%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP532-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:08:02 AM UTC 2025
% Result : Unsatisfiable 0.22s 0.59s
% Output : Proof 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 48
% Syntax : Number of formulae : 271 ( 227 unt; 0 typ; 0 def)
% Number of atoms : 321 ( 317 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 88 ( 41 ~; 37 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 176 ( 168 !; 0 ?; 176 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(divide_type,type,
divide: ( $i * $i ) > $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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(5,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(b,a) = divide(b,divide(divide(b,b),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
multiply(b,a) = divide(b,divide(divide(b,b),a)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
divide(b,divide(divide(b,b),a)) = multiply(b,a),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
<=> ( divide(divide(A,divide(B,C)),divide(A,B)) = C ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
<=> ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
<=> ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(divide(b,b),a)),divide(b,divide(divide(b,b),a)))),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),a)))) = divide(b,divide(divide(b,b),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
divide(divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(divide(b,b),a)),divide(b,divide(divide(b,b),a)))),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),a)))) = divide(b,divide(divide(b,b),a)),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,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(21,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)],[20]) ).
tff(22,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(23,axiom,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
tff(24,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(divide(b,b),a)) = divide(divide(b,b),divide(divide(b,b),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
inverse(divide(divide(b,b),a)) = divide(divide(b,b),divide(divide(b,b),a)),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(divide(b,b),a)) = divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
inverse(divide(divide(b,b),a)) = divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),
inference(unit_resolution,[status(thm)],[29,26]) ).
tff(31,plain,
divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)) = inverse(divide(divide(b,b),a)),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(divide(a,a),divide(a,a)),a) = divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
multiply(divide(divide(a,a),divide(a,a)),a) = divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),
inference(unit_resolution,[status(thm)],[32,7]) ).
tff(34,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(divide(a,a),divide(a,a)),a) = divide(divide(divide(a,a),divide(a,a)),divide(divide(a,a),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
multiply(divide(divide(a,a),divide(a,a)),a) = divide(divide(divide(a,a),divide(a,a)),divide(divide(a,a),a)),
inference(unit_resolution,[status(thm)],[34,7]) ).
tff(36,plain,
divide(divide(divide(a,a),divide(a,a)),divide(divide(a,a),a)) = multiply(divide(divide(a,a),divide(a,a)),a),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(divide(a,a),divide(a,a)),divide(divide(a,a),a)) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
divide(divide(divide(a,a),divide(a,a)),divide(divide(a,a),a)) = a,
inference(unit_resolution,[status(thm)],[37,17]) ).
tff(39,plain,
a = divide(divide(divide(a,a),divide(a,a)),divide(divide(a,a),a)),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
a = divide(divide(b,b),divide(divide(b,b),a)),
inference(transitivity,[status(thm)],[39,36,33,31,28]) ).
tff(41,plain,
a = divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),
inference(transitivity,[status(thm)],[39,36,33]) ).
tff(42,plain,
divide(a,a) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),
inference(monotonicity,[status(thm)],[41,40]) ).
tff(43,plain,
divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))) = divide(a,a),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),a))) = divide(divide(a,a),divide(b,divide(divide(b,b),a))),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)) = multiply(divide(divide(a,a),divide(a,a)),a),
inference(symmetry,[status(thm)],[33]) ).
tff(46,plain,
divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)) = a,
inference(transitivity,[status(thm)],[45,35,38]) ).
tff(47,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a))) = divide(divide(a,a),a),
inference(monotonicity,[status(thm)],[43,46]) ).
tff(48,plain,
divide(divide(a,a),a) = divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a))),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(a) = divide(divide(a,a),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
inverse(a) = divide(divide(a,a),a),
inference(unit_resolution,[status(thm)],[49,26]) ).
tff(51,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(a) = divide(divide(b,b),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
inverse(a) = divide(divide(b,b),a),
inference(unit_resolution,[status(thm)],[51,26]) ).
tff(53,plain,
divide(divide(b,b),a) = inverse(a),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
divide(divide(b,b),a) = divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a))),
inference(transitivity,[status(thm)],[53,50,48]) ).
tff(55,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(a,divide(b,a)),divide(a,b)) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
divide(divide(a,divide(b,a)),divide(a,b)) = a,
inference(unit_resolution,[status(thm)],[55,17]) ).
tff(57,plain,
divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(a,divide(b,a)),divide(a,b))) = divide(a,a),
inference(monotonicity,[status(thm)],[46,56]) ).
tff(58,plain,
divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(a,divide(b,a)),divide(a,b))) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),
inference(transitivity,[status(thm)],[57,42]) ).
tff(59,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(a,divide(b,a)),divide(a,b))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(a,divide(b,a)))) = divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(a,divide(b,a)))),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(a,divide(b,a)),divide(a,b))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(a,divide(b,a)))) = divide(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(a,divide(b,a)),divide(a,b))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(a,divide(b,a)))) = divide(a,b),
inference(unit_resolution,[status(thm)],[60,17]) ).
tff(62,plain,
divide(a,b) = divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(a,divide(b,a)),divide(a,b))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(a,divide(b,a)))),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
divide(a,b) = divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(a,divide(b,a)))),
inference(transitivity,[status(thm)],[62,59]) ).
tff(64,plain,
divide(divide(a,b),divide(divide(b,b),a)) = divide(divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(a,divide(b,a)))),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))),
inference(monotonicity,[status(thm)],[63,54]) ).
tff(65,plain,
divide(divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(a,divide(b,a)))),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))) = divide(divide(a,b),divide(divide(b,b),a)),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(a,divide(b,a)))),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))) = divide(a,divide(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
divide(divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(a,divide(b,a)))),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))) = divide(a,divide(b,a)),
inference(unit_resolution,[status(thm)],[66,17]) ).
tff(68,plain,
divide(a,divide(b,a)) = divide(divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(a,divide(b,a)))),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
divide(a,divide(b,a)) = divide(divide(a,b),divide(divide(b,b),a)),
inference(transitivity,[status(thm)],[68,65]) ).
tff(70,plain,
divide(divide(a,divide(b,a)),divide(a,divide(b,a))) = divide(divide(a,divide(b,a)),divide(divide(a,b),divide(divide(b,b),a))),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
divide(divide(a,divide(b,a)),divide(divide(a,b),divide(divide(b,b),a))) = divide(divide(a,divide(b,a)),divide(a,divide(b,a))),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),a)) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
multiply(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),a)) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a))),
inference(unit_resolution,[status(thm)],[72,7]) ).
tff(74,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),a)) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(75,plain,
multiply(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),a)) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),
inference(unit_resolution,[status(thm)],[74,7]) ).
tff(76,plain,
divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))) = multiply(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),a)),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a))),
inference(transitivity,[status(thm)],[76,73]) ).
tff(78,plain,
divide(b,a) = divide(b,divide(divide(b,b),divide(divide(b,b),a))),
inference(monotonicity,[status(thm)],[40]) ).
tff(79,plain,
divide(b,divide(divide(b,b),divide(divide(b,b),a))) = divide(b,a),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))) = divide(b,divide(divide(b,b),divide(divide(b,b),a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(81,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))) = divide(b,divide(divide(b,b),divide(divide(b,b),a))),
inference(unit_resolution,[status(thm)],[80,17]) ).
tff(82,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(divide(b,b),a)) = divide(divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),divide(divide(b,b),a)))),divide(divide(b,b),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
inverse(divide(divide(b,b),a)) = divide(divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),divide(divide(b,b),a)))),divide(divide(b,b),a)),
inference(unit_resolution,[status(thm)],[82,26]) ).
tff(84,plain,
divide(divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),divide(divide(b,b),a)))),divide(divide(b,b),a)) = inverse(divide(divide(b,b),a)),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b))) = divide(divide(b,b),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b))) = divide(divide(b,b),a),
inference(unit_resolution,[status(thm)],[85,17]) ).
tff(87,plain,
divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),divide(divide(b,b),a)))) = divide(divide(b,a),divide(b,a)),
inference(monotonicity,[status(thm)],[79,79]) ).
tff(88,plain,
divide(divide(b,a),divide(b,a)) = divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),divide(divide(b,b),a)))),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a)))) = divide(a,divide(a,a)),
inference(monotonicity,[status(thm)],[46,43]) ).
tff(90,plain,
divide(a,divide(a,a)) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a)))),
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
divide(divide(b,b),divide(b,divide(divide(b,b),divide(divide(b,b),a)))) = divide(divide(b,b),divide(b,a)),
inference(monotonicity,[status(thm)],[79]) ).
tff(92,plain,
divide(divide(b,b),divide(b,a)) = divide(divide(b,b),divide(b,divide(divide(b,b),divide(divide(b,b),a)))),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(b,a)) = divide(divide(b,b),divide(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(94,plain,
inverse(divide(b,a)) = divide(divide(b,b),divide(b,a)),
inference(unit_resolution,[status(thm)],[93,26]) ).
tff(95,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(b,a)) = divide(divide(a,a),divide(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
inverse(divide(b,a)) = divide(divide(a,a),divide(b,a)),
inference(unit_resolution,[status(thm)],[95,26]) ).
tff(97,plain,
divide(divide(a,a),divide(b,a)) = inverse(divide(b,a)),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),divide(divide(b,b),a)))) = divide(divide(a,a),divide(b,a)),
inference(monotonicity,[status(thm)],[43,79]) ).
tff(99,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),divide(divide(b,b),a)))) = divide(divide(b,b),divide(b,divide(divide(b,b),divide(divide(b,b),a)))),
inference(transitivity,[status(thm)],[98,97,94,92]) ).
tff(100,plain,
divide(divide(b,b),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b)))) = divide(divide(b,b),divide(divide(b,b),a)),
inference(monotonicity,[status(thm)],[86]) ).
tff(101,plain,
divide(divide(b,b),divide(divide(b,b),a)) = divide(divide(b,b),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b)))),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)) = divide(divide(b,b),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b)))),
inference(transitivity,[status(thm)],[31,28,101]) ).
tff(103,plain,
divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),divide(divide(b,b),a))))) = divide(divide(divide(b,b),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b)))),divide(divide(b,b),divide(b,divide(divide(b,b),divide(divide(b,b),a))))),
inference(monotonicity,[status(thm)],[102,99]) ).
tff(104,plain,
divide(divide(divide(b,b),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b)))),divide(divide(b,b),divide(b,divide(divide(b,b),divide(divide(b,b),a))))) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),divide(divide(b,b),a))))),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(divide(b,b),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b)))),divide(divide(b,b),divide(b,divide(divide(b,b),divide(divide(b,b),a))))) = divide(b,divide(b,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
divide(divide(divide(b,b),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b)))),divide(divide(b,b),divide(b,divide(divide(b,b),divide(divide(b,b),a))))) = divide(b,divide(b,b)),
inference(unit_resolution,[status(thm)],[105,17]) ).
tff(107,plain,
divide(b,divide(b,b)) = divide(divide(divide(b,b),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b)))),divide(divide(b,b),divide(b,divide(divide(b,b),divide(divide(b,b),a))))),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
divide(b,divide(b,b)) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),divide(divide(b,b),a))))),
inference(transitivity,[status(thm)],[107,104]) ).
tff(109,plain,
divide(divide(b,divide(b,b)),divide(a,divide(a,a))) = divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),
inference(monotonicity,[status(thm)],[108,90]) ).
tff(110,plain,
divide(divide(b,divide(b,b)),divide(a,divide(a,a))) = divide(b,a),
inference(transitivity,[status(thm)],[109,81,79]) ).
tff(111,plain,
divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(a,divide(a,a)))) = divide(divide(b,a),divide(b,a)),
inference(monotonicity,[status(thm)],[79,110]) ).
tff(112,plain,
divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(a,divide(a,a)))) = divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),divide(divide(b,b),a)))),
inference(transitivity,[status(thm)],[111,88]) ).
tff(113,plain,
divide(divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(a,divide(a,a)))),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b)))) = divide(divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),divide(divide(b,b),a)))),divide(divide(b,b),a)),
inference(monotonicity,[status(thm)],[112,86]) ).
tff(114,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(a,divide(a,a)))),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b)))) = divide(a,divide(a,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
divide(divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(a,divide(a,a)))),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b)))) = divide(a,divide(a,a)),
inference(unit_resolution,[status(thm)],[114,17]) ).
tff(116,plain,
divide(a,divide(a,a)) = divide(divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(a,divide(a,a)))),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b)))),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a)))) = divide(divide(b,b),divide(divide(b,b),a)),
inference(transitivity,[status(thm)],[89,116,113,84,28]) ).
tff(118,plain,
divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),divide(divide(b,b),a))))) = divide(b,divide(b,b)),
inference(transitivity,[status(thm)],[103,106]) ).
tff(119,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))) = divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))),
inference(monotonicity,[status(thm)],[118,117]) ).
tff(120,plain,
divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))) = divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(b,divide(divide(b,b),divide(divide(b,b),a))))) = divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(122,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(b,divide(divide(b,b),divide(divide(b,b),a))))) = divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))),
inference(unit_resolution,[status(thm)],[121,17]) ).
tff(123,plain,
divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(b,divide(divide(b,b),divide(divide(b,b),a)))) = divide(a,divide(b,a)),
inference(monotonicity,[status(thm)],[46,79]) ).
tff(124,plain,
divide(a,divide(b,a)) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(b,divide(divide(b,b),divide(divide(b,b),a)))),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(divide(b,divide(b,b)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(b,divide(b,b)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(126,plain,
divide(divide(divide(b,divide(b,b)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(b,divide(b,b)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),
inference(unit_resolution,[status(thm)],[125,17]) ).
tff(127,plain,
divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)) = divide(divide(b,b),divide(divide(b,b),a)),
inference(transitivity,[status(thm)],[31,28]) ).
tff(128,plain,
divide(divide(b,divide(b,b)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a))) = divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))) = divide(divide(b,divide(b,b)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a))),
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
divide(divide(b,divide(b,b)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))) = divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),
inference(monotonicity,[status(thm)],[108]) ).
tff(131,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))) = divide(divide(b,divide(b,b)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
divide(b,divide(divide(b,b),divide(divide(b,b),a))) = divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),
inference(symmetry,[status(thm)],[81]) ).
tff(133,plain,
divide(b,divide(divide(b,b),divide(divide(b,b),a))) = divide(divide(b,divide(b,b)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),
inference(transitivity,[status(thm)],[132,131]) ).
tff(134,plain,
divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a)))) = divide(divide(divide(b,divide(b,b)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(b,divide(b,b)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))),
inference(monotonicity,[status(thm)],[133,129]) ).
tff(135,plain,
divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a)))) = divide(a,a),
inference(transitivity,[status(thm)],[134,126,43]) ).
tff(136,plain,
divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))))) = divide(a,divide(a,a)),
inference(monotonicity,[status(thm)],[46,135]) ).
tff(137,plain,
divide(a,divide(a,a)) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))))),
inference(symmetry,[status(thm)],[136]) ).
tff(138,plain,
divide(divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),divide(divide(b,b),a)))),divide(divide(b,b),a)) = divide(divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(a,divide(a,a)))),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b)))),
inference(symmetry,[status(thm)],[113]) ).
tff(139,plain,
divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))))),
inference(transitivity,[status(thm)],[31,83,138,115,137]) ).
tff(140,plain,
divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(a,divide(b,a))) = divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(b,divide(divide(b,b),divide(divide(b,b),a))))),
inference(monotonicity,[status(thm)],[139,124]) ).
tff(141,plain,
divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(a,divide(b,a))) = divide(b,a),
inference(transitivity,[status(thm)],[140,122,120,81,79]) ).
tff(142,plain,
divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(a,divide(b,a)))) = divide(a,divide(b,a)),
inference(monotonicity,[status(thm)],[46,141]) ).
tff(143,plain,
divide(a,divide(b,a)) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(a,divide(b,a)))),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
divide(divide(a,divide(b,a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a)))) = divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(a,divide(b,a)))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))),
inference(monotonicity,[status(thm)],[143,77]) ).
tff(145,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(a,divide(b,a)))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))) = divide(divide(a,divide(b,a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a)))),
inference(symmetry,[status(thm)],[144]) ).
tff(146,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(a,divide(b,a)))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))) = divide(a,divide(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(147,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(a,divide(b,a)))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))) = divide(a,divide(b,a)),
inference(unit_resolution,[status(thm)],[146,17]) ).
tff(148,plain,
divide(a,divide(b,a)) = divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(a,divide(b,a)))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))),
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
divide(divide(a,b),divide(divide(b,b),a)) = divide(divide(a,divide(b,a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a)))),
inference(transitivity,[status(thm)],[64,67,148,145]) ).
tff(150,plain,
divide(divide(a,divide(b,a)),divide(divide(a,b),divide(divide(b,b),a))) = divide(divide(a,divide(b,a)),divide(divide(a,divide(b,a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),
inference(monotonicity,[status(thm)],[149]) ).
tff(151,plain,
divide(divide(a,divide(b,a)),divide(divide(a,divide(b,a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))) = divide(divide(a,divide(b,a)),divide(divide(a,b),divide(divide(b,b),a))),
inference(symmetry,[status(thm)],[150]) ).
tff(152,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(153,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),
inference(unit_resolution,[status(thm)],[152,17]) ).
tff(154,plain,
divide(a,a) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a))),
inference(transitivity,[status(thm)],[42,76,73]) ).
tff(155,plain,
divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a)))) = a,
inference(transitivity,[status(thm)],[89,116,113,84,30,45,35,38]) ).
tff(156,plain,
divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))) = divide(a,a),
inference(monotonicity,[status(thm)],[46,155]) ).
tff(157,plain,
divide(a,a) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),
inference(symmetry,[status(thm)],[156]) ).
tff(158,plain,
divide(divide(a,a),divide(a,a)) = divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))),
inference(monotonicity,[status(thm)],[157,154]) ).
tff(159,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a)))) = divide(divide(a,a),divide(a,a)),
inference(monotonicity,[status(thm)],[43,43]) ).
tff(160,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a)))) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a))),
inference(transitivity,[status(thm)],[159,158,153,76,73]) ).
tff(161,plain,
divide(divide(a,divide(b,a)),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))) = divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(a,divide(b,a)))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))),
inference(monotonicity,[status(thm)],[143,160]) ).
tff(162,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(a,divide(b,a)))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))) = divide(divide(a,divide(b,a)),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),
inference(symmetry,[status(thm)],[161]) ).
tff(163,plain,
divide(a,divide(b,a)) = divide(divide(a,divide(b,a)),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),
inference(transitivity,[status(thm)],[148,162]) ).
tff(164,plain,
divide(divide(a,divide(b,a)),divide(divide(a,divide(b,a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))) = divide(divide(divide(a,divide(b,a)),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(a,divide(b,a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),
inference(monotonicity,[status(thm)],[163]) ).
tff(165,plain,
divide(divide(divide(a,divide(b,a)),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(a,divide(b,a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))) = divide(divide(a,divide(b,a)),divide(divide(a,divide(b,a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),
inference(symmetry,[status(thm)],[164]) ).
tff(166,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(divide(a,divide(b,a)),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(a,divide(b,a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(167,plain,
divide(divide(divide(a,divide(b,a)),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(a,divide(b,a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),
inference(unit_resolution,[status(thm)],[166,17]) ).
tff(168,plain,
divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))) = divide(divide(divide(a,divide(b,a)),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(a,divide(b,a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(divide(b,divide(b,b)),divide(divide(divide(b,b),a),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(b,divide(b,b)),divide(divide(b,b),a))) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(170,plain,
divide(divide(divide(b,divide(b,b)),divide(divide(divide(b,b),a),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(b,divide(b,b)),divide(divide(b,b),a))) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),
inference(unit_resolution,[status(thm)],[169,17]) ).
tff(171,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))),b)),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))))) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(172,plain,
divide(divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))),b)),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))))) = b,
inference(unit_resolution,[status(thm)],[171,17]) ).
tff(173,plain,
divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))) = divide(b,a),
inference(transitivity,[status(thm)],[120,81,79]) ).
tff(174,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a)))) = divide(divide(a,a),divide(b,a)),
inference(monotonicity,[status(thm)],[43,173]) ).
tff(175,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a)))) = divide(divide(b,b),divide(b,divide(divide(b,b),divide(divide(b,b),a)))),
inference(transitivity,[status(thm)],[174,97,94,92]) ).
tff(176,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b)))) = divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(177,plain,
divide(divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b)))) = divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),
inference(unit_resolution,[status(thm)],[176,17]) ).
tff(178,plain,
divide(divide(b,b),a) = divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b))),
inference(symmetry,[status(thm)],[86]) ).
tff(179,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(b,b))) = divide(divide(b,b),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(180,plain,
divide(divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(b,b))) = divide(divide(b,b),a),
inference(unit_resolution,[status(thm)],[179,17]) ).
tff(181,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(b,divide(b,b)),divide(b,b)) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(182,plain,
divide(divide(b,divide(b,b)),divide(b,b)) = b,
inference(unit_resolution,[status(thm)],[181,17]) ).
tff(183,plain,
b = divide(divide(b,divide(b,b)),divide(b,b)),
inference(symmetry,[status(thm)],[182]) ).
tff(184,plain,
divide(divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))),b) = divide(divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(b,b))),
inference(monotonicity,[status(thm)],[183]) ).
tff(185,plain,
divide(divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))),b) = divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b))),
inference(transitivity,[status(thm)],[184,180,178]) ).
tff(186,plain,
divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))) = divide(divide(divide(b,divide(b,b)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(b,divide(b,b)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))),
inference(monotonicity,[status(thm)],[133]) ).
tff(187,plain,
divide(divide(divide(b,divide(b,b)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(b,divide(b,b)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))) = divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))),
inference(symmetry,[status(thm)],[186]) ).
tff(188,plain,
divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))) = divide(divide(divide(b,divide(b,b)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(b,divide(b,b)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))),
inference(symmetry,[status(thm)],[126]) ).
tff(189,plain,
divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))) = divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))),
inference(transitivity,[status(thm)],[188,187]) ).
tff(190,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))),b)) = divide(divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b)))),
inference(monotonicity,[status(thm)],[189,185]) ).
tff(191,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))),b)) = divide(divide(b,b),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b)))),
inference(transitivity,[status(thm)],[190,177,31,28,101]) ).
tff(192,plain,
divide(divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))),b)),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))))) = divide(divide(divide(b,b),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b)))),divide(divide(b,b),divide(b,divide(divide(b,b),divide(divide(b,b),a))))),
inference(monotonicity,[status(thm)],[191,175]) ).
tff(193,plain,
divide(divide(divide(b,b),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b)))),divide(divide(b,b),divide(b,divide(divide(b,b),divide(divide(b,b),a))))) = divide(divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))),b)),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))))),
inference(symmetry,[status(thm)],[192]) ).
tff(194,plain,
divide(b,divide(b,b)) = b,
inference(transitivity,[status(thm)],[107,193,172]) ).
tff(195,plain,
divide(divide(b,divide(b,b)),divide(divide(b,b),a)) = divide(b,divide(divide(b,b),a)),
inference(monotonicity,[status(thm)],[194]) ).
tff(196,plain,
divide(b,divide(divide(b,b),a)) = divide(divide(b,divide(b,b)),divide(divide(b,b),a)),
inference(symmetry,[status(thm)],[195]) ).
tff(197,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,b),a))),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))) = divide(divide(b,b),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(198,plain,
divide(divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,b),a))),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))) = divide(divide(b,b),a),
inference(unit_resolution,[status(thm)],[197,17]) ).
tff(199,plain,
divide(divide(a,a),divide(a,a)) = divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a)))),
inference(symmetry,[status(thm)],[159]) ).
tff(200,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))) = divide(divide(a,a),divide(a,a)),
inference(symmetry,[status(thm)],[158]) ).
tff(201,plain,
divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))) = divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))),
inference(symmetry,[status(thm)],[153]) ).
tff(202,plain,
divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))) = divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a)))),
inference(transitivity,[status(thm)],[201,200,199]) ).
tff(203,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,b),a)) = divide(divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b)))),
inference(monotonicity,[status(thm)],[189,178]) ).
tff(204,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,b),a)) = a,
inference(transitivity,[status(thm)],[203,177,45,35,38]) ).
tff(205,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,b),a))) = divide(divide(a,a),a),
inference(monotonicity,[status(thm)],[43,204]) ).
tff(206,plain,
divide(divide(a,a),a) = divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,b),a))),
inference(symmetry,[status(thm)],[205]) ).
tff(207,plain,
divide(divide(b,b),a) = divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,b),a))),
inference(transitivity,[status(thm)],[53,50,206]) ).
tff(208,plain,
divide(divide(divide(b,b),a),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a)))) = divide(divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,b),a))),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),
inference(monotonicity,[status(thm)],[207,202]) ).
tff(209,plain,
divide(divide(divide(b,b),a),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a)))) = divide(divide(b,b),a),
inference(transitivity,[status(thm)],[208,198]) ).
tff(210,plain,
divide(divide(b,divide(b,b)),divide(divide(divide(b,b),a),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))) = divide(b,divide(divide(b,b),a)),
inference(monotonicity,[status(thm)],[194,209]) ).
tff(211,plain,
divide(b,divide(divide(b,b),a)) = divide(divide(b,divide(b,b)),divide(divide(divide(b,b),a),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),
inference(symmetry,[status(thm)],[210]) ).
tff(212,plain,
divide(divide(b,divide(divide(b,b),a)),divide(b,divide(divide(b,b),a))) = divide(divide(divide(b,divide(b,b)),divide(divide(divide(b,b),a),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(b,divide(b,b)),divide(divide(b,b),a))),
inference(monotonicity,[status(thm)],[211,196]) ).
tff(213,plain,
divide(divide(b,divide(divide(b,b),a)),divide(b,divide(divide(b,b),a))) = divide(a,a),
inference(transitivity,[status(thm)],[212,170,43]) ).
tff(214,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(divide(b,b),a)),divide(b,divide(divide(b,b),a)))) = divide(divide(a,a),divide(a,a)),
inference(monotonicity,[status(thm)],[43,213]) ).
tff(215,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(divide(b,b),a)),divide(b,divide(divide(b,b),a)))) = divide(divide(a,divide(b,a)),divide(a,divide(b,a))),
inference(transitivity,[status(thm)],[214,158,153,168,165,151,71]) ).
tff(216,plain,
divide(divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(divide(b,b),a)),divide(b,divide(divide(b,b),a)))),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),a)))) = divide(divide(divide(a,divide(b,a)),divide(a,divide(b,a))),divide(divide(a,a),divide(b,divide(divide(b,b),a)))),
inference(monotonicity,[status(thm)],[215,44]) ).
tff(217,plain,
divide(divide(divide(a,divide(b,a)),divide(a,divide(b,a))),divide(divide(a,a),divide(b,divide(divide(b,b),a)))) = divide(divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(divide(b,b),a)),divide(b,divide(divide(b,b),a)))),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(divide(b,b),a)))),
inference(symmetry,[status(thm)],[216]) ).
tff(218,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(divide(a,divide(b,a)),divide(a,divide(b,a))),divide(divide(a,a),divide(b,divide(divide(b,b),a)))))),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b)))) = divide(divide(divide(a,divide(b,a)),divide(a,divide(b,a))),divide(divide(a,a),divide(b,divide(divide(b,b),a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(219,plain,
divide(divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(divide(a,divide(b,a)),divide(a,divide(b,a))),divide(divide(a,a),divide(b,divide(divide(b,b),a)))))),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b)))) = divide(divide(divide(a,divide(b,a)),divide(a,divide(b,a))),divide(divide(a,a),divide(b,divide(divide(b,b),a)))),
inference(unit_resolution,[status(thm)],[218,17]) ).
tff(220,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b))) = divide(divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a)))),divide(b,divide(b,b))),
inference(monotonicity,[status(thm)],[202]) ).
tff(221,plain,
divide(divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a)))),divide(b,divide(b,b))) = divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b))),
inference(symmetry,[status(thm)],[220]) ).
tff(222,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(divide(b,divide(b,b)),divide(divide(divide(b,b),a),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(b,b),a))) = divide(divide(b,b),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(223,plain,
divide(divide(divide(b,divide(b,b)),divide(divide(divide(b,b),a),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(b,b),a))) = divide(divide(b,b),a),
inference(unit_resolution,[status(thm)],[222,17]) ).
tff(224,plain,
divide(divide(divide(a,divide(b,a)),divide(a,divide(b,a))),divide(divide(a,a),divide(b,divide(divide(b,b),a)))) = divide(divide(b,divide(b,b)),divide(divide(b,b),a)),
inference(transitivity,[status(thm)],[217,19,196]) ).
tff(225,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(divide(b,b),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(b,b),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(226,plain,
divide(divide(divide(b,b),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(b,b),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),
inference(unit_resolution,[status(thm)],[225,17]) ).
tff(227,plain,
divide(divide(b,b),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a))) = divide(divide(b,b),divide(divide(b,b),divide(divide(b,b),a))),
inference(monotonicity,[status(thm)],[127]) ).
tff(228,plain,
divide(divide(b,b),divide(divide(b,b),divide(divide(b,b),a))) = divide(divide(b,b),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a))),
inference(symmetry,[status(thm)],[227]) ).
tff(229,plain,
divide(divide(b,b),divide(divide(b,b),a)) = inverse(divide(divide(b,b),a)),
inference(symmetry,[status(thm)],[28]) ).
tff(230,plain,
divide(divide(b,b),divide(divide(b,b),a)) = a,
inference(transitivity,[status(thm)],[229,30,45,35,38]) ).
tff(231,plain,
divide(divide(b,b),divide(divide(b,b),divide(divide(b,b),a))) = divide(divide(b,b),a),
inference(monotonicity,[status(thm)],[230]) ).
tff(232,plain,
divide(divide(b,b),a) = divide(divide(b,b),divide(divide(b,b),divide(divide(b,b),a))),
inference(symmetry,[status(thm)],[231]) ).
tff(233,plain,
divide(divide(b,b),a) = divide(divide(b,b),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a))),
inference(transitivity,[status(thm)],[232,228]) ).
tff(234,plain,
divide(divide(b,b),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))) = divide(divide(b,b),divide(divide(b,b),divide(divide(b,b),a))),
inference(monotonicity,[status(thm)],[117]) ).
tff(235,plain,
divide(divide(b,b),divide(divide(b,b),divide(divide(b,b),a))) = divide(divide(b,b),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),
inference(symmetry,[status(thm)],[234]) ).
tff(236,plain,
divide(divide(b,b),a) = divide(divide(b,b),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),
inference(transitivity,[status(thm)],[232,235]) ).
tff(237,plain,
divide(divide(divide(b,b),a),divide(divide(b,b),a)) = divide(divide(divide(b,b),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(b,b),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))),
inference(monotonicity,[status(thm)],[236,233]) ).
tff(238,plain,
divide(divide(divide(b,b),a),divide(divide(b,b),a)) = divide(a,a),
inference(transitivity,[status(thm)],[237,226,43]) ).
tff(239,plain,
divide(divide(b,divide(b,b)),divide(divide(divide(b,b),a),divide(divide(b,b),a))) = divide(divide(b,divide(b,b)),divide(a,a)),
inference(monotonicity,[status(thm)],[238]) ).
tff(240,plain,
divide(divide(b,divide(b,b)),divide(a,a)) = divide(divide(b,divide(b,b)),divide(divide(divide(b,b),a),divide(divide(b,b),a))),
inference(symmetry,[status(thm)],[239]) ).
tff(241,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(B,C)),divide(A,B)) = C )
| ( divide(divide(divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b))),divide(divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))),b)) = divide(b,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(242,plain,
divide(divide(divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b))),divide(divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))),b)) = divide(b,b),
inference(unit_resolution,[status(thm)],[241,17]) ).
tff(243,plain,
divide(divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))),b) = divide(divide(b,b),a),
inference(transitivity,[status(thm)],[184,180]) ).
tff(244,plain,
divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))) = divide(b,divide(divide(b,b),divide(divide(b,b),a))),
inference(transitivity,[status(thm)],[120,81]) ).
tff(245,plain,
divide(divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b))) = divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b))),
inference(monotonicity,[status(thm)],[244]) ).
tff(246,plain,
divide(divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b))) = divide(divide(b,b),a),
inference(transitivity,[status(thm)],[245,86]) ).
tff(247,plain,
divide(divide(divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b))),divide(divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))),b)) = divide(divide(divide(b,b),a),divide(divide(b,b),a)),
inference(monotonicity,[status(thm)],[246,243]) ).
tff(248,plain,
divide(divide(divide(b,b),a),divide(divide(b,b),a)) = divide(divide(divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b))),divide(divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))),b)),
inference(symmetry,[status(thm)],[247]) ).
tff(249,plain,
divide(divide(divide(b,b),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(b,b),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))) = divide(divide(divide(b,b),a),divide(divide(b,b),a)),
inference(symmetry,[status(thm)],[237]) ).
tff(250,plain,
divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))) = divide(divide(divide(b,b),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))))),divide(divide(b,b),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))),
inference(symmetry,[status(thm)],[226]) ).
tff(251,plain,
divide(a,a) = divide(b,b),
inference(transitivity,[status(thm)],[42,250,249,248,242]) ).
tff(252,plain,
divide(divide(b,divide(b,b)),divide(a,a)) = divide(divide(b,divide(b,b)),divide(b,b)),
inference(monotonicity,[status(thm)],[251]) ).
tff(253,plain,
divide(divide(b,divide(b,b)),divide(b,b)) = divide(divide(b,divide(b,b)),divide(a,a)),
inference(symmetry,[status(thm)],[252]) ).
tff(254,plain,
divide(b,divide(b,b)) = divide(divide(b,divide(b,b)),divide(divide(divide(b,b),a),divide(divide(b,b),a))),
inference(transitivity,[status(thm)],[107,193,172,183,253,240]) ).
tff(255,plain,
divide(divide(b,divide(b,b)),divide(divide(divide(a,divide(b,a)),divide(a,divide(b,a))),divide(divide(a,a),divide(b,divide(divide(b,b),a))))) = divide(divide(divide(b,divide(b,b)),divide(divide(divide(b,b),a),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(b,b),a))),
inference(monotonicity,[status(thm)],[254,224]) ).
tff(256,plain,
divide(divide(b,divide(b,b)),divide(divide(divide(a,divide(b,a)),divide(a,divide(b,a))),divide(divide(a,a),divide(b,divide(divide(b,b),a))))) = divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b))),
inference(transitivity,[status(thm)],[255,223,178]) ).
tff(257,plain,
divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(divide(a,divide(b,a)),divide(a,divide(b,a))),divide(divide(a,a),divide(b,divide(divide(b,b),a)))))) = divide(divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b)))),
inference(monotonicity,[status(thm)],[189,256]) ).
tff(258,plain,
divide(divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b)))) = divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(divide(a,divide(b,a)),divide(a,divide(b,a))),divide(divide(a,a),divide(b,divide(divide(b,b),a)))))),
inference(symmetry,[status(thm)],[257]) ).
tff(259,plain,
divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)) = divide(divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)))),divide(divide(b,divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b)))),
inference(symmetry,[status(thm)],[177]) ).
tff(260,plain,
divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)) = divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(divide(a,divide(b,a)),divide(a,divide(b,a))),divide(divide(a,a),divide(b,divide(divide(b,b),a)))))),
inference(transitivity,[status(thm)],[259,258]) ).
tff(261,plain,
divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a)))),divide(b,divide(b,b)))) = divide(divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(divide(a,divide(b,a)),divide(a,divide(b,a))),divide(divide(a,a),divide(b,divide(divide(b,b),a)))))),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(b,divide(b,b)))),
inference(monotonicity,[status(thm)],[260,221]) ).
tff(262,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(b,divide(b,b))) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a)))),divide(b,divide(b,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(263,plain,
multiply(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(b,divide(b,b))) = divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a)))),divide(b,divide(b,b)))),
inference(unit_resolution,[status(thm)],[262,7]) ).
tff(264,plain,
b = divide(divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))),b)),divide(divide(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(divide(b,b),divide(divide(b,b),a))),divide(divide(b,divide(b,b)),divide(divide(b,b),divide(divide(b,b),a))))),
inference(symmetry,[status(thm)],[172]) ).
tff(265,plain,
b = divide(b,divide(b,b)),
inference(transitivity,[status(thm)],[264,192,106]) ).
tff(266,plain,
multiply(a,b) = multiply(divide(divide(divide(a,a),divide(a,a)),divide(divide(b,b),a)),divide(b,divide(b,b))),
inference(monotonicity,[status(thm)],[41,265]) ).
tff(267,plain,
multiply(a,b) = multiply(b,a),
inference(transitivity,[status(thm)],[266,263,261,219,217,19,10]) ).
tff(268,plain,
( ( multiply(a,b) != multiply(b,a) )
<=> ( multiply(a,b) != multiply(b,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(269,axiom,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_4) ).
tff(270,plain,
multiply(a,b) != multiply(b,a),
inference(modus_ponens,[status(thm)],[269,268]) ).
tff(271,plain,
$false,
inference(unit_resolution,[status(thm)],[270,267]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GRP532-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Jun 19 16:15:39 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.22/0.59 % SZS status Unsatisfiable
% 0.22/0.59 % SZS output start Proof
% See solution above
% 0.47/0.66 % E exiting
%------------------------------------------------------------------------------