%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP544-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 : Sat Jun 21 05:08:03 AM UTC 2025
% Result : Unsatisfiable 0.37s 0.57s
% Output : Proof 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 36
% Syntax : Number of formulae : 203 ( 171 unt; 0 typ; 0 def)
% Number of atoms : 241 ( 237 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 64 ( 29 ~; 25 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of FOOLs : 3 ( 3 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 121 ( 115 !; 0 ?; 121 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(divide_type,type,
divide: ( $i * $i ) > $i ).
tff(identity_type,type,
identity: $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(( ( multiply(A,B) = divide(A,divide(identity,B)) )
<=> ( multiply(A,B) = divide(A,divide(identity,B)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) )
<=> ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) )
<=> ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
tff(5,plain,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) )
| ( multiply(b,a) = divide(b,divide(identity,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
multiply(b,a) = divide(b,divide(identity,a)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
divide(b,divide(identity,a)) = multiply(b,a),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
<=> ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)),identity)),divide(identity,b)) = divide(b,divide(identity,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
divide(divide(identity,divide(divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)),identity)),divide(identity,b)) = divide(b,divide(identity,a)),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
^ [A: $i] :
refl(( ( identity = divide(A,A) )
<=> ( identity = divide(A,A) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [A: $i] : ( identity = divide(A,A) )
<=> ! [A: $i] : ( identity = divide(A,A) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [A: $i] : ( identity = divide(A,A) )
<=> ! [A: $i] : ( identity = divide(A,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
! [A: $i] : ( identity = divide(A,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
tff(24,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [A: $i] : ( identity = divide(A,A) )
| ( identity = divide(identity,identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
identity = divide(identity,identity),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
divide(identity,identity) = identity,
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
( ~ ! [A: $i] : ( identity = divide(A,A) )
| ( identity = divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
identity = divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),
inference(unit_resolution,[status(thm)],[30,26]) ).
tff(32,plain,
divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))) = identity,
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity) = divide(identity,identity),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity) = identity,
inference(transitivity,[status(thm)],[33,29]) ).
tff(35,plain,
divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity),divide(identity,divide(identity,a))) = divide(identity,divide(identity,divide(identity,a))),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
divide(identity,divide(identity,divide(identity,a))) = divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity),divide(identity,divide(identity,a))),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(identity,divide(identity,divide(identity,divide(identity,a)))),identity),identity)),identity) = divide(identity,divide(identity,divide(identity,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
divide(divide(identity,divide(divide(divide(identity,divide(identity,divide(identity,divide(identity,a)))),identity),identity)),identity) = divide(identity,divide(identity,divide(identity,a))),
inference(unit_resolution,[status(thm)],[37,17]) ).
tff(39,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity),divide(identity,divide(identity,a)))),identity) = divide(identity,divide(identity,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity),divide(identity,divide(identity,a)))),identity) = divide(identity,divide(identity,a)),
inference(unit_resolution,[status(thm)],[39,17]) ).
tff(41,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity)),divide(identity,divide(identity,a))) = divide(identity,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
divide(divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity)),divide(identity,divide(identity,a))) = divide(identity,a),
inference(unit_resolution,[status(thm)],[41,17]) ).
tff(43,plain,
divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity)) = divide(identity,identity),
inference(monotonicity,[status(thm)],[34]) ).
tff(44,plain,
divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity)) = identity,
inference(transitivity,[status(thm)],[43,29]) ).
tff(45,plain,
divide(divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity)),divide(identity,divide(identity,a))) = divide(identity,divide(identity,divide(identity,a))),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
divide(identity,divide(identity,divide(identity,a))) = divide(divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity)),divide(identity,divide(identity,a))),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity),divide(identity,divide(identity,a))) = divide(identity,a),
inference(transitivity,[status(thm)],[35,46,42]) ).
tff(48,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(b,identity),divide(identity,a)),b)),divide(identity,a)) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
divide(divide(identity,divide(divide(divide(b,identity),divide(identity,a)),b)),divide(identity,a)) = identity,
inference(unit_resolution,[status(thm)],[48,17]) ).
tff(50,plain,
divide(divide(divide(identity,divide(divide(divide(b,identity),divide(identity,a)),b)),divide(identity,a)),identity) = divide(identity,identity),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
divide(divide(divide(identity,divide(divide(divide(b,identity),divide(identity,a)),b)),divide(identity,a)),identity) = identity,
inference(transitivity,[status(thm)],[50,29]) ).
tff(52,plain,
divide(identity,divide(divide(divide(identity,divide(divide(divide(b,identity),divide(identity,a)),b)),divide(identity,a)),identity)) = divide(identity,identity),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
divide(identity,identity) = divide(identity,divide(divide(divide(identity,divide(divide(divide(b,identity),divide(identity,a)),b)),divide(identity,a)),identity)),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
identity = divide(identity,divide(divide(divide(identity,divide(divide(divide(b,identity),divide(identity,a)),b)),divide(identity,a)),identity)),
inference(transitivity,[status(thm)],[28,53]) ).
tff(55,plain,
divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity),divide(identity,divide(identity,a)))) = divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(b,identity),divide(identity,a)),b)),divide(identity,a)),identity)),divide(identity,a)),
inference(monotonicity,[status(thm)],[54,47]) ).
tff(56,plain,
divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(b,identity),divide(identity,a)),b)),divide(identity,a)),identity)),divide(identity,a)) = divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity),divide(identity,divide(identity,a)))),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
divide(identity,divide(divide(divide(identity,divide(divide(divide(b,identity),divide(identity,a)),b)),divide(identity,a)),identity)) = identity,
inference(transitivity,[status(thm)],[52,29]) ).
tff(58,plain,
divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(b,identity),divide(identity,a)),b)),divide(identity,a)),identity)),divide(identity,a)) = divide(identity,divide(identity,a)),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
divide(identity,divide(identity,a)) = divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(b,identity),divide(identity,a)),b)),divide(identity,a)),identity)),divide(identity,a)),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
divide(identity,divide(identity,divide(identity,divide(identity,a)))) = divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity),divide(identity,divide(identity,a)))),
inference(monotonicity,[status(thm)],[36]) ).
tff(61,plain,
divide(divide(identity,divide(identity,divide(identity,divide(identity,a)))),identity) = divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity),divide(identity,divide(identity,a)))),identity),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
divide(divide(identity,divide(identity,divide(identity,divide(identity,a)))),identity) = divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity),divide(identity,divide(identity,a)))),
inference(transitivity,[status(thm)],[61,40,59,56]) ).
tff(63,plain,
divide(divide(divide(identity,divide(identity,divide(identity,divide(identity,a)))),identity),identity) = divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity),divide(identity,divide(identity,a)))),identity),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
divide(divide(divide(identity,divide(identity,divide(identity,divide(identity,a)))),identity),identity) = divide(identity,divide(identity,a)),
inference(transitivity,[status(thm)],[63,40]) ).
tff(65,plain,
divide(identity,divide(divide(divide(identity,divide(identity,divide(identity,divide(identity,a)))),identity),identity)) = divide(identity,divide(identity,divide(identity,a))),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
divide(identity,divide(identity,divide(identity,a))) = divide(identity,divide(divide(divide(identity,divide(identity,divide(identity,divide(identity,a)))),identity),identity)),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,divide(identity,divide(identity,a)))),divide(identity,b)),divide(identity,divide(identity,divide(identity,a))))),divide(identity,b)) = divide(identity,divide(identity,divide(identity,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,divide(identity,divide(identity,a)))),divide(identity,b)),divide(identity,divide(identity,divide(identity,a))))),divide(identity,b)) = divide(identity,divide(identity,divide(identity,a))),
inference(unit_resolution,[status(thm)],[67,17]) ).
tff(69,plain,
divide(identity,divide(identity,divide(identity,a))) = divide(identity,a),
inference(transitivity,[status(thm)],[46,42]) ).
tff(70,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(identity,b),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),identity)),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
divide(divide(identity,divide(divide(divide(identity,b),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),identity)),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))) = b,
inference(unit_resolution,[status(thm)],[70,17]) ).
tff(72,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),identity)),identity) = divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),identity)),identity) = divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),
inference(unit_resolution,[status(thm)],[72,17]) ).
tff(74,plain,
divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),divide(identity,identity)) = divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),identity),
inference(monotonicity,[status(thm)],[29]) ).
tff(75,plain,
divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),identity) = divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),divide(identity,identity)),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(identity,identity),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),identity)),identity)),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),identity)) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
divide(divide(identity,divide(divide(divide(identity,identity),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),identity)),identity)),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),identity)) = identity,
inference(unit_resolution,[status(thm)],[76,17]) ).
tff(78,plain,
divide(divide(identity,identity),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),identity)) = divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),identity)),
inference(monotonicity,[status(thm)],[29]) ).
tff(79,plain,
divide(divide(divide(identity,identity),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),identity)),identity) = divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),identity)),identity),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
divide(divide(divide(identity,identity),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),identity)),identity) = divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),
inference(transitivity,[status(thm)],[79,73]) ).
tff(81,plain,
divide(identity,divide(divide(divide(identity,identity),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),identity)),identity)) = divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))) = divide(identity,divide(divide(divide(identity,identity),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),identity)),identity)),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),divide(identity,identity))) = divide(divide(identity,divide(divide(divide(identity,identity),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),identity)),identity)),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),identity)),
inference(monotonicity,[status(thm)],[82,74]) ).
tff(84,plain,
divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),divide(identity,identity))) = identity,
inference(transitivity,[status(thm)],[83,77]) ).
tff(85,plain,
divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),divide(identity,identity))),identity) = divide(identity,identity),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),divide(identity,identity))),identity) = identity,
inference(transitivity,[status(thm)],[85,29]) ).
tff(87,plain,
divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),divide(identity,identity))),identity)) = divide(identity,identity),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
divide(identity,identity) = divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),divide(identity,identity))),identity)),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
identity = divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),divide(identity,identity))),identity)),
inference(transitivity,[status(thm)],[28,88]) ).
tff(90,plain,
divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),identity)) = divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),divide(identity,identity))),identity)),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),divide(identity,identity))),
inference(monotonicity,[status(thm)],[89,75]) ).
tff(91,plain,
divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),divide(identity,identity))),identity)),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),divide(identity,identity))) = divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),identity)),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),divide(identity,identity))),identity)),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),divide(identity,identity))) = divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(93,plain,
divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),divide(identity,identity))),identity)),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),divide(identity,identity))) = divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),
inference(unit_resolution,[status(thm)],[92,17]) ).
tff(94,plain,
divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))) = divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),divide(identity,identity))),identity)),divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),divide(identity,identity))),
inference(symmetry,[status(thm)],[93]) ).
tff(95,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))) = divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
divide(divide(identity,divide(divide(divide(divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))) = divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),
inference(unit_resolution,[status(thm)],[95,17]) ).
tff(97,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))) = divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
divide(divide(identity,divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))) = divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),
inference(unit_resolution,[status(thm)],[97,17]) ).
tff(99,plain,
( ~ ! [A: $i] : ( identity = divide(A,A) )
| ( identity = divide(divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(100,plain,
identity = divide(divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),
inference(unit_resolution,[status(thm)],[99,26]) ).
tff(101,plain,
divide(divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))) = identity,
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
divide(divide(divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))) = divide(identity,divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
divide(divide(divide(divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))) = divide(divide(identity,divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
divide(divide(divide(divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))) = divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),
inference(transitivity,[status(thm)],[103,98]) ).
tff(105,plain,
divide(identity,divide(divide(divide(divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))))) = divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))) = divide(identity,divide(divide(divide(divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))))),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
divide(divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))) = divide(divide(identity,divide(divide(divide(divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
divide(divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))) = divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),identity)),
inference(transitivity,[status(thm)],[107,96,94,91]) ).
tff(109,plain,
divide(divide(divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),identity) = divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),identity)),identity),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
divide(divide(divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),identity) = divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),
inference(transitivity,[status(thm)],[109,73]) ).
tff(111,plain,
divide(identity,divide(divide(divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),identity)) = divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))) = divide(identity,divide(divide(divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),identity)),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(identity,divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity)),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))) = divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(114,plain,
divide(divide(identity,divide(divide(divide(identity,divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity)),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))) = divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),
inference(unit_resolution,[status(thm)],[113,17]) ).
tff(115,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(identity,b)),identity)),divide(identity,b)) = divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(116,plain,
divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(identity,b)),identity)),divide(identity,b)) = divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),
inference(unit_resolution,[status(thm)],[115,17]) ).
tff(117,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(identity,b)) = divide(identity,divide(identity,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(118,plain,
divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(identity,b)) = divide(identity,divide(identity,a)),
inference(unit_resolution,[status(thm)],[117,17]) ).
tff(119,plain,
divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(identity,b)) = divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity),divide(identity,divide(identity,a)))),
inference(transitivity,[status(thm)],[118,59,56]) ).
tff(120,plain,
divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(identity,b)),identity) = divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity),divide(identity,divide(identity,a)))),identity),
inference(monotonicity,[status(thm)],[119]) ).
tff(121,plain,
divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(identity,b)),identity) = divide(identity,divide(identity,a)),
inference(transitivity,[status(thm)],[120,40]) ).
tff(122,plain,
divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(identity,b)),identity)) = divide(identity,divide(identity,divide(identity,a))),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
divide(identity,divide(identity,divide(identity,a))) = divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(identity,b)),identity)),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,b)) = divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(identity,b)),identity)),divide(identity,b)),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,b)) = divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),
inference(transitivity,[status(thm)],[124,116]) ).
tff(126,plain,
divide(divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,b)),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))) = divide(divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,plain,
divide(divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,b)),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))) = identity,
inference(transitivity,[status(thm)],[126,101]) ).
tff(128,plain,
divide(divide(divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,b)),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(identity,divide(identity,divide(identity,a)))) = divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity),divide(identity,divide(identity,a)))),
inference(monotonicity,[status(thm)],[127,36]) ).
tff(129,plain,
divide(divide(divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,b)),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(identity,divide(identity,divide(identity,a)))) = divide(identity,divide(identity,a)),
inference(transitivity,[status(thm)],[128,55,58]) ).
tff(130,plain,
divide(identity,divide(divide(divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,b)),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(identity,divide(identity,divide(identity,a))))) = divide(identity,divide(identity,divide(identity,a))),
inference(monotonicity,[status(thm)],[129]) ).
tff(131,plain,
divide(identity,divide(identity,divide(identity,a))) = divide(identity,divide(divide(divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,b)),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(identity,divide(identity,divide(identity,a))))),
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))) = divide(identity,divide(identity,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(133,plain,
divide(divide(identity,divide(divide(divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))) = divide(identity,divide(identity,a)),
inference(unit_resolution,[status(thm)],[132,17]) ).
tff(134,plain,
divide(divide(identity,divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))) = divide(divide(divide(divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),
inference(symmetry,[status(thm)],[103]) ).
tff(135,plain,
divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)) = divide(divide(identity,divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),
inference(symmetry,[status(thm)],[98]) ).
tff(136,plain,
divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)) = divide(divide(divide(divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),
inference(transitivity,[status(thm)],[135,134]) ).
tff(137,plain,
divide(divide(divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))) = divide(identity,divide(divide(divide(divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))))),
inference(monotonicity,[status(thm)],[101,136]) ).
tff(138,plain,
divide(identity,divide(divide(divide(divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))))) = divide(divide(divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))) = divide(divide(divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),
inference(transitivity,[status(thm)],[106,138]) ).
tff(140,plain,
divide(identity,divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)))) = divide(identity,divide(divide(divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)))),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
divide(divide(identity,divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))) = divide(divide(identity,divide(divide(divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),
inference(monotonicity,[status(thm)],[140]) ).
tff(142,plain,
divide(divide(identity,divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))) = divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity),divide(identity,divide(identity,a)))),
inference(transitivity,[status(thm)],[141,133,59,56]) ).
tff(143,plain,
divide(divide(divide(identity,divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity) = divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity),divide(identity,divide(identity,a)))),identity),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
divide(divide(divide(identity,divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity) = divide(identity,divide(identity,a)),
inference(transitivity,[status(thm)],[143,40]) ).
tff(145,plain,
divide(identity,divide(divide(divide(identity,divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity)) = divide(identity,divide(identity,divide(identity,a))),
inference(monotonicity,[status(thm)],[144]) ).
tff(146,plain,
divide(identity,divide(divide(divide(identity,divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity)) = divide(identity,divide(divide(divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,b)),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(identity,divide(identity,divide(identity,a))))),
inference(transitivity,[status(thm)],[145,131]) ).
tff(147,plain,
divide(divide(identity,divide(divide(divide(identity,divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity)),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))) = divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,b)),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(identity,divide(identity,divide(identity,a))))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),
inference(monotonicity,[status(thm)],[146]) ).
tff(148,plain,
divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,b)),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(identity,divide(identity,divide(identity,a))))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))) = divide(divide(identity,divide(divide(divide(identity,divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity)),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,b)),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(identity,divide(identity,divide(identity,a))))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))) = divide(identity,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(150,plain,
divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,b)),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(identity,divide(identity,divide(identity,a))))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))) = divide(identity,b),
inference(unit_resolution,[status(thm)],[149,17]) ).
tff(151,plain,
divide(identity,b) = divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,b)),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(identity,divide(identity,divide(identity,a))))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),
inference(symmetry,[status(thm)],[150]) ).
tff(152,plain,
divide(identity,b) = divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),
inference(transitivity,[status(thm)],[151,148,114]) ).
tff(153,plain,
divide(divide(identity,b),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))) = divide(divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
divide(divide(identity,b),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))) = divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),identity)),
inference(transitivity,[status(thm)],[153,107,96,94,91]) ).
tff(155,plain,
divide(divide(divide(identity,b),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),identity) = divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),identity),identity)),identity),
inference(monotonicity,[status(thm)],[154]) ).
tff(156,plain,
divide(divide(divide(identity,b),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),identity) = divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a))),
inference(transitivity,[status(thm)],[155,73]) ).
tff(157,plain,
divide(identity,divide(divide(divide(identity,b),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),identity)) = divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),
inference(monotonicity,[status(thm)],[156]) ).
tff(158,plain,
divide(identity,divide(divide(divide(identity,b),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),identity)) = divide(identity,divide(divide(divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),identity)),
inference(transitivity,[status(thm)],[157,112]) ).
tff(159,plain,
divide(divide(identity,divide(divide(divide(identity,b),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),identity)),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))) = divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),identity)),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),
inference(monotonicity,[status(thm)],[158]) ).
tff(160,plain,
divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),identity)),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))) = divide(divide(identity,divide(divide(divide(identity,b),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),identity)),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),identity)),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))) = divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(162,plain,
divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),identity)),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))) = divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),
inference(unit_resolution,[status(thm)],[161,17]) ).
tff(163,plain,
divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)) = divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),identity)),divide(divide(divide(divide(b,divide(identity,identity)),divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b))),divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),divide(identity,divide(identity,a)))),divide(b,divide(identity,identity)))),
inference(symmetry,[status(thm)],[162]) ).
tff(164,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(b,identity),divide(identity,a)),b)),divide(identity,a)),identity)),divide(identity,a)) = divide(divide(divide(b,identity),divide(identity,a)),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(165,plain,
divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(b,identity),divide(identity,a)),b)),divide(identity,a)),identity)),divide(identity,a)) = divide(divide(divide(b,identity),divide(identity,a)),b),
inference(unit_resolution,[status(thm)],[164,17]) ).
tff(166,plain,
divide(divide(divide(b,identity),divide(identity,a)),b) = divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(b,identity),divide(identity,a)),b)),divide(identity,a)),identity)),divide(identity,a)),
inference(symmetry,[status(thm)],[165]) ).
tff(167,plain,
divide(divide(divide(b,identity),divide(identity,a)),b) = divide(identity,divide(identity,a)),
inference(transitivity,[status(thm)],[166,58]) ).
tff(168,plain,
divide(identity,divide(divide(divide(b,identity),divide(identity,a)),b)) = divide(identity,divide(identity,divide(identity,a))),
inference(monotonicity,[status(thm)],[167]) ).
tff(169,plain,
divide(identity,divide(identity,divide(identity,a))) = divide(identity,divide(divide(divide(b,identity),divide(identity,a)),b)),
inference(symmetry,[status(thm)],[168]) ).
tff(170,plain,
divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,divide(identity,divide(identity,a)))) = divide(divide(identity,divide(divide(divide(b,identity),divide(identity,a)),b)),divide(identity,a)),
inference(monotonicity,[status(thm)],[169,69]) ).
tff(171,plain,
divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,divide(identity,divide(identity,a)))) = divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),
inference(transitivity,[status(thm)],[170,49,31]) ).
tff(172,plain,
divide(divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,divide(identity,divide(identity,a)))),divide(identity,b)) = divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),divide(identity,b)),
inference(monotonicity,[status(thm)],[171]) ).
tff(173,plain,
divide(divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,divide(identity,divide(identity,a)))),divide(identity,b)) = b,
inference(transitivity,[status(thm)],[172,163,160,71]) ).
tff(174,plain,
divide(divide(divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,divide(identity,divide(identity,a)))),divide(identity,b)),divide(identity,divide(identity,divide(identity,a)))) = divide(b,divide(identity,a)),
inference(monotonicity,[status(thm)],[173,69]) ).
tff(175,plain,
divide(identity,divide(divide(divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,divide(identity,divide(identity,a)))),divide(identity,b)),divide(identity,divide(identity,divide(identity,a))))) = divide(identity,divide(b,divide(identity,a))),
inference(monotonicity,[status(thm)],[174]) ).
tff(176,plain,
divide(identity,divide(b,divide(identity,a))) = divide(identity,divide(divide(divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,divide(identity,divide(identity,a)))),divide(identity,b)),divide(identity,divide(identity,divide(identity,a))))),
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)) = divide(divide(identity,divide(divide(divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,divide(identity,divide(identity,a)))),divide(identity,b)),divide(identity,divide(identity,divide(identity,a))))),divide(identity,b)),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,plain,
divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)) = divide(identity,divide(divide(divide(identity,divide(identity,divide(identity,divide(identity,a)))),identity),identity)),
inference(transitivity,[status(thm)],[177,68,66]) ).
tff(179,plain,
divide(divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)),identity) = divide(divide(identity,divide(divide(divide(identity,divide(identity,divide(identity,divide(identity,a)))),identity),identity)),identity),
inference(monotonicity,[status(thm)],[178]) ).
tff(180,plain,
divide(divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)),identity) = divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity),divide(identity,divide(identity,a))),
inference(transitivity,[status(thm)],[179,38,36]) ).
tff(181,plain,
divide(identity,divide(divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)),identity)) = divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity),divide(identity,divide(identity,a)))),
inference(monotonicity,[status(thm)],[180]) ).
tff(182,plain,
divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity),divide(identity,divide(identity,a)))) = divide(identity,divide(divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)),identity)),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
divide(identity,a) = divide(divide(identity,divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity)),divide(identity,divide(identity,a))),
inference(symmetry,[status(thm)],[42]) ).
tff(184,plain,
divide(identity,a) = divide(identity,divide(divide(divide(b,identity),divide(identity,a)),b)),
inference(transitivity,[status(thm)],[183,45,169]) ).
tff(185,plain,
divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))) = divide(divide(identity,divide(divide(divide(b,identity),divide(identity,a)),b)),divide(identity,a)),
inference(monotonicity,[status(thm)],[184,69]) ).
tff(186,plain,
divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))) = identity,
inference(transitivity,[status(thm)],[185,49]) ).
tff(187,plain,
divide(divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))),identity) = divide(identity,identity),
inference(monotonicity,[status(thm)],[186]) ).
tff(188,plain,
divide(divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))),identity) = identity,
inference(transitivity,[status(thm)],[187,29]) ).
tff(189,plain,
divide(identity,divide(divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))),identity)) = divide(identity,identity),
inference(monotonicity,[status(thm)],[188]) ).
tff(190,plain,
divide(identity,divide(divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))),identity)) = identity,
inference(transitivity,[status(thm)],[189,29]) ).
tff(191,plain,
divide(divide(identity,divide(divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))),identity)),divide(identity,divide(identity,divide(identity,a)))) = divide(identity,divide(divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),identity),divide(identity,divide(identity,a)))),
inference(monotonicity,[status(thm)],[190,36]) ).
tff(192,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))),identity)),divide(identity,divide(identity,divide(identity,a)))) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(193,plain,
divide(divide(identity,divide(divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))),identity)),divide(identity,divide(identity,divide(identity,a)))) = a,
inference(unit_resolution,[status(thm)],[192,17]) ).
tff(194,plain,
a = divide(divide(identity,divide(divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))),identity)),divide(identity,divide(identity,divide(identity,a)))),
inference(symmetry,[status(thm)],[193]) ).
tff(195,plain,
a = divide(identity,divide(divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)),identity)),
inference(transitivity,[status(thm)],[194,191,182]) ).
tff(196,plain,
divide(a,divide(identity,b)) = divide(divide(identity,divide(divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)),identity)),divide(identity,b)),
inference(monotonicity,[status(thm)],[195]) ).
tff(197,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) )
| ( multiply(a,b) = divide(a,divide(identity,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(198,plain,
multiply(a,b) = divide(a,divide(identity,b)),
inference(unit_resolution,[status(thm)],[197,7]) ).
tff(199,plain,
multiply(a,b) = multiply(b,a),
inference(transitivity,[status(thm)],[198,196,19,10]) ).
tff(200,plain,
( ( multiply(a,b) != multiply(b,a) )
<=> ( multiply(a,b) != multiply(b,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(201,axiom,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_4) ).
tff(202,plain,
multiply(a,b) != multiply(b,a),
inference(modus_ponens,[status(thm)],[201,200]) ).
tff(203,plain,
$false,
inference(unit_resolution,[status(thm)],[202,199]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP544-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 16:15:56 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.37/0.57 % SZS status Unsatisfiable
% 0.37/0.57 % SZS output start Proof
% See solution above
% 0.48/0.63 % E exiting
%------------------------------------------------------------------------------