) = if_minus(le(s(s(s(d(d(e(zero)))))),s(zero)),s(s(s(d(d(e(zero)))))),s(zero)),
inference(unit_resolution,[status(thm)],[372,61]) ).
tff(374,plain,
minus(s(d(s(s(s(zero))))),s(zero)) = minus(s(s(s(d(d(e(zero)))))),s(zero)),
inference(monotonicity,[status(thm)],[346]) ).
tff(375,plain,
minus(s(d(s(s(s(zero))))),s(zero)) = s(s(d(d(e(zero))))),
inference(transitivity,[status(thm)],[374,373,371,367,365]) ).
tff(376,plain,
quot(minus(s(d(s(s(s(zero))))),s(zero)),s(s(zero))) = quot(s(s(d(d(e(zero))))),s(s(zero))),
inference(monotonicity,[status(thm)],[375]) ).
tff(377,plain,
quot(minus(s(d(s(s(s(zero))))),s(zero)),s(s(zero))) = s(s(s(zero))),
inference(transitivity,[status(thm)],[376,270,266,264]) ).
tff(378,plain,
s(quot(minus(s(d(s(s(s(zero))))),s(zero)),s(s(zero)))) = s(s(s(s(zero)))),
inference(monotonicity,[status(thm)],[377]) ).
tff(379,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(s(zero))) = s(quot(minus(s(d(s(s(s(zero))))),s(zero)),s(s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(380,plain,
quot(s(s(d(s(s(s(zero)))))),s(s(zero))) = s(quot(minus(s(d(s(s(s(zero))))),s(zero)),s(s(zero)))),
inference(unit_resolution,[status(thm)],[379,74]) ).
tff(381,plain,
d(e(d(e(zero)))) = s(s(d(s(s(s(zero)))))),
inference(transitivity,[status(thm)],[309,289]) ).
tff(382,plain,
quot(d(e(d(e(zero)))),s(s(zero))) = quot(s(s(d(s(s(s(zero)))))),s(s(zero))),
inference(monotonicity,[status(thm)],[381]) ).
tff(383,plain,
minus(s(d(s(s(s(zero))))),s(zero)) = d(s(s(s(zero)))),
inference(transitivity,[status(thm)],[374,373,371,367,365,283,280]) ).
tff(384,plain,
s(minus(s(d(s(s(s(zero))))),s(zero))) = s(d(s(s(s(zero))))),
inference(monotonicity,[status(thm)],[383]) ).
tff(385,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(s(d(s(s(s(zero)))))),s(zero)) = s(minus(s(d(s(s(s(zero))))),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(386,plain,
if_minus(false,s(s(d(s(s(s(zero)))))),s(zero)) = s(minus(s(d(s(s(s(zero))))),s(zero))),
inference(unit_resolution,[status(thm)],[385,119]) ).
tff(387,plain,
le(s(d(s(s(s(zero))))),zero) = le(s(s(s(d(d(e(zero)))))),zero),
inference(monotonicity,[status(thm)],[346]) ).
tff(388,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(389,plain,
le(s(s(d(s(s(s(zero)))))),s(zero)) = le(s(d(s(s(s(zero))))),zero),
inference(unit_resolution,[status(thm)],[388,50]) ).
tff(390,plain,
le(s(s(d(s(s(s(zero)))))),s(zero)) = false,
inference(transitivity,[status(thm)],[389,387,340]) ).
tff(391,plain,
if_minus(le(s(s(d(s(s(s(zero)))))),s(zero)),s(s(d(s(s(s(zero)))))),s(zero)) = if_minus(false,s(s(d(s(s(s(zero)))))),s(zero)),
inference(monotonicity,[status(thm)],[390]) ).
tff(392,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(d(s(s(s(zero)))))),s(zero)) = if_minus(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(393,plain,
minus(s(s(d(s(s(s(zero)))))),s(zero)) = if_minus(le(s(s(d(s(s(s(zero)))))),s(zero)),s(s(d(s(s(s(zero)))))),s(zero)),
inference(unit_resolution,[status(thm)],[392,61]) ).
tff(394,plain,
minus(d(e(d(e(zero)))),s(zero)) = minus(s(s(d(s(s(s(zero)))))),s(zero)),
inference(monotonicity,[status(thm)],[381]) ).
tff(395,plain,
minus(d(e(d(e(zero)))),s(zero)) = minus(s(d(s(s(s(zero))))),zero),
inference(transitivity,[status(thm)],[394,393,391,386,384,335,352,342,351,350]) ).
tff(396,plain,
s(minus(d(e(d(e(zero)))),s(zero))) = s(minus(s(d(s(s(s(zero))))),zero)),
inference(monotonicity,[status(thm)],[395]) ).
tff(397,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(d(e(d(e(zero))))),s(zero)) = s(minus(d(e(d(e(zero)))),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(398,plain,
if_minus(false,s(d(e(d(e(zero))))),s(zero)) = s(minus(d(e(d(e(zero)))),s(zero))),
inference(unit_resolution,[status(thm)],[397,119]) ).
tff(399,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(d(s(s(s(zero)))))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(400,plain,
le(s(s(d(s(s(s(zero)))))),zero) = false,
inference(unit_resolution,[status(thm)],[399,128]) ).
tff(401,plain,
le(d(e(d(e(zero)))),zero) = le(s(s(d(s(s(s(zero)))))),zero),
inference(monotonicity,[status(thm)],[381]) ).
tff(402,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(d(e(d(e(zero))))),s(zero)) = le(d(e(d(e(zero)))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(403,plain,
le(s(d(e(d(e(zero))))),s(zero)) = le(d(e(d(e(zero)))),zero),
inference(unit_resolution,[status(thm)],[402,50]) ).
tff(404,plain,
le(s(d(e(d(e(zero))))),s(zero)) = false,
inference(transitivity,[status(thm)],[403,401,400]) ).
tff(405,plain,
if_minus(le(s(d(e(d(e(zero))))),s(zero)),s(d(e(d(e(zero))))),s(zero)) = if_minus(false,s(d(e(d(e(zero))))),s(zero)),
inference(monotonicity,[status(thm)],[404]) ).
tff(406,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(d(e(d(e(zero))))),s(zero)) = if_minus(le(s(d(e(d(e(zero))))),s(zero)),s(d(e(d(e(zero))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(407,plain,
minus(s(d(e(d(e(zero))))),s(zero)) = if_minus(le(s(d(e(d(e(zero))))),s(zero)),s(d(e(d(e(zero))))),s(zero)),
inference(unit_resolution,[status(thm)],[406,61]) ).
tff(408,plain,
s(d(e(d(e(zero))))) = s(s(s(d(s(s(s(zero))))))),
inference(monotonicity,[status(thm)],[381]) ).
tff(409,plain,
s(s(s(d(s(s(s(zero))))))) = s(d(e(d(e(zero))))),
inference(symmetry,[status(thm)],[408]) ).
tff(410,plain,
minus(d(e(d(e(zero)))),zero) = minus(s(s(d(s(s(s(zero)))))),zero),
inference(monotonicity,[status(thm)],[381]) ).
tff(411,plain,
minus(s(s(d(s(s(s(zero)))))),zero) = minus(d(e(d(e(zero)))),zero),
inference(symmetry,[status(thm)],[410]) ).
tff(412,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(d(s(s(s(zero)))))),zero) = if_minus(le(s(s(d(s(s(s(zero)))))),zero),s(s(d(s(s(s(zero)))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(413,plain,
minus(s(s(d(s(s(s(zero)))))),zero) = if_minus(le(s(s(d(s(s(s(zero)))))),zero),s(s(d(s(s(s(zero)))))),zero),
inference(unit_resolution,[status(thm)],[412,61]) ).
tff(414,plain,
if_minus(le(s(s(d(s(s(s(zero)))))),zero),s(s(d(s(s(s(zero)))))),zero) = minus(s(s(d(s(s(s(zero)))))),zero),
inference(symmetry,[status(thm)],[413]) ).
tff(415,plain,
if_minus(le(s(s(d(s(s(s(zero)))))),zero),s(s(d(s(s(s(zero)))))),zero) = if_minus(false,s(s(d(s(s(s(zero)))))),zero),
inference(monotonicity,[status(thm)],[400]) ).
tff(416,plain,
if_minus(false,s(s(d(s(s(s(zero)))))),zero) = if_minus(le(s(s(d(s(s(s(zero)))))),zero),s(s(d(s(s(s(zero)))))),zero),
inference(symmetry,[status(thm)],[415]) ).
tff(417,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(s(d(s(s(s(zero)))))),zero) = s(minus(s(d(s(s(s(zero))))),zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(418,plain,
if_minus(false,s(s(d(s(s(s(zero)))))),zero) = s(minus(s(d(s(s(s(zero))))),zero)),
inference(unit_resolution,[status(thm)],[417,119]) ).
tff(419,plain,
s(minus(s(d(s(s(s(zero))))),zero)) = if_minus(false,s(s(d(s(s(s(zero)))))),zero),
inference(symmetry,[status(thm)],[418]) ).
tff(420,plain,
s(s(d(s(s(s(zero)))))) = s(minus(s(d(s(s(s(zero))))),zero)),
inference(symmetry,[status(thm)],[349]) ).
tff(421,plain,
s(s(d(s(s(s(zero)))))) = minus(d(e(d(e(zero)))),zero),
inference(transitivity,[status(thm)],[420,419,416,414,411]) ).
tff(422,plain,
s(s(s(d(s(s(s(zero))))))) = s(minus(d(e(d(e(zero)))),zero)),
inference(monotonicity,[status(thm)],[421]) ).
tff(423,plain,
s(minus(d(e(d(e(zero)))),zero)) = s(s(s(d(s(s(s(zero))))))),
inference(symmetry,[status(thm)],[422]) ).
tff(424,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(d(e(d(e(zero))))),zero) = s(minus(d(e(d(e(zero)))),zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(425,plain,
if_minus(false,s(d(e(d(e(zero))))),zero) = s(minus(d(e(d(e(zero)))),zero)),
inference(unit_resolution,[status(thm)],[424,119]) ).
tff(426,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(d(e(d(e(zero))))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(427,plain,
le(s(d(e(d(e(zero))))),zero) = false,
inference(unit_resolution,[status(thm)],[426,128]) ).
tff(428,plain,
false = le(s(d(e(d(e(zero))))),zero),
inference(symmetry,[status(thm)],[427]) ).
tff(429,plain,
if_minus(false,s(d(e(d(e(zero))))),zero) = if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero),
inference(monotonicity,[status(thm)],[428]) ).
tff(430,plain,
if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero) = if_minus(false,s(d(e(d(e(zero))))),zero),
inference(symmetry,[status(thm)],[429]) ).
tff(431,plain,
if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero) = s(d(e(d(e(zero))))),
inference(transitivity,[status(thm)],[430,425,423,409]) ).
tff(432,plain,
minus(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero),s(zero)) = minus(s(d(e(d(e(zero))))),s(zero)),
inference(monotonicity,[status(thm)],[431]) ).
tff(433,plain,
minus(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero),s(zero)) = d(e(d(e(zero)))),
inference(transitivity,[status(thm)],[432,407,405,398,396,349,317,308]) ).
tff(434,plain,
quot(minus(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero),s(zero)),s(s(zero))) = quot(d(e(d(e(zero)))),s(s(zero))),
inference(monotonicity,[status(thm)],[433]) ).
tff(435,plain,
quot(minus(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero),s(zero)),s(s(zero))) = d(d(e(zero))),
inference(transitivity,[status(thm)],[434,382,380,378,162,196,193]) ).
tff(436,plain,
s(quot(minus(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero),s(zero)),s(s(zero)))) = s(d(d(e(zero)))),
inference(monotonicity,[status(thm)],[435]) ).
tff(437,plain,
( ~ ! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) )
| ( quot(s(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero)),s(s(zero))) = s(quot(minus(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero),s(zero)),s(s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(438,plain,
quot(s(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero)),s(s(zero))) = s(quot(minus(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero),s(zero)),s(s(zero)))),
inference(unit_resolution,[status(thm)],[437,74]) ).
tff(439,plain,
s(s(d(s(zero)))) = e(d(e(zero))),
inference(transitivity,[status(thm)],[196,306,301,291]) ).
tff(440,plain,
d(s(s(d(s(zero))))) = d(e(d(e(zero)))),
inference(monotonicity,[status(thm)],[439]) ).
tff(441,plain,
d(s(s(d(s(zero))))) = s(s(d(s(s(s(zero)))))),
inference(transitivity,[status(thm)],[440,309,289]) ).
tff(442,plain,
s(d(s(s(d(s(zero)))))) = s(s(s(d(s(s(s(zero))))))),
inference(monotonicity,[status(thm)],[441]) ).
tff(443,plain,
s(s(s(d(s(s(s(zero))))))) = s(d(s(s(d(s(zero)))))),
inference(symmetry,[status(thm)],[442]) ).
tff(444,plain,
if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero) = s(d(s(s(d(s(zero)))))),
inference(transitivity,[status(thm)],[430,425,423,443]) ).
tff(445,plain,
s(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero)) = s(s(d(s(s(d(s(zero))))))),
inference(monotonicity,[status(thm)],[444]) ).
tff(446,plain,
s(s(d(s(s(d(s(zero))))))) = s(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero)),
inference(symmetry,[status(thm)],[445]) ).
tff(447,plain,
quot(s(s(d(s(s(d(s(zero))))))),s(s(zero))) = quot(s(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero)),s(s(zero))),
inference(monotonicity,[status(thm)],[446]) ).
tff(448,plain,
minus(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero),s(zero)) = s(s(d(s(s(s(zero)))))),
inference(transitivity,[status(thm)],[432,407,405,398,396,349]) ).
tff(449,plain,
s(minus(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero),s(zero))) = s(s(s(d(s(s(s(zero))))))),
inference(monotonicity,[status(thm)],[448]) ).
tff(450,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero)),s(zero)) = s(minus(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(451,plain,
if_minus(false,s(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero)),s(zero)) = s(minus(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero),s(zero))),
inference(unit_resolution,[status(thm)],[450,119]) ).
tff(452,plain,
s(s(s(s(d(s(s(s(zero)))))))) = s(s(d(s(s(d(s(zero))))))),
inference(monotonicity,[status(thm)],[443]) ).
tff(453,plain,
s(s(s(s(d(s(s(s(zero)))))))) = s(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero)),
inference(transitivity,[status(thm)],[452,446]) ).
tff(454,plain,
le(s(s(s(d(s(s(s(zero))))))),zero) = le(s(d(e(d(e(zero))))),zero),
inference(monotonicity,[status(thm)],[409]) ).
tff(455,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(s(d(s(s(s(zero)))))))),s(zero)) = le(s(s(s(d(s(s(s(zero))))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(456,plain,
le(s(s(s(s(d(s(s(s(zero)))))))),s(zero)) = le(s(s(s(d(s(s(s(zero))))))),zero),
inference(unit_resolution,[status(thm)],[455,50]) ).
tff(457,plain,
le(s(s(s(s(d(s(s(s(zero)))))))),s(zero)) = false,
inference(transitivity,[status(thm)],[456,454,427]) ).
tff(458,plain,
if_minus(le(s(s(s(s(d(s(s(s(zero)))))))),s(zero)),s(s(s(s(d(s(s(s(zero)))))))),s(zero)) = if_minus(false,s(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero)),s(zero)),
inference(monotonicity,[status(thm)],[457,453]) ).
tff(459,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(s(s(d(s(s(s(zero)))))))),s(zero)) = if_minus(le(s(s(s(s(d(s(s(s(zero)))))))),s(zero)),s(s(s(s(d(s(s(s(zero)))))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(460,plain,
minus(s(s(s(s(d(s(s(s(zero)))))))),s(zero)) = if_minus(le(s(s(s(s(d(s(s(s(zero)))))))),s(zero)),s(s(s(s(d(s(s(s(zero)))))))),s(zero)),
inference(unit_resolution,[status(thm)],[459,61]) ).
tff(461,plain,
s(s(d(s(s(d(s(zero))))))) = s(s(s(s(d(s(s(s(zero)))))))),
inference(symmetry,[status(thm)],[452]) ).
tff(462,plain,
minus(s(s(d(s(s(d(s(zero))))))),s(zero)) = minus(s(s(s(s(d(s(s(s(zero)))))))),s(zero)),
inference(monotonicity,[status(thm)],[461]) ).
tff(463,plain,
minus(s(s(d(s(s(d(s(zero))))))),s(zero)) = s(d(s(s(d(s(zero)))))),
inference(transitivity,[status(thm)],[462,460,458,451,449,443]) ).
tff(464,plain,
s(minus(s(s(d(s(s(d(s(zero))))))),s(zero))) = s(s(d(s(s(d(s(zero))))))),
inference(monotonicity,[status(thm)],[463]) ).
tff(465,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(s(s(d(s(s(d(s(zero)))))))),s(zero)) = s(minus(s(s(d(s(s(d(s(zero))))))),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(466,plain,
if_minus(false,s(s(s(d(s(s(d(s(zero)))))))),s(zero)) = s(minus(s(s(d(s(s(d(s(zero))))))),s(zero))),
inference(unit_resolution,[status(thm)],[465,119]) ).
tff(467,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(s(s(d(s(s(s(zero)))))))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(468,plain,
le(s(s(s(s(d(s(s(s(zero)))))))),zero) = false,
inference(unit_resolution,[status(thm)],[467,128]) ).
tff(469,plain,
le(s(s(d(s(s(d(s(zero))))))),zero) = le(s(s(s(s(d(s(s(s(zero)))))))),zero),
inference(monotonicity,[status(thm)],[461]) ).
tff(470,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(d(s(s(d(s(zero)))))))),s(zero)) = le(s(s(d(s(s(d(s(zero))))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(471,plain,
le(s(s(s(d(s(s(d(s(zero)))))))),s(zero)) = le(s(s(d(s(s(d(s(zero))))))),zero),
inference(unit_resolution,[status(thm)],[470,50]) ).
tff(472,plain,
le(s(s(s(d(s(s(d(s(zero)))))))),s(zero)) = false,
inference(transitivity,[status(thm)],[471,469,468]) ).
tff(473,plain,
if_minus(le(s(s(s(d(s(s(d(s(zero)))))))),s(zero)),s(s(s(d(s(s(d(s(zero)))))))),s(zero)) = if_minus(false,s(s(s(d(s(s(d(s(zero)))))))),s(zero)),
inference(monotonicity,[status(thm)],[472]) ).
tff(474,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(s(d(s(s(d(s(zero)))))))),s(zero)) = if_minus(le(s(s(s(d(s(s(d(s(zero)))))))),s(zero)),s(s(s(d(s(s(d(s(zero)))))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(475,plain,
minus(s(s(s(d(s(s(d(s(zero)))))))),s(zero)) = if_minus(le(s(s(s(d(s(s(d(s(zero)))))))),s(zero)),s(s(s(d(s(s(d(s(zero)))))))),s(zero)),
inference(unit_resolution,[status(thm)],[474,61]) ).
tff(476,plain,
d(s(d(d(e(zero))))) = d(s(s(s(d(s(zero)))))),
inference(monotonicity,[status(thm)],[199]) ).
tff(477,plain,
d(s(s(s(d(s(zero)))))) = d(s(d(d(e(zero))))),
inference(symmetry,[status(thm)],[476]) ).
tff(478,plain,
( ~ ! [X: $i] : ( d(s(X)) = s(s(d(X))) )
| ( d(s(s(s(d(s(zero)))))) = s(s(d(s(s(d(s(zero))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(479,plain,
d(s(s(s(d(s(zero)))))) = s(s(d(s(s(d(s(zero))))))),
inference(unit_resolution,[status(thm)],[478,90]) ).
tff(480,plain,
s(s(d(s(s(d(s(zero))))))) = d(s(s(s(d(s(zero)))))),
inference(symmetry,[status(thm)],[479]) ).
tff(481,plain,
s(s(d(s(s(d(s(zero))))))) = d(s(d(d(e(zero))))),
inference(transitivity,[status(thm)],[480,477]) ).
tff(482,plain,
s(s(s(d(s(s(d(s(zero)))))))) = s(d(s(d(d(e(zero)))))),
inference(monotonicity,[status(thm)],[481]) ).
tff(483,plain,
s(d(s(d(d(e(zero)))))) = s(s(s(d(s(s(d(s(zero)))))))),
inference(symmetry,[status(thm)],[482]) ).
tff(484,plain,
minus(s(d(s(d(d(e(zero)))))),s(zero)) = minus(s(s(s(d(s(s(d(s(zero)))))))),s(zero)),
inference(monotonicity,[status(thm)],[483]) ).
tff(485,plain,
minus(s(d(s(d(d(e(zero)))))),s(zero)) = s(s(d(s(s(d(s(zero))))))),
inference(transitivity,[status(thm)],[484,475,473,466,464]) ).
tff(486,plain,
quot(minus(s(d(s(d(d(e(zero)))))),s(zero)),s(s(zero))) = quot(s(s(d(s(s(d(s(zero))))))),s(s(zero))),
inference(monotonicity,[status(thm)],[485]) ).
tff(487,plain,
quot(minus(s(d(s(d(d(e(zero)))))),s(zero)),s(s(zero))) = s(d(d(e(zero)))),
inference(transitivity,[status(thm)],[486,447,438,436]) ).
tff(488,plain,
s(quot(minus(s(d(s(d(d(e(zero)))))),s(zero)),s(s(zero)))) = s(s(d(d(e(zero))))),
inference(monotonicity,[status(thm)],[487]) ).
tff(489,plain,
( ~ ! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) )
| ( quot(s(s(d(s(d(d(e(zero))))))),s(s(zero))) = s(quot(minus(s(d(s(d(d(e(zero)))))),s(zero)),s(s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(490,plain,
quot(s(s(d(s(d(d(e(zero))))))),s(s(zero))) = s(quot(minus(s(d(s(d(d(e(zero)))))),s(zero)),s(s(zero)))),
inference(unit_resolution,[status(thm)],[489,74]) ).
tff(491,plain,
minus(s(s(d(s(s(d(s(zero))))))),zero) = minus(s(s(s(s(d(s(s(s(zero)))))))),zero),
inference(monotonicity,[status(thm)],[461]) ).
tff(492,plain,
minus(s(s(s(s(d(s(s(s(zero)))))))),zero) = minus(s(s(d(s(s(d(s(zero))))))),zero),
inference(symmetry,[status(thm)],[491]) ).
tff(493,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(s(s(d(s(s(s(zero)))))))),zero) = if_minus(le(s(s(s(s(d(s(s(s(zero)))))))),zero),s(s(s(s(d(s(s(s(zero)))))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(494,plain,
minus(s(s(s(s(d(s(s(s(zero)))))))),zero) = if_minus(le(s(s(s(s(d(s(s(s(zero)))))))),zero),s(s(s(s(d(s(s(s(zero)))))))),zero),
inference(unit_resolution,[status(thm)],[493,61]) ).
tff(495,plain,
if_minus(le(s(s(s(s(d(s(s(s(zero)))))))),zero),s(s(s(s(d(s(s(s(zero)))))))),zero) = minus(s(s(s(s(d(s(s(s(zero)))))))),zero),
inference(symmetry,[status(thm)],[494]) ).
tff(496,plain,
if_minus(le(s(s(s(s(d(s(s(s(zero)))))))),zero),s(s(s(s(d(s(s(s(zero)))))))),zero) = if_minus(false,s(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero)),zero),
inference(monotonicity,[status(thm)],[468,453]) ).
tff(497,plain,
if_minus(false,s(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero)),zero) = if_minus(le(s(s(s(s(d(s(s(s(zero)))))))),zero),s(s(s(s(d(s(s(s(zero)))))))),zero),
inference(symmetry,[status(thm)],[496]) ).
tff(498,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero)),zero) = s(minus(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero),zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(499,plain,
if_minus(false,s(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero)),zero) = s(minus(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero),zero)),
inference(unit_resolution,[status(thm)],[498,119]) ).
tff(500,plain,
s(minus(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero),zero)) = if_minus(false,s(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero)),zero),
inference(symmetry,[status(thm)],[499]) ).
tff(501,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(d(e(d(e(zero))))),zero) = if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(502,plain,
minus(s(d(e(d(e(zero))))),zero) = if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero),
inference(unit_resolution,[status(thm)],[501,61]) ).
tff(503,plain,
minus(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero),zero) = minus(s(d(e(d(e(zero))))),zero),
inference(monotonicity,[status(thm)],[431]) ).
tff(504,plain,
minus(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero),zero) = s(d(s(s(d(s(zero)))))),
inference(transitivity,[status(thm)],[503,502,430,425,423,443]) ).
tff(505,plain,
s(minus(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero),zero)) = s(s(d(s(s(d(s(zero))))))),
inference(monotonicity,[status(thm)],[504]) ).
tff(506,plain,
s(s(d(s(s(d(s(zero))))))) = s(minus(if_minus(le(s(d(e(d(e(zero))))),zero),s(d(e(d(e(zero))))),zero),zero)),
inference(symmetry,[status(thm)],[505]) ).
tff(507,plain,
d(s(d(d(e(zero))))) = minus(s(s(d(s(s(d(s(zero))))))),zero),
inference(transitivity,[status(thm)],[476,479,506,500,497,495,492]) ).
tff(508,plain,
s(d(s(d(d(e(zero)))))) = s(minus(s(s(d(s(s(d(s(zero))))))),zero)),
inference(monotonicity,[status(thm)],[507]) ).
tff(509,plain,
s(minus(s(s(d(s(s(d(s(zero))))))),zero)) = s(d(s(d(d(e(zero)))))),
inference(symmetry,[status(thm)],[508]) ).
tff(510,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(s(s(d(s(s(d(s(zero)))))))),zero) = s(minus(s(s(d(s(s(d(s(zero))))))),zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(511,plain,
if_minus(false,s(s(s(d(s(s(d(s(zero)))))))),zero) = s(minus(s(s(d(s(s(d(s(zero))))))),zero)),
inference(unit_resolution,[status(thm)],[510,119]) ).
tff(512,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(s(d(s(s(d(s(zero)))))))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(513,plain,
le(s(s(s(d(s(s(d(s(zero)))))))),zero) = false,
inference(unit_resolution,[status(thm)],[512,128]) ).
tff(514,plain,
false = le(s(s(s(d(s(s(d(s(zero)))))))),zero),
inference(symmetry,[status(thm)],[513]) ).
tff(515,plain,
if_minus(false,s(s(s(d(s(s(d(s(zero)))))))),zero) = if_minus(le(s(s(s(d(s(s(d(s(zero)))))))),zero),s(s(s(d(s(s(d(s(zero)))))))),zero),
inference(monotonicity,[status(thm)],[514]) ).
tff(516,plain,
if_minus(le(s(s(s(d(s(s(d(s(zero)))))))),zero),s(s(s(d(s(s(d(s(zero)))))))),zero) = if_minus(false,s(s(s(d(s(s(d(s(zero)))))))),zero),
inference(symmetry,[status(thm)],[515]) ).
tff(517,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(s(d(s(s(d(s(zero)))))))),zero) = if_minus(le(s(s(s(d(s(s(d(s(zero)))))))),zero),s(s(s(d(s(s(d(s(zero)))))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(518,plain,
minus(s(s(s(d(s(s(d(s(zero)))))))),zero) = if_minus(le(s(s(s(d(s(s(d(s(zero)))))))),zero),s(s(s(d(s(s(d(s(zero)))))))),zero),
inference(unit_resolution,[status(thm)],[517,61]) ).
tff(519,plain,
minus(s(d(s(d(d(e(zero)))))),zero) = minus(s(s(s(d(s(s(d(s(zero)))))))),zero),
inference(monotonicity,[status(thm)],[483]) ).
tff(520,plain,
minus(s(d(s(d(d(e(zero)))))),zero) = s(d(s(d(d(e(zero)))))),
inference(transitivity,[status(thm)],[519,518,516,511,509]) ).
tff(521,plain,
s(minus(s(d(s(d(d(e(zero)))))),zero)) = s(s(d(s(d(d(e(zero))))))),
inference(monotonicity,[status(thm)],[520]) ).
tff(522,plain,
minus(s(s(s(d(s(s(d(s(zero)))))))),zero) = minus(s(d(s(d(d(e(zero)))))),zero),
inference(symmetry,[status(thm)],[519]) ).
tff(523,plain,
if_minus(le(s(s(s(d(s(s(d(s(zero)))))))),zero),s(s(s(d(s(s(d(s(zero)))))))),zero) = minus(s(s(s(d(s(s(d(s(zero)))))))),zero),
inference(symmetry,[status(thm)],[518]) ).
tff(524,plain,
s(minus(s(s(d(s(s(d(s(zero))))))),zero)) = if_minus(false,s(s(s(d(s(s(d(s(zero)))))))),zero),
inference(symmetry,[status(thm)],[511]) ).
tff(525,plain,
minus(s(d(s(d(d(e(zero)))))),s(zero)) = d(s(d(d(e(zero))))),
inference(transitivity,[status(thm)],[484,475,473,466,464,480,477]) ).
tff(526,plain,
s(minus(s(d(s(d(d(e(zero)))))),s(zero))) = s(d(s(d(d(e(zero)))))),
inference(monotonicity,[status(thm)],[525]) ).
tff(527,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(s(d(s(d(d(e(zero))))))),s(zero)) = s(minus(s(d(s(d(d(e(zero)))))),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(528,plain,
if_minus(false,s(s(d(s(d(d(e(zero))))))),s(zero)) = s(minus(s(d(s(d(d(e(zero)))))),s(zero))),
inference(unit_resolution,[status(thm)],[527,119]) ).
tff(529,plain,
le(s(d(s(d(d(e(zero)))))),zero) = le(s(s(s(d(s(s(d(s(zero)))))))),zero),
inference(monotonicity,[status(thm)],[483]) ).
tff(530,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(d(s(d(d(e(zero))))))),s(zero)) = le(s(d(s(d(d(e(zero)))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(531,plain,
le(s(s(d(s(d(d(e(zero))))))),s(zero)) = le(s(d(s(d(d(e(zero)))))),zero),
inference(unit_resolution,[status(thm)],[530,50]) ).
tff(532,plain,
le(s(s(d(s(d(d(e(zero))))))),s(zero)) = false,
inference(transitivity,[status(thm)],[531,529,513]) ).
tff(533,plain,
if_minus(le(s(s(d(s(d(d(e(zero))))))),s(zero)),s(s(d(s(d(d(e(zero))))))),s(zero)) = if_minus(false,s(s(d(s(d(d(e(zero))))))),s(zero)),
inference(monotonicity,[status(thm)],[532]) ).
tff(534,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(d(s(d(d(e(zero))))))),s(zero)) = if_minus(le(s(s(d(s(d(d(e(zero))))))),s(zero)),s(s(d(s(d(d(e(zero))))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(535,plain,
minus(s(s(d(s(d(d(e(zero))))))),s(zero)) = if_minus(le(s(s(d(s(d(d(e(zero))))))),s(zero)),s(s(d(s(d(d(e(zero))))))),s(zero)),
inference(unit_resolution,[status(thm)],[534,61]) ).
tff(536,plain,
minus(s(s(d(s(d(d(e(zero))))))),s(zero)) = minus(s(d(s(d(d(e(zero)))))),zero),
inference(transitivity,[status(thm)],[535,533,528,526,508,524,515,523,522]) ).
tff(537,plain,
s(minus(s(s(d(s(d(d(e(zero))))))),s(zero))) = s(minus(s(d(s(d(d(e(zero)))))),zero)),
inference(monotonicity,[status(thm)],[536]) ).
tff(538,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(s(s(d(s(d(d(e(zero)))))))),s(zero)) = s(minus(s(s(d(s(d(d(e(zero))))))),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(539,plain,
if_minus(false,s(s(s(d(s(d(d(e(zero)))))))),s(zero)) = s(minus(s(s(d(s(d(d(e(zero))))))),s(zero))),
inference(unit_resolution,[status(thm)],[538,119]) ).
tff(540,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(d(s(d(d(e(zero))))))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(541,plain,
le(s(s(d(s(d(d(e(zero))))))),zero) = false,
inference(unit_resolution,[status(thm)],[540,128]) ).
tff(542,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(d(s(d(d(e(zero)))))))),s(zero)) = le(s(s(d(s(d(d(e(zero))))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(543,plain,
le(s(s(s(d(s(d(d(e(zero)))))))),s(zero)) = le(s(s(d(s(d(d(e(zero))))))),zero),
inference(unit_resolution,[status(thm)],[542,50]) ).
tff(544,plain,
le(s(s(s(d(s(d(d(e(zero)))))))),s(zero)) = false,
inference(transitivity,[status(thm)],[543,541]) ).
tff(545,plain,
if_minus(le(s(s(s(d(s(d(d(e(zero)))))))),s(zero)),s(s(s(d(s(d(d(e(zero)))))))),s(zero)) = if_minus(false,s(s(s(d(s(d(d(e(zero)))))))),s(zero)),
inference(monotonicity,[status(thm)],[544]) ).
tff(546,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(s(d(s(d(d(e(zero)))))))),s(zero)) = if_minus(le(s(s(s(d(s(d(d(e(zero)))))))),s(zero)),s(s(s(d(s(d(d(e(zero)))))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(547,plain,
minus(s(s(s(d(s(d(d(e(zero)))))))),s(zero)) = if_minus(le(s(s(s(d(s(d(d(e(zero)))))))),s(zero)),s(s(s(d(s(d(d(e(zero)))))))),s(zero)),
inference(unit_resolution,[status(thm)],[546,61]) ).
tff(548,plain,
( ~ ! [X: $i] : ( d(s(X)) = s(s(d(X))) )
| ( d(s(s(d(d(e(zero)))))) = s(s(d(s(d(d(e(zero))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(549,plain,
d(s(s(d(d(e(zero)))))) = s(s(d(s(d(d(e(zero))))))),
inference(unit_resolution,[status(thm)],[548,90]) ).
tff(550,plain,
s(s(d(s(d(d(e(zero))))))) = d(s(s(d(d(e(zero)))))),
inference(symmetry,[status(thm)],[549]) ).
tff(551,plain,
s(s(s(d(s(d(d(e(zero)))))))) = s(d(s(s(d(d(e(zero))))))),
inference(monotonicity,[status(thm)],[550]) ).
tff(552,plain,
s(d(s(s(d(d(e(zero))))))) = s(s(s(d(s(d(d(e(zero)))))))),
inference(symmetry,[status(thm)],[551]) ).
tff(553,plain,
minus(s(d(s(s(d(d(e(zero))))))),s(zero)) = minus(s(s(s(d(s(d(d(e(zero)))))))),s(zero)),
inference(monotonicity,[status(thm)],[552]) ).
tff(554,plain,
minus(s(d(s(s(d(d(e(zero))))))),s(zero)) = s(s(d(s(d(d(e(zero))))))),
inference(transitivity,[status(thm)],[553,547,545,539,537,521]) ).
tff(555,plain,
quot(minus(s(d(s(s(d(d(e(zero))))))),s(zero)),s(s(zero))) = quot(s(s(d(s(d(d(e(zero))))))),s(s(zero))),
inference(monotonicity,[status(thm)],[554]) ).
tff(556,plain,
quot(minus(s(d(s(s(d(d(e(zero))))))),s(zero)),s(s(zero))) = d(s(s(s(zero)))),
inference(transitivity,[status(thm)],[555,490,488,283,280]) ).
tff(557,plain,
s(quot(minus(s(d(s(s(d(d(e(zero))))))),s(zero)),s(s(zero)))) = s(d(s(s(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(d(s(s(d(d(e(zero)))))))),s(s(zero))) = s(quot(minus(s(d(s(s(d(d(e(zero))))))),s(zero)),s(s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(559,plain,
quot(s(s(d(s(s(d(d(e(zero)))))))),s(s(zero))) = s(quot(minus(s(d(s(s(d(d(e(zero))))))),s(zero)),s(s(zero)))),
inference(unit_resolution,[status(thm)],[558,74]) ).
tff(560,plain,
quot(s(s(d(s(s(d(d(e(zero)))))))),s(s(zero))) = minus(s(d(s(s(s(zero))))),zero),
inference(transitivity,[status(thm)],[559,557,335,352,342,351,350]) ).
tff(561,plain,
s(quot(s(s(d(s(s(d(d(e(zero)))))))),s(s(zero)))) = s(minus(s(d(s(s(s(zero))))),zero)),
inference(monotonicity,[status(thm)],[560]) ).
tff(562,plain,
s(quot(s(s(d(s(s(d(d(e(zero)))))))),s(s(zero)))) = e(s(s(s(zero)))),
inference(transitivity,[status(thm)],[561,349,317,308,316,315]) ).
tff(563,plain,
log(s(quot(s(s(d(s(s(d(d(e(zero)))))))),s(s(zero))))) = log(e(s(s(s(zero))))),
inference(monotonicity,[status(thm)],[562]) ).
tff(564,plain,
log(s(quot(s(s(d(s(s(d(d(e(zero)))))))),s(s(zero))))) = s(s(s(zero))),
inference(transitivity,[status(thm)],[563,314,278,276]) ).
tff(565,plain,
s(log(s(quot(s(s(d(s(s(d(d(e(zero)))))))),s(s(zero)))))) = s(s(s(s(zero)))),
inference(monotonicity,[status(thm)],[564]) ).
tff(566,plain,
( ~ ! [X: $i] : ( log(s(s(X))) = s(log(s(quot(X,s(s(zero)))))) )
| ( log(s(s(s(s(d(s(s(d(d(e(zero))))))))))) = s(log(s(quot(s(s(d(s(s(d(d(e(zero)))))))),s(s(zero)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(567,plain,
log(s(s(s(s(d(s(s(d(d(e(zero))))))))))) = s(log(s(quot(s(s(d(s(s(d(d(e(zero)))))))),s(s(zero)))))),
inference(unit_resolution,[status(thm)],[566,23]) ).
tff(568,plain,
d(s(d(s(s(s(zero)))))) = d(s(s(s(d(d(e(zero))))))),
inference(monotonicity,[status(thm)],[346]) ).
tff(569,plain,
d(s(s(s(d(d(e(zero))))))) = d(s(d(s(s(s(zero)))))),
inference(symmetry,[status(thm)],[568]) ).
tff(570,plain,
( ~ ! [X: $i] : ( d(s(X)) = s(s(d(X))) )
| ( d(s(s(s(d(d(e(zero))))))) = s(s(d(s(s(d(d(e(zero)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(571,plain,
d(s(s(s(d(d(e(zero))))))) = s(s(d(s(s(d(d(e(zero)))))))),
inference(unit_resolution,[status(thm)],[570,90]) ).
tff(572,plain,
s(s(d(s(s(d(d(e(zero)))))))) = d(s(s(s(d(d(e(zero))))))),
inference(symmetry,[status(thm)],[571]) ).
tff(573,plain,
s(s(d(s(s(d(d(e(zero)))))))) = d(s(d(s(s(s(zero)))))),
inference(transitivity,[status(thm)],[572,569]) ).
tff(574,plain,
s(s(s(d(s(s(d(d(e(zero))))))))) = s(d(s(d(s(s(s(zero))))))),
inference(monotonicity,[status(thm)],[573]) ).
tff(575,plain,
s(s(s(s(d(s(s(d(d(e(zero)))))))))) = s(s(d(s(d(s(s(s(zero)))))))),
inference(monotonicity,[status(thm)],[574]) ).
tff(576,plain,
s(s(d(s(d(s(s(s(zero)))))))) = s(s(s(s(d(s(s(d(d(e(zero)))))))))),
inference(symmetry,[status(thm)],[575]) ).
tff(577,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(578,plain,
d(s(s(d(s(s(s(zero))))))) = s(s(d(s(d(s(s(s(zero)))))))),
inference(unit_resolution,[status(thm)],[577,90]) ).
tff(579,plain,
s(s(d(s(s(s(zero)))))) = e(s(s(s(zero)))),
inference(transitivity,[status(thm)],[317,308,316,315]) ).
tff(580,plain,
d(s(s(d(s(s(s(zero))))))) = d(e(s(s(s(zero))))),
inference(monotonicity,[status(thm)],[579]) ).
tff(581,plain,
d(e(s(s(s(zero))))) = d(s(s(d(s(s(s(zero))))))),
inference(symmetry,[status(thm)],[580]) ).
tff(582,plain,
( ~ ! [X: $i] : ( e(s(X)) = d(e(X)) )
| ( e(s(s(s(s(zero))))) = d(e(s(s(s(zero))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(583,plain,
e(s(s(s(s(zero))))) = d(e(s(s(s(zero))))),
inference(unit_resolution,[status(thm)],[582,298]) ).
tff(584,plain,
e(s(s(d(s(zero))))) = e(s(s(s(s(zero))))),
inference(monotonicity,[status(thm)],[163]) ).
tff(585,plain,
e(s(s(d(s(zero))))) = s(s(s(s(d(s(s(d(d(e(zero)))))))))),
inference(transitivity,[status(thm)],[584,583,581,578,576]) ).
tff(586,plain,
log(e(s(s(d(s(zero)))))) = log(s(s(s(s(d(s(s(d(d(e(zero))))))))))),
inference(monotonicity,[status(thm)],[585]) ).
tff(587,plain,
log(e(s(s(d(s(zero)))))) = s(s(s(s(zero)))),
inference(transitivity,[status(thm)],[586,567,565]) ).
tff(588,plain,
^ [X: $i] :
refl(( ( log(e(X)) != s(s(s(s(zero)))) )
<=> ( log(e(X)) != s(s(s(s(zero)))) ) )),
inference(bind,[status(th)],[]) ).
tff(589,plain,
( ! [X: $i] : ( log(e(X)) != s(s(s(s(zero)))) )
<=> ! [X: $i] : ( log(e(X)) != s(s(s(s(zero)))) ) ),
inference(quant_intro,[status(thm)],[588]) ).
tff(590,plain,
( ! [X: $i] : ( log(e(X)) != s(s(s(s(zero)))) )
<=> ! [X: $i] : ( log(e(X)) != s(s(s(s(zero)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(591,axiom,
! [X: $i] : ( log(e(X)) != s(s(s(s(zero)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tff(592,plain,
! [X: $i] : ( log(e(X)) != s(s(s(s(zero)))) ),
inference(modus_ponens,[status(thm)],[591,590]) ).
tff(593,plain,
! [X: $i] : ( log(e(X)) != s(s(s(s(zero)))) ),
inference(skolemize,[status(sab)],[592]) ).
tff(594,plain,
! [X: $i] : ( log(e(X)) != s(s(s(s(zero)))) ),
inference(modus_ponens,[status(thm)],[593,589]) ).
tff(595,plain,
( ~ ! [X: $i] : ( log(e(X)) != s(s(s(s(zero)))) )
| ( log(e(s(s(d(s(zero)))))) != s(s(s(s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(596,plain,
log(e(s(s(d(s(zero)))))) != s(s(s(s(zero)))),
inference(unit_resolution,[status(thm)],[595,594]) ).
tff(597,plain,
$false,
inference(unit_resolution,[status(thm)],[596,587]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ARI765-2 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.14/0.32 % Computer : n025.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 18:44:15 EDT 2026
% 0.14/0.33 % CPUTime :
% 23.86/24.10 % SZS status Unsatisfiable
% 23.86/24.10 % SZS output start Proof
% See solution above
% 24.04/24.23 % E exiting
%------------------------------------------------------------------------------