TSTP Solution File: GRP196-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP196-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 22:26:44 EDT 2022
% Result : Unsatisfiable 44.45s 28.72s
% Output : Proof 44.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 227
% Syntax : Number of formulae : 954 ( 730 unt; 3 typ; 0 def)
% Number of atoms : 1176 (1173 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 443 ( 220 ~; 216 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 18 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 672 ( 667 !; 0 ?; 672 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP008-0.ax',associativity_of_multiply) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,a),multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))))) = multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
multiply(multiply(a,a),multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))))) = multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))))))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
multiply(a,multiply(multiply(a,a),multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))))))) = multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))))))),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))))) = multiply(a,multiply(multiply(a,a),multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))))) = multiply(a,multiply(multiply(a,a),multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))))))),
inference(unit_resolution,[status(thm)],[11,7]) ).
tff(13,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,a),multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))) = multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(14,plain,
multiply(multiply(a,a),multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))) = multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))),
inference(unit_resolution,[status(thm)],[13,7]) ).
tff(15,plain,
multiply(a,multiply(multiply(a,a),multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))) = multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))))),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))) = multiply(a,multiply(multiply(a,a),multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(17,plain,
multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))) = multiply(a,multiply(multiply(a,a),multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))),
inference(unit_resolution,[status(thm)],[16,7]) ).
tff(18,plain,
multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))) = multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))))),
inference(transitivity,[status(thm)],[17,15]) ).
tff(19,plain,
multiply(multiply(a,multiply(a,a)),multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))) = multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))))),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,a))),multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))) = multiply(multiply(a,multiply(a,a)),multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
multiply(multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,a))),multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))) = multiply(multiply(a,multiply(a,a)),multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))),
inference(unit_resolution,[status(thm)],[20,7]) ).
tff(22,plain,
^ [Y: $i,X: $i] :
refl(
( ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) )
<=> ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) )
<=> ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) )
<=> ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,axiom,
! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition) ).
tff(26,plain,
! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) )
| ( multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))),multiply(a,multiply(a,a))) = multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))),multiply(a,multiply(a,a))) = multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))),
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))),a),multiply(a,a)) = multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))),multiply(a,multiply(a,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
multiply(multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))),a),multiply(a,a)) = multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))),multiply(a,multiply(a,a))),
inference(unit_resolution,[status(thm)],[31,7]) ).
tff(33,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))),a) = multiply(b,multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))),a) = multiply(b,multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),a)),
inference(unit_resolution,[status(thm)],[33,7]) ).
tff(35,plain,
multiply(b,multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),a)) = multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))),a),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
multiply(multiply(b,multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),a)),multiply(a,a)) = multiply(multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))),a),multiply(a,a)),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
multiply(multiply(b,multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),a)),multiply(a,a)) = multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))),
inference(transitivity,[status(thm)],[36,32,30]) ).
tff(38,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,a))) = multiply(a,multiply(multiply(a,a),multiply(a,multiply(a,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,a))) = multiply(a,multiply(multiply(a,a),multiply(a,multiply(a,a)))),
inference(unit_resolution,[status(thm)],[38,7]) ).
tff(40,plain,
multiply(a,multiply(multiply(a,a),multiply(a,multiply(a,a)))) = multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,a))),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
multiply(multiply(a,multiply(multiply(a,a),multiply(a,multiply(a,a)))),multiply(multiply(b,multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),a)),multiply(a,a))) = multiply(multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,a))),multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))),
inference(monotonicity,[status(thm)],[40,37]) ).
tff(42,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(multiply(a,a),multiply(a,multiply(a,a)))),multiply(b,multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),a))),multiply(a,a)) = multiply(multiply(a,multiply(multiply(a,a),multiply(a,multiply(a,a)))),multiply(multiply(b,multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),a)),multiply(a,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
multiply(multiply(multiply(a,multiply(multiply(a,a),multiply(a,multiply(a,a)))),multiply(b,multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),a))),multiply(a,a)) = multiply(multiply(a,multiply(multiply(a,a),multiply(a,multiply(a,a)))),multiply(multiply(b,multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),a)),multiply(a,a))),
inference(unit_resolution,[status(thm)],[42,7]) ).
tff(44,plain,
multiply(multiply(a,multiply(multiply(a,a),multiply(a,multiply(a,a)))),multiply(b,multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),a))) = multiply(multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,a))),multiply(b,multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),a))),
inference(monotonicity,[status(thm)],[40]) ).
tff(45,plain,
multiply(multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,a))),multiply(b,multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),a))) = multiply(multiply(a,multiply(multiply(a,a),multiply(a,multiply(a,a)))),multiply(b,multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),a))),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) )
| ( multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))),multiply(b,multiply(b,b))) = multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))),multiply(b,multiply(b,b))) = multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))),
inference(unit_resolution,[status(thm)],[46,28]) ).
tff(48,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) )
| ( multiply(multiply(b,multiply(b,b)),multiply(b,multiply(b,b))) = multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
multiply(multiply(b,multiply(b,b)),multiply(b,multiply(b,b))) = multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))),
inference(unit_resolution,[status(thm)],[48,28]) ).
tff(50,plain,
multiply(multiply(multiply(b,multiply(b,b)),multiply(b,multiply(b,b))),multiply(b,multiply(b,b))) = multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))),multiply(b,multiply(b,b))),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(b,b)),multiply(b,multiply(b,b))),multiply(b,multiply(b,b))) = multiply(multiply(b,multiply(b,b)),multiply(multiply(b,multiply(b,b)),multiply(b,multiply(b,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
multiply(multiply(multiply(b,multiply(b,b)),multiply(b,multiply(b,b))),multiply(b,multiply(b,b))) = multiply(multiply(b,multiply(b,b)),multiply(multiply(b,multiply(b,b)),multiply(b,multiply(b,b)))),
inference(unit_resolution,[status(thm)],[51,7]) ).
tff(53,plain,
multiply(multiply(b,multiply(b,b)),multiply(multiply(b,multiply(b,b)),multiply(b,multiply(b,b)))) = multiply(multiply(multiply(b,multiply(b,b)),multiply(b,multiply(b,b))),multiply(b,multiply(b,b))),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
multiply(multiply(b,multiply(b,b)),multiply(multiply(b,multiply(b,b)),multiply(b,multiply(b,b)))) = multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))),
inference(transitivity,[status(thm)],[53,50,47]) ).
tff(55,plain,
multiply(a,multiply(multiply(b,multiply(b,b)),multiply(multiply(b,multiply(b,b)),multiply(b,multiply(b,b))))) = multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) )
| ( multiply(a,multiply(multiply(b,multiply(b,b)),multiply(multiply(b,multiply(b,b)),multiply(b,multiply(b,b))))) = multiply(multiply(b,multiply(b,b)),multiply(multiply(b,multiply(b,b)),multiply(multiply(b,multiply(b,b)),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
multiply(a,multiply(multiply(b,multiply(b,b)),multiply(multiply(b,multiply(b,b)),multiply(b,multiply(b,b))))) = multiply(multiply(b,multiply(b,b)),multiply(multiply(b,multiply(b,b)),multiply(multiply(b,multiply(b,b)),a))),
inference(unit_resolution,[status(thm)],[56,28]) ).
tff(58,plain,
multiply(multiply(b,multiply(b,b)),multiply(multiply(b,multiply(b,b)),multiply(multiply(b,multiply(b,b)),a))) = multiply(a,multiply(multiply(b,multiply(b,b)),multiply(multiply(b,multiply(b,b)),multiply(b,multiply(b,b))))),
inference(symmetry,[status(thm)],[57]) ).
tff(59,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(b,b)),multiply(b,multiply(b,b))),multiply(multiply(b,multiply(b,b)),a)) = multiply(multiply(b,multiply(b,b)),multiply(multiply(b,multiply(b,b)),multiply(multiply(b,multiply(b,b)),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
multiply(multiply(multiply(b,multiply(b,b)),multiply(b,multiply(b,b))),multiply(multiply(b,multiply(b,b)),a)) = multiply(multiply(b,multiply(b,b)),multiply(multiply(b,multiply(b,b)),multiply(multiply(b,multiply(b,b)),a))),
inference(unit_resolution,[status(thm)],[59,7]) ).
tff(61,plain,
multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))) = multiply(multiply(b,multiply(b,b)),multiply(b,multiply(b,b))),
inference(symmetry,[status(thm)],[49]) ).
tff(62,plain,
multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))),multiply(multiply(b,multiply(b,b)),a)) = multiply(multiply(multiply(b,multiply(b,b)),multiply(b,multiply(b,b))),multiply(multiply(b,multiply(b,b)),a)),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))),multiply(b,multiply(b,b))),a) = multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))),multiply(multiply(b,multiply(b,b)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
multiply(multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))),multiply(b,multiply(b,b))),a) = multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))),multiply(multiply(b,multiply(b,b)),a)),
inference(unit_resolution,[status(thm)],[63,7]) ).
tff(65,plain,
multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))) = multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))),multiply(b,multiply(b,b))),
inference(symmetry,[status(thm)],[47]) ).
tff(66,plain,
multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))),a) = multiply(multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))),multiply(b,multiply(b,b))),a),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
multiply(b,multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),a)) = multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))),
inference(transitivity,[status(thm)],[35,66,64,62,60,58,55]) ).
tff(68,plain,
multiply(multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,a))),multiply(b,multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),a))) = multiply(multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,a))),multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
multiply(multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,a))),multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))) = multiply(multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,a))),multiply(b,multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),a))),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,a))),multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))) = multiply(multiply(a,multiply(a,a)),multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
multiply(multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,a))),multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))) = multiply(multiply(a,multiply(a,a)),multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))),
inference(unit_resolution,[status(thm)],[70,7]) ).
tff(72,plain,
multiply(multiply(a,multiply(a,a)),multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))) = multiply(multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,a))),multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,a),multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))) = multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(74,plain,
multiply(multiply(a,a),multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))) = multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))),
inference(unit_resolution,[status(thm)],[73,7]) ).
tff(75,plain,
multiply(a,multiply(multiply(a,a),multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))) = multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))) = multiply(a,multiply(multiply(a,a),multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(77,plain,
multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))) = multiply(a,multiply(multiply(a,a),multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))),
inference(unit_resolution,[status(thm)],[76,7]) ).
tff(78,plain,
multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))) = multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))),
inference(transitivity,[status(thm)],[77,75]) ).
tff(79,plain,
multiply(multiply(a,multiply(a,a)),multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))) = multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))) = multiply(multiply(a,multiply(a,a)),multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))) = multiply(a,multiply(multiply(a,a),multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))) = multiply(a,multiply(multiply(a,a),multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))))),
inference(unit_resolution,[status(thm)],[81,7]) ).
tff(83,plain,
multiply(a,multiply(multiply(a,a),multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))))) = multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,a),multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))) = multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
multiply(multiply(a,a),multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))) = multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))))),
inference(unit_resolution,[status(thm)],[84,7]) ).
tff(86,plain,
multiply(a,multiply(multiply(a,a),multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))))) = multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))))),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))))) = multiply(a,multiply(multiply(a,a),multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))))),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) )
| ( multiply(multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))),multiply(a,multiply(a,a))) = multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(89,plain,
multiply(multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))),multiply(a,multiply(a,a))) = multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))))),
inference(unit_resolution,[status(thm)],[88,28]) ).
tff(90,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,a),multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))) = multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
multiply(multiply(a,a),multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))) = multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))),
inference(unit_resolution,[status(thm)],[90,7]) ).
tff(92,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))) = multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))) = multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))),
inference(unit_resolution,[status(thm)],[92,7]) ).
tff(94,plain,
multiply(multiply(a,a),multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))),multiply(b,multiply(b,b)))) = multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))),
inference(monotonicity,[status(thm)],[47]) ).
tff(95,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))),multiply(b,multiply(b,b))) = multiply(multiply(a,a),multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))),multiply(b,multiply(b,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(96,plain,
multiply(multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))),multiply(b,multiply(b,b))) = multiply(multiply(a,a),multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))),multiply(b,multiply(b,b)))),
inference(unit_resolution,[status(thm)],[95,7]) ).
tff(97,plain,
multiply(multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))),multiply(b,multiply(b,b))) = multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))),
inference(transitivity,[status(thm)],[96,94,93]) ).
tff(98,plain,
multiply(multiply(a,a),multiply(multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))),multiply(b,multiply(b,b)))) = multiply(multiply(a,a),multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,a),multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),multiply(b,multiply(b,b))) = multiply(multiply(a,a),multiply(multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))),multiply(b,multiply(b,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(100,plain,
multiply(multiply(multiply(a,a),multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),multiply(b,multiply(b,b))) = multiply(multiply(a,a),multiply(multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))),multiply(b,multiply(b,b)))),
inference(unit_resolution,[status(thm)],[99,7]) ).
tff(101,plain,
multiply(multiply(multiply(a,a),multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),multiply(b,multiply(b,b))) = multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))),
inference(transitivity,[status(thm)],[100,98,91]) ).
tff(102,plain,
multiply(multiply(multiply(multiply(a,a),multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),multiply(b,multiply(b,b))),multiply(a,multiply(a,a))) = multiply(multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))))))),multiply(a,multiply(a,a))),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(a,a),multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),multiply(b,multiply(b,b))),multiply(a,multiply(a,a))) = multiply(multiply(multiply(a,a),multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
multiply(multiply(multiply(multiply(a,a),multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),multiply(b,multiply(b,b))),multiply(a,multiply(a,a))) = multiply(multiply(multiply(a,a),multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,a)))),
inference(unit_resolution,[status(thm)],[103,7]) ).
tff(105,plain,
multiply(multiply(multiply(a,a),multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,a)))) = multiply(multiply(multiply(multiply(a,a),multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),multiply(b,multiply(b,b))),multiply(a,multiply(a,a))),
inference(symmetry,[status(thm)],[104]) ).
tff(106,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,a))) = multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(107,plain,
multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,a))) = multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a)))),
inference(unit_resolution,[status(thm)],[106,7]) ).
tff(108,plain,
multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a)))) = multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,a))),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,a),multiply(a,a)),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))) = multiply(multiply(a,a),multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(110,plain,
multiply(multiply(multiply(a,a),multiply(a,a)),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))) = multiply(multiply(a,a),multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),
inference(unit_resolution,[status(thm)],[109,7]) ).
tff(111,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,a),multiply(a,a)) = multiply(a,multiply(a,multiply(a,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(112,plain,
multiply(multiply(a,a),multiply(a,a)) = multiply(a,multiply(a,multiply(a,a))),
inference(unit_resolution,[status(thm)],[111,7]) ).
tff(113,plain,
multiply(multiply(multiply(a,a),multiply(a,a)),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))) = multiply(multiply(a,multiply(a,multiply(a,a))),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
multiply(multiply(a,multiply(a,multiply(a,a))),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))) = multiply(multiply(multiply(a,a),multiply(a,a)),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(a,multiply(a,a))),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))) = multiply(a,multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(116,plain,
multiply(multiply(a,multiply(a,multiply(a,a))),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))) = multiply(a,multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),
inference(unit_resolution,[status(thm)],[115,7]) ).
tff(117,plain,
multiply(a,multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))) = multiply(multiply(a,multiply(a,multiply(a,a))),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
multiply(a,multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))) = multiply(multiply(a,a),multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),
inference(transitivity,[status(thm)],[117,114,110]) ).
tff(119,plain,
multiply(multiply(a,multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a))))) = multiply(multiply(multiply(a,a),multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,a)))),
inference(monotonicity,[status(thm)],[118,108]) ).
tff(120,plain,
multiply(multiply(a,multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a))))) = multiply(multiply(a,multiply(multiply(a,a),multiply(a,multiply(a,a)))),multiply(b,multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),a))),
inference(transitivity,[status(thm)],[119,105,102,89,87,83,80,72,69,45]) ).
tff(121,plain,
multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a))))),multiply(a,a)) = multiply(multiply(multiply(a,multiply(multiply(a,a),multiply(a,multiply(a,a)))),multiply(b,multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),a))),multiply(a,a)),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a))))),multiply(a,a)) = multiply(multiply(a,multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),multiply(multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a)))),multiply(a,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(123,plain,
multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a))))),multiply(a,a)) = multiply(multiply(a,multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),multiply(multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a)))),multiply(a,a))),
inference(unit_resolution,[status(thm)],[122,7]) ).
tff(124,plain,
multiply(multiply(a,multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),multiply(multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a)))),multiply(a,a))) = multiply(multiply(multiply(a,multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a))))),multiply(a,a)),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) )
| ( multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,b))) = multiply(b,multiply(b,multiply(b,multiply(a,multiply(a,a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(126,plain,
multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,b))) = multiply(b,multiply(b,multiply(b,multiply(a,multiply(a,a))))),
inference(unit_resolution,[status(thm)],[125,28]) ).
tff(127,plain,
multiply(b,multiply(b,multiply(b,multiply(a,multiply(a,a))))) = multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,b))),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,b),multiply(b,multiply(a,multiply(a,a)))) = multiply(b,multiply(b,multiply(b,multiply(a,multiply(a,a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
multiply(multiply(b,b),multiply(b,multiply(a,multiply(a,a)))) = multiply(b,multiply(b,multiply(b,multiply(a,multiply(a,a))))),
inference(unit_resolution,[status(thm)],[128,7]) ).
tff(130,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,b),b),multiply(a,multiply(a,a))) = multiply(multiply(b,b),multiply(b,multiply(a,multiply(a,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(131,plain,
multiply(multiply(multiply(b,b),b),multiply(a,multiply(a,a))) = multiply(multiply(b,b),multiply(b,multiply(a,multiply(a,a)))),
inference(unit_resolution,[status(thm)],[130,7]) ).
tff(132,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,b),b) = multiply(b,multiply(b,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(133,plain,
multiply(multiply(b,b),b) = multiply(b,multiply(b,b)),
inference(unit_resolution,[status(thm)],[132,7]) ).
tff(134,plain,
multiply(multiply(multiply(b,b),b),multiply(a,multiply(a,a))) = multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,a))),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,a))) = multiply(multiply(multiply(b,b),b),multiply(a,multiply(a,a))),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a)))) = multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,b))),
inference(transitivity,[status(thm)],[108,135,131,129,127]) ).
tff(137,plain,
multiply(multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a)))),multiply(a,a)) = multiply(multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,b))),multiply(a,a)),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
multiply(multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,b))),multiply(a,a)) = multiply(multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a)))),multiply(a,a)),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,b))),multiply(a,a)) = multiply(multiply(a,multiply(a,a)),multiply(multiply(b,multiply(b,b)),multiply(a,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(140,plain,
multiply(multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,b))),multiply(a,a)) = multiply(multiply(a,multiply(a,a)),multiply(multiply(b,multiply(b,b)),multiply(a,a))),
inference(unit_resolution,[status(thm)],[139,7]) ).
tff(141,plain,
multiply(multiply(a,multiply(a,a)),multiply(multiply(b,multiply(b,b)),multiply(a,a))) = multiply(multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,b))),multiply(a,a)),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,a),multiply(b,multiply(b,b))) = multiply(a,multiply(a,multiply(b,multiply(b,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(143,plain,
multiply(multiply(a,a),multiply(b,multiply(b,b))) = multiply(a,multiply(a,multiply(b,multiply(b,b)))),
inference(unit_resolution,[status(thm)],[142,7]) ).
tff(144,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) )
| ( multiply(multiply(a,a),multiply(b,multiply(b,b))) = multiply(b,multiply(b,multiply(b,multiply(a,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(145,plain,
multiply(multiply(a,a),multiply(b,multiply(b,b))) = multiply(b,multiply(b,multiply(b,multiply(a,a)))),
inference(unit_resolution,[status(thm)],[144,28]) ).
tff(146,plain,
multiply(b,multiply(b,multiply(b,multiply(a,a)))) = multiply(multiply(a,a),multiply(b,multiply(b,b))),
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,b),multiply(a,a)) = multiply(b,multiply(b,multiply(a,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(148,plain,
multiply(multiply(b,b),multiply(a,a)) = multiply(b,multiply(b,multiply(a,a))),
inference(unit_resolution,[status(thm)],[147,7]) ).
tff(149,plain,
multiply(b,multiply(multiply(b,b),multiply(a,a))) = multiply(b,multiply(b,multiply(b,multiply(a,a)))),
inference(monotonicity,[status(thm)],[148]) ).
tff(150,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,multiply(b,b)),multiply(a,a)) = multiply(b,multiply(multiply(b,b),multiply(a,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(151,plain,
multiply(multiply(b,multiply(b,b)),multiply(a,a)) = multiply(b,multiply(multiply(b,b),multiply(a,a))),
inference(unit_resolution,[status(thm)],[150,7]) ).
tff(152,plain,
multiply(multiply(b,multiply(b,b)),multiply(a,a)) = multiply(a,multiply(a,multiply(b,multiply(b,b)))),
inference(transitivity,[status(thm)],[151,149,146,143]) ).
tff(153,plain,
multiply(multiply(a,multiply(a,a)),multiply(multiply(b,multiply(b,b)),multiply(a,a))) = multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,multiply(b,multiply(b,b))))),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,multiply(b,multiply(b,b))))) = multiply(multiply(a,multiply(a,a)),multiply(multiply(b,multiply(b,b)),multiply(a,a))),
inference(symmetry,[status(thm)],[153]) ).
tff(155,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(a,a)),a),multiply(a,multiply(b,multiply(b,b)))) = multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,multiply(b,multiply(b,b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(156,plain,
multiply(multiply(multiply(a,multiply(a,a)),a),multiply(a,multiply(b,multiply(b,b)))) = multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,multiply(b,multiply(b,b))))),
inference(unit_resolution,[status(thm)],[155,7]) ).
tff(157,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,b),multiply(b,b)) = multiply(a,multiply(b,multiply(b,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(158,plain,
multiply(multiply(a,b),multiply(b,b)) = multiply(a,multiply(b,multiply(b,b))),
inference(unit_resolution,[status(thm)],[157,7]) ).
tff(159,plain,
multiply(a,multiply(b,multiply(b,b))) = multiply(multiply(a,b),multiply(b,b)),
inference(symmetry,[status(thm)],[158]) ).
tff(160,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,a),a),a) = multiply(multiply(a,a),multiply(a,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(161,plain,
multiply(multiply(multiply(a,a),a),a) = multiply(multiply(a,a),multiply(a,a)),
inference(unit_resolution,[status(thm)],[160,7]) ).
tff(162,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,a),a) = multiply(a,multiply(a,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(163,plain,
multiply(multiply(a,a),a) = multiply(a,multiply(a,a)),
inference(unit_resolution,[status(thm)],[162,7]) ).
tff(164,plain,
multiply(a,multiply(a,a)) = multiply(multiply(a,a),a),
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
multiply(multiply(a,multiply(a,a)),a) = multiply(multiply(multiply(a,a),a),a),
inference(monotonicity,[status(thm)],[164]) ).
tff(166,plain,
multiply(multiply(a,multiply(a,a)),a) = multiply(multiply(a,a),multiply(a,a)),
inference(transitivity,[status(thm)],[165,161]) ).
tff(167,plain,
multiply(multiply(multiply(a,multiply(a,a)),a),multiply(a,multiply(b,multiply(b,b)))) = multiply(multiply(multiply(a,a),multiply(a,a)),multiply(multiply(a,b),multiply(b,b))),
inference(monotonicity,[status(thm)],[166,159]) ).
tff(168,plain,
multiply(multiply(multiply(a,a),multiply(a,a)),multiply(multiply(a,b),multiply(b,b))) = multiply(multiply(multiply(a,multiply(a,a)),a),multiply(a,multiply(b,multiply(b,b)))),
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
multiply(multiply(multiply(a,a),multiply(a,a)),multiply(a,multiply(b,multiply(b,b)))) = multiply(multiply(multiply(a,a),multiply(a,a)),multiply(multiply(a,b),multiply(b,b))),
inference(monotonicity,[status(thm)],[159]) ).
tff(170,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,a),multiply(a,a)),multiply(a,multiply(b,multiply(b,b)))) = multiply(multiply(a,a),multiply(multiply(a,a),multiply(a,multiply(b,multiply(b,b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(171,plain,
multiply(multiply(multiply(a,a),multiply(a,a)),multiply(a,multiply(b,multiply(b,b)))) = multiply(multiply(a,a),multiply(multiply(a,a),multiply(a,multiply(b,multiply(b,b))))),
inference(unit_resolution,[status(thm)],[170,7]) ).
tff(172,plain,
multiply(multiply(a,a),multiply(multiply(a,a),multiply(a,multiply(b,multiply(b,b))))) = multiply(multiply(multiply(a,a),multiply(a,a)),multiply(a,multiply(b,multiply(b,b)))),
inference(symmetry,[status(thm)],[171]) ).
tff(173,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,a),multiply(a,multiply(b,multiply(b,b)))) = multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(174,plain,
multiply(multiply(a,a),multiply(a,multiply(b,multiply(b,b)))) = multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,b))))),
inference(unit_resolution,[status(thm)],[173,7]) ).
tff(175,plain,
multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,b))))) = multiply(multiply(a,a),multiply(a,multiply(b,multiply(b,b)))),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) )
| ( multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,a))) = multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(177,plain,
multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,a))) = multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,b))))),
inference(unit_resolution,[status(thm)],[176,28]) ).
tff(178,plain,
multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a)))) = multiply(multiply(a,a),multiply(a,multiply(b,multiply(b,b)))),
inference(transitivity,[status(thm)],[108,177,175]) ).
tff(179,plain,
multiply(multiply(a,a),multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a))))) = multiply(multiply(a,a),multiply(multiply(a,a),multiply(a,multiply(b,multiply(b,b))))),
inference(monotonicity,[status(thm)],[178]) ).
tff(180,plain,
multiply(multiply(a,a),multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a))))) = multiply(multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a)))),multiply(a,a)),
inference(transitivity,[status(thm)],[179,172,169,168,156,154,141,138]) ).
tff(181,plain,
multiply(a,multiply(a,multiply(a,a))) = multiply(multiply(a,a),multiply(a,a)),
inference(symmetry,[status(thm)],[112]) ).
tff(182,plain,
multiply(multiply(a,multiply(a,multiply(a,a))),multiply(multiply(b,multiply(b,b)),multiply(b,multiply(b,b)))) = multiply(multiply(multiply(a,a),multiply(a,a)),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))),
inference(monotonicity,[status(thm)],[181,49]) ).
tff(183,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(a,multiply(a,a))),multiply(b,multiply(b,b))),multiply(b,multiply(b,b))) = multiply(multiply(a,multiply(a,multiply(a,a))),multiply(multiply(b,multiply(b,b)),multiply(b,multiply(b,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(184,plain,
multiply(multiply(multiply(a,multiply(a,multiply(a,a))),multiply(b,multiply(b,b))),multiply(b,multiply(b,b))) = multiply(multiply(a,multiply(a,multiply(a,a))),multiply(multiply(b,multiply(b,b)),multiply(b,multiply(b,b)))),
inference(unit_resolution,[status(thm)],[183,7]) ).
tff(185,plain,
multiply(multiply(multiply(a,a),multiply(a,a)),multiply(b,multiply(b,b))) = multiply(multiply(a,multiply(a,multiply(a,a))),multiply(b,multiply(b,b))),
inference(monotonicity,[status(thm)],[112]) ).
tff(186,plain,
multiply(multiply(multiply(a,multiply(a,a)),a),multiply(b,multiply(b,b))) = multiply(multiply(multiply(a,a),multiply(a,a)),multiply(b,multiply(b,b))),
inference(monotonicity,[status(thm)],[166]) ).
tff(187,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(a,a)),a),multiply(b,multiply(b,b))) = multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(188,plain,
multiply(multiply(multiply(a,multiply(a,a)),a),multiply(b,multiply(b,b))) = multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b)))),
inference(unit_resolution,[status(thm)],[187,7]) ).
tff(189,plain,
multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b)))) = multiply(multiply(multiply(a,multiply(a,a)),a),multiply(b,multiply(b,b))),
inference(symmetry,[status(thm)],[188]) ).
tff(190,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b)))) = multiply(a,multiply(multiply(a,a),multiply(a,multiply(b,multiply(b,b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(191,plain,
multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b)))) = multiply(a,multiply(multiply(a,a),multiply(a,multiply(b,multiply(b,b))))),
inference(unit_resolution,[status(thm)],[190,7]) ).
tff(192,plain,
multiply(a,multiply(multiply(a,a),multiply(a,multiply(b,multiply(b,b))))) = multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b)))),
inference(symmetry,[status(thm)],[191]) ).
tff(193,plain,
multiply(a,multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a))))) = multiply(a,multiply(multiply(a,a),multiply(a,multiply(b,multiply(b,b))))),
inference(monotonicity,[status(thm)],[178]) ).
tff(194,plain,
multiply(multiply(b,multiply(b,b)),multiply(multiply(a,a),a)) = multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,a))),
inference(monotonicity,[status(thm)],[163]) ).
tff(195,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(b,b)),multiply(a,a)),a) = multiply(multiply(b,multiply(b,b)),multiply(multiply(a,a),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(196,plain,
multiply(multiply(multiply(b,multiply(b,b)),multiply(a,a)),a) = multiply(multiply(b,multiply(b,b)),multiply(multiply(a,a),a)),
inference(unit_resolution,[status(thm)],[195,7]) ).
tff(197,plain,
multiply(b,multiply(multiply(b,b),multiply(a,a))) = multiply(multiply(b,multiply(b,b)),multiply(a,a)),
inference(symmetry,[status(thm)],[151]) ).
tff(198,plain,
multiply(b,multiply(b,multiply(b,multiply(a,a)))) = multiply(b,multiply(multiply(b,b),multiply(a,a))),
inference(symmetry,[status(thm)],[149]) ).
tff(199,plain,
multiply(a,multiply(a,multiply(b,multiply(b,b)))) = multiply(multiply(a,a),multiply(b,multiply(b,b))),
inference(symmetry,[status(thm)],[143]) ).
tff(200,plain,
multiply(a,multiply(a,multiply(b,multiply(b,b)))) = multiply(multiply(b,multiply(b,b)),multiply(a,a)),
inference(transitivity,[status(thm)],[199,145,198,197]) ).
tff(201,plain,
multiply(multiply(a,multiply(a,multiply(b,multiply(b,b)))),a) = multiply(multiply(multiply(b,multiply(b,b)),multiply(a,a)),a),
inference(monotonicity,[status(thm)],[200]) ).
tff(202,plain,
multiply(multiply(a,multiply(a,multiply(b,multiply(b,b)))),a) = multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a)))),
inference(transitivity,[status(thm)],[201,196,194,107]) ).
tff(203,plain,
multiply(a,multiply(multiply(a,multiply(a,multiply(b,multiply(b,b)))),a)) = multiply(a,multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a))))),
inference(monotonicity,[status(thm)],[202]) ).
tff(204,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,b))))),a) = multiply(a,multiply(multiply(a,multiply(a,multiply(b,multiply(b,b)))),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(205,plain,
multiply(multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,b))))),a) = multiply(a,multiply(multiply(a,multiply(a,multiply(b,multiply(b,b)))),a)),
inference(unit_resolution,[status(thm)],[204,7]) ).
tff(206,plain,
multiply(multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,a))),a) = multiply(multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,b))))),a),
inference(monotonicity,[status(thm)],[177]) ).
tff(207,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,a))),a) = multiply(multiply(b,multiply(b,b)),multiply(multiply(a,multiply(a,a)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(208,plain,
multiply(multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,a))),a) = multiply(multiply(b,multiply(b,b)),multiply(multiply(a,multiply(a,a)),a)),
inference(unit_resolution,[status(thm)],[207,7]) ).
tff(209,plain,
multiply(multiply(b,multiply(b,b)),multiply(multiply(a,multiply(a,a)),a)) = multiply(multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,a))),a),
inference(symmetry,[status(thm)],[208]) ).
tff(210,plain,
multiply(multiply(multiply(a,a),a),a) = multiply(multiply(a,multiply(a,a)),a),
inference(symmetry,[status(thm)],[165]) ).
tff(211,plain,
multiply(multiply(a,a),multiply(a,a)) = multiply(multiply(multiply(a,a),a),a),
inference(symmetry,[status(thm)],[161]) ).
tff(212,plain,
multiply(multiply(a,a),multiply(a,a)) = multiply(multiply(a,multiply(a,a)),a),
inference(transitivity,[status(thm)],[211,210]) ).
tff(213,plain,
multiply(multiply(b,multiply(b,b)),multiply(multiply(a,a),multiply(a,a))) = multiply(multiply(b,multiply(b,b)),multiply(multiply(a,multiply(a,a)),a)),
inference(monotonicity,[status(thm)],[212]) ).
tff(214,plain,
multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,multiply(a,a)))) = multiply(multiply(b,multiply(b,b)),multiply(multiply(a,a),multiply(a,a))),
inference(monotonicity,[status(thm)],[181]) ).
tff(215,plain,
multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,multiply(a,a)))) = multiply(multiply(a,multiply(a,multiply(a,a))),multiply(b,multiply(b,b))),
inference(transitivity,[status(thm)],[214,213,209,206,205,203,193,192,189,186,185]) ).
tff(216,plain,
multiply(multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,multiply(a,a)))),multiply(b,multiply(b,b))) = multiply(multiply(multiply(a,multiply(a,multiply(a,a))),multiply(b,multiply(b,b))),multiply(b,multiply(b,b))),
inference(monotonicity,[status(thm)],[215]) ).
tff(217,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,multiply(a,a)))),multiply(b,multiply(b,b))) = multiply(multiply(b,multiply(b,b)),multiply(multiply(a,multiply(a,multiply(a,a))),multiply(b,multiply(b,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(218,plain,
multiply(multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,multiply(a,a)))),multiply(b,multiply(b,b))) = multiply(multiply(b,multiply(b,b)),multiply(multiply(a,multiply(a,multiply(a,a))),multiply(b,multiply(b,b)))),
inference(unit_resolution,[status(thm)],[217,7]) ).
tff(219,plain,
multiply(multiply(b,multiply(b,b)),multiply(multiply(a,multiply(a,multiply(a,a))),multiply(b,multiply(b,b)))) = multiply(multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,multiply(a,a)))),multiply(b,multiply(b,b))),
inference(symmetry,[status(thm)],[218]) ).
tff(220,plain,
multiply(multiply(b,multiply(b,b)),multiply(multiply(a,a),multiply(a,a))) = multiply(multiply(a,multiply(a,multiply(a,a))),multiply(b,multiply(b,b))),
inference(transitivity,[status(thm)],[213,209,206,205,203,193,192,189,186,185]) ).
tff(221,plain,
multiply(multiply(b,multiply(b,b)),multiply(multiply(b,multiply(b,b)),multiply(multiply(a,a),multiply(a,a)))) = multiply(multiply(b,multiply(b,b)),multiply(multiply(a,multiply(a,multiply(a,a))),multiply(b,multiply(b,b)))),
inference(monotonicity,[status(thm)],[220]) ).
tff(222,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,multiply(b,b)),multiply(multiply(b,multiply(b,b)),multiply(multiply(a,a),multiply(a,a)))) = multiply(b,multiply(multiply(b,b),multiply(multiply(b,multiply(b,b)),multiply(multiply(a,a),multiply(a,a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(223,plain,
multiply(multiply(b,multiply(b,b)),multiply(multiply(b,multiply(b,b)),multiply(multiply(a,a),multiply(a,a)))) = multiply(b,multiply(multiply(b,b),multiply(multiply(b,multiply(b,b)),multiply(multiply(a,a),multiply(a,a))))),
inference(unit_resolution,[status(thm)],[222,7]) ).
tff(224,plain,
multiply(b,multiply(multiply(b,b),multiply(multiply(b,multiply(b,b)),multiply(multiply(a,a),multiply(a,a))))) = multiply(multiply(b,multiply(b,b)),multiply(multiply(b,multiply(b,b)),multiply(multiply(a,a),multiply(a,a)))),
inference(symmetry,[status(thm)],[223]) ).
tff(225,plain,
multiply(b,multiply(multiply(b,b),multiply(multiply(b,multiply(b,b)),multiply(multiply(a,a),multiply(a,a))))) = multiply(a,multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),
inference(transitivity,[status(thm)],[224,221,219,216,184,182,113,116]) ).
tff(226,plain,
multiply(multiply(b,multiply(multiply(b,b),multiply(multiply(b,multiply(b,b)),multiply(multiply(a,a),multiply(a,a))))),multiply(multiply(a,a),multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a)))))) = multiply(multiply(a,multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),multiply(multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a)))),multiply(a,a))),
inference(monotonicity,[status(thm)],[225,180]) ).
tff(227,plain,
multiply(multiply(a,a),multiply(multiply(a,a),multiply(a,multiply(b,multiply(b,b))))) = multiply(multiply(a,a),multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a))))),
inference(symmetry,[status(thm)],[179]) ).
tff(228,plain,
multiply(multiply(multiply(a,a),multiply(a,a)),multiply(multiply(a,b),multiply(b,b))) = multiply(multiply(multiply(a,a),multiply(a,a)),multiply(a,multiply(b,multiply(b,b)))),
inference(symmetry,[status(thm)],[169]) ).
tff(229,plain,
multiply(multiply(multiply(a,a),multiply(a,a)),multiply(multiply(a,b),multiply(b,b))) = multiply(multiply(a,multiply(a,multiply(a,a))),multiply(a,multiply(b,multiply(b,b)))),
inference(monotonicity,[status(thm)],[112,158]) ).
tff(230,plain,
multiply(multiply(a,multiply(a,multiply(a,a))),multiply(a,multiply(b,multiply(b,b)))) = multiply(multiply(multiply(a,a),multiply(a,a)),multiply(multiply(a,b),multiply(b,b))),
inference(symmetry,[status(thm)],[229]) ).
tff(231,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(a,multiply(a,a))),multiply(a,multiply(b,multiply(b,b)))) = multiply(a,multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(232,plain,
multiply(multiply(a,multiply(a,multiply(a,a))),multiply(a,multiply(b,multiply(b,b)))) = multiply(a,multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b))))),
inference(unit_resolution,[status(thm)],[231,7]) ).
tff(233,plain,
multiply(a,multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b))))) = multiply(multiply(a,multiply(a,multiply(a,a))),multiply(a,multiply(b,multiply(b,b)))),
inference(symmetry,[status(thm)],[232]) ).
tff(234,plain,
multiply(a,multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b))))) = multiply(multiply(a,a),multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a))))),
inference(transitivity,[status(thm)],[233,230,228,171,227]) ).
tff(235,plain,
multiply(multiply(b,multiply(b,b)),multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,multiply(a,a))))) = multiply(multiply(b,multiply(b,b)),multiply(multiply(b,multiply(b,b)),multiply(multiply(a,a),multiply(a,a)))),
inference(monotonicity,[status(thm)],[214]) ).
tff(236,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(b,b)),multiply(b,multiply(b,b))),multiply(a,multiply(a,multiply(a,a)))) = multiply(multiply(b,multiply(b,b)),multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,multiply(a,a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(237,plain,
multiply(multiply(multiply(b,multiply(b,b)),multiply(b,multiply(b,b))),multiply(a,multiply(a,multiply(a,a)))) = multiply(multiply(b,multiply(b,b)),multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,multiply(a,a))))),
inference(unit_resolution,[status(thm)],[236,7]) ).
tff(238,plain,
multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))),multiply(a,multiply(a,multiply(a,a)))) = multiply(multiply(multiply(b,multiply(b,b)),multiply(b,multiply(b,b))),multiply(a,multiply(a,multiply(a,a)))),
inference(monotonicity,[status(thm)],[61]) ).
tff(239,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))),a),multiply(a,multiply(a,a))) = multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))),multiply(a,multiply(a,multiply(a,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(240,plain,
multiply(multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))),a),multiply(a,multiply(a,a))) = multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))),multiply(a,multiply(a,multiply(a,a)))),
inference(unit_resolution,[status(thm)],[239,7]) ).
tff(241,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,b),multiply(b,b)) = multiply(b,multiply(b,multiply(b,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(242,plain,
multiply(multiply(b,b),multiply(b,b)) = multiply(b,multiply(b,multiply(b,b))),
inference(unit_resolution,[status(thm)],[241,7]) ).
tff(243,plain,
multiply(b,multiply(b,multiply(b,b))) = multiply(multiply(b,b),multiply(b,b)),
inference(symmetry,[status(thm)],[242]) ).
tff(244,plain,
multiply(multiply(b,multiply(b,multiply(b,b))),multiply(b,b)) = multiply(multiply(multiply(b,b),multiply(b,b)),multiply(b,b)),
inference(monotonicity,[status(thm)],[243]) ).
tff(245,plain,
multiply(multiply(multiply(b,b),multiply(b,b)),multiply(b,b)) = multiply(multiply(b,multiply(b,multiply(b,b))),multiply(b,b)),
inference(symmetry,[status(thm)],[244]) ).
tff(246,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,b),multiply(b,b)),multiply(b,b)) = multiply(multiply(b,b),multiply(multiply(b,b),multiply(b,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(247,plain,
multiply(multiply(multiply(b,b),multiply(b,b)),multiply(b,b)) = multiply(multiply(b,b),multiply(multiply(b,b),multiply(b,b))),
inference(unit_resolution,[status(thm)],[246,7]) ).
tff(248,plain,
multiply(multiply(b,b),multiply(multiply(b,b),multiply(b,b))) = multiply(multiply(multiply(b,b),multiply(b,b)),multiply(b,b)),
inference(symmetry,[status(thm)],[247]) ).
tff(249,plain,
multiply(multiply(b,b),multiply(multiply(b,b),multiply(b,b))) = multiply(multiply(b,b),multiply(b,multiply(b,multiply(b,b)))),
inference(monotonicity,[status(thm)],[242]) ).
tff(250,plain,
multiply(multiply(b,b),multiply(b,multiply(b,multiply(b,b)))) = multiply(multiply(b,b),multiply(multiply(b,b),multiply(b,b))),
inference(symmetry,[status(thm)],[249]) ).
tff(251,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,b),multiply(b,multiply(b,multiply(b,b)))) = multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(252,plain,
multiply(multiply(b,b),multiply(b,multiply(b,multiply(b,b)))) = multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))),
inference(unit_resolution,[status(thm)],[251,7]) ).
tff(253,plain,
multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))) = multiply(multiply(b,b),multiply(b,multiply(b,multiply(b,b)))),
inference(symmetry,[status(thm)],[252]) ).
tff(254,plain,
multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))) = multiply(multiply(b,multiply(b,multiply(b,b))),multiply(b,b)),
inference(transitivity,[status(thm)],[253,250,248,245]) ).
tff(255,plain,
multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))),a) = multiply(multiply(multiply(b,multiply(b,multiply(b,b))),multiply(b,b)),a),
inference(monotonicity,[status(thm)],[254]) ).
tff(256,plain,
multiply(multiply(multiply(b,multiply(b,multiply(b,b))),multiply(b,b)),a) = multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))),a),
inference(symmetry,[status(thm)],[255]) ).
tff(257,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(b,multiply(b,b))),multiply(b,b)),a) = multiply(multiply(b,multiply(b,multiply(b,b))),multiply(multiply(b,b),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(258,plain,
multiply(multiply(multiply(b,multiply(b,multiply(b,b))),multiply(b,b)),a) = multiply(multiply(b,multiply(b,multiply(b,b))),multiply(multiply(b,b),a)),
inference(unit_resolution,[status(thm)],[257,7]) ).
tff(259,plain,
multiply(multiply(b,multiply(b,multiply(b,b))),multiply(multiply(b,b),a)) = multiply(multiply(multiply(b,multiply(b,multiply(b,b))),multiply(b,b)),a),
inference(symmetry,[status(thm)],[258]) ).
tff(260,plain,
multiply(multiply(b,multiply(b,multiply(b,b))),multiply(multiply(b,b),a)) = multiply(multiply(multiply(b,b),multiply(b,b)),multiply(multiply(b,b),a)),
inference(monotonicity,[status(thm)],[243]) ).
tff(261,plain,
multiply(multiply(multiply(b,b),multiply(b,b)),multiply(multiply(b,b),a)) = multiply(multiply(b,multiply(b,multiply(b,b))),multiply(multiply(b,b),a)),
inference(symmetry,[status(thm)],[260]) ).
tff(262,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,b),multiply(b,b)),multiply(multiply(b,b),a)) = multiply(multiply(b,b),multiply(multiply(b,b),multiply(multiply(b,b),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(263,plain,
multiply(multiply(multiply(b,b),multiply(b,b)),multiply(multiply(b,b),a)) = multiply(multiply(b,b),multiply(multiply(b,b),multiply(multiply(b,b),a))),
inference(unit_resolution,[status(thm)],[262,7]) ).
tff(264,plain,
multiply(multiply(b,b),multiply(multiply(b,b),multiply(multiply(b,b),a))) = multiply(multiply(multiply(b,b),multiply(b,b)),multiply(multiply(b,b),a)),
inference(symmetry,[status(thm)],[263]) ).
tff(265,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) )
| ( multiply(a,multiply(multiply(b,b),multiply(multiply(b,b),multiply(b,b)))) = multiply(multiply(b,b),multiply(multiply(b,b),multiply(multiply(b,b),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(266,plain,
multiply(a,multiply(multiply(b,b),multiply(multiply(b,b),multiply(b,b)))) = multiply(multiply(b,b),multiply(multiply(b,b),multiply(multiply(b,b),a))),
inference(unit_resolution,[status(thm)],[265,28]) ).
tff(267,plain,
multiply(multiply(b,b),multiply(multiply(b,b),multiply(b,b))) = multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))),
inference(transitivity,[status(thm)],[249,252]) ).
tff(268,plain,
multiply(a,multiply(multiply(b,b),multiply(multiply(b,b),multiply(b,b)))) = multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))),
inference(monotonicity,[status(thm)],[267]) ).
tff(269,plain,
multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))) = multiply(a,multiply(multiply(b,b),multiply(multiply(b,b),multiply(b,b)))),
inference(symmetry,[status(thm)],[268]) ).
tff(270,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,b),multiply(b,multiply(b,multiply(b,multiply(b,b))))) = multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(271,plain,
multiply(multiply(a,b),multiply(b,multiply(b,multiply(b,multiply(b,b))))) = multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b)))))),
inference(unit_resolution,[status(thm)],[270,7]) ).
tff(272,plain,
multiply(multiply(a,b),multiply(b,multiply(b,multiply(b,multiply(b,b))))) = multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))),a),
inference(transitivity,[status(thm)],[271,269,266,264,261,259,256]) ).
tff(273,plain,
multiply(multiply(multiply(a,b),multiply(b,multiply(b,multiply(b,multiply(b,b))))),multiply(a,multiply(a,a))) = multiply(multiply(multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))),a),multiply(a,multiply(a,a))),
inference(monotonicity,[status(thm)],[272]) ).
tff(274,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,b),multiply(b,multiply(b,multiply(b,multiply(b,b))))),multiply(a,multiply(a,a))) = multiply(multiply(a,b),multiply(multiply(b,multiply(b,multiply(b,multiply(b,b)))),multiply(a,multiply(a,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(275,plain,
multiply(multiply(multiply(a,b),multiply(b,multiply(b,multiply(b,multiply(b,b))))),multiply(a,multiply(a,a))) = multiply(multiply(a,b),multiply(multiply(b,multiply(b,multiply(b,multiply(b,b)))),multiply(a,multiply(a,a)))),
inference(unit_resolution,[status(thm)],[274,7]) ).
tff(276,plain,
multiply(multiply(a,b),multiply(multiply(b,multiply(b,multiply(b,multiply(b,b)))),multiply(a,multiply(a,a)))) = multiply(multiply(multiply(a,b),multiply(b,multiply(b,multiply(b,multiply(b,b))))),multiply(a,multiply(a,a))),
inference(symmetry,[status(thm)],[275]) ).
tff(277,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) )
| ( multiply(multiply(b,multiply(b,multiply(b,multiply(b,b)))),multiply(a,multiply(a,a))) = multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,b))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(278,plain,
multiply(multiply(b,multiply(b,multiply(b,multiply(b,b)))),multiply(a,multiply(a,a))) = multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),
inference(unit_resolution,[status(thm)],[277,28]) ).
tff(279,plain,
multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,b))))))) = multiply(multiply(b,multiply(b,multiply(b,multiply(b,b)))),multiply(a,multiply(a,a))),
inference(symmetry,[status(thm)],[278]) ).
tff(280,plain,
multiply(multiply(a,b),multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))) = multiply(multiply(a,b),multiply(multiply(b,multiply(b,multiply(b,multiply(b,b)))),multiply(a,multiply(a,a)))),
inference(monotonicity,[status(thm)],[279]) ).
tff(281,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,b),a),multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,b))))))) = multiply(multiply(a,b),multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(282,plain,
multiply(multiply(multiply(a,b),a),multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,b))))))) = multiply(multiply(a,b),multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,b)))))))),
inference(unit_resolution,[status(thm)],[281,7]) ).
tff(283,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,b),a) = multiply(a,multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(284,plain,
multiply(multiply(a,b),a) = multiply(a,multiply(b,a)),
inference(unit_resolution,[status(thm)],[283,7]) ).
tff(285,plain,
multiply(a,multiply(b,a)) = multiply(multiply(a,b),a),
inference(symmetry,[status(thm)],[284]) ).
tff(286,plain,
multiply(multiply(a,multiply(b,a)),multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,b))))))) = multiply(multiply(multiply(a,b),a),multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),
inference(monotonicity,[status(thm)],[285]) ).
tff(287,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,b),multiply(b,multiply(b,multiply(b,b)))) = multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(288,plain,
multiply(multiply(a,b),multiply(b,multiply(b,multiply(b,b)))) = multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,b))))),
inference(unit_resolution,[status(thm)],[287,7]) ).
tff(289,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,b),b),multiply(b,multiply(b,b))) = multiply(multiply(a,b),multiply(b,multiply(b,multiply(b,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(290,plain,
multiply(multiply(multiply(a,b),b),multiply(b,multiply(b,b))) = multiply(multiply(a,b),multiply(b,multiply(b,multiply(b,b)))),
inference(unit_resolution,[status(thm)],[289,7]) ).
tff(291,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,b),b) = multiply(a,multiply(b,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(292,plain,
multiply(multiply(a,b),b) = multiply(a,multiply(b,b)),
inference(unit_resolution,[status(thm)],[291,7]) ).
tff(293,plain,
multiply(a,multiply(b,b)) = multiply(multiply(a,b),b),
inference(symmetry,[status(thm)],[292]) ).
tff(294,plain,
multiply(multiply(a,multiply(b,b)),multiply(b,multiply(b,b))) = multiply(multiply(multiply(a,b),b),multiply(b,multiply(b,b))),
inference(monotonicity,[status(thm)],[293]) ).
tff(295,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) )
| ( multiply(multiply(a,multiply(b,b)),multiply(b,multiply(b,b))) = multiply(b,multiply(b,multiply(b,multiply(a,multiply(b,b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(296,plain,
multiply(multiply(a,multiply(b,b)),multiply(b,multiply(b,b))) = multiply(b,multiply(b,multiply(b,multiply(a,multiply(b,b))))),
inference(unit_resolution,[status(thm)],[295,28]) ).
tff(297,plain,
multiply(b,multiply(b,multiply(b,multiply(a,multiply(b,b))))) = multiply(multiply(a,multiply(b,b)),multiply(b,multiply(b,b))),
inference(symmetry,[status(thm)],[296]) ).
tff(298,plain,
multiply(b,multiply(b,multiply(b,multiply(a,multiply(b,b))))) = multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,b))))),
inference(transitivity,[status(thm)],[297,294,290,288]) ).
tff(299,plain,
multiply(a,multiply(b,multiply(b,multiply(b,multiply(a,multiply(b,b)))))) = multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,b)))))),
inference(monotonicity,[status(thm)],[298]) ).
tff(300,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,b),multiply(b,multiply(b,multiply(a,multiply(b,b))))) = multiply(a,multiply(b,multiply(b,multiply(b,multiply(a,multiply(b,b)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(301,plain,
multiply(multiply(a,b),multiply(b,multiply(b,multiply(a,multiply(b,b))))) = multiply(a,multiply(b,multiply(b,multiply(b,multiply(a,multiply(b,b)))))),
inference(unit_resolution,[status(thm)],[300,7]) ).
tff(302,plain,
multiply(multiply(a,b),multiply(b,multiply(b,multiply(a,multiply(b,b))))) = multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,b)))))),
inference(transitivity,[status(thm)],[301,299]) ).
tff(303,plain,
multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),multiply(b,multiply(b,multiply(a,multiply(b,b)))))) = multiply(multiply(a,multiply(b,a)),multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),
inference(monotonicity,[status(thm)],[302]) ).
tff(304,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(b,multiply(b,multiply(a,multiply(b,b))))) = multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),multiply(b,multiply(b,multiply(a,multiply(b,b)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(305,plain,
multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(b,multiply(b,multiply(a,multiply(b,b))))) = multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),multiply(b,multiply(b,multiply(a,multiply(b,b)))))),
inference(unit_resolution,[status(thm)],[304,7]) ).
tff(306,plain,
multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(b,multiply(b,multiply(a,multiply(b,b))))) = multiply(b,multiply(multiply(b,b),multiply(multiply(b,multiply(b,b)),multiply(multiply(a,a),multiply(a,a))))),
inference(transitivity,[status(thm)],[305,303,286,282,280,276,273,240,238,237,235,223]) ).
tff(307,plain,
multiply(multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(b,multiply(b,multiply(a,multiply(b,b))))),multiply(a,multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b)))))) = multiply(multiply(b,multiply(multiply(b,b),multiply(multiply(b,multiply(b,b)),multiply(multiply(a,a),multiply(a,a))))),multiply(multiply(a,a),multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a)))))),
inference(monotonicity,[status(thm)],[306,234]) ).
tff(308,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(b,multiply(b,multiply(a,multiply(b,b))))),multiply(a,multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b)))))) = multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(multiply(b,multiply(b,multiply(a,multiply(b,b)))),multiply(a,multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(309,plain,
multiply(multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(b,multiply(b,multiply(a,multiply(b,b))))),multiply(a,multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b)))))) = multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(multiply(b,multiply(b,multiply(a,multiply(b,b)))),multiply(a,multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b))))))),
inference(unit_resolution,[status(thm)],[308,7]) ).
tff(310,plain,
multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(multiply(b,multiply(b,multiply(a,multiply(b,b)))),multiply(a,multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b))))))) = multiply(multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(b,multiply(b,multiply(a,multiply(b,b))))),multiply(a,multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b)))))),
inference(symmetry,[status(thm)],[309]) ).
tff(311,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,b),multiply(a,multiply(b,b))) = multiply(b,multiply(b,multiply(a,multiply(b,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(312,plain,
multiply(multiply(b,b),multiply(a,multiply(b,b))) = multiply(b,multiply(b,multiply(a,multiply(b,b)))),
inference(unit_resolution,[status(thm)],[311,7]) ).
tff(313,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,b),a),multiply(b,b)) = multiply(multiply(b,b),multiply(a,multiply(b,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(314,plain,
multiply(multiply(multiply(b,b),a),multiply(b,b)) = multiply(multiply(b,b),multiply(a,multiply(b,b))),
inference(unit_resolution,[status(thm)],[313,7]) ).
tff(315,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,b),a) = multiply(b,multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(316,plain,
multiply(multiply(b,b),a) = multiply(b,multiply(b,a)),
inference(unit_resolution,[status(thm)],[315,7]) ).
tff(317,plain,
multiply(b,multiply(b,a)) = multiply(multiply(b,b),a),
inference(symmetry,[status(thm)],[316]) ).
tff(318,plain,
multiply(multiply(b,multiply(b,a)),multiply(b,b)) = multiply(multiply(multiply(b,b),a),multiply(b,b)),
inference(monotonicity,[status(thm)],[317]) ).
tff(319,plain,
multiply(multiply(b,multiply(b,a)),multiply(b,b)) = multiply(b,multiply(b,multiply(a,multiply(b,b)))),
inference(transitivity,[status(thm)],[318,314,312]) ).
tff(320,plain,
multiply(multiply(multiply(b,multiply(b,a)),multiply(b,b)),multiply(a,multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b)))))) = multiply(multiply(b,multiply(b,multiply(a,multiply(b,b)))),multiply(a,multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b)))))),
inference(monotonicity,[status(thm)],[319]) ).
tff(321,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(b,a)),multiply(b,b)),multiply(a,multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b)))))) = multiply(multiply(b,multiply(b,a)),multiply(multiply(b,b),multiply(a,multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(322,plain,
multiply(multiply(multiply(b,multiply(b,a)),multiply(b,b)),multiply(a,multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b)))))) = multiply(multiply(b,multiply(b,a)),multiply(multiply(b,b),multiply(a,multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b))))))),
inference(unit_resolution,[status(thm)],[321,7]) ).
tff(323,plain,
multiply(multiply(b,multiply(b,a)),multiply(multiply(b,b),multiply(a,multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b))))))) = multiply(multiply(multiply(b,multiply(b,a)),multiply(b,b)),multiply(a,multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b)))))),
inference(symmetry,[status(thm)],[322]) ).
tff(324,plain,
multiply(a,multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b))))) = multiply(multiply(multiply(a,a),multiply(a,a)),multiply(multiply(a,b),multiply(b,b))),
inference(transitivity,[status(thm)],[233,230]) ).
tff(325,plain,
multiply(multiply(b,b),multiply(a,multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b)))))) = multiply(multiply(b,b),multiply(multiply(multiply(a,a),multiply(a,a)),multiply(multiply(a,b),multiply(b,b)))),
inference(monotonicity,[status(thm)],[324]) ).
tff(326,plain,
multiply(multiply(b,b),multiply(multiply(multiply(a,a),multiply(a,a)),multiply(multiply(a,b),multiply(b,b)))) = multiply(multiply(b,b),multiply(a,multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b)))))),
inference(symmetry,[status(thm)],[325]) ).
tff(327,plain,
multiply(multiply(multiply(a,a),multiply(a,a)),multiply(multiply(a,b),multiply(b,b))) = multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,multiply(b,multiply(b,b))))),
inference(transitivity,[status(thm)],[168,156]) ).
tff(328,plain,
multiply(multiply(b,b),multiply(multiply(multiply(a,a),multiply(a,a)),multiply(multiply(a,b),multiply(b,b)))) = multiply(multiply(b,b),multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,multiply(b,multiply(b,b)))))),
inference(monotonicity,[status(thm)],[327]) ).
tff(329,plain,
multiply(multiply(b,b),multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,multiply(b,multiply(b,b)))))) = multiply(multiply(b,b),multiply(multiply(multiply(a,a),multiply(a,a)),multiply(multiply(a,b),multiply(b,b)))),
inference(symmetry,[status(thm)],[328]) ).
tff(330,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,b),multiply(a,multiply(a,a))),multiply(a,multiply(a,multiply(b,multiply(b,b))))) = multiply(multiply(b,b),multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,multiply(b,multiply(b,b)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(331,plain,
multiply(multiply(multiply(b,b),multiply(a,multiply(a,a))),multiply(a,multiply(a,multiply(b,multiply(b,b))))) = multiply(multiply(b,b),multiply(multiply(a,multiply(a,a)),multiply(a,multiply(a,multiply(b,multiply(b,b)))))),
inference(unit_resolution,[status(thm)],[330,7]) ).
tff(332,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,b),multiply(a,multiply(a,a))) = multiply(b,multiply(b,multiply(a,multiply(a,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(333,plain,
multiply(multiply(b,b),multiply(a,multiply(a,a))) = multiply(b,multiply(b,multiply(a,multiply(a,a)))),
inference(unit_resolution,[status(thm)],[332,7]) ).
tff(334,plain,
multiply(multiply(multiply(b,b),multiply(a,multiply(a,a))),multiply(a,multiply(a,multiply(b,multiply(b,b))))) = multiply(multiply(b,multiply(b,multiply(a,multiply(a,a)))),multiply(multiply(b,multiply(b,b)),multiply(a,a))),
inference(monotonicity,[status(thm)],[333,200]) ).
tff(335,plain,
multiply(multiply(b,multiply(b,multiply(a,multiply(a,a)))),multiply(multiply(b,multiply(b,b)),multiply(a,a))) = multiply(multiply(multiply(b,b),multiply(a,multiply(a,a))),multiply(a,multiply(a,multiply(b,multiply(b,b))))),
inference(symmetry,[status(thm)],[334]) ).
tff(336,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(b,multiply(a,multiply(a,a)))),multiply(b,multiply(b,b))),multiply(a,a)) = multiply(multiply(b,multiply(b,multiply(a,multiply(a,a)))),multiply(multiply(b,multiply(b,b)),multiply(a,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(337,plain,
multiply(multiply(multiply(b,multiply(b,multiply(a,multiply(a,a)))),multiply(b,multiply(b,b))),multiply(a,a)) = multiply(multiply(b,multiply(b,multiply(a,multiply(a,a)))),multiply(multiply(b,multiply(b,b)),multiply(a,a))),
inference(unit_resolution,[status(thm)],[336,7]) ).
tff(338,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,b))))) = multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,b)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(339,plain,
multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,b))))) = multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,b)))))),
inference(unit_resolution,[status(thm)],[338,7]) ).
tff(340,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,a),b),multiply(b,multiply(b,multiply(b,b)))) = multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(341,plain,
multiply(multiply(multiply(a,a),b),multiply(b,multiply(b,multiply(b,b)))) = multiply(multiply(a,a),multiply(b,multiply(b,multiply(b,multiply(b,b))))),
inference(unit_resolution,[status(thm)],[340,7]) ).
tff(342,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,a),b) = multiply(a,multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(343,plain,
multiply(multiply(a,a),b) = multiply(a,multiply(a,b)),
inference(unit_resolution,[status(thm)],[342,7]) ).
tff(344,plain,
multiply(a,multiply(a,b)) = multiply(multiply(a,a),b),
inference(symmetry,[status(thm)],[343]) ).
tff(345,plain,
multiply(multiply(a,multiply(a,b)),multiply(b,multiply(b,multiply(b,b)))) = multiply(multiply(multiply(a,a),b),multiply(b,multiply(b,multiply(b,b)))),
inference(monotonicity,[status(thm)],[344]) ).
tff(346,plain,
multiply(multiply(a,multiply(a,b)),multiply(b,multiply(b,multiply(b,b)))) = multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,b)))))),
inference(transitivity,[status(thm)],[345,341,339]) ).
tff(347,plain,
multiply(a,multiply(multiply(a,multiply(a,b)),multiply(b,multiply(b,multiply(b,b))))) = multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,b))))))),
inference(monotonicity,[status(thm)],[346]) ).
tff(348,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(a,multiply(a,b))),multiply(b,multiply(b,multiply(b,b)))) = multiply(a,multiply(multiply(a,multiply(a,b)),multiply(b,multiply(b,multiply(b,b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(349,plain,
multiply(multiply(a,multiply(a,multiply(a,b))),multiply(b,multiply(b,multiply(b,b)))) = multiply(a,multiply(multiply(a,multiply(a,b)),multiply(b,multiply(b,multiply(b,b))))),
inference(unit_resolution,[status(thm)],[348,7]) ).
tff(350,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(a,multiply(a,b))),b),multiply(b,multiply(b,b))) = multiply(multiply(a,multiply(a,multiply(a,b))),multiply(b,multiply(b,multiply(b,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(351,plain,
multiply(multiply(multiply(a,multiply(a,multiply(a,b))),b),multiply(b,multiply(b,b))) = multiply(multiply(a,multiply(a,multiply(a,b))),multiply(b,multiply(b,multiply(b,b)))),
inference(unit_resolution,[status(thm)],[350,7]) ).
tff(352,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,a),multiply(a,b)) = multiply(a,multiply(a,multiply(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(353,plain,
multiply(multiply(a,a),multiply(a,b)) = multiply(a,multiply(a,multiply(a,b))),
inference(unit_resolution,[status(thm)],[352,7]) ).
tff(354,plain,
multiply(a,multiply(a,multiply(a,b))) = multiply(multiply(a,a),multiply(a,b)),
inference(symmetry,[status(thm)],[353]) ).
tff(355,plain,
multiply(multiply(a,multiply(a,multiply(a,b))),b) = multiply(multiply(multiply(a,a),multiply(a,b)),b),
inference(monotonicity,[status(thm)],[354]) ).
tff(356,plain,
multiply(multiply(multiply(a,a),multiply(a,b)),b) = multiply(multiply(a,multiply(a,multiply(a,b))),b),
inference(symmetry,[status(thm)],[355]) ).
tff(357,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,a),multiply(a,b)),b) = multiply(multiply(a,a),multiply(multiply(a,b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(358,plain,
multiply(multiply(multiply(a,a),multiply(a,b)),b) = multiply(multiply(a,a),multiply(multiply(a,b),b)),
inference(unit_resolution,[status(thm)],[357,7]) ).
tff(359,plain,
multiply(multiply(a,a),multiply(multiply(a,b),b)) = multiply(multiply(multiply(a,a),multiply(a,b)),b),
inference(symmetry,[status(thm)],[358]) ).
tff(360,plain,
multiply(multiply(a,a),multiply(multiply(a,b),b)) = multiply(multiply(a,a),multiply(a,multiply(b,b))),
inference(monotonicity,[status(thm)],[292]) ).
tff(361,plain,
multiply(multiply(a,a),multiply(a,multiply(b,b))) = multiply(multiply(a,a),multiply(multiply(a,b),b)),
inference(symmetry,[status(thm)],[360]) ).
tff(362,plain,
multiply(multiply(a,a),multiply(a,multiply(b,b))) = multiply(multiply(a,multiply(a,multiply(a,b))),b),
inference(transitivity,[status(thm)],[361,359,356]) ).
tff(363,plain,
multiply(multiply(multiply(a,a),multiply(a,multiply(b,b))),multiply(b,multiply(b,b))) = multiply(multiply(multiply(a,multiply(a,multiply(a,b))),b),multiply(b,multiply(b,b))),
inference(monotonicity,[status(thm)],[362]) ).
tff(364,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,a),multiply(a,multiply(b,b))) = multiply(a,multiply(a,multiply(a,multiply(b,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(365,plain,
multiply(multiply(a,a),multiply(a,multiply(b,b))) = multiply(a,multiply(a,multiply(a,multiply(b,b)))),
inference(unit_resolution,[status(thm)],[364,7]) ).
tff(366,plain,
multiply(a,multiply(a,multiply(a,multiply(b,b)))) = multiply(multiply(a,a),multiply(a,multiply(b,b))),
inference(symmetry,[status(thm)],[365]) ).
tff(367,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) )
| ( multiply(multiply(b,b),multiply(a,multiply(a,a))) = multiply(a,multiply(a,multiply(a,multiply(b,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(368,plain,
multiply(multiply(b,b),multiply(a,multiply(a,a))) = multiply(a,multiply(a,multiply(a,multiply(b,b)))),
inference(unit_resolution,[status(thm)],[367,28]) ).
tff(369,plain,
multiply(b,multiply(b,multiply(a,multiply(a,a)))) = multiply(multiply(b,b),multiply(a,multiply(a,a))),
inference(symmetry,[status(thm)],[333]) ).
tff(370,plain,
multiply(b,multiply(b,multiply(a,multiply(a,a)))) = multiply(multiply(a,a),multiply(a,multiply(b,b))),
inference(transitivity,[status(thm)],[369,368,366]) ).
tff(371,plain,
multiply(multiply(b,multiply(b,multiply(a,multiply(a,a)))),multiply(b,multiply(b,b))) = multiply(multiply(multiply(a,a),multiply(a,multiply(b,b))),multiply(b,multiply(b,b))),
inference(monotonicity,[status(thm)],[370]) ).
tff(372,plain,
multiply(multiply(b,multiply(b,multiply(a,multiply(a,a)))),multiply(b,multiply(b,b))) = multiply(multiply(b,multiply(b,multiply(b,multiply(b,b)))),multiply(a,multiply(a,a))),
inference(transitivity,[status(thm)],[371,363,351,349,347,279]) ).
tff(373,plain,
multiply(multiply(multiply(b,multiply(b,multiply(a,multiply(a,a)))),multiply(b,multiply(b,b))),multiply(a,a)) = multiply(multiply(multiply(b,multiply(b,multiply(b,multiply(b,b)))),multiply(a,multiply(a,a))),multiply(a,a)),
inference(monotonicity,[status(thm)],[372]) ).
tff(374,plain,
multiply(multiply(multiply(b,multiply(b,multiply(b,multiply(b,b)))),multiply(a,multiply(a,a))),multiply(a,a)) = multiply(multiply(multiply(b,multiply(b,multiply(a,multiply(a,a)))),multiply(b,multiply(b,b))),multiply(a,a)),
inference(symmetry,[status(thm)],[373]) ).
tff(375,plain,
multiply(multiply(multiply(b,multiply(b,multiply(b,multiply(b,b)))),multiply(a,multiply(a,a))),multiply(a,a)) = multiply(multiply(b,b),multiply(a,multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b)))))),
inference(transitivity,[status(thm)],[374,337,335,331,329,326]) ).
tff(376,plain,
multiply(multiply(b,multiply(b,a)),multiply(multiply(multiply(b,multiply(b,multiply(b,multiply(b,b)))),multiply(a,multiply(a,a))),multiply(a,a))) = multiply(multiply(b,multiply(b,a)),multiply(multiply(b,b),multiply(a,multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b))))))),
inference(monotonicity,[status(thm)],[375]) ).
tff(377,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,b),multiply(b,multiply(b,b))) = multiply(b,multiply(b,multiply(b,multiply(b,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(378,plain,
multiply(multiply(b,b),multiply(b,multiply(b,b))) = multiply(b,multiply(b,multiply(b,multiply(b,b)))),
inference(unit_resolution,[status(thm)],[377,7]) ).
tff(379,plain,
multiply(multiply(multiply(b,b),multiply(b,multiply(b,b))),multiply(a,multiply(a,a))) = multiply(multiply(b,multiply(b,multiply(b,multiply(b,b)))),multiply(a,multiply(a,a))),
inference(monotonicity,[status(thm)],[378]) ).
tff(380,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,b),multiply(b,multiply(b,b))),multiply(a,multiply(a,a))) = multiply(multiply(b,b),multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(381,plain,
multiply(multiply(multiply(b,b),multiply(b,multiply(b,b))),multiply(a,multiply(a,a))) = multiply(multiply(b,b),multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,a)))),
inference(unit_resolution,[status(thm)],[380,7]) ).
tff(382,plain,
multiply(multiply(b,b),multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,a)))) = multiply(multiply(multiply(b,b),multiply(b,multiply(b,b))),multiply(a,multiply(a,a))),
inference(symmetry,[status(thm)],[381]) ).
tff(383,plain,
multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,b))))) = multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,a))),
inference(symmetry,[status(thm)],[177]) ).
tff(384,plain,
multiply(multiply(b,b),multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,b)))))) = multiply(multiply(b,b),multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,a)))),
inference(monotonicity,[status(thm)],[383]) ).
tff(385,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,b),a),multiply(a,multiply(a,multiply(b,multiply(b,b))))) = multiply(multiply(b,b),multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,b)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(386,plain,
multiply(multiply(multiply(b,b),a),multiply(a,multiply(a,multiply(b,multiply(b,b))))) = multiply(multiply(b,b),multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,b)))))),
inference(unit_resolution,[status(thm)],[385,7]) ).
tff(387,plain,
multiply(multiply(b,multiply(b,a)),multiply(a,multiply(a,multiply(b,multiply(b,b))))) = multiply(multiply(multiply(b,b),a),multiply(a,multiply(a,multiply(b,multiply(b,b))))),
inference(monotonicity,[status(thm)],[317]) ).
tff(388,plain,
multiply(multiply(b,multiply(b,a)),multiply(a,multiply(a,multiply(b,multiply(b,b))))) = multiply(multiply(b,multiply(b,multiply(b,multiply(b,b)))),multiply(a,multiply(a,a))),
inference(transitivity,[status(thm)],[387,386,384,382,379]) ).
tff(389,plain,
multiply(multiply(multiply(b,multiply(b,a)),multiply(a,multiply(a,multiply(b,multiply(b,b))))),multiply(a,a)) = multiply(multiply(multiply(b,multiply(b,multiply(b,multiply(b,b)))),multiply(a,multiply(a,a))),multiply(a,a)),
inference(monotonicity,[status(thm)],[388]) ).
tff(390,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(b,a)),multiply(a,multiply(a,multiply(b,multiply(b,b))))),multiply(a,a)) = multiply(multiply(b,multiply(b,a)),multiply(multiply(a,multiply(a,multiply(b,multiply(b,b)))),multiply(a,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(391,plain,
multiply(multiply(multiply(b,multiply(b,a)),multiply(a,multiply(a,multiply(b,multiply(b,b))))),multiply(a,a)) = multiply(multiply(b,multiply(b,a)),multiply(multiply(a,multiply(a,multiply(b,multiply(b,b)))),multiply(a,a))),
inference(unit_resolution,[status(thm)],[390,7]) ).
tff(392,plain,
multiply(multiply(b,multiply(b,a)),multiply(multiply(a,multiply(a,multiply(b,multiply(b,b)))),multiply(a,a))) = multiply(multiply(multiply(b,multiply(b,a)),multiply(a,multiply(a,multiply(b,multiply(b,b))))),multiply(a,a)),
inference(symmetry,[status(thm)],[391]) ).
tff(393,plain,
multiply(multiply(a,multiply(a,multiply(b,multiply(b,b)))),multiply(a,a)) = multiply(multiply(multiply(b,multiply(b,b)),multiply(a,a)),multiply(a,a)),
inference(monotonicity,[status(thm)],[200]) ).
tff(394,plain,
multiply(multiply(multiply(b,multiply(b,b)),multiply(a,a)),multiply(a,a)) = multiply(multiply(a,multiply(a,multiply(b,multiply(b,b)))),multiply(a,a)),
inference(symmetry,[status(thm)],[393]) ).
tff(395,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(b,b)),multiply(a,a)),multiply(a,a)) = multiply(multiply(b,multiply(b,b)),multiply(multiply(a,a),multiply(a,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(396,plain,
multiply(multiply(multiply(b,multiply(b,b)),multiply(a,a)),multiply(a,a)) = multiply(multiply(b,multiply(b,b)),multiply(multiply(a,a),multiply(a,a))),
inference(unit_resolution,[status(thm)],[395,7]) ).
tff(397,plain,
multiply(multiply(b,multiply(b,b)),multiply(multiply(a,a),multiply(a,a))) = multiply(multiply(multiply(b,multiply(b,b)),multiply(a,a)),multiply(a,a)),
inference(symmetry,[status(thm)],[396]) ).
tff(398,plain,
multiply(multiply(b,multiply(b,b)),multiply(multiply(a,multiply(a,a)),a)) = multiply(multiply(b,multiply(b,b)),multiply(multiply(a,a),multiply(a,a))),
inference(symmetry,[status(thm)],[213]) ).
tff(399,plain,
multiply(multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,b))))),a) = multiply(multiply(multiply(b,multiply(b,b)),multiply(a,multiply(a,a))),a),
inference(symmetry,[status(thm)],[206]) ).
tff(400,plain,
multiply(a,multiply(multiply(a,multiply(a,multiply(b,multiply(b,b)))),a)) = multiply(multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,b))))),a),
inference(symmetry,[status(thm)],[205]) ).
tff(401,plain,
multiply(a,multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a))))) = multiply(a,multiply(multiply(a,multiply(a,multiply(b,multiply(b,b)))),a)),
inference(symmetry,[status(thm)],[203]) ).
tff(402,plain,
multiply(a,multiply(multiply(a,a),multiply(a,multiply(b,multiply(b,b))))) = multiply(a,multiply(b,multiply(multiply(b,b),multiply(a,multiply(a,a))))),
inference(symmetry,[status(thm)],[193]) ).
tff(403,plain,
multiply(multiply(multiply(a,a),multiply(a,a)),multiply(b,multiply(b,b))) = multiply(multiply(multiply(a,multiply(a,a)),a),multiply(b,multiply(b,b))),
inference(symmetry,[status(thm)],[186]) ).
tff(404,plain,
multiply(multiply(a,multiply(a,multiply(a,a))),multiply(b,multiply(b,b))) = multiply(multiply(multiply(a,a),multiply(a,a)),multiply(b,multiply(b,b))),
inference(symmetry,[status(thm)],[185]) ).
tff(405,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(a,multiply(a,a))),multiply(b,multiply(b,b))) = multiply(a,multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(406,plain,
multiply(multiply(a,multiply(a,multiply(a,a))),multiply(b,multiply(b,b))) = multiply(a,multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,b)))),
inference(unit_resolution,[status(thm)],[405,7]) ).
tff(407,plain,
multiply(a,multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,b)))) = multiply(multiply(a,multiply(a,multiply(a,a))),multiply(b,multiply(b,b))),
inference(symmetry,[status(thm)],[406]) ).
tff(408,plain,
multiply(a,multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,b)))) = multiply(multiply(a,multiply(a,multiply(b,multiply(b,b)))),multiply(a,a)),
inference(transitivity,[status(thm)],[407,404,403,188,191,402,401,400,399,208,398,397,394]) ).
tff(409,plain,
multiply(multiply(multiply(b,b),a),multiply(a,multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,b))))) = multiply(multiply(b,multiply(b,a)),multiply(multiply(a,multiply(a,multiply(b,multiply(b,b)))),multiply(a,a))),
inference(monotonicity,[status(thm)],[316,408]) ).
tff(410,plain,
multiply(multiply(a,multiply(a,a)),multiply(multiply(a,b),multiply(b,b))) = multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b)))),
inference(monotonicity,[status(thm)],[158]) ).
tff(411,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) )
| ( multiply(a,multiply(b,multiply(b,b))) = multiply(b,multiply(b,multiply(b,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(412,plain,
multiply(a,multiply(b,multiply(b,b))) = multiply(b,multiply(b,multiply(b,a))),
inference(unit_resolution,[status(thm)],[411,28]) ).
tff(413,plain,
multiply(b,multiply(b,multiply(b,a))) = multiply(a,multiply(b,multiply(b,b))),
inference(symmetry,[status(thm)],[412]) ).
tff(414,plain,
multiply(b,multiply(multiply(b,b),a)) = multiply(b,multiply(b,multiply(b,a))),
inference(monotonicity,[status(thm)],[316]) ).
tff(415,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,multiply(b,b)),a) = multiply(b,multiply(multiply(b,b),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(416,plain,
multiply(multiply(b,multiply(b,b)),a) = multiply(b,multiply(multiply(b,b),a)),
inference(unit_resolution,[status(thm)],[415,7]) ).
tff(417,plain,
multiply(multiply(multiply(b,b),b),a) = multiply(multiply(b,multiply(b,b)),a),
inference(monotonicity,[status(thm)],[133]) ).
tff(418,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,b),b),a) = multiply(multiply(b,b),multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(419,plain,
multiply(multiply(multiply(b,b),b),a) = multiply(multiply(b,b),multiply(b,a)),
inference(unit_resolution,[status(thm)],[418,7]) ).
tff(420,plain,
multiply(multiply(b,b),multiply(b,a)) = multiply(multiply(multiply(b,b),b),a),
inference(symmetry,[status(thm)],[419]) ).
tff(421,plain,
multiply(multiply(b,b),multiply(b,a)) = multiply(multiply(a,b),multiply(b,b)),
inference(transitivity,[status(thm)],[420,417,416,414,413,159]) ).
tff(422,plain,
multiply(multiply(a,multiply(a,a)),multiply(multiply(b,b),multiply(b,a))) = multiply(multiply(a,multiply(a,a)),multiply(multiply(a,b),multiply(b,b))),
inference(monotonicity,[status(thm)],[421]) ).
tff(423,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(a,a)),multiply(b,b)),multiply(b,a)) = multiply(multiply(a,multiply(a,a)),multiply(multiply(b,b),multiply(b,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(424,plain,
multiply(multiply(multiply(a,multiply(a,a)),multiply(b,b)),multiply(b,a)) = multiply(multiply(a,multiply(a,a)),multiply(multiply(b,b),multiply(b,a))),
inference(unit_resolution,[status(thm)],[423,7]) ).
tff(425,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(a,a)),multiply(b,b)) = multiply(a,multiply(multiply(a,a),multiply(b,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(426,plain,
multiply(multiply(a,multiply(a,a)),multiply(b,b)) = multiply(a,multiply(multiply(a,a),multiply(b,b))),
inference(unit_resolution,[status(thm)],[425,7]) ).
tff(427,plain,
multiply(a,multiply(multiply(a,a),multiply(b,b))) = multiply(multiply(a,multiply(a,a)),multiply(b,b)),
inference(symmetry,[status(thm)],[426]) ).
tff(428,plain,
multiply(multiply(a,multiply(a,b)),b) = multiply(multiply(multiply(a,a),b),b),
inference(monotonicity,[status(thm)],[344]) ).
tff(429,plain,
multiply(multiply(multiply(a,a),b),b) = multiply(multiply(a,multiply(a,b)),b),
inference(symmetry,[status(thm)],[428]) ).
tff(430,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,a),b),b) = multiply(multiply(a,a),multiply(b,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(431,plain,
multiply(multiply(multiply(a,a),b),b) = multiply(multiply(a,a),multiply(b,b)),
inference(unit_resolution,[status(thm)],[430,7]) ).
tff(432,plain,
multiply(multiply(a,a),multiply(b,b)) = multiply(multiply(multiply(a,a),b),b),
inference(symmetry,[status(thm)],[431]) ).
tff(433,plain,
multiply(multiply(a,a),multiply(b,b)) = multiply(multiply(a,multiply(a,b)),b),
inference(transitivity,[status(thm)],[432,429]) ).
tff(434,plain,
multiply(a,multiply(multiply(a,a),multiply(b,b))) = multiply(a,multiply(multiply(a,multiply(a,b)),b)),
inference(monotonicity,[status(thm)],[433]) ).
tff(435,plain,
multiply(a,multiply(multiply(a,multiply(a,b)),b)) = multiply(a,multiply(multiply(a,a),multiply(b,b))),
inference(symmetry,[status(thm)],[434]) ).
tff(436,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(a,multiply(a,b))),b) = multiply(a,multiply(multiply(a,multiply(a,b)),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(437,plain,
multiply(multiply(a,multiply(a,multiply(a,b))),b) = multiply(a,multiply(multiply(a,multiply(a,b)),b)),
inference(unit_resolution,[status(thm)],[436,7]) ).
tff(438,plain,
multiply(b,multiply(b,multiply(a,multiply(a,a)))) = multiply(multiply(a,multiply(a,a)),multiply(b,b)),
inference(transitivity,[status(thm)],[369,368,366,361,359,356,437,435,427]) ).
tff(439,plain,
multiply(multiply(b,multiply(b,multiply(a,multiply(a,a)))),multiply(b,a)) = multiply(multiply(multiply(a,multiply(a,a)),multiply(b,b)),multiply(b,a)),
inference(monotonicity,[status(thm)],[438]) ).
tff(440,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,b),a),multiply(a,a)) = multiply(multiply(b,b),multiply(a,multiply(a,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(441,plain,
multiply(multiply(multiply(b,b),a),multiply(a,a)) = multiply(multiply(b,b),multiply(a,multiply(a,a))),
inference(unit_resolution,[status(thm)],[440,7]) ).
tff(442,plain,
multiply(multiply(b,multiply(b,a)),multiply(a,a)) = multiply(multiply(multiply(b,b),a),multiply(a,a)),
inference(monotonicity,[status(thm)],[317]) ).
tff(443,plain,
multiply(multiply(b,multiply(b,a)),multiply(a,a)) = multiply(b,multiply(b,multiply(a,multiply(a,a)))),
inference(transitivity,[status(thm)],[442,441,333]) ).
tff(444,plain,
multiply(multiply(multiply(b,multiply(b,a)),multiply(a,a)),multiply(b,a)) = multiply(multiply(b,multiply(b,multiply(a,multiply(a,a)))),multiply(b,a)),
inference(monotonicity,[status(thm)],[443]) ).
tff(445,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(b,a)),multiply(a,a)),multiply(b,a)) = multiply(multiply(b,multiply(b,a)),multiply(multiply(a,a),multiply(b,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(446,plain,
multiply(multiply(multiply(b,multiply(b,a)),multiply(a,a)),multiply(b,a)) = multiply(multiply(b,multiply(b,a)),multiply(multiply(a,a),multiply(b,a))),
inference(unit_resolution,[status(thm)],[445,7]) ).
tff(447,plain,
multiply(multiply(b,multiply(b,a)),multiply(multiply(a,a),multiply(b,a))) = multiply(multiply(multiply(b,multiply(b,a)),multiply(a,a)),multiply(b,a)),
inference(symmetry,[status(thm)],[446]) ).
tff(448,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,a),b),a) = multiply(multiply(a,a),multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(449,plain,
multiply(multiply(multiply(a,a),b),a) = multiply(multiply(a,a),multiply(b,a)),
inference(unit_resolution,[status(thm)],[448,7]) ).
tff(450,plain,
multiply(multiply(multiply(a,a),b),a) = multiply(multiply(a,multiply(a,b)),a),
inference(monotonicity,[status(thm)],[343]) ).
tff(451,plain,
multiply(multiply(a,multiply(a,b)),a) = multiply(multiply(multiply(a,a),b),a),
inference(symmetry,[status(thm)],[450]) ).
tff(452,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(a,b)),a) = multiply(a,multiply(multiply(a,b),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(453,plain,
multiply(multiply(a,multiply(a,b)),a) = multiply(a,multiply(multiply(a,b),a)),
inference(unit_resolution,[status(thm)],[452,7]) ).
tff(454,plain,
multiply(a,multiply(multiply(a,b),a)) = multiply(multiply(a,multiply(a,b)),a),
inference(symmetry,[status(thm)],[453]) ).
tff(455,plain,
multiply(a,multiply(multiply(a,b),a)) = multiply(multiply(a,a),multiply(b,a)),
inference(transitivity,[status(thm)],[454,451,449]) ).
tff(456,plain,
multiply(multiply(b,multiply(b,a)),multiply(a,multiply(multiply(a,b),a))) = multiply(multiply(b,multiply(b,a)),multiply(multiply(a,a),multiply(b,a))),
inference(monotonicity,[status(thm)],[455]) ).
tff(457,plain,
multiply(multiply(b,multiply(b,a)),multiply(a,multiply(multiply(a,b),a))) = multiply(a,multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,b)))),
inference(transitivity,[status(thm)],[456,447,444,439,424,422,410,189,186,185,406]) ).
tff(458,plain,
multiply(multiply(b,multiply(b,a)),multiply(multiply(b,multiply(b,a)),multiply(a,multiply(multiply(a,b),a)))) = multiply(multiply(multiply(b,b),a),multiply(a,multiply(multiply(a,multiply(a,a)),multiply(b,multiply(b,b))))),
inference(monotonicity,[status(thm)],[317,457]) ).
tff(459,plain,
multiply(multiply(b,multiply(b,a)),multiply(multiply(b,multiply(b,a)),multiply(a,multiply(multiply(a,b),a)))) = multiply(multiply(multiply(b,multiply(b,multiply(b,multiply(b,b)))),multiply(a,multiply(a,a))),multiply(a,a)),
inference(transitivity,[status(thm)],[458,409,392,389]) ).
tff(460,plain,
multiply(multiply(b,multiply(b,a)),multiply(multiply(b,multiply(b,a)),multiply(multiply(b,multiply(b,a)),multiply(a,multiply(multiply(a,b),a))))) = multiply(multiply(b,multiply(b,a)),multiply(multiply(multiply(b,multiply(b,multiply(b,multiply(b,b)))),multiply(a,multiply(a,a))),multiply(a,a))),
inference(monotonicity,[status(thm)],[459]) ).
tff(461,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) )
| ( multiply(multiply(a,multiply(multiply(a,b),a)),multiply(multiply(b,multiply(b,a)),multiply(multiply(b,multiply(b,a)),multiply(b,multiply(b,a))))) = multiply(multiply(b,multiply(b,a)),multiply(multiply(b,multiply(b,a)),multiply(multiply(b,multiply(b,a)),multiply(a,multiply(multiply(a,b),a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(462,plain,
multiply(multiply(a,multiply(multiply(a,b),a)),multiply(multiply(b,multiply(b,a)),multiply(multiply(b,multiply(b,a)),multiply(b,multiply(b,a))))) = multiply(multiply(b,multiply(b,a)),multiply(multiply(b,multiply(b,a)),multiply(multiply(b,multiply(b,a)),multiply(a,multiply(multiply(a,b),a))))),
inference(unit_resolution,[status(thm)],[461,28]) ).
tff(463,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,b),multiply(b,a)) = multiply(a,multiply(b,multiply(b,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(464,plain,
multiply(multiply(a,b),multiply(b,a)) = multiply(a,multiply(b,multiply(b,a))),
inference(unit_resolution,[status(thm)],[463,7]) ).
tff(465,plain,
multiply(a,multiply(b,multiply(b,a))) = multiply(multiply(a,b),multiply(b,a)),
inference(symmetry,[status(thm)],[464]) ).
tff(466,plain,
multiply(multiply(b,b),multiply(a,multiply(b,multiply(b,a)))) = multiply(multiply(b,b),multiply(multiply(a,b),multiply(b,a))),
inference(monotonicity,[status(thm)],[465]) ).
tff(467,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,b),a),multiply(b,multiply(b,a))) = multiply(multiply(b,b),multiply(a,multiply(b,multiply(b,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(468,plain,
multiply(multiply(multiply(b,b),a),multiply(b,multiply(b,a))) = multiply(multiply(b,b),multiply(a,multiply(b,multiply(b,a)))),
inference(unit_resolution,[status(thm)],[467,7]) ).
tff(469,plain,
multiply(multiply(b,multiply(b,a)),multiply(b,multiply(b,a))) = multiply(multiply(multiply(b,b),a),multiply(b,multiply(b,a))),
inference(monotonicity,[status(thm)],[317]) ).
tff(470,plain,
multiply(multiply(b,multiply(b,a)),multiply(b,multiply(b,a))) = multiply(multiply(b,b),multiply(multiply(a,b),multiply(b,a))),
inference(transitivity,[status(thm)],[469,468,466]) ).
tff(471,plain,
multiply(multiply(b,multiply(b,a)),multiply(multiply(b,multiply(b,a)),multiply(b,multiply(b,a)))) = multiply(multiply(b,multiply(b,a)),multiply(multiply(b,b),multiply(multiply(a,b),multiply(b,a)))),
inference(monotonicity,[status(thm)],[470]) ).
tff(472,plain,
multiply(multiply(b,multiply(b,a)),multiply(multiply(b,b),multiply(multiply(a,b),multiply(b,a)))) = multiply(multiply(b,multiply(b,a)),multiply(multiply(b,multiply(b,a)),multiply(b,multiply(b,a)))),
inference(symmetry,[status(thm)],[471]) ).
tff(473,plain,
multiply(multiply(a,multiply(multiply(a,b),a)),multiply(multiply(b,multiply(b,a)),multiply(multiply(b,b),multiply(multiply(a,b),multiply(b,a))))) = multiply(multiply(a,multiply(multiply(a,b),a)),multiply(multiply(b,multiply(b,a)),multiply(multiply(b,multiply(b,a)),multiply(b,multiply(b,a))))),
inference(monotonicity,[status(thm)],[472]) ).
tff(474,plain,
multiply(multiply(a,multiply(multiply(a,b),a)),multiply(multiply(b,multiply(b,a)),multiply(multiply(b,b),multiply(multiply(a,b),multiply(b,a))))) = multiply(multiply(b,multiply(b,multiply(a,multiply(b,b)))),multiply(a,multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b)))))),
inference(transitivity,[status(thm)],[473,462,460,376,323,320]) ).
tff(475,plain,
multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(multiply(a,multiply(multiply(a,b),a)),multiply(multiply(b,multiply(b,a)),multiply(multiply(b,b),multiply(multiply(a,b),multiply(b,a)))))) = multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(multiply(b,multiply(b,multiply(a,multiply(b,b)))),multiply(a,multiply(multiply(a,multiply(a,a)),multiply(a,multiply(b,multiply(b,b))))))),
inference(monotonicity,[status(thm)],[474]) ).
tff(476,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(a,multiply(multiply(a,b),a))),multiply(multiply(b,multiply(b,a)),multiply(multiply(b,b),multiply(multiply(a,b),multiply(b,a))))) = multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(multiply(a,multiply(multiply(a,b),a)),multiply(multiply(b,multiply(b,a)),multiply(multiply(b,b),multiply(multiply(a,b),multiply(b,a)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(477,plain,
multiply(multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(a,multiply(multiply(a,b),a))),multiply(multiply(b,multiply(b,a)),multiply(multiply(b,b),multiply(multiply(a,b),multiply(b,a))))) = multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(multiply(a,multiply(multiply(a,b),a)),multiply(multiply(b,multiply(b,a)),multiply(multiply(b,b),multiply(multiply(a,b),multiply(b,a)))))),
inference(unit_resolution,[status(thm)],[476,7]) ).
tff(478,plain,
multiply(multiply(b,b),multiply(multiply(a,b),multiply(b,a))) = multiply(multiply(b,b),multiply(a,multiply(b,multiply(b,a)))),
inference(symmetry,[status(thm)],[466]) ).
tff(479,plain,
multiply(multiply(b,multiply(b,a)),multiply(multiply(b,b),multiply(multiply(a,b),multiply(b,a)))) = multiply(multiply(b,multiply(b,a)),multiply(multiply(b,b),multiply(a,multiply(b,multiply(b,a))))),
inference(monotonicity,[status(thm)],[478]) ).
tff(480,plain,
multiply(multiply(b,multiply(b,a)),multiply(multiply(b,b),multiply(a,multiply(b,multiply(b,a))))) = multiply(multiply(b,multiply(b,a)),multiply(multiply(b,b),multiply(multiply(a,b),multiply(b,a)))),
inference(symmetry,[status(thm)],[479]) ).
tff(481,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(b,a)),multiply(b,b)),multiply(a,multiply(b,multiply(b,a)))) = multiply(multiply(b,multiply(b,a)),multiply(multiply(b,b),multiply(a,multiply(b,multiply(b,a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(482,plain,
multiply(multiply(multiply(b,multiply(b,a)),multiply(b,b)),multiply(a,multiply(b,multiply(b,a)))) = multiply(multiply(b,multiply(b,a)),multiply(multiply(b,b),multiply(a,multiply(b,multiply(b,a))))),
inference(unit_resolution,[status(thm)],[481,7]) ).
tff(483,plain,
multiply(multiply(multiply(b,multiply(b,a)),multiply(b,b)),multiply(a,multiply(b,multiply(b,a)))) = multiply(multiply(b,multiply(b,multiply(a,multiply(b,b)))),multiply(a,multiply(b,multiply(b,a)))),
inference(monotonicity,[status(thm)],[319]) ).
tff(484,plain,
multiply(multiply(b,multiply(b,multiply(a,multiply(b,b)))),multiply(a,multiply(b,multiply(b,a)))) = multiply(multiply(multiply(b,multiply(b,a)),multiply(b,b)),multiply(a,multiply(b,multiply(b,a)))),
inference(symmetry,[status(thm)],[483]) ).
tff(485,plain,
multiply(b,multiply(a,multiply(b,b))) = multiply(b,multiply(multiply(a,b),b)),
inference(monotonicity,[status(thm)],[293]) ).
tff(486,plain,
multiply(b,multiply(multiply(a,b),b)) = multiply(b,multiply(a,multiply(b,b))),
inference(symmetry,[status(thm)],[485]) ).
tff(487,plain,
multiply(b,multiply(b,multiply(multiply(a,b),b))) = multiply(b,multiply(b,multiply(a,multiply(b,b)))),
inference(monotonicity,[status(thm)],[486]) ).
tff(488,plain,
multiply(multiply(b,multiply(b,multiply(multiply(a,b),b))),multiply(a,multiply(b,multiply(b,a)))) = multiply(multiply(b,multiply(b,multiply(a,multiply(b,b)))),multiply(a,multiply(b,multiply(b,a)))),
inference(monotonicity,[status(thm)],[487]) ).
tff(489,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,multiply(b,multiply(multiply(a,b),b))),multiply(a,multiply(b,multiply(b,a)))) = multiply(b,multiply(multiply(b,multiply(multiply(a,b),b)),multiply(a,multiply(b,multiply(b,a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(490,plain,
multiply(multiply(b,multiply(b,multiply(multiply(a,b),b))),multiply(a,multiply(b,multiply(b,a)))) = multiply(b,multiply(multiply(b,multiply(multiply(a,b),b)),multiply(a,multiply(b,multiply(b,a))))),
inference(unit_resolution,[status(thm)],[489,7]) ).
tff(491,plain,
multiply(b,multiply(multiply(b,multiply(multiply(a,b),b)),multiply(a,multiply(b,multiply(b,a))))) = multiply(multiply(b,multiply(b,multiply(multiply(a,b),b))),multiply(a,multiply(b,multiply(b,a)))),
inference(symmetry,[status(thm)],[490]) ).
tff(492,plain,
multiply(multiply(b,multiply(multiply(a,b),b)),multiply(a,multiply(b,multiply(b,a)))) = multiply(multiply(b,multiply(multiply(a,b),b)),multiply(multiply(a,b),multiply(b,a))),
inference(monotonicity,[status(thm)],[465]) ).
tff(493,plain,
multiply(multiply(b,multiply(multiply(a,b),b)),multiply(multiply(a,b),multiply(b,a))) = multiply(multiply(b,multiply(multiply(a,b),b)),multiply(a,multiply(b,multiply(b,a)))),
inference(symmetry,[status(thm)],[492]) ).
tff(494,plain,
multiply(b,multiply(multiply(b,multiply(multiply(a,b),b)),multiply(multiply(a,b),multiply(b,a)))) = multiply(b,multiply(multiply(b,multiply(multiply(a,b),b)),multiply(a,multiply(b,multiply(b,a))))),
inference(monotonicity,[status(thm)],[493]) ).
tff(495,plain,
multiply(b,multiply(multiply(b,multiply(multiply(a,b),b)),multiply(multiply(a,b),multiply(b,a)))) = multiply(multiply(b,multiply(b,a)),multiply(multiply(b,b),multiply(multiply(a,b),multiply(b,a)))),
inference(transitivity,[status(thm)],[494,491,488,484,482,480]) ).
tff(496,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,a),multiply(a,b)) = multiply(b,multiply(a,multiply(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(497,plain,
multiply(multiply(b,a),multiply(a,b)) = multiply(b,multiply(a,multiply(a,b))),
inference(unit_resolution,[status(thm)],[496,7]) ).
tff(498,plain,
multiply(b,multiply(a,multiply(a,b))) = multiply(multiply(b,a),multiply(a,b)),
inference(symmetry,[status(thm)],[497]) ).
tff(499,plain,
multiply(a,multiply(b,multiply(a,multiply(a,b)))) = multiply(a,multiply(multiply(b,a),multiply(a,b))),
inference(monotonicity,[status(thm)],[498]) ).
tff(500,plain,
multiply(a,multiply(multiply(b,a),multiply(a,b))) = multiply(a,multiply(b,multiply(a,multiply(a,b)))),
inference(symmetry,[status(thm)],[499]) ).
tff(501,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(b,a)),multiply(a,b)) = multiply(a,multiply(multiply(b,a),multiply(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(502,plain,
multiply(multiply(a,multiply(b,a)),multiply(a,b)) = multiply(a,multiply(multiply(b,a),multiply(a,b))),
inference(unit_resolution,[status(thm)],[501,7]) ).
tff(503,plain,
multiply(multiply(a,multiply(b,a)),multiply(a,b)) = multiply(a,multiply(b,multiply(a,multiply(a,b)))),
inference(transitivity,[status(thm)],[502,500]) ).
tff(504,plain,
multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(a,multiply(multiply(a,b),a))) = multiply(multiply(a,multiply(b,multiply(a,multiply(a,b)))),multiply(a,multiply(multiply(a,b),a))),
inference(monotonicity,[status(thm)],[503]) ).
tff(505,plain,
multiply(multiply(a,multiply(b,multiply(a,multiply(a,b)))),multiply(a,multiply(multiply(a,b),a))) = multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(a,multiply(multiply(a,b),a))),
inference(symmetry,[status(thm)],[504]) ).
tff(506,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(b,multiply(a,multiply(a,b)))),multiply(a,multiply(multiply(a,b),a))) = multiply(a,multiply(multiply(b,multiply(a,multiply(a,b))),multiply(a,multiply(multiply(a,b),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(507,plain,
multiply(multiply(a,multiply(b,multiply(a,multiply(a,b)))),multiply(a,multiply(multiply(a,b),a))) = multiply(a,multiply(multiply(b,multiply(a,multiply(a,b))),multiply(a,multiply(multiply(a,b),a)))),
inference(unit_resolution,[status(thm)],[506,7]) ).
tff(508,plain,
multiply(a,multiply(multiply(b,multiply(a,multiply(a,b))),multiply(a,multiply(multiply(a,b),a)))) = multiply(multiply(a,multiply(b,multiply(a,multiply(a,b)))),multiply(a,multiply(multiply(a,b),a))),
inference(symmetry,[status(thm)],[507]) ).
tff(509,plain,
multiply(multiply(multiply(a,b),a),multiply(a,b)) = multiply(multiply(a,multiply(b,a)),multiply(a,b)),
inference(monotonicity,[status(thm)],[284]) ).
tff(510,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,b),a),multiply(a,b)) = multiply(multiply(a,b),multiply(a,multiply(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(511,plain,
multiply(multiply(multiply(a,b),a),multiply(a,b)) = multiply(multiply(a,b),multiply(a,multiply(a,b))),
inference(unit_resolution,[status(thm)],[510,7]) ).
tff(512,plain,
multiply(multiply(a,b),multiply(a,multiply(a,b))) = multiply(multiply(multiply(a,b),a),multiply(a,b)),
inference(symmetry,[status(thm)],[511]) ).
tff(513,plain,
multiply(multiply(a,b),multiply(a,multiply(a,b))) = multiply(multiply(a,multiply(b,a)),multiply(a,b)),
inference(transitivity,[status(thm)],[512,509]) ).
tff(514,plain,
multiply(multiply(multiply(a,b),multiply(a,multiply(a,b))),a) = multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a),
inference(monotonicity,[status(thm)],[513]) ).
tff(515,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,b),multiply(a,multiply(a,b))),a) = multiply(multiply(a,b),multiply(multiply(a,multiply(a,b)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(516,plain,
multiply(multiply(multiply(a,b),multiply(a,multiply(a,b))),a) = multiply(multiply(a,b),multiply(multiply(a,multiply(a,b)),a)),
inference(unit_resolution,[status(thm)],[515,7]) ).
tff(517,plain,
multiply(multiply(a,b),multiply(multiply(a,multiply(a,b)),a)) = multiply(multiply(multiply(a,b),multiply(a,multiply(a,b))),a),
inference(symmetry,[status(thm)],[516]) ).
tff(518,plain,
multiply(multiply(a,b),multiply(a,multiply(multiply(a,b),a))) = multiply(multiply(a,b),multiply(multiply(a,multiply(a,b)),a)),
inference(monotonicity,[status(thm)],[454]) ).
tff(519,plain,
multiply(multiply(a,b),multiply(a,multiply(multiply(a,b),a))) = multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a),
inference(transitivity,[status(thm)],[518,517,514]) ).
tff(520,plain,
multiply(multiply(b,a),multiply(multiply(a,b),multiply(a,multiply(multiply(a,b),a)))) = multiply(multiply(b,a),multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a)),
inference(monotonicity,[status(thm)],[519]) ).
tff(521,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,a),multiply(a,b)),multiply(a,multiply(multiply(a,b),a))) = multiply(multiply(b,a),multiply(multiply(a,b),multiply(a,multiply(multiply(a,b),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(522,plain,
multiply(multiply(multiply(b,a),multiply(a,b)),multiply(a,multiply(multiply(a,b),a))) = multiply(multiply(b,a),multiply(multiply(a,b),multiply(a,multiply(multiply(a,b),a)))),
inference(unit_resolution,[status(thm)],[521,7]) ).
tff(523,plain,
multiply(multiply(b,multiply(a,multiply(a,b))),multiply(a,multiply(multiply(a,b),a))) = multiply(multiply(multiply(b,a),multiply(a,b)),multiply(a,multiply(multiply(a,b),a))),
inference(monotonicity,[status(thm)],[498]) ).
tff(524,plain,
multiply(multiply(b,multiply(a,multiply(a,b))),multiply(a,multiply(multiply(a,b),a))) = multiply(multiply(b,a),multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a)),
inference(transitivity,[status(thm)],[523,522,520]) ).
tff(525,plain,
multiply(a,multiply(multiply(b,multiply(a,multiply(a,b))),multiply(a,multiply(multiply(a,b),a)))) = multiply(a,multiply(multiply(b,a),multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a))),
inference(monotonicity,[status(thm)],[524]) ).
tff(526,plain,
multiply(a,multiply(multiply(b,a),multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a))) = multiply(a,multiply(multiply(b,multiply(a,multiply(a,b))),multiply(a,multiply(multiply(a,b),a)))),
inference(symmetry,[status(thm)],[525]) ).
tff(527,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a) = multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(528,plain,
multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a) = multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a)),
inference(unit_resolution,[status(thm)],[527,7]) ).
tff(529,plain,
multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a)) = multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a),
inference(symmetry,[status(thm)],[528]) ).
tff(530,plain,
multiply(multiply(b,a),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a))) = multiply(multiply(b,a),multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a)),
inference(monotonicity,[status(thm)],[529]) ).
tff(531,plain,
multiply(multiply(b,a),multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a)) = multiply(multiply(b,a),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a))),
inference(symmetry,[status(thm)],[530]) ).
tff(532,plain,
multiply(a,multiply(multiply(b,a),multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a))) = multiply(a,multiply(multiply(b,a),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a)))),
inference(monotonicity,[status(thm)],[531]) ).
tff(533,plain,
multiply(a,multiply(multiply(b,a),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a)))) = multiply(a,multiply(multiply(b,a),multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a))),
inference(symmetry,[status(thm)],[532]) ).
tff(534,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a))) = multiply(a,multiply(multiply(b,a),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(535,plain,
multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a))) = multiply(a,multiply(multiply(b,a),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a)))),
inference(unit_resolution,[status(thm)],[534,7]) ).
tff(536,plain,
multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a))) = multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(a,multiply(multiply(a,b),a))),
inference(transitivity,[status(thm)],[535,533,526,508,505]) ).
tff(537,plain,
multiply(multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a))),multiply(b,multiply(multiply(b,multiply(multiply(a,b),b)),multiply(multiply(a,b),multiply(b,a))))) = multiply(multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(a,multiply(multiply(a,b),a))),multiply(multiply(b,multiply(b,a)),multiply(multiply(b,b),multiply(multiply(a,b),multiply(b,a))))),
inference(monotonicity,[status(thm)],[536,495]) ).
tff(538,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a))),b),multiply(multiply(b,multiply(multiply(a,b),b)),multiply(multiply(a,b),multiply(b,a)))) = multiply(multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a))),multiply(b,multiply(multiply(b,multiply(multiply(a,b),b)),multiply(multiply(a,b),multiply(b,a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(539,plain,
multiply(multiply(multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a))),b),multiply(multiply(b,multiply(multiply(a,b),b)),multiply(multiply(a,b),multiply(b,a)))) = multiply(multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a))),multiply(b,multiply(multiply(b,multiply(multiply(a,b),b)),multiply(multiply(a,b),multiply(b,a))))),
inference(unit_resolution,[status(thm)],[538,7]) ).
tff(540,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a))),b) = multiply(multiply(a,multiply(b,a)),multiply(multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a)),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(541,plain,
multiply(multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a))),b) = multiply(multiply(a,multiply(b,a)),multiply(multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a)),b)),
inference(unit_resolution,[status(thm)],[540,7]) ).
tff(542,plain,
multiply(multiply(a,multiply(b,a)),multiply(multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a)),b)) = multiply(multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a))),b),
inference(symmetry,[status(thm)],[541]) ).
tff(543,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(b,a)),multiply(a,multiply(b,multiply(a,b)))) = multiply(a,multiply(multiply(b,a),multiply(a,multiply(b,multiply(a,b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(544,plain,
multiply(multiply(a,multiply(b,a)),multiply(a,multiply(b,multiply(a,b)))) = multiply(a,multiply(multiply(b,a),multiply(a,multiply(b,multiply(a,b))))),
inference(unit_resolution,[status(thm)],[543,7]) ).
tff(545,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,b),multiply(a,b)) = multiply(a,multiply(b,multiply(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(546,plain,
multiply(multiply(a,b),multiply(a,b)) = multiply(a,multiply(b,multiply(a,b))),
inference(unit_resolution,[status(thm)],[545,7]) ).
tff(547,plain,
multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),multiply(a,b))) = multiply(multiply(a,multiply(b,a)),multiply(a,multiply(b,multiply(a,b)))),
inference(monotonicity,[status(thm)],[546]) ).
tff(548,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(a,b)) = multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),multiply(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(549,plain,
multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(a,b)) = multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),multiply(a,b))),
inference(unit_resolution,[status(thm)],[548,7]) ).
tff(550,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a),b) = multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(551,plain,
multiply(multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a),b) = multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(a,b)),
inference(unit_resolution,[status(thm)],[550,7]) ).
tff(552,plain,
multiply(multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a)),b) = multiply(multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a),b),
inference(monotonicity,[status(thm)],[529]) ).
tff(553,plain,
multiply(multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a)),b) = multiply(a,multiply(multiply(b,a),multiply(a,multiply(b,multiply(a,b))))),
inference(transitivity,[status(thm)],[552,551,549,547,544]) ).
tff(554,plain,
multiply(multiply(a,multiply(b,a)),multiply(multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a)),b)) = multiply(multiply(a,multiply(b,a)),multiply(a,multiply(multiply(b,a),multiply(a,multiply(b,multiply(a,b)))))),
inference(monotonicity,[status(thm)],[553]) ).
tff(555,plain,
multiply(multiply(a,multiply(b,a)),multiply(a,multiply(multiply(b,a),multiply(a,multiply(b,multiply(a,b)))))) = multiply(multiply(a,multiply(b,a)),multiply(multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a)),b)),
inference(symmetry,[status(thm)],[554]) ).
tff(556,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,a),b) = multiply(b,multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(557,plain,
multiply(multiply(b,a),b) = multiply(b,multiply(a,b)),
inference(unit_resolution,[status(thm)],[556,7]) ).
tff(558,plain,
multiply(a,multiply(multiply(b,a),b)) = multiply(a,multiply(b,multiply(a,b))),
inference(monotonicity,[status(thm)],[557]) ).
tff(559,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(b,a)),b) = multiply(a,multiply(multiply(b,a),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(560,plain,
multiply(multiply(a,multiply(b,a)),b) = multiply(a,multiply(multiply(b,a),b)),
inference(unit_resolution,[status(thm)],[559,7]) ).
tff(561,plain,
multiply(multiply(a,multiply(b,a)),b) = multiply(a,multiply(b,multiply(a,b))),
inference(transitivity,[status(thm)],[560,558]) ).
tff(562,plain,
multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),b)) = multiply(multiply(a,multiply(b,a)),multiply(a,multiply(b,multiply(a,b)))),
inference(monotonicity,[status(thm)],[561]) ).
tff(563,plain,
multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),b)) = multiply(a,multiply(multiply(b,a),multiply(a,multiply(b,multiply(a,b))))),
inference(transitivity,[status(thm)],[562,544]) ).
tff(564,plain,
multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),b))) = multiply(multiply(a,multiply(b,a)),multiply(a,multiply(multiply(b,a),multiply(a,multiply(b,multiply(a,b)))))),
inference(monotonicity,[status(thm)],[563]) ).
tff(565,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) )
| ( multiply(b,multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),multiply(a,multiply(b,a))))) = multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(566,plain,
multiply(b,multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),multiply(a,multiply(b,a))))) = multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),b))),
inference(unit_resolution,[status(thm)],[565,28]) ).
tff(567,plain,
multiply(multiply(a,multiply(b,a)),multiply(a,multiply(b,a))) = multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a)),
inference(monotonicity,[status(thm)],[285]) ).
tff(568,plain,
multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),multiply(a,multiply(b,a)))) = multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a))),
inference(monotonicity,[status(thm)],[567]) ).
tff(569,plain,
multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a))) = multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),multiply(a,multiply(b,a)))),
inference(symmetry,[status(thm)],[568]) ).
tff(570,plain,
multiply(b,multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a)))) = multiply(b,multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),multiply(a,multiply(b,a))))),
inference(monotonicity,[status(thm)],[569]) ).
tff(571,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a))) = multiply(b,multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(572,plain,
multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a))) = multiply(b,multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a)))),
inference(unit_resolution,[status(thm)],[571,7]) ).
tff(573,plain,
multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a)) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a))),
inference(monotonicity,[status(thm)],[528]) ).
tff(574,plain,
multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(a,b),multiply(a,multiply(multiply(a,b),a)))) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a)),
inference(monotonicity,[status(thm)],[519]) ).
tff(575,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(a,b)),multiply(a,multiply(multiply(a,b),a))) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(a,b),multiply(a,multiply(multiply(a,b),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(576,plain,
multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(a,b)),multiply(a,multiply(multiply(a,b),a))) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(a,b),multiply(a,multiply(multiply(a,b),a)))),
inference(unit_resolution,[status(thm)],[575,7]) ).
tff(577,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,multiply(a,multiply(b,a))),multiply(a,b)) = multiply(b,multiply(multiply(a,multiply(b,a)),multiply(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(578,plain,
multiply(multiply(b,multiply(a,multiply(b,a))),multiply(a,b)) = multiply(b,multiply(multiply(a,multiply(b,a)),multiply(a,b))),
inference(unit_resolution,[status(thm)],[577,7]) ).
tff(579,plain,
multiply(b,multiply(multiply(a,multiply(b,a)),multiply(a,b))) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(a,b)),
inference(symmetry,[status(thm)],[578]) ).
tff(580,plain,
multiply(multiply(b,multiply(multiply(a,multiply(b,a)),multiply(a,b))),multiply(a,multiply(multiply(a,b),a))) = multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(a,b)),multiply(a,multiply(multiply(a,b),a))),
inference(monotonicity,[status(thm)],[579]) ).
tff(581,plain,
multiply(multiply(b,multiply(multiply(a,multiply(b,a)),multiply(a,b))),multiply(a,multiply(multiply(a,b),a))) = multiply(multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a))),b),
inference(transitivity,[status(thm)],[580,576,574,573,572,570,566,564,555,542]) ).
tff(582,plain,
multiply(multiply(multiply(b,multiply(multiply(a,multiply(b,a)),multiply(a,b))),multiply(a,multiply(multiply(a,b),a))),multiply(multiply(b,multiply(multiply(a,b),b)),multiply(multiply(a,b),multiply(b,a)))) = multiply(multiply(multiply(multiply(a,multiply(b,a)),multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),a))),b),multiply(multiply(b,multiply(multiply(a,b),b)),multiply(multiply(a,b),multiply(b,a)))),
inference(monotonicity,[status(thm)],[581]) ).
tff(583,plain,
multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(a,b)),multiply(a,multiply(multiply(a,b),a))) = multiply(multiply(b,multiply(multiply(a,multiply(b,a)),multiply(a,b))),multiply(a,multiply(multiply(a,b),a))),
inference(symmetry,[status(thm)],[580]) ).
tff(584,plain,
multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(a,b),multiply(a,multiply(multiply(a,b),a)))) = multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(a,b)),multiply(a,multiply(multiply(a,b),a))),
inference(symmetry,[status(thm)],[576]) ).
tff(585,plain,
multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a)) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(a,b),multiply(a,multiply(multiply(a,b),a)))),
inference(symmetry,[status(thm)],[574]) ).
tff(586,plain,
multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a)) = multiply(multiply(b,multiply(multiply(a,multiply(b,a)),multiply(a,b))),multiply(a,multiply(multiply(a,b),a))),
inference(transitivity,[status(thm)],[585,584,583]) ).
tff(587,plain,
multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a)),multiply(multiply(b,multiply(multiply(a,b),b)),multiply(a,multiply(b,multiply(b,a))))) = multiply(multiply(multiply(b,multiply(multiply(a,multiply(b,a)),multiply(a,b))),multiply(a,multiply(multiply(a,b),a))),multiply(multiply(b,multiply(multiply(a,b),b)),multiply(multiply(a,b),multiply(b,a)))),
inference(monotonicity,[status(thm)],[586,492]) ).
tff(588,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a)),multiply(b,multiply(multiply(a,b),b))),multiply(a,multiply(b,multiply(b,a)))) = multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a)),multiply(multiply(b,multiply(multiply(a,b),b)),multiply(a,multiply(b,multiply(b,a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(589,plain,
multiply(multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a)),multiply(b,multiply(multiply(a,b),b))),multiply(a,multiply(b,multiply(b,a)))) = multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a)),multiply(multiply(b,multiply(multiply(a,b),b)),multiply(a,multiply(b,multiply(b,a))))),
inference(unit_resolution,[status(thm)],[588,7]) ).
tff(590,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a)),multiply(b,multiply(multiply(a,b),b))) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a),multiply(b,multiply(multiply(a,b),b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(591,plain,
multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a)),multiply(b,multiply(multiply(a,b),b))) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a),multiply(b,multiply(multiply(a,b),b)))),
inference(unit_resolution,[status(thm)],[590,7]) ).
tff(592,plain,
multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a),multiply(b,multiply(multiply(a,b),b)))) = multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a)),multiply(b,multiply(multiply(a,b),b))),
inference(symmetry,[status(thm)],[591]) ).
tff(593,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))) = multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(594,plain,
multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))) = multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))),
inference(unit_resolution,[status(thm)],[593,7]) ).
tff(595,plain,
multiply(a,multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))) = multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))),
inference(monotonicity,[status(thm)],[594]) ).
tff(596,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))) = multiply(a,multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(597,plain,
multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))) = multiply(a,multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))),
inference(unit_resolution,[status(thm)],[596,7]) ).
tff(598,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,b)))) = multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(599,plain,
multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,b)))) = multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),
inference(unit_resolution,[status(thm)],[598,7]) ).
tff(600,plain,
multiply(multiply(a,b),multiply(multiply(a,b),multiply(a,b))) = multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,b)))),
inference(monotonicity,[status(thm)],[546]) ).
tff(601,plain,
multiply(multiply(a,b),multiply(multiply(a,b),multiply(a,b))) = multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),
inference(transitivity,[status(thm)],[600,599]) ).
tff(602,plain,
multiply(b,multiply(multiply(a,b),multiply(multiply(a,b),multiply(a,b)))) = multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),
inference(monotonicity,[status(thm)],[601]) ).
tff(603,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) )
| ( multiply(b,multiply(multiply(a,b),multiply(multiply(a,b),multiply(a,b)))) = multiply(multiply(a,b),multiply(multiply(a,b),multiply(multiply(a,b),b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(604,plain,
multiply(b,multiply(multiply(a,b),multiply(multiply(a,b),multiply(a,b)))) = multiply(multiply(a,b),multiply(multiply(a,b),multiply(multiply(a,b),b))),
inference(unit_resolution,[status(thm)],[603,28]) ).
tff(605,plain,
multiply(multiply(a,b),multiply(multiply(a,b),multiply(multiply(a,b),b))) = multiply(b,multiply(multiply(a,b),multiply(multiply(a,b),multiply(a,b)))),
inference(symmetry,[status(thm)],[604]) ).
tff(606,plain,
multiply(multiply(a,b),multiply(multiply(a,b),multiply(multiply(a,b),b))) = multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),
inference(transitivity,[status(thm)],[605,602]) ).
tff(607,plain,
multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),multiply(multiply(a,b),multiply(multiply(a,b),b)))) = multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))),
inference(monotonicity,[status(thm)],[606]) ).
tff(608,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(multiply(a,b),multiply(multiply(a,b),b))) = multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),multiply(multiply(a,b),multiply(multiply(a,b),b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(609,plain,
multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(multiply(a,b),multiply(multiply(a,b),b))) = multiply(multiply(a,multiply(b,a)),multiply(multiply(a,b),multiply(multiply(a,b),multiply(multiply(a,b),b)))),
inference(unit_resolution,[status(thm)],[608,7]) ).
tff(610,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,b),multiply(multiply(a,b),b)) = multiply(a,multiply(b,multiply(multiply(a,b),b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(611,plain,
multiply(multiply(a,b),multiply(multiply(a,b),b)) = multiply(a,multiply(b,multiply(multiply(a,b),b))),
inference(unit_resolution,[status(thm)],[610,7]) ).
tff(612,plain,
multiply(a,multiply(b,multiply(multiply(a,b),b))) = multiply(multiply(a,b),multiply(multiply(a,b),b)),
inference(symmetry,[status(thm)],[611]) ).
tff(613,plain,
multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(a,multiply(b,multiply(multiply(a,b),b)))) = multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(multiply(a,b),multiply(multiply(a,b),b))),
inference(monotonicity,[status(thm)],[612]) ).
tff(614,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a),multiply(b,multiply(multiply(a,b),b))) = multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(a,multiply(b,multiply(multiply(a,b),b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(615,plain,
multiply(multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a),multiply(b,multiply(multiply(a,b),b))) = multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),multiply(a,multiply(b,multiply(multiply(a,b),b)))),
inference(unit_resolution,[status(thm)],[614,7]) ).
tff(616,plain,
multiply(multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a),multiply(b,multiply(multiply(a,b),b))) = multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))),
inference(transitivity,[status(thm)],[615,613,609,607,597,595]) ).
tff(617,plain,
multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a),multiply(b,multiply(multiply(a,b),b)))) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))),
inference(monotonicity,[status(thm)],[616]) ).
tff(618,plain,
multiply(multiply(b,multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a),multiply(b,multiply(multiply(a,b),b)))),
inference(symmetry,[status(thm)],[617]) ).
tff(619,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,a),multiply(b,a)) = multiply(b,multiply(a,multiply(b,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(620,plain,
multiply(multiply(b,a),multiply(b,a)) = multiply(b,multiply(a,multiply(b,a))),
inference(unit_resolution,[status(thm)],[619,7]) ).
tff(621,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,a),b),a) = multiply(multiply(b,a),multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(622,plain,
multiply(multiply(multiply(b,a),b),a) = multiply(multiply(b,a),multiply(b,a)),
inference(unit_resolution,[status(thm)],[621,7]) ).
tff(623,plain,
multiply(b,multiply(a,b)) = multiply(multiply(b,a),b),
inference(symmetry,[status(thm)],[557]) ).
tff(624,plain,
multiply(multiply(b,multiply(a,b)),a) = multiply(multiply(multiply(b,a),b),a),
inference(monotonicity,[status(thm)],[623]) ).
tff(625,plain,
multiply(multiply(b,multiply(a,b)),a) = multiply(b,multiply(a,multiply(b,a))),
inference(transitivity,[status(thm)],[624,622,620]) ).
tff(626,plain,
multiply(multiply(multiply(b,multiply(a,b)),a),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))),
inference(monotonicity,[status(thm)],[625]) ).
tff(627,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(a,b)),a),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))) = multiply(multiply(b,multiply(a,b)),multiply(a,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(628,plain,
multiply(multiply(multiply(b,multiply(a,b)),a),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))) = multiply(multiply(b,multiply(a,b)),multiply(a,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))),
inference(unit_resolution,[status(thm)],[627,7]) ).
tff(629,plain,
multiply(multiply(b,multiply(a,b)),multiply(a,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))) = multiply(multiply(multiply(b,multiply(a,b)),a),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))),
inference(symmetry,[status(thm)],[628]) ).
tff(630,plain,
multiply(b,multiply(a,multiply(b,a))) = multiply(multiply(b,a),multiply(b,a)),
inference(symmetry,[status(thm)],[620]) ).
tff(631,plain,
multiply(multiply(b,multiply(a,multiply(b,a))),multiply(b,a)) = multiply(multiply(multiply(b,a),multiply(b,a)),multiply(b,a)),
inference(monotonicity,[status(thm)],[630]) ).
tff(632,plain,
multiply(multiply(multiply(b,a),multiply(b,a)),multiply(b,a)) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(b,a)),
inference(symmetry,[status(thm)],[631]) ).
tff(633,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,a),multiply(b,a)),multiply(b,a)) = multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(634,plain,
multiply(multiply(multiply(b,a),multiply(b,a)),multiply(b,a)) = multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a))),
inference(unit_resolution,[status(thm)],[633,7]) ).
tff(635,plain,
multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a))) = multiply(multiply(multiply(b,a),multiply(b,a)),multiply(b,a)),
inference(symmetry,[status(thm)],[634]) ).
tff(636,plain,
multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a))) = multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,a)))),
inference(monotonicity,[status(thm)],[620]) ).
tff(637,plain,
multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,a)))) = multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a))),
inference(symmetry,[status(thm)],[636]) ).
tff(638,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,a),b),multiply(a,multiply(b,a))) = multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(639,plain,
multiply(multiply(multiply(b,a),b),multiply(a,multiply(b,a))) = multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,a)))),
inference(unit_resolution,[status(thm)],[638,7]) ).
tff(640,plain,
multiply(multiply(multiply(b,a),b),multiply(a,multiply(b,a))) = multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a))),
inference(monotonicity,[status(thm)],[557]) ).
tff(641,plain,
multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a))) = multiply(multiply(multiply(b,a),b),multiply(a,multiply(b,a))),
inference(symmetry,[status(thm)],[640]) ).
tff(642,plain,
multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a))) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(b,a)),
inference(transitivity,[status(thm)],[641,639,637,635,632]) ).
tff(643,plain,
multiply(multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,b)))) = multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(b,a)),multiply(a,multiply(b,multiply(a,b)))),
inference(monotonicity,[status(thm)],[642]) ).
tff(644,plain,
multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(b,a)),multiply(a,multiply(b,multiply(a,b)))) = multiply(multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,b)))),
inference(symmetry,[status(thm)],[643]) ).
tff(645,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(b,a)),multiply(a,multiply(b,multiply(a,b)))) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(b,a),multiply(a,multiply(b,multiply(a,b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(646,plain,
multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(b,a)),multiply(a,multiply(b,multiply(a,b)))) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(b,a),multiply(a,multiply(b,multiply(a,b))))),
inference(unit_resolution,[status(thm)],[645,7]) ).
tff(647,plain,
multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(b,a),multiply(a,multiply(b,multiply(a,b))))) = multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(b,a)),multiply(a,multiply(b,multiply(a,b)))),
inference(symmetry,[status(thm)],[646]) ).
tff(648,plain,
multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(b,a),multiply(a,multiply(b,multiply(a,b))))) = multiply(multiply(multiply(b,a),multiply(b,a)),multiply(multiply(b,a),multiply(a,multiply(b,multiply(a,b))))),
inference(monotonicity,[status(thm)],[630]) ).
tff(649,plain,
multiply(multiply(multiply(b,a),multiply(b,a)),multiply(multiply(b,a),multiply(a,multiply(b,multiply(a,b))))) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(b,a),multiply(a,multiply(b,multiply(a,b))))),
inference(symmetry,[status(thm)],[648]) ).
tff(650,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,a),multiply(b,a)),multiply(multiply(b,a),multiply(a,multiply(b,multiply(a,b))))) = multiply(multiply(b,a),multiply(multiply(b,a),multiply(multiply(b,a),multiply(a,multiply(b,multiply(a,b)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(651,plain,
multiply(multiply(multiply(b,a),multiply(b,a)),multiply(multiply(b,a),multiply(a,multiply(b,multiply(a,b))))) = multiply(multiply(b,a),multiply(multiply(b,a),multiply(multiply(b,a),multiply(a,multiply(b,multiply(a,b)))))),
inference(unit_resolution,[status(thm)],[650,7]) ).
tff(652,plain,
multiply(multiply(b,a),multiply(multiply(b,a),multiply(multiply(b,a),multiply(a,multiply(b,multiply(a,b)))))) = multiply(multiply(multiply(b,a),multiply(b,a)),multiply(multiply(b,a),multiply(a,multiply(b,multiply(a,b))))),
inference(symmetry,[status(thm)],[651]) ).
tff(653,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) )
| ( multiply(multiply(a,multiply(b,multiply(a,b))),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(b,a),multiply(multiply(b,a),multiply(multiply(b,a),multiply(a,multiply(b,multiply(a,b)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(654,plain,
multiply(multiply(a,multiply(b,multiply(a,b))),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(b,a),multiply(multiply(b,a),multiply(multiply(b,a),multiply(a,multiply(b,multiply(a,b)))))),
inference(unit_resolution,[status(thm)],[653,28]) ).
tff(655,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,b),a),b) = multiply(multiply(a,b),multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(656,plain,
multiply(multiply(multiply(a,b),a),b) = multiply(multiply(a,b),multiply(a,b)),
inference(unit_resolution,[status(thm)],[655,7]) ).
tff(657,plain,
multiply(multiply(a,b),multiply(a,b)) = multiply(multiply(multiply(a,b),a),b),
inference(symmetry,[status(thm)],[656]) ).
tff(658,plain,
multiply(a,multiply(b,multiply(a,b))) = multiply(multiply(a,b),multiply(a,b)),
inference(symmetry,[status(thm)],[546]) ).
tff(659,plain,
multiply(a,multiply(b,multiply(a,b))) = multiply(multiply(multiply(a,b),a),b),
inference(transitivity,[status(thm)],[658,657]) ).
tff(660,plain,
multiply(multiply(a,multiply(b,multiply(a,b))),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(multiply(multiply(a,b),a),b),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))),
inference(monotonicity,[status(thm)],[659]) ).
tff(661,plain,
multiply(multiply(multiply(multiply(a,b),a),b),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(a,multiply(b,multiply(a,b))),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))),
inference(symmetry,[status(thm)],[660]) ).
tff(662,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(a,b),a),b),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(multiply(a,b),a),multiply(b,multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(663,plain,
multiply(multiply(multiply(multiply(a,b),a),b),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(multiply(a,b),a),multiply(b,multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a))))),
inference(unit_resolution,[status(thm)],[662,7]) ).
tff(664,plain,
multiply(multiply(multiply(a,b),a),multiply(b,multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a))))) = multiply(multiply(multiply(multiply(a,b),a),b),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))),
inference(symmetry,[status(thm)],[663]) ).
tff(665,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,b))))) = multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(666,plain,
multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,b))))) = multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),
inference(unit_resolution,[status(thm)],[665,7]) ).
tff(667,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,a),multiply(b,multiply(a,b))) = multiply(b,multiply(a,multiply(b,multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(668,plain,
multiply(multiply(b,a),multiply(b,multiply(a,b))) = multiply(b,multiply(a,multiply(b,multiply(a,b)))),
inference(unit_resolution,[status(thm)],[667,7]) ).
tff(669,plain,
multiply(multiply(b,a),multiply(multiply(b,a),b)) = multiply(multiply(b,a),multiply(b,multiply(a,b))),
inference(monotonicity,[status(thm)],[557]) ).
tff(670,plain,
multiply(multiply(b,a),multiply(multiply(b,a),b)) = multiply(b,multiply(a,multiply(b,multiply(a,b)))),
inference(transitivity,[status(thm)],[669,668]) ).
tff(671,plain,
multiply(multiply(b,a),multiply(multiply(b,a),multiply(multiply(b,a),b))) = multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,b))))),
inference(monotonicity,[status(thm)],[670]) ).
tff(672,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) )
| ( multiply(b,multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(b,a),multiply(multiply(b,a),multiply(multiply(b,a),b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(673,plain,
multiply(b,multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(b,a),multiply(multiply(b,a),multiply(multiply(b,a),b))),
inference(unit_resolution,[status(thm)],[672,28]) ).
tff(674,plain,
multiply(b,multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))) = multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),
inference(transitivity,[status(thm)],[673,671,666]) ).
tff(675,plain,
multiply(multiply(multiply(a,b),a),multiply(b,multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a))))) = multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))),
inference(monotonicity,[status(thm)],[674]) ).
tff(676,plain,
multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))) = multiply(multiply(multiply(a,b),a),multiply(b,multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a))))),
inference(symmetry,[status(thm)],[675]) ).
tff(677,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))) = multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(678,plain,
multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))) = multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))),
inference(unit_resolution,[status(thm)],[677,7]) ).
tff(679,plain,
multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))) = multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))),
inference(symmetry,[status(thm)],[678]) ).
tff(680,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))) = multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(681,plain,
multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))) = multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))),
inference(unit_resolution,[status(thm)],[680,7]) ).
tff(682,plain,
multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))) = multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))),
inference(symmetry,[status(thm)],[681]) ).
tff(683,plain,
multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))) = multiply(multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,b)))),
inference(transitivity,[status(thm)],[682,679,676,664,661,654,652,649,647,644]) ).
tff(684,plain,
multiply(a,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))) = multiply(a,multiply(multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,b))))),
inference(monotonicity,[status(thm)],[683]) ).
tff(685,plain,
multiply(a,multiply(multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,b))))) = multiply(a,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))),
inference(symmetry,[status(thm)],[684]) ).
tff(686,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a)))),multiply(a,multiply(b,multiply(a,b)))) = multiply(a,multiply(multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(687,plain,
multiply(multiply(a,multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a)))),multiply(a,multiply(b,multiply(a,b)))) = multiply(a,multiply(multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,b))))),
inference(unit_resolution,[status(thm)],[686,7]) ).
tff(688,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a))) = multiply(a,multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(689,plain,
multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a))) = multiply(a,multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a)))),
inference(unit_resolution,[status(thm)],[688,7]) ).
tff(690,plain,
multiply(a,multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a)))) = multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a))),
inference(symmetry,[status(thm)],[689]) ).
tff(691,plain,
multiply(multiply(a,multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a)))),multiply(a,multiply(b,multiply(a,b)))) = multiply(multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,b)))),
inference(monotonicity,[status(thm)],[690]) ).
tff(692,plain,
multiply(multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,b)))) = multiply(multiply(a,multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a)))),multiply(a,multiply(b,multiply(a,b)))),
inference(symmetry,[status(thm)],[691]) ).
tff(693,plain,
multiply(multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,b)))) = multiply(a,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))),
inference(transitivity,[status(thm)],[692,687,685]) ).
tff(694,plain,
multiply(multiply(b,multiply(a,b)),multiply(multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,b))))) = multiply(multiply(b,multiply(a,b)),multiply(a,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))),
inference(monotonicity,[status(thm)],[693]) ).
tff(695,plain,
multiply(multiply(b,multiply(a,b)),multiply(multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,b))))) = multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a)),multiply(b,multiply(multiply(a,b),b))),
inference(transitivity,[status(thm)],[694,629,626,618,592]) ).
tff(696,plain,
multiply(multiply(multiply(b,multiply(a,b)),multiply(multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,b))))),multiply(a,multiply(b,multiply(b,a)))) = multiply(multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(multiply(a,multiply(b,a)),multiply(a,b)),a)),multiply(b,multiply(multiply(a,b),b))),multiply(a,multiply(b,multiply(b,a)))),
inference(monotonicity,[status(thm)],[695]) ).
tff(697,plain,
multiply(multiply(b,multiply(a,b)),multiply(a,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))) = multiply(multiply(b,multiply(a,b)),multiply(multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,b))))),
inference(symmetry,[status(thm)],[694]) ).
tff(698,plain,
multiply(multiply(b,multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))) = multiply(multiply(multiply(b,multiply(a,b)),a),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))),
inference(symmetry,[status(thm)],[626]) ).
tff(699,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,a),b),multiply(a,multiply(b,multiply(a,b)))) = multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(700,plain,
multiply(multiply(multiply(b,a),b),multiply(a,multiply(b,multiply(a,b)))) = multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,b))))),
inference(unit_resolution,[status(thm)],[699,7]) ).
tff(701,plain,
multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,multiply(a,b)))) = multiply(multiply(multiply(b,a),b),multiply(a,multiply(b,multiply(a,b)))),
inference(monotonicity,[status(thm)],[623]) ).
tff(702,plain,
multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,multiply(a,b)))) = multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),
inference(transitivity,[status(thm)],[701,700,666]) ).
tff(703,plain,
multiply(multiply(multiply(a,b),a),multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,multiply(a,b))))) = multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))),
inference(monotonicity,[status(thm)],[702]) ).
tff(704,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,b))),multiply(a,multiply(b,multiply(a,b)))) = multiply(multiply(multiply(a,b),a),multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,multiply(a,b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(705,plain,
multiply(multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,b))),multiply(a,multiply(b,multiply(a,b)))) = multiply(multiply(multiply(a,b),a),multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,multiply(a,b))))),
inference(unit_resolution,[status(thm)],[704,7]) ).
tff(706,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,b))) = multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(707,plain,
multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,b))) = multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,b)))),
inference(unit_resolution,[status(thm)],[706,7]) ).
tff(708,plain,
multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,b)))) = multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,b))),
inference(symmetry,[status(thm)],[707]) ).
tff(709,plain,
multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))) = multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,b)))),
inference(symmetry,[status(thm)],[599]) ).
tff(710,plain,
multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))) = multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,b))),
inference(transitivity,[status(thm)],[709,708]) ).
tff(711,plain,
multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),multiply(a,multiply(b,multiply(a,b)))) = multiply(multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,b))),multiply(a,multiply(b,multiply(a,b)))),
inference(monotonicity,[status(thm)],[710]) ).
tff(712,plain,
multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),multiply(a,multiply(b,multiply(a,b)))) = multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))),
inference(transitivity,[status(thm)],[711,705,703,678,681]) ).
tff(713,plain,
multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),multiply(a,multiply(b,multiply(a,b))))) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))),
inference(monotonicity,[status(thm)],[712]) ).
tff(714,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),multiply(a,multiply(b,multiply(a,b)))) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),multiply(a,multiply(b,multiply(a,b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(715,plain,
multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),multiply(a,multiply(b,multiply(a,b)))) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),multiply(a,multiply(b,multiply(a,b))))),
inference(unit_resolution,[status(thm)],[714,7]) ).
tff(716,plain,
multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,b)))) = multiply(multiply(a,b),multiply(multiply(a,b),multiply(a,b))),
inference(symmetry,[status(thm)],[600]) ).
tff(717,plain,
multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))) = multiply(multiply(a,b),multiply(multiply(a,b),multiply(a,b))),
inference(transitivity,[status(thm)],[709,716]) ).
tff(718,plain,
multiply(multiply(b,multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(a,b),multiply(multiply(a,b),multiply(a,b)))),
inference(monotonicity,[status(thm)],[717]) ).
tff(719,plain,
multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(a,b),multiply(multiply(a,b),multiply(a,b)))) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),
inference(symmetry,[status(thm)],[718]) ).
tff(720,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) )
| ( multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(a,b),multiply(multiply(a,b),multiply(a,b)))) = multiply(multiply(a,b),multiply(multiply(a,b),multiply(multiply(a,b),multiply(b,multiply(a,multiply(b,a)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(721,plain,
multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(a,b),multiply(multiply(a,b),multiply(a,b)))) = multiply(multiply(a,b),multiply(multiply(a,b),multiply(multiply(a,b),multiply(b,multiply(a,multiply(b,a)))))),
inference(unit_resolution,[status(thm)],[720,28]) ).
tff(722,plain,
multiply(multiply(a,b),multiply(multiply(a,b),multiply(multiply(a,b),multiply(b,multiply(a,multiply(b,a)))))) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(a,b),multiply(multiply(a,b),multiply(a,b)))),
inference(symmetry,[status(thm)],[721]) ).
tff(723,plain,
multiply(multiply(multiply(a,b),multiply(a,b)),multiply(b,multiply(a,multiply(b,a)))) = multiply(multiply(a,multiply(b,multiply(a,b))),multiply(b,multiply(a,multiply(b,a)))),
inference(monotonicity,[status(thm)],[546]) ).
tff(724,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,b),multiply(a,b)),multiply(b,multiply(a,multiply(b,a)))) = multiply(multiply(a,b),multiply(multiply(a,b),multiply(b,multiply(a,multiply(b,a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(725,plain,
multiply(multiply(multiply(a,b),multiply(a,b)),multiply(b,multiply(a,multiply(b,a)))) = multiply(multiply(a,b),multiply(multiply(a,b),multiply(b,multiply(a,multiply(b,a))))),
inference(unit_resolution,[status(thm)],[724,7]) ).
tff(726,plain,
multiply(multiply(a,b),multiply(multiply(a,b),multiply(b,multiply(a,multiply(b,a))))) = multiply(multiply(multiply(a,b),multiply(a,b)),multiply(b,multiply(a,multiply(b,a)))),
inference(symmetry,[status(thm)],[725]) ).
tff(727,plain,
multiply(multiply(a,b),multiply(multiply(a,b),multiply(b,multiply(a,multiply(b,a))))) = multiply(multiply(a,multiply(b,multiply(a,b))),multiply(b,multiply(a,multiply(b,a)))),
inference(transitivity,[status(thm)],[726,723]) ).
tff(728,plain,
multiply(multiply(a,b),multiply(multiply(a,b),multiply(multiply(a,b),multiply(b,multiply(a,multiply(b,a)))))) = multiply(multiply(a,b),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(b,multiply(a,multiply(b,a))))),
inference(monotonicity,[status(thm)],[727]) ).
tff(729,plain,
multiply(multiply(a,b),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(b,multiply(a,multiply(b,a))))) = multiply(multiply(a,b),multiply(multiply(a,b),multiply(multiply(a,b),multiply(b,multiply(a,multiply(b,a)))))),
inference(symmetry,[status(thm)],[728]) ).
tff(730,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,b)))),multiply(b,multiply(a,multiply(b,a)))) = multiply(multiply(a,b),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(b,multiply(a,multiply(b,a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(731,plain,
multiply(multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,b)))),multiply(b,multiply(a,multiply(b,a)))) = multiply(multiply(a,b),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(b,multiply(a,multiply(b,a))))),
inference(unit_resolution,[status(thm)],[730,7]) ).
tff(732,plain,
multiply(multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,b)))),multiply(b,multiply(a,multiply(b,a)))) = multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),multiply(b,multiply(a,multiply(b,a)))),
inference(monotonicity,[status(thm)],[599]) ).
tff(733,plain,
multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),multiply(b,multiply(a,multiply(b,a)))) = multiply(multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,b)))),multiply(b,multiply(a,multiply(b,a)))),
inference(symmetry,[status(thm)],[732]) ).
tff(734,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),b),multiply(a,multiply(b,a))) = multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),multiply(b,multiply(a,multiply(b,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(735,plain,
multiply(multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),b),multiply(a,multiply(b,a))) = multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),multiply(b,multiply(a,multiply(b,a)))),
inference(unit_resolution,[status(thm)],[734,7]) ).
tff(736,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,b),multiply(a,b)),multiply(multiply(a,b),b)) = multiply(multiply(a,b),multiply(multiply(a,b),multiply(multiply(a,b),b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(737,plain,
multiply(multiply(multiply(a,b),multiply(a,b)),multiply(multiply(a,b),b)) = multiply(multiply(a,b),multiply(multiply(a,b),multiply(multiply(a,b),b))),
inference(unit_resolution,[status(thm)],[736,7]) ).
tff(738,plain,
multiply(multiply(a,multiply(b,multiply(a,b))),multiply(multiply(a,b),b)) = multiply(multiply(multiply(a,b),multiply(a,b)),multiply(multiply(a,b),b)),
inference(monotonicity,[status(thm)],[658]) ).
tff(739,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,b)),b) = multiply(multiply(a,multiply(b,multiply(a,b))),multiply(multiply(a,b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(740,plain,
multiply(multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,b)),b) = multiply(multiply(a,multiply(b,multiply(a,b))),multiply(multiply(a,b),b)),
inference(unit_resolution,[status(thm)],[739,7]) ).
tff(741,plain,
multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,b)) = multiply(multiply(multiply(a,b),multiply(a,b)),multiply(a,b)),
inference(monotonicity,[status(thm)],[658]) ).
tff(742,plain,
multiply(multiply(multiply(a,b),multiply(a,b)),multiply(a,b)) = multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,b)),
inference(symmetry,[status(thm)],[741]) ).
tff(743,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,b),multiply(a,b)),multiply(a,b)) = multiply(multiply(a,b),multiply(multiply(a,b),multiply(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(744,plain,
multiply(multiply(multiply(a,b),multiply(a,b)),multiply(a,b)) = multiply(multiply(a,b),multiply(multiply(a,b),multiply(a,b))),
inference(unit_resolution,[status(thm)],[743,7]) ).
tff(745,plain,
multiply(multiply(a,b),multiply(multiply(a,b),multiply(a,b))) = multiply(multiply(multiply(a,b),multiply(a,b)),multiply(a,b)),
inference(symmetry,[status(thm)],[744]) ).
tff(746,plain,
multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))) = multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,b)),
inference(transitivity,[status(thm)],[709,716,745,742]) ).
tff(747,plain,
multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),b) = multiply(multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,b)),b),
inference(monotonicity,[status(thm)],[746]) ).
tff(748,plain,
multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),b) = multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),
inference(transitivity,[status(thm)],[747,740,738,737,605,602]) ).
tff(749,plain,
multiply(multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),b),multiply(a,multiply(b,a))) = multiply(multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),multiply(a,multiply(b,a))),
inference(monotonicity,[status(thm)],[748]) ).
tff(750,plain,
multiply(multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),multiply(a,multiply(b,a))) = multiply(multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),b),multiply(a,multiply(b,a))),
inference(symmetry,[status(thm)],[749]) ).
tff(751,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),multiply(a,multiply(b,a))) = multiply(b,multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),multiply(a,multiply(b,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(752,plain,
multiply(multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),multiply(a,multiply(b,a))) = multiply(b,multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),multiply(a,multiply(b,a)))),
inference(unit_resolution,[status(thm)],[751,7]) ).
tff(753,plain,
multiply(b,multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),multiply(a,multiply(b,a)))) = multiply(multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),multiply(a,multiply(b,a))),
inference(symmetry,[status(thm)],[752]) ).
tff(754,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(a,b),multiply(a,multiply(b,a))),b),multiply(a,multiply(b,a))) = multiply(multiply(multiply(a,b),multiply(a,multiply(b,a))),multiply(b,multiply(a,multiply(b,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(755,plain,
multiply(multiply(multiply(multiply(a,b),multiply(a,multiply(b,a))),b),multiply(a,multiply(b,a))) = multiply(multiply(multiply(a,b),multiply(a,multiply(b,a))),multiply(b,multiply(a,multiply(b,a)))),
inference(unit_resolution,[status(thm)],[754,7]) ).
tff(756,plain,
multiply(multiply(a,b),multiply(multiply(a,multiply(b,a)),b)) = multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,b)))),
inference(monotonicity,[status(thm)],[561]) ).
tff(757,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,b),multiply(a,multiply(b,a))),b) = multiply(multiply(a,b),multiply(multiply(a,multiply(b,a)),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(758,plain,
multiply(multiply(multiply(a,b),multiply(a,multiply(b,a))),b) = multiply(multiply(a,b),multiply(multiply(a,multiply(b,a)),b)),
inference(unit_resolution,[status(thm)],[757,7]) ).
tff(759,plain,
multiply(multiply(multiply(a,b),multiply(a,multiply(b,a))),b) = multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),
inference(transitivity,[status(thm)],[758,756,599]) ).
tff(760,plain,
multiply(multiply(multiply(multiply(a,b),multiply(a,multiply(b,a))),b),multiply(a,multiply(b,a))) = multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),multiply(a,multiply(b,a))),
inference(monotonicity,[status(thm)],[759]) ).
tff(761,plain,
multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),multiply(a,multiply(b,a))) = multiply(multiply(multiply(multiply(a,b),multiply(a,multiply(b,a))),b),multiply(a,multiply(b,a))),
inference(symmetry,[status(thm)],[760]) ).
tff(762,plain,
multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),multiply(a,multiply(b,a))) = multiply(multiply(multiply(a,b),multiply(a,multiply(b,a))),multiply(b,multiply(a,multiply(b,a)))),
inference(transitivity,[status(thm)],[761,755]) ).
tff(763,plain,
multiply(b,multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),multiply(a,multiply(b,a)))) = multiply(b,multiply(multiply(multiply(a,b),multiply(a,multiply(b,a))),multiply(b,multiply(a,multiply(b,a))))),
inference(monotonicity,[status(thm)],[762]) ).
tff(764,plain,
multiply(b,multiply(multiply(multiply(a,b),multiply(a,multiply(b,a))),multiply(b,multiply(a,multiply(b,a))))) = multiply(b,multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),multiply(a,multiply(b,a)))),
inference(symmetry,[status(thm)],[763]) ).
tff(765,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,multiply(multiply(a,b),multiply(a,multiply(b,a)))),multiply(b,multiply(a,multiply(b,a)))) = multiply(b,multiply(multiply(multiply(a,b),multiply(a,multiply(b,a))),multiply(b,multiply(a,multiply(b,a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(766,plain,
multiply(multiply(b,multiply(multiply(a,b),multiply(a,multiply(b,a)))),multiply(b,multiply(a,multiply(b,a)))) = multiply(b,multiply(multiply(multiply(a,b),multiply(a,multiply(b,a))),multiply(b,multiply(a,multiply(b,a))))),
inference(unit_resolution,[status(thm)],[765,7]) ).
tff(767,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a))) = multiply(b,multiply(multiply(a,b),multiply(a,multiply(b,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(768,plain,
multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a))) = multiply(b,multiply(multiply(a,b),multiply(a,multiply(b,a)))),
inference(unit_resolution,[status(thm)],[767,7]) ).
tff(769,plain,
multiply(b,multiply(multiply(a,b),multiply(a,multiply(b,a)))) = multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a))),
inference(symmetry,[status(thm)],[768]) ).
tff(770,plain,
multiply(multiply(b,multiply(multiply(a,b),multiply(a,multiply(b,a)))),multiply(b,multiply(a,multiply(b,a)))) = multiply(multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a))),multiply(b,multiply(a,multiply(b,a)))),
inference(monotonicity,[status(thm)],[769]) ).
tff(771,plain,
multiply(multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a))),multiply(b,multiply(a,multiply(b,a)))) = multiply(multiply(b,multiply(multiply(a,b),multiply(a,multiply(b,a)))),multiply(b,multiply(a,multiply(b,a)))),
inference(symmetry,[status(thm)],[770]) ).
tff(772,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a))),multiply(b,multiply(a,multiply(b,a)))) = multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,multiply(b,a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(773,plain,
multiply(multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a))),multiply(b,multiply(a,multiply(b,a)))) = multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,multiply(b,a))))),
inference(unit_resolution,[status(thm)],[772,7]) ).
tff(774,plain,
multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,multiply(b,a))))) = multiply(multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a))),multiply(b,multiply(a,multiply(b,a)))),
inference(symmetry,[status(thm)],[773]) ).
tff(775,plain,
multiply(multiply(multiply(a,multiply(b,a)),b),multiply(a,multiply(b,a))) = multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a))),
inference(monotonicity,[status(thm)],[561]) ).
tff(776,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(b,a)),b),multiply(a,multiply(b,a))) = multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,multiply(b,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(777,plain,
multiply(multiply(multiply(a,multiply(b,a)),b),multiply(a,multiply(b,a))) = multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,multiply(b,a)))),
inference(unit_resolution,[status(thm)],[776,7]) ).
tff(778,plain,
multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,multiply(b,a)))) = multiply(multiply(multiply(a,multiply(b,a)),b),multiply(a,multiply(b,a))),
inference(symmetry,[status(thm)],[777]) ).
tff(779,plain,
multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,multiply(b,a)))) = multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a))),
inference(transitivity,[status(thm)],[778,775]) ).
tff(780,plain,
multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,multiply(b,a))))) = multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a)))),
inference(monotonicity,[status(thm)],[779]) ).
tff(781,plain,
multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a)))) = multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,multiply(b,a))))),
inference(symmetry,[status(thm)],[780]) ).
tff(782,plain,
multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a)))) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),
inference(transitivity,[status(thm)],[781,774,771,766,764,753,750,735,733,731,729,722,719]) ).
tff(783,plain,
multiply(multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a)))),multiply(a,multiply(b,multiply(a,b)))) = multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),multiply(a,multiply(b,multiply(a,b)))),
inference(monotonicity,[status(thm)],[782]) ).
tff(784,plain,
multiply(multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a)))),multiply(a,multiply(b,multiply(a,b)))) = multiply(multiply(b,multiply(a,b)),multiply(multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,b))))),
inference(transitivity,[status(thm)],[783,715,713,698,628,697]) ).
tff(785,plain,
multiply(multiply(multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a)))),multiply(a,multiply(b,multiply(a,b)))),multiply(a,multiply(b,multiply(b,a)))) = multiply(multiply(multiply(b,multiply(a,b)),multiply(multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a))),multiply(a,multiply(b,multiply(a,b))))),multiply(a,multiply(b,multiply(b,a)))),
inference(monotonicity,[status(thm)],[784]) ).
tff(786,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a)))),multiply(a,multiply(b,multiply(a,b)))),multiply(a,multiply(b,multiply(b,a)))) = multiply(multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a)))),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,multiply(b,a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(787,plain,
multiply(multiply(multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a)))),multiply(a,multiply(b,multiply(a,b)))),multiply(a,multiply(b,multiply(b,a)))) = multiply(multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a)))),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,multiply(b,a))))),
inference(unit_resolution,[status(thm)],[786,7]) ).
tff(788,plain,
multiply(multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a)))),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,multiply(b,a))))) = multiply(multiply(multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a)))),multiply(a,multiply(b,multiply(a,b)))),multiply(a,multiply(b,multiply(b,a)))),
inference(symmetry,[status(thm)],[787]) ).
tff(789,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(b,multiply(a,b))),a),multiply(b,multiply(b,a))) = multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,multiply(b,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(790,plain,
multiply(multiply(multiply(a,multiply(b,multiply(a,b))),a),multiply(b,multiply(b,a))) = multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,multiply(b,a)))),
inference(unit_resolution,[status(thm)],[789,7]) ).
tff(791,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,b),a),multiply(b,a)) = multiply(multiply(a,b),multiply(a,multiply(b,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(792,plain,
multiply(multiply(multiply(a,b),a),multiply(b,a)) = multiply(multiply(a,b),multiply(a,multiply(b,a))),
inference(unit_resolution,[status(thm)],[791,7]) ).
tff(793,plain,
multiply(multiply(a,multiply(b,a)),multiply(b,a)) = multiply(multiply(multiply(a,b),a),multiply(b,a)),
inference(monotonicity,[status(thm)],[285]) ).
tff(794,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(b,a)),multiply(b,a)) = multiply(a,multiply(multiply(b,a),multiply(b,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(795,plain,
multiply(multiply(a,multiply(b,a)),multiply(b,a)) = multiply(a,multiply(multiply(b,a),multiply(b,a))),
inference(unit_resolution,[status(thm)],[794,7]) ).
tff(796,plain,
multiply(a,multiply(multiply(b,a),multiply(b,a))) = multiply(multiply(a,multiply(b,a)),multiply(b,a)),
inference(symmetry,[status(thm)],[795]) ).
tff(797,plain,
multiply(multiply(b,multiply(a,b)),a) = multiply(multiply(b,a),multiply(b,a)),
inference(transitivity,[status(thm)],[624,622]) ).
tff(798,plain,
multiply(a,multiply(multiply(b,multiply(a,b)),a)) = multiply(a,multiply(multiply(b,a),multiply(b,a))),
inference(monotonicity,[status(thm)],[797]) ).
tff(799,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(b,multiply(a,b))),a) = multiply(a,multiply(multiply(b,multiply(a,b)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(800,plain,
multiply(multiply(a,multiply(b,multiply(a,b))),a) = multiply(a,multiply(multiply(b,multiply(a,b)),a)),
inference(unit_resolution,[status(thm)],[799,7]) ).
tff(801,plain,
multiply(multiply(a,multiply(b,multiply(a,b))),a) = multiply(multiply(a,b),multiply(a,multiply(b,a))),
inference(transitivity,[status(thm)],[800,798,796,793,792]) ).
tff(802,plain,
multiply(multiply(multiply(a,multiply(b,multiply(a,b))),a),multiply(b,multiply(b,a))) = multiply(multiply(multiply(a,b),multiply(a,multiply(b,a))),multiply(b,multiply(b,a))),
inference(monotonicity,[status(thm)],[801]) ).
tff(803,plain,
multiply(multiply(multiply(a,b),multiply(a,multiply(b,a))),multiply(b,multiply(b,a))) = multiply(multiply(multiply(a,multiply(b,multiply(a,b))),a),multiply(b,multiply(b,a))),
inference(symmetry,[status(thm)],[802]) ).
tff(804,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(a,b),multiply(a,multiply(b,a))),b),multiply(b,a)) = multiply(multiply(multiply(a,b),multiply(a,multiply(b,a))),multiply(b,multiply(b,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(805,plain,
multiply(multiply(multiply(multiply(a,b),multiply(a,multiply(b,a))),b),multiply(b,a)) = multiply(multiply(multiply(a,b),multiply(a,multiply(b,a))),multiply(b,multiply(b,a))),
inference(unit_resolution,[status(thm)],[804,7]) ).
tff(806,plain,
multiply(multiply(multiply(multiply(a,b),multiply(a,multiply(b,a))),b),multiply(b,a)) = multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),multiply(b,a)),
inference(monotonicity,[status(thm)],[759]) ).
tff(807,plain,
multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),multiply(b,a)) = multiply(multiply(multiply(multiply(a,b),multiply(a,multiply(b,a))),b),multiply(b,a)),
inference(symmetry,[status(thm)],[806]) ).
tff(808,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),b),a) = multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(809,plain,
multiply(multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),b),a) = multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),multiply(b,a)),
inference(unit_resolution,[status(thm)],[808,7]) ).
tff(810,plain,
multiply(multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),b),a) = multiply(multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),a),
inference(monotonicity,[status(thm)],[748]) ).
tff(811,plain,
multiply(multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),a) = multiply(multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),b),a),
inference(symmetry,[status(thm)],[810]) ).
tff(812,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,multiply(a,multiply(b,a))),multiply(b,multiply(a,b))) = multiply(b,multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(813,plain,
multiply(multiply(b,multiply(a,multiply(b,a))),multiply(b,multiply(a,b))) = multiply(b,multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,b)))),
inference(unit_resolution,[status(thm)],[812,7]) ).
tff(814,plain,
multiply(b,multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,b)))) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(b,multiply(a,b))),
inference(symmetry,[status(thm)],[813]) ).
tff(815,plain,
multiply(a,multiply(multiply(b,a),multiply(b,multiply(a,b)))) = multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),
inference(monotonicity,[status(thm)],[668]) ).
tff(816,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,b))) = multiply(a,multiply(multiply(b,a),multiply(b,multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(817,plain,
multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,b))) = multiply(a,multiply(multiply(b,a),multiply(b,multiply(a,b)))),
inference(unit_resolution,[status(thm)],[816,7]) ).
tff(818,plain,
multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,b))) = multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),
inference(transitivity,[status(thm)],[817,815]) ).
tff(819,plain,
multiply(b,multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,b)))) = multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),
inference(monotonicity,[status(thm)],[818]) ).
tff(820,plain,
multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))) = multiply(b,multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,b)))),
inference(symmetry,[status(thm)],[819]) ).
tff(821,plain,
multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(b,multiply(a,b))),
inference(transitivity,[status(thm)],[820,814]) ).
tff(822,plain,
multiply(multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),a) = multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(b,multiply(a,b))),a),
inference(monotonicity,[status(thm)],[821]) ).
tff(823,plain,
multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(b,multiply(a,b))),a) = multiply(multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),a),
inference(symmetry,[status(thm)],[822]) ).
tff(824,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(b,multiply(a,b))),a) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(b,multiply(a,b)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(825,plain,
multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(b,multiply(a,b))),a) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(b,multiply(a,b)),a)),
inference(unit_resolution,[status(thm)],[824,7]) ).
tff(826,plain,
multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(b,multiply(a,b)),a)) = multiply(multiply(multiply(b,multiply(a,multiply(b,a))),multiply(b,multiply(a,b))),a),
inference(symmetry,[status(thm)],[825]) ).
tff(827,plain,
multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(b,multiply(a,b)),a)) = multiply(multiply(multiply(b,a),multiply(b,a)),multiply(multiply(b,a),multiply(b,a))),
inference(monotonicity,[status(thm)],[630,797]) ).
tff(828,plain,
multiply(multiply(multiply(b,a),multiply(b,a)),multiply(multiply(b,a),multiply(b,a))) = multiply(multiply(b,multiply(a,multiply(b,a))),multiply(multiply(b,multiply(a,b)),a)),
inference(symmetry,[status(thm)],[827]) ).
tff(829,plain,
multiply(multiply(multiply(b,multiply(a,b)),a),multiply(b,multiply(a,multiply(b,a)))) = multiply(multiply(multiply(b,a),multiply(b,a)),multiply(multiply(b,a),multiply(b,a))),
inference(monotonicity,[status(thm)],[797,630]) ).
tff(830,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(a,b)),a),multiply(b,multiply(a,multiply(b,a)))) = multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,multiply(a,multiply(b,a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(831,plain,
multiply(multiply(multiply(b,multiply(a,b)),a),multiply(b,multiply(a,multiply(b,a)))) = multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,multiply(a,multiply(b,a))))),
inference(unit_resolution,[status(thm)],[830,7]) ).
tff(832,plain,
multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,multiply(a,multiply(b,a))))) = multiply(multiply(multiply(b,multiply(a,b)),a),multiply(b,multiply(a,multiply(b,a)))),
inference(symmetry,[status(thm)],[831]) ).
tff(833,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,b),multiply(a,multiply(b,a))) = multiply(a,multiply(b,multiply(a,multiply(b,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(834,plain,
multiply(multiply(a,b),multiply(a,multiply(b,a))) = multiply(a,multiply(b,multiply(a,multiply(b,a)))),
inference(unit_resolution,[status(thm)],[833,7]) ).
tff(835,plain,
multiply(multiply(b,multiply(a,b)),multiply(multiply(a,b),multiply(a,multiply(b,a)))) = multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,multiply(a,multiply(b,a))))),
inference(monotonicity,[status(thm)],[834]) ).
tff(836,plain,
multiply(multiply(b,multiply(a,b)),multiply(multiply(a,b),multiply(a,multiply(b,a)))) = multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,multiply(b,a)))),
inference(transitivity,[status(thm)],[835,832,829,828,826,823,811,809,807,805,803,790]) ).
tff(837,plain,
multiply(multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a)))),multiply(multiply(b,multiply(a,b)),multiply(multiply(a,b),multiply(a,multiply(b,a))))) = multiply(multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a)))),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,multiply(b,a))))),
inference(monotonicity,[status(thm)],[836]) ).
tff(838,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a)))),multiply(b,multiply(a,b))),multiply(multiply(a,b),multiply(a,multiply(b,a)))) = multiply(multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a)))),multiply(multiply(b,multiply(a,b)),multiply(multiply(a,b),multiply(a,multiply(b,a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(839,plain,
multiply(multiply(multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a)))),multiply(b,multiply(a,b))),multiply(multiply(a,b),multiply(a,multiply(b,a)))) = multiply(multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a)))),multiply(multiply(b,multiply(a,b)),multiply(multiply(a,b),multiply(a,multiply(b,a))))),
inference(unit_resolution,[status(thm)],[838,7]) ).
tff(840,plain,
multiply(a,multiply(multiply(b,a),multiply(b,a))) = multiply(multiply(a,b),multiply(a,multiply(b,a))),
inference(transitivity,[status(thm)],[796,793,792]) ).
tff(841,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a)))),multiply(b,multiply(a,b))) = multiply(multiply(b,multiply(a,b)),multiply(multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a))),multiply(b,multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(842,plain,
multiply(multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a)))),multiply(b,multiply(a,b))) = multiply(multiply(b,multiply(a,b)),multiply(multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a))),multiply(b,multiply(a,b)))),
inference(unit_resolution,[status(thm)],[841,7]) ).
tff(843,plain,
multiply(multiply(b,multiply(a,b)),multiply(multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a))),multiply(b,multiply(a,b)))) = multiply(multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a)))),multiply(b,multiply(a,b))),
inference(symmetry,[status(thm)],[842]) ).
tff(844,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))) = multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(845,plain,
multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))) = multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))),
inference(unit_resolution,[status(thm)],[844,7]) ).
tff(846,plain,
multiply(multiply(a,b),multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))) = multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))),
inference(monotonicity,[status(thm)],[845]) ).
tff(847,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,b),multiply(a,b)),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))) = multiply(multiply(a,b),multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(848,plain,
multiply(multiply(multiply(a,b),multiply(a,b)),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))) = multiply(multiply(a,b),multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))),
inference(unit_resolution,[status(thm)],[847,7]) ).
tff(849,plain,
multiply(multiply(a,multiply(b,multiply(a,b))),multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,b)))) = multiply(multiply(multiply(a,b),multiply(a,b)),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),
inference(monotonicity,[status(thm)],[658,818]) ).
tff(850,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a))),multiply(b,multiply(a,b))) = multiply(multiply(a,multiply(b,multiply(a,b))),multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(851,plain,
multiply(multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a))),multiply(b,multiply(a,b))) = multiply(multiply(a,multiply(b,multiply(a,b))),multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,b)))),
inference(unit_resolution,[status(thm)],[850,7]) ).
tff(852,plain,
multiply(multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a))),multiply(b,multiply(a,b))) = multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))),
inference(transitivity,[status(thm)],[851,849,848,846,681]) ).
tff(853,plain,
multiply(multiply(b,multiply(a,b)),multiply(multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a))),multiply(b,multiply(a,b)))) = multiply(multiply(multiply(b,a),b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))),
inference(monotonicity,[status(thm)],[623,852]) ).
tff(854,plain,
multiply(multiply(multiply(b,a),b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))) = multiply(multiply(b,multiply(a,b)),multiply(multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a))),multiply(b,multiply(a,b)))),
inference(symmetry,[status(thm)],[853]) ).
tff(855,plain,
multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))) = multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))),
inference(transitivity,[status(thm)],[597,595]) ).
tff(856,plain,
multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))) = multiply(multiply(multiply(b,a),b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))),
inference(monotonicity,[status(thm)],[623,855]) ).
tff(857,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a))),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))) = multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(858,plain,
multiply(multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a))),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))) = multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,a)),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))),
inference(unit_resolution,[status(thm)],[857,7]) ).
tff(859,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,a),multiply(b,a)),b) = multiply(multiply(b,a),multiply(multiply(b,a),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(860,plain,
multiply(multiply(multiply(b,a),multiply(b,a)),b) = multiply(multiply(b,a),multiply(multiply(b,a),b)),
inference(unit_resolution,[status(thm)],[859,7]) ).
tff(861,plain,
multiply(multiply(multiply(b,a),multiply(b,a)),b) = multiply(b,multiply(a,multiply(b,multiply(a,b)))),
inference(transitivity,[status(thm)],[860,669,668]) ).
tff(862,plain,
multiply(multiply(b,a),multiply(multiply(multiply(b,a),multiply(b,a)),b)) = multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,b))))),
inference(monotonicity,[status(thm)],[861]) ).
tff(863,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a))),b) = multiply(multiply(b,a),multiply(multiply(multiply(b,a),multiply(b,a)),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(864,plain,
multiply(multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a))),b) = multiply(multiply(b,a),multiply(multiply(multiply(b,a),multiply(b,a)),b)),
inference(unit_resolution,[status(thm)],[863,7]) ).
tff(865,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a))) = multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(866,plain,
multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a))) = multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a)))),
inference(unit_resolution,[status(thm)],[865,7]) ).
tff(867,plain,
multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a))),
inference(symmetry,[status(thm)],[866]) ).
tff(868,plain,
multiply(multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a)))),b) = multiply(multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a))),b),
inference(monotonicity,[status(thm)],[867]) ).
tff(869,plain,
multiply(multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a)))),b) = multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),
inference(transitivity,[status(thm)],[868,864,862,666]) ).
tff(870,plain,
multiply(multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a))),multiply(multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a)))),b)) = multiply(multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a))),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))),
inference(monotonicity,[status(thm)],[869]) ).
tff(871,plain,
multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,a)))) = multiply(multiply(multiply(b,a),b),multiply(a,multiply(b,a))),
inference(symmetry,[status(thm)],[639]) ).
tff(872,plain,
multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a))),
inference(transitivity,[status(thm)],[867,636,871,640]) ).
tff(873,plain,
multiply(multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a)))),multiply(multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a)))),b)) = multiply(multiply(multiply(b,multiply(a,b)),multiply(a,multiply(b,a))),multiply(multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a)))),b)),
inference(monotonicity,[status(thm)],[872]) ).
tff(874,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a)))),multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a))))),b) = multiply(multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a)))),multiply(multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a)))),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(875,plain,
multiply(multiply(multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a)))),multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a))))),b) = multiply(multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a)))),multiply(multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a)))),b)),
inference(unit_resolution,[status(thm)],[874,7]) ).
tff(876,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a)))),b),multiply(a,multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a)))),multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(877,plain,
multiply(multiply(multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a)))),b),multiply(a,multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a)))),multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a))))),
inference(unit_resolution,[status(thm)],[876,7]) ).
tff(878,plain,
multiply(multiply(multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a)))),b),multiply(a,multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),multiply(multiply(a,b),multiply(a,multiply(b,a)))),
inference(monotonicity,[status(thm)],[869,840]) ).
tff(879,plain,
multiply(multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),multiply(multiply(a,b),multiply(a,multiply(b,a)))) = multiply(multiply(multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a)))),b),multiply(a,multiply(multiply(b,a),multiply(b,a)))),
inference(symmetry,[status(thm)],[878]) ).
tff(880,plain,
multiply(multiply(multiply(a,b),a),multiply(b,a)) = multiply(multiply(a,multiply(b,a)),multiply(b,a)),
inference(symmetry,[status(thm)],[793]) ).
tff(881,plain,
multiply(multiply(a,b),multiply(a,multiply(b,a))) = multiply(multiply(multiply(a,b),a),multiply(b,a)),
inference(symmetry,[status(thm)],[792]) ).
tff(882,plain,
multiply(multiply(a,b),multiply(a,multiply(b,a))) = multiply(a,multiply(multiply(b,a),multiply(b,a))),
inference(transitivity,[status(thm)],[881,880,795]) ).
tff(883,plain,
multiply(multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,b)),b) = multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),b),
inference(symmetry,[status(thm)],[747]) ).
tff(884,plain,
multiply(multiply(a,multiply(b,multiply(a,b))),multiply(multiply(a,b),b)) = multiply(multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,b)),b),
inference(symmetry,[status(thm)],[740]) ).
tff(885,plain,
multiply(multiply(multiply(a,b),multiply(a,b)),multiply(multiply(a,b),b)) = multiply(multiply(a,multiply(b,multiply(a,b))),multiply(multiply(a,b),b)),
inference(symmetry,[status(thm)],[738]) ).
tff(886,plain,
multiply(multiply(a,b),multiply(multiply(a,b),multiply(multiply(a,b),b))) = multiply(multiply(multiply(a,b),multiply(a,b)),multiply(multiply(a,b),b)),
inference(symmetry,[status(thm)],[737]) ).
tff(887,plain,
multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))) = multiply(b,multiply(multiply(a,b),multiply(multiply(a,b),multiply(a,b)))),
inference(symmetry,[status(thm)],[602]) ).
tff(888,plain,
multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))) = multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),b),
inference(transitivity,[status(thm)],[887,604,886,885,884,883]) ).
tff(889,plain,
multiply(multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),multiply(multiply(a,b),multiply(a,multiply(b,a)))) = multiply(multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),b),multiply(a,multiply(multiply(b,a),multiply(b,a)))),
inference(monotonicity,[status(thm)],[888,882]) ).
tff(890,plain,
multiply(multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),b),multiply(a,multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),multiply(multiply(a,b),multiply(a,multiply(b,a)))),
inference(symmetry,[status(thm)],[889]) ).
tff(891,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),b),multiply(a,multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(892,plain,
multiply(multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),b),multiply(a,multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a))))),
inference(unit_resolution,[status(thm)],[891,7]) ).
tff(893,plain,
multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a))))) = multiply(multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),b),multiply(a,multiply(multiply(b,a),multiply(b,a)))),
inference(symmetry,[status(thm)],[892]) ).
tff(894,plain,
multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a))))) = multiply(multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,b))),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))),
inference(monotonicity,[status(thm)],[710,867]) ).
tff(895,plain,
multiply(multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,b))),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))),multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a))))),
inference(symmetry,[status(thm)],[894]) ).
tff(896,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,b))),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(multiply(a,b),a),multiply(multiply(b,multiply(a,b)),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(897,plain,
multiply(multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,b))),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(multiply(a,b),a),multiply(multiply(b,multiply(a,b)),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a))))),
inference(unit_resolution,[status(thm)],[896,7]) ).
tff(898,plain,
multiply(multiply(multiply(a,b),a),multiply(multiply(b,multiply(a,b)),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a))))) = multiply(multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,b))),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))),
inference(symmetry,[status(thm)],[897]) ).
tff(899,plain,
multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,multiply(a,b)))) = multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,b))))),
inference(monotonicity,[status(thm)],[668]) ).
tff(900,plain,
multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,multiply(a,b)))) = multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),
inference(transitivity,[status(thm)],[899,666]) ).
tff(901,plain,
multiply(multiply(b,a),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,multiply(a,b))))) = multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))),
inference(monotonicity,[status(thm)],[900]) ).
tff(902,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) )
| ( multiply(multiply(b,multiply(a,b)),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(b,a),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,multiply(a,b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(903,plain,
multiply(multiply(b,multiply(a,b)),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(b,a),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,multiply(a,b))))),
inference(unit_resolution,[status(thm)],[902,28]) ).
tff(904,plain,
multiply(multiply(b,multiply(a,b)),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))) = multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))),
inference(transitivity,[status(thm)],[903,901,594]) ).
tff(905,plain,
multiply(multiply(multiply(a,b),a),multiply(multiply(b,multiply(a,b)),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a))))) = multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))),
inference(monotonicity,[status(thm)],[904]) ).
tff(906,plain,
multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))) = multiply(multiply(multiply(a,b),a),multiply(multiply(b,multiply(a,b)),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a))))),
inference(symmetry,[status(thm)],[905]) ).
tff(907,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))) = multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(908,plain,
multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))) = multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))),
inference(unit_resolution,[status(thm)],[907,7]) ).
tff(909,plain,
multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))) = multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))),
inference(symmetry,[status(thm)],[908]) ).
tff(910,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))) = multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(911,plain,
multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))) = multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))),
inference(unit_resolution,[status(thm)],[910,7]) ).
tff(912,plain,
multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))) = multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))),
inference(symmetry,[status(thm)],[911]) ).
tff(913,plain,
multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))) = multiply(multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a)))),multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a))))),
inference(transitivity,[status(thm)],[912,909,906,898,895,893,890,879,877]) ).
tff(914,plain,
multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))),b) = multiply(multiply(multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a)))),multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a))))),b),
inference(monotonicity,[status(thm)],[913]) ).
tff(915,plain,
multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))),b) = multiply(multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a)))),multiply(b,multiply(a,b))),
inference(transitivity,[status(thm)],[914,875,873,870,858,856,854,843]) ).
tff(916,plain,
multiply(multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))),b),multiply(a,multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(multiply(multiply(b,multiply(a,b)),multiply(multiply(a,multiply(b,multiply(a,b))),multiply(a,multiply(b,a)))),multiply(b,multiply(a,b))),multiply(multiply(a,b),multiply(a,multiply(b,a)))),
inference(monotonicity,[status(thm)],[915,840]) ).
tff(917,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))),b),multiply(a,multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))),multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(918,plain,
multiply(multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))),b),multiply(a,multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))),multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a))))),
inference(unit_resolution,[status(thm)],[917,7]) ).
tff(919,plain,
multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))),multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a))))) = multiply(multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))),b),multiply(a,multiply(multiply(b,a),multiply(b,a)))),
inference(symmetry,[status(thm)],[918]) ).
tff(920,plain,
multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))) = multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))),
inference(transitivity,[status(thm)],[908,911]) ).
tff(921,plain,
multiply(multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))),multiply(b,multiply(a,multiply(multiply(b,a),multiply(b,a))))),
inference(monotonicity,[status(thm)],[920,866]) ).
tff(922,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(multiply(a,b),a),multiply(multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(923,plain,
multiply(multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(multiply(a,b),a),multiply(multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a))))),
inference(unit_resolution,[status(thm)],[922,7]) ).
tff(924,plain,
multiply(multiply(multiply(a,b),a),multiply(multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a))))) = multiply(multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))),
inference(symmetry,[status(thm)],[923]) ).
tff(925,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,multiply(Y,Y))) = multiply(Y,multiply(Y,multiply(Y,X))) )
| ( multiply(multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(b,a),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(926,plain,
multiply(multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))) = multiply(multiply(b,a),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))),
inference(unit_resolution,[status(thm)],[925,28]) ).
tff(927,plain,
multiply(multiply(b,a),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))) = multiply(multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))),
inference(symmetry,[status(thm)],[926]) ).
tff(928,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))) = multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(929,plain,
multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))) = multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))))),
inference(unit_resolution,[status(thm)],[928,7]) ).
tff(930,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))) = multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(931,plain,
multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))) = multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))),
inference(unit_resolution,[status(thm)],[930,7]) ).
tff(932,plain,
multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))) = multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))),
inference(monotonicity,[status(thm)],[931]) ).
tff(933,plain,
multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))) = multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))))),
inference(transitivity,[status(thm)],[932,929]) ).
tff(934,plain,
multiply(multiply(b,a),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))) = multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))))),
inference(monotonicity,[status(thm)],[933]) ).
tff(935,plain,
multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))))) = multiply(multiply(b,a),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))),
inference(symmetry,[status(thm)],[934]) ).
tff(936,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))))) = multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(937,plain,
multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))))) = multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))))))),
inference(unit_resolution,[status(thm)],[936,7]) ).
tff(938,plain,
multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))))))) = multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))))),
inference(symmetry,[status(thm)],[937]) ).
tff(939,plain,
multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))))))) = multiply(multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a)))),
inference(transitivity,[status(thm)],[938,935,927]) ).
tff(940,plain,
multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))))))) = multiply(multiply(multiply(a,b),a),multiply(multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))),multiply(multiply(b,a),multiply(multiply(b,a),multiply(b,a))))),
inference(monotonicity,[status(thm)],[939]) ).
tff(941,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))))))) = multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(942,plain,
multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))))))) = multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))))))))),
inference(unit_resolution,[status(thm)],[941,7]) ).
tff(943,plain,
multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))))))))) = multiply(multiply(multiply(a,b),a),multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))))))),
inference(symmetry,[status(thm)],[942]) ).
tff(944,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))))))))) = multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(945,plain,
multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))))))))) = multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))))))))),
inference(unit_resolution,[status(thm)],[944,7]) ).
tff(946,plain,
multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))))))))) = multiply(multiply(a,b),multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))))))))))))),
inference(symmetry,[status(thm)],[945]) ).
tff(947,plain,
multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))))))))) = multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))))))),
inference(transitivity,[status(thm)],[946,943,940,924,921,919,916,839,837,788,785,696,589,587,582,539,537,477,475,310,307,226,124,121,43,41,21,19,12,10]) ).
tff(948,plain,
( ( multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))))))))) != multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))))))) )
<=> ( multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))))))))) != multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(949,axiom,
multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))))))))) != multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(950,plain,
multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))))))))))))) != multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,multiply(b,b))))))))))))))))),
inference(modus_ponens,[status(thm)],[949,948]) ).
tff(951,plain,
$false,
inference(unit_resolution,[status(thm)],[950,947]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP196-1 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 31 16:04:47 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 44.45/28.72 % SZS status Unsatisfiable
% 44.45/28.72 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------