%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP509-1 : 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 05:07:57 AM UTC 2025
% Result : Unsatisfiable 0.77s 0.97s
% Output : Proof 1.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 113
% Number of leaves : 124
% Syntax : Number of formulae : 1070 ( 948 unt; 0 typ; 0 def)
% Number of atoms : 1194 (1192 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 246 ( 123 ~; 119 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 17 ( 3 avg)
% Number of FOOLs : 1 ( 1 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 384 ( 381 !; 0 ?; 384 :)
% 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(1,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
<=> ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
<=> ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
<=> ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
tff(5,plain,
! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1)),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1)),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))) = inverse(multiply(a1,inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(11,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))) = inverse(multiply(a1,inverse(a1))),
inference(unit_resolution,[status(thm)],[10,7]) ).
tff(12,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),
inference(unit_resolution,[status(thm)],[12,7]) ).
tff(14,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(15,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(unit_resolution,[status(thm)],[14,7]) ).
tff(16,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))) = a1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(17,plain,
multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))) = a1,
inference(unit_resolution,[status(thm)],[16,7]) ).
tff(18,plain,
inverse(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1)))) = inverse(a1),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
inverse(a1) = inverse(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1)))),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
a1 = multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),
inference(symmetry,[status(thm)],[17]) ).
tff(21,plain,
multiply(a1,inverse(multiply(inverse(a1),a1))) = multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(a1)) = multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))))),
inference(monotonicity,[status(thm)],[21,19]) ).
tff(23,plain,
multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))))) = multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(a1)),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))))) = inverse(multiply(inverse(a1),a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))))) = inverse(multiply(inverse(a1),a1)),
inference(unit_resolution,[status(thm)],[24,7]) ).
tff(26,plain,
inverse(multiply(inverse(a1),a1)) = multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))))),
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(a1)),inverse(multiply(a1,inverse(a1)))) = inverse(multiply(inverse(a1),a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
multiply(multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(a1)),inverse(multiply(a1,inverse(a1)))) = inverse(multiply(inverse(a1),a1)),
inference(unit_resolution,[status(thm)],[27,7]) ).
tff(29,plain,
inverse(multiply(inverse(a1),a1)) = multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(a1)),
inference(transitivity,[status(thm)],[26,23]) ).
tff(30,plain,
multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(a1)),inverse(multiply(a1,inverse(a1)))),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(a1)),
inference(transitivity,[status(thm)],[30,28,26,23]) ).
tff(32,plain,
multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(a1)),inverse(multiply(a1,inverse(a1)))),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
multiply(multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(a1)),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
inverse(multiply(inverse(a1),a1)) = multiply(multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(a1)),inverse(multiply(a1,inverse(a1)))),
inference(symmetry,[status(thm)],[28]) ).
tff(35,plain,
inverse(multiply(inverse(a1),a1)) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[34,33]) ).
tff(36,plain,
multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(a1,inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(a1,inverse(a1))),
inference(unit_resolution,[status(thm)],[38,7]) ).
tff(40,plain,
inverse(multiply(a1,inverse(a1))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(a1,inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(a1,inverse(a1))),
inference(unit_resolution,[status(thm)],[41,7]) ).
tff(43,plain,
multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[30,33]) ).
tff(44,plain,
multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
inverse(multiply(a1,inverse(a1))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[40,45]) ).
tff(47,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[47,42,40,37]) ).
tff(49,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[47,42,40,45]) ).
tff(51,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[51,42,40,45]) ).
tff(53,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[52,49]) ).
tff(54,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
inverse(multiply(a1,inverse(a1))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[42]) ).
tff(56,plain,
inverse(multiply(a1,inverse(a1))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(transitivity,[status(thm)],[55,54,15]) ).
tff(57,plain,
multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[36,45]) ).
tff(58,plain,
multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[57,56]) ).
tff(59,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(a1,inverse(a1)))),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[36,39,55,59]) ).
tff(61,plain,
multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),
inference(unit_resolution,[status(thm)],[63,7]) ).
tff(65,plain,
inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[65,62]) ).
tff(67,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[66,56]) ).
tff(68,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),
inference(transitivity,[status(thm)],[67,13]) ).
tff(69,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))),b1) = multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))),b1),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))) = inverse(multiply(a1,inverse(a1))),
inference(transitivity,[status(thm)],[71,11]) ).
tff(73,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))) = multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = inverse(multiply(a1,inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = inverse(multiply(a1,inverse(a1))),
inference(unit_resolution,[status(thm)],[75,7]) ).
tff(77,plain,
multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))) = inverse(multiply(inverse(a1),a1)),
inference(transitivity,[status(thm)],[30,28]) ).
tff(78,plain,
multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))) = multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[80,76,40,45]) ).
tff(82,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[81,56]) ).
tff(83,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
inverse(multiply(a1,inverse(a1))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[55,83]) ).
tff(85,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
multiply(multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(88,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),
inference(unit_resolution,[status(thm)],[87,7]) ).
tff(89,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = inverse(a1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(90,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = inverse(a1),
inference(unit_resolution,[status(thm)],[89,7]) ).
tff(91,plain,
inverse(multiply(a1,inverse(a1))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[55,59]) ).
tff(92,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))) = multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[67,13,65,93]) ).
tff(95,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1))))),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(a1,inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(a1,inverse(a1))),
inference(unit_resolution,[status(thm)],[97,7]) ).
tff(99,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[46,56]) ).
tff(100,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[99,59]) ).
tff(101,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[65,102]) ).
tff(104,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[104,98,40,45]) ).
tff(106,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[105,56]) ).
tff(107,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = inverse(multiply(a1,inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(109,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = inverse(multiply(a1,inverse(a1))),
inference(unit_resolution,[status(thm)],[108,7]) ).
tff(110,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))) = inverse(multiply(a1,inverse(a1))),
inference(transitivity,[status(thm)],[99,42]) ).
tff(111,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(a1)) = multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(a1)),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[113,109,55,107]) ).
tff(115,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[114,96]) ).
tff(116,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(118,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(unit_resolution,[status(thm)],[117,7]) ).
tff(119,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(transitivity,[status(thm)],[119,116]) ).
tff(121,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(symmetry,[status(thm)],[121]) ).
tff(123,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(124,plain,
multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),
inference(unit_resolution,[status(thm)],[123,7]) ).
tff(125,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))) = multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(symmetry,[status(thm)],[124]) ).
tff(126,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(127,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),
inference(unit_resolution,[status(thm)],[126,7]) ).
tff(128,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(a1,inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(129,plain,
multiply(multiply(multiply(inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(a1,inverse(a1))),
inference(unit_resolution,[status(thm)],[128,7]) ).
tff(130,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))) = a1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,plain,
multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))) = a1,
inference(unit_resolution,[status(thm)],[130,7]) ).
tff(132,plain,
multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))) = multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),
inference(monotonicity,[status(thm)],[20]) ).
tff(133,plain,
multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))) = a1,
inference(transitivity,[status(thm)],[132,131]) ).
tff(134,plain,
inverse(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))))) = inverse(a1),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
inverse(a1) = inverse(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))))),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))) = multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),
inference(transitivity,[status(thm)],[132,131,20]) ).
tff(137,plain,
multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))) = multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))) = multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
a1 = multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),
inference(symmetry,[status(thm)],[131]) ).
tff(140,plain,
a1 = multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),
inference(transitivity,[status(thm)],[139,138]) ).
tff(141,plain,
multiply(a1,inverse(a1)) = multiply(multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))))),
inference(monotonicity,[status(thm)],[140,135]) ).
tff(142,plain,
multiply(multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))))) = multiply(a1,inverse(a1)),
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))))) = inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(144,plain,
multiply(multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))))) = inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))),
inference(unit_resolution,[status(thm)],[143,7]) ).
tff(145,plain,
inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))) = multiply(multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))))),
inference(symmetry,[status(thm)],[144]) ).
tff(146,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(a1)),inverse(multiply(a1,inverse(a1)))) = inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(147,plain,
multiply(multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(a1)),inverse(multiply(a1,inverse(a1)))) = inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))),
inference(unit_resolution,[status(thm)],[146,7]) ).
tff(148,plain,
multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(a1)) = multiply(a1,inverse(a1)),
inference(monotonicity,[status(thm)],[133]) ).
tff(149,plain,
multiply(a1,inverse(a1)) = multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(a1)),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))) = multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(a1)),
inference(transitivity,[status(thm)],[145,142,149]) ).
tff(151,plain,
multiply(inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(a1)),inverse(multiply(a1,inverse(a1)))),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
multiply(inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(a1,inverse(a1)))) = multiply(a1,inverse(a1)),
inference(transitivity,[status(thm)],[151,147,145,142]) ).
tff(153,plain,
inverse(multiply(inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(a1,inverse(a1))))) = inverse(multiply(a1,inverse(a1))),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
inverse(multiply(a1,inverse(a1))) = inverse(multiply(inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(a1,inverse(a1))))),
inference(symmetry,[status(thm)],[153]) ).
tff(155,plain,
multiply(inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(a1)),
inference(transitivity,[status(thm)],[151,147,145,142,149]) ).
tff(156,plain,
multiply(multiply(inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(a1)),inverse(multiply(a1,inverse(a1)))),
inference(monotonicity,[status(thm)],[155]) ).
tff(157,plain,
multiply(multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(a1)),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))),
inference(symmetry,[status(thm)],[156]) ).
tff(158,plain,
inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))) = multiply(multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(a1)),inverse(multiply(a1,inverse(a1)))),
inference(symmetry,[status(thm)],[147]) ).
tff(159,plain,
multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(a1)) = multiply(multiply(inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[148,141,144,158,157]) ).
tff(160,plain,
multiply(multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(a1)),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[159,154]) ).
tff(161,plain,
multiply(a1,inverse(a1)) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[141,144,158,160,129,55,107]) ).
tff(162,plain,
multiply(multiply(a1,inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[161,96]) ).
tff(163,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(a1,inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[162]) ).
tff(164,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = multiply(multiply(a1,inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(transitivity,[status(thm)],[119,163]) ).
tff(165,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(multiply(a1,inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(monotonicity,[status(thm)],[164]) ).
tff(166,plain,
multiply(multiply(multiply(a1,inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(symmetry,[status(thm)],[165]) ).
tff(167,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(a1,inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(a1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(168,plain,
multiply(multiply(multiply(a1,inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(a1),
inference(unit_resolution,[status(thm)],[167,7]) ).
tff(169,plain,
inverse(a1) = multiply(multiply(multiply(a1,inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(symmetry,[status(thm)],[168]) ).
tff(170,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(a1,inverse(a1)),inverse(a1)),inverse(multiply(a1,inverse(a1)))) = inverse(a1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(171,plain,
multiply(multiply(multiply(a1,inverse(a1)),inverse(a1)),inverse(multiply(a1,inverse(a1)))) = inverse(a1),
inference(unit_resolution,[status(thm)],[170,7]) ).
tff(172,plain,
multiply(a1,inverse(a1)) = inverse(multiply(a1,inverse(a1))),
inference(transitivity,[status(thm)],[141,144,158,160,129]) ).
tff(173,plain,
multiply(multiply(a1,inverse(a1)),inverse(a1)) = multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),
inference(monotonicity,[status(thm)],[172]) ).
tff(174,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)) = multiply(multiply(a1,inverse(a1)),inverse(a1)),
inference(symmetry,[status(thm)],[173]) ).
tff(175,plain,
multiply(multiply(multiply(inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(a1)),inverse(multiply(a1,inverse(a1)))),
inference(symmetry,[status(thm)],[160]) ).
tff(176,plain,
inverse(multiply(a1,inverse(a1))) = multiply(multiply(multiply(inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[129]) ).
tff(177,plain,
inverse(multiply(a1,inverse(a1))) = inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))),
inference(transitivity,[status(thm)],[176,175,147]) ).
tff(178,plain,
multiply(a1,inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),
inference(monotonicity,[status(thm)],[20,177]) ).
tff(179,plain,
multiply(a1,inverse(multiply(a1,inverse(a1)))) = a1,
inference(transitivity,[status(thm)],[178,131]) ).
tff(180,plain,
inverse(multiply(a1,inverse(multiply(a1,inverse(a1))))) = inverse(a1),
inference(monotonicity,[status(thm)],[179]) ).
tff(181,plain,
inverse(a1) = inverse(multiply(a1,inverse(multiply(a1,inverse(a1))))),
inference(symmetry,[status(thm)],[180]) ).
tff(182,plain,
multiply(a1,inverse(a1)) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[141,144,158,160,129,40,45]) ).
tff(183,plain,
multiply(multiply(a1,inverse(a1)),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[182,56]) ).
tff(184,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(a1,inverse(a1)),inverse(multiply(a1,inverse(a1)))),
inference(symmetry,[status(thm)],[183]) ).
tff(185,plain,
inverse(multiply(a1,inverse(a1))) = multiply(multiply(a1,inverse(a1)),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[55,184]) ).
tff(186,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)) = multiply(multiply(multiply(a1,inverse(a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[185,181]) ).
tff(187,plain,
multiply(multiply(multiply(a1,inverse(a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(multiply(a1,inverse(a1)))))) = multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),
inference(symmetry,[status(thm)],[186]) ).
tff(188,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(a1,inverse(a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(multiply(a1,inverse(a1)))))) = inverse(a1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(189,plain,
multiply(multiply(multiply(a1,inverse(a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(multiply(a1,inverse(a1)))))) = inverse(a1),
inference(unit_resolution,[status(thm)],[188,7]) ).
tff(190,plain,
inverse(a1) = multiply(multiply(multiply(a1,inverse(a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[189]) ).
tff(191,plain,
inverse(a1) = multiply(multiply(a1,inverse(a1)),inverse(a1)),
inference(transitivity,[status(thm)],[190,187,174]) ).
tff(192,plain,
multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(a1,inverse(a1)),inverse(a1)),inverse(multiply(a1,inverse(a1)))),
inference(monotonicity,[status(thm)],[191]) ).
tff(193,plain,
multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))) = multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(transitivity,[status(thm)],[192,171,169,166]) ).
tff(194,plain,
inverse(multiply(inverse(a1),inverse(multiply(a1,inverse(a1))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))),
inference(monotonicity,[status(thm)],[193]) ).
tff(195,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))) = inverse(multiply(inverse(a1),inverse(multiply(a1,inverse(a1))))),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),
inference(transitivity,[status(thm)],[165,168,190,187]) ).
tff(197,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),
inference(monotonicity,[status(thm)],[196]) ).
tff(198,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))),
inference(symmetry,[status(thm)],[197]) ).
tff(199,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))) = inverse(multiply(inverse(a1),inverse(multiply(a1,inverse(a1))))),
inference(transitivity,[status(thm)],[198,195]) ).
tff(200,plain,
inverse(a1) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(a1)),
inference(transitivity,[status(thm)],[190,187,112]) ).
tff(201,plain,
multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(monotonicity,[status(thm)],[200]) ).
tff(202,plain,
multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[201,109,40,45]) ).
tff(203,plain,
multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[202,56]) ).
tff(204,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(a1,inverse(a1)))),
inference(symmetry,[status(thm)],[203]) ).
tff(205,plain,
inverse(multiply(a1,inverse(a1))) = multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[55,204]) ).
tff(206,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[205,199]) ).
tff(207,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(transitivity,[status(thm)],[206,127,125,122]) ).
tff(208,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))),
inference(monotonicity,[status(thm)],[207]) ).
tff(209,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))),
inference(symmetry,[status(thm)],[208]) ).
tff(210,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(211,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),
inference(unit_resolution,[status(thm)],[210,7]) ).
tff(212,plain,
multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[201,109,40,37]) ).
tff(213,plain,
inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(monotonicity,[status(thm)],[212]) ).
tff(214,plain,
inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))),
inference(symmetry,[status(thm)],[213]) ).
tff(215,plain,
inverse(multiply(a1,inverse(a1))) = inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))),
inference(transitivity,[status(thm)],[55,54,15,214]) ).
tff(216,plain,
multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[201,109,55,204]) ).
tff(217,plain,
multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[216,199]) ).
tff(218,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(symmetry,[status(thm)],[217]) ).
tff(219,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[127]) ).
tff(220,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))) = multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(transitivity,[status(thm)],[219,218]) ).
tff(221,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(monotonicity,[status(thm)],[220,215]) ).
tff(222,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))) = multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(transitivity,[status(thm)],[221,211,125,122]) ).
tff(223,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))),
inference(monotonicity,[status(thm)],[222]) ).
tff(224,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))),
inference(transitivity,[status(thm)],[223,209]) ).
tff(225,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(symmetry,[status(thm)],[113]) ).
tff(226,plain,
inverse(multiply(a1,inverse(a1))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(symmetry,[status(thm)],[109]) ).
tff(227,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))) = inverse(multiply(a1,inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(228,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))) = inverse(multiply(a1,inverse(a1))),
inference(unit_resolution,[status(thm)],[227,7]) ).
tff(229,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(230,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(unit_resolution,[status(thm)],[229,7]) ).
tff(231,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[104,98,40,37]) ).
tff(232,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(monotonicity,[status(thm)],[231]) ).
tff(233,plain,
inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))),
inference(symmetry,[status(thm)],[232]) ).
tff(234,plain,
inverse(multiply(a1,inverse(a1))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))),
inference(transitivity,[status(thm)],[55,54,15,233]) ).
tff(235,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[104,98,55,107]) ).
tff(236,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[235,96]) ).
tff(237,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[236]) ).
tff(238,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(transitivity,[status(thm)],[119,237]) ).
tff(239,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(monotonicity,[status(thm)],[238,234]) ).
tff(240,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(transitivity,[status(thm)],[239,230,119,116]) ).
tff(241,plain,
multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(monotonicity,[status(thm)],[240]) ).
tff(242,plain,
multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(symmetry,[status(thm)],[241]) ).
tff(243,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(transitivity,[status(thm)],[125,242]) ).
tff(244,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),
inference(monotonicity,[status(thm)],[243]) ).
tff(245,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[244,228,40,45]) ).
tff(246,plain,
multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[245,56]) ).
tff(247,plain,
multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(transitivity,[status(thm)],[246,42,226,225]) ).
tff(248,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(monotonicity,[status(thm)],[247,224]) ).
tff(249,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(250,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))),
inference(unit_resolution,[status(thm)],[249,7]) ).
tff(251,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[250]) ).
tff(252,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))) = inverse(a1),
inference(transitivity,[status(thm)],[208,251,248,90]) ).
tff(253,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = a1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(254,plain,
multiply(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = a1,
inference(unit_resolution,[status(thm)],[253,7]) ).
tff(255,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(256,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),
inference(unit_resolution,[status(thm)],[255,7]) ).
tff(257,plain,
inverse(a1) = multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),
inference(transitivity,[status(thm)],[190,187]) ).
tff(258,plain,
multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[257]) ).
tff(259,plain,
inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))) = inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))),
inference(monotonicity,[status(thm)],[258]) ).
tff(260,plain,
inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))) = inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))),
inference(symmetry,[status(thm)],[259]) ).
tff(261,plain,
multiply(multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(a1)),inverse(multiply(a1,inverse(a1)))) = multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),
inference(symmetry,[status(thm)],[30]) ).
tff(262,plain,
multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(a1)) = multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))))),
inference(monotonicity,[status(thm)],[19]) ).
tff(263,plain,
multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(a1)) = multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[262,25,34,261]) ).
tff(264,plain,
inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(a1))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),
inference(monotonicity,[status(thm)],[263]) ).
tff(265,plain,
inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))) = inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(a1))),
inference(symmetry,[status(thm)],[264]) ).
tff(266,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))) = inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(267,plain,
multiply(multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))) = inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))),
inference(unit_resolution,[status(thm)],[266,7]) ).
tff(268,plain,
multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(a1),a1))) = multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),
inference(monotonicity,[status(thm)],[136]) ).
tff(269,plain,
multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))) = multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(a1),a1))),
inference(symmetry,[status(thm)],[268]) ).
tff(270,plain,
multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))) = multiply(multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),
inference(monotonicity,[status(thm)],[269]) ).
tff(271,plain,
multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))) = inverse(multiply(a1,inverse(a1))),
inference(transitivity,[status(thm)],[270,267,158,160,129]) ).
tff(272,plain,
multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(a1)) = multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),
inference(monotonicity,[status(thm)],[271]) ).
tff(273,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)) = multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(a1)),
inference(symmetry,[status(thm)],[272]) ).
tff(274,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(a1)),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(a1)))),
inference(monotonicity,[status(thm)],[273,265]) ).
tff(275,plain,
multiply(multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(a1)),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(a1)))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[274]) ).
tff(276,plain,
inverse(a1) = multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(a1)),
inference(transitivity,[status(thm)],[190,187,273]) ).
tff(277,plain,
multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(a1)),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(a1)))),
inference(monotonicity,[status(thm)],[276,265]) ).
tff(278,plain,
multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[277,275]) ).
tff(279,plain,
multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[278]) ).
tff(280,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[279]) ).
tff(281,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = inverse(a1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(282,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = inverse(a1),
inference(unit_resolution,[status(thm)],[281,7]) ).
tff(283,plain,
inverse(a1) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[282]) ).
tff(284,plain,
inverse(a1) = multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(transitivity,[status(thm)],[283,280]) ).
tff(285,plain,
multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(monotonicity,[status(thm)],[284,260]) ).
tff(286,plain,
multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[285,256,65,102]) ).
tff(287,plain,
multiply(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[286]) ).
tff(288,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[287]) ).
tff(289,plain,
inverse(multiply(a1,inverse(a1))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[98]) ).
tff(290,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),a1),inverse(multiply(inverse(a1),a1))) = inverse(multiply(a1,inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(291,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),a1),inverse(multiply(inverse(a1),a1))) = inverse(multiply(a1,inverse(a1))),
inference(unit_resolution,[status(thm)],[290,7]) ).
tff(292,plain,
multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))) = inverse(a1),
inference(transitivity,[status(thm)],[192,171]) ).
tff(293,plain,
multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),a1) = multiply(inverse(a1),a1),
inference(monotonicity,[status(thm)],[292]) ).
tff(294,plain,
multiply(inverse(a1),a1) = multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),a1),
inference(symmetry,[status(thm)],[293]) ).
tff(295,plain,
multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),a1),inverse(multiply(inverse(a1),a1))),
inference(monotonicity,[status(thm)],[294]) ).
tff(296,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))))) = inverse(multiply(inverse(a1),a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(297,plain,
multiply(multiply(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))))) = inverse(multiply(inverse(a1),a1)),
inference(unit_resolution,[status(thm)],[296,7]) ).
tff(298,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(299,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(unit_resolution,[status(thm)],[298,7]) ).
tff(300,plain,
multiply(multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(a1)),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(a1)))) = multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[277]) ).
tff(301,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(a1,inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(302,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(a1,inverse(a1))),
inference(unit_resolution,[status(thm)],[301,7]) ).
tff(303,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[99,107]) ).
tff(304,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[303,96]) ).
tff(305,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[304]) ).
tff(306,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(transitivity,[status(thm)],[119,305]) ).
tff(307,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(monotonicity,[status(thm)],[306]) ).
tff(308,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[307,302,40,37]) ).
tff(309,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(monotonicity,[status(thm)],[308]) ).
tff(310,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(311,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),
inference(unit_resolution,[status(thm)],[310,7]) ).
tff(312,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[92,102]) ).
tff(313,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[312]) ).
tff(314,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[313]) ).
tff(315,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(transitivity,[status(thm)],[307,302,289,314]) ).
tff(316,plain,
multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(monotonicity,[status(thm)],[315]) ).
tff(317,plain,
multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[316,311,65,62]) ).
tff(318,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[317,309]) ).
tff(319,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(320,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))),
inference(unit_resolution,[status(thm)],[319,7]) ).
tff(321,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),
inference(symmetry,[status(thm)],[320]) ).
tff(322,plain,
inverse(multiply(a1,inverse(a1))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[55,107]) ).
tff(323,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[322,96]) ).
tff(324,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[323]) ).
tff(325,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))) = multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(transitivity,[status(thm)],[239,230,119,324]) ).
tff(326,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))),
inference(monotonicity,[status(thm)],[325]) ).
tff(327,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1))))) = inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(a1))),
inference(transitivity,[status(thm)],[326,321,318,13,265]) ).
tff(328,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(a1,inverse(a1)),inverse(a1)),
inference(transitivity,[status(thm)],[165,168,190,187,174]) ).
tff(329,plain,
multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(a1,inverse(a1)),inverse(a1)),inverse(multiply(a1,inverse(a1)))),
inference(monotonicity,[status(thm)],[328]) ).
tff(330,plain,
multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(a1)),
inference(transitivity,[status(thm)],[329,171,190,187,273]) ).
tff(331,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(a1)),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(a1)))),
inference(monotonicity,[status(thm)],[330,327]) ).
tff(332,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(333,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))),
inference(unit_resolution,[status(thm)],[332,7]) ).
tff(334,plain,
inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[333]) ).
tff(335,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(336,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))),
inference(unit_resolution,[status(thm)],[335,7]) ).
tff(337,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),
inference(symmetry,[status(thm)],[318]) ).
tff(338,plain,
inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[13]) ).
tff(339,plain,
inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))),
inference(transitivity,[status(thm)],[338,337,320]) ).
tff(340,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(monotonicity,[status(thm)],[306,339]) ).
tff(341,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[340,302,40,37]) ).
tff(342,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(monotonicity,[status(thm)],[341]) ).
tff(343,plain,
inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(symmetry,[status(thm)],[342]) ).
tff(344,plain,
inverse(multiply(a1,inverse(a1))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(transitivity,[status(thm)],[55,54,15,343]) ).
tff(345,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(a1)),
inference(transitivity,[status(thm)],[165,168,190,187,273]) ).
tff(346,plain,
multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(a1)),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(a1)))),
inference(monotonicity,[status(thm)],[345,265]) ).
tff(347,plain,
multiply(multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(a1)),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(a1)))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[346]) ).
tff(348,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(a1)),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(a1)))) = inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(349,plain,
multiply(multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(a1)),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(a1)))) = inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),
inference(unit_resolution,[status(thm)],[348,7]) ).
tff(350,plain,
inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))) = multiply(multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(a1)),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(a1)))),
inference(symmetry,[status(thm)],[349]) ).
tff(351,plain,
inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[350,347]) ).
tff(352,plain,
multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[351,344]) ).
tff(353,plain,
multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(a1,inverse(a1)))) = multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[352,336,334,331,300]) ).
tff(354,plain,
inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(a1,inverse(a1))))) = inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(monotonicity,[status(thm)],[353]) ).
tff(355,plain,
inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(a1,inverse(a1))))),
inference(symmetry,[status(thm)],[354]) ).
tff(356,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(a1,inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(357,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(a1,inverse(a1))),
inference(unit_resolution,[status(thm)],[356,7]) ).
tff(358,plain,
multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(a1)),
inference(transitivity,[status(thm)],[192,171,190,187,273]) ).
tff(359,plain,
multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(a1)),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(a1)))),
inference(monotonicity,[status(thm)],[358,265]) ).
tff(360,plain,
multiply(multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(a1)),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(a1)))) = multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[359]) ).
tff(361,plain,
inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))) = multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[350,360]) ).
tff(362,plain,
multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[361]) ).
tff(363,plain,
multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[362,357,40,45]) ).
tff(364,plain,
multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[363,56]) ).
tff(365,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),
inference(symmetry,[status(thm)],[364]) ).
tff(366,plain,
multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(transitivity,[status(thm)],[295,291,226,225]) ).
tff(367,plain,
multiply(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(monotonicity,[status(thm)],[366,209]) ).
tff(368,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = multiply(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),
inference(symmetry,[status(thm)],[367]) ).
tff(369,plain,
inverse(a1) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(symmetry,[status(thm)],[90]) ).
tff(370,plain,
inverse(a1) = multiply(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),
inference(transitivity,[status(thm)],[369,368]) ).
tff(371,plain,
multiply(inverse(a1),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))))) = multiply(multiply(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))))),
inference(monotonicity,[status(thm)],[370]) ).
tff(372,plain,
multiply(inverse(a1),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[371,297,34,33]) ).
tff(373,plain,
multiply(multiply(inverse(a1),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[372]) ).
tff(374,plain,
multiply(multiply(inverse(a1),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[373,39,55,365]) ).
tff(375,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[374,355]) ).
tff(376,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(a1),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(377,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))))),
inference(unit_resolution,[status(thm)],[376,7]) ).
tff(378,plain,
inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[377]) ).
tff(379,plain,
inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))))) = inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(transitivity,[status(thm)],[378,375,299]) ).
tff(380,plain,
multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(monotonicity,[status(thm)],[258,339]) ).
tff(381,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[380]) ).
tff(382,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(a1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(383,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(a1),
inference(unit_resolution,[status(thm)],[382,7]) ).
tff(384,plain,
inverse(a1) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(symmetry,[status(thm)],[383]) ).
tff(385,plain,
multiply(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))) = multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[367,90,384,381]) ).
tff(386,plain,
multiply(multiply(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[385,379]) ).
tff(387,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))))),
inference(symmetry,[status(thm)],[386]) ).
tff(388,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(389,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(unit_resolution,[status(thm)],[388,7]) ).
tff(390,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[389]) ).
tff(391,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = inverse(multiply(inverse(a1),a1)),
inference(transitivity,[status(thm)],[390,387,297]) ).
tff(392,plain,
multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))),
inference(monotonicity,[status(thm)],[391]) ).
tff(393,plain,
multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(transitivity,[status(thm)],[392,295,291,289,288]) ).
tff(394,plain,
multiply(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(monotonicity,[status(thm)],[393]) ).
tff(395,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(symmetry,[status(thm)],[394]) ).
tff(396,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(397,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))),
inference(unit_resolution,[status(thm)],[396,7]) ).
tff(398,plain,
inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(symmetry,[status(thm)],[397]) ).
tff(399,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(400,plain,
multiply(multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))),
inference(unit_resolution,[status(thm)],[399,7]) ).
tff(401,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(monotonicity,[status(thm)],[339]) ).
tff(402,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(transitivity,[status(thm)],[401,383,169,166]) ).
tff(403,plain,
inverse(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))),
inference(monotonicity,[status(thm)],[402]) ).
tff(404,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))) = inverse(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(symmetry,[status(thm)],[403]) ).
tff(405,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))) = inverse(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(transitivity,[status(thm)],[198,404]) ).
tff(406,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(a1,inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(407,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(a1,inverse(a1))),
inference(unit_resolution,[status(thm)],[406,7]) ).
tff(408,plain,
multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))) = multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),
inference(transitivity,[status(thm)],[192,171,190,187]) ).
tff(409,plain,
multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[408]) ).
tff(410,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[409]) ).
tff(411,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(monotonicity,[status(thm)],[410,260]) ).
tff(412,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[411,407,55,59]) ).
tff(413,plain,
multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[412]) ).
tff(414,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[413]) ).
tff(415,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[92,414]) ).
tff(416,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[415,405]) ).
tff(417,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = a1,
inference(transitivity,[status(thm)],[416,400,398,395,254]) ).
tff(418,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = multiply(a1,inverse(a1)),
inference(monotonicity,[status(thm)],[417,252]) ).
tff(419,plain,
multiply(a1,inverse(a1)) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(symmetry,[status(thm)],[418]) ).
tff(420,plain,
inverse(multiply(a1,inverse(a1))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),
inference(transitivity,[status(thm)],[176,175,147,145,142,419,88]) ).
tff(421,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(monotonicity,[status(thm)],[420]) ).
tff(422,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))),
inference(monotonicity,[status(thm)],[421]) ).
tff(423,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))),
inference(symmetry,[status(thm)],[422]) ).
tff(424,plain,
multiply(multiply(a1,inverse(a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))) = multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(monotonicity,[status(thm)],[172]) ).
tff(425,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))) = multiply(multiply(a1,inverse(a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(symmetry,[status(thm)],[424]) ).
tff(426,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(multiply(multiply(a1,inverse(a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(monotonicity,[status(thm)],[425]) ).
tff(427,plain,
multiply(multiply(multiply(a1,inverse(a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(symmetry,[status(thm)],[426]) ).
tff(428,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(a1,inverse(a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = inverse(a1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(429,plain,
multiply(multiply(multiply(a1,inverse(a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = inverse(a1),
inference(unit_resolution,[status(thm)],[428,7]) ).
tff(430,plain,
inverse(a1) = multiply(multiply(multiply(a1,inverse(a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(symmetry,[status(thm)],[429]) ).
tff(431,plain,
inverse(a1) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(transitivity,[status(thm)],[430,427]) ).
tff(432,plain,
multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),
inference(monotonicity,[status(thm)],[431,423]) ).
tff(433,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))) = multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),
inference(symmetry,[status(thm)],[432]) ).
tff(434,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(435,plain,
multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))),
inference(unit_resolution,[status(thm)],[434,7]) ).
tff(436,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(437,plain,
multiply(multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1)))),
inference(unit_resolution,[status(thm)],[436,7]) ).
tff(438,plain,
multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))) = multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(monotonicity,[status(thm)],[133]) ).
tff(439,plain,
multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))) = multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(symmetry,[status(thm)],[438]) ).
tff(440,plain,
multiply(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(multiply(multiply(a1,inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(monotonicity,[status(thm)],[439]) ).
tff(441,plain,
multiply(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(a1,inverse(a1)),
inference(transitivity,[status(thm)],[440,437,145,142]) ).
tff(442,plain,
multiply(multiply(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(a1,inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[441]) ).
tff(443,plain,
multiply(multiply(a1,inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[442]) ).
tff(444,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = multiply(multiply(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(transitivity,[status(thm)],[119,163,443]) ).
tff(445,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(multiply(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(monotonicity,[status(thm)],[444]) ).
tff(446,plain,
multiply(multiply(multiply(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(symmetry,[status(thm)],[445]) ).
tff(447,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(448,plain,
multiply(multiply(multiply(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),
inference(unit_resolution,[status(thm)],[447,7]) ).
tff(449,plain,
inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))) = multiply(multiply(multiply(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(symmetry,[status(thm)],[448]) ).
tff(450,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(451,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),
inference(unit_resolution,[status(thm)],[450,7]) ).
tff(452,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(transitivity,[status(thm)],[426,429,169,166]) ).
tff(453,plain,
inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))),
inference(monotonicity,[status(thm)],[452]) ).
tff(454,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))) = inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))),
inference(symmetry,[status(thm)],[453]) ).
tff(455,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))) = inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))),
inference(transitivity,[status(thm)],[198,454]) ).
tff(456,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(457,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),
inference(unit_resolution,[status(thm)],[456,7]) ).
tff(458,plain,
multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(a1,inverse(a1))),
inference(transitivity,[status(thm)],[36,39]) ).
tff(459,plain,
multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))) = multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(monotonicity,[status(thm)],[458]) ).
tff(460,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(symmetry,[status(thm)],[459]) ).
tff(461,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(monotonicity,[status(thm)],[460]) ).
tff(462,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),
inference(transitivity,[status(thm)],[461,457]) ).
tff(463,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(monotonicity,[status(thm)],[462]) ).
tff(464,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(symmetry,[status(thm)],[463]) ).
tff(465,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),
inference(monotonicity,[status(thm)],[464,455]) ).
tff(466,plain,
multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(symmetry,[status(thm)],[465]) ).
tff(467,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(468,plain,
multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),
inference(unit_resolution,[status(thm)],[467,7]) ).
tff(469,plain,
inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))) = multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),
inference(symmetry,[status(thm)],[468]) ).
tff(470,plain,
inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(transitivity,[status(thm)],[469,466]) ).
tff(471,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(monotonicity,[status(thm)],[470]) ).
tff(472,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(transitivity,[status(thm)],[471,451,449,446]) ).
tff(473,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))),
inference(monotonicity,[status(thm)],[472]) ).
tff(474,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))))),
inference(symmetry,[status(thm)],[473]) ).
tff(475,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))) = inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(476,plain,
multiply(multiply(multiply(multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))) = inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),
inference(unit_resolution,[status(thm)],[475,7]) ).
tff(477,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[248]) ).
tff(478,plain,
inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))) = multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[65,414]) ).
tff(479,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[478,405]) ).
tff(480,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = a1,
inference(transitivity,[status(thm)],[479,400,398,395,254]) ).
tff(481,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))) = inverse(a1),
inference(monotonicity,[status(thm)],[480]) ).
tff(482,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))),
inference(transitivity,[status(thm)],[481,369,477,250]) ).
tff(483,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[104,98,55,204]) ).
tff(484,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[483,199]) ).
tff(485,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(transitivity,[status(thm)],[484,127,125,242]) ).
tff(486,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),
inference(monotonicity,[status(thm)],[485,482]) ).
tff(487,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(488,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(unit_resolution,[status(thm)],[487,7]) ).
tff(489,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(symmetry,[status(thm)],[488]) ).
tff(490,plain,
inverse(multiply(inverse(a1),a1)) = multiply(multiply(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))))),
inference(symmetry,[status(thm)],[297]) ).
tff(491,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = inverse(multiply(inverse(a1),a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(492,plain,
multiply(multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = inverse(multiply(inverse(a1),a1)),
inference(unit_resolution,[status(thm)],[491,7]) ).
tff(493,plain,
multiply(multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[492,490,386,389,489,486,228,40,37]) ).
tff(494,plain,
inverse(multiply(multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(monotonicity,[status(thm)],[493]) ).
tff(495,plain,
inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = inverse(multiply(multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))),
inference(symmetry,[status(thm)],[494]) ).
tff(496,plain,
inverse(multiply(a1,inverse(a1))) = inverse(multiply(multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))),
inference(transitivity,[status(thm)],[55,54,15,495]) ).
tff(497,plain,
multiply(multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),
inference(transitivity,[status(thm)],[492,490,386,389,489,486,228,176,175,147,145,142,419,88]) ).
tff(498,plain,
multiply(multiply(multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(monotonicity,[status(thm)],[497]) ).
tff(499,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(multiply(multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(symmetry,[status(thm)],[498]) ).
tff(500,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),
inference(monotonicity,[status(thm)],[499,496]) ).
tff(501,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))) = multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(transitivity,[status(thm)],[500,476,449,446]) ).
tff(502,plain,
inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))),
inference(monotonicity,[status(thm)],[501]) ).
tff(503,plain,
inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))))),
inference(transitivity,[status(thm)],[502,474]) ).
tff(504,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(symmetry,[status(thm)],[484]) ).
tff(505,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(506,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),
inference(unit_resolution,[status(thm)],[505,7]) ).
tff(507,plain,
multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[201,109,55,83]) ).
tff(508,plain,
multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[507]) ).
tff(509,plain,
multiply(multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[508]) ).
tff(510,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(511,plain,
multiply(multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),
inference(unit_resolution,[status(thm)],[510,7]) ).
tff(512,plain,
inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))) = multiply(multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[511]) ).
tff(513,plain,
inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))) = multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[512,509]) ).
tff(514,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[513]) ).
tff(515,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(transitivity,[status(thm)],[514,506,219,504]) ).
tff(516,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(monotonicity,[status(thm)],[515]) ).
tff(517,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(symmetry,[status(thm)],[516]) ).
tff(518,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(symmetry,[status(thm)],[486]) ).
tff(519,plain,
inverse(multiply(a1,inverse(a1))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),
inference(symmetry,[status(thm)],[228]) ).
tff(520,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))) = inverse(multiply(a1,inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(521,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))) = inverse(multiply(a1,inverse(a1))),
inference(unit_resolution,[status(thm)],[520,7]) ).
tff(522,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(monotonicity,[status(thm)],[68]) ).
tff(523,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(symmetry,[status(thm)],[522]) ).
tff(524,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),
inference(monotonicity,[status(thm)],[523]) ).
tff(525,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[524,521,40,45]) ).
tff(526,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[525,56]) ).
tff(527,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(transitivity,[status(thm)],[526,42,519,518,517]) ).
tff(528,plain,
multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))))),
inference(monotonicity,[status(thm)],[527,503]) ).
tff(529,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))))) = multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[528]) ).
tff(530,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))))) = inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(531,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))))) = inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),
inference(unit_resolution,[status(thm)],[530,7]) ).
tff(532,plain,
inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))))),
inference(symmetry,[status(thm)],[531]) ).
tff(533,plain,
inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))),
inference(transitivity,[status(thm)],[532,529,435,423]) ).
tff(534,plain,
multiply(inverse(a1),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),
inference(monotonicity,[status(thm)],[431,533]) ).
tff(535,plain,
multiply(inverse(a1),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),
inference(transitivity,[status(thm)],[534,433]) ).
tff(536,plain,
inverse(multiply(inverse(a1),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))))) = inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))))),
inference(monotonicity,[status(thm)],[535]) ).
tff(537,plain,
inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))))) = inverse(multiply(inverse(a1),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))))),
inference(symmetry,[status(thm)],[536]) ).
tff(538,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(539,plain,
multiply(multiply(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))))),
inference(unit_resolution,[status(thm)],[538,7]) ).
tff(540,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(a1,inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(541,plain,
multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(a1,inverse(a1))),
inference(unit_resolution,[status(thm)],[540,7]) ).
tff(542,plain,
inverse(multiply(inverse(a1),a1)) = inverse(multiply(a1,inverse(a1))),
inference(transitivity,[status(thm)],[490,386,389,489,486,228]) ).
tff(543,plain,
multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))) = multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(monotonicity,[status(thm)],[542]) ).
tff(544,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))) = multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(symmetry,[status(thm)],[543]) ).
tff(545,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))),
inference(monotonicity,[status(thm)],[544]) ).
tff(546,plain,
inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))) = inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))),
inference(monotonicity,[status(thm)],[545]) ).
tff(547,plain,
inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))) = inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))),
inference(symmetry,[status(thm)],[546]) ).
tff(548,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[545,420]) ).
tff(549,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))),
inference(symmetry,[status(thm)],[548]) ).
tff(550,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(551,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),
inference(unit_resolution,[status(thm)],[550,7]) ).
tff(552,plain,
inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[551]) ).
tff(553,plain,
inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[552,549]) ).
tff(554,plain,
multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[553,547]) ).
tff(555,plain,
multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[554,541,55,83]) ).
tff(556,plain,
multiply(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[555]) ).
tff(557,plain,
multiply(multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[556]) ).
tff(558,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))))) = inverse(multiply(a1,inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(559,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))))) = inverse(multiply(a1,inverse(a1))),
inference(unit_resolution,[status(thm)],[558,7]) ).
tff(560,plain,
multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(transitivity,[status(thm)],[192,171,430,427]) ).
tff(561,plain,
multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),
inference(monotonicity,[status(thm)],[560,423]) ).
tff(562,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))) = multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),
inference(symmetry,[status(thm)],[561]) ).
tff(563,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))) = inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(564,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))) = inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),
inference(unit_resolution,[status(thm)],[563,7]) ).
tff(565,plain,
inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),
inference(symmetry,[status(thm)],[564]) ).
tff(566,plain,
inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))) = multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),
inference(transitivity,[status(thm)],[565,562]) ).
tff(567,plain,
multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))))),
inference(monotonicity,[status(thm)],[566]) ).
tff(568,plain,
multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[567,559,55,83]) ).
tff(569,plain,
multiply(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[568]) ).
tff(570,plain,
multiply(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[569,557]) ).
tff(571,plain,
multiply(multiply(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[570]) ).
tff(572,plain,
multiply(multiply(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[571]) ).
tff(573,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(574,plain,
multiply(multiply(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))),
inference(unit_resolution,[status(thm)],[573,7]) ).
tff(575,plain,
inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))) = multiply(multiply(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[574]) ).
tff(576,plain,
inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))) = inverse(multiply(inverse(a1),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))))),
inference(transitivity,[status(thm)],[575,572,539,537]) ).
tff(577,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = inverse(a1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(578,plain,
multiply(multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = inverse(a1),
inference(unit_resolution,[status(thm)],[577,7]) ).
tff(579,plain,
multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(a1)) = inverse(multiply(inverse(a1),a1)),
inference(transitivity,[status(thm)],[262,25]) ).
tff(580,plain,
multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))) = multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(monotonicity,[status(thm)],[579]) ).
tff(581,plain,
multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))) = multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(symmetry,[status(thm)],[580]) ).
tff(582,plain,
multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(monotonicity,[status(thm)],[581]) ).
tff(583,plain,
multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(multiply(a1,inverse(a1)),inverse(a1)),
inference(transitivity,[status(thm)],[582,578,190,187,174]) ).
tff(584,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(a1,inverse(a1)),inverse(a1)),inverse(multiply(a1,inverse(a1)))),
inference(monotonicity,[status(thm)],[583]) ).
tff(585,plain,
multiply(multiply(multiply(a1,inverse(a1)),inverse(a1)),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),
inference(symmetry,[status(thm)],[584]) ).
tff(586,plain,
multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[192,585]) ).
tff(587,plain,
multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[586]) ).
tff(588,plain,
multiply(multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[587]) ).
tff(589,plain,
inverse(a1) = multiply(multiply(multiply(a1,inverse(a1)),inverse(a1)),inverse(multiply(a1,inverse(a1)))),
inference(symmetry,[status(thm)],[171]) ).
tff(590,plain,
inverse(a1) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[589,585]) ).
tff(591,plain,
multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[590]) ).
tff(592,plain,
multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[591,588]) ).
tff(593,plain,
multiply(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[592]) ).
tff(594,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[593]) ).
tff(595,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(a1,inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(596,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(a1,inverse(a1))),
inference(unit_resolution,[status(thm)],[595,7]) ).
tff(597,plain,
inverse(multiply(a1,inverse(a1))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[596]) ).
tff(598,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),
inference(transitivity,[status(thm)],[82,42,597,594]) ).
tff(599,plain,
multiply(multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))))),
inference(monotonicity,[status(thm)],[598,576]) ).
tff(600,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[599]) ).
tff(601,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(602,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))),
inference(unit_resolution,[status(thm)],[601,7]) ).
tff(603,plain,
inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))))),
inference(symmetry,[status(thm)],[602]) ).
tff(604,plain,
multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[554,541,40,37]) ).
tff(605,plain,
inverse(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(monotonicity,[status(thm)],[604]) ).
tff(606,plain,
inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = inverse(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),
inference(symmetry,[status(thm)],[605]) ).
tff(607,plain,
inverse(multiply(a1,inverse(a1))) = inverse(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),
inference(transitivity,[status(thm)],[55,54,15,606]) ).
tff(608,plain,
inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))) = multiply(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[512,557]) ).
tff(609,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[608,607]) ).
tff(610,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(a1,inverse(a1)))) = multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[609,574,603,600,86]) ).
tff(611,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(a1,inverse(a1))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),
inference(monotonicity,[status(thm)],[610]) ).
tff(612,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(a1,inverse(a1))))),
inference(symmetry,[status(thm)],[611]) ).
tff(613,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(614,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),
inference(unit_resolution,[status(thm)],[613,7]) ).
tff(615,plain,
multiply(multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[591]) ).
tff(616,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(617,plain,
multiply(multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),
inference(unit_resolution,[status(thm)],[616,7]) ).
tff(618,plain,
inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))) = multiply(multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[617]) ).
tff(619,plain,
multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))) = multiply(a1,inverse(multiply(inverse(a1),a1))),
inference(symmetry,[status(thm)],[21]) ).
tff(620,plain,
inverse(multiply(inverse(a1),a1)) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(transitivity,[status(thm)],[490,386,389]) ).
tff(621,plain,
multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))) = multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[17,620]) ).
tff(622,plain,
multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),
inference(symmetry,[status(thm)],[621]) ).
tff(623,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(624,plain,
multiply(multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),
inference(unit_resolution,[status(thm)],[623,7]) ).
tff(625,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(a1)),
inference(transitivity,[status(thm)],[401,383,190,187,273]) ).
tff(626,plain,
multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(a1)),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(a1)))),
inference(monotonicity,[status(thm)],[625,265]) ).
tff(627,plain,
multiply(multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(a1)),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(a1)))) = multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[626]) ).
tff(628,plain,
inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))) = multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[350,627]) ).
tff(629,plain,
multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[628,405]) ).
tff(630,plain,
multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[629,624,65,93]) ).
tff(631,plain,
inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(monotonicity,[status(thm)],[630]) ).
tff(632,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))),
inference(symmetry,[status(thm)],[631]) ).
tff(633,plain,
multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[629,624,65,414]) ).
tff(634,plain,
multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[633,405]) ).
tff(635,plain,
multiply(multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(symmetry,[status(thm)],[634]) ).
tff(636,plain,
inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))) = multiply(multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[400]) ).
tff(637,plain,
a1 = multiply(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(symmetry,[status(thm)],[254]) ).
tff(638,plain,
a1 = multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(transitivity,[status(thm)],[637,394,397,636,635]) ).
tff(639,plain,
multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(monotonicity,[status(thm)],[638,632]) ).
tff(640,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[639]) ).
tff(641,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(642,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),
inference(unit_resolution,[status(thm)],[641,7]) ).
tff(643,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(symmetry,[status(thm)],[642]) ).
tff(644,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(645,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))),
inference(unit_resolution,[status(thm)],[644,7]) ).
tff(646,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(647,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),
inference(unit_resolution,[status(thm)],[646,7]) ).
tff(648,plain,
multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[362,357,55,204]) ).
tff(649,plain,
multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[648,199]) ).
tff(650,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(symmetry,[status(thm)],[649]) ).
tff(651,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))) = multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(transitivity,[status(thm)],[219,650]) ).
tff(652,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(monotonicity,[status(thm)],[651,632]) ).
tff(653,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[652]) ).
tff(654,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(655,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(unit_resolution,[status(thm)],[654,7]) ).
tff(656,plain,
inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(symmetry,[status(thm)],[655]) ).
tff(657,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(658,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(unit_resolution,[status(thm)],[657,7]) ).
tff(659,plain,
inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[350,275]) ).
tff(660,plain,
multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[659]) ).
tff(661,plain,
multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(transitivity,[status(thm)],[660,282,169,166]) ).
tff(662,plain,
inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))),
inference(monotonicity,[status(thm)],[661]) ).
tff(663,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))) = inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))),
inference(symmetry,[status(thm)],[662]) ).
tff(664,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))) = inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))),
inference(transitivity,[status(thm)],[198,663]) ).
tff(665,plain,
multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[362,357,55,107]) ).
tff(666,plain,
multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[665,96]) ).
tff(667,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[666]) ).
tff(668,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(transitivity,[status(thm)],[119,667]) ).
tff(669,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(monotonicity,[status(thm)],[668,664]) ).
tff(670,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(transitivity,[status(thm)],[669,658,656,653]) ).
tff(671,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))),
inference(monotonicity,[status(thm)],[670]) ).
tff(672,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))),
inference(symmetry,[status(thm)],[671]) ).
tff(673,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[340,302,55,204]) ).
tff(674,plain,
multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[673,199]) ).
tff(675,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(symmetry,[status(thm)],[674]) ).
tff(676,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(transitivity,[status(thm)],[219,675]) ).
tff(677,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(monotonicity,[status(thm)],[676,672]) ).
tff(678,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[677,647,65,93]) ).
tff(679,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(monotonicity,[status(thm)],[678]) ).
tff(680,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))),
inference(symmetry,[status(thm)],[679]) ).
tff(681,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[244,228,55,107]) ).
tff(682,plain,
multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[681,96]) ).
tff(683,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[682]) ).
tff(684,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(transitivity,[status(thm)],[219,504]) ).
tff(685,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(monotonicity,[status(thm)],[684]) ).
tff(686,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(transitivity,[status(thm)],[685,488,119,683]) ).
tff(687,plain,
multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(monotonicity,[status(thm)],[686]) ).
tff(688,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(symmetry,[status(thm)],[687]) ).
tff(689,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(690,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))),
inference(unit_resolution,[status(thm)],[689,7]) ).
tff(691,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(symmetry,[status(thm)],[690]) ).
tff(692,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(transitivity,[status(thm)],[186,189,369,477,250,691,688]) ).
tff(693,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),
inference(monotonicity,[status(thm)],[692,680]) ).
tff(694,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(transitivity,[status(thm)],[693,645,481,169,166]) ).
tff(695,plain,
inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))),
inference(monotonicity,[status(thm)],[694]) ).
tff(696,plain,
a1 = multiply(a1,inverse(multiply(inverse(a1),a1))),
inference(transitivity,[status(thm)],[637,394,397,695,197,643,640,622,619]) ).
tff(697,plain,
multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))) = multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(monotonicity,[status(thm)],[696]) ).
tff(698,plain,
multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))) = multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(symmetry,[status(thm)],[697]) ).
tff(699,plain,
multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))) = multiply(multiply(a1,inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(monotonicity,[status(thm)],[619]) ).
tff(700,plain,
multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))) = multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(transitivity,[status(thm)],[699,698]) ).
tff(701,plain,
inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))) = inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),
inference(monotonicity,[status(thm)],[700]) ).
tff(702,plain,
inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))) = inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),
inference(symmetry,[status(thm)],[701]) ).
tff(703,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[445,448,702,618,615]) ).
tff(704,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))) = inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),
inference(monotonicity,[status(thm)],[703]) ).
tff(705,plain,
inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))),
inference(symmetry,[status(thm)],[704]) ).
tff(706,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))) = multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[435]) ).
tff(707,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))))),
inference(transitivity,[status(thm)],[422,706,528,531,705,474]) ).
tff(708,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(a1,inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(709,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(a1,inverse(a1))),
inference(unit_resolution,[status(thm)],[708,7]) ).
tff(710,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[99,83]) ).
tff(711,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[710]) ).
tff(712,plain,
multiply(multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[711]) ).
tff(713,plain,
inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[512,712]) ).
tff(714,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[713]) ).
tff(715,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(a1,inverse(a1))),
inference(transitivity,[status(thm)],[714,709]) ).
tff(716,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),
inference(monotonicity,[status(thm)],[715,481]) ).
tff(717,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(symmetry,[status(thm)],[716]) ).
tff(718,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(transitivity,[status(thm)],[426,429,190,187,717]) ).
tff(719,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))))),
inference(monotonicity,[status(thm)],[718,707]) ).
tff(720,plain,
inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(a1,inverse(a1))))),
inference(transitivity,[status(thm)],[565,719,614,612]) ).
tff(721,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[714,709,40,45]) ).
tff(722,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[721,56]) ).
tff(723,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),
inference(symmetry,[status(thm)],[722]) ).
tff(724,plain,
inverse(multiply(a1,inverse(a1))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[55,723]) ).
tff(725,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[724,720]) ).
tff(726,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(a1,inverse(a1)))))) = multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(symmetry,[status(thm)],[725]) ).
tff(727,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(728,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),
inference(unit_resolution,[status(thm)],[727,7]) ).
tff(729,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[728]) ).
tff(730,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(transitivity,[status(thm)],[729,726,74]) ).
tff(731,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(monotonicity,[status(thm)],[730]) ).
tff(732,plain,
multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(symmetry,[status(thm)],[731]) ).
tff(733,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(734,plain,
multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1)),
inference(unit_resolution,[status(thm)],[733,7]) ).
tff(735,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1)) = multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(symmetry,[status(thm)],[734]) ).
tff(736,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(737,plain,
multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1)),
inference(unit_resolution,[status(thm)],[736,7]) ).
tff(738,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))) = multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[71,11,40,37]) ).
tff(739,plain,
inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1)))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(monotonicity,[status(thm)],[738]) ).
tff(740,plain,
inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1)))),
inference(symmetry,[status(thm)],[739]) ).
tff(741,plain,
inverse(multiply(a1,inverse(a1))) = inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1)))),
inference(transitivity,[status(thm)],[55,54,15,740]) ).
tff(742,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))) = multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),
inference(monotonicity,[status(thm)],[72]) ).
tff(743,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),
inference(symmetry,[status(thm)],[742]) ).
tff(744,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))),
inference(monotonicity,[status(thm)],[743,741]) ).
tff(745,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(a1,inverse(a1)))) = multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(transitivity,[status(thm)],[744,737,735,732]) ).
tff(746,plain,
inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(a1,inverse(a1))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))),
inference(monotonicity,[status(thm)],[745]) ).
tff(747,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))) = inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(a1,inverse(a1))))),
inference(symmetry,[status(thm)],[746]) ).
tff(748,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(749,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1)),
inference(unit_resolution,[status(thm)],[748,7]) ).
tff(750,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(multiply(inverse(a1),a1),a1),b1),inverse(multiply(multiply(inverse(a1),a1),b1))) = a1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(751,plain,
multiply(multiply(multiply(multiply(inverse(a1),a1),a1),b1),inverse(multiply(multiply(inverse(a1),a1),b1))) = a1,
inference(unit_resolution,[status(thm)],[750,7]) ).
tff(752,plain,
a1 = inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))),
inference(transitivity,[status(thm)],[637,394,397,260]) ).
tff(753,plain,
multiply(inverse(a1),a1) = multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(monotonicity,[status(thm)],[284,752]) ).
tff(754,plain,
multiply(inverse(a1),a1) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),
inference(transitivity,[status(thm)],[753,256]) ).
tff(755,plain,
multiply(multiply(inverse(a1),a1),b1) = multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),
inference(monotonicity,[status(thm)],[754]) ).
tff(756,plain,
inverse(multiply(multiply(inverse(a1),a1),b1)) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1)),
inference(monotonicity,[status(thm)],[755]) ).
tff(757,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1)) = inverse(multiply(multiply(inverse(a1),a1),b1)),
inference(symmetry,[status(thm)],[756]) ).
tff(758,plain,
multiply(multiply(multiply(multiply(inverse(a1),a1),a1),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))) = multiply(multiply(multiply(multiply(inverse(a1),a1),a1),b1),inverse(multiply(multiply(inverse(a1),a1),b1))),
inference(monotonicity,[status(thm)],[757]) ).
tff(759,plain,
multiply(multiply(multiply(multiply(inverse(a1),a1),a1),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))) = multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(transitivity,[status(thm)],[758,751,637,394,397,695,197,125,122]) ).
tff(760,plain,
inverse(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1)))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))),
inference(monotonicity,[status(thm)],[759]) ).
tff(761,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))) = inverse(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1)))),
inference(symmetry,[status(thm)],[760]) ).
tff(762,plain,
inverse(a1) = inverse(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1)))),
inference(transitivity,[status(thm)],[369,477,250,761]) ).
tff(763,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))),b1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1))) = inverse(multiply(a1,inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(764,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))),b1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1))) = inverse(multiply(a1,inverse(a1))),
inference(unit_resolution,[status(thm)],[763,7]) ).
tff(765,plain,
inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(symmetry,[status(thm)],[88]) ).
tff(766,plain,
multiply(inverse(a1),a1) = multiply(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(transitivity,[status(thm)],[753,256,765,418,141,144,158,160,129,289,288]) ).
tff(767,plain,
multiply(multiply(inverse(a1),a1),a1) = multiply(multiply(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(monotonicity,[status(thm)],[766,752]) ).
tff(768,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(inverse(a1),a1),a1),
inference(symmetry,[status(thm)],[767]) ).
tff(769,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))) = inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))),
inference(symmetry,[status(thm)],[695]) ).
tff(770,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(inverse(a1),a1),a1),
inference(transitivity,[status(thm)],[221,211,198,769,398,768]) ).
tff(771,plain,
multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))),b1) = multiply(multiply(multiply(inverse(a1),a1),a1),b1),
inference(monotonicity,[status(thm)],[770]) ).
tff(772,plain,
multiply(multiply(multiply(inverse(a1),a1),a1),b1) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))),b1),
inference(symmetry,[status(thm)],[771]) ).
tff(773,plain,
multiply(multiply(multiply(multiply(inverse(a1),a1),a1),b1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))),b1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1))),
inference(monotonicity,[status(thm)],[772]) ).
tff(774,plain,
multiply(multiply(multiply(multiply(inverse(a1),a1),a1),b1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1))) = inverse(multiply(a1,inverse(a1))),
inference(transitivity,[status(thm)],[773,764]) ).
tff(775,plain,
multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),b1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))) = multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),
inference(monotonicity,[status(thm)],[774]) ).
tff(776,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))) = multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),b1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),
inference(symmetry,[status(thm)],[775]) ).
tff(777,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(a1)) = multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),b1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))),
inference(monotonicity,[status(thm)],[776,762]) ).
tff(778,plain,
multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),b1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(a1)),
inference(symmetry,[status(thm)],[777]) ).
tff(779,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),b1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(780,plain,
multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),b1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1)),
inference(unit_resolution,[status(thm)],[779,7]) ).
tff(781,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1)) = multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),b1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))),
inference(symmetry,[status(thm)],[780]) ).
tff(782,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1)) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(a1)),
inference(transitivity,[status(thm)],[781,778]) ).
tff(783,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(monotonicity,[status(thm)],[782]) ).
tff(784,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(transitivity,[status(thm)],[783,749,735,732]) ).
tff(785,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))),
inference(monotonicity,[status(thm)],[784]) ).
tff(786,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))) = inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(a1,inverse(a1))))),
inference(transitivity,[status(thm)],[785,747]) ).
tff(787,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))) = inverse(multiply(a1,inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(788,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))) = inverse(multiply(a1,inverse(a1))),
inference(unit_resolution,[status(thm)],[787,7]) ).
tff(789,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))) = multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),
inference(monotonicity,[status(thm)],[110]) ).
tff(790,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),
inference(symmetry,[status(thm)],[789]) ).
tff(791,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))),
inference(monotonicity,[status(thm)],[790]) ).
tff(792,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[791,788,40,45]) ).
tff(793,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[792,56]) ).
tff(794,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))),inverse(multiply(a1,inverse(a1)))),
inference(symmetry,[status(thm)],[793]) ).
tff(795,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(a1)),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))) = inverse(a1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(796,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(a1)),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))) = inverse(a1),
inference(unit_resolution,[status(thm)],[795,7]) ).
tff(797,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),
inference(symmetry,[status(thm)],[719]) ).
tff(798,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))))),
inference(symmetry,[status(thm)],[614]) ).
tff(799,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))) = inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),
inference(transitivity,[status(thm)],[798,797,564]) ).
tff(800,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(monotonicity,[status(thm)],[799]) ).
tff(801,plain,
inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))))) = inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),
inference(monotonicity,[status(thm)],[800]) ).
tff(802,plain,
inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))) = inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))))),
inference(symmetry,[status(thm)],[801]) ).
tff(803,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(804,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))),
inference(unit_resolution,[status(thm)],[803,7]) ).
tff(805,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(a1,inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(806,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(a1,inverse(a1))),
inference(unit_resolution,[status(thm)],[805,7]) ).
tff(807,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(transitivity,[status(thm)],[221,211,219,650]) ).
tff(808,plain,
multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(monotonicity,[status(thm)],[807,632]) ).
tff(809,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[808]) ).
tff(810,plain,
inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(transitivity,[status(thm)],[656,809]) ).
tff(811,plain,
multiply(inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(monotonicity,[status(thm)],[810]) ).
tff(812,plain,
multiply(inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[811,806,40,37]) ).
tff(813,plain,
inverse(multiply(inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(monotonicity,[status(thm)],[812]) ).
tff(814,plain,
inverse(multiply(inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(transitivity,[status(thm)],[813,343]) ).
tff(815,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(816,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),
inference(unit_resolution,[status(thm)],[815,7]) ).
tff(817,plain,
multiply(multiply(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(a1)),inverse(multiply(multiply(multiply(multiply(multiply(inverse(a1),a1),a1),inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1))),inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[331]) ).
tff(818,plain,
inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))) = inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))),
inference(transitivity,[status(thm)],[350,817,333]) ).
tff(819,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))) = multiply(multiply(multiply(a1,inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(monotonicity,[status(thm)],[164,818]) ).
tff(820,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(a1)),
inference(transitivity,[status(thm)],[819,168,190,187,112]) ).
tff(821,plain,
multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(monotonicity,[status(thm)],[820]) ).
tff(822,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(symmetry,[status(thm)],[821]) ).
tff(823,plain,
multiply(inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(transitivity,[status(thm)],[811,806,226,822]) ).
tff(824,plain,
multiply(multiply(inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(monotonicity,[status(thm)],[823,672]) ).
tff(825,plain,
multiply(multiply(inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[824,816,350,347]) ).
tff(826,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[825,814]) ).
tff(827,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),
inference(symmetry,[status(thm)],[826]) ).
tff(828,plain,
inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[336]) ).
tff(829,plain,
inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))),
inference(transitivity,[status(thm)],[350,817,333,828,827,804,672]) ).
tff(830,plain,
inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(transitivity,[status(thm)],[765,418,141,144,158,160,129,226,822]) ).
tff(831,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(monotonicity,[status(thm)],[830,829]) ).
tff(832,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),
inference(symmetry,[status(thm)],[831]) ).
tff(833,plain,
inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(symmetry,[status(thm)],[816]) ).
tff(834,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))) = inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(835,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))) = inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))),
inference(unit_resolution,[status(thm)],[834,7]) ).
tff(836,plain,
multiply(multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(symmetry,[status(thm)],[479]) ).
tff(837,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(838,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))),
inference(unit_resolution,[status(thm)],[837,7]) ).
tff(839,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1))))),
inference(symmetry,[status(thm)],[326]) ).
tff(840,plain,
inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1))))),
inference(transitivity,[status(thm)],[338,337,320,839]) ).
tff(841,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(transitivity,[status(thm)],[121,124,219,218]) ).
tff(842,plain,
multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(monotonicity,[status(thm)],[841,215]) ).
tff(843,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(a1,inverse(a1)))),
inference(symmetry,[status(thm)],[842]) ).
tff(844,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(symmetry,[status(thm)],[211]) ).
tff(845,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[844,843]) ).
tff(846,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[845,840]) ).
tff(847,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(transitivity,[status(thm)],[846,838,636,836]) ).
tff(848,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))),
inference(monotonicity,[status(thm)],[847]) ).
tff(849,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(symmetry,[status(thm)],[848]) ).
tff(850,plain,
inverse(a1) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))),
inference(symmetry,[status(thm)],[481]) ).
tff(851,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(transitivity,[status(thm)],[251,248,90,850,849]) ).
tff(852,plain,
inverse(a1) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))),
inference(transitivity,[status(thm)],[369,477,250]) ).
tff(853,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(a1)) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),
inference(monotonicity,[status(thm)],[243,852]) ).
tff(854,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(a1)) = multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[853,228,55,59]) ).
tff(855,plain,
multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[854]) ).
tff(856,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[855]) ).
tff(857,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))) = multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(transitivity,[status(thm)],[819,168,283,280]) ).
tff(858,plain,
multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(monotonicity,[status(thm)],[857,260]) ).
tff(859,plain,
multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[858,256,65,856]) ).
tff(860,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[859,851]) ).
tff(861,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),
inference(symmetry,[status(thm)],[860]) ).
tff(862,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = inverse(a1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(863,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))) = inverse(a1),
inference(unit_resolution,[status(thm)],[862,7]) ).
tff(864,plain,
inverse(a1) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[863]) ).
tff(865,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(a1)),b1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1))) = inverse(a1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(866,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(a1)),b1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1))) = inverse(a1),
inference(unit_resolution,[status(thm)],[865,7]) ).
tff(867,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(a1)) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),
inference(transitivity,[status(thm)],[853,228,176,175,147,145,142,419,88]) ).
tff(868,plain,
multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(a1)),b1) = multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),
inference(monotonicity,[status(thm)],[867]) ).
tff(869,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(a1)),b1),
inference(symmetry,[status(thm)],[868]) ).
tff(870,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(a1)),b1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1))),
inference(monotonicity,[status(thm)],[869]) ).
tff(871,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1))) = multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),
inference(transitivity,[status(thm)],[870,866,864,861,835,833,832]) ).
tff(872,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(monotonicity,[status(thm)],[871,799]) ).
tff(873,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[872]) ).
tff(874,plain,
multiply(multiply(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(a1,inverse(a1)))),
inference(symmetry,[status(thm)],[609]) ).
tff(875,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(876,plain,
multiply(multiply(multiply(inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))),
inference(unit_resolution,[status(thm)],[875,7]) ).
tff(877,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(878,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),
inference(unit_resolution,[status(thm)],[877,7]) ).
tff(879,plain,
inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))) = inverse(multiply(inverse(a1),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))))),
inference(transitivity,[status(thm)],[546,575,572,539,537]) ).
tff(880,plain,
inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))))),
inference(transitivity,[status(thm)],[705,474]) ).
tff(881,plain,
multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(transitivity,[status(thm)],[201,109,519,518,517]) ).
tff(882,plain,
multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))))),
inference(monotonicity,[status(thm)],[881,880]) ).
tff(883,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))))) = multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[882]) ).
tff(884,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(885,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),
inference(unit_resolution,[status(thm)],[884,7]) ).
tff(886,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[714,709,40,37]) ).
tff(887,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(monotonicity,[status(thm)],[886]) ).
tff(888,plain,
inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))))),
inference(symmetry,[status(thm)],[887]) ).
tff(889,plain,
inverse(multiply(a1,inverse(a1))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))))),
inference(transitivity,[status(thm)],[55,54,15,888]) ).
tff(890,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[465,468,512,86]) ).
tff(891,plain,
inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),
inference(monotonicity,[status(thm)],[890]) ).
tff(892,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))) = inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))))),
inference(symmetry,[status(thm)],[891]) ).
tff(893,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))) = multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[524,521,55,204]) ).
tff(894,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[893,199]) ).
tff(895,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(symmetry,[status(thm)],[894]) ).
tff(896,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(transitivity,[status(thm)],[514,506,219,895]) ).
tff(897,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(monotonicity,[status(thm)],[896,892]) ).
tff(898,plain,
multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[897]) ).
tff(899,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(900,plain,
multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))),
inference(unit_resolution,[status(thm)],[899,7]) ).
tff(901,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))) = multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(symmetry,[status(thm)],[900]) ).
tff(902,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(903,plain,
multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))),
inference(unit_resolution,[status(thm)],[902,7]) ).
tff(904,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))) = inverse(multiply(a1,inverse(a1))),
inference(transitivity,[status(thm)],[524,521]) ).
tff(905,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))) = multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(monotonicity,[status(thm)],[904]) ).
tff(906,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(symmetry,[status(thm)],[905]) ).
tff(907,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(monotonicity,[status(thm)],[906]) ).
tff(908,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),
inference(transitivity,[status(thm)],[907,903,901,898]) ).
tff(909,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))))),
inference(monotonicity,[status(thm)],[908,889]) ).
tff(910,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),
inference(transitivity,[status(thm)],[909,885,532,883]) ).
tff(911,plain,
multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(a1),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))))),
inference(monotonicity,[status(thm)],[910,879]) ).
tff(912,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),
inference(symmetry,[status(thm)],[909]) ).
tff(913,plain,
inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))))),
inference(symmetry,[status(thm)],[885]) ).
tff(914,plain,
inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[913,912]) ).
tff(915,plain,
multiply(inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[914,547]) ).
tff(916,plain,
multiply(inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(transitivity,[status(thm)],[915,911,878,125,122]) ).
tff(917,plain,
inverse(multiply(inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))),
inference(monotonicity,[status(thm)],[916]) ).
tff(918,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))) = inverse(multiply(inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),
inference(symmetry,[status(thm)],[917]) ).
tff(919,plain,
inverse(a1) = inverse(multiply(inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),
inference(transitivity,[status(thm)],[369,477,250,918]) ).
tff(920,plain,
inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))))),
inference(symmetry,[status(thm)],[835]) ).
tff(921,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))) = multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(transitivity,[status(thm)],[831,816,920,860,863,169,166]) ).
tff(922,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))),
inference(monotonicity,[status(thm)],[921]) ).
tff(923,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(924,plain,
multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))))),
inference(unit_resolution,[status(thm)],[923,7]) ).
tff(925,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))))) = inverse(multiply(a1,inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(926,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))))) = inverse(multiply(a1,inverse(a1))),
inference(unit_resolution,[status(thm)],[925,7]) ).
tff(927,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))) = multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),
inference(monotonicity,[status(thm)],[68]) ).
tff(928,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),
inference(symmetry,[status(thm)],[927]) ).
tff(929,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))))),
inference(monotonicity,[status(thm)],[928]) ).
tff(930,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))))) = inverse(multiply(a1,inverse(a1))),
inference(transitivity,[status(thm)],[929,926]) ).
tff(931,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))) = multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(monotonicity,[status(thm)],[930]) ).
tff(932,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(symmetry,[status(thm)],[931]) ).
tff(933,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(monotonicity,[status(thm)],[932]) ).
tff(934,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(transitivity,[status(thm)],[933,924,922,197,219,218]) ).
tff(935,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(monotonicity,[status(thm)],[934,215]) ).
tff(936,plain,
multiply(multiply(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(a1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),
inference(symmetry,[status(thm)],[935]) ).
tff(937,plain,
multiply(inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[915,911,878,844,936]) ).
tff(938,plain,
multiply(multiply(inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[937,547]) ).
tff(939,plain,
multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[938]) ).
tff(940,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(941,plain,
multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),
inference(unit_resolution,[status(thm)],[940,7]) ).
tff(942,plain,
inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))) = multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[941]) ).
tff(943,plain,
inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))) = multiply(multiply(inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[942,939]) ).
tff(944,plain,
multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(a1)) = multiply(multiply(multiply(inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[943,919]) ).
tff(945,plain,
multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(a1)) = multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[944,876,575,874]) ).
tff(946,plain,
inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(a1))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(a1,inverse(a1))))),
inference(monotonicity,[status(thm)],[945]) ).
tff(947,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(a1,inverse(a1))))) = inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(a1))),
inference(symmetry,[status(thm)],[946]) ).
tff(948,plain,
inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))) = inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(a1))),
inference(transitivity,[status(thm)],[565,719,614,612,947]) ).
tff(949,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(a1,inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(950,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(a1,inverse(a1))),
inference(unit_resolution,[status(thm)],[949,7]) ).
tff(951,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[221,936]) ).
tff(952,plain,
multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[951,547]) ).
tff(953,plain,
multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[952]) ).
tff(954,plain,
inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[942,953]) ).
tff(955,plain,
multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[954]) ).
tff(956,plain,
multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(a1,inverse(a1))),
inference(transitivity,[status(thm)],[955,950]) ).
tff(957,plain,
multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(a1)) = multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),
inference(monotonicity,[status(thm)],[956]) ).
tff(958,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)) = multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(a1)),
inference(symmetry,[status(thm)],[957]) ).
tff(959,plain,
multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))) = multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(a1)),
inference(transitivity,[status(thm)],[831,816,920,860,863,190,187,958]) ).
tff(960,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))) = multiply(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(a1)),inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(a1)))),
inference(monotonicity,[status(thm)],[959,948]) ).
tff(961,plain,
multiply(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(a1)),inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(a1)))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(symmetry,[status(thm)],[960]) ).
tff(962,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(a1)),inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(a1)))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(963,plain,
multiply(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(a1)),inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(a1)))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),
inference(unit_resolution,[status(thm)],[962,7]) ).
tff(964,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))) = multiply(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(a1)),inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(a1)))),
inference(symmetry,[status(thm)],[963]) ).
tff(965,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(966,plain,
multiply(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),
inference(unit_resolution,[status(thm)],[965,7]) ).
tff(967,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(968,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),
inference(unit_resolution,[status(thm)],[967,7]) ).
tff(969,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[206,127,844,936]) ).
tff(970,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[969,547]) ).
tff(971,plain,
multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[970]) ).
tff(972,plain,
inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[942,971]) ).
tff(973,plain,
multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),
inference(monotonicity,[status(thm)],[972]) ).
tff(974,plain,
multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))))))),
inference(transitivity,[status(thm)],[973,968,125,122]) ).
tff(975,plain,
inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))),
inference(monotonicity,[status(thm)],[974]) ).
tff(976,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))) = inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))))),
inference(symmetry,[status(thm)],[975]) ).
tff(977,plain,
inverse(a1) = inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))))),
inference(transitivity,[status(thm)],[369,477,250,976]) ).
tff(978,plain,
multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(monotonicity,[status(thm)],[956,799]) ).
tff(979,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))) = multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),
inference(symmetry,[status(thm)],[978]) ).
tff(980,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))) = multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),
inference(transitivity,[status(thm)],[729,726,979]) ).
tff(981,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(a1)) = multiply(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(a1),a1))))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))))),
inference(monotonicity,[status(thm)],[980,977]) ).
tff(982,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(a1)) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),
inference(transitivity,[status(thm)],[981,966,964,961,873]) ).
tff(983,plain,
multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(a1)),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))))),
inference(monotonicity,[status(thm)],[982,802]) ).
tff(984,plain,
multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(a1)),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(symmetry,[status(thm)],[983]) ).
tff(985,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(986,plain,
multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1)),
inference(unit_resolution,[status(thm)],[985,7]) ).
tff(987,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1)) = multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))))),
inference(symmetry,[status(thm)],[986]) ).
tff(988,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1)) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(a1)),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(transitivity,[status(thm)],[987,984]) ).
tff(989,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1)),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(a1)),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),
inference(monotonicity,[status(thm)],[988]) ).
tff(990,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1)),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(a1)),
inference(transitivity,[status(thm)],[989,796,190,187,112]) ).
tff(991,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1)),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(monotonicity,[status(thm)],[990]) ).
tff(992,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1)),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[991,109,55,794]) ).
tff(993,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1)),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))) = multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[992,786]) ).
tff(994,plain,
multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1)),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),b1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(symmetry,[status(thm)],[993]) ).
tff(995,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(996,plain,
multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1)))),
inference(unit_resolution,[status(thm)],[995,7]) ).
tff(997,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1)))) = multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[996]) ).
tff(998,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1)))) = inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(a1,inverse(a1))))),
inference(transitivity,[status(thm)],[997,994,9,747]) ).
tff(999,plain,
multiply(inverse(multiply(a1,inverse(a1))),b1) = multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),
inference(monotonicity,[status(thm)],[420]) ).
tff(1000,plain,
multiply(inverse(multiply(a1,inverse(a1))),b1) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))),b1),
inference(transitivity,[status(thm)],[999,70]) ).
tff(1001,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),
inference(monotonicity,[status(thm)],[1000]) ).
tff(1002,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[1001,11,55,794]) ).
tff(1003,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))) = multiply(multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[1002,998]) ).
tff(1004,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))) = b1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1005,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))) = b1,
inference(unit_resolution,[status(thm)],[1004,7]) ).
tff(1006,plain,
b1 = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))),
inference(symmetry,[status(thm)],[1005]) ).
tff(1007,plain,
b1 = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))))),
inference(transitivity,[status(thm)],[1006,1003,994,9]) ).
tff(1008,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(a1)),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(a1)))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1009,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(a1)),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(a1)))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),
inference(unit_resolution,[status(thm)],[1008,7]) ).
tff(1010,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(a1)) = multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[853,228,40,37]) ).
tff(1011,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(a1))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(monotonicity,[status(thm)],[1010]) ).
tff(1012,plain,
inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(a1))),
inference(symmetry,[status(thm)],[1011]) ).
tff(1013,plain,
inverse(multiply(a1,inverse(a1))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(a1))),
inference(transitivity,[status(thm)],[55,54,15,1012]) ).
tff(1014,plain,
inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))))))) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1))))),
inference(symmetry,[status(thm)],[223]) ).
tff(1015,plain,
inverse(a1) = inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1))))),
inference(transitivity,[status(thm)],[369,477,250,1014]) ).
tff(1016,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),
inference(transitivity,[status(thm)],[219,895]) ).
tff(1017,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)))))),
inference(monotonicity,[status(thm)],[1016,892]) ).
tff(1018,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),
inference(transitivity,[status(thm)],[1017,898]) ).
tff(1019,plain,
multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))))),
inference(monotonicity,[status(thm)],[1018,889]) ).
tff(1020,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(a1),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1)))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),
inference(symmetry,[status(thm)],[1019]) ).
tff(1021,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[1017,900,706,528,531,913,1020]) ).
tff(1022,plain,
multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(a1)) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[1021,1015]) ).
tff(1023,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(a1)),
inference(symmetry,[status(thm)],[1022]) ).
tff(1024,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1025,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),
inference(unit_resolution,[status(thm)],[1024,7]) ).
tff(1026,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[1025]) ).
tff(1027,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(a1)),
inference(transitivity,[status(thm)],[1026,1023]) ).
tff(1028,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1)))))))),inverse(a1)),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))),inverse(a1)))),
inference(monotonicity,[status(thm)],[1027,1013]) ).
tff(1029,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),
inference(transitivity,[status(thm)],[1028,1009,729,726,74]) ).
tff(1030,plain,
multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(monotonicity,[status(thm)],[1029]) ).
tff(1031,plain,
multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(symmetry,[status(thm)],[1030]) ).
tff(1032,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1033,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1)),
inference(unit_resolution,[status(thm)],[1032,7]) ).
tff(1034,plain,
multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(a1,inverse(a1)))),
inference(symmetry,[status(thm)],[744]) ).
tff(1035,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1)) = multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))),
inference(symmetry,[status(thm)],[737]) ).
tff(1036,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))) = multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1)))))),
inference(transitivity,[status(thm)],[99,42,40,37]) ).
tff(1037,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1))))) = inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))),
inference(monotonicity,[status(thm)],[1036]) ).
tff(1038,plain,
inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1))))),
inference(symmetry,[status(thm)],[1037]) ).
tff(1039,plain,
inverse(multiply(a1,inverse(a1))) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1))))),
inference(transitivity,[status(thm)],[55,54,15,1038]) ).
tff(1040,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1041,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1)),
inference(unit_resolution,[status(thm)],[1040,7]) ).
tff(1042,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),
inference(symmetry,[status(thm)],[1001]) ).
tff(1043,plain,
inverse(multiply(a1,inverse(a1))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),inverse(multiply(a1,inverse(a1)))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),
inference(symmetry,[status(thm)],[11]) ).
tff(1044,plain,
inverse(multiply(a1,inverse(a1))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),
inference(transitivity,[status(thm)],[1043,1042]) ).
tff(1045,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),b1),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))),
inference(monotonicity,[status(thm)],[1044]) ).
tff(1046,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))) = b1,
inference(transitivity,[status(thm)],[1045,1005]) ).
tff(1047,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1)))))) = inverse(b1),
inference(monotonicity,[status(thm)],[1046]) ).
tff(1048,plain,
inverse(b1) = inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1)))))),
inference(symmetry,[status(thm)],[1047]) ).
tff(1049,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))),
inference(symmetry,[status(thm)],[791]) ).
tff(1050,plain,
inverse(multiply(a1,inverse(a1))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))),
inference(symmetry,[status(thm)],[788]) ).
tff(1051,plain,
inverse(multiply(a1,inverse(a1))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))),
inference(transitivity,[status(thm)],[1050,1049]) ).
tff(1052,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(b1)) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))))))),
inference(monotonicity,[status(thm)],[1051,1048]) ).
tff(1053,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(b1)) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[1052,1041,1035,1034]) ).
tff(1054,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(b1)),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[1053,1039]) ).
tff(1055,plain,
multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(b1)),inverse(multiply(a1,inverse(a1)))) = multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[1054,1033,1035,1034]) ).
tff(1056,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(b1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))))) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))))),
inference(monotonicity,[status(thm)],[1055]) ).
tff(1057,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(b1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))))) = inverse(b1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1058,plain,
multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(b1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))))) = inverse(b1),
inference(unit_resolution,[status(thm)],[1057,7]) ).
tff(1059,plain,
inverse(b1) = multiply(multiply(multiply(inverse(multiply(a1,inverse(a1))),inverse(b1)),inverse(multiply(a1,inverse(a1)))),inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(a1,inverse(a1)))))),
inference(symmetry,[status(thm)],[1058]) ).
tff(1060,plain,
inverse(b1) = multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),
inference(transitivity,[status(thm)],[1059,1056,1033,735,1031]) ).
tff(1061,plain,
multiply(inverse(b1),b1) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),
inference(monotonicity,[status(thm)],[1060,1007]) ).
tff(1062,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))) = multiply(inverse(b1),b1),
inference(symmetry,[status(thm)],[1061]) ).
tff(1063,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B )
| ( multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))) = inverse(multiply(a1,inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1064,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))) = inverse(multiply(a1,inverse(a1))),
inference(unit_resolution,[status(thm)],[1063,7]) ).
tff(1065,plain,
inverse(multiply(a1,inverse(a1))) = multiply(multiply(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(a1,inverse(a1)))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))),inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(multiply(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))),inverse(multiply(a1,inverse(a1))))))),inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,inverse(a1))))),b1),inverse(multiply(inverse(b1),inverse(multiply(inverse(a1),a1))))))))),
inference(symmetry,[status(thm)],[1064]) ).
tff(1066,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(transitivity,[status(thm)],[753,256,765,418,141,144,158,160,129,1065,1062]) ).
tff(1067,plain,
( ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1) )
<=> ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1068,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_1) ).
tff(1069,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(modus_ponens,[status(thm)],[1068,1067]) ).
tff(1070,plain,
$false,
inference(unit_resolution,[status(thm)],[1069,1066]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP509-1 : TPTP v9.0.0. Released v2.6.0.
% 0.08/0.13 % 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 16:16:18 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.77/0.97 % SZS status Unsatisfiable
% 0.77/0.97 % SZS output start Proof
% See solution above
% 1.04/1.22 % E exiting
%------------------------------------------------------------------------------