TSTP Solution File: BOO022-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : BOO022-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 : Tue Sep 6 17:18:46 EDT 2022
% Result : Unsatisfiable 1.35s 1.09s
% Output : Proof 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 65
% Syntax : Number of formulae : 297 ( 237 unt; 5 typ; 0 def)
% Number of atoms : 355 ( 350 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 109 ( 50 ~; 46 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 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 : 205 ( 195 !; 0 ?; 205 :)
% 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/sandbox/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(a,multiply(b,c)),multiply(b,c)) = multiply(b,c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
add(multiply(a,multiply(b,c)),multiply(b,c)) = multiply(b,c),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
multiply(b,c) = add(multiply(a,multiply(b,c)),multiply(b,c)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,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)],[10]) ).
tff(12,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)],[11]) ).
tff(13,plain,
^ [Y: $i,X: $i] :
refl(
( ( multiply(add(X,Y),Y) = Y )
<=> ( multiply(add(X,Y),Y) = Y ) )),
inference(bind,[status(th)],]) ).
tff(14,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)],[13]) ).
tff(15,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(16,axiom,
! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_add) ).
tff(17,plain,
! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,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(21,plain,
multiply(add(multiply(a,multiply(b,c)),multiply(b,c)),multiply(b,c)) = multiply(b,c),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
multiply(b,c) = multiply(add(multiply(a,multiply(b,c)),multiply(b,c)),multiply(b,c)),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
multiply(b,c) = multiply(multiply(b,c),multiply(b,c)),
inference(transitivity,[status(thm)],[22,12]) ).
tff(24,plain,
add(multiply(b,c),multiply(b,c)) = add(multiply(multiply(b,c),multiply(b,c)),multiply(b,c)),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
add(multiply(multiply(b,c),multiply(b,c)),multiply(b,c)) = add(multiply(b,c),multiply(b,c)),
inference(symmetry,[status(thm)],[24]) ).
tff(26,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(27,plain,
add(multiply(multiply(b,c),multiply(b,c)),multiply(b,c)) = multiply(b,c),
inference(unit_resolution,[status(thm)],[26,7]) ).
tff(28,plain,
multiply(b,c) = add(multiply(multiply(b,c),multiply(b,c)),multiply(b,c)),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
multiply(b,c) = add(multiply(b,c),multiply(b,c)),
inference(transitivity,[status(thm)],[28,25]) ).
tff(30,plain,
multiply(a,multiply(b,c)) = multiply(a,add(multiply(b,c),multiply(b,c))),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
multiply(a,add(multiply(b,c),multiply(b,c))) = multiply(a,multiply(b,c)),
inference(symmetry,[status(thm)],[30]) ).
tff(32,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(33,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)],[32]) ).
tff(34,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(35,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_add_property) ).
tff(36,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,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(40,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)],[39,38]) ).
tff(41,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)],[40]) ).
tff(42,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(43,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)],[42,19]) ).
tff(44,plain,
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(symmetry,[status(thm)],[43]) ).
tff(45,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(monotonicity,[status(thm)],[44]) ).
tff(46,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(symmetry,[status(thm)],[45]) ).
tff(47,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(48,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)],[47,7]) ).
tff(49,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)],[48]) ).
tff(50,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(b,a),a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
add(multiply(b,a),a) = a,
inference(unit_resolution,[status(thm)],[50,7]) ).
tff(52,plain,
a = add(multiply(b,a),a),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
multiply(multiply(b,c),a) = multiply(multiply(b,c),add(multiply(b,a),a)),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
multiply(multiply(b,c),add(multiply(b,a),a)) = multiply(multiply(b,c),a),
inference(symmetry,[status(thm)],[53]) ).
tff(55,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(56,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)],[55,38]) ).
tff(57,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)],[56]) ).
tff(58,plain,
multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),multiply(b,c)) = multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(multiply(b,c),multiply(b,c))),
inference(monotonicity,[status(thm)],[29]) ).
tff(59,plain,
multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(multiply(b,c),multiply(b,c))) = multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),multiply(b,c)),
inference(symmetry,[status(thm)],[58]) ).
tff(60,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(multiply(b,c),multiply(b,c))) = add(multiply(multiply(b,c),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),multiply(multiply(b,c),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),add(multiply(b,c),multiply(b,c))) = add(multiply(multiply(b,c),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),multiply(multiply(b,c),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)))),
inference(unit_resolution,[status(thm)],[60,38]) ).
tff(62,plain,
add(multiply(multiply(b,c),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),multiply(multiply(b,c),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(b,c),multiply(b,c))),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y )
| ( multiply(add(multiply(b,c),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(64,plain,
multiply(add(multiply(b,c),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)],[63,19]) ).
tff(65,plain,
multiply(a,add(multiply(a,multiply(b,c)),multiply(b,c))) = multiply(a,multiply(b,c)),
inference(monotonicity,[status(thm)],[9]) ).
tff(66,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(67,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)],[66,38]) ).
tff(68,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)],[67]) ).
tff(69,plain,
add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)) = multiply(a,multiply(b,c)),
inference(transitivity,[status(thm)],[68,65]) ).
tff(70,plain,
add(multiply(b,c),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))) = add(multiply(b,c),multiply(a,multiply(b,c))),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
add(multiply(b,c),multiply(a,multiply(b,c))) = add(multiply(b,c),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),
inference(symmetry,[status(thm)],[70]) ).
tff(72,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(73,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)],[72]) ).
tff(74,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(75,axiom,
! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_multiply_property) ).
tff(76,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) )
| ( add(multiply(b,c),multiply(a,multiply(b,c))) = multiply(add(a,multiply(b,c)),add(multiply(b,c),multiply(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
add(multiply(b,c),multiply(a,multiply(b,c))) = multiply(add(a,multiply(b,c)),add(multiply(b,c),multiply(b,c))),
inference(unit_resolution,[status(thm)],[79,78]) ).
tff(81,plain,
multiply(add(a,multiply(b,c)),add(multiply(b,c),multiply(b,c))) = add(multiply(b,c),multiply(a,multiply(b,c))),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(add(a,multiply(b,c)),add(multiply(b,c),multiply(b,c))) = add(multiply(multiply(b,c),add(a,multiply(b,c))),multiply(multiply(b,c),add(a,multiply(b,c)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(83,plain,
multiply(add(a,multiply(b,c)),add(multiply(b,c),multiply(b,c))) = add(multiply(multiply(b,c),add(a,multiply(b,c))),multiply(multiply(b,c),add(a,multiply(b,c)))),
inference(unit_resolution,[status(thm)],[82,38]) ).
tff(84,plain,
add(multiply(multiply(b,c),add(a,multiply(b,c))),multiply(multiply(b,c),add(a,multiply(b,c)))) = multiply(add(a,multiply(b,c)),add(multiply(b,c),multiply(b,c))),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
multiply(multiply(b,c),multiply(b,c)) = multiply(b,c),
inference(transitivity,[status(thm)],[11,21]) ).
tff(86,plain,
add(multiply(a,multiply(b,c)),multiply(multiply(b,c),multiply(b,c))) = add(multiply(a,multiply(b,c)),multiply(b,c)),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(multiply(b,c),add(a,multiply(b,c))) = add(multiply(a,multiply(b,c)),multiply(multiply(b,c),multiply(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(88,plain,
multiply(multiply(b,c),add(a,multiply(b,c))) = add(multiply(a,multiply(b,c)),multiply(multiply(b,c),multiply(b,c))),
inference(unit_resolution,[status(thm)],[87,38]) ).
tff(89,plain,
multiply(multiply(b,c),add(a,multiply(b,c))) = multiply(b,c),
inference(transitivity,[status(thm)],[88,86,9]) ).
tff(90,plain,
multiply(multiply(b,c),add(a,multiply(b,c))) = multiply(multiply(b,c),multiply(b,c)),
inference(transitivity,[status(thm)],[88,86,9,22,12]) ).
tff(91,plain,
add(multiply(multiply(b,c),add(a,multiply(b,c))),multiply(multiply(b,c),add(a,multiply(b,c)))) = add(multiply(multiply(b,c),multiply(b,c)),multiply(b,c)),
inference(monotonicity,[status(thm)],[90,89]) ).
tff(92,plain,
add(multiply(multiply(b,c),multiply(b,c)),multiply(b,c)) = add(multiply(multiply(b,c),add(a,multiply(b,c))),multiply(multiply(b,c),add(a,multiply(b,c)))),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
multiply(b,c) = add(multiply(b,c),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),
inference(transitivity,[status(thm)],[28,92,84,81,71]) ).
tff(94,plain,
multiply(multiply(b,c),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))) = multiply(add(multiply(b,c),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)],[93]) ).
tff(95,plain,
multiply(multiply(b,c),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)],[94,64]) ).
tff(96,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)],[69]) ).
tff(97,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)],[96]) ).
tff(98,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(99,plain,
add(b,multiply(a,multiply(b,c))) = multiply(add(a,b),add(multiply(b,c),b)),
inference(unit_resolution,[status(thm)],[98,78]) ).
tff(100,plain,
multiply(add(a,b),add(multiply(b,c),b)) = add(b,multiply(a,multiply(b,c))),
inference(symmetry,[status(thm)],[99]) ).
tff(101,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)],[100,97]) ).
tff(102,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)],[101]) ).
tff(103,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)],[102]) ).
tff(104,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(105,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)],[104,19]) ).
tff(106,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)],[105]) ).
tff(107,plain,
multiply(multiply(b,c),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)],[94,64,106,103]) ).
tff(108,plain,
add(multiply(multiply(b,c),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),multiply(multiply(b,c),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)],[107,95]) ).
tff(109,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(b,c),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),multiply(multiply(b,c),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)))),
inference(symmetry,[status(thm)],[108]) ).
tff(110,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(111,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)],[110,7]) ).
tff(112,plain,
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(symmetry,[status(thm)],[111]) ).
tff(113,plain,
multiply(a,multiply(b,c)) = multiply(a,add(multiply(a,multiply(b,c)),multiply(b,c))),
inference(symmetry,[status(thm)],[65]) ).
tff(114,plain,
multiply(a,multiply(b,c)) = multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),multiply(b,c)),
inference(transitivity,[status(thm)],[113,67,112,109,62,59]) ).
tff(115,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(116,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)],[115,7]) ).
tff(117,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(118,plain,
multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,a)) = multiply(b,a),
inference(unit_resolution,[status(thm)],[117,19]) ).
tff(119,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)],[118]) ).
tff(120,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)],[119]) ).
tff(121,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(122,plain,
multiply(a,add(b,b)) = add(multiply(b,a),multiply(b,a)),
inference(unit_resolution,[status(thm)],[121,38]) ).
tff(123,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(b,b),b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(124,plain,
add(multiply(b,b),b) = b,
inference(unit_resolution,[status(thm)],[123,7]) ).
tff(125,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(a,b),b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(126,plain,
add(multiply(a,b),b) = b,
inference(unit_resolution,[status(thm)],[125,7]) ).
tff(127,plain,
b = add(multiply(a,b),b),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
multiply(b,b) = multiply(add(multiply(a,b),b),b),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
multiply(add(multiply(a,b),b),b) = multiply(b,b),
inference(symmetry,[status(thm)],[128]) ).
tff(130,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(131,plain,
multiply(add(multiply(a,b),b),b) = b,
inference(unit_resolution,[status(thm)],[130,19]) ).
tff(132,plain,
b = multiply(add(multiply(a,b),b),b),
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
b = multiply(b,b),
inference(transitivity,[status(thm)],[132,129]) ).
tff(134,plain,
add(b,b) = add(multiply(b,b),b),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
add(b,b) = b,
inference(transitivity,[status(thm)],[134,124]) ).
tff(136,plain,
multiply(a,add(b,b)) = multiply(a,b),
inference(monotonicity,[status(thm)],[135]) ).
tff(137,plain,
multiply(a,b) = multiply(a,add(b,b)),
inference(symmetry,[status(thm)],[136]) ).
tff(138,plain,
multiply(a,b) = multiply(a,add(multiply(a,b),b)),
inference(monotonicity,[status(thm)],[127]) ).
tff(139,plain,
multiply(a,add(multiply(a,b),b)) = multiply(a,b),
inference(symmetry,[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(a,add(multiply(a,b),b)) = add(multiply(multiply(a,b),a),multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(141,plain,
multiply(a,add(multiply(a,b),b)) = add(multiply(multiply(a,b),a),multiply(b,a)),
inference(unit_resolution,[status(thm)],[140,38]) ).
tff(142,plain,
add(multiply(multiply(a,b),a),multiply(b,a)) = multiply(a,add(multiply(a,b),b)),
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
add(multiply(multiply(a,b),a),multiply(b,a)) = multiply(b,a),
inference(transitivity,[status(thm)],[142,139,137,122,120,116]) ).
tff(144,plain,
multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,c)) = multiply(multiply(b,a),multiply(b,c)),
inference(monotonicity,[status(thm)],[143]) ).
tff(145,plain,
multiply(multiply(b,a),multiply(b,c)) = multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,c)),
inference(symmetry,[status(thm)],[144]) ).
tff(146,plain,
add(multiply(multiply(b,a),multiply(b,c)),multiply(a,multiply(b,c))) = add(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,c)),multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),multiply(b,c))),
inference(monotonicity,[status(thm)],[145,114]) ).
tff(147,plain,
add(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,c)),multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),multiply(b,c))) = add(multiply(multiply(b,a),multiply(b,c)),multiply(a,multiply(b,c))),
inference(symmetry,[status(thm)],[146]) ).
tff(148,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,multiply(b,c)),a),multiply(multiply(b,c),a)))) = add(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,c)),multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),multiply(b,c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(149,plain,
multiply(multiply(b,c),add(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)))) = add(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(b,c)),multiply(add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)),multiply(b,c))),
inference(unit_resolution,[status(thm)],[148,38]) ).
tff(150,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(c,b),b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(151,plain,
add(multiply(c,b),b) = b,
inference(unit_resolution,[status(thm)],[150,7]) ).
tff(152,plain,
add(multiply(c,b),b) = add(multiply(a,b),b),
inference(transitivity,[status(thm)],[151,127]) ).
tff(153,plain,
multiply(add(multiply(c,b),b),add(multiply(c,b),b)) = multiply(add(multiply(a,b),b),b),
inference(monotonicity,[status(thm)],[152,151]) ).
tff(154,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) )
| ( add(b,multiply(multiply(c,b),multiply(c,b))) = multiply(add(multiply(c,b),b),add(multiply(c,b),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(155,plain,
add(b,multiply(multiply(c,b),multiply(c,b))) = multiply(add(multiply(c,b),b),add(multiply(c,b),b)),
inference(unit_resolution,[status(thm)],[154,78]) ).
tff(156,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(157,plain,
multiply(c,add(b,b)) = add(multiply(b,c),multiply(b,c)),
inference(unit_resolution,[status(thm)],[156,38]) ).
tff(158,plain,
add(multiply(b,b),b) = add(b,b),
inference(symmetry,[status(thm)],[134]) ).
tff(159,plain,
b = add(multiply(b,b),b),
inference(symmetry,[status(thm)],[124]) ).
tff(160,plain,
b = add(b,b),
inference(transitivity,[status(thm)],[159,158]) ).
tff(161,plain,
multiply(c,b) = multiply(c,add(b,b)),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
multiply(c,b) = multiply(b,c),
inference(transitivity,[status(thm)],[161,157,24,27]) ).
tff(163,plain,
multiply(c,b) = add(multiply(a,multiply(b,c)),multiply(b,c)),
inference(transitivity,[status(thm)],[161,157,24,27,10]) ).
tff(164,plain,
multiply(multiply(c,b),multiply(c,b)) = multiply(add(multiply(a,multiply(b,c)),multiply(b,c)),multiply(b,c)),
inference(monotonicity,[status(thm)],[163,162]) ).
tff(165,plain,
multiply(add(multiply(a,multiply(b,c)),multiply(b,c)),multiply(b,c)) = multiply(multiply(c,b),multiply(c,b)),
inference(symmetry,[status(thm)],[164]) ).
tff(166,plain,
multiply(b,c) = multiply(multiply(c,b),multiply(c,b)),
inference(transitivity,[status(thm)],[22,165]) ).
tff(167,plain,
add(b,multiply(b,c)) = add(b,multiply(multiply(c,b),multiply(c,b))),
inference(monotonicity,[status(thm)],[166]) ).
tff(168,plain,
add(b,multiply(b,c)) = b,
inference(transitivity,[status(thm)],[167,155,153,131]) ).
tff(169,plain,
multiply(a,add(b,multiply(b,c))) = multiply(a,b),
inference(monotonicity,[status(thm)],[168]) ).
tff(170,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(a,add(b,multiply(b,c))) = add(multiply(b,a),multiply(multiply(b,c),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(171,plain,
multiply(a,add(b,multiply(b,c))) = add(multiply(b,a),multiply(multiply(b,c),a)),
inference(unit_resolution,[status(thm)],[170,38]) ).
tff(172,plain,
add(multiply(b,a),multiply(multiply(b,c),a)) = multiply(a,add(b,multiply(b,c))),
inference(symmetry,[status(thm)],[171]) ).
tff(173,plain,
multiply(multiply(b,c),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))) = multiply(multiply(b,c),a),
inference(transitivity,[status(thm)],[94,64,68,65,30,40,45,48]) ).
tff(174,plain,
add(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(multiply(b,c),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)))) = add(multiply(b,a),multiply(multiply(b,c),a)),
inference(monotonicity,[status(thm)],[143,173]) ).
tff(175,plain,
multiply(add(multiply(b,c),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(b,c),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),
inference(symmetry,[status(thm)],[94]) ).
tff(176,plain,
add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)) = multiply(add(multiply(b,c),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)],[64]) ).
tff(177,plain,
add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)) = multiply(multiply(b,c),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))),
inference(transitivity,[status(thm)],[176,175]) ).
tff(178,plain,
add(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))) = add(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(multiply(b,c),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)))),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
add(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a))) = multiply(a,b),
inference(transitivity,[status(thm)],[178,174,172,169]) ).
tff(180,plain,
multiply(multiply(b,c),add(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(b,c),a)))) = multiply(multiply(b,c),multiply(a,b)),
inference(monotonicity,[status(thm)],[179]) ).
tff(181,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,multiply(b,c)),a),multiply(multiply(b,c),a)))),
inference(symmetry,[status(thm)],[180]) ).
tff(182,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(183,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)],[182,38]) ).
tff(184,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(b,c),c) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(185,plain,
add(multiply(b,c),c) = c,
inference(unit_resolution,[status(thm)],[184,7]) ).
tff(186,plain,
c = add(multiply(b,c),c),
inference(symmetry,[status(thm)],[185]) ).
tff(187,plain,
multiply(multiply(a,b),c) = multiply(multiply(a,b),add(multiply(b,c),c)),
inference(monotonicity,[status(thm)],[186]) ).
tff(188,plain,
( ~ ! [Y: $i,X: $i] : ( add(multiply(X,Y),Y) = Y )
| ( add(multiply(c,c),c) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(189,plain,
add(multiply(c,c),c) = c,
inference(unit_resolution,[status(thm)],[188,7]) ).
tff(190,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(191,plain,
add(multiply(multiply(a,b),c),c) = c,
inference(unit_resolution,[status(thm)],[190,7]) ).
tff(192,plain,
c = add(multiply(multiply(a,b),c),c),
inference(symmetry,[status(thm)],[191]) ).
tff(193,plain,
multiply(c,c) = multiply(add(multiply(multiply(a,b),c),c),c),
inference(monotonicity,[status(thm)],[192]) ).
tff(194,plain,
multiply(add(multiply(multiply(a,b),c),c),c) = multiply(c,c),
inference(symmetry,[status(thm)],[193]) ).
tff(195,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(196,plain,
multiply(add(multiply(multiply(a,b),c),c),c) = c,
inference(unit_resolution,[status(thm)],[195,19]) ).
tff(197,plain,
c = multiply(add(multiply(multiply(a,b),c),c),c),
inference(symmetry,[status(thm)],[196]) ).
tff(198,plain,
c = multiply(c,c),
inference(transitivity,[status(thm)],[197,194]) ).
tff(199,plain,
add(c,c) = add(multiply(c,c),c),
inference(monotonicity,[status(thm)],[198]) ).
tff(200,plain,
add(c,c) = c,
inference(transitivity,[status(thm)],[199,189]) ).
tff(201,plain,
add(multiply(multiply(a,b),a),multiply(b,a)) = multiply(a,b),
inference(transitivity,[status(thm)],[142,139]) ).
tff(202,plain,
multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(c,c)) = multiply(multiply(a,b),c),
inference(monotonicity,[status(thm)],[201,200]) ).
tff(203,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(204,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)],[203,38]) ).
tff(205,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)],[204]) ).
tff(206,plain,
multiply(c,add(multiply(multiply(a,b),a),multiply(b,a))) = multiply(c,multiply(a,b)),
inference(monotonicity,[status(thm)],[201]) ).
tff(207,plain,
multiply(c,multiply(a,b)) = multiply(c,add(multiply(multiply(a,b),a),multiply(b,a))),
inference(symmetry,[status(thm)],[206]) ).
tff(208,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(209,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)],[208,19]) ).
tff(210,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)],[209,207]) ).
tff(211,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)],[210,207]) ).
tff(212,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(213,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)],[212,7]) ).
tff(214,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)],[213]) ).
tff(215,plain,
multiply(c,multiply(a,b)) = add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),
inference(transitivity,[status(thm)],[214,211,205,202,187,183]) ).
tff(216,plain,
multiply(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(monotonicity,[status(thm)],[215,215]) ).
tff(217,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(multiply(c,multiply(a,b)),multiply(c,multiply(a,b))),
inference(symmetry,[status(thm)],[216]) ).
tff(218,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)],[211]) ).
tff(219,plain,
multiply(multiply(a,b),c) = multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(c,c)),
inference(symmetry,[status(thm)],[202]) ).
tff(220,plain,
multiply(multiply(a,b),add(multiply(b,c),c)) = multiply(multiply(a,b),c),
inference(symmetry,[status(thm)],[187]) ).
tff(221,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)],[183]) ).
tff(222,plain,
add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))) = multiply(c,multiply(a,b)),
inference(transitivity,[status(thm)],[221,220,219,204,218,213]) ).
tff(223,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)],[222]) ).
tff(224,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)],[223]) ).
tff(225,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)],[209]) ).
tff(226,plain,
add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))) = multiply(multiply(c,multiply(a,b)),multiply(c,multiply(a,b))),
inference(transitivity,[status(thm)],[221,220,219,204,218,213,225,224,217]) ).
tff(227,plain,
add(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(a,b),a),multiply(b,a)),multiply(multiply(c,multiply(a,b)),multiply(c,multiply(a,b)))),
inference(monotonicity,[status(thm)],[226]) ).
tff(228,plain,
add(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(multiply(c,multiply(a,b)),multiply(c,multiply(a,b)))) = add(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)],[227]) ).
tff(229,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) )
| ( add(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(multiply(c,multiply(a,b)),multiply(c,multiply(a,b)))) = multiply(add(multiply(c,multiply(a,b)),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(quant_inst,[status(thm)],]) ).
tff(230,plain,
add(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(multiply(c,multiply(a,b)),multiply(c,multiply(a,b)))) = multiply(add(multiply(c,multiply(a,b)),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(unit_resolution,[status(thm)],[229,78]) ).
tff(231,plain,
multiply(add(multiply(c,multiply(a,b)),add(multiply(multiply(a,b),a),multiply(b,a))),add(multiply(c,multiply(a,b)),add(multiply(multiply(a,b),a),multiply(b,a)))) = add(add(multiply(multiply(a,b),a),multiply(b,a)),multiply(multiply(c,multiply(a,b)),multiply(c,multiply(a,b)))),
inference(symmetry,[status(thm)],[230]) ).
tff(232,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(233,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)],[232,7]) ).
tff(234,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)],[207]) ).
tff(235,plain,
add(multiply(c,multiply(a,b)),add(multiply(multiply(a,b),a),multiply(b,a))) = add(multiply(multiply(a,b),a),multiply(b,a)),
inference(transitivity,[status(thm)],[234,233]) ).
tff(236,plain,
multiply(add(multiply(c,multiply(a,b)),add(multiply(multiply(a,b),a),multiply(b,a))),add(multiply(c,multiply(a,b)),add(multiply(multiply(a,b),a),multiply(b,a)))) = multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a))),
inference(monotonicity,[status(thm)],[235,235]) ).
tff(237,plain,
multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a))) = multiply(add(multiply(c,multiply(a,b)),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)],[236]) ).
tff(238,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)],[234]) ).
tff(239,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)],[233]) ).
tff(240,plain,
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(transitivity,[status(thm)],[239,238]) ).
tff(241,plain,
multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a))) = multiply(add(multiply(c,multiply(a,b)),add(multiply(multiply(a,b),a),multiply(b,a))),add(multiply(multiply(a,b),a),multiply(b,a))),
inference(monotonicity,[status(thm)],[240]) ).
tff(242,plain,
multiply(add(multiply(c,multiply(a,b)),add(multiply(multiply(a,b),a),multiply(b,a))),add(multiply(multiply(a,b),a),multiply(b,a))) = multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a))),
inference(symmetry,[status(thm)],[241]) ).
tff(243,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(add(X,Y),Y) = Y )
| ( multiply(add(multiply(c,multiply(a,b)),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(244,plain,
multiply(add(multiply(c,multiply(a,b)),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)],[243,19]) ).
tff(245,plain,
add(multiply(multiply(a,b),a),multiply(b,a)) = multiply(add(multiply(c,multiply(a,b)),add(multiply(multiply(a,b),a),multiply(b,a))),add(multiply(multiply(a,b),a),multiply(b,a))),
inference(symmetry,[status(thm)],[244]) ).
tff(246,plain,
multiply(a,b) = add(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)],[138,141,245,242,237,231,228]) ).
tff(247,plain,
multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a))) = multiply(a,b),
inference(transitivity,[status(thm)],[241,244,142,139]) ).
tff(248,plain,
multiply(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a))),c) = multiply(multiply(a,b),c),
inference(monotonicity,[status(thm)],[247]) ).
tff(249,plain,
multiply(multiply(a,b),c) = multiply(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a))),c),
inference(symmetry,[status(thm)],[248]) ).
tff(250,plain,
add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))) = multiply(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a))),c),
inference(transitivity,[status(thm)],[221,220,249]) ).
tff(251,plain,
add(multiply(b,c),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))) = add(multiply(b,c),multiply(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a))),c)),
inference(monotonicity,[status(thm)],[250]) ).
tff(252,plain,
add(multiply(b,c),multiply(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a))),c)) = add(multiply(b,c),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),
inference(symmetry,[status(thm)],[251]) ).
tff(253,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )
| ( multiply(c,add(b,multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a))))) = add(multiply(b,c),multiply(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a))),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(254,plain,
multiply(c,add(b,multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a))))) = add(multiply(b,c),multiply(multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a))),c)),
inference(unit_resolution,[status(thm)],[253,38]) ).
tff(255,plain,
add(add(multiply(multiply(a,b),a),multiply(b,a)),b) = add(multiply(a,b),b),
inference(monotonicity,[status(thm)],[201]) ).
tff(256,plain,
add(add(multiply(multiply(a,b),a),multiply(b,a)),b) = b,
inference(transitivity,[status(thm)],[255,126]) ).
tff(257,plain,
multiply(add(add(multiply(multiply(a,b),a),multiply(b,a)),b),add(add(multiply(multiply(a,b),a),multiply(b,a)),b)) = multiply(add(multiply(a,b),b),b),
inference(monotonicity,[status(thm)],[255,256]) ).
tff(258,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) )
| ( add(b,multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a)))) = multiply(add(add(multiply(multiply(a,b),a),multiply(b,a)),b),add(add(multiply(multiply(a,b),a),multiply(b,a)),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(259,plain,
add(b,multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a)))) = multiply(add(add(multiply(multiply(a,b),a),multiply(b,a)),b),add(add(multiply(multiply(a,b),a),multiply(b,a)),b)),
inference(unit_resolution,[status(thm)],[258,78]) ).
tff(260,plain,
add(b,multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a)))) = b,
inference(transitivity,[status(thm)],[259,257,131]) ).
tff(261,plain,
multiply(c,add(b,multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a))))) = multiply(c,b),
inference(monotonicity,[status(thm)],[260]) ).
tff(262,plain,
multiply(c,b) = multiply(c,add(b,multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(multiply(multiply(a,b),a),multiply(b,a))))),
inference(symmetry,[status(thm)],[261]) ).
tff(263,plain,
multiply(c,add(b,b)) = multiply(c,b),
inference(symmetry,[status(thm)],[161]) ).
tff(264,plain,
add(multiply(b,c),multiply(b,c)) = multiply(c,add(b,b)),
inference(symmetry,[status(thm)],[157]) ).
tff(265,plain,
multiply(b,c) = add(multiply(b,c),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),
inference(transitivity,[status(thm)],[28,25,264,263,262,254,252]) ).
tff(266,plain,
multiply(multiply(b,c),multiply(a,b)) = multiply(add(multiply(b,c),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),add(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)],[265,246]) ).
tff(267,plain,
multiply(add(multiply(b,c),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),add(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,c),multiply(a,b)),
inference(symmetry,[status(thm)],[266]) ).
tff(268,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(multiply(b,c),add(multiply(multiply(a,b),a),multiply(b,a)))) = multiply(add(multiply(b,c),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),add(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(269,plain,
add(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(multiply(b,c),add(multiply(multiply(a,b),a),multiply(b,a)))) = multiply(add(multiply(b,c),add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b)))),add(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)],[268,78]) ).
tff(270,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(271,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)],[270,38]) ).
tff(272,plain,
add(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),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)],[271]) ).
tff(273,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(add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))),multiply(multiply(b,c),add(multiply(multiply(a,b),a),multiply(b,a)))),
inference(symmetry,[status(thm)],[272]) ).
tff(274,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)],[271]) ).
tff(275,plain,
add(multiply(multiply(b,c),multiply(a,b)),multiply(c,multiply(a,b))) = multiply(c,add(multiply(multiply(a,b),a),multiply(b,a))),
inference(transitivity,[status(thm)],[221,220,219,204,218,213,207]) ).
tff(276,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(c,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)],[275,274]) ).
tff(277,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(symmetry,[status(thm)],[276]) ).
tff(278,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(279,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)],[278,38]) ).
tff(280,plain,
add(multiply(b,c),c) = add(multiply(multiply(a,b),c),c),
inference(transitivity,[status(thm)],[185,192]) ).
tff(281,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)],[280,185]) ).
tff(282,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(283,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)],[282,78]) ).
tff(284,plain,
add(c,multiply(b,c)) = add(c,multiply(multiply(b,c),multiply(b,c))),
inference(monotonicity,[status(thm)],[23]) ).
tff(285,plain,
add(c,multiply(b,c)) = c,
inference(transitivity,[status(thm)],[284,283,281,196]) ).
tff(286,plain,
multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(c,multiply(b,c))) = multiply(multiply(a,b),c),
inference(monotonicity,[status(thm)],[201,285]) ).
tff(287,plain,
multiply(multiply(a,b),c) = multiply(add(multiply(multiply(a,b),a),multiply(b,a)),add(c,multiply(b,c))),
inference(symmetry,[status(thm)],[286]) ).
tff(288,plain,
multiply(multiply(a,b),c) = multiply(a,multiply(b,c)),
inference(transitivity,[status(thm)],[287,279,277,273,269,267,181,149,147,57,54,49,46,41,31]) ).
tff(289,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(290,axiom,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_associativity_of_multiply) ).
tff(291,plain,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
inference(modus_ponens,[status(thm)],[290,289]) ).
tff(292,plain,
$false,
inference(unit_resolution,[status(thm)],[291,288]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : BOO022-1 : TPTP v8.1.0. Released v2.2.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 30 03:14:15 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 1.35/1.09 % SZS status Unsatisfiable
% 1.35/1.09 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------