TSTP Solution File: GRP524-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP524-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 22:27:58 EDT 2022
% Result : Unsatisfiable 0.54s 0.60s
% Output : Proof 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 50
% Syntax : Number of formulae : 244 ( 198 unt; 5 typ; 0 def)
% Number of atoms : 286 ( 282 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 82 ( 38 ~; 34 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 164 ( 156 !; 0 ?; 164 :)
% 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(
( ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
<=> ( divide(A,divide(B,divide(C,divide(A,B)))) = C ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
<=> ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
<=> ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
tff(5,plain,
! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))))) = divide(b,divide(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))))) = divide(b,divide(b,a)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(b,divide(b,a)),divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(b,divide(b,a)))))) = divide(a,divide(divide(b,b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(11,plain,
divide(divide(b,divide(b,a)),divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(b,divide(b,a)))))) = divide(a,divide(divide(b,b),b)),
inference(unit_resolution,[status(thm)],[10,7]) ).
tff(12,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))))) = divide(a,divide(divide(b,b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))))) = divide(a,divide(divide(b,b),b)),
inference(unit_resolution,[status(thm)],[12,7]) ).
tff(14,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a))))))) = divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(15,plain,
divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a))))))) = divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),
inference(unit_resolution,[status(thm)],[14,7]) ).
tff(16,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(b,b),divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),b)))) = divide(a,divide(b,divide(b,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(17,plain,
divide(divide(b,b),divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),b)))) = divide(a,divide(b,divide(b,a))),
inference(unit_resolution,[status(thm)],[16,7]) ).
tff(18,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(19,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)],[18]) ).
tff(20,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(21,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(22,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(a,divide(b,divide(b,a))),b) = divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(26,plain,
multiply(divide(a,divide(b,divide(b,a))),b) = divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(a,divide(b,divide(b,a))),b) = divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
multiply(divide(a,divide(b,divide(b,a))),b) = divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),b)),
inference(unit_resolution,[status(thm)],[27,24]) ).
tff(29,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),b)) = multiply(divide(a,divide(b,divide(b,a))),b),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),b)) = divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),
inference(transitivity,[status(thm)],[29,26]) ).
tff(31,plain,
divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),b))) = divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),b))),
inference(symmetry,[status(thm)],[31]) ).
tff(33,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(34,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)],[33]) ).
tff(35,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(36,axiom,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
tff(37,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(b) = divide(divide(divide(b,b),divide(b,b)),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
inverse(b) = divide(divide(divide(b,b),divide(b,b)),b),
inference(unit_resolution,[status(thm)],[40,39]) ).
tff(42,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(43,plain,
inverse(b) = divide(divide(b,b),b),
inference(unit_resolution,[status(thm)],[42,39]) ).
tff(44,plain,
divide(divide(b,b),b) = inverse(b),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(b,divide(a,divide(b,divide(b,a)))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
divide(b,divide(a,divide(b,divide(b,a)))) = b,
inference(unit_resolution,[status(thm)],[45,7]) ).
tff(47,plain,
divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a))))) = divide(divide(b,b),b),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a))))) = divide(divide(divide(b,b),divide(b,b)),b),
inference(transitivity,[status(thm)],[47,44,41]) ).
tff(49,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a)))))) = divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a))))))) = divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a))))))) = divide(b,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a))))))) = divide(b,b),
inference(unit_resolution,[status(thm)],[51,7]) ).
tff(53,plain,
divide(b,b) = divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a))))))),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
divide(b,b) = divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),b))),
inference(transitivity,[status(thm)],[53,50,32]) ).
tff(55,plain,
divide(divide(b,b),divide(b,b)) = divide(divide(b,b),divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),b)))),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),divide(b,divide(a,divide(b,divide(b,a))))))) = divide(divide(b,b),divide(b,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),divide(b,divide(a,divide(b,divide(b,a))))))) = divide(divide(b,b),divide(b,b)),
inference(unit_resolution,[status(thm)],[56,7]) ).
tff(58,plain,
divide(divide(b,b),b) = divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a))))),
inference(symmetry,[status(thm)],[47]) ).
tff(59,plain,
divide(divide(divide(b,b),divide(b,b)),b) = inverse(b),
inference(symmetry,[status(thm)],[41]) ).
tff(60,plain,
divide(divide(divide(b,b),divide(b,b)),divide(b,divide(a,divide(b,divide(b,a))))) = divide(divide(divide(b,b),divide(b,b)),b),
inference(monotonicity,[status(thm)],[46]) ).
tff(61,plain,
divide(divide(divide(b,b),divide(b,b)),divide(b,divide(a,divide(b,divide(b,a))))) = divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a))))),
inference(transitivity,[status(thm)],[60,59,43,58]) ).
tff(62,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),divide(b,divide(a,divide(b,divide(b,a)))))) = divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a)))))),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a)))))) = divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),divide(b,divide(a,divide(b,divide(b,a)))))),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)) = divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a)))))),
inference(symmetry,[status(thm)],[49]) ).
tff(65,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)) = divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),divide(b,divide(a,divide(b,divide(b,a)))))),
inference(transitivity,[status(thm)],[64,63]) ).
tff(66,plain,
divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),divide(b,divide(a,divide(b,divide(b,a))))))),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(b) = divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
inverse(b) = divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),b),
inference(unit_resolution,[status(thm)],[67,39]) ).
tff(69,plain,
divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),b) = inverse(b),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(b,divide(a,divide(b,divide(b,a))))) = divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),b),
inference(monotonicity,[status(thm)],[46]) ).
tff(71,plain,
divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(b,divide(a,divide(b,divide(b,a))))) = divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a))))),
inference(transitivity,[status(thm)],[70,69,43,58]) ).
tff(72,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(b,divide(a,divide(b,divide(b,a)))))) = divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a)))))),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(b,divide(a,divide(b,divide(b,a)))))) = divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),
inference(transitivity,[status(thm)],[72,49]) ).
tff(74,plain,
divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(b,divide(a,divide(b,divide(b,a))))))) = divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(b,divide(a,divide(b,divide(b,a))))))) = divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,plain,
divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(b,divide(a,divide(b,divide(b,a))))))) = divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),
inference(unit_resolution,[status(thm)],[75,7]) ).
tff(77,plain,
divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))) = divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(b,divide(a,divide(b,divide(b,a))))))),
inference(symmetry,[status(thm)],[76]) ).
tff(78,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(79,plain,
inverse(divide(b,b)) = divide(divide(b,b),divide(b,b)),
inference(unit_resolution,[status(thm)],[78,39]) ).
tff(80,plain,
divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a))))))),
inference(symmetry,[status(thm)],[50]) ).
tff(81,plain,
divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),divide(b,divide(a,divide(b,divide(b,a))))))) = divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))),
inference(symmetry,[status(thm)],[66]) ).
tff(82,plain,
divide(divide(b,b),divide(b,b)) = divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),divide(b,divide(a,divide(b,divide(b,a))))))),
inference(symmetry,[status(thm)],[57]) ).
tff(83,plain,
divide(divide(b,b),divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),b)))) = divide(divide(b,b),divide(b,b)),
inference(symmetry,[status(thm)],[55]) ).
tff(84,plain,
divide(a,divide(b,divide(b,a))) = divide(divide(b,b),divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),b)))),
inference(symmetry,[status(thm)],[17]) ).
tff(85,plain,
divide(a,divide(b,divide(b,a))) = divide(b,b),
inference(transitivity,[status(thm)],[84,83,82,81,80,52]) ).
tff(86,plain,
inverse(divide(a,divide(b,divide(b,a)))) = inverse(divide(b,b)),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(a,divide(b,divide(b,a)))) = divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(88,plain,
inverse(divide(a,divide(b,divide(b,a)))) = divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a)))),
inference(unit_resolution,[status(thm)],[87,39]) ).
tff(89,plain,
divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a)))) = inverse(divide(a,divide(b,divide(b,a)))),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a)))) = divide(a,divide(b,divide(b,a))),
inference(transitivity,[status(thm)],[89,86,79,55,17]) ).
tff(91,plain,
divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a))))) = divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a)))),
inference(monotonicity,[status(thm)],[90]) ).
tff(92,plain,
divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a))))) = divide(a,divide(b,divide(b,a))),
inference(transitivity,[status(thm)],[91,89,86,79,55,17]) ).
tff(93,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a)))))) = divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a)))))) = divide(a,divide(b,divide(b,a))),
inference(transitivity,[status(thm)],[93,77,74,66,57,55,17]) ).
tff(95,plain,
divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a))))))) = divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a)))),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a)))) = divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a))))))),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
inverse(divide(b,b)) = inverse(divide(a,divide(b,divide(b,a)))),
inference(symmetry,[status(thm)],[86]) ).
tff(98,plain,
divide(divide(b,b),divide(b,b)) = inverse(divide(b,b)),
inference(symmetry,[status(thm)],[79]) ).
tff(99,plain,
divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))) = divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a))))))),
inference(symmetry,[status(thm)],[15]) ).
tff(100,plain,
divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))) = divide(a,divide(b,divide(b,a))),
inference(transitivity,[status(thm)],[99,95,89,86,79,55,17]) ).
tff(101,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))) = divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))) = divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),
inference(transitivity,[status(thm)],[101,77,74,66,57,98,97,88,96,15]) ).
tff(103,plain,
divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))))),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))))),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))))),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))))) = divide(a,divide(b,divide(b,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))))) = divide(a,divide(b,divide(b,a))),
inference(unit_resolution,[status(thm)],[107,7]) ).
tff(109,plain,
divide(a,divide(b,divide(b,a))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))))),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))))),
inference(transitivity,[status(thm)],[99,95,89,86,79,55,17,109,106]) ).
tff(111,plain,
divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))))),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(b,divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a))))))) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(113,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(b,divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a))))))) = b,
inference(unit_resolution,[status(thm)],[112,7]) ).
tff(114,plain,
divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))) = divide(a,divide(b,divide(b,a))),
inference(transitivity,[status(thm)],[77,74,66,57,55,17]) ).
tff(115,plain,
divide(b,divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a))))) = divide(b,divide(a,divide(b,divide(b,a)))),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
divide(b,divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a))))) = b,
inference(transitivity,[status(thm)],[115,46]) ).
tff(117,plain,
divide(a,divide(b,divide(b,a))) = divide(divide(b,b),divide(b,b)),
inference(transitivity,[status(thm)],[84,83]) ).
tff(118,plain,
divide(divide(a,divide(b,divide(b,a))),divide(b,divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))))) = divide(divide(divide(b,b),divide(b,b)),b),
inference(monotonicity,[status(thm)],[117,116]) ).
tff(119,plain,
divide(divide(a,divide(b,divide(b,a))),divide(b,divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))))) = divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a))))),
inference(transitivity,[status(thm)],[118,59,43,58]) ).
tff(120,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(b,divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a))))))) = divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a)))))),
inference(monotonicity,[status(thm)],[119]) ).
tff(121,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a)))))) = divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(b,divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a))))))),
inference(symmetry,[status(thm)],[120]) ).
tff(122,plain,
divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(divide(b,b),b)) = divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a)))))),
inference(monotonicity,[status(thm)],[114,58]) ).
tff(123,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(divide(b,b),b)) = divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(divide(b,b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(124,plain,
inverse(divide(divide(b,b),b)) = divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(divide(b,b),b)),
inference(unit_resolution,[status(thm)],[123,39]) ).
tff(125,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(divide(b,b),b)) = divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(divide(b,b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(126,plain,
inverse(divide(divide(b,b),b)) = divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(divide(b,b),b)),
inference(unit_resolution,[status(thm)],[125,39]) ).
tff(127,plain,
divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(divide(b,b),b)) = inverse(divide(divide(b,b),b)),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)) = b,
inference(transitivity,[status(thm)],[64,121,113]) ).
tff(129,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = divide(divide(divide(b,b),divide(b,b)),b),
inference(monotonicity,[status(thm)],[117,128]) ).
tff(130,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = divide(divide(b,b),b),
inference(transitivity,[status(thm)],[129,59,43]) ).
tff(131,plain,
divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))) = divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(divide(b,b),b)),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))) = b,
inference(transitivity,[status(thm)],[131,127,124,122,121,113]) ).
tff(133,plain,
divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))) = divide(b,b),
inference(monotonicity,[status(thm)],[128,132]) ).
tff(134,plain,
divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))) = divide(a,divide(b,divide(b,a))),
inference(transitivity,[status(thm)],[133,53,50,66,57,55,17]) ).
tff(135,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))) = divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),
inference(monotonicity,[status(thm)],[134]) ).
tff(136,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))) = divide(divide(b,divide(b,a)),divide(b,divide(b,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(137,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))) = divide(divide(b,divide(b,a)),divide(b,divide(b,a))),
inference(unit_resolution,[status(thm)],[136,7]) ).
tff(138,plain,
divide(divide(b,divide(b,a)),divide(b,divide(b,a))) = divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
divide(divide(b,divide(b,a)),divide(b,divide(b,a))) = divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),
inference(transitivity,[status(thm)],[138,135,77,74,66,57,98,97,88,96,15]) ).
tff(140,plain,
divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(b,divide(b,a)))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(b,divide(b,a)))) = divide(a,divide(divide(b,b),b)),
inference(transitivity,[status(thm)],[140,111,13]) ).
tff(142,plain,
divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(b,divide(b,a))))) = divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b))),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,plain,
divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b))) = divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(b,divide(b,a))))),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
divide(divide(b,divide(b,a)),divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))) = divide(divide(b,divide(b,a)),divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(b,divide(b,a)))))),
inference(monotonicity,[status(thm)],[143]) ).
tff(145,plain,
divide(divide(b,divide(b,a)),divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))) = divide(a,divide(divide(b,b),b)),
inference(transitivity,[status(thm)],[144,11]) ).
tff(146,plain,
divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b))))) = divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b))))),
inference(symmetry,[status(thm)],[146]) ).
tff(148,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(a,divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(b,divide(b,a)))))) = divide(a,divide(divide(b,b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(149,plain,
divide(a,divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(b,divide(b,a)))))) = divide(a,divide(divide(b,b),b)),
inference(unit_resolution,[status(thm)],[148,7]) ).
tff(150,plain,
divide(a,divide(b,divide(b,a))) = divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),
inference(transitivity,[status(thm)],[84,83,98,97,88,96,15]) ).
tff(151,plain,
divide(divide(a,divide(divide(b,b),b)),divide(a,divide(b,divide(b,a)))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
divide(divide(a,divide(divide(b,b),b)),divide(a,divide(b,divide(b,a)))) = divide(a,divide(divide(b,b),b)),
inference(transitivity,[status(thm)],[151,111,13]) ).
tff(153,plain,
divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(b,divide(b,a))))) = divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b))),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b))) = divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(b,divide(b,a))))),
inference(symmetry,[status(thm)],[153]) ).
tff(155,plain,
divide(a,divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))) = divide(a,divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(b,divide(b,a)))))),
inference(monotonicity,[status(thm)],[154]) ).
tff(156,plain,
divide(a,divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))) = divide(a,divide(divide(b,b),b)),
inference(transitivity,[status(thm)],[155,149]) ).
tff(157,plain,
divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b))))) = divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),
inference(monotonicity,[status(thm)],[156]) ).
tff(158,plain,
divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b))))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b))))),
inference(transitivity,[status(thm)],[157,147]) ).
tff(159,plain,
divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))))) = divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))))),
inference(monotonicity,[status(thm)],[158]) ).
tff(160,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(161,plain,
divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))))) = a,
inference(unit_resolution,[status(thm)],[160,7]) ).
tff(162,plain,
a = divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))))),
inference(symmetry,[status(thm)],[161]) ).
tff(163,plain,
a = divide(b,divide(b,a)),
inference(transitivity,[status(thm)],[162,159,9]) ).
tff(164,plain,
multiply(b,a) = multiply(b,divide(b,divide(b,a))),
inference(monotonicity,[status(thm)],[163]) ).
tff(165,plain,
multiply(b,divide(b,divide(b,a))) = multiply(b,a),
inference(symmetry,[status(thm)],[164]) ).
tff(166,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(b,divide(b,divide(b,a))) = divide(b,divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(b,divide(b,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(167,plain,
multiply(b,divide(b,divide(b,a))) = divide(b,divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(b,divide(b,a)))),
inference(unit_resolution,[status(thm)],[166,24]) ).
tff(168,plain,
divide(b,divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(b,divide(b,a)))) = multiply(b,divide(b,divide(b,a))),
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))) = divide(divide(b,b),divide(b,b)),
inference(transitivity,[status(thm)],[77,74,66,57]) ).
tff(170,plain,
divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = divide(divide(divide(b,b),divide(b,b)),b),
inference(monotonicity,[status(thm)],[169,128]) ).
tff(171,plain,
divide(divide(divide(b,b),divide(b,b)),b) = divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))),
inference(symmetry,[status(thm)],[170]) ).
tff(172,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))),
inference(transitivity,[status(thm)],[129,171]) ).
tff(173,plain,
divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))) = divide(divide(b,divide(b,a)),divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))),
inference(monotonicity,[status(thm)],[172]) ).
tff(174,plain,
divide(divide(b,divide(b,a)),divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))) = divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))),
inference(symmetry,[status(thm)],[173]) ).
tff(175,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = divide(divide(b,divide(b,a)),divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(176,plain,
multiply(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = divide(divide(b,divide(b,a)),divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))),
inference(unit_resolution,[status(thm)],[175,24]) ).
tff(177,plain,
divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))))) = divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))))),
inference(symmetry,[status(thm)],[159]) ).
tff(178,plain,
divide(b,divide(b,a)) = divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))))),
inference(symmetry,[status(thm)],[9]) ).
tff(179,plain,
divide(b,divide(b,a)) = a,
inference(transitivity,[status(thm)],[178,177,161]) ).
tff(180,plain,
multiply(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = multiply(a,b),
inference(monotonicity,[status(thm)],[179,128]) ).
tff(181,plain,
multiply(a,b) = multiply(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))),
inference(symmetry,[status(thm)],[180]) ).
tff(182,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(a,b) = divide(a,divide(divide(b,b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(183,plain,
multiply(a,b) = divide(a,divide(divide(b,b),b)),
inference(unit_resolution,[status(thm)],[182,24]) ).
tff(184,plain,
divide(a,divide(divide(b,b),b)) = multiply(a,b),
inference(symmetry,[status(thm)],[183]) ).
tff(185,plain,
divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = divide(b,b),
inference(monotonicity,[status(thm)],[128,128]) ).
tff(186,plain,
divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),
inference(transitivity,[status(thm)],[185,53,50,66,57,98,97,88,96,15]) ).
tff(187,plain,
divide(divide(a,divide(divide(b,b),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))),
inference(monotonicity,[status(thm)],[186]) ).
tff(188,plain,
divide(divide(a,divide(divide(b,b),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))) = divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))),
inference(transitivity,[status(thm)],[187,111,13,184,181,176,174]) ).
tff(189,plain,
divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))) = divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),
inference(monotonicity,[status(thm)],[188]) ).
tff(190,plain,
divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))) = divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),
inference(symmetry,[status(thm)],[189]) ).
tff(191,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a))))))) = divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(192,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a))))))) = divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),
inference(unit_resolution,[status(thm)],[191,7]) ).
tff(193,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))))))) = divide(b,divide(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(194,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))))))) = divide(b,divide(b,a)),
inference(unit_resolution,[status(thm)],[193,7]) ).
tff(195,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,a),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(a,divide(b,divide(b,a))))))) = divide(a,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(196,plain,
divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,a),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(a,divide(b,divide(b,a))))))) = divide(a,a),
inference(unit_resolution,[status(thm)],[195,7]) ).
tff(197,plain,
inverse(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = inverse(b),
inference(monotonicity,[status(thm)],[128]) ).
tff(198,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = divide(divide(a,a),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(199,plain,
inverse(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = divide(divide(a,a),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))),
inference(unit_resolution,[status(thm)],[198,39]) ).
tff(200,plain,
divide(divide(a,a),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = inverse(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))),
inference(symmetry,[status(thm)],[199]) ).
tff(201,plain,
b = divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(b,divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a))))))),
inference(symmetry,[status(thm)],[113]) ).
tff(202,plain,
divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(a,divide(b,divide(b,a)))) = divide(b,divide(a,divide(b,divide(b,a)))),
inference(monotonicity,[status(thm)],[128]) ).
tff(203,plain,
divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(a,divide(b,divide(b,a)))) = divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),
inference(transitivity,[status(thm)],[202,46,201,120,49]) ).
tff(204,plain,
divide(divide(a,a),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(a,divide(b,divide(b,a))))) = divide(divide(a,a),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))),
inference(monotonicity,[status(thm)],[203]) ).
tff(205,plain,
divide(divide(a,a),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(a,divide(b,divide(b,a))))) = divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a))))),
inference(transitivity,[status(thm)],[204,200,197,43,58]) ).
tff(206,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(a,a),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(a,divide(b,divide(b,a)))))) = divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a)))))),
inference(monotonicity,[status(thm)],[205]) ).
tff(207,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(a,a),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(a,divide(b,divide(b,a)))))) = b,
inference(transitivity,[status(thm)],[206,121,113]) ).
tff(208,plain,
divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,a),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(a,divide(b,divide(b,a))))))) = divide(b,b),
inference(monotonicity,[status(thm)],[128,207]) ).
tff(209,plain,
divide(b,b) = divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,a),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(a,divide(b,divide(b,a))))))),
inference(symmetry,[status(thm)],[208]) ).
tff(210,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))) = divide(b,divide(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(211,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))) = divide(b,divide(b,a)),
inference(unit_resolution,[status(thm)],[210,7]) ).
tff(212,plain,
divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))))) = divide(divide(b,divide(b,a)),divide(b,divide(b,a))),
inference(monotonicity,[status(thm)],[211]) ).
tff(213,plain,
divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))))) = divide(a,a),
inference(transitivity,[status(thm)],[212,138,135,77,74,80,52,209,196]) ).
tff(214,plain,
divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))))) = divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(a,a)),
inference(monotonicity,[status(thm)],[213]) ).
tff(215,plain,
divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(a,a)) = divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))))),
inference(symmetry,[status(thm)],[214]) ).
tff(216,plain,
divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))) = divide(a,a),
inference(transitivity,[status(thm)],[77,74,80,52,209,196]) ).
tff(217,plain,
divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a))))) = divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(a,a)),
inference(monotonicity,[status(thm)],[216]) ).
tff(218,plain,
divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a))))) = divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))))),
inference(transitivity,[status(thm)],[217,215]) ).
tff(219,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))))) = divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))))))),
inference(monotonicity,[status(thm)],[218]) ).
tff(220,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))))) = divide(b,divide(b,a)),
inference(transitivity,[status(thm)],[219,194]) ).
tff(221,plain,
divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a))))))) = divide(divide(divide(b,b),divide(b,b)),divide(b,divide(b,a))),
inference(monotonicity,[status(thm)],[117,220]) ).
tff(222,plain,
divide(divide(divide(b,b),divide(b,b)),divide(b,divide(b,a))) = divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a))))))),
inference(symmetry,[status(thm)],[221]) ).
tff(223,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(b,divide(b,a))) = divide(divide(divide(b,b),divide(b,b)),divide(b,divide(b,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(224,plain,
inverse(divide(b,divide(b,a))) = divide(divide(divide(b,b),divide(b,b)),divide(b,divide(b,a))),
inference(unit_resolution,[status(thm)],[223,39]) ).
tff(225,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(b,divide(b,a))) = divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(b,divide(b,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(226,plain,
inverse(divide(b,divide(b,a))) = divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(b,divide(b,a))),
inference(unit_resolution,[status(thm)],[225,39]) ).
tff(227,plain,
divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(b,divide(b,a))) = inverse(divide(b,divide(b,a))),
inference(symmetry,[status(thm)],[226]) ).
tff(228,plain,
divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(b,divide(b,a))) = divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),
inference(transitivity,[status(thm)],[227,224,222,192,190]) ).
tff(229,plain,
b = divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),
inference(transitivity,[status(thm)],[201,120,49]) ).
tff(230,plain,
divide(b,divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(b,divide(b,a)))) = divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))),
inference(monotonicity,[status(thm)],[229,228]) ).
tff(231,plain,
divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))) = divide(b,divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(b,divide(b,a)))),
inference(symmetry,[status(thm)],[230]) ).
tff(232,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))) = divide(a,divide(divide(b,b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(233,plain,
divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))) = divide(a,divide(divide(b,b),b)),
inference(unit_resolution,[status(thm)],[232,7]) ).
tff(234,plain,
divide(a,divide(divide(b,b),b)) = divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))),
inference(symmetry,[status(thm)],[233]) ).
tff(235,plain,
multiply(a,b) = multiply(b,a),
inference(transitivity,[status(thm)],[183,234,231,168,165]) ).
tff(236,plain,
( ( multiply(a,b) != multiply(b,a) )
<=> ( multiply(a,b) != multiply(b,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(237,axiom,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_4) ).
tff(238,plain,
multiply(a,b) != multiply(b,a),
inference(modus_ponens,[status(thm)],[237,236]) ).
tff(239,plain,
$false,
inference(unit_resolution,[status(thm)],[238,235]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP524-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % 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 : Wed Aug 31 17:41:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.54/0.60 % SZS status Unsatisfiable
% 0.54/0.60 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------