%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP585-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:08:08 AM UTC 2025
% Result : Unsatisfiable 30.73s 30.91s
% Output : Proof 30.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 32
% Syntax : Number of formulae : 159 ( 130 unt; 0 typ; 0 def)
% Number of atoms : 192 ( 189 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 59 ( 28 ~; 24 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 18 ( 4 avg)
% Number of FOOLs : 2 ( 2 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 : 115 ( 110 !; 0 ?; 115 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(b1_type,type,
b1: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(a1_type,type,
a1: $i ).
tff(double_divide_type,type,
double_divide: ( $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(( ( multiply(A,B) = inverse(double_divide(B,A)) )
<=> ( multiply(A,B) = inverse(double_divide(B,A)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,A: $i] : ( multiply(A,B) = inverse(double_divide(B,A)) )
<=> ! [B: $i,A: $i] : ( multiply(A,B) = inverse(double_divide(B,A)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i] : ( multiply(A,B) = inverse(double_divide(B,A)) )
<=> ! [B: $i,A: $i] : ( multiply(A,B) = inverse(double_divide(B,A)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i,A: $i] : ( multiply(A,B) = inverse(double_divide(B,A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
tff(5,plain,
! [B: $i,A: $i] : ( multiply(A,B) = inverse(double_divide(B,A)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( multiply(A,B) = inverse(double_divide(B,A)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( multiply(A,B) = inverse(double_divide(B,A)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = inverse(double_divide(B,A)) )
| ( multiply(inverse(b1),b1) = inverse(double_divide(b1,inverse(b1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
multiply(inverse(b1),b1) = inverse(double_divide(b1,inverse(b1))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
inverse(double_divide(b1,inverse(b1))) = multiply(inverse(b1),b1),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C )
<=> ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C )
<=> ! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C )
<=> ! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C )
| ( double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))) = double_divide(b1,inverse(b1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))) = double_divide(b1,inverse(b1)),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C )
| ( double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),inverse(a1))),inverse(a1)))) = a1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),inverse(a1))),inverse(a1)))) = a1,
inference(unit_resolution,[status(thm)],[20,17]) ).
tff(22,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C )
| ( double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1)))) = double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1)))) = double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1)))),
inference(unit_resolution,[status(thm)],[22,17]) ).
tff(24,plain,
double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1)))) = double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1)))),
inference(monotonicity,[status(thm)],[21]) ).
tff(25,plain,
double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1)))) = double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1)))),
inference(transitivity,[status(thm)],[24,23]) ).
tff(26,plain,
inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1))))) = inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),inverse(a1))),inverse(a1)))) = double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),inverse(a1))),inverse(a1)))),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),inverse(a1))),inverse(a1)))) = a1,
inference(transitivity,[status(thm)],[27,21]) ).
tff(29,plain,
inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),inverse(a1))),inverse(a1))))) = inverse(a1),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
inverse(a1) = inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),inverse(a1))),inverse(a1))))),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)) = double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),inverse(a1))),inverse(a1)))))),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),inverse(a1))),inverse(a1)))))) = double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C )
| ( double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),inverse(a1))),inverse(a1)))))) = double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),inverse(a1))),inverse(a1)))))) = double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1)),
inference(unit_resolution,[status(thm)],[33,17]) ).
tff(35,plain,
double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1)) = double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),inverse(a1))),inverse(a1)))))),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C )
| ( double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))))) = double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))))) = double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1)),
inference(unit_resolution,[status(thm)],[36,17]) ).
tff(38,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C )
| ( double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))) = a1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))) = a1,
inference(unit_resolution,[status(thm)],[38,17]) ).
tff(40,plain,
double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1)))) = double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1)))),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1)))) = double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1)))),
inference(transitivity,[status(thm)],[40,23]) ).
tff(42,plain,
inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1))))) = inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))) = inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1))))),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C )
| ( double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))))) = double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))))) = double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1)))),
inference(unit_resolution,[status(thm)],[44,17]) ).
tff(46,plain,
double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))))) = double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))))),
inference(monotonicity,[status(thm)],[39]) ).
tff(47,plain,
double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))))) = double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1)))),
inference(transitivity,[status(thm)],[46,45]) ).
tff(48,plain,
inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1))))))) = inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1))))))) = inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1))))),
inference(transitivity,[status(thm)],[48,43]) ).
tff(50,plain,
double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))) = double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1))))) = inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1))))),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1))))) = inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1))))),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))))) = double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))))),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))))) = double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))))),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C )
| ( double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))))) = double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))))) = double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),
inference(unit_resolution,[status(thm)],[55,17]) ).
tff(57,plain,
double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))) = double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))))),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C )
| ( double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1))))))),inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))))))) = double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1))))))),inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))))))) = double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),
inference(unit_resolution,[status(thm)],[58,17]) ).
tff(60,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C )
| ( double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))) = a1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))) = a1,
inference(unit_resolution,[status(thm)],[60,17]) ).
tff(62,plain,
a1 = double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
inverse(a1) = inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1))))),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1))))) = inverse(a1),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C )
| ( double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))),inverse(a1))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))))) = a1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))),inverse(a1))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))))) = a1,
inference(unit_resolution,[status(thm)],[65,17]) ).
tff(67,plain,
double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))),inverse(a1)) = double_divide(a1,inverse(a1)),
inference(monotonicity,[status(thm)],[61]) ).
tff(68,plain,
inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))),inverse(a1))) = inverse(double_divide(a1,inverse(a1))),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
inverse(double_divide(a1,inverse(a1))) = inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))),inverse(a1))),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C )
| ( double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)))) = double_divide(a1,inverse(a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)))) = double_divide(a1,inverse(a1)),
inference(unit_resolution,[status(thm)],[70,17]) ).
tff(72,plain,
double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)))) = double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)))),
inference(monotonicity,[status(thm)],[61]) ).
tff(73,plain,
double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)))) = double_divide(a1,inverse(a1)),
inference(transitivity,[status(thm)],[72,71]) ).
tff(74,plain,
inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1))))) = inverse(double_divide(a1,inverse(a1))),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1))))) = inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))),inverse(a1))),
inference(transitivity,[status(thm)],[74,69]) ).
tff(76,plain,
double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))) = double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))),inverse(a1))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1))))) = inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))),inverse(a1))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1))))),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))))) = double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))),inverse(a1))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))))),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C )
| ( double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))))) = double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))))) = double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),
inference(unit_resolution,[status(thm)],[79,17]) ).
tff(81,plain,
double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)) = double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))))),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))))) = double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),
inference(monotonicity,[status(thm)],[64]) ).
tff(83,plain,
double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))))) = a1,
inference(transitivity,[status(thm)],[82,81,78,66]) ).
tff(84,plain,
double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))))) = double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))))),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))))) = double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1)))),
inference(transitivity,[status(thm)],[84,45]) ).
tff(86,plain,
inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1))))))) = inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1))))))),inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))))) = double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),
inference(monotonicity,[status(thm)],[86,64]) ).
tff(88,plain,
inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1))))))),inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1))))))) = inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1))),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C )
| ( double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1)))))) = double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(90,plain,
double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1)))))) = double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1)))),
inference(unit_resolution,[status(thm)],[89,17]) ).
tff(91,plain,
double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1)))))) = double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[19]) ).
tff(92,plain,
double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1)))))) = double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[91,90]) ).
tff(93,plain,
inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1))))))) = inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))) = inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1))))))),
inference(symmetry,[status(thm)],[93]) ).
tff(95,plain,
double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1))))))),inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))))))) = double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),
inference(monotonicity,[status(thm)],[94,88]) ).
tff(96,plain,
double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))) = double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1))))))),inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(a1))),inverse(a1)))))))),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))) = double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)),
inference(transitivity,[status(thm)],[96,59,57,54,37,35,32]) ).
tff(98,plain,
inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1))))) = inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1))),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))))) = double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C )
| ( double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))))) = double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))))) = double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1)))),
inference(unit_resolution,[status(thm)],[100,17]) ).
tff(102,plain,
double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1)))) = double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(b1,inverse(b1))))),inverse(a1)))))),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C )
| ( double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1)))))),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1)))))))) = double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(104,plain,
double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1)))))),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1)))))))) = double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1)))),
inference(unit_resolution,[status(thm)],[103,17]) ).
tff(105,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C )
| ( double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(b1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(b1))),inverse(a1)))))) = double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(b1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(b1))),inverse(a1)))))) = double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))),
inference(unit_resolution,[status(thm)],[105,17]) ).
tff(107,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C )
| ( double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1)))) = b1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(108,plain,
double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1)))) = b1,
inference(unit_resolution,[status(thm)],[107,17]) ).
tff(109,plain,
b1 = double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1)))),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
inverse(b1) = inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1))))),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C )
| ( double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(b1))),inverse(a1)))) = b1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(b1))),inverse(a1)))) = b1,
inference(unit_resolution,[status(thm)],[111,17]) ).
tff(113,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C )
| ( double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))))) = double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(114,plain,
double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))))) = double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1)))),
inference(unit_resolution,[status(thm)],[113,17]) ).
tff(115,plain,
double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(b1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))))) = double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))))),
inference(monotonicity,[status(thm)],[112]) ).
tff(116,plain,
double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(b1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))))) = double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[115,114]) ).
tff(117,plain,
inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(b1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1))))))) = inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(b1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(b1))),inverse(a1)))) = double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(b1))),inverse(a1)))),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(b1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(b1))),inverse(a1)))) = b1,
inference(transitivity,[status(thm)],[118,112]) ).
tff(120,plain,
inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(b1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(b1))),inverse(a1))))) = inverse(b1),
inference(monotonicity,[status(thm)],[119]) ).
tff(121,plain,
inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(b1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(b1))),inverse(a1))))) = inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1))))),
inference(transitivity,[status(thm)],[120,110]) ).
tff(122,plain,
inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1))))) = inverse(b1),
inference(symmetry,[status(thm)],[110]) ).
tff(123,plain,
double_divide(b1,inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1)))))) = double_divide(b1,inverse(b1)),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,plain,
double_divide(double_divide(b1,inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1)))))),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1)))))) = double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
double_divide(double_divide(b1,inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1)))))),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1)))))) = double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[124,90]) ).
tff(126,plain,
inverse(double_divide(double_divide(b1,inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1)))))),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1))))))) = inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,plain,
inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))) = inverse(double_divide(double_divide(b1,inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1)))))),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1))))))),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(b1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(b1))),inverse(a1)))))) = double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1)))))),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1)))))),
inference(monotonicity,[status(thm)],[127,121]) ).
tff(129,plain,
double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1)))))),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1)))))) = double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(b1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1))))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(b1))),inverse(a1)))))),
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1)))))),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1)))))) = double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))),
inference(transitivity,[status(thm)],[129,106]) ).
tff(131,plain,
inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1)))))),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1))))))) = inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1))))),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1))))) = inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1)))))),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1))))))),
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))))) = double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1)))))),inverse(double_divide(inverse(double_divide(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(b1))),inverse(a1)))))))),
inference(monotonicity,[status(thm)],[132]) ).
tff(134,plain,
double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1)))) = double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(double_divide(inverse(double_divide(double_divide(b1,inverse(b1)),inverse(double_divide(a1,inverse(a1))))),inverse(b1)))))),
inference(symmetry,[status(thm)],[114]) ).
tff(135,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C )
| ( double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(a1)))) = double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(136,plain,
double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(a1)))) = double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1)))),
inference(unit_resolution,[status(thm)],[135,17]) ).
tff(137,plain,
double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(a1)))) = double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(a1)))),
inference(monotonicity,[status(thm)],[39]) ).
tff(138,plain,
double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(a1)))) = double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[137,136]) ).
tff(139,plain,
inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(a1))))) = inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),
inference(monotonicity,[status(thm)],[138]) ).
tff(140,plain,
double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))) = double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))) = a1,
inference(transitivity,[status(thm)],[140,39]) ).
tff(142,plain,
inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1))))) = inverse(a1),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,plain,
double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))))) = double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C )
| ( double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))))) = double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))))) = double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(a1)),
inference(unit_resolution,[status(thm)],[144,17]) ).
tff(146,plain,
double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(a1)) = double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))),inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(a1))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))),inverse(a1)),inverse(a1))),inverse(a1)))))),
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(a1)) = a1,
inference(transitivity,[status(thm)],[146,143,81,78,66]) ).
tff(148,plain,
inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(a1))) = inverse(a1),
inference(monotonicity,[status(thm)],[147]) ).
tff(149,plain,
inverse(a1) = inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(a1))),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
double_divide(a1,inverse(a1)) = double_divide(a1,inverse(double_divide(inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1))))))),inverse(a1)))),
inference(monotonicity,[status(thm)],[149]) ).
tff(151,plain,
double_divide(a1,inverse(a1)) = double_divide(b1,inverse(b1)),
inference(transitivity,[status(thm)],[150,136,134,133,104,102,99,19]) ).
tff(152,plain,
inverse(double_divide(a1,inverse(a1))) = inverse(double_divide(b1,inverse(b1))),
inference(monotonicity,[status(thm)],[151]) ).
tff(153,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = inverse(double_divide(B,A)) )
| ( multiply(inverse(a1),a1) = inverse(double_divide(a1,inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(154,plain,
multiply(inverse(a1),a1) = inverse(double_divide(a1,inverse(a1))),
inference(unit_resolution,[status(thm)],[153,7]) ).
tff(155,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(transitivity,[status(thm)],[154,152,10]) ).
tff(156,plain,
( ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1) )
<=> ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(157,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
tff(158,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(modus_ponens,[status(thm)],[157,156]) ).
tff(159,plain,
$false,
inference(unit_resolution,[status(thm)],[158,155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : GRP585-1 : TPTP v9.0.0. Released v2.6.0.
% 0.13/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n001.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Jun 19 16:24:03 EDT 2025
% 0.13/0.35 % CPUTime :
% 30.73/30.91 % SZS status Unsatisfiable
% 30.73/30.91 % SZS output start Proof
% See solution above
% 30.82/31.06 % E exiting
%------------------------------------------------------------------------------