%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : BOO022-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:00:10 AM UTC 2025
% Result : Unsatisfiable 0.42s 0.60s
% Output : Proof 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 72
% Syntax : Number of formulae : 342 ( 275 unt; 0 typ; 0 def)
% Number of atoms : 417 ( 412 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 133 ( 62 ~; 58 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 236 ( 226 !; 0 ?; 236 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( add(multiply(X,Y),Y) = Y )
<=> ( add(multiply(X,Y),Y) = Y ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
<=> ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
<=> ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_multiply) ).
tff(5,plain,
! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(multiply(b,c),multiply(b,c)),multiply(b,c)) = multiply(b,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
add(multiply(multiply(b,c),multiply(b,c)),multiply(b,c)) = multiply(b,c),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(a,multiply(b,c)),multiply(b,c)) = multiply(b,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(11,plain,
add(multiply(a,multiply(b,c)),multiply(b,c)) = multiply(b,c),
inference(unit_resolution,[status(thm)],[10,7]) ).
tff(12,plain,
multiply(b,c) = add(multiply(a,multiply(b,c)),multiply(b,c)),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
multiply(multiply(b,c),multiply(b,c)) = multiply(add(multiply(a,multiply(b,c)),multiply(b,c)),multiply(b,c)),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
multiply(add(multiply(a,multiply(b,c)),multiply(b,c)),multiply(b,c)) = multiply(multiply(b,c),multiply(b,c)),
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
^ [Y: $i,X: $i] :
refl(( ( multiply(add(X,Y),Y) = Y )
<=> ( multiply(add(X,Y),Y) = Y ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y )
<=> ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y )
<=> ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_add) ).
tff(19,plain,
! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y )
| ( multiply(add(multiply(a,multiply(b,c)),multiply(b,c)),multiply(b,c)) = multiply(b,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
multiply(add(multiply(a,multiply(b,c)),multiply(b,c)),multiply(b,c)) = multiply(b,c),
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
multiply(b,c) = multiply(add(multiply(a,multiply(b,c)),multiply(b,c)),multiply(b,c)),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
multiply(b,c) = multiply(multiply(b,c),multiply(b,c)),
inference(transitivity,[status(thm)],[24,14]) ).
tff(26,plain,
add(multiply(b,c),multiply(b,c)) = add(multiply(multiply(b,c),multiply(b,c)),multiply(b,c)),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
add(multiply(b,c),multiply(b,c)) = multiply(b,c),
inference(transitivity,[status(thm)],[26,9]) ).
tff(28,plain,
multiply(a,add(multiply(b,c),multiply(b,c))) = multiply(a,multiply(b,c)),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
<=> ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_add_property) ).
tff(33,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(a,add(multiply(b,c),multiply(b,c))) = add(multiply(multiply(b,c),a),multiply(multiply(b,c),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
multiply(a,add(multiply(b,c),multiply(b,c))) = add(multiply(multiply(b,c),a),multiply(multiply(b,c),a)),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
add(multiply(multiply(b,c),a),multiply(multiply(b,c),a)) = multiply(a,add(multiply(b,c),multiply(b,c))),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y )
| ( multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),multiply(multiply(b,c),a)) = multiply(multiply(b,c),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),multiply(multiply(b,c),a)) = multiply(multiply(b,c),a),
inference(unit_resolution,[status(thm)],[39,21]) ).
tff(41,plain,
add(multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),multiply(multiply(b,c),a)),multiply(multiply(b,c),a)) = add(multiply(multiply(b,c),a),multiply(multiply(b,c),a)),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),multiply(multiply(b,c),a)),multiply(multiply(b,c),a)) = multiply(multiply(b,c),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
add(multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),multiply(multiply(b,c),a)),multiply(multiply(b,c),a)) = multiply(multiply(b,c),a),
inference(unit_resolution,[status(thm)],[42,7]) ).
tff(44,plain,
multiply(multiply(b,c),a) = add(multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),multiply(multiply(b,c),a)),multiply(multiply(b,c),a)),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(b,a),a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
add(multiply(b,a),a) = a,
inference(unit_resolution,[status(thm)],[45,7]) ).
tff(47,plain,
multiply(multiply(b,c),add(multiply(b,a),a)) = multiply(multiply(b,c),a),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(multiply(b,c),add(multiply(b,a),a)) = add(multiply(multiply(b,a),multiply(b,c)),multiply(a,multiply(b,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
multiply(multiply(b,c),add(multiply(b,a),a)) = add(multiply(multiply(b,a),multiply(b,c)),multiply(a,multiply(b,c))),
inference(unit_resolution,[status(thm)],[48,35]) ).
tff(50,plain,
add(multiply(multiply(b,a),multiply(b,c)),multiply(a,multiply(b,c))) = multiply(multiply(b,c),add(multiply(b,a),a)),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
multiply(a,multiply(b,c)) = multiply(a,add(multiply(a,multiply(b,c)),multiply(b,c))),
inference(monotonicity,[status(thm)],[12]) ).
tff(52,plain,
multiply(a,add(multiply(a,multiply(b,c)),multiply(b,c))) = multiply(a,multiply(b,c)),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(a,add(multiply(a,multiply(b,c)),multiply(b,c))) = add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
multiply(a,add(multiply(a,multiply(b,c)),multiply(b,c))) = add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),
inference(unit_resolution,[status(thm)],[53,35]) ).
tff(55,plain,
add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)) = multiply(a,add(multiply(a,multiply(b,c)),multiply(b,c))),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(multiply(add(a,b),add(multiply(b,c),b)),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))) = add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
add(multiply(multiply(add(a,b),add(multiply(b,c),b)),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))) = add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),
inference(unit_resolution,[status(thm)],[56,7]) ).
tff(58,plain,
add(multiply(multiply(b,c),a),multiply(multiply(b,c),a)) = add(multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),multiply(multiply(b,c),a)),multiply(multiply(b,c),a)),
inference(symmetry,[status(thm)],[41]) ).
tff(59,plain,
multiply(a,multiply(b,c)) = multiply(a,add(multiply(b,c),multiply(b,c))),
inference(symmetry,[status(thm)],[28]) ).
tff(60,plain,
add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)) = multiply(multiply(b,c),a),
inference(transitivity,[status(thm)],[55,52,59,37,58,43]) ).
tff(61,plain,
multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))) = multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),multiply(multiply(b,c),a)),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))) = add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),
inference(transitivity,[status(thm)],[61,40,44,41,38,28,51,54]) ).
tff(63,plain,
add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)) = multiply(a,multiply(b,c)),
inference(transitivity,[status(thm)],[55,52]) ).
tff(64,plain,
add(b,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))) = add(b,multiply(a,multiply(b,c))),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
add(b,multiply(a,multiply(b,c))) = add(b,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) )
<=> ( add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) ) )),
inference(bind,[status(th)],[]) ).
tff(67,plain,
( ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,axiom,
! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_multiply_property) ).
tff(70,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) ),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) )
| ( add(b,multiply(a,multiply(b,c))) = multiply(add(a,b),add(multiply(b,c),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
add(b,multiply(a,multiply(b,c))) = multiply(add(a,b),add(multiply(b,c),b)),
inference(unit_resolution,[status(thm)],[73,72]) ).
tff(75,plain,
multiply(add(a,b),add(multiply(b,c),b)) = add(b,multiply(a,multiply(b,c))),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
multiply(add(a,b),add(multiply(b,c),b)) = add(b,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),
inference(transitivity,[status(thm)],[75,65]) ).
tff(77,plain,
multiply(multiply(add(a,b),add(multiply(b,c),b)),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))) = multiply(add(b,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
multiply(add(b,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))) = multiply(multiply(add(a,b),add(multiply(b,c),b)),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),
inference(symmetry,[status(thm)],[77]) ).
tff(79,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y )
| ( multiply(add(multiply(b,c),b),b) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
multiply(add(multiply(b,c),b),b) = b,
inference(unit_resolution,[status(thm)],[79,21]) ).
tff(81,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(b,b),b) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
add(multiply(b,b),b) = b,
inference(unit_resolution,[status(thm)],[81,7]) ).
tff(83,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(a,b),b) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
add(multiply(a,b),b) = b,
inference(unit_resolution,[status(thm)],[83,7]) ).
tff(85,plain,
b = add(multiply(a,b),b),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
multiply(b,b) = multiply(add(multiply(a,b),b),b),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
multiply(add(multiply(a,b),b),b) = multiply(b,b),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y )
| ( multiply(add(multiply(a,b),b),b) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(89,plain,
multiply(add(multiply(a,b),b),b) = b,
inference(unit_resolution,[status(thm)],[88,21]) ).
tff(90,plain,
b = multiply(add(multiply(a,b),b),b),
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
b = multiply(b,b),
inference(transitivity,[status(thm)],[90,87]) ).
tff(92,plain,
add(b,b) = add(multiply(b,b),b),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
add(b,b) = b,
inference(transitivity,[status(thm)],[92,82]) ).
tff(94,plain,
multiply(add(multiply(b,c),b),add(b,b)) = multiply(add(multiply(b,c),b),b),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) )
| ( add(b,multiply(multiply(b,c),b)) = multiply(add(multiply(b,c),b),add(b,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
add(b,multiply(multiply(b,c),b)) = multiply(add(multiply(b,c),b),add(b,b)),
inference(unit_resolution,[status(thm)],[95,72]) ).
tff(97,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(add(c,multiply(multiply(b,c),b)),add(b,multiply(multiply(b,c),b))),add(b,multiply(multiply(b,c),b))) = add(b,multiply(multiply(b,c),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
add(multiply(add(c,multiply(multiply(b,c),b)),add(b,multiply(multiply(b,c),b))),add(b,multiply(multiply(b,c),b))) = add(b,multiply(multiply(b,c),b)),
inference(unit_resolution,[status(thm)],[97,7]) ).
tff(99,plain,
multiply(add(multiply(b,c),b),add(b,b)) = add(b,multiply(multiply(b,c),b)),
inference(symmetry,[status(thm)],[96]) ).
tff(100,plain,
multiply(add(multiply(b,c),b),b) = multiply(add(multiply(b,c),b),add(b,b)),
inference(symmetry,[status(thm)],[94]) ).
tff(101,plain,
b = multiply(add(multiply(b,c),b),b),
inference(symmetry,[status(thm)],[80]) ).
tff(102,plain,
b = add(b,multiply(multiply(b,c),b)),
inference(transitivity,[status(thm)],[101,100,99]) ).
tff(103,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) )
| ( add(multiply(multiply(b,c),b),multiply(c,b)) = multiply(add(c,multiply(multiply(b,c),b)),add(b,multiply(multiply(b,c),b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(104,plain,
add(multiply(multiply(b,c),b),multiply(c,b)) = multiply(add(c,multiply(multiply(b,c),b)),add(b,multiply(multiply(b,c),b))),
inference(unit_resolution,[status(thm)],[103,72]) ).
tff(105,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(b,add(multiply(b,c),c)) = add(multiply(multiply(b,c),b),multiply(c,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
multiply(b,add(multiply(b,c),c)) = add(multiply(multiply(b,c),b),multiply(c,b)),
inference(unit_resolution,[status(thm)],[105,35]) ).
tff(107,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(b,c),c) = c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(108,plain,
add(multiply(b,c),c) = c,
inference(unit_resolution,[status(thm)],[107,7]) ).
tff(109,plain,
multiply(b,add(multiply(b,c),c)) = multiply(b,c),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
multiply(b,c) = multiply(b,add(multiply(b,c),c)),
inference(symmetry,[status(thm)],[109]) ).
tff(111,plain,
multiply(b,c) = multiply(add(c,multiply(multiply(b,c),b)),add(b,multiply(multiply(b,c),b))),
inference(transitivity,[status(thm)],[110,106,104]) ).
tff(112,plain,
add(multiply(b,c),b) = add(multiply(add(c,multiply(multiply(b,c),b)),add(b,multiply(multiply(b,c),b))),add(b,multiply(multiply(b,c),b))),
inference(monotonicity,[status(thm)],[111,102]) ).
tff(113,plain,
add(multiply(b,c),b) = b,
inference(transitivity,[status(thm)],[112,98,96,94,80]) ).
tff(114,plain,
multiply(add(a,b),add(multiply(b,c),b)) = multiply(add(a,b),b),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
multiply(add(a,b),b) = multiply(add(a,b),add(multiply(b,c),b)),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y )
| ( multiply(add(a,b),b) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(117,plain,
multiply(add(a,b),b) = b,
inference(unit_resolution,[status(thm)],[116,21]) ).
tff(118,plain,
b = multiply(add(a,b),b),
inference(symmetry,[status(thm)],[117]) ).
tff(119,plain,
b = add(b,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),
inference(transitivity,[status(thm)],[118,115,75,65]) ).
tff(120,plain,
multiply(b,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))) = multiply(add(b,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),
inference(monotonicity,[status(thm)],[119]) ).
tff(121,plain,
multiply(b,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))) = multiply(multiply(add(a,b),add(multiply(b,c),b)),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),
inference(transitivity,[status(thm)],[120,78]) ).
tff(122,plain,
add(multiply(b,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)))) = add(multiply(multiply(add(a,b),add(multiply(b,c),b)),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),
inference(monotonicity,[status(thm)],[121,62]) ).
tff(123,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(b,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)))) = add(multiply(b,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(124,plain,
multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(b,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)))) = add(multiply(b,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)))),
inference(unit_resolution,[status(thm)],[123,35]) ).
tff(125,plain,
multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(b,multiply(a,multiply(b,c)))) = multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(b,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)))),
inference(monotonicity,[status(thm)],[65]) ).
tff(126,plain,
b = add(b,multiply(a,multiply(b,c))),
inference(transitivity,[status(thm)],[118,115,75]) ).
tff(127,plain,
multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),b) = multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(b,multiply(a,multiply(b,c)))),
inference(monotonicity,[status(thm)],[126]) ).
tff(128,plain,
multiply(add(a,b),add(b,b)) = multiply(add(a,b),b),
inference(monotonicity,[status(thm)],[93]) ).
tff(129,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) )
| ( add(b,multiply(a,b)) = multiply(add(a,b),add(b,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(130,plain,
add(b,multiply(a,b)) = multiply(add(a,b),add(b,b)),
inference(unit_resolution,[status(thm)],[129,72]) ).
tff(131,plain,
multiply(a,b) = multiply(a,add(multiply(a,b),b)),
inference(monotonicity,[status(thm)],[85]) ).
tff(132,plain,
multiply(a,add(multiply(a,b),b)) = multiply(a,b),
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(a,add(multiply(a,b),b)) = add(multiply(multiply(a,b),a),multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(134,plain,
multiply(a,add(multiply(a,b),b)) = add(multiply(multiply(a,b),a),multiply(b,a)),
inference(unit_resolution,[status(thm)],[133,35]) ).
tff(135,plain,
add(multiply(multiply(a,b),a),multiply(b,a)) = multiply(a,add(multiply(a,b),b)),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
add(multiply(multiply(a,b),a),multiply(b,a)) = multiply(a,b),
inference(transitivity,[status(thm)],[135,132]) ).
tff(137,plain,
add(b,add(multiply(multiply(a,b),a),multiply(b,a))) = add(b,multiply(a,b)),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
add(b,add(multiply(multiply(a,b),a),multiply(b,a))) = b,
inference(transitivity,[status(thm)],[137,130,128,117]) ).
tff(139,plain,
multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(b,add(multiply(multiply(a,b),a),multiply(b,a)))) = multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),b),
inference(monotonicity,[status(thm)],[138]) ).
tff(140,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(b,add(multiply(multiply(a,b),a),multiply(b,a)))) = add(multiply(b,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(141,plain,
multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(b,add(multiply(multiply(a,b),a),multiply(b,a)))) = add(multiply(b,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)))),
inference(unit_resolution,[status(thm)],[140,35]) ).
tff(142,plain,
add(multiply(b,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)))) = multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(b,add(multiply(multiply(a,b),a),multiply(b,a)))),
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
multiply(add(b,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))) = multiply(b,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),
inference(symmetry,[status(thm)],[120]) ).
tff(144,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y )
| ( multiply(add(b,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))) = add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
multiply(add(b,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))) = add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),
inference(unit_resolution,[status(thm)],[144,21]) ).
tff(146,plain,
add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)) = multiply(add(b,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))) = multiply(b,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),
inference(transitivity,[status(thm)],[61,40,44,41,38,28,51,54,146,143]) ).
tff(148,plain,
add(multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)))) = add(multiply(b,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)))),
inference(monotonicity,[status(thm)],[147]) ).
tff(149,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(multiply(multiply(a,b),a),multiply(b,a)))) = add(multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(150,plain,
multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(multiply(multiply(a,b),a),multiply(b,a)))) = add(multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)))),
inference(unit_resolution,[status(thm)],[149,35]) ).
tff(151,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,a)),multiply(b,a)) = multiply(b,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(152,plain,
add(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,a)),multiply(b,a)) = multiply(b,a),
inference(unit_resolution,[status(thm)],[151,7]) ).
tff(153,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y )
| ( multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,a)) = multiply(b,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(154,plain,
multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,a)) = multiply(b,a),
inference(unit_resolution,[status(thm)],[153,21]) ).
tff(155,plain,
add(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,a)),multiply(b,a)) = add(multiply(b,a),multiply(b,a)),
inference(monotonicity,[status(thm)],[154]) ).
tff(156,plain,
add(multiply(b,a),multiply(b,a)) = add(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,a)),multiply(b,a)),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(a,add(b,b)) = add(multiply(b,a),multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(158,plain,
multiply(a,add(b,b)) = add(multiply(b,a),multiply(b,a)),
inference(unit_resolution,[status(thm)],[157,35]) ).
tff(159,plain,
multiply(a,add(b,b)) = multiply(a,b),
inference(monotonicity,[status(thm)],[93]) ).
tff(160,plain,
multiply(a,b) = multiply(a,add(b,b)),
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
add(multiply(multiply(a,b),a),multiply(b,a)) = multiply(b,a),
inference(transitivity,[status(thm)],[135,132,160,158,156,152]) ).
tff(162,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(c,add(b,b)) = add(multiply(b,c),multiply(b,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(163,plain,
multiply(c,add(b,b)) = add(multiply(b,c),multiply(b,c)),
inference(unit_resolution,[status(thm)],[162,35]) ).
tff(164,plain,
add(multiply(b,b),b) = add(b,b),
inference(symmetry,[status(thm)],[92]) ).
tff(165,plain,
b = add(multiply(b,b),b),
inference(symmetry,[status(thm)],[82]) ).
tff(166,plain,
b = add(b,b),
inference(transitivity,[status(thm)],[165,164]) ).
tff(167,plain,
multiply(c,b) = multiply(c,add(b,b)),
inference(monotonicity,[status(thm)],[166]) ).
tff(168,plain,
multiply(c,b) = multiply(b,c),
inference(transitivity,[status(thm)],[167,163,26,9]) ).
tff(169,plain,
multiply(multiply(c,b),a) = multiply(multiply(b,c),a),
inference(monotonicity,[status(thm)],[168]) ).
tff(170,plain,
multiply(multiply(b,c),a) = multiply(multiply(c,b),a),
inference(symmetry,[status(thm)],[169]) ).
tff(171,plain,
add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)) = multiply(multiply(c,b),a),
inference(transitivity,[status(thm)],[55,52,59,37,58,43,170]) ).
tff(172,plain,
add(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(multiply(multiply(a,b),a),multiply(b,a))) = add(multiply(multiply(c,b),a),multiply(b,a)),
inference(monotonicity,[status(thm)],[171,161]) ).
tff(173,plain,
add(multiply(multiply(c,b),a),multiply(b,a)) = add(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(multiply(multiply(a,b),a),multiply(b,a))),
inference(symmetry,[status(thm)],[172]) ).
tff(174,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(a,add(multiply(c,b),b)) = add(multiply(multiply(c,b),a),multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(175,plain,
multiply(a,add(multiply(c,b),b)) = add(multiply(multiply(c,b),a),multiply(b,a)),
inference(unit_resolution,[status(thm)],[174,35]) ).
tff(176,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(c,b),b) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(177,plain,
add(multiply(c,b),b) = b,
inference(unit_resolution,[status(thm)],[176,7]) ).
tff(178,plain,
multiply(a,add(multiply(c,b),b)) = multiply(a,b),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
multiply(a,b) = multiply(a,add(multiply(c,b),b)),
inference(symmetry,[status(thm)],[178]) ).
tff(180,plain,
add(multiply(multiply(a,b),a),multiply(b,a)) = add(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(multiply(multiply(a,b),a),multiply(b,a))),
inference(transitivity,[status(thm)],[135,132,179,175,173]) ).
tff(181,plain,
multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(multiply(multiply(a,b),a),multiply(b,a))) = multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(multiply(multiply(a,b),a),multiply(b,a)))),
inference(monotonicity,[status(thm)],[180]) ).
tff(182,plain,
multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(b,multiply(a,multiply(b,c)))) = add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),
inference(transitivity,[status(thm)],[125,124,122,57]) ).
tff(183,plain,
multiply(multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(b,multiply(a,multiply(b,c)))),add(multiply(multiply(a,b),a),multiply(b,a))) = multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(multiply(multiply(a,b),a),multiply(b,a))),
inference(monotonicity,[status(thm)],[182]) ).
tff(184,plain,
multiply(multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(b,multiply(a,multiply(b,c)))),add(multiply(multiply(a,b),a),multiply(b,a))) = multiply(a,multiply(b,c)),
inference(transitivity,[status(thm)],[183,181,150,148,142,139,127,125,124,122,57,55,52]) ).
tff(185,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(add(multiply(multiply(multiply(a,b),a),multiply(b,c)),multiply(multiply(b,a),multiply(b,c))),multiply(multiply(b,a),multiply(b,c))),multiply(multiply(b,a),multiply(b,c))) = multiply(multiply(b,a),multiply(b,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(186,plain,
add(multiply(add(multiply(multiply(multiply(a,b),a),multiply(b,c)),multiply(multiply(b,a),multiply(b,c))),multiply(multiply(b,a),multiply(b,c))),multiply(multiply(b,a),multiply(b,c))) = multiply(multiply(b,a),multiply(b,c)),
inference(unit_resolution,[status(thm)],[185,7]) ).
tff(187,plain,
add(multiply(b,a),multiply(b,a)) = multiply(a,add(b,b)),
inference(symmetry,[status(thm)],[158]) ).
tff(188,plain,
multiply(b,a) = add(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,a)),multiply(b,a)),
inference(symmetry,[status(thm)],[152]) ).
tff(189,plain,
multiply(b,a) = add(multiply(multiply(a,b),a),multiply(b,a)),
inference(transitivity,[status(thm)],[188,155,187,159,131,134]) ).
tff(190,plain,
multiply(multiply(b,a),multiply(b,c)) = multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,c)),
inference(monotonicity,[status(thm)],[189]) ).
tff(191,plain,
multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,c)) = multiply(multiply(b,a),multiply(b,c)),
inference(symmetry,[status(thm)],[190]) ).
tff(192,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y )
| ( multiply(add(multiply(multiply(multiply(a,b),a),multiply(b,c)),multiply(multiply(b,a),multiply(b,c))),multiply(multiply(b,a),multiply(b,c))) = multiply(multiply(b,a),multiply(b,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(193,plain,
multiply(add(multiply(multiply(multiply(a,b),a),multiply(b,c)),multiply(multiply(b,a),multiply(b,c))),multiply(multiply(b,a),multiply(b,c))) = multiply(multiply(b,a),multiply(b,c)),
inference(unit_resolution,[status(thm)],[192,21]) ).
tff(194,plain,
multiply(multiply(b,a),multiply(b,c)) = multiply(add(multiply(multiply(multiply(a,b),a),multiply(b,c)),multiply(multiply(b,a),multiply(b,c))),multiply(multiply(b,a),multiply(b,c))),
inference(symmetry,[status(thm)],[193]) ).
tff(195,plain,
multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,c)) = multiply(add(multiply(multiply(multiply(a,b),a),multiply(b,c)),multiply(multiply(b,a),multiply(b,c))),multiply(multiply(b,a),multiply(b,c))),
inference(transitivity,[status(thm)],[191,194]) ).
tff(196,plain,
add(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,c)),multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,c))) = add(multiply(add(multiply(multiply(multiply(a,b),a),multiply(b,c)),multiply(multiply(b,a),multiply(b,c))),multiply(multiply(b,a),multiply(b,c))),multiply(multiply(b,a),multiply(b,c))),
inference(monotonicity,[status(thm)],[195,191]) ).
tff(197,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(multiply(b,c),add(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a)))) = add(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,c)),multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(198,plain,
multiply(multiply(b,c),add(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a)))) = add(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,c)),multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,c))),
inference(unit_resolution,[status(thm)],[197,35]) ).
tff(199,plain,
multiply(b,a) = multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,a)),
inference(symmetry,[status(thm)],[154]) ).
tff(200,plain,
add(multiply(multiply(a,b),a),multiply(b,a)) = multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,a)),
inference(transitivity,[status(thm)],[135,132,160,158,156,152,199]) ).
tff(201,plain,
add(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a))) = add(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,a)),multiply(b,a)),
inference(monotonicity,[status(thm)],[200,161]) ).
tff(202,plain,
add(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,a)),multiply(b,a)) = add(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a))),
inference(symmetry,[status(thm)],[201]) ).
tff(203,plain,
multiply(a,b) = add(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a))),
inference(transitivity,[status(thm)],[160,158,156,202]) ).
tff(204,plain,
multiply(multiply(b,c),multiply(a,b)) = multiply(multiply(b,c),add(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a)))),
inference(monotonicity,[status(thm)],[203]) ).
tff(205,plain,
add(b,multiply(a,multiply(b,c))) = b,
inference(transitivity,[status(thm)],[74,114,117]) ).
tff(206,plain,
multiply(c,add(b,multiply(a,multiply(b,c)))) = multiply(c,b),
inference(monotonicity,[status(thm)],[205]) ).
tff(207,plain,
multiply(c,add(b,multiply(a,multiply(b,c)))) = multiply(b,c),
inference(transitivity,[status(thm)],[206,167,163,26,9]) ).
tff(208,plain,
multiply(multiply(c,add(b,multiply(a,multiply(b,c)))),add(multiply(multiply(a,b),a),multiply(b,a))) = multiply(multiply(b,c),multiply(a,b)),
inference(monotonicity,[status(thm)],[207,136]) ).
tff(209,plain,
multiply(multiply(c,add(b,multiply(a,multiply(b,c)))),add(multiply(multiply(a,b),a),multiply(b,a))) = multiply(multiply(b,a),multiply(b,c)),
inference(transitivity,[status(thm)],[208,204,198,196,186]) ).
tff(210,plain,
add(multiply(multiply(c,add(b,multiply(a,multiply(b,c)))),add(multiply(multiply(a,b),a),multiply(b,a))),multiply(multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(b,multiply(a,multiply(b,c)))),add(multiply(multiply(a,b),a),multiply(b,a)))) = add(multiply(multiply(b,a),multiply(b,c)),multiply(a,multiply(b,c))),
inference(monotonicity,[status(thm)],[209,184]) ).
tff(211,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(c,add(b,multiply(a,multiply(b,c)))),multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(b,multiply(a,multiply(b,c)))))) = add(multiply(multiply(c,add(b,multiply(a,multiply(b,c)))),add(multiply(multiply(a,b),a),multiply(b,a))),multiply(multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(b,multiply(a,multiply(b,c)))),add(multiply(multiply(a,b),a),multiply(b,a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(212,plain,
multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(c,add(b,multiply(a,multiply(b,c)))),multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(b,multiply(a,multiply(b,c)))))) = add(multiply(multiply(c,add(b,multiply(a,multiply(b,c)))),add(multiply(multiply(a,b),a),multiply(b,a))),multiply(multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(b,multiply(a,multiply(b,c)))),add(multiply(multiply(a,b),a),multiply(b,a)))),
inference(unit_resolution,[status(thm)],[211,35]) ).
tff(213,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(add(b,multiply(a,multiply(b,c))),add(c,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)))) = add(multiply(c,add(b,multiply(a,multiply(b,c)))),multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(b,multiply(a,multiply(b,c))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(214,plain,
multiply(add(b,multiply(a,multiply(b,c))),add(c,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)))) = add(multiply(c,add(b,multiply(a,multiply(b,c)))),multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(b,multiply(a,multiply(b,c))))),
inference(unit_resolution,[status(thm)],[213,35]) ).
tff(215,plain,
add(c,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))) = add(c,multiply(a,multiply(b,c))),
inference(monotonicity,[status(thm)],[63]) ).
tff(216,plain,
multiply(add(b,multiply(a,multiply(b,c))),add(c,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)))) = multiply(add(b,multiply(a,multiply(b,c))),add(c,multiply(a,multiply(b,c)))),
inference(monotonicity,[status(thm)],[215]) ).
tff(217,plain,
multiply(add(b,multiply(a,multiply(b,c))),add(c,multiply(a,multiply(b,c)))) = multiply(add(b,multiply(a,multiply(b,c))),add(c,add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)))),
inference(symmetry,[status(thm)],[216]) ).
tff(218,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) )
| ( add(multiply(a,multiply(b,c)),multiply(b,c)) = multiply(add(b,multiply(a,multiply(b,c))),add(c,multiply(a,multiply(b,c)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(219,plain,
add(multiply(a,multiply(b,c)),multiply(b,c)) = multiply(add(b,multiply(a,multiply(b,c))),add(c,multiply(a,multiply(b,c)))),
inference(unit_resolution,[status(thm)],[218,72]) ).
tff(220,plain,
multiply(b,c) = add(multiply(c,add(b,multiply(a,multiply(b,c)))),multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(b,multiply(a,multiply(b,c))))),
inference(transitivity,[status(thm)],[12,219,217,214]) ).
tff(221,plain,
multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,c)) = multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(c,add(b,multiply(a,multiply(b,c)))),multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(b,multiply(a,multiply(b,c)))))),
inference(monotonicity,[status(thm)],[220]) ).
tff(222,plain,
add(add(multiply(multiply(a,b),a),multiply(b,a)),b) = add(multiply(a,b),b),
inference(monotonicity,[status(thm)],[136]) ).
tff(223,plain,
add(add(multiply(multiply(a,b),a),multiply(b,a)),b) = b,
inference(transitivity,[status(thm)],[222,84]) ).
tff(224,plain,
multiply(c,add(add(multiply(multiply(a,b),a),multiply(b,a)),b)) = multiply(c,b),
inference(monotonicity,[status(thm)],[223]) ).
tff(225,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(c,add(add(multiply(multiply(a,b),a),multiply(b,a)),b)) = add(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),c),multiply(b,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(226,plain,
multiply(c,add(add(multiply(multiply(a,b),a),multiply(b,a)),b)) = add(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),c),multiply(b,c)),
inference(unit_resolution,[status(thm)],[225,35]) ).
tff(227,plain,
add(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),c),multiply(b,c)) = multiply(c,add(add(multiply(multiply(a,b),a),multiply(b,a)),b)),
inference(symmetry,[status(thm)],[226]) ).
tff(228,plain,
multiply(add(multiply(multiply(a,b),a),multiply(b,a)),c) = multiply(multiply(a,b),c),
inference(monotonicity,[status(thm)],[136]) ).
tff(229,plain,
multiply(multiply(a,b),c) = multiply(add(multiply(multiply(a,b),a),multiply(b,a)),c),
inference(symmetry,[status(thm)],[228]) ).
tff(230,plain,
multiply(multiply(a,b),add(multiply(b,c),c)) = multiply(multiply(a,b),c),
inference(monotonicity,[status(thm)],[108]) ).
tff(231,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(multiply(a,b),add(multiply(b,c),c)) = add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(232,plain,
multiply(multiply(a,b),add(multiply(b,c),c)) = add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),
inference(unit_resolution,[status(thm)],[231,35]) ).
tff(233,plain,
add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))) = multiply(multiply(a,b),add(multiply(b,c),c)),
inference(symmetry,[status(thm)],[232]) ).
tff(234,plain,
add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))) = multiply(add(multiply(multiply(a,b),a),multiply(b,a)),c),
inference(transitivity,[status(thm)],[233,230,229]) ).
tff(235,plain,
add(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(b,c)) = add(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),c),multiply(b,c)),
inference(monotonicity,[status(thm)],[234]) ).
tff(236,plain,
add(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(b,c)) = multiply(b,c),
inference(transitivity,[status(thm)],[235,227,224,167,163,26,9]) ).
tff(237,plain,
multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(b,c))) = multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,c)),
inference(monotonicity,[status(thm)],[236]) ).
tff(238,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(b,c))) = add(multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),add(multiply(multiply(a,b),a),multiply(b,a))),multiply(multiply(b,c),add(multiply(multiply(a,b),a),multiply(b,a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(239,plain,
multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(b,c))) = add(multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),add(multiply(multiply(a,b),a),multiply(b,a))),multiply(multiply(b,c),add(multiply(multiply(a,b),a),multiply(b,a)))),
inference(unit_resolution,[status(thm)],[238,35]) ).
tff(240,plain,
add(multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),add(multiply(multiply(a,b),a),multiply(b,a))),multiply(multiply(b,c),add(multiply(multiply(a,b),a),multiply(b,a)))) = multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(b,c))),
inference(symmetry,[status(thm)],[239]) ).
tff(241,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(multiply(b,c),add(multiply(multiply(a,b),a),multiply(b,a))) = add(multiply(multiply(multiply(a,b),a),multiply(b,c)),multiply(multiply(b,a),multiply(b,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(242,plain,
multiply(multiply(b,c),add(multiply(multiply(a,b),a),multiply(b,a))) = add(multiply(multiply(multiply(a,b),a),multiply(b,c)),multiply(multiply(b,a),multiply(b,c))),
inference(unit_resolution,[status(thm)],[241,35]) ).
tff(243,plain,
add(multiply(multiply(multiply(a,b),a),multiply(b,c)),multiply(multiply(b,a),multiply(b,c))) = multiply(multiply(b,c),add(multiply(multiply(a,b),a),multiply(b,a))),
inference(symmetry,[status(thm)],[242]) ).
tff(244,plain,
add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))) = multiply(multiply(a,b),c),
inference(transitivity,[status(thm)],[233,230]) ).
tff(245,plain,
multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),add(multiply(multiply(a,b),a),multiply(b,a))) = multiply(multiply(multiply(a,b),c),multiply(a,b)),
inference(monotonicity,[status(thm)],[244,136]) ).
tff(246,plain,
multiply(multiply(multiply(a,b),c),multiply(a,b)) = multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),add(multiply(multiply(a,b),a),multiply(b,a))),
inference(symmetry,[status(thm)],[245]) ).
tff(247,plain,
multiply(c,add(multiply(multiply(a,b),a),multiply(b,a))) = multiply(c,multiply(a,b)),
inference(monotonicity,[status(thm)],[136]) ).
tff(248,plain,
multiply(c,multiply(a,b)) = multiply(c,add(multiply(multiply(a,b),a),multiply(b,a))),
inference(symmetry,[status(thm)],[247]) ).
tff(249,plain,
add(multiply(c,multiply(a,b)),add(multiply(multiply(a,b),a),multiply(b,a))) = add(multiply(c,add(multiply(multiply(a,b),a),multiply(b,a))),add(multiply(multiply(a,b),a),multiply(b,a))),
inference(monotonicity,[status(thm)],[248]) ).
tff(250,plain,
add(multiply(c,add(multiply(multiply(a,b),a),multiply(b,a))),add(multiply(multiply(a,b),a),multiply(b,a))) = add(multiply(c,multiply(a,b)),add(multiply(multiply(a,b),a),multiply(b,a))),
inference(symmetry,[status(thm)],[249]) ).
tff(251,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(c,add(multiply(multiply(a,b),a),multiply(b,a))),add(multiply(multiply(a,b),a),multiply(b,a))) = add(multiply(multiply(a,b),a),multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(252,plain,
add(multiply(c,add(multiply(multiply(a,b),a),multiply(b,a))),add(multiply(multiply(a,b),a),multiply(b,a))) = add(multiply(multiply(a,b),a),multiply(b,a)),
inference(unit_resolution,[status(thm)],[251,7]) ).
tff(253,plain,
add(multiply(multiply(a,b),a),multiply(b,a)) = add(multiply(c,add(multiply(multiply(a,b),a),multiply(b,a))),add(multiply(multiply(a,b),a),multiply(b,a))),
inference(symmetry,[status(thm)],[252]) ).
tff(254,plain,
multiply(a,b) = add(multiply(c,multiply(a,b)),add(multiply(multiply(a,b),a),multiply(b,a))),
inference(transitivity,[status(thm)],[131,134,253,250]) ).
tff(255,plain,
multiply(multiply(a,b),c) = multiply(multiply(a,b),add(multiply(b,c),c)),
inference(symmetry,[status(thm)],[230]) ).
tff(256,plain,
multiply(multiply(a,b),c) = add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),
inference(transitivity,[status(thm)],[255,232]) ).
tff(257,plain,
multiply(multiply(multiply(a,b),c),multiply(a,b)) = multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),add(multiply(c,multiply(a,b)),add(multiply(multiply(a,b),a),multiply(b,a)))),
inference(monotonicity,[status(thm)],[256,254]) ).
tff(258,plain,
multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),add(multiply(c,multiply(a,b)),add(multiply(multiply(a,b),a),multiply(b,a)))) = multiply(multiply(multiply(a,b),c),multiply(a,b)),
inference(symmetry,[status(thm)],[257]) ).
tff(259,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),add(multiply(c,multiply(a,b)),add(multiply(multiply(a,b),a),multiply(b,a)))) = add(multiply(multiply(c,multiply(a,b)),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(260,plain,
multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),add(multiply(c,multiply(a,b)),add(multiply(multiply(a,b),a),multiply(b,a)))) = add(multiply(multiply(c,multiply(a,b)),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))),
inference(unit_resolution,[status(thm)],[259,35]) ).
tff(261,plain,
add(multiply(multiply(c,multiply(a,b)),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))) = multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),add(multiply(c,multiply(a,b)),add(multiply(multiply(a,b),a),multiply(b,a)))),
inference(symmetry,[status(thm)],[260]) ).
tff(262,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(c,c),c) = c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(263,plain,
add(multiply(c,c),c) = c,
inference(unit_resolution,[status(thm)],[262,7]) ).
tff(264,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(multiply(a,b),c),c) = c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(265,plain,
add(multiply(multiply(a,b),c),c) = c,
inference(unit_resolution,[status(thm)],[264,7]) ).
tff(266,plain,
c = add(multiply(multiply(a,b),c),c),
inference(symmetry,[status(thm)],[265]) ).
tff(267,plain,
multiply(c,c) = multiply(add(multiply(multiply(a,b),c),c),c),
inference(monotonicity,[status(thm)],[266]) ).
tff(268,plain,
multiply(add(multiply(multiply(a,b),c),c),c) = multiply(c,c),
inference(symmetry,[status(thm)],[267]) ).
tff(269,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y )
| ( multiply(add(multiply(multiply(a,b),c),c),c) = c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(270,plain,
multiply(add(multiply(multiply(a,b),c),c),c) = c,
inference(unit_resolution,[status(thm)],[269,21]) ).
tff(271,plain,
c = multiply(add(multiply(multiply(a,b),c),c),c),
inference(symmetry,[status(thm)],[270]) ).
tff(272,plain,
c = multiply(c,c),
inference(transitivity,[status(thm)],[271,268]) ).
tff(273,plain,
add(c,c) = add(multiply(c,c),c),
inference(monotonicity,[status(thm)],[272]) ).
tff(274,plain,
add(c,c) = c,
inference(transitivity,[status(thm)],[273,263]) ).
tff(275,plain,
multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(c,c)) = multiply(multiply(a,b),c),
inference(monotonicity,[status(thm)],[136,274]) ).
tff(276,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(c,c)) = add(multiply(c,add(multiply(multiply(a,b),a),multiply(b,a))),multiply(c,add(multiply(multiply(a,b),a),multiply(b,a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(277,plain,
multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(c,c)) = add(multiply(c,add(multiply(multiply(a,b),a),multiply(b,a))),multiply(c,add(multiply(multiply(a,b),a),multiply(b,a)))),
inference(unit_resolution,[status(thm)],[276,35]) ).
tff(278,plain,
add(multiply(c,add(multiply(multiply(a,b),a),multiply(b,a))),multiply(c,add(multiply(multiply(a,b),a),multiply(b,a)))) = multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(c,c)),
inference(symmetry,[status(thm)],[277]) ).
tff(279,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y )
| ( multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(c,multiply(a,b))) = multiply(c,multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(280,plain,
multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(c,multiply(a,b))) = multiply(c,multiply(a,b)),
inference(unit_resolution,[status(thm)],[279,21]) ).
tff(281,plain,
multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(c,multiply(a,b))) = multiply(c,add(multiply(multiply(a,b),a),multiply(b,a))),
inference(transitivity,[status(thm)],[280,248]) ).
tff(282,plain,
add(multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(c,multiply(a,b))),multiply(c,multiply(a,b))) = add(multiply(c,add(multiply(multiply(a,b),a),multiply(b,a))),multiply(c,add(multiply(multiply(a,b),a),multiply(b,a)))),
inference(monotonicity,[status(thm)],[281,248]) ).
tff(283,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(c,multiply(a,b))),multiply(c,multiply(a,b))) = multiply(c,multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(284,plain,
add(multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(c,multiply(a,b))),multiply(c,multiply(a,b))) = multiply(c,multiply(a,b)),
inference(unit_resolution,[status(thm)],[283,7]) ).
tff(285,plain,
multiply(c,multiply(a,b)) = add(multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(c,multiply(a,b))),multiply(c,multiply(a,b))),
inference(symmetry,[status(thm)],[284]) ).
tff(286,plain,
add(multiply(c,add(multiply(multiply(a,b),a),multiply(b,a))),multiply(c,add(multiply(multiply(a,b),a),multiply(b,a)))) = add(multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(c,multiply(a,b))),multiply(c,multiply(a,b))),
inference(symmetry,[status(thm)],[282]) ).
tff(287,plain,
multiply(multiply(a,b),c) = multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(c,c)),
inference(symmetry,[status(thm)],[275]) ).
tff(288,plain,
add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))) = multiply(c,multiply(a,b)),
inference(transitivity,[status(thm)],[233,230,287,277,286,284]) ).
tff(289,plain,
multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))) = multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(c,multiply(a,b))),
inference(monotonicity,[status(thm)],[288]) ).
tff(290,plain,
multiply(c,multiply(a,b)) = add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),
inference(transitivity,[status(thm)],[285,282,278,275,255,232]) ).
tff(291,plain,
multiply(multiply(c,multiply(a,b)),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))) = multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),
inference(monotonicity,[status(thm)],[290]) ).
tff(292,plain,
multiply(multiply(c,multiply(a,b)),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))) = add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),
inference(transitivity,[status(thm)],[291,289,280,285,282,278,275,255,232]) ).
tff(293,plain,
add(multiply(multiply(c,multiply(a,b)),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))) = add(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))),
inference(monotonicity,[status(thm)],[292]) ).
tff(294,plain,
add(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))) = add(multiply(multiply(c,multiply(a,b)),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))),
inference(symmetry,[status(thm)],[293]) ).
tff(295,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y )
| ( multiply(add(multiply(multiply(multiply(a,b),a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))) = multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(296,plain,
multiply(add(multiply(multiply(multiply(a,b),a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))) = multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),
inference(unit_resolution,[status(thm)],[295,21]) ).
tff(297,plain,
multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))) = multiply(add(multiply(multiply(multiply(a,b),a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))),
inference(symmetry,[status(thm)],[296]) ).
tff(298,plain,
multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))) = multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),
inference(monotonicity,[status(thm)],[161]) ).
tff(299,plain,
multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))) = multiply(add(multiply(multiply(multiply(a,b),a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))),
inference(transitivity,[status(thm)],[298,297]) ).
tff(300,plain,
add(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))) = add(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(add(multiply(multiply(multiply(a,b),a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))))),
inference(monotonicity,[status(thm)],[299]) ).
tff(301,plain,
add(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(add(multiply(multiply(multiply(a,b),a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))))) = add(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))),
inference(symmetry,[status(thm)],[300]) ).
tff(302,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) )
| ( add(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(add(multiply(multiply(multiply(a,b),a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))))) = multiply(add(add(multiply(multiply(multiply(a,b),a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),add(multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(303,plain,
add(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(add(multiply(multiply(multiply(a,b),a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))))) = multiply(add(add(multiply(multiply(multiply(a,b),a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),add(multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))),
inference(unit_resolution,[status(thm)],[302,72]) ).
tff(304,plain,
multiply(add(add(multiply(multiply(multiply(a,b),a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),add(multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))) = add(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(add(multiply(multiply(multiply(a,b),a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))))),
inference(symmetry,[status(thm)],[303]) ).
tff(305,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))) = add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(306,plain,
add(multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))) = add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),
inference(unit_resolution,[status(thm)],[305,7]) ).
tff(307,plain,
multiply(multiply(a,b),add(multiply(multiply(a,b),c),c)) = multiply(multiply(a,b),c),
inference(monotonicity,[status(thm)],[265]) ).
tff(308,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(multiply(a,b),add(multiply(multiply(a,b),c),c)) = add(multiply(multiply(multiply(a,b),c),multiply(a,b)),multiply(c,multiply(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(309,plain,
multiply(multiply(a,b),add(multiply(multiply(a,b),c),c)) = add(multiply(multiply(multiply(a,b),c),multiply(a,b)),multiply(c,multiply(a,b))),
inference(unit_resolution,[status(thm)],[308,35]) ).
tff(310,plain,
add(multiply(multiply(multiply(a,b),c),multiply(a,b)),multiply(c,multiply(a,b))) = multiply(multiply(a,b),add(multiply(multiply(a,b),c),c)),
inference(symmetry,[status(thm)],[309]) ).
tff(311,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),add(multiply(multiply(a,b),a),multiply(b,a))) = add(multiply(multiply(multiply(a,b),a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(312,plain,
multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),add(multiply(multiply(a,b),a),multiply(b,a))) = add(multiply(multiply(multiply(a,b),a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))),
inference(unit_resolution,[status(thm)],[311,35]) ).
tff(313,plain,
add(multiply(multiply(multiply(a,b),a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))) = multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),add(multiply(multiply(a,b),a),multiply(b,a))),
inference(symmetry,[status(thm)],[312]) ).
tff(314,plain,
add(multiply(multiply(multiply(a,b),a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))) = multiply(multiply(multiply(a,b),c),multiply(a,b)),
inference(transitivity,[status(thm)],[313,245]) ).
tff(315,plain,
add(add(multiply(multiply(multiply(a,b),a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))) = add(multiply(multiply(multiply(a,b),c),multiply(a,b)),multiply(c,multiply(a,b))),
inference(monotonicity,[status(thm)],[314,288]) ).
tff(316,plain,
add(add(multiply(multiply(multiply(a,b),a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))) = add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),
inference(transitivity,[status(thm)],[315,310,307,255,232]) ).
tff(317,plain,
multiply(add(add(multiply(multiply(multiply(a,b),a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),add(multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))) = multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),
inference(monotonicity,[status(thm)],[316,306]) ).
tff(318,plain,
multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))) = multiply(add(add(multiply(multiply(multiply(a,b),a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),add(multiply(multiply(b,a),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))))),
inference(symmetry,[status(thm)],[317]) ).
tff(319,plain,
multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(c,multiply(a,b))) = multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),
inference(symmetry,[status(thm)],[289]) ).
tff(320,plain,
multiply(c,multiply(a,b)) = multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(c,multiply(a,b))),
inference(symmetry,[status(thm)],[280]) ).
tff(321,plain,
add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))) = multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),add(multiply(multiply(a,b),a),multiply(b,a))),
inference(transitivity,[status(thm)],[233,230,287,277,286,284,320,319,318,304,301,294,261,258,246]) ).
tff(322,plain,
add(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),add(multiply(multiply(multiply(a,b),a),multiply(b,c)),multiply(multiply(b,a),multiply(b,c)))) = add(multiply(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),add(multiply(multiply(a,b),a),multiply(b,a))),multiply(multiply(b,c),add(multiply(multiply(a,b),a),multiply(b,a)))),
inference(monotonicity,[status(thm)],[321,243]) ).
tff(323,plain,
multiply(c,add(multiply(multiply(a,b),a),multiply(b,a))) = add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),
inference(transitivity,[status(thm)],[247,285,282,278,275,255,232]) ).
tff(324,plain,
add(multiply(c,add(multiply(multiply(a,b),a),multiply(b,a))),multiply(multiply(b,c),add(multiply(multiply(a,b),a),multiply(b,a)))) = add(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),add(multiply(multiply(multiply(a,b),a),multiply(b,c)),multiply(multiply(b,a),multiply(b,c)))),
inference(monotonicity,[status(thm)],[323,242]) ).
tff(325,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(c,multiply(b,c))) = add(multiply(c,add(multiply(multiply(a,b),a),multiply(b,a))),multiply(multiply(b,c),add(multiply(multiply(a,b),a),multiply(b,a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(326,plain,
multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(c,multiply(b,c))) = add(multiply(c,add(multiply(multiply(a,b),a),multiply(b,a))),multiply(multiply(b,c),add(multiply(multiply(a,b),a),multiply(b,a)))),
inference(unit_resolution,[status(thm)],[325,35]) ).
tff(327,plain,
add(c,multiply(b,c)) = add(c,multiply(multiply(b,c),multiply(b,c))),
inference(monotonicity,[status(thm)],[25]) ).
tff(328,plain,
add(c,multiply(multiply(b,c),multiply(b,c))) = add(c,multiply(b,c)),
inference(symmetry,[status(thm)],[327]) ).
tff(329,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) )
| ( add(c,multiply(multiply(b,c),multiply(b,c))) = multiply(add(multiply(b,c),c),add(multiply(b,c),c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(330,plain,
add(c,multiply(multiply(b,c),multiply(b,c))) = multiply(add(multiply(b,c),c),add(multiply(b,c),c)),
inference(unit_resolution,[status(thm)],[329,72]) ).
tff(331,plain,
multiply(add(multiply(b,c),c),add(multiply(b,c),c)) = add(c,multiply(multiply(b,c),multiply(b,c))),
inference(symmetry,[status(thm)],[330]) ).
tff(332,plain,
add(multiply(b,c),c) = add(multiply(multiply(a,b),c),c),
inference(transitivity,[status(thm)],[108,266]) ).
tff(333,plain,
multiply(add(multiply(b,c),c),add(multiply(b,c),c)) = multiply(add(multiply(multiply(a,b),c),c),c),
inference(monotonicity,[status(thm)],[332,108]) ).
tff(334,plain,
multiply(add(multiply(multiply(a,b),c),c),c) = multiply(add(multiply(b,c),c),add(multiply(b,c),c)),
inference(symmetry,[status(thm)],[333]) ).
tff(335,plain,
c = add(c,multiply(b,c)),
inference(transitivity,[status(thm)],[271,334,331,328]) ).
tff(336,plain,
multiply(a,b) = add(multiply(multiply(a,b),a),multiply(b,a)),
inference(transitivity,[status(thm)],[131,134]) ).
tff(337,plain,
multiply(multiply(a,b),c) = multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(c,multiply(b,c))),
inference(monotonicity,[status(thm)],[336,335]) ).
tff(338,plain,
multiply(multiply(a,b),c) = multiply(a,multiply(b,c)),
inference(transitivity,[status(thm)],[337,326,324,322,240,237,221,212,210,50,47,44,41,38,28]) ).
tff(339,plain,
( ( multiply(multiply(a,b),c) != multiply(a,multiply(b,c)) )
<=> ( multiply(multiply(a,b),c) != multiply(a,multiply(b,c)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(340,axiom,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity_of_multiply) ).
tff(341,plain,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
inference(modus_ponens,[status(thm)],[340,339]) ).
tff(342,plain,
$false,
inference(unit_resolution,[status(thm)],[341,338]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO022-1 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n008.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 11:37:33 EDT 2025
% 0.11/0.34 % CPUTime :
% 0.42/0.60 % SZS status Unsatisfiable
% 0.42/0.60 % SZS output start Proof
% See solution above
% 0.51/0.66 % E exiting
%------------------------------------------------------------------------------