TSTP Solution File: GRP522-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP522-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 : Fri Sep 16 22:27:55 EDT 2022
% Result : Unsatisfiable 0.20s 0.52s
% Output : Proof 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 44
% Syntax : Number of formulae : 199 ( 159 unt; 5 typ; 0 def)
% Number of atoms : 235 ( 231 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 70 ( 32 ~; 28 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 17 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 146 ( 138 !; 0 ?; 146 :)
% Comments :
%------------------------------------------------------------------------------
tff(a2_type,type,
a2: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(b2_type,type,
b2: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(divide_type,type,
divide: ( $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
<=> ( divide(A,divide(B,divide(C,divide(A,B)))) = C ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
<=> ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
<=> ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
tff(5,plain,
! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(multiply(inverse(b2),b2),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))) = a2 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(multiply(inverse(b2),b2),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))) = a2,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
<=> ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
<=> ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
<=> ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
tff(14,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(b2,divide(b2,b2)) = divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
multiply(b2,divide(b2,b2)) = divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(b2,divide(b2,divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2)))) = divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(20,plain,
divide(b2,divide(b2,divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2)))) = divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),
inference(unit_resolution,[status(thm)],[19,7]) ).
tff(21,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(inverse(b2),b2) = divide(inverse(b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),b2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
multiply(inverse(b2),b2) = divide(inverse(b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),b2)),
inference(unit_resolution,[status(thm)],[21,16]) ).
tff(23,plain,
divide(inverse(b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),b2)) = multiply(inverse(b2),b2),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
^ [B: $i,A: $i] :
refl(
( ( inverse(A) = divide(divide(B,B),A) )
<=> ( inverse(A) = divide(divide(B,B),A) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
<=> ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
<=> ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
tff(28,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(b2) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),b2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
inverse(b2) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),b2),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(b2) = divide(divide(b2,b2),b2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
inverse(b2) = divide(divide(b2,b2),b2),
inference(unit_resolution,[status(thm)],[33,30]) ).
tff(35,plain,
divide(divide(b2,b2),b2) = inverse(b2),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
divide(divide(b2,b2),b2) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),b2),
inference(transitivity,[status(thm)],[35,32]) ).
tff(37,plain,
divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)) = divide(inverse(b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),b2)),
inference(monotonicity,[status(thm)],[35,36]) ).
tff(38,plain,
divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)) = multiply(inverse(b2),b2),
inference(transitivity,[status(thm)],[37,23]) ).
tff(39,plain,
divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)) = divide(multiply(inverse(b2),b2),divide(b2,b2)),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
divide(multiply(inverse(b2),b2),divide(b2,b2)) = divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
divide(b2,divide(multiply(inverse(b2),b2),divide(b2,b2))) = divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))) = divide(b2,divide(multiply(inverse(b2),b2),divide(b2,b2))),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(b2,b2)) = divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
inverse(divide(b2,b2)) = divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),
inference(unit_resolution,[status(thm)],[43,30]) ).
tff(45,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(b2,b2)) = divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
inverse(divide(b2,b2)) = divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2)),
inference(unit_resolution,[status(thm)],[45,30]) ).
tff(47,plain,
divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2)) = inverse(divide(b2,b2)),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2)) = divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),
inference(transitivity,[status(thm)],[47,44]) ).
tff(49,plain,
divide(b2,divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))) = divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
divide(b2,divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))) = divide(b2,divide(multiply(inverse(b2),b2),divide(b2,b2))),
inference(transitivity,[status(thm)],[49,42]) ).
tff(51,plain,
divide(b2,divide(b2,divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2)))) = divide(b2,divide(b2,divide(multiply(inverse(b2),b2),divide(b2,b2)))),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
divide(b2,divide(b2,divide(multiply(inverse(b2),b2),divide(b2,b2)))) = divide(b2,divide(b2,divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2)))),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(b2,b2)) = divide(divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),divide(b2,b2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
inverse(divide(b2,b2)) = divide(divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),divide(b2,b2)),
inference(unit_resolution,[status(thm)],[53,30]) ).
tff(55,plain,
divide(divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),divide(b2,b2)) = inverse(divide(b2,b2)),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
divide(divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),divide(b2,b2)) = divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),
inference(transitivity,[status(thm)],[55,44]) ).
tff(57,plain,
divide(b2,divide(divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),divide(b2,b2))) = divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
divide(b2,divide(divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),divide(b2,b2))) = divide(b2,divide(multiply(inverse(b2),b2),divide(b2,b2))),
inference(transitivity,[status(thm)],[57,42]) ).
tff(59,plain,
divide(b2,divide(b2,divide(divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),divide(b2,b2)))) = divide(b2,divide(b2,divide(multiply(inverse(b2),b2),divide(b2,b2)))),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(b2,divide(b2,divide(divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),divide(b2,b2)))) = divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
divide(b2,divide(b2,divide(divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),divide(b2,b2)))) = divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),
inference(unit_resolution,[status(thm)],[60,7]) ).
tff(62,plain,
divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))) = divide(b2,divide(b2,divide(divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),divide(b2,b2)))),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(b2,divide(b2,divide(multiply(inverse(b2),b2),divide(b2,b2)))) = multiply(inverse(b2),b2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
divide(b2,divide(b2,divide(multiply(inverse(b2),b2),divide(b2,b2)))) = multiply(inverse(b2),b2),
inference(unit_resolution,[status(thm)],[63,7]) ).
tff(65,plain,
multiply(inverse(b2),b2) = divide(b2,divide(b2,divide(multiply(inverse(b2),b2),divide(b2,b2)))),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
multiply(inverse(b2),b2) = divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),
inference(transitivity,[status(thm)],[65,52,20]) ).
tff(67,plain,
divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)) = divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),
inference(monotonicity,[status(thm)],[66,66]) ).
tff(68,plain,
divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)) = divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),
inference(monotonicity,[status(thm)],[38]) ).
tff(69,plain,
divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)) = multiply(inverse(b2),b2),
inference(transitivity,[status(thm)],[68,67,62,59,64]) ).
tff(70,plain,
divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))) = divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),
inference(monotonicity,[status(thm)],[69,69]) ).
tff(71,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(b2,b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))))) = divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(b2,b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))))) = divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),
inference(unit_resolution,[status(thm)],[71,7]) ).
tff(73,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))) = divide(divide(b2,b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(74,plain,
inverse(divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))) = divide(divide(b2,b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))),
inference(unit_resolution,[status(thm)],[73,30]) ).
tff(75,plain,
divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)) = inverse(divide(b2,b2)),
inference(symmetry,[status(thm)],[44]) ).
tff(76,plain,
divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)) = divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2)),
inference(transitivity,[status(thm)],[75,46]) ).
tff(77,plain,
inverse(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))) = inverse(divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))) = divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(79,plain,
inverse(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))) = divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),
inference(unit_resolution,[status(thm)],[78,30]) ).
tff(80,plain,
divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))) = inverse(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))) = divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),
inference(monotonicity,[status(thm)],[48]) ).
tff(82,plain,
divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))) = divide(divide(b2,b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))),
inference(transitivity,[status(thm)],[81,80,77,74]) ).
tff(83,plain,
divide(divide(b2,b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2)))) = divide(divide(b2,b2),divide(divide(b2,b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2)))),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
divide(divide(b2,b2),divide(divide(b2,b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2)))) = divide(divide(b2,b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2)))),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(b2,b2),divide(divide(b2,b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))))) = divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(b2,b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))))),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(b2,b2),divide(divide(b2,b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))))) = divide(b2,b2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(87,plain,
divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(b2,b2),divide(divide(b2,b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))))) = divide(b2,b2),
inference(unit_resolution,[status(thm)],[86,7]) ).
tff(88,plain,
divide(b2,b2) = divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(b2,b2),divide(divide(b2,b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))))),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
divide(b2,b2) = divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),
inference(transitivity,[status(thm)],[88,85,72,70,67,62,59,52,20]) ).
tff(90,plain,
multiply(b2,divide(b2,b2)) = multiply(b2,divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
multiply(b2,divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))) = multiply(b2,divide(b2,b2)),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(b2,divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))) = divide(b2,divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
multiply(b2,divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))) = divide(b2,divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))))),
inference(unit_resolution,[status(thm)],[92,16]) ).
tff(94,plain,
divide(b2,divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))))) = multiply(b2,divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),
inference(symmetry,[status(thm)],[93]) ).
tff(95,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(b2) = divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(96,plain,
inverse(b2) = divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2),
inference(unit_resolution,[status(thm)],[95,30]) ).
tff(97,plain,
divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2) = inverse(b2),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),b2),
inference(transitivity,[status(thm)],[97,32]) ).
tff(99,plain,
divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)) = divide(inverse(b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),b2)),
inference(monotonicity,[status(thm)],[35,98]) ).
tff(100,plain,
divide(inverse(b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),b2)) = divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)),
inference(symmetry,[status(thm)],[99]) ).
tff(101,plain,
divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))) = divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)),
inference(transitivity,[status(thm)],[62,59,64,22,100]) ).
tff(102,plain,
divide(b2,divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))))) = divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))) = divide(b2,divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))))),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))) = divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),
inference(transitivity,[status(thm)],[103,94,91,18]) ).
tff(105,plain,
divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))) = divide(divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),
inference(monotonicity,[status(thm)],[104,104]) ).
tff(106,plain,
divide(divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))) = divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(b2,b2),divide(divide(divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))))) = divide(divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(b2,b2),divide(divide(divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))))) = divide(divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),
inference(unit_resolution,[status(thm)],[107,7]) ).
tff(109,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))) = divide(divide(divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(110,plain,
inverse(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))) = divide(divide(divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),
inference(unit_resolution,[status(thm)],[109,30]) ).
tff(111,plain,
divide(divide(divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))) = inverse(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
divide(divide(divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))) = divide(divide(divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),
inference(monotonicity,[status(thm)],[48]) ).
tff(113,plain,
divide(divide(divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))) = divide(divide(b2,b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))),
inference(transitivity,[status(thm)],[112,111,77,74]) ).
tff(114,plain,
divide(divide(b2,b2),divide(divide(divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2)))) = divide(divide(b2,b2),divide(divide(b2,b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2)))),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(b2,b2),divide(divide(divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))))) = divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(b2,b2),divide(divide(b2,b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))))),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(b2,b2),divide(divide(b2,b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))))) = divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(b2,b2),divide(divide(divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))))),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(b2,b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))))) = divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(b2,b2),divide(divide(b2,b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))))),
inference(symmetry,[status(thm)],[85]) ).
tff(118,plain,
divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))) = divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(b2,b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))))),
inference(symmetry,[status(thm)],[72]) ).
tff(119,plain,
divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)) = divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),
inference(symmetry,[status(thm)],[70]) ).
tff(120,plain,
divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))) = divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),
inference(symmetry,[status(thm)],[67]) ).
tff(121,plain,
divide(b2,divide(b2,divide(multiply(inverse(b2),b2),divide(b2,b2)))) = divide(b2,divide(b2,divide(divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),divide(b2,b2)))),
inference(symmetry,[status(thm)],[59]) ).
tff(122,plain,
multiply(inverse(b2),b2) = divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),
inference(transitivity,[status(thm)],[65,121,61,120,119,118,117,116,108,106]) ).
tff(123,plain,
divide(multiply(inverse(b2),b2),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2)))) = divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2)))),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,plain,
divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(multiply(inverse(b2),b2),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))) = divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))) = divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(multiply(inverse(b2),b2),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),
inference(symmetry,[status(thm)],[124]) ).
tff(126,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(multiply(inverse(b2),b2),divide(multiply(inverse(b2),b2),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))))) = divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(127,plain,
divide(multiply(inverse(b2),b2),divide(multiply(inverse(b2),b2),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))))) = divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),
inference(unit_resolution,[status(thm)],[126,7]) ).
tff(128,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))))))) = divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))))))) = divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),
inference(unit_resolution,[status(thm)],[128,7]) ).
tff(130,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(a2,divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(a2,a2)))) = divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(131,plain,
divide(a2,divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(a2,a2)))) = divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),
inference(unit_resolution,[status(thm)],[130,7]) ).
tff(132,plain,
divide(b2,divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))) = divide(b2,divide(b2,divide(multiply(inverse(b2),b2),divide(b2,b2)))),
inference(monotonicity,[status(thm)],[42]) ).
tff(133,plain,
divide(b2,divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))) = multiply(inverse(b2),b2),
inference(transitivity,[status(thm)],[132,64]) ).
tff(134,plain,
divide(multiply(inverse(b2),b2),divide(b2,divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))))) = divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)) = divide(multiply(inverse(b2),b2),divide(b2,divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))))),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
multiply(inverse(b2),b2) = divide(multiply(inverse(b2),b2),divide(b2,divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))))),
inference(transitivity,[status(thm)],[65,121,61,120,135]) ).
tff(137,plain,
divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2)) = divide(divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(multiply(inverse(b2),b2),divide(b2,divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))))),
inference(monotonicity,[status(thm)],[104,136]) ).
tff(138,plain,
divide(divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(multiply(inverse(b2),b2),divide(b2,divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))))) = divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2)),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))) = divide(divide(a2,a2),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(140,plain,
inverse(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))) = divide(divide(a2,a2),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),
inference(unit_resolution,[status(thm)],[139,30]) ).
tff(141,plain,
divide(divide(a2,a2),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))) = inverse(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
divide(divide(a2,a2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))) = divide(divide(a2,a2),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),
inference(monotonicity,[status(thm)],[48]) ).
tff(143,plain,
divide(divide(a2,a2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))) = divide(divide(b2,b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))),
inference(transitivity,[status(thm)],[142,141,77,74]) ).
tff(144,plain,
divide(divide(b2,b2),divide(divide(a2,a2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2)))) = divide(divide(b2,b2),divide(divide(b2,b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2)))),
inference(monotonicity,[status(thm)],[143]) ).
tff(145,plain,
divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(b2,b2),divide(divide(a2,a2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))))) = divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(b2,b2),divide(divide(b2,b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))))),
inference(monotonicity,[status(thm)],[144]) ).
tff(146,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(b2,b2),divide(divide(a2,a2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))))) = divide(a2,a2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(147,plain,
divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(b2,b2),divide(divide(a2,a2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))))) = divide(a2,a2),
inference(unit_resolution,[status(thm)],[146,7]) ).
tff(148,plain,
divide(a2,a2) = divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(b2,b2),divide(divide(a2,a2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2))))),
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
divide(a2,a2) = divide(multiply(inverse(b2),b2),divide(b2,divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))))),
inference(transitivity,[status(thm)],[148,145,85,72,70,135]) ).
tff(150,plain,
divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(a2,a2)) = divide(divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(multiply(inverse(b2),b2),divide(b2,divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))))),
inference(monotonicity,[status(thm)],[104,149]) ).
tff(151,plain,
divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(a2,a2)) = divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2)),
inference(transitivity,[status(thm)],[150,138]) ).
tff(152,plain,
divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(a2,a2))) = divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))),
inference(monotonicity,[status(thm)],[151]) ).
tff(153,plain,
divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))) = divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(a2,a2))),
inference(symmetry,[status(thm)],[152]) ).
tff(154,plain,
divide(multiply(inverse(b2),b2),divide(b2,divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))))) = divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)),
inference(transitivity,[status(thm)],[134,67,62,59,64,22,100]) ).
tff(155,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(b2,divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(b2,divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))))) = b2 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(156,plain,
divide(b2,divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(b2,divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))))) = b2,
inference(unit_resolution,[status(thm)],[155,7]) ).
tff(157,plain,
divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))) = divide(b2,divide(b2,divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,b2)))),
inference(symmetry,[status(thm)],[20]) ).
tff(158,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(b2,b2)) = divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(159,plain,
multiply(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(b2,b2)) = divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),
inference(unit_resolution,[status(thm)],[158,16]) ).
tff(160,plain,
divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))) = divide(b2,b2),
inference(transitivity,[status(thm)],[157,51,121,61,120,119,118,117,87]) ).
tff(161,plain,
multiply(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))) = multiply(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(b2,b2)),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))) = divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(163,plain,
multiply(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))) = divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))))),
inference(unit_resolution,[status(thm)],[162,16]) ).
tff(164,plain,
divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))))) = multiply(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
divide(b2,divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))) = divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),
inference(transitivity,[status(thm)],[132,121,61]) ).
tff(166,plain,
divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(b2,divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))))) = divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))))),
inference(monotonicity,[status(thm)],[165]) ).
tff(167,plain,
divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(b2,divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))))) = divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)),
inference(transitivity,[status(thm)],[166,164,161,159,157,51,64,22,100]) ).
tff(168,plain,
divide(b2,divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(b2,divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))))) = divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),
inference(monotonicity,[status(thm)],[167]) ).
tff(169,plain,
divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))) = divide(b2,divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)),divide(b2,divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))))),
inference(symmetry,[status(thm)],[168]) ).
tff(170,plain,
divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))) = multiply(b2,divide(b2,b2)),
inference(symmetry,[status(thm)],[18]) ).
tff(171,plain,
divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))) = b2,
inference(transitivity,[status(thm)],[170,90,93,102,169,156]) ).
tff(172,plain,
divide(divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(multiply(inverse(b2),b2),divide(b2,divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))))) = divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),
inference(monotonicity,[status(thm)],[171,154]) ).
tff(173,plain,
divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))) = divide(divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(multiply(inverse(b2),b2),divide(b2,divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))))),
inference(symmetry,[status(thm)],[172]) ).
tff(174,plain,
divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))) = divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2)),
inference(transitivity,[status(thm)],[173,138]) ).
tff(175,plain,
divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))) = a2,
inference(transitivity,[status(thm)],[125,9]) ).
tff(176,plain,
divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))) = divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))),
inference(monotonicity,[status(thm)],[175,174]) ).
tff(177,plain,
divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))) = divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(a2,a2))),
inference(transitivity,[status(thm)],[176,153]) ).
tff(178,plain,
divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))))) = divide(a2,divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(a2,a2)))),
inference(monotonicity,[status(thm)],[175,177]) ).
tff(179,plain,
divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))))) = divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),
inference(transitivity,[status(thm)],[178,131,103,94,91,18]) ).
tff(180,plain,
divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))))) = divide(divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))),
inference(monotonicity,[status(thm)],[104,179]) ).
tff(181,plain,
divide(divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2))),divide(b2,divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),divide(b2,b2)))) = divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))))),
inference(symmetry,[status(thm)],[180]) ).
tff(182,plain,
divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)) = divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))))),
inference(transitivity,[status(thm)],[119,118,117,116,108,181]) ).
tff(183,plain,
divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) = divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))))))),
inference(monotonicity,[status(thm)],[182]) ).
tff(184,plain,
divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) = a2,
inference(transitivity,[status(thm)],[183,129,125,9]) ).
tff(185,plain,
divide(multiply(inverse(b2),b2),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)))) = divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),a2),
inference(monotonicity,[status(thm)],[122,184]) ).
tff(186,plain,
divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),a2) = divide(multiply(inverse(b2),b2),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)))),
inference(symmetry,[status(thm)],[185]) ).
tff(187,plain,
divide(multiply(inverse(b2),b2),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),a2)) = divide(multiply(inverse(b2),b2),divide(multiply(inverse(b2),b2),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),divide(a2,divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),multiply(inverse(b2),b2))))),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))))),
inference(monotonicity,[status(thm)],[186]) ).
tff(188,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(multiply(inverse(b2),b2),a2) = divide(multiply(inverse(b2),b2),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),a2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(189,plain,
multiply(multiply(inverse(b2),b2),a2) = divide(multiply(inverse(b2),b2),divide(divide(divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2))),divide(b2,divide(divide(divide(b2,b2),b2),divide(divide(divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2)),divide(divide(divide(divide(b2,b2),b2),divide(divide(b2,b2),b2)),multiply(inverse(b2),b2))),b2)))),a2)),
inference(unit_resolution,[status(thm)],[188,16]) ).
tff(190,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(transitivity,[status(thm)],[189,187,127,125,9]) ).
tff(191,plain,
( ( multiply(multiply(inverse(b2),b2),a2) != a2 )
<=> ( multiply(multiply(inverse(b2),b2),a2) != a2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(192,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
tff(193,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(modus_ponens,[status(thm)],[192,191]) ).
tff(194,plain,
$false,
inference(unit_resolution,[status(thm)],[193,190]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP522-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 17:30:44 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.52 % SZS status Unsatisfiable
% 0.20/0.52 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------