%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ARI765-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 25.73s 25.92s
% Output : Proof 25.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 143
% Syntax : Number of formulae : 569 ( 442 unt; 0 typ; 0 def)
% Number of atoms : 720 ( 707 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 242 ( 103 ~; 99 |; 0 &)
% ( 40 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of FOOLs : 12 ( 12 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 : 320 ( 303 !; 0 ?; 320 :)
% 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(minus_type,type,
minus: ( $i * $i ) > $i ).
tff(if_minus_type,type,
if_minus: ( $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(quot_type,type,
quot: ( $i * $i ) > $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/sandbox/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/sandbox/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(zero) = s(d(zero)),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
s(s(zero)) = s(s(d(zero))),
inference(monotonicity,[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,
( ~ ! [X: $i] : ( d(s(X)) = s(s(d(X))) )
| ( d(s(s(zero))) = s(s(d(s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
d(s(s(zero))) = s(s(d(s(zero)))),
inference(unit_resolution,[status(thm)],[21,7]) ).
tff(23,plain,
s(s(d(zero))) = s(s(zero)),
inference(symmetry,[status(thm)],[16]) ).
tff(24,plain,
( ( e(zero) = s(zero) )
<=> ( e(zero) = s(zero) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
e(zero) = s(zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exp1) ).
tff(26,plain,
e(zero) = s(zero),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
s(zero) = e(zero),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
d(s(zero)) = d(e(zero)),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
d(e(zero)) = d(s(zero)),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
^ [X: $i] :
refl(( ( e(s(X)) = d(e(X)) )
<=> ( e(s(X)) = d(e(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [X: $i] : ( e(s(X)) = d(e(X)) )
<=> ! [X: $i] : ( e(s(X)) = d(e(X)) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [X: $i] : ( e(s(X)) = d(e(X)) )
<=> ! [X: $i] : ( e(s(X)) = d(e(X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
! [X: $i] : ( e(s(X)) = d(e(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exp2) ).
tff(34,plain,
! [X: $i] : ( e(s(X)) = d(e(X)) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [X: $i] : ( e(s(X)) = d(e(X)) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [X: $i] : ( e(s(X)) = d(e(X)) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ~ ! [X: $i] : ( e(s(X)) = d(e(X)) )
| ( e(s(zero)) = d(e(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
e(s(zero)) = d(e(zero)),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
e(s(zero)) = s(s(zero)),
inference(transitivity,[status(thm)],[38,29,9,23]) ).
tff(40,plain,
d(e(s(zero))) = d(s(s(zero))),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
d(e(s(zero))) = s(s(d(s(zero)))),
inference(transitivity,[status(thm)],[40,22]) ).
tff(42,plain,
minus(d(e(s(zero))),s(zero)) = minus(s(s(d(s(zero)))),s(zero)),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
minus(s(s(d(s(zero)))),s(zero)) = minus(d(e(s(zero))),s(zero)),
inference(symmetry,[status(thm)],[42]) ).
tff(44,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(45,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)],[44]) ).
tff(46,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(47,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(48,plain,
! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(d(s(zero)))),s(zero)) = if_minus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
minus(s(s(d(s(zero)))),s(zero)) = if_minus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)),
inference(unit_resolution,[status(thm)],[51,50]) ).
tff(53,plain,
if_minus(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)],[52]) ).
tff(54,plain,
le(s(s(d(s(zero)))),s(zero)) = le(s(s(s(s(zero)))),s(zero)),
inference(monotonicity,[status(thm)],[20]) ).
tff(55,plain,
le(s(s(s(s(zero)))),s(zero)) = le(s(s(d(s(zero)))),s(zero)),
inference(symmetry,[status(thm)],[54]) ).
tff(56,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(57,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)],[56]) ).
tff(58,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(59,axiom,
! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule3) ).
tff(60,plain,
! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) ),
inference(skolemize,[status(sab)],[60]) ).
tff(62,plain,
! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,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(64,plain,
le(s(s(s(s(zero)))),s(zero)) = le(s(s(s(zero))),zero),
inference(unit_resolution,[status(thm)],[63,62]) ).
tff(65,plain,
le(s(s(s(zero))),zero) = le(s(s(s(s(zero)))),s(zero)),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
^ [X: $i] :
refl(( ( le(s(X),zero) = false )
<=> ( le(s(X),zero) = false ) )),
inference(bind,[status(th)],[]) ).
tff(67,plain,
( ! [X: $i] : ( le(s(X),zero) = false )
<=> ! [X: $i] : ( le(s(X),zero) = false ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [X: $i] : ( le(s(X),zero) = false )
<=> ! [X: $i] : ( le(s(X),zero) = false ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,axiom,
! [X: $i] : ( le(s(X),zero) = false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule2) ).
tff(70,plain,
! [X: $i] : ( le(s(X),zero) = false ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [X: $i] : ( le(s(X),zero) = false ),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [X: $i] : ( le(s(X),zero) = false ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(s(zero))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
le(s(s(s(zero))),zero) = false,
inference(unit_resolution,[status(thm)],[73,72]) ).
tff(75,plain,
false = le(s(s(s(zero))),zero),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
false = le(s(s(d(s(zero)))),s(zero)),
inference(transitivity,[status(thm)],[75,65,55]) ).
tff(77,plain,
if_minus(false,s(s(d(s(zero)))),s(zero)) = if_minus(le(s(s(d(s(zero)))),s(zero)),s(s(d(s(zero)))),s(zero)),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,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(79,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)],[78]) ).
tff(80,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(81,axiom,
! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule7) ).
tff(82,plain,
! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) ),
inference(modus_ponens,[status(thm)],[83,79]) ).
tff(85,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(s(d(s(zero)))),s(zero)) = s(minus(s(d(s(zero))),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
if_minus(false,s(s(d(s(zero)))),s(zero)) = s(minus(s(d(s(zero))),s(zero))),
inference(unit_resolution,[status(thm)],[85,84]) ).
tff(87,plain,
s(minus(s(d(s(zero))),s(zero))) = if_minus(false,s(s(d(s(zero)))),s(zero)),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
s(d(e(zero))) = s(d(s(zero))),
inference(monotonicity,[status(thm)],[29]) ).
tff(89,plain,
s(d(s(zero))) = s(d(e(zero))),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
minus(s(d(s(zero))),s(zero)) = minus(s(d(e(zero))),s(zero)),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
minus(s(d(e(zero))),s(zero)) = minus(s(d(s(zero))),s(zero)),
inference(symmetry,[status(thm)],[90]) ).
tff(92,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(93,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)],[92,50]) ).
tff(94,plain,
if_minus(le(s(d(e(zero))),s(zero)),s(d(e(zero))),s(zero)) = minus(s(d(e(zero))),s(zero)),
inference(symmetry,[status(thm)],[93]) ).
tff(95,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(zero)),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
le(s(s(zero)),zero) = false,
inference(unit_resolution,[status(thm)],[95,72]) ).
tff(97,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(98,plain,
le(s(s(s(zero))),s(zero)) = le(s(s(zero)),zero),
inference(unit_resolution,[status(thm)],[97,62]) ).
tff(99,plain,
s(d(s(zero))) = s(s(s(zero))),
inference(symmetry,[status(thm)],[18]) ).
tff(100,plain,
s(d(e(zero))) = s(s(s(zero))),
inference(transitivity,[status(thm)],[88,99]) ).
tff(101,plain,
le(s(d(e(zero))),s(zero)) = le(s(s(s(zero))),s(zero)),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
le(s(d(e(zero))),s(zero)) = false,
inference(transitivity,[status(thm)],[101,98,96]) ).
tff(103,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)],[102]) ).
tff(104,plain,
if_minus(false,s(d(e(zero))),s(zero)) = if_minus(le(s(d(e(zero))),s(zero)),s(d(e(zero))),s(zero)),
inference(symmetry,[status(thm)],[103]) ).
tff(105,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(106,plain,
if_minus(false,s(d(e(zero))),s(zero)) = s(minus(d(e(zero)),s(zero))),
inference(unit_resolution,[status(thm)],[105,84]) ).
tff(107,plain,
s(minus(d(e(zero)),s(zero))) = if_minus(false,s(d(e(zero))),s(zero)),
inference(symmetry,[status(thm)],[106]) ).
tff(108,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(109,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)],[108]) ).
tff(110,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(111,axiom,
! [Y: $i,X: $i] : ( if_minus(true,s(X),Y) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule6) ).
tff(112,plain,
! [Y: $i,X: $i] : ( if_minus(true,s(X),Y) = zero ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
! [Y: $i,X: $i] : ( if_minus(true,s(X),Y) = zero ),
inference(skolemize,[status(sab)],[112]) ).
tff(114,plain,
! [Y: $i,X: $i] : ( if_minus(true,s(X),Y) = zero ),
inference(modus_ponens,[status(thm)],[113,109]) ).
tff(115,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(116,plain,
if_minus(true,s(zero),s(zero)) = zero,
inference(unit_resolution,[status(thm)],[115,114]) ).
tff(117,plain,
^ [Y: $i] :
refl(( ( le(zero,Y) = true )
<=> ( le(zero,Y) = true ) )),
inference(bind,[status(th)],[]) ).
tff(118,plain,
( ! [Y: $i] : ( le(zero,Y) = true )
<=> ! [Y: $i] : ( le(zero,Y) = true ) ),
inference(quant_intro,[status(thm)],[117]) ).
tff(119,plain,
( ! [Y: $i] : ( le(zero,Y) = true )
<=> ! [Y: $i] : ( le(zero,Y) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(120,axiom,
! [Y: $i] : ( le(zero,Y) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule1) ).
tff(121,plain,
! [Y: $i] : ( le(zero,Y) = true ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
! [Y: $i] : ( le(zero,Y) = true ),
inference(skolemize,[status(sab)],[121]) ).
tff(123,plain,
! [Y: $i] : ( le(zero,Y) = true ),
inference(modus_ponens,[status(thm)],[122,118]) ).
tff(124,plain,
( ~ ! [Y: $i] : ( le(zero,Y) = true )
| ( le(zero,zero) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(125,plain,
le(zero,zero) = true,
inference(unit_resolution,[status(thm)],[124,123]) ).
tff(126,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(127,plain,
le(s(zero),s(zero)) = le(zero,zero),
inference(unit_resolution,[status(thm)],[126,62]) ).
tff(128,plain,
le(s(zero),s(zero)) = true,
inference(transitivity,[status(thm)],[127,125]) ).
tff(129,plain,
if_minus(le(s(zero),s(zero)),s(zero),s(zero)) = if_minus(true,s(zero),s(zero)),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,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(131,plain,
minus(s(zero),s(zero)) = if_minus(le(s(zero),s(zero)),s(zero),s(zero)),
inference(unit_resolution,[status(thm)],[130,50]) ).
tff(132,plain,
minus(s(zero),s(zero)) = zero,
inference(transitivity,[status(thm)],[131,129,116]) ).
tff(133,plain,
s(minus(s(zero),s(zero))) = s(zero),
inference(monotonicity,[status(thm)],[132]) ).
tff(134,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(135,plain,
if_minus(false,s(s(zero)),s(zero)) = s(minus(s(zero),s(zero))),
inference(unit_resolution,[status(thm)],[134,84]) ).
tff(136,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(zero),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
le(s(zero),zero) = false,
inference(unit_resolution,[status(thm)],[136,72]) ).
tff(138,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(139,plain,
le(s(s(zero)),s(zero)) = le(s(zero),zero),
inference(unit_resolution,[status(thm)],[138,62]) ).
tff(140,plain,
le(s(s(zero)),s(zero)) = false,
inference(transitivity,[status(thm)],[139,137]) ).
tff(141,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)],[140]) ).
tff(142,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(143,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)],[142,50]) ).
tff(144,plain,
d(e(zero)) = s(s(zero)),
inference(transitivity,[status(thm)],[29,9,23]) ).
tff(145,plain,
minus(d(e(zero)),s(zero)) = minus(s(s(zero)),s(zero)),
inference(monotonicity,[status(thm)],[144]) ).
tff(146,plain,
minus(d(e(zero)),s(zero)) = s(zero),
inference(transitivity,[status(thm)],[145,143,141,135,133]) ).
tff(147,plain,
s(minus(d(e(zero)),s(zero))) = s(s(zero)),
inference(monotonicity,[status(thm)],[146]) ).
tff(148,plain,
s(s(zero)) = s(minus(d(e(zero)),s(zero))),
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
d(s(zero)) = minus(s(d(s(zero))),s(zero)),
inference(transitivity,[status(thm)],[9,23,148,107,104,94,91]) ).
tff(150,plain,
s(d(s(zero))) = s(minus(s(d(s(zero))),s(zero))),
inference(monotonicity,[status(thm)],[149]) ).
tff(151,plain,
s(d(s(zero))) = minus(d(e(s(zero))),s(zero)),
inference(transitivity,[status(thm)],[150,87,77,53,43]) ).
tff(152,plain,
s(s(d(s(zero)))) = s(minus(d(e(s(zero))),s(zero))),
inference(monotonicity,[status(thm)],[151]) ).
tff(153,plain,
s(minus(d(e(s(zero))),s(zero))) = s(s(d(s(zero)))),
inference(symmetry,[status(thm)],[152]) ).
tff(154,plain,
( ( log(s(zero)) = zero )
<=> ( log(s(zero)) = zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(155,axiom,
log(s(zero)) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule10) ).
tff(156,plain,
log(s(zero)) = zero,
inference(modus_ponens,[status(thm)],[155,154]) ).
tff(157,plain,
^ [Y: $i] :
refl(( ( quot(zero,s(Y)) = zero )
<=> ( quot(zero,s(Y)) = zero ) )),
inference(bind,[status(th)],[]) ).
tff(158,plain,
( ! [Y: $i] : ( quot(zero,s(Y)) = zero )
<=> ! [Y: $i] : ( quot(zero,s(Y)) = zero ) ),
inference(quant_intro,[status(thm)],[157]) ).
tff(159,plain,
( ! [Y: $i] : ( quot(zero,s(Y)) = zero )
<=> ! [Y: $i] : ( quot(zero,s(Y)) = zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(160,axiom,
! [Y: $i] : ( quot(zero,s(Y)) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule8) ).
tff(161,plain,
! [Y: $i] : ( quot(zero,s(Y)) = zero ),
inference(modus_ponens,[status(thm)],[160,159]) ).
tff(162,plain,
! [Y: $i] : ( quot(zero,s(Y)) = zero ),
inference(skolemize,[status(sab)],[161]) ).
tff(163,plain,
! [Y: $i] : ( quot(zero,s(Y)) = zero ),
inference(modus_ponens,[status(thm)],[162,158]) ).
tff(164,plain,
( ~ ! [Y: $i] : ( quot(zero,s(Y)) = zero )
| ( quot(zero,s(s(zero))) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(165,plain,
quot(zero,s(s(zero))) = zero,
inference(unit_resolution,[status(thm)],[164,163]) ).
tff(166,plain,
s(quot(zero,s(s(zero)))) = s(zero),
inference(monotonicity,[status(thm)],[165]) ).
tff(167,plain,
log(s(quot(zero,s(s(zero))))) = log(s(zero)),
inference(monotonicity,[status(thm)],[166]) ).
tff(168,plain,
log(s(quot(zero,s(s(zero))))) = zero,
inference(transitivity,[status(thm)],[167,156]) ).
tff(169,plain,
s(log(s(quot(zero,s(s(zero)))))) = s(zero),
inference(monotonicity,[status(thm)],[168]) ).
tff(170,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(171,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)],[170]) ).
tff(172,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(173,axiom,
! [X: $i] : ( log(s(s(X))) = s(log(s(quot(X,s(s(zero)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule11) ).
tff(174,plain,
! [X: $i] : ( log(s(s(X))) = s(log(s(quot(X,s(s(zero)))))) ),
inference(modus_ponens,[status(thm)],[173,172]) ).
tff(175,plain,
! [X: $i] : ( log(s(s(X))) = s(log(s(quot(X,s(s(zero)))))) ),
inference(skolemize,[status(sab)],[174]) ).
tff(176,plain,
! [X: $i] : ( log(s(s(X))) = s(log(s(quot(X,s(s(zero)))))) ),
inference(modus_ponens,[status(thm)],[175,171]) ).
tff(177,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(178,plain,
log(s(s(zero))) = s(log(s(quot(zero,s(s(zero)))))),
inference(unit_resolution,[status(thm)],[177,176]) ).
tff(179,plain,
quot(minus(s(zero),s(zero)),s(s(zero))) = quot(zero,s(s(zero))),
inference(monotonicity,[status(thm)],[132]) ).
tff(180,plain,
quot(minus(s(zero),s(zero)),s(s(zero))) = zero,
inference(transitivity,[status(thm)],[179,165]) ).
tff(181,plain,
s(quot(minus(s(zero),s(zero)),s(s(zero)))) = s(zero),
inference(monotonicity,[status(thm)],[180]) ).
tff(182,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(183,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)],[182]) ).
tff(184,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(185,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(186,plain,
! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) ),
inference(modus_ponens,[status(thm)],[185,184]) ).
tff(187,plain,
! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) ),
inference(skolemize,[status(sab)],[186]) ).
tff(188,plain,
! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) ),
inference(modus_ponens,[status(thm)],[187,183]) ).
tff(189,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(190,plain,
quot(s(s(zero)),s(s(zero))) = s(quot(minus(s(zero),s(zero)),s(s(zero)))),
inference(unit_resolution,[status(thm)],[189,188]) ).
tff(191,plain,
quot(s(s(zero)),s(s(zero))) = s(zero),
inference(transitivity,[status(thm)],[190,181]) ).
tff(192,plain,
s(quot(s(s(zero)),s(s(zero)))) = s(s(zero)),
inference(monotonicity,[status(thm)],[191]) ).
tff(193,plain,
log(s(quot(s(s(zero)),s(s(zero))))) = log(s(s(zero))),
inference(monotonicity,[status(thm)],[192]) ).
tff(194,plain,
log(s(quot(s(s(zero)),s(s(zero))))) = s(zero),
inference(transitivity,[status(thm)],[193,178,169]) ).
tff(195,plain,
s(log(s(quot(s(s(zero)),s(s(zero)))))) = s(s(zero)),
inference(monotonicity,[status(thm)],[194]) ).
tff(196,plain,
( ~ ! [X: $i] : ( log(s(s(X))) = s(log(s(quot(X,s(s(zero)))))) )
| ( log(s(s(s(s(zero))))) = s(log(s(quot(s(s(zero)),s(s(zero)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(197,plain,
log(s(s(s(s(zero))))) = s(log(s(quot(s(s(zero)),s(s(zero)))))),
inference(unit_resolution,[status(thm)],[196,176]) ).
tff(198,plain,
minus(s(d(s(zero))),s(zero)) = s(s(zero)),
inference(transitivity,[status(thm)],[90,93,103,106,147]) ).
tff(199,plain,
quot(minus(s(d(s(zero))),s(zero)),s(s(zero))) = quot(s(s(zero)),s(s(zero))),
inference(monotonicity,[status(thm)],[198]) ).
tff(200,plain,
quot(minus(s(d(s(zero))),s(zero)),s(s(zero))) = s(zero),
inference(transitivity,[status(thm)],[199,190,181]) ).
tff(201,plain,
s(quot(minus(s(d(s(zero))),s(zero)),s(s(zero)))) = s(s(zero)),
inference(monotonicity,[status(thm)],[200]) ).
tff(202,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(zero))) = s(quot(minus(s(d(s(zero))),s(zero)),s(s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(203,plain,
quot(s(s(d(s(zero)))),s(s(zero))) = s(quot(minus(s(d(s(zero))),s(zero)),s(s(zero)))),
inference(unit_resolution,[status(thm)],[202,188]) ).
tff(204,plain,
quot(d(e(s(zero))),s(s(zero))) = quot(s(s(d(s(zero)))),s(s(zero))),
inference(monotonicity,[status(thm)],[41]) ).
tff(205,plain,
d(s(s(zero))) = d(e(s(zero))),
inference(symmetry,[status(thm)],[40]) ).
tff(206,plain,
s(s(d(s(zero)))) = d(s(s(zero))),
inference(symmetry,[status(thm)],[22]) ).
tff(207,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(d(e(s(zero)))),s(zero)) = s(minus(d(e(s(zero))),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(208,plain,
if_minus(false,s(d(e(s(zero)))),s(zero)) = s(minus(d(e(s(zero))),s(zero))),
inference(unit_resolution,[status(thm)],[207,84]) ).
tff(209,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(d(e(s(zero)))),s(zero)) = le(d(e(s(zero))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(210,plain,
le(s(d(e(s(zero)))),s(zero)) = le(d(e(s(zero))),zero),
inference(unit_resolution,[status(thm)],[209,62]) ).
tff(211,plain,
le(d(e(s(zero))),zero) = le(s(d(e(s(zero)))),s(zero)),
inference(symmetry,[status(thm)],[210]) ).
tff(212,plain,
d(e(s(zero))) = s(s(s(s(zero)))),
inference(transitivity,[status(thm)],[40,22,20]) ).
tff(213,plain,
le(d(e(s(zero))),zero) = le(s(s(s(s(zero)))),zero),
inference(monotonicity,[status(thm)],[212]) ).
tff(214,plain,
le(s(s(s(s(zero)))),zero) = le(d(e(s(zero))),zero),
inference(symmetry,[status(thm)],[213]) ).
tff(215,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(s(s(zero)))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(216,plain,
le(s(s(s(s(zero)))),zero) = false,
inference(unit_resolution,[status(thm)],[215,72]) ).
tff(217,plain,
false = le(s(s(s(s(zero)))),zero),
inference(symmetry,[status(thm)],[216]) ).
tff(218,plain,
false = le(s(d(e(s(zero)))),s(zero)),
inference(transitivity,[status(thm)],[217,214,211]) ).
tff(219,plain,
if_minus(false,s(d(e(s(zero)))),s(zero)) = if_minus(le(s(d(e(s(zero)))),s(zero)),s(d(e(s(zero)))),s(zero)),
inference(monotonicity,[status(thm)],[218]) ).
tff(220,plain,
if_minus(le(s(d(e(s(zero)))),s(zero)),s(d(e(s(zero)))),s(zero)) = if_minus(false,s(d(e(s(zero)))),s(zero)),
inference(symmetry,[status(thm)],[219]) ).
tff(221,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(d(e(s(zero)))),s(zero)) = if_minus(le(s(d(e(s(zero)))),s(zero)),s(d(e(s(zero)))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(222,plain,
minus(s(d(e(s(zero)))),s(zero)) = if_minus(le(s(d(e(s(zero)))),s(zero)),s(d(e(s(zero)))),s(zero)),
inference(unit_resolution,[status(thm)],[221,50]) ).
tff(223,plain,
s(d(e(s(zero)))) = s(d(s(s(zero)))),
inference(monotonicity,[status(thm)],[40]) ).
tff(224,plain,
s(d(s(s(zero)))) = s(d(e(s(zero)))),
inference(symmetry,[status(thm)],[223]) ).
tff(225,plain,
minus(s(d(s(s(zero)))),s(zero)) = minus(s(d(e(s(zero)))),s(zero)),
inference(monotonicity,[status(thm)],[224]) ).
tff(226,plain,
minus(s(d(s(s(zero)))),s(zero)) = d(e(s(zero))),
inference(transitivity,[status(thm)],[225,222,220,208,153,206,205]) ).
tff(227,plain,
quot(minus(s(d(s(s(zero)))),s(zero)),s(s(zero))) = quot(d(e(s(zero))),s(s(zero))),
inference(monotonicity,[status(thm)],[226]) ).
tff(228,plain,
quot(minus(s(d(s(s(zero)))),s(zero)),s(s(zero))) = d(s(zero)),
inference(transitivity,[status(thm)],[227,204,203,201,16,10]) ).
tff(229,plain,
s(quot(minus(s(d(s(s(zero)))),s(zero)),s(s(zero)))) = s(d(s(zero))),
inference(monotonicity,[status(thm)],[228]) ).
tff(230,plain,
( ~ ! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) )
| ( quot(s(s(d(s(s(zero))))),s(s(zero))) = s(quot(minus(s(d(s(s(zero)))),s(zero)),s(s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(231,plain,
quot(s(s(d(s(s(zero))))),s(s(zero))) = s(quot(minus(s(d(s(s(zero)))),s(zero)),s(s(zero)))),
inference(unit_resolution,[status(thm)],[230,188]) ).
tff(232,plain,
quot(s(s(d(s(s(zero))))),s(s(zero))) = minus(d(e(s(zero))),s(zero)),
inference(transitivity,[status(thm)],[231,229,150,87,77,53,43]) ).
tff(233,plain,
s(quot(s(s(d(s(s(zero))))),s(s(zero)))) = s(minus(d(e(s(zero))),s(zero))),
inference(monotonicity,[status(thm)],[232]) ).
tff(234,plain,
s(quot(s(s(d(s(s(zero))))),s(s(zero)))) = s(s(s(s(zero)))),
inference(transitivity,[status(thm)],[233,153,20]) ).
tff(235,plain,
log(s(quot(s(s(d(s(s(zero))))),s(s(zero))))) = log(s(s(s(s(zero))))),
inference(monotonicity,[status(thm)],[234]) ).
tff(236,plain,
log(s(quot(s(s(d(s(s(zero))))),s(s(zero))))) = d(s(zero)),
inference(transitivity,[status(thm)],[235,197,195,16,10]) ).
tff(237,plain,
s(log(s(quot(s(s(d(s(s(zero))))),s(s(zero)))))) = s(d(s(zero))),
inference(monotonicity,[status(thm)],[236]) ).
tff(238,plain,
( ~ ! [X: $i] : ( log(s(s(X))) = s(log(s(quot(X,s(s(zero)))))) )
| ( log(s(s(s(s(d(s(s(zero)))))))) = s(log(s(quot(s(s(d(s(s(zero))))),s(s(zero)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(239,plain,
log(s(s(s(s(d(s(s(zero)))))))) = s(log(s(quot(s(s(d(s(s(zero))))),s(s(zero)))))),
inference(unit_resolution,[status(thm)],[238,176]) ).
tff(240,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(241,plain,
d(s(s(s(zero)))) = s(s(d(s(s(zero))))),
inference(unit_resolution,[status(thm)],[240,7]) ).
tff(242,plain,
s(s(d(s(s(zero))))) = d(s(s(s(zero)))),
inference(symmetry,[status(thm)],[241]) ).
tff(243,plain,
s(s(s(d(s(s(zero)))))) = s(d(s(s(s(zero))))),
inference(monotonicity,[status(thm)],[242]) ).
tff(244,plain,
s(s(s(s(d(s(s(zero))))))) = s(s(d(s(s(s(zero)))))),
inference(monotonicity,[status(thm)],[243]) ).
tff(245,plain,
s(s(d(s(s(s(zero)))))) = s(s(s(s(d(s(s(zero))))))),
inference(symmetry,[status(thm)],[244]) ).
tff(246,plain,
s(d(s(s(s(zero))))) = s(s(s(d(s(s(zero)))))),
inference(symmetry,[status(thm)],[243]) ).
tff(247,plain,
minus(s(d(s(s(s(zero))))),s(zero)) = minus(s(s(s(d(s(s(zero)))))),s(zero)),
inference(monotonicity,[status(thm)],[246]) ).
tff(248,plain,
minus(s(s(s(d(s(s(zero)))))),s(zero)) = minus(s(d(s(s(s(zero))))),s(zero)),
inference(symmetry,[status(thm)],[247]) ).
tff(249,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(zero)))))),s(zero)) = if_minus(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(250,plain,
minus(s(s(s(d(s(s(zero)))))),s(zero)) = if_minus(le(s(s(s(d(s(s(zero)))))),s(zero)),s(s(s(d(s(s(zero)))))),s(zero)),
inference(unit_resolution,[status(thm)],[249,50]) ).
tff(251,plain,
if_minus(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)],[250]) ).
tff(252,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(d(s(s(zero))))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(253,plain,
le(s(s(d(s(s(zero))))),zero) = false,
inference(unit_resolution,[status(thm)],[252,72]) ).
tff(254,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(255,plain,
le(s(s(s(d(s(s(zero)))))),s(zero)) = le(s(s(d(s(s(zero))))),zero),
inference(unit_resolution,[status(thm)],[254,62]) ).
tff(256,plain,
le(s(s(s(d(s(s(zero)))))),s(zero)) = false,
inference(transitivity,[status(thm)],[255,253]) ).
tff(257,plain,
if_minus(le(s(s(s(d(s(s(zero)))))),s(zero)),s(s(s(d(s(s(zero)))))),s(zero)) = if_minus(false,s(s(s(d(s(s(zero)))))),s(zero)),
inference(monotonicity,[status(thm)],[256]) ).
tff(258,plain,
if_minus(false,s(s(s(d(s(s(zero)))))),s(zero)) = if_minus(le(s(s(s(d(s(s(zero)))))),s(zero)),s(s(s(d(s(s(zero)))))),s(zero)),
inference(symmetry,[status(thm)],[257]) ).
tff(259,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(s(s(d(s(s(zero)))))),s(zero)) = s(minus(s(s(d(s(s(zero))))),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(260,plain,
if_minus(false,s(s(s(d(s(s(zero)))))),s(zero)) = s(minus(s(s(d(s(s(zero))))),s(zero))),
inference(unit_resolution,[status(thm)],[259,84]) ).
tff(261,plain,
s(minus(s(s(d(s(s(zero))))),s(zero))) = if_minus(false,s(s(s(d(s(s(zero)))))),s(zero)),
inference(symmetry,[status(thm)],[260]) ).
tff(262,plain,
minus(s(d(s(s(zero)))),s(zero)) = d(s(s(zero))),
inference(transitivity,[status(thm)],[225,222,220,208,153,206]) ).
tff(263,plain,
s(minus(s(d(s(s(zero)))),s(zero))) = s(d(s(s(zero)))),
inference(monotonicity,[status(thm)],[262]) ).
tff(264,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(s(d(s(s(zero))))),s(zero)) = s(minus(s(d(s(s(zero)))),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(265,plain,
if_minus(false,s(s(d(s(s(zero))))),s(zero)) = s(minus(s(d(s(s(zero)))),s(zero))),
inference(unit_resolution,[status(thm)],[264,84]) ).
tff(266,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(d(e(s(zero)))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(267,plain,
le(s(d(e(s(zero)))),zero) = false,
inference(unit_resolution,[status(thm)],[266,72]) ).
tff(268,plain,
le(s(d(s(s(zero)))),zero) = le(s(d(e(s(zero)))),zero),
inference(monotonicity,[status(thm)],[224]) ).
tff(269,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(270,plain,
le(s(s(d(s(s(zero))))),s(zero)) = le(s(d(s(s(zero)))),zero),
inference(unit_resolution,[status(thm)],[269,62]) ).
tff(271,plain,
le(s(s(d(s(s(zero))))),s(zero)) = false,
inference(transitivity,[status(thm)],[270,268,267]) ).
tff(272,plain,
if_minus(le(s(s(d(s(s(zero))))),s(zero)),s(s(d(s(s(zero))))),s(zero)) = if_minus(false,s(s(d(s(s(zero))))),s(zero)),
inference(monotonicity,[status(thm)],[271]) ).
tff(273,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(d(s(s(zero))))),s(zero)) = if_minus(le(s(s(d(s(s(zero))))),s(zero)),s(s(d(s(s(zero))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(274,plain,
minus(s(s(d(s(s(zero))))),s(zero)) = if_minus(le(s(s(d(s(s(zero))))),s(zero)),s(s(d(s(s(zero))))),s(zero)),
inference(unit_resolution,[status(thm)],[273,50]) ).
tff(275,plain,
minus(s(s(d(s(s(zero))))),s(zero)) = s(d(s(s(zero)))),
inference(transitivity,[status(thm)],[274,272,265,263]) ).
tff(276,plain,
s(minus(s(s(d(s(s(zero))))),s(zero))) = s(s(d(s(s(zero))))),
inference(monotonicity,[status(thm)],[275]) ).
tff(277,plain,
s(s(d(s(s(zero))))) = s(minus(s(s(d(s(s(zero))))),s(zero))),
inference(symmetry,[status(thm)],[276]) ).
tff(278,plain,
d(s(s(s(zero)))) = minus(s(d(s(s(s(zero))))),s(zero)),
inference(transitivity,[status(thm)],[241,277,261,258,251,248]) ).
tff(279,plain,
s(d(s(s(s(zero))))) = s(minus(s(d(s(s(s(zero))))),s(zero))),
inference(monotonicity,[status(thm)],[278]) ).
tff(280,plain,
s(minus(s(d(s(s(s(zero))))),s(zero))) = s(d(s(s(s(zero))))),
inference(symmetry,[status(thm)],[279]) ).
tff(281,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(282,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)],[281,84]) ).
tff(283,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(284,plain,
le(s(s(d(s(s(s(zero)))))),s(zero)) = le(s(d(s(s(s(zero))))),zero),
inference(unit_resolution,[status(thm)],[283,62]) ).
tff(285,plain,
le(s(d(s(s(s(zero))))),zero) = le(s(s(d(s(s(s(zero)))))),s(zero)),
inference(symmetry,[status(thm)],[284]) ).
tff(286,plain,
le(s(d(s(s(s(zero))))),zero) = le(s(s(s(d(s(s(zero)))))),zero),
inference(monotonicity,[status(thm)],[246]) ).
tff(287,plain,
le(s(s(s(d(s(s(zero)))))),zero) = le(s(d(s(s(s(zero))))),zero),
inference(symmetry,[status(thm)],[286]) ).
tff(288,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(s(d(s(s(zero)))))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(289,plain,
le(s(s(s(d(s(s(zero)))))),zero) = false,
inference(unit_resolution,[status(thm)],[288,72]) ).
tff(290,plain,
false = le(s(s(s(d(s(s(zero)))))),zero),
inference(symmetry,[status(thm)],[289]) ).
tff(291,plain,
false = le(s(s(d(s(s(s(zero)))))),s(zero)),
inference(transitivity,[status(thm)],[290,287,285]) ).
tff(292,plain,
if_minus(false,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(monotonicity,[status(thm)],[291]) ).
tff(293,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(symmetry,[status(thm)],[292]) ).
tff(294,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(295,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)],[294,50]) ).
tff(296,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(297,plain,
d(s(s(s(s(zero))))) = s(s(d(s(s(s(zero)))))),
inference(unit_resolution,[status(thm)],[296,7]) ).
tff(298,plain,
( ~ ! [X: $i] : ( e(s(X)) = d(e(X)) )
| ( e(s(s(zero))) = d(e(s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(299,plain,
e(s(s(zero))) = d(e(s(zero))),
inference(unit_resolution,[status(thm)],[298,36]) ).
tff(300,plain,
d(e(s(zero))) = e(s(s(zero))),
inference(symmetry,[status(thm)],[299]) ).
tff(301,plain,
s(s(s(s(zero)))) = e(s(s(zero))),
inference(transitivity,[status(thm)],[19,206,205,300]) ).
tff(302,plain,
d(s(s(s(s(zero))))) = d(e(s(s(zero)))),
inference(monotonicity,[status(thm)],[301]) ).
tff(303,plain,
d(e(s(s(zero)))) = d(s(s(s(s(zero))))),
inference(symmetry,[status(thm)],[302]) ).
tff(304,plain,
d(e(s(s(zero)))) = s(s(d(s(s(s(zero)))))),
inference(transitivity,[status(thm)],[303,297]) ).
tff(305,plain,
minus(d(e(s(s(zero)))),s(zero)) = minus(s(s(d(s(s(s(zero)))))),s(zero)),
inference(monotonicity,[status(thm)],[304]) ).
tff(306,plain,
minus(d(e(s(s(zero)))),s(zero)) = s(d(s(s(s(zero))))),
inference(transitivity,[status(thm)],[305,295,293,282,280]) ).
tff(307,plain,
s(minus(d(e(s(s(zero)))),s(zero))) = s(s(d(s(s(s(zero)))))),
inference(monotonicity,[status(thm)],[306]) ).
tff(308,plain,
minus(s(s(d(s(s(s(zero)))))),s(zero)) = minus(d(e(s(s(zero)))),s(zero)),
inference(symmetry,[status(thm)],[305]) ).
tff(309,plain,
if_minus(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)],[295]) ).
tff(310,plain,
s(minus(s(d(s(s(s(zero))))),s(zero))) = if_minus(false,s(s(d(s(s(s(zero)))))),s(zero)),
inference(symmetry,[status(thm)],[282]) ).
tff(311,plain,
minus(s(d(s(s(s(zero))))),s(zero)) = s(s(d(s(s(zero))))),
inference(transitivity,[status(thm)],[247,250,257,260,276]) ).
tff(312,plain,
quot(minus(s(d(s(s(s(zero))))),s(zero)),s(s(zero))) = quot(s(s(d(s(s(zero))))),s(s(zero))),
inference(monotonicity,[status(thm)],[311]) ).
tff(313,plain,
quot(minus(s(d(s(s(s(zero))))),s(zero)),s(s(zero))) = minus(d(e(s(zero))),s(zero)),
inference(transitivity,[status(thm)],[312,231,229,150,87,77,53,43]) ).
tff(314,plain,
s(quot(minus(s(d(s(s(s(zero))))),s(zero)),s(s(zero)))) = s(minus(d(e(s(zero))),s(zero))),
inference(monotonicity,[status(thm)],[313]) ).
tff(315,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(316,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)],[315,188]) ).
tff(317,plain,
quot(d(e(s(s(zero)))),s(s(zero))) = quot(s(s(d(s(s(s(zero)))))),s(s(zero))),
inference(monotonicity,[status(thm)],[304]) ).
tff(318,plain,
s(s(d(s(s(s(zero)))))) = d(s(s(s(s(zero))))),
inference(symmetry,[status(thm)],[297]) ).
tff(319,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(d(e(s(s(zero))))),s(zero)) = s(minus(d(e(s(s(zero)))),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(320,plain,
if_minus(false,s(d(e(s(s(zero))))),s(zero)) = s(minus(d(e(s(s(zero)))),s(zero))),
inference(unit_resolution,[status(thm)],[319,84]) ).
tff(321,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(d(s(s(s(zero)))))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(322,plain,
le(s(s(d(s(s(s(zero)))))),zero) = false,
inference(unit_resolution,[status(thm)],[321,72]) ).
tff(323,plain,
le(d(e(s(s(zero)))),zero) = le(s(s(d(s(s(s(zero)))))),zero),
inference(monotonicity,[status(thm)],[304]) ).
tff(324,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(d(e(s(s(zero))))),s(zero)) = le(d(e(s(s(zero)))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(325,plain,
le(s(d(e(s(s(zero))))),s(zero)) = le(d(e(s(s(zero)))),zero),
inference(unit_resolution,[status(thm)],[324,62]) ).
tff(326,plain,
le(s(d(e(s(s(zero))))),s(zero)) = false,
inference(transitivity,[status(thm)],[325,323,322]) ).
tff(327,plain,
if_minus(le(s(d(e(s(s(zero))))),s(zero)),s(d(e(s(s(zero))))),s(zero)) = if_minus(false,s(d(e(s(s(zero))))),s(zero)),
inference(monotonicity,[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(d(e(s(s(zero))))),s(zero)) = if_minus(le(s(d(e(s(s(zero))))),s(zero)),s(d(e(s(s(zero))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(329,plain,
minus(s(d(e(s(s(zero))))),s(zero)) = if_minus(le(s(d(e(s(s(zero))))),s(zero)),s(d(e(s(s(zero))))),s(zero)),
inference(unit_resolution,[status(thm)],[328,50]) ).
tff(330,plain,
minus(s(d(e(s(s(zero))))),s(zero)) = d(e(s(s(zero)))),
inference(transitivity,[status(thm)],[329,327,320,307,318,302]) ).
tff(331,plain,
quot(minus(s(d(e(s(s(zero))))),s(zero)),s(s(zero))) = quot(d(e(s(s(zero)))),s(s(zero))),
inference(monotonicity,[status(thm)],[330]) ).
tff(332,plain,
quot(minus(s(d(e(s(s(zero))))),s(zero)),s(s(zero))) = d(s(s(zero))),
inference(transitivity,[status(thm)],[331,317,316,314,153,206]) ).
tff(333,plain,
s(quot(minus(s(d(e(s(s(zero))))),s(zero)),s(s(zero)))) = s(d(s(s(zero)))),
inference(monotonicity,[status(thm)],[332]) ).
tff(334,plain,
( ~ ! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) )
| ( quot(s(s(d(e(s(s(zero)))))),s(s(zero))) = s(quot(minus(s(d(e(s(s(zero))))),s(zero)),s(s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(335,plain,
quot(s(s(d(e(s(s(zero)))))),s(s(zero))) = s(quot(minus(s(d(e(s(s(zero))))),s(zero)),s(s(zero)))),
inference(unit_resolution,[status(thm)],[334,188]) ).
tff(336,plain,
d(d(e(s(zero)))) = d(e(s(s(zero)))),
inference(monotonicity,[status(thm)],[300]) ).
tff(337,plain,
s(d(d(e(s(zero))))) = s(d(e(s(s(zero))))),
inference(monotonicity,[status(thm)],[336]) ).
tff(338,plain,
s(d(e(s(s(zero))))) = s(d(d(e(s(zero))))),
inference(symmetry,[status(thm)],[337]) ).
tff(339,plain,
s(s(d(e(s(s(zero)))))) = s(s(d(d(e(s(zero)))))),
inference(monotonicity,[status(thm)],[338]) ).
tff(340,plain,
s(s(d(d(e(s(zero)))))) = s(s(d(e(s(s(zero)))))),
inference(symmetry,[status(thm)],[339]) ).
tff(341,plain,
quot(s(s(d(d(e(s(zero)))))),s(s(zero))) = quot(s(s(d(e(s(s(zero)))))),s(s(zero))),
inference(monotonicity,[status(thm)],[340]) ).
tff(342,plain,
s(minus(s(d(e(s(s(zero))))),s(zero))) = s(d(e(s(s(zero))))),
inference(monotonicity,[status(thm)],[330]) ).
tff(343,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(s(d(e(s(s(zero)))))),s(zero)) = s(minus(s(d(e(s(s(zero))))),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(344,plain,
if_minus(false,s(s(d(e(s(s(zero)))))),s(zero)) = s(minus(s(d(e(s(s(zero))))),s(zero))),
inference(unit_resolution,[status(thm)],[343,84]) ).
tff(345,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(d(e(s(s(zero))))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(346,plain,
le(s(d(e(s(s(zero))))),zero) = false,
inference(unit_resolution,[status(thm)],[345,72]) ).
tff(347,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(d(e(s(s(zero)))))),s(zero)) = le(s(d(e(s(s(zero))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(348,plain,
le(s(s(d(e(s(s(zero)))))),s(zero)) = le(s(d(e(s(s(zero))))),zero),
inference(unit_resolution,[status(thm)],[347,62]) ).
tff(349,plain,
le(s(s(d(e(s(s(zero)))))),s(zero)) = false,
inference(transitivity,[status(thm)],[348,346]) ).
tff(350,plain,
if_minus(le(s(s(d(e(s(s(zero)))))),s(zero)),s(s(d(e(s(s(zero)))))),s(zero)) = if_minus(false,s(s(d(e(s(s(zero)))))),s(zero)),
inference(monotonicity,[status(thm)],[349]) ).
tff(351,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(d(e(s(s(zero)))))),s(zero)) = if_minus(le(s(s(d(e(s(s(zero)))))),s(zero)),s(s(d(e(s(s(zero)))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(352,plain,
minus(s(s(d(e(s(s(zero)))))),s(zero)) = if_minus(le(s(s(d(e(s(s(zero)))))),s(zero)),s(s(d(e(s(s(zero)))))),s(zero)),
inference(unit_resolution,[status(thm)],[351,50]) ).
tff(353,plain,
minus(s(s(d(d(e(s(zero)))))),s(zero)) = minus(s(s(d(e(s(s(zero)))))),s(zero)),
inference(monotonicity,[status(thm)],[340]) ).
tff(354,plain,
minus(s(s(d(d(e(s(zero)))))),s(zero)) = s(d(d(e(s(zero))))),
inference(transitivity,[status(thm)],[353,352,350,344,342,338]) ).
tff(355,plain,
s(minus(s(s(d(d(e(s(zero)))))),s(zero))) = s(s(d(d(e(s(zero)))))),
inference(monotonicity,[status(thm)],[354]) ).
tff(356,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(s(s(d(d(e(s(zero))))))),s(zero)) = s(minus(s(s(d(d(e(s(zero)))))),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(357,plain,
if_minus(false,s(s(s(d(d(e(s(zero))))))),s(zero)) = s(minus(s(s(d(d(e(s(zero)))))),s(zero))),
inference(unit_resolution,[status(thm)],[356,84]) ).
tff(358,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(d(e(s(s(zero)))))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(359,plain,
le(s(s(d(e(s(s(zero)))))),zero) = false,
inference(unit_resolution,[status(thm)],[358,72]) ).
tff(360,plain,
le(s(s(d(d(e(s(zero)))))),zero) = le(s(s(d(e(s(s(zero)))))),zero),
inference(monotonicity,[status(thm)],[340]) ).
tff(361,plain,
( ~ ! [Y: $i,X: $i] : ( le(s(X),s(Y)) = le(X,Y) )
| ( le(s(s(s(d(d(e(s(zero))))))),s(zero)) = le(s(s(d(d(e(s(zero)))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(362,plain,
le(s(s(s(d(d(e(s(zero))))))),s(zero)) = le(s(s(d(d(e(s(zero)))))),zero),
inference(unit_resolution,[status(thm)],[361,62]) ).
tff(363,plain,
le(s(s(s(d(d(e(s(zero))))))),s(zero)) = false,
inference(transitivity,[status(thm)],[362,360,359]) ).
tff(364,plain,
if_minus(le(s(s(s(d(d(e(s(zero))))))),s(zero)),s(s(s(d(d(e(s(zero))))))),s(zero)) = if_minus(false,s(s(s(d(d(e(s(zero))))))),s(zero)),
inference(monotonicity,[status(thm)],[363]) ).
tff(365,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(s(zero))))))),s(zero)) = if_minus(le(s(s(s(d(d(e(s(zero))))))),s(zero)),s(s(s(d(d(e(s(zero))))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(366,plain,
minus(s(s(s(d(d(e(s(zero))))))),s(zero)) = if_minus(le(s(s(s(d(d(e(s(zero))))))),s(zero)),s(s(s(d(d(e(s(zero))))))),s(zero)),
inference(unit_resolution,[status(thm)],[365,50]) ).
tff(367,plain,
d(s(d(s(s(zero))))) = d(s(d(e(s(zero))))),
inference(monotonicity,[status(thm)],[224]) ).
tff(368,plain,
d(s(d(e(s(zero))))) = d(s(d(s(s(zero))))),
inference(symmetry,[status(thm)],[367]) ).
tff(369,plain,
( ~ ! [X: $i] : ( d(s(X)) = s(s(d(X))) )
| ( d(s(d(e(s(zero))))) = s(s(d(d(e(s(zero)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(370,plain,
d(s(d(e(s(zero))))) = s(s(d(d(e(s(zero)))))),
inference(unit_resolution,[status(thm)],[369,7]) ).
tff(371,plain,
s(s(d(d(e(s(zero)))))) = d(s(d(e(s(zero))))),
inference(symmetry,[status(thm)],[370]) ).
tff(372,plain,
s(s(d(d(e(s(zero)))))) = d(s(d(s(s(zero))))),
inference(transitivity,[status(thm)],[371,368]) ).
tff(373,plain,
s(s(s(d(d(e(s(zero))))))) = s(d(s(d(s(s(zero)))))),
inference(monotonicity,[status(thm)],[372]) ).
tff(374,plain,
s(d(s(d(s(s(zero)))))) = s(s(s(d(d(e(s(zero))))))),
inference(symmetry,[status(thm)],[373]) ).
tff(375,plain,
minus(s(d(s(d(s(s(zero)))))),s(zero)) = minus(s(s(s(d(d(e(s(zero))))))),s(zero)),
inference(monotonicity,[status(thm)],[374]) ).
tff(376,plain,
minus(s(d(s(d(s(s(zero)))))),s(zero)) = s(s(d(d(e(s(zero)))))),
inference(transitivity,[status(thm)],[375,366,364,357,355]) ).
tff(377,plain,
quot(minus(s(d(s(d(s(s(zero)))))),s(zero)),s(s(zero))) = quot(s(s(d(d(e(s(zero)))))),s(s(zero))),
inference(monotonicity,[status(thm)],[376]) ).
tff(378,plain,
quot(minus(s(d(s(d(s(s(zero)))))),s(zero)),s(s(zero))) = s(d(s(s(zero)))),
inference(transitivity,[status(thm)],[377,341,335,333]) ).
tff(379,plain,
s(quot(minus(s(d(s(d(s(s(zero)))))),s(zero)),s(s(zero)))) = s(s(d(s(s(zero))))),
inference(monotonicity,[status(thm)],[378]) ).
tff(380,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(zero))))))),s(s(zero))) = s(quot(minus(s(d(s(d(s(s(zero)))))),s(zero)),s(s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(381,plain,
quot(s(s(d(s(d(s(s(zero))))))),s(s(zero))) = s(quot(minus(s(d(s(d(s(s(zero)))))),s(zero)),s(s(zero)))),
inference(unit_resolution,[status(thm)],[380,188]) ).
tff(382,plain,
minus(s(s(d(d(e(s(zero)))))),zero) = minus(s(s(d(e(s(s(zero)))))),zero),
inference(monotonicity,[status(thm)],[340]) ).
tff(383,plain,
minus(s(s(d(e(s(s(zero)))))),zero) = minus(s(s(d(d(e(s(zero)))))),zero),
inference(symmetry,[status(thm)],[382]) ).
tff(384,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(d(e(s(s(zero)))))),zero) = if_minus(le(s(s(d(e(s(s(zero)))))),zero),s(s(d(e(s(s(zero)))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(385,plain,
minus(s(s(d(e(s(s(zero)))))),zero) = if_minus(le(s(s(d(e(s(s(zero)))))),zero),s(s(d(e(s(s(zero)))))),zero),
inference(unit_resolution,[status(thm)],[384,50]) ).
tff(386,plain,
if_minus(le(s(s(d(e(s(s(zero)))))),zero),s(s(d(e(s(s(zero)))))),zero) = minus(s(s(d(e(s(s(zero)))))),zero),
inference(symmetry,[status(thm)],[385]) ).
tff(387,plain,
if_minus(le(s(s(d(e(s(s(zero)))))),zero),s(s(d(e(s(s(zero)))))),zero) = if_minus(false,s(s(d(e(s(s(zero)))))),zero),
inference(monotonicity,[status(thm)],[359]) ).
tff(388,plain,
if_minus(false,s(s(d(e(s(s(zero)))))),zero) = if_minus(le(s(s(d(e(s(s(zero)))))),zero),s(s(d(e(s(s(zero)))))),zero),
inference(symmetry,[status(thm)],[387]) ).
tff(389,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(s(d(e(s(s(zero)))))),zero) = s(minus(s(d(e(s(s(zero))))),zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(390,plain,
if_minus(false,s(s(d(e(s(s(zero)))))),zero) = s(minus(s(d(e(s(s(zero))))),zero)),
inference(unit_resolution,[status(thm)],[389,84]) ).
tff(391,plain,
s(minus(s(d(e(s(s(zero))))),zero)) = if_minus(false,s(s(d(e(s(s(zero)))))),zero),
inference(symmetry,[status(thm)],[390]) ).
tff(392,plain,
^ [Y: $i] :
refl(( ( minus(zero,Y) = zero )
<=> ( minus(zero,Y) = zero ) )),
inference(bind,[status(th)],[]) ).
tff(393,plain,
( ! [Y: $i] : ( minus(zero,Y) = zero )
<=> ! [Y: $i] : ( minus(zero,Y) = zero ) ),
inference(quant_intro,[status(thm)],[392]) ).
tff(394,plain,
( ! [Y: $i] : ( minus(zero,Y) = zero )
<=> ! [Y: $i] : ( minus(zero,Y) = zero ) ),
inference(rewrite,[status(thm)],[]) ).
tff(395,axiom,
! [Y: $i] : ( minus(zero,Y) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule4) ).
tff(396,plain,
! [Y: $i] : ( minus(zero,Y) = zero ),
inference(modus_ponens,[status(thm)],[395,394]) ).
tff(397,plain,
! [Y: $i] : ( minus(zero,Y) = zero ),
inference(skolemize,[status(sab)],[396]) ).
tff(398,plain,
! [Y: $i] : ( minus(zero,Y) = zero ),
inference(modus_ponens,[status(thm)],[397,393]) ).
tff(399,plain,
( ~ ! [Y: $i] : ( minus(zero,Y) = zero )
| ( minus(zero,zero) = zero ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(400,plain,
minus(zero,zero) = zero,
inference(unit_resolution,[status(thm)],[399,398]) ).
tff(401,plain,
s(minus(zero,zero)) = s(zero),
inference(monotonicity,[status(thm)],[400]) ).
tff(402,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(403,plain,
if_minus(false,s(zero),zero) = s(minus(zero,zero)),
inference(unit_resolution,[status(thm)],[402,84]) ).
tff(404,plain,
if_minus(le(s(zero),zero),s(zero),zero) = if_minus(false,s(zero),zero),
inference(monotonicity,[status(thm)],[137]) ).
tff(405,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(406,plain,
minus(s(zero),zero) = if_minus(le(s(zero),zero),s(zero),zero),
inference(unit_resolution,[status(thm)],[405,50]) ).
tff(407,plain,
minus(s(zero),zero) = s(zero),
inference(transitivity,[status(thm)],[406,404,403,401]) ).
tff(408,plain,
s(minus(s(zero),zero)) = s(s(zero)),
inference(monotonicity,[status(thm)],[407]) ).
tff(409,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(410,plain,
if_minus(false,s(s(zero)),zero) = s(minus(s(zero),zero)),
inference(unit_resolution,[status(thm)],[409,84]) ).
tff(411,plain,
if_minus(le(s(s(zero)),zero),s(s(zero)),zero) = if_minus(false,s(s(zero)),zero),
inference(monotonicity,[status(thm)],[96]) ).
tff(412,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(413,plain,
minus(s(s(zero)),zero) = if_minus(le(s(s(zero)),zero),s(s(zero)),zero),
inference(unit_resolution,[status(thm)],[412,50]) ).
tff(414,plain,
minus(d(e(zero)),zero) = minus(s(s(zero)),zero),
inference(monotonicity,[status(thm)],[144]) ).
tff(415,plain,
minus(d(e(zero)),zero) = d(s(zero)),
inference(transitivity,[status(thm)],[414,413,411,410,408,16,10]) ).
tff(416,plain,
s(minus(d(e(zero)),zero)) = s(d(s(zero))),
inference(monotonicity,[status(thm)],[415]) ).
tff(417,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(418,plain,
if_minus(false,s(d(e(zero))),zero) = s(minus(d(e(zero)),zero)),
inference(unit_resolution,[status(thm)],[417,84]) ).
tff(419,plain,
le(s(d(e(zero))),zero) = le(s(s(s(zero))),zero),
inference(monotonicity,[status(thm)],[100]) ).
tff(420,plain,
le(s(d(e(zero))),zero) = false,
inference(transitivity,[status(thm)],[419,74]) ).
tff(421,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)],[420]) ).
tff(422,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(423,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)],[422,50]) ).
tff(424,plain,
minus(s(d(s(zero))),zero) = minus(s(d(e(zero))),zero),
inference(monotonicity,[status(thm)],[89]) ).
tff(425,plain,
minus(s(d(s(zero))),zero) = minus(d(e(s(zero))),s(zero)),
inference(transitivity,[status(thm)],[424,423,421,418,416,150,87,77,53,43]) ).
tff(426,plain,
s(minus(s(d(s(zero))),zero)) = s(minus(d(e(s(zero))),s(zero))),
inference(monotonicity,[status(thm)],[425]) ).
tff(427,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(s(d(s(zero)))),zero) = s(minus(s(d(s(zero))),zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(428,plain,
if_minus(false,s(s(d(s(zero)))),zero) = s(minus(s(d(s(zero))),zero)),
inference(unit_resolution,[status(thm)],[427,84]) ).
tff(429,plain,
le(s(s(d(s(zero)))),zero) = le(s(s(s(s(zero)))),zero),
inference(monotonicity,[status(thm)],[20]) ).
tff(430,plain,
le(s(s(d(s(zero)))),zero) = false,
inference(transitivity,[status(thm)],[429,216]) ).
tff(431,plain,
if_minus(le(s(s(d(s(zero)))),zero),s(s(d(s(zero)))),zero) = if_minus(false,s(s(d(s(zero)))),zero),
inference(monotonicity,[status(thm)],[430]) ).
tff(432,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(d(s(zero)))),zero) = if_minus(le(s(s(d(s(zero)))),zero),s(s(d(s(zero)))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(433,plain,
minus(s(s(d(s(zero)))),zero) = if_minus(le(s(s(d(s(zero)))),zero),s(s(d(s(zero)))),zero),
inference(unit_resolution,[status(thm)],[432,50]) ).
tff(434,plain,
minus(d(e(s(zero))),zero) = minus(s(s(d(s(zero)))),zero),
inference(monotonicity,[status(thm)],[41]) ).
tff(435,plain,
minus(d(e(s(zero))),zero) = d(s(s(zero))),
inference(transitivity,[status(thm)],[434,433,431,428,426,153,206]) ).
tff(436,plain,
s(minus(d(e(s(zero))),zero)) = s(d(s(s(zero)))),
inference(monotonicity,[status(thm)],[435]) ).
tff(437,plain,
minus(s(s(d(s(zero)))),zero) = minus(d(e(s(zero))),zero),
inference(symmetry,[status(thm)],[434]) ).
tff(438,plain,
if_minus(le(s(s(d(s(zero)))),zero),s(s(d(s(zero)))),zero) = minus(s(s(d(s(zero)))),zero),
inference(symmetry,[status(thm)],[433]) ).
tff(439,plain,
if_minus(le(s(s(d(s(zero)))),zero),s(s(d(s(zero)))),zero) = minus(d(e(s(zero))),zero),
inference(transitivity,[status(thm)],[438,437]) ).
tff(440,plain,
s(if_minus(le(s(s(d(s(zero)))),zero),s(s(d(s(zero)))),zero)) = s(minus(d(e(s(zero))),zero)),
inference(monotonicity,[status(thm)],[439]) ).
tff(441,plain,
s(if_minus(le(s(s(d(s(zero)))),zero),s(s(d(s(zero)))),zero)) = s(d(s(s(zero)))),
inference(transitivity,[status(thm)],[440,436]) ).
tff(442,plain,
s(s(if_minus(le(s(s(d(s(zero)))),zero),s(s(d(s(zero)))),zero))) = s(s(d(s(s(zero))))),
inference(monotonicity,[status(thm)],[441]) ).
tff(443,plain,
s(minus(d(e(s(zero))),zero)) = s(if_minus(le(s(s(d(s(zero)))),zero),s(s(d(s(zero)))),zero)),
inference(symmetry,[status(thm)],[440]) ).
tff(444,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(d(e(s(zero)))),zero) = s(minus(d(e(s(zero))),zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(445,plain,
if_minus(false,s(d(e(s(zero)))),zero) = s(minus(d(e(s(zero))),zero)),
inference(unit_resolution,[status(thm)],[444,84]) ).
tff(446,plain,
if_minus(le(s(d(e(s(zero)))),zero),s(d(e(s(zero)))),zero) = if_minus(false,s(d(e(s(zero)))),zero),
inference(monotonicity,[status(thm)],[267]) ).
tff(447,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(d(e(s(zero)))),zero) = if_minus(le(s(d(e(s(zero)))),zero),s(d(e(s(zero)))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(448,plain,
minus(s(d(e(s(zero)))),zero) = if_minus(le(s(d(e(s(zero)))),zero),s(d(e(s(zero)))),zero),
inference(unit_resolution,[status(thm)],[447,50]) ).
tff(449,plain,
minus(s(d(s(s(zero)))),zero) = minus(s(d(e(s(zero)))),zero),
inference(monotonicity,[status(thm)],[224]) ).
tff(450,plain,
minus(s(d(s(s(zero)))),zero) = s(if_minus(le(s(s(d(s(zero)))),zero),s(s(d(s(zero)))),zero)),
inference(transitivity,[status(thm)],[449,448,446,445,443]) ).
tff(451,plain,
s(minus(s(d(s(s(zero)))),zero)) = s(s(if_minus(le(s(s(d(s(zero)))),zero),s(s(d(s(zero)))),zero))),
inference(monotonicity,[status(thm)],[450]) ).
tff(452,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(s(d(s(s(zero))))),zero) = s(minus(s(d(s(s(zero)))),zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(453,plain,
if_minus(false,s(s(d(s(s(zero))))),zero) = s(minus(s(d(s(s(zero)))),zero)),
inference(unit_resolution,[status(thm)],[452,84]) ).
tff(454,plain,
if_minus(le(s(s(d(s(s(zero))))),zero),s(s(d(s(s(zero))))),zero) = if_minus(false,s(s(d(s(s(zero))))),zero),
inference(monotonicity,[status(thm)],[253]) ).
tff(455,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(d(s(s(zero))))),zero) = if_minus(le(s(s(d(s(s(zero))))),zero),s(s(d(s(s(zero))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(456,plain,
minus(s(s(d(s(s(zero))))),zero) = if_minus(le(s(s(d(s(s(zero))))),zero),s(s(d(s(s(zero))))),zero),
inference(unit_resolution,[status(thm)],[455,50]) ).
tff(457,plain,
minus(s(s(d(s(s(zero))))),zero) = d(s(s(s(zero)))),
inference(transitivity,[status(thm)],[456,454,453,451,442,242]) ).
tff(458,plain,
s(minus(s(s(d(s(s(zero))))),zero)) = s(d(s(s(s(zero))))),
inference(monotonicity,[status(thm)],[457]) ).
tff(459,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(s(s(d(s(s(zero)))))),zero) = s(minus(s(s(d(s(s(zero))))),zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(460,plain,
if_minus(false,s(s(s(d(s(s(zero)))))),zero) = s(minus(s(s(d(s(s(zero))))),zero)),
inference(unit_resolution,[status(thm)],[459,84]) ).
tff(461,plain,
if_minus(le(s(s(s(d(s(s(zero)))))),zero),s(s(s(d(s(s(zero)))))),zero) = if_minus(false,s(s(s(d(s(s(zero)))))),zero),
inference(monotonicity,[status(thm)],[289]) ).
tff(462,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(zero)))))),zero) = if_minus(le(s(s(s(d(s(s(zero)))))),zero),s(s(s(d(s(s(zero)))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(463,plain,
minus(s(s(s(d(s(s(zero)))))),zero) = if_minus(le(s(s(s(d(s(s(zero)))))),zero),s(s(s(d(s(s(zero)))))),zero),
inference(unit_resolution,[status(thm)],[462,50]) ).
tff(464,plain,
minus(s(d(s(s(s(zero))))),zero) = minus(s(s(s(d(s(s(zero)))))),zero),
inference(monotonicity,[status(thm)],[246]) ).
tff(465,plain,
minus(s(d(s(s(s(zero))))),zero) = minus(d(e(s(s(zero)))),s(zero)),
inference(transitivity,[status(thm)],[464,463,461,460,458,279,310,292,309,308]) ).
tff(466,plain,
s(minus(s(d(s(s(s(zero))))),zero)) = s(minus(d(e(s(s(zero)))),s(zero))),
inference(monotonicity,[status(thm)],[465]) ).
tff(467,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(468,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)],[467,84]) ).
tff(469,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)],[322]) ).
tff(470,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(471,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)],[470,50]) ).
tff(472,plain,
minus(d(e(s(s(zero)))),zero) = minus(s(s(d(s(s(s(zero)))))),zero),
inference(monotonicity,[status(thm)],[304]) ).
tff(473,plain,
minus(d(e(s(s(zero)))),zero) = d(e(s(s(zero)))),
inference(transitivity,[status(thm)],[472,471,469,468,466,307,318,302]) ).
tff(474,plain,
s(minus(d(e(s(s(zero)))),zero)) = s(d(e(s(s(zero))))),
inference(monotonicity,[status(thm)],[473]) ).
tff(475,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(d(e(s(s(zero))))),zero) = s(minus(d(e(s(s(zero)))),zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(476,plain,
if_minus(false,s(d(e(s(s(zero))))),zero) = s(minus(d(e(s(s(zero)))),zero)),
inference(unit_resolution,[status(thm)],[475,84]) ).
tff(477,plain,
if_minus(le(s(d(e(s(s(zero))))),zero),s(d(e(s(s(zero))))),zero) = if_minus(false,s(d(e(s(s(zero))))),zero),
inference(monotonicity,[status(thm)],[346]) ).
tff(478,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(d(e(s(s(zero))))),zero) = if_minus(le(s(d(e(s(s(zero))))),zero),s(d(e(s(s(zero))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(479,plain,
minus(s(d(e(s(s(zero))))),zero) = if_minus(le(s(d(e(s(s(zero))))),zero),s(d(e(s(s(zero))))),zero),
inference(unit_resolution,[status(thm)],[478,50]) ).
tff(480,plain,
minus(s(d(e(s(s(zero))))),zero) = s(d(d(e(s(zero))))),
inference(transitivity,[status(thm)],[479,477,476,474,338]) ).
tff(481,plain,
s(minus(s(d(e(s(s(zero))))),zero)) = s(s(d(d(e(s(zero)))))),
inference(monotonicity,[status(thm)],[480]) ).
tff(482,plain,
s(s(d(d(e(s(zero)))))) = s(minus(s(d(e(s(s(zero))))),zero)),
inference(symmetry,[status(thm)],[481]) ).
tff(483,plain,
d(s(d(s(s(zero))))) = minus(s(s(d(d(e(s(zero)))))),zero),
inference(transitivity,[status(thm)],[367,370,482,391,388,386,383]) ).
tff(484,plain,
s(d(s(d(s(s(zero)))))) = s(minus(s(s(d(d(e(s(zero)))))),zero)),
inference(monotonicity,[status(thm)],[483]) ).
tff(485,plain,
s(minus(s(s(d(d(e(s(zero)))))),zero)) = s(d(s(d(s(s(zero)))))),
inference(symmetry,[status(thm)],[484]) ).
tff(486,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(s(s(d(d(e(s(zero))))))),zero) = s(minus(s(s(d(d(e(s(zero)))))),zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(487,plain,
if_minus(false,s(s(s(d(d(e(s(zero))))))),zero) = s(minus(s(s(d(d(e(s(zero)))))),zero)),
inference(unit_resolution,[status(thm)],[486,84]) ).
tff(488,plain,
( ~ ! [X: $i] : ( le(s(X),zero) = false )
| ( le(s(s(s(d(d(e(s(zero))))))),zero) = false ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(489,plain,
le(s(s(s(d(d(e(s(zero))))))),zero) = false,
inference(unit_resolution,[status(thm)],[488,72]) ).
tff(490,plain,
false = le(s(s(s(d(d(e(s(zero))))))),zero),
inference(symmetry,[status(thm)],[489]) ).
tff(491,plain,
if_minus(false,s(s(s(d(d(e(s(zero))))))),zero) = if_minus(le(s(s(s(d(d(e(s(zero))))))),zero),s(s(s(d(d(e(s(zero))))))),zero),
inference(monotonicity,[status(thm)],[490]) ).
tff(492,plain,
if_minus(le(s(s(s(d(d(e(s(zero))))))),zero),s(s(s(d(d(e(s(zero))))))),zero) = if_minus(false,s(s(s(d(d(e(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(d(d(e(s(zero))))))),zero) = if_minus(le(s(s(s(d(d(e(s(zero))))))),zero),s(s(s(d(d(e(s(zero))))))),zero) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(494,plain,
minus(s(s(s(d(d(e(s(zero))))))),zero) = if_minus(le(s(s(s(d(d(e(s(zero))))))),zero),s(s(s(d(d(e(s(zero))))))),zero),
inference(unit_resolution,[status(thm)],[493,50]) ).
tff(495,plain,
minus(s(d(s(d(s(s(zero)))))),zero) = minus(s(s(s(d(d(e(s(zero))))))),zero),
inference(monotonicity,[status(thm)],[374]) ).
tff(496,plain,
minus(s(d(s(d(s(s(zero)))))),zero) = s(d(s(d(s(s(zero)))))),
inference(transitivity,[status(thm)],[495,494,492,487,485]) ).
tff(497,plain,
s(minus(s(d(s(d(s(s(zero)))))),zero)) = s(s(d(s(d(s(s(zero))))))),
inference(monotonicity,[status(thm)],[496]) ).
tff(498,plain,
minus(s(s(s(d(d(e(s(zero))))))),zero) = minus(s(d(s(d(s(s(zero)))))),zero),
inference(symmetry,[status(thm)],[495]) ).
tff(499,plain,
if_minus(le(s(s(s(d(d(e(s(zero))))))),zero),s(s(s(d(d(e(s(zero))))))),zero) = minus(s(s(s(d(d(e(s(zero))))))),zero),
inference(symmetry,[status(thm)],[494]) ).
tff(500,plain,
s(minus(s(s(d(d(e(s(zero)))))),zero)) = if_minus(false,s(s(s(d(d(e(s(zero))))))),zero),
inference(symmetry,[status(thm)],[487]) ).
tff(501,plain,
minus(s(d(s(d(s(s(zero)))))),s(zero)) = d(s(d(s(s(zero))))),
inference(transitivity,[status(thm)],[375,366,364,357,355,371,368]) ).
tff(502,plain,
s(minus(s(d(s(d(s(s(zero)))))),s(zero))) = s(d(s(d(s(s(zero)))))),
inference(monotonicity,[status(thm)],[501]) ).
tff(503,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(s(d(s(d(s(s(zero))))))),s(zero)) = s(minus(s(d(s(d(s(s(zero)))))),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(504,plain,
if_minus(false,s(s(d(s(d(s(s(zero))))))),s(zero)) = s(minus(s(d(s(d(s(s(zero)))))),s(zero))),
inference(unit_resolution,[status(thm)],[503,84]) ).
tff(505,plain,
le(s(d(s(d(s(s(zero)))))),zero) = le(s(s(s(d(d(e(s(zero))))))),zero),
inference(monotonicity,[status(thm)],[374]) ).
tff(506,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(507,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)],[506,62]) ).
tff(508,plain,
le(s(s(d(s(d(s(s(zero))))))),s(zero)) = false,
inference(transitivity,[status(thm)],[507,505,489]) ).
tff(509,plain,
if_minus(le(s(s(d(s(d(s(s(zero))))))),s(zero)),s(s(d(s(d(s(s(zero))))))),s(zero)) = if_minus(false,s(s(d(s(d(s(s(zero))))))),s(zero)),
inference(monotonicity,[status(thm)],[508]) ).
tff(510,plain,
( ~ ! [Y: $i,X: $i] : ( minus(s(X),Y) = if_minus(le(s(X),Y),s(X),Y) )
| ( minus(s(s(d(s(d(s(s(zero))))))),s(zero)) = if_minus(le(s(s(d(s(d(s(s(zero))))))),s(zero)),s(s(d(s(d(s(s(zero))))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(511,plain,
minus(s(s(d(s(d(s(s(zero))))))),s(zero)) = if_minus(le(s(s(d(s(d(s(s(zero))))))),s(zero)),s(s(d(s(d(s(s(zero))))))),s(zero)),
inference(unit_resolution,[status(thm)],[510,50]) ).
tff(512,plain,
minus(s(s(d(s(d(s(s(zero))))))),s(zero)) = minus(s(d(s(d(s(s(zero)))))),zero),
inference(transitivity,[status(thm)],[511,509,504,502,484,500,491,499,498]) ).
tff(513,plain,
s(minus(s(s(d(s(d(s(s(zero))))))),s(zero))) = s(minus(s(d(s(d(s(s(zero)))))),zero)),
inference(monotonicity,[status(thm)],[512]) ).
tff(514,plain,
( ~ ! [Y: $i,X: $i] : ( if_minus(false,s(X),Y) = s(minus(X,Y)) )
| ( if_minus(false,s(s(s(d(s(d(s(s(zero)))))))),s(zero)) = s(minus(s(s(d(s(d(s(s(zero))))))),s(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(515,plain,
if_minus(false,s(s(s(d(s(d(s(s(zero)))))))),s(zero)) = s(minus(s(s(d(s(d(s(s(zero))))))),s(zero))),
inference(unit_resolution,[status(thm)],[514,84]) ).
tff(516,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(517,plain,
le(s(s(d(s(d(s(s(zero))))))),zero) = false,
inference(unit_resolution,[status(thm)],[516,72]) ).
tff(518,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(519,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)],[518,62]) ).
tff(520,plain,
le(s(s(s(d(s(d(s(s(zero)))))))),s(zero)) = false,
inference(transitivity,[status(thm)],[519,517]) ).
tff(521,plain,
if_minus(le(s(s(s(d(s(d(s(s(zero)))))))),s(zero)),s(s(s(d(s(d(s(s(zero)))))))),s(zero)) = if_minus(false,s(s(s(d(s(d(s(s(zero)))))))),s(zero)),
inference(monotonicity,[status(thm)],[520]) ).
tff(522,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(s(s(zero)))))))),s(zero)) = if_minus(le(s(s(s(d(s(d(s(s(zero)))))))),s(zero)),s(s(s(d(s(d(s(s(zero)))))))),s(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(523,plain,
minus(s(s(s(d(s(d(s(s(zero)))))))),s(zero)) = if_minus(le(s(s(s(d(s(d(s(s(zero)))))))),s(zero)),s(s(s(d(s(d(s(s(zero)))))))),s(zero)),
inference(unit_resolution,[status(thm)],[522,50]) ).
tff(524,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(525,plain,
d(s(s(d(s(s(zero)))))) = s(s(d(s(d(s(s(zero))))))),
inference(unit_resolution,[status(thm)],[524,7]) ).
tff(526,plain,
s(s(d(s(d(s(s(zero))))))) = d(s(s(d(s(s(zero)))))),
inference(symmetry,[status(thm)],[525]) ).
tff(527,plain,
s(s(s(d(s(d(s(s(zero)))))))) = s(d(s(s(d(s(s(zero))))))),
inference(monotonicity,[status(thm)],[526]) ).
tff(528,plain,
s(d(s(s(d(s(s(zero))))))) = s(s(s(d(s(d(s(s(zero)))))))),
inference(symmetry,[status(thm)],[527]) ).
tff(529,plain,
minus(s(d(s(s(d(s(s(zero))))))),s(zero)) = minus(s(s(s(d(s(d(s(s(zero)))))))),s(zero)),
inference(monotonicity,[status(thm)],[528]) ).
tff(530,plain,
minus(s(d(s(s(d(s(s(zero))))))),s(zero)) = s(s(d(s(d(s(s(zero))))))),
inference(transitivity,[status(thm)],[529,523,521,515,513,497]) ).
tff(531,plain,
quot(minus(s(d(s(s(d(s(s(zero))))))),s(zero)),s(s(zero))) = quot(s(s(d(s(d(s(s(zero))))))),s(s(zero))),
inference(monotonicity,[status(thm)],[530]) ).
tff(532,plain,
quot(minus(s(d(s(s(d(s(s(zero))))))),s(zero)),s(s(zero))) = d(s(s(s(zero)))),
inference(transitivity,[status(thm)],[531,381,379,242]) ).
tff(533,plain,
s(quot(minus(s(d(s(s(d(s(s(zero))))))),s(zero)),s(s(zero)))) = s(d(s(s(s(zero))))),
inference(monotonicity,[status(thm)],[532]) ).
tff(534,plain,
( ~ ! [Y: $i,X: $i] : ( quot(s(X),s(Y)) = s(quot(minus(X,Y),s(Y))) )
| ( quot(s(s(d(s(s(d(s(s(zero)))))))),s(s(zero))) = s(quot(minus(s(d(s(s(d(s(s(zero))))))),s(zero)),s(s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(535,plain,
quot(s(s(d(s(s(d(s(s(zero)))))))),s(s(zero))) = s(quot(minus(s(d(s(s(d(s(s(zero))))))),s(zero)),s(s(zero)))),
inference(unit_resolution,[status(thm)],[534,188]) ).
tff(536,plain,
quot(s(s(d(s(s(d(s(s(zero)))))))),s(s(zero))) = minus(d(e(s(s(zero)))),s(zero)),
inference(transitivity,[status(thm)],[535,533,279,310,292,309,308]) ).
tff(537,plain,
s(quot(s(s(d(s(s(d(s(s(zero)))))))),s(s(zero)))) = s(minus(d(e(s(s(zero)))),s(zero))),
inference(monotonicity,[status(thm)],[536]) ).
tff(538,plain,
s(quot(s(s(d(s(s(d(s(s(zero)))))))),s(s(zero)))) = s(s(s(s(d(s(s(zero))))))),
inference(transitivity,[status(thm)],[537,307,245]) ).
tff(539,plain,
log(s(quot(s(s(d(s(s(d(s(s(zero)))))))),s(s(zero))))) = log(s(s(s(s(d(s(s(zero)))))))),
inference(monotonicity,[status(thm)],[538]) ).
tff(540,plain,
log(s(quot(s(s(d(s(s(d(s(s(zero)))))))),s(s(zero))))) = minus(d(e(s(zero))),s(zero)),
inference(transitivity,[status(thm)],[539,239,237,150,87,77,53,43]) ).
tff(541,plain,
s(log(s(quot(s(s(d(s(s(d(s(s(zero)))))))),s(s(zero)))))) = s(minus(d(e(s(zero))),s(zero))),
inference(monotonicity,[status(thm)],[540]) ).
tff(542,plain,
( ~ ! [X: $i] : ( log(s(s(X))) = s(log(s(quot(X,s(s(zero)))))) )
| ( log(s(s(s(s(d(s(s(d(s(s(zero))))))))))) = s(log(s(quot(s(s(d(s(s(d(s(s(zero)))))))),s(s(zero)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(543,plain,
log(s(s(s(s(d(s(s(d(s(s(zero))))))))))) = s(log(s(quot(s(s(d(s(s(d(s(s(zero)))))))),s(s(zero)))))),
inference(unit_resolution,[status(thm)],[542,176]) ).
tff(544,plain,
d(s(d(s(s(s(zero)))))) = d(s(s(s(d(s(s(zero))))))),
inference(monotonicity,[status(thm)],[246]) ).
tff(545,plain,
d(s(s(s(d(s(s(zero))))))) = d(s(d(s(s(s(zero)))))),
inference(symmetry,[status(thm)],[544]) ).
tff(546,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(547,plain,
d(s(s(s(d(s(s(zero))))))) = s(s(d(s(s(d(s(s(zero)))))))),
inference(unit_resolution,[status(thm)],[546,7]) ).
tff(548,plain,
s(s(d(s(s(d(s(s(zero)))))))) = d(s(s(s(d(s(s(zero))))))),
inference(symmetry,[status(thm)],[547]) ).
tff(549,plain,
s(s(d(s(s(d(s(s(zero)))))))) = d(s(d(s(s(s(zero)))))),
inference(transitivity,[status(thm)],[548,545]) ).
tff(550,plain,
s(s(s(d(s(s(d(s(s(zero))))))))) = s(d(s(d(s(s(s(zero))))))),
inference(monotonicity,[status(thm)],[549]) ).
tff(551,plain,
s(s(s(s(d(s(s(d(s(s(zero)))))))))) = s(s(d(s(d(s(s(s(zero)))))))),
inference(monotonicity,[status(thm)],[550]) ).
tff(552,plain,
s(s(d(s(d(s(s(s(zero)))))))) = s(s(s(s(d(s(s(d(s(s(zero)))))))))),
inference(symmetry,[status(thm)],[551]) ).
tff(553,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(554,plain,
d(s(s(d(s(s(s(zero))))))) = s(s(d(s(d(s(s(s(zero)))))))),
inference(unit_resolution,[status(thm)],[553,7]) ).
tff(555,plain,
( ~ ! [X: $i] : ( e(s(X)) = d(e(X)) )
| ( e(s(s(s(zero)))) = d(e(s(s(zero)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(556,plain,
e(s(s(s(zero)))) = d(e(s(s(zero)))),
inference(unit_resolution,[status(thm)],[555,36]) ).
tff(557,plain,
d(e(s(s(zero)))) = e(s(s(s(zero)))),
inference(symmetry,[status(thm)],[556]) ).
tff(558,plain,
s(s(d(s(s(s(zero)))))) = e(s(s(s(zero)))),
inference(transitivity,[status(thm)],[318,302,557]) ).
tff(559,plain,
d(s(s(d(s(s(s(zero))))))) = d(e(s(s(s(zero))))),
inference(monotonicity,[status(thm)],[558]) ).
tff(560,plain,
d(e(s(s(s(zero))))) = d(s(s(d(s(s(s(zero))))))),
inference(symmetry,[status(thm)],[559]) ).
tff(561,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(562,plain,
e(s(s(s(s(zero))))) = d(e(s(s(s(zero))))),
inference(unit_resolution,[status(thm)],[561,36]) ).
tff(563,plain,
e(s(s(s(s(zero))))) = s(s(s(s(d(s(s(d(s(s(zero)))))))))),
inference(transitivity,[status(thm)],[562,560,554,552]) ).
tff(564,plain,
log(e(s(s(s(s(zero)))))) = log(s(s(s(s(d(s(s(d(s(s(zero))))))))))),
inference(monotonicity,[status(thm)],[563]) ).
tff(565,plain,
log(e(s(s(s(s(zero)))))) = s(s(s(s(zero)))),
inference(transitivity,[status(thm)],[564,543,541,153,20]) ).
tff(566,plain,
( ( log(e(s(s(s(s(zero)))))) != s(s(s(s(zero)))) )
<=> ( log(e(s(s(s(s(zero)))))) != s(s(s(s(zero)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(567,axiom,
log(e(s(s(s(s(zero)))))) != s(s(s(s(zero)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tff(568,plain,
log(e(s(s(s(s(zero)))))) != s(s(s(s(zero)))),
inference(modus_ponens,[status(thm)],[567,566]) ).
tff(569,plain,
$false,
inference(unit_resolution,[status(thm)],[568,565]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ARI765-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.15/0.32 % Computer : n011.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 18:42:04 EDT 2026
% 0.15/0.33 % CPUTime :
% 25.73/25.92 % SZS status Unsatisfiable
% 25.73/25.92 % SZS output start Proof
% See solution above
% 0.18/26.04 % E exiting
%------------------------------------------------------------------------------