%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP540-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:08:03 AM UTC 2025
% Result : Unsatisfiable 0.39s 0.61s
% Output : Proof 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 37
% Syntax : Number of formulae : 174 ( 141 unt; 0 typ; 0 def)
% Number of atoms : 213 ( 209 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 66 ( 30 ~; 26 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 142 ( 134 !; 0 ?; 142 :)
% 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] :
refl(( ( inverse(A) = divide(divide(B,B),A) )
<=> ( inverse(A) = divide(divide(B,B),A) ) )),
inference(bind,[status(th)],[]) ).
tff(2,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)],[1]) ).
tff(3,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(4,axiom,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
tff(5,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(divide(b,b),b)) = divide(divide(b,b),divide(divide(b,b),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
inverse(divide(divide(b,b),b)) = divide(divide(b,b),divide(divide(b,b),b)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(divide(b,b),b)) = divide(divide(a,a),divide(divide(b,b),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(11,plain,
inverse(divide(divide(b,b),b)) = divide(divide(a,a),divide(divide(b,b),b)),
inference(unit_resolution,[status(thm)],[10,7]) ).
tff(12,plain,
divide(divide(a,a),divide(divide(b,b),b)) = inverse(divide(divide(b,b),b)),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
divide(divide(a,a),divide(divide(b,b),b)) = divide(divide(b,b),divide(divide(b,b),b)),
inference(transitivity,[status(thm)],[12,9]) ).
tff(14,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(15,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)],[14]) ).
tff(16,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(17,axiom,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
tff(18,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(a,b) = divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
multiply(a,b) = divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),
inference(unit_resolution,[status(thm)],[21,20]) ).
tff(23,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(a,b) = divide(a,divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
multiply(a,b) = divide(a,divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),b)),
inference(unit_resolution,[status(thm)],[23,20]) ).
tff(25,plain,
divide(a,divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),b)) = multiply(a,b),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( divide(divide(A,B),divide(divide(A,C),B)) = C )
<=> ( divide(divide(A,B),divide(divide(A,C),B)) = C ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(divide(A,B),divide(divide(A,C),B)) = C )
<=> ! [B: $i,A: $i,C: $i] : ( divide(divide(A,B),divide(divide(A,C),B)) = C ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(divide(A,B),divide(divide(A,C),B)) = C )
<=> ! [B: $i,A: $i,C: $i] : ( divide(divide(A,B),divide(divide(A,C),B)) = C ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
! [B: $i,A: $i,C: $i] : ( divide(divide(A,B),divide(divide(A,C),B)) = C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
tff(30,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(A,B),divide(divide(A,C),B)) = C ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(A,B),divide(divide(A,C),B)) = C ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(A,B),divide(divide(A,C),B)) = C ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,B),divide(divide(A,C),B)) = C )
| ( divide(divide(b,divide(divide(b,b),b)),divide(divide(b,divide(b,b)),divide(divide(b,b),b))) = divide(b,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
divide(divide(b,divide(divide(b,b),b)),divide(divide(b,divide(b,b)),divide(divide(b,b),b))) = divide(b,b),
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,B),divide(divide(A,C),B)) = C )
| ( divide(divide(divide(b,divide(divide(b,b),b)),b),divide(divide(divide(b,divide(divide(b,b),b)),b),b)) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
divide(divide(divide(b,divide(divide(b,b),b)),b),divide(divide(divide(b,divide(divide(b,b),b)),b),b)) = b,
inference(unit_resolution,[status(thm)],[35,32]) ).
tff(37,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,B),divide(divide(A,C),B)) = C )
| ( divide(divide(b,divide(divide(b,b),b)),divide(divide(b,b),divide(divide(b,b),b))) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
divide(divide(b,divide(divide(b,b),b)),divide(divide(b,b),divide(divide(b,b),b))) = b,
inference(unit_resolution,[status(thm)],[37,32]) ).
tff(39,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,B),divide(divide(A,C),B)) = C )
| ( divide(divide(b,b),divide(divide(b,b),b)) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
divide(divide(b,b),divide(divide(b,b),b)) = b,
inference(unit_resolution,[status(thm)],[39,32]) ).
tff(41,plain,
b = divide(divide(b,b),divide(divide(b,b),b)),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
divide(divide(b,divide(divide(b,b),b)),b) = divide(divide(b,divide(divide(b,b),b)),divide(divide(b,b),divide(divide(b,b),b))),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
divide(divide(b,divide(divide(b,b),b)),b) = b,
inference(transitivity,[status(thm)],[42,38]) ).
tff(44,plain,
divide(divide(divide(b,divide(divide(b,b),b)),b),b) = divide(b,b),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
divide(b,b) = divide(divide(divide(b,divide(divide(b,b),b)),b),b),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
divide(divide(b,divide(divide(b,b),b)),divide(divide(b,b),divide(divide(b,b),b))) = divide(divide(b,divide(divide(b,b),b)),b),
inference(symmetry,[status(thm)],[42]) ).
tff(47,plain,
b = divide(divide(b,divide(divide(b,b),b)),divide(divide(b,b),divide(divide(b,b),b))),
inference(symmetry,[status(thm)],[38]) ).
tff(48,plain,
b = divide(divide(b,divide(divide(b,b),b)),b),
inference(transitivity,[status(thm)],[47,46]) ).
tff(49,plain,
divide(b,divide(b,b)) = divide(divide(divide(b,divide(divide(b,b),b)),b),divide(divide(divide(b,divide(divide(b,b),b)),b),b)),
inference(monotonicity,[status(thm)],[48,45]) ).
tff(50,plain,
divide(b,divide(b,b)) = b,
inference(transitivity,[status(thm)],[49,36]) ).
tff(51,plain,
divide(divide(b,divide(b,b)),divide(divide(b,b),b)) = divide(b,divide(divide(b,b),b)),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
divide(b,divide(divide(b,b),b)) = divide(divide(b,divide(b,b)),divide(divide(b,b),b)),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,B),divide(divide(A,C),B)) = C )
| ( divide(divide(b,divide(divide(b,b),b)),divide(divide(b,divide(b,divide(divide(b,b),b))),divide(divide(b,b),b))) = divide(b,divide(divide(b,b),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
divide(divide(b,divide(divide(b,b),b)),divide(divide(b,divide(b,divide(divide(b,b),b))),divide(divide(b,b),b))) = divide(b,divide(divide(b,b),b)),
inference(unit_resolution,[status(thm)],[53,32]) ).
tff(55,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(b,b)) = divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
inverse(divide(b,b)) = divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)),
inference(unit_resolution,[status(thm)],[55,7]) ).
tff(57,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(b,b)) = divide(divide(b,b),divide(b,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
inverse(divide(b,b)) = divide(divide(b,b),divide(b,b)),
inference(unit_resolution,[status(thm)],[57,7]) ).
tff(59,plain,
divide(divide(b,b),divide(b,b)) = inverse(divide(b,b)),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
divide(divide(divide(b,b),divide(divide(b,b),b)),b) = divide(b,b),
inference(monotonicity,[status(thm)],[40]) ).
tff(61,plain,
divide(b,b) = divide(divide(divide(b,b),divide(divide(b,b),b)),b),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,B),divide(divide(A,C),B)) = C )
| ( divide(divide(divide(b,b),b),divide(divide(divide(b,b),divide(divide(b,b),b)),b)) = divide(divide(b,b),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
divide(divide(divide(b,b),b),divide(divide(divide(b,b),divide(divide(b,b),b)),b)) = divide(divide(b,b),b),
inference(unit_resolution,[status(thm)],[62,32]) ).
tff(64,plain,
divide(divide(divide(b,b),b),divide(b,b)) = divide(divide(divide(b,b),b),divide(divide(divide(b,b),divide(divide(b,b),b)),b)),
inference(monotonicity,[status(thm)],[61]) ).
tff(65,plain,
divide(divide(divide(b,b),b),divide(b,b)) = divide(divide(b,b),b),
inference(transitivity,[status(thm)],[64,63]) ).
tff(66,plain,
divide(divide(divide(divide(b,b),b),divide(b,b)),divide(b,b)) = divide(divide(divide(b,b),b),divide(divide(divide(b,b),divide(divide(b,b),b)),b)),
inference(monotonicity,[status(thm)],[65,61]) ).
tff(67,plain,
divide(divide(divide(b,b),b),divide(divide(divide(b,b),divide(divide(b,b),b)),b)) = divide(divide(divide(divide(b,b),b),divide(b,b)),divide(b,b)),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
divide(divide(b,b),b) = divide(divide(divide(b,b),b),divide(divide(divide(b,b),divide(divide(b,b),b)),b)),
inference(symmetry,[status(thm)],[63]) ).
tff(69,plain,
divide(divide(b,b),b) = divide(divide(divide(divide(b,b),b),divide(b,b)),divide(b,b)),
inference(transitivity,[status(thm)],[68,67]) ).
tff(70,plain,
divide(divide(divide(divide(b,b),b),divide(b,b)),divide(divide(b,b),b)) = divide(divide(divide(divide(b,b),b),divide(b,b)),divide(divide(divide(divide(b,b),b),divide(b,b)),divide(b,b))),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
divide(divide(divide(divide(b,b),b),divide(b,b)),divide(divide(divide(divide(b,b),b),divide(b,b)),divide(b,b))) = divide(divide(divide(divide(b,b),b),divide(b,b)),divide(divide(b,b),b)),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,B),divide(divide(A,C),B)) = C )
| ( divide(divide(divide(divide(b,b),b),divide(b,b)),divide(divide(divide(divide(b,b),b),divide(b,b)),divide(b,b))) = divide(b,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
divide(divide(divide(divide(b,b),b),divide(b,b)),divide(divide(divide(divide(b,b),b),divide(b,b)),divide(b,b))) = divide(b,b),
inference(unit_resolution,[status(thm)],[72,32]) ).
tff(74,plain,
divide(b,b) = divide(divide(divide(divide(b,b),b),divide(b,b)),divide(divide(divide(divide(b,b),b),divide(b,b)),divide(b,b))),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
divide(b,b) = divide(divide(divide(divide(b,b),b),divide(b,b)),divide(divide(b,b),b)),
inference(transitivity,[status(thm)],[74,71]) ).
tff(76,plain,
divide(divide(divide(b,b),b),divide(divide(divide(b,b),divide(divide(b,b),b)),b)) = divide(divide(divide(b,b),b),divide(b,b)),
inference(symmetry,[status(thm)],[64]) ).
tff(77,plain,
divide(divide(b,b),b) = divide(divide(divide(b,b),b),divide(b,b)),
inference(transitivity,[status(thm)],[68,76]) ).
tff(78,plain,
divide(divide(divide(b,b),b),divide(divide(b,b),b)) = divide(divide(divide(divide(b,b),b),divide(b,b)),divide(divide(divide(divide(b,b),b),divide(b,b)),divide(b,b))),
inference(monotonicity,[status(thm)],[77,69]) ).
tff(79,plain,
divide(divide(divide(divide(b,b),b),divide(b,b)),divide(divide(divide(divide(b,b),b),divide(b,b)),divide(b,b))) = divide(divide(divide(b,b),b),divide(divide(b,b),b)),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
divide(b,b) = divide(divide(divide(b,b),b),divide(divide(b,b),b)),
inference(transitivity,[status(thm)],[74,79]) ).
tff(81,plain,
divide(divide(b,b),divide(b,b)) = divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(divide(b,b),b),divide(b,b)),divide(divide(b,b),b))),
inference(monotonicity,[status(thm)],[80,75]) ).
tff(82,plain,
divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(divide(b,b),b),divide(b,b)),divide(divide(b,b),b))) = divide(divide(b,b),divide(b,b)),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,B),divide(divide(A,C),B)) = C )
| ( divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(divide(b,b),b),divide(b,b)),divide(divide(b,b),b))) = divide(b,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(divide(b,b),b),divide(b,b)),divide(divide(b,b),b))) = divide(b,b),
inference(unit_resolution,[status(thm)],[83,32]) ).
tff(85,plain,
divide(b,b) = divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(divide(b,b),b),divide(b,b)),divide(divide(b,b),b))),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,B),divide(divide(A,C),B)) = C )
| ( divide(divide(divide(b,b),divide(divide(b,b),b)),divide(divide(divide(b,b),divide(divide(b,b),b)),divide(divide(b,b),b))) = divide(divide(b,b),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
divide(divide(divide(b,b),divide(divide(b,b),b)),divide(divide(divide(b,b),divide(divide(b,b),b)),divide(divide(b,b),b))) = divide(divide(b,b),b),
inference(unit_resolution,[status(thm)],[86,32]) ).
tff(88,plain,
divide(divide(divide(b,b),divide(divide(b,b),b)),divide(divide(b,b),b)) = divide(b,divide(divide(b,b),b)),
inference(monotonicity,[status(thm)],[40]) ).
tff(89,plain,
divide(b,divide(divide(b,b),b)) = divide(divide(divide(b,b),divide(divide(b,b),b)),divide(divide(b,b),b)),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
divide(b,divide(b,divide(divide(b,b),b))) = divide(divide(divide(b,b),divide(divide(b,b),b)),divide(divide(divide(b,b),divide(divide(b,b),b)),divide(divide(b,b),b))),
inference(monotonicity,[status(thm)],[41,89]) ).
tff(91,plain,
divide(b,divide(b,divide(divide(b,b),b))) = divide(divide(divide(b,b),b),divide(b,b)),
inference(transitivity,[status(thm)],[90,87,68,76]) ).
tff(92,plain,
divide(divide(b,divide(b,divide(divide(b,b),b))),divide(divide(b,b),b)) = divide(divide(divide(divide(b,b),b),divide(b,b)),divide(divide(divide(divide(b,b),b),divide(b,b)),divide(b,b))),
inference(monotonicity,[status(thm)],[91,69]) ).
tff(93,plain,
divide(divide(b,divide(b,divide(divide(b,b),b))),divide(divide(b,b),b)) = divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)),
inference(transitivity,[status(thm)],[92,73,85,82,59,56]) ).
tff(94,plain,
divide(divide(b,divide(divide(b,b),b)),divide(divide(b,divide(b,divide(divide(b,b),b))),divide(divide(b,b),b))) = divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))) = divide(divide(b,divide(divide(b,b),b)),divide(divide(b,divide(b,divide(divide(b,b),b))),divide(divide(b,b),b))),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))) = divide(divide(b,divide(b,b)),divide(divide(b,b),b)),
inference(transitivity,[status(thm)],[95,54,52]) ).
tff(97,plain,
divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))) = divide(b,divide(divide(b,b),b)),
inference(transitivity,[status(thm)],[95,54]) ).
tff(98,plain,
divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))) = divide(divide(b,divide(divide(b,b),b)),divide(divide(b,divide(b,b)),divide(divide(b,b),b))),
inference(monotonicity,[status(thm)],[97,96]) ).
tff(99,plain,
divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))) = divide(b,b),
inference(transitivity,[status(thm)],[98,34]) ).
tff(100,plain,
divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),b) = divide(divide(b,b),b),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
divide(divide(b,b),b) = divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),b),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
divide(a,divide(divide(b,b),b)) = divide(a,divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),b)),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
divide(a,divide(divide(b,b),b)) = divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),
inference(transitivity,[status(thm)],[102,25,22]) ).
tff(104,plain,
divide(divide(a,divide(divide(b,b),b)),divide(divide(a,a),divide(divide(b,b),b))) = divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b))),
inference(monotonicity,[status(thm)],[103,13]) ).
tff(105,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,B),divide(divide(A,C),B)) = C )
| ( divide(divide(a,divide(divide(b,b),b)),divide(divide(a,a),divide(divide(b,b),b))) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
divide(divide(a,divide(divide(b,b),b)),divide(divide(a,a),divide(divide(b,b),b))) = a,
inference(unit_resolution,[status(thm)],[105,32]) ).
tff(107,plain,
a = divide(divide(a,divide(divide(b,b),b)),divide(divide(a,a),divide(divide(b,b),b))),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
a = divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b))),
inference(transitivity,[status(thm)],[107,104]) ).
tff(109,plain,
multiply(b,a) = multiply(b,divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b)))),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
multiply(b,divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b)))) = multiply(b,a),
inference(symmetry,[status(thm)],[109]) ).
tff(111,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(b,divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b)))) = divide(b,divide(divide(divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(a,divide(divide(b,b),divide(divide(b,b),b))))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
multiply(b,divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b)))) = divide(b,divide(divide(divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(a,divide(divide(b,b),divide(divide(b,b),b))))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b))))),
inference(unit_resolution,[status(thm)],[111,20]) ).
tff(113,plain,
divide(b,divide(divide(divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(a,divide(divide(b,b),divide(divide(b,b),b))))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b))))) = multiply(b,divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b)))),
inference(symmetry,[status(thm)],[112]) ).
tff(114,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b)))) = divide(divide(divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b)))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
inverse(divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b)))) = divide(divide(divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b)))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b)))),
inference(unit_resolution,[status(thm)],[114,7]) ).
tff(116,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b)))) = divide(divide(divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(a,divide(divide(b,b),divide(divide(b,b),b))))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(117,plain,
inverse(divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b)))) = divide(divide(divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(a,divide(divide(b,b),divide(divide(b,b),b))))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b)))),
inference(unit_resolution,[status(thm)],[116,7]) ).
tff(118,plain,
divide(divide(divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(a,divide(divide(b,b),divide(divide(b,b),b))))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b)))) = inverse(divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b)))),
inference(symmetry,[status(thm)],[117]) ).
tff(119,plain,
divide(divide(divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(a,divide(divide(b,b),divide(divide(b,b),b))))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b)))) = divide(divide(divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b)))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b)))),
inference(transitivity,[status(thm)],[118,115]) ).
tff(120,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(b) = divide(divide(a,a),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(121,plain,
inverse(b) = divide(divide(a,a),b),
inference(unit_resolution,[status(thm)],[120,7]) ).
tff(122,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(b) = divide(divide(b,b),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(123,plain,
inverse(b) = divide(divide(b,b),b),
inference(unit_resolution,[status(thm)],[122,7]) ).
tff(124,plain,
divide(divide(b,b),b) = inverse(b),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
divide(divide(b,b),b) = divide(divide(a,a),b),
inference(transitivity,[status(thm)],[124,121]) ).
tff(126,plain,
divide(divide(a,b),divide(divide(b,b),b)) = divide(divide(a,b),divide(divide(a,a),b)),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,plain,
divide(divide(a,b),divide(divide(a,a),b)) = divide(divide(a,b),divide(divide(b,b),b)),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,B),divide(divide(A,C),B)) = C )
| ( divide(divide(a,b),divide(divide(a,a),b)) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(129,plain,
divide(divide(a,b),divide(divide(a,a),b)) = a,
inference(unit_resolution,[status(thm)],[128,32]) ).
tff(130,plain,
a = divide(divide(a,b),divide(divide(a,a),b)),
inference(symmetry,[status(thm)],[129]) ).
tff(131,plain,
divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(a,a),divide(divide(b,b),b))),
inference(symmetry,[status(thm)],[104]) ).
tff(132,plain,
divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b))) = divide(divide(a,b),divide(divide(b,b),b)),
inference(transitivity,[status(thm)],[131,106,130,127]) ).
tff(133,plain,
divide(a,divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),b)) = divide(a,divide(divide(b,b),b)),
inference(symmetry,[status(thm)],[102]) ).
tff(134,plain,
divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)) = multiply(a,b),
inference(symmetry,[status(thm)],[22]) ).
tff(135,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,B),divide(divide(A,C),B)) = C )
| ( divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b))),divide(divide(b,b),b))) = divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(136,plain,
divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b))),divide(divide(b,b),b))) = divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),
inference(unit_resolution,[status(thm)],[135,32]) ).
tff(137,plain,
divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))) = divide(divide(divide(b,b),b),divide(divide(b,b),b)),
inference(transitivity,[status(thm)],[98,34,74,79]) ).
tff(138,plain,
divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b)) = divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(divide(b,b),b),divide(b,b)),divide(divide(b,b),b))),
inference(monotonicity,[status(thm)],[137,75]) ).
tff(139,plain,
divide(divide(divide(divide(b,b),b),divide(divide(b,b),b)),divide(divide(divide(divide(b,b),b),divide(b,b)),divide(divide(b,b),b))) = divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b)),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,B),divide(divide(A,C),B)) = C )
| ( divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(divide(b,b),b)),divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(divide(b,b),b)),divide(divide(b,b),b))) = divide(divide(b,b),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(141,plain,
divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(divide(b,b),b)),divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(divide(b,b),b)),divide(divide(b,b),b))) = divide(divide(b,b),b),
inference(unit_resolution,[status(thm)],[140,32]) ).
tff(142,plain,
divide(a,b) = divide(a,divide(divide(b,b),divide(divide(b,b),b))),
inference(monotonicity,[status(thm)],[41]) ).
tff(143,plain,
divide(a,divide(divide(b,b),divide(divide(b,b),b))) = divide(a,b),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(divide(b,b),b)) = divide(divide(a,b),divide(divide(a,a),b)),
inference(monotonicity,[status(thm)],[143,125]) ).
tff(145,plain,
divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(divide(b,b),b)) = a,
inference(transitivity,[status(thm)],[144,129]) ).
tff(146,plain,
divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(divide(b,b),b)),divide(divide(b,b),b)) = divide(a,divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),b)),
inference(monotonicity,[status(thm)],[145,101]) ).
tff(147,plain,
divide(a,divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),b)) = divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(divide(b,b),b)),divide(divide(b,b),b)),
inference(symmetry,[status(thm)],[146]) ).
tff(148,plain,
divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)) = divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(divide(b,b),b)),divide(divide(b,b),b)),
inference(transitivity,[status(thm)],[134,24,147]) ).
tff(149,plain,
divide(divide(a,b),divide(divide(a,a),b)) = divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(divide(b,b),b)),
inference(symmetry,[status(thm)],[144]) ).
tff(150,plain,
a = divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(divide(b,b),b)),
inference(transitivity,[status(thm)],[130,149]) ).
tff(151,plain,
divide(a,divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b))) = divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(divide(b,b),b)),divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(divide(b,b),b)),divide(divide(b,b),b))),
inference(monotonicity,[status(thm)],[150,148]) ).
tff(152,plain,
divide(a,divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b))) = divide(divide(divide(b,b),b),divide(b,b)),
inference(transitivity,[status(thm)],[151,141,68,76]) ).
tff(153,plain,
divide(divide(a,divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b))),divide(divide(b,b),b)) = divide(divide(divide(divide(b,b),b),divide(b,b)),divide(divide(divide(divide(b,b),b),divide(b,b)),divide(b,b))),
inference(monotonicity,[status(thm)],[152,69]) ).
tff(154,plain,
divide(divide(a,divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b))),divide(divide(b,b),b)) = divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b)),
inference(transitivity,[status(thm)],[153,73,85,139]) ).
tff(155,plain,
divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b))),divide(divide(b,b),b))) = divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b))),
inference(monotonicity,[status(thm)],[103,154]) ).
tff(156,plain,
divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b))),divide(divide(b,b),b))),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b))) = divide(a,divide(divide(b,b),b)),
inference(transitivity,[status(thm)],[156,136,134,24,133]) ).
tff(158,plain,
divide(divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b)))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(a,b),divide(divide(b,b),b))),
inference(monotonicity,[status(thm)],[157,132]) ).
tff(159,plain,
divide(divide(a,divide(divide(b,b),b)),divide(divide(a,b),divide(divide(b,b),b))) = divide(divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b)))),
inference(symmetry,[status(thm)],[158]) ).
tff(160,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,B),divide(divide(A,C),B)) = C )
| ( divide(divide(a,divide(divide(b,b),b)),divide(divide(a,b),divide(divide(b,b),b))) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(161,plain,
divide(divide(a,divide(divide(b,b),b)),divide(divide(a,b),divide(divide(b,b),b))) = b,
inference(unit_resolution,[status(thm)],[160,32]) ).
tff(162,plain,
b = divide(divide(a,divide(divide(b,b),b)),divide(divide(a,b),divide(divide(b,b),b))),
inference(symmetry,[status(thm)],[161]) ).
tff(163,plain,
b = divide(divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b)))),
inference(transitivity,[status(thm)],[162,159]) ).
tff(164,plain,
divide(b,divide(divide(divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(a,divide(divide(b,b),divide(divide(b,b),b))))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b))))) = divide(divide(divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b)))),divide(divide(divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b)))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b))))),
inference(monotonicity,[status(thm)],[163,119]) ).
tff(165,plain,
divide(divide(divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b)))),divide(divide(divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b)))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b))))) = divide(b,divide(divide(divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(a,divide(divide(b,b),divide(divide(b,b),b))))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b))))),
inference(symmetry,[status(thm)],[164]) ).
tff(166,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,B),divide(divide(A,C),B)) = C )
| ( divide(divide(divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b)))),divide(divide(divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b)))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b))))) = divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(167,plain,
divide(divide(divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b)))),divide(divide(divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b)))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b))))) = divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b))),
inference(unit_resolution,[status(thm)],[166,32]) ).
tff(168,plain,
divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b))) = divide(divide(divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b)))),divide(divide(divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b))),divide(divide(b,divide(divide(b,b),b)),divide(divide(divide(b,divide(divide(b,b),b)),divide(b,divide(divide(b,b),b))),divide(b,b)))),divide(b,b)))),divide(divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)),divide(divide(b,b),divide(divide(b,b),b))))),
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b)) = divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(a,divide(divide(divide(a,divide(divide(b,b),divide(divide(b,b),b))),divide(a,divide(divide(b,b),divide(divide(b,b),b)))),b))),divide(divide(b,b),b))),
inference(symmetry,[status(thm)],[136]) ).
tff(170,plain,
multiply(a,b) = multiply(b,a),
inference(transitivity,[status(thm)],[22,169,155,168,165,113,110]) ).
tff(171,plain,
( ( multiply(a,b) != multiply(b,a) )
<=> ( multiply(a,b) != multiply(b,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(172,axiom,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_4) ).
tff(173,plain,
multiply(a,b) != multiply(b,a),
inference(modus_ponens,[status(thm)],[172,171]) ).
tff(174,plain,
$false,
inference(unit_resolution,[status(thm)],[173,170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP540-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 16:16:47 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.39/0.61 % SZS status Unsatisfiable
% 0.39/0.61 % SZS output start Proof
% See solution above
% 0.47/0.66 % E exiting
%------------------------------------------------------------------------------