%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG008-4 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:23:52 AM UTC 2025
% Result : Unsatisfiable 58.58s 58.81s
% Output : Proof 58.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 127
% Syntax : Number of formulae : 546 ( 434 unt; 0 typ; 0 def)
% Number of atoms : 680 ( 668 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 212 ( 89 ~; 85 |; 0 &)
% ( 38 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 11 ( 11 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 398 ( 375 !; 0 ?; 398 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_type,type,
c: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(additive_inverse_type,type,
additive_inverse: $i > $i ).
tff(1,plain,
( ( multiply(a,b) = c )
<=> ( multiply(a,b) = c ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
multiply(a,b) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
tff(3,plain,
multiply(a,b) = c,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Y: $i,X: $i] :
refl(( ( add(X,Y) = add(Y,X) )
<=> ( add(X,Y) = add(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
<=> ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
<=> ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',commutative_addition) ).
tff(8,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(additive_identity,b) = add(b,additive_identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
add(additive_identity,b) = add(b,additive_identity),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
( ! [X: $i] : ( additive_inverse(additive_inverse(X)) = X )
<=> ! [X: $i] : ( additive_inverse(additive_inverse(X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,plain,
( ! [X: $i] : ( additive_inverse(additive_inverse(X)) = X )
<=> ! [X: $i] : ( additive_inverse(additive_inverse(X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
! [X: $i] : ( additive_inverse(additive_inverse(X)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',additive_inverse_additive_inverse) ).
tff(16,plain,
! [X: $i] : ( additive_inverse(additive_inverse(X)) = X ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X: $i] : ( additive_inverse(additive_inverse(X)) = X ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [X: $i] : ( additive_inverse(additive_inverse(X)) = X ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
( ~ ! [X: $i] : ( additive_inverse(additive_inverse(X)) = X )
| ( additive_inverse(additive_inverse(b)) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
additive_inverse(additive_inverse(b)) = b,
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
( ( additive_inverse(additive_identity) = additive_identity )
<=> ( additive_inverse(additive_identity) = additive_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
additive_inverse(additive_identity) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',additive_inverse_identity) ).
tff(23,plain,
additive_inverse(additive_identity) = additive_identity,
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
add(additive_inverse(additive_identity),additive_inverse(additive_inverse(b))) = add(additive_identity,b),
inference(monotonicity,[status(thm)],[23,20]) ).
tff(25,plain,
^ [Y: $i,X: $i] :
refl(( ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) )
<=> ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [Y: $i,X: $i] : ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) )
<=> ! [Y: $i,X: $i] : ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [Y: $i,X: $i] : ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) )
<=> ! [Y: $i,X: $i] : ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
! [Y: $i,X: $i] : ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',distribute_additive_inverse) ).
tff(29,plain,
! [Y: $i,X: $i] : ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [Y: $i,X: $i] : ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [Y: $i,X: $i] : ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
( ~ ! [Y: $i,X: $i] : ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) )
| ( additive_inverse(add(additive_identity,additive_inverse(b))) = add(additive_inverse(additive_identity),additive_inverse(additive_inverse(b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
additive_inverse(add(additive_identity,additive_inverse(b))) = add(additive_inverse(additive_identity),additive_inverse(additive_inverse(b))),
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,plain,
^ [X: $i] :
refl(( ( add(additive_identity,X) = X )
<=> ( add(additive_identity,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [X: $i] : ( add(additive_identity,X) = X )
<=> ! [X: $i] : ( add(additive_identity,X) = X ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [X: $i] : ( add(additive_identity,X) = X )
<=> ! [X: $i] : ( add(additive_identity,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
! [X: $i] : ( add(additive_identity,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',left_identity) ).
tff(38,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [X: $i] : ( add(additive_identity,X) = X ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ~ ! [X: $i] : ( add(additive_identity,X) = X )
| ( add(additive_identity,additive_inverse(b)) = additive_inverse(b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
add(additive_identity,additive_inverse(b)) = additive_inverse(b),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
additive_inverse(b) = add(additive_identity,additive_inverse(b)),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
additive_inverse(additive_inverse(b)) = additive_inverse(add(additive_identity,additive_inverse(b))),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
b = additive_inverse(additive_inverse(b)),
inference(symmetry,[status(thm)],[20]) ).
tff(46,plain,
b = add(b,additive_identity),
inference(transitivity,[status(thm)],[45,44,33,24,12]) ).
tff(47,plain,
^ [X: $i] :
refl(( ( multiply(X,X) = X )
<=> ( multiply(X,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [X: $i] : ( multiply(X,X) = X )
<=> ! [X: $i] : ( multiply(X,X) = X ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [X: $i] : ( multiply(X,X) = X )
<=> ! [X: $i] : ( multiply(X,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
! [X: $i] : ( multiply(X,X) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boolean_ring) ).
tff(51,plain,
! [X: $i] : ( multiply(X,X) = X ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [X: $i] : ( multiply(X,X) = X ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [X: $i] : ( multiply(X,X) = X ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
( ~ ! [X: $i] : ( multiply(X,X) = X )
| ( multiply(add(a,additive_identity),add(a,additive_identity)) = add(a,additive_identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
multiply(add(a,additive_identity),add(a,additive_identity)) = add(a,additive_identity),
inference(unit_resolution,[status(thm)],[54,53]) ).
tff(56,plain,
add(a,additive_identity) = multiply(add(a,additive_identity),add(a,additive_identity)),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(additive_identity,a) = add(a,additive_identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
add(additive_identity,a) = add(a,additive_identity),
inference(unit_resolution,[status(thm)],[57,10]) ).
tff(59,plain,
( ~ ! [X: $i] : ( additive_inverse(additive_inverse(X)) = X )
| ( additive_inverse(additive_inverse(a)) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
additive_inverse(additive_inverse(a)) = a,
inference(unit_resolution,[status(thm)],[59,18]) ).
tff(61,plain,
add(additive_inverse(additive_identity),additive_inverse(additive_inverse(a))) = add(additive_identity,a),
inference(monotonicity,[status(thm)],[23,60]) ).
tff(62,plain,
( ~ ! [Y: $i,X: $i] : ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) )
| ( additive_inverse(add(additive_identity,additive_inverse(a))) = add(additive_inverse(additive_identity),additive_inverse(additive_inverse(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
additive_inverse(add(additive_identity,additive_inverse(a))) = add(additive_inverse(additive_identity),additive_inverse(additive_inverse(a))),
inference(unit_resolution,[status(thm)],[62,31]) ).
tff(64,plain,
( ~ ! [X: $i] : ( add(additive_identity,X) = X )
| ( add(additive_identity,additive_inverse(a)) = additive_inverse(a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
add(additive_identity,additive_inverse(a)) = additive_inverse(a),
inference(unit_resolution,[status(thm)],[64,40]) ).
tff(66,plain,
additive_inverse(a) = add(additive_identity,additive_inverse(a)),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
additive_inverse(additive_inverse(a)) = additive_inverse(add(additive_identity,additive_inverse(a))),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
a = additive_inverse(additive_inverse(a)),
inference(symmetry,[status(thm)],[60]) ).
tff(69,plain,
a = multiply(add(a,additive_identity),add(a,additive_identity)),
inference(transitivity,[status(thm)],[68,67,63,61,58,56]) ).
tff(70,plain,
multiply(a,b) = multiply(multiply(add(a,additive_identity),add(a,additive_identity)),add(b,additive_identity)),
inference(monotonicity,[status(thm)],[69,46]) ).
tff(71,plain,
multiply(multiply(add(a,additive_identity),add(a,additive_identity)),add(b,additive_identity)) = multiply(a,b),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(73,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',associative_multiplication) ).
tff(76,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(add(a,additive_identity),add(a,additive_identity)),add(b,additive_identity)) = multiply(add(a,additive_identity),multiply(add(a,additive_identity),add(b,additive_identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
multiply(multiply(add(a,additive_identity),add(a,additive_identity)),add(b,additive_identity)) = multiply(add(a,additive_identity),multiply(add(a,additive_identity),add(b,additive_identity))),
inference(unit_resolution,[status(thm)],[79,78]) ).
tff(81,plain,
multiply(add(a,additive_identity),multiply(add(a,additive_identity),add(b,additive_identity))) = multiply(multiply(add(a,additive_identity),add(a,additive_identity)),add(b,additive_identity)),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(additive_identity,additive_inverse(multiply(additive_inverse(a),b))) = add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
add(additive_identity,additive_inverse(multiply(additive_inverse(a),b))) = add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity),
inference(unit_resolution,[status(thm)],[82,10]) ).
tff(84,plain,
^ [Y: $i,X: $i] :
refl(( ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) )
<=> ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(85,plain,
( ! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) )
<=> ! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,plain,
( ! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) )
<=> ! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,axiom,
! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',multiply_additive_inverse2) ).
tff(88,plain,
! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ),
inference(skolemize,[status(sab)],[88]) ).
tff(90,plain,
! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) )
| ( multiply(additive_inverse(a),b) = additive_inverse(multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
multiply(additive_inverse(a),b) = additive_inverse(multiply(a,b)),
inference(unit_resolution,[status(thm)],[91,90]) ).
tff(93,plain,
additive_inverse(multiply(a,b)) = multiply(additive_inverse(a),b),
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
additive_inverse(additive_inverse(multiply(a,b))) = additive_inverse(multiply(additive_inverse(a),b)),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
additive_inverse(multiply(additive_inverse(a),b)) = additive_inverse(additive_inverse(multiply(a,b))),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
additive_identity = additive_inverse(additive_identity),
inference(symmetry,[status(thm)],[23]) ).
tff(97,plain,
add(additive_identity,additive_inverse(multiply(additive_inverse(a),b))) = add(additive_inverse(additive_identity),additive_inverse(additive_inverse(multiply(a,b)))),
inference(monotonicity,[status(thm)],[96,95]) ).
tff(98,plain,
add(additive_inverse(additive_identity),additive_inverse(additive_inverse(multiply(a,b)))) = add(additive_identity,additive_inverse(multiply(additive_inverse(a),b))),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
( ~ ! [Y: $i,X: $i] : ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) )
| ( additive_inverse(add(additive_identity,additive_inverse(multiply(a,b)))) = add(additive_inverse(additive_identity),additive_inverse(additive_inverse(multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(100,plain,
additive_inverse(add(additive_identity,additive_inverse(multiply(a,b)))) = add(additive_inverse(additive_identity),additive_inverse(additive_inverse(multiply(a,b)))),
inference(unit_resolution,[status(thm)],[99,31]) ).
tff(101,plain,
( ~ ! [X: $i] : ( add(additive_identity,X) = X )
| ( add(additive_identity,additive_inverse(multiply(a,b))) = additive_inverse(multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
add(additive_identity,additive_inverse(multiply(a,b))) = additive_inverse(multiply(a,b)),
inference(unit_resolution,[status(thm)],[101,40]) ).
tff(103,plain,
add(additive_identity,additive_inverse(multiply(a,b))) = multiply(additive_inverse(a),b),
inference(transitivity,[status(thm)],[102,93]) ).
tff(104,plain,
additive_inverse(add(additive_identity,additive_inverse(multiply(a,b)))) = additive_inverse(multiply(additive_inverse(a),b)),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
additive_inverse(multiply(additive_inverse(a),b)) = additive_inverse(add(additive_identity,additive_inverse(multiply(a,b)))),
inference(symmetry,[status(thm)],[104]) ).
tff(106,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) )
| ( multiply(additive_inverse(additive_inverse(a)),b) = additive_inverse(multiply(additive_inverse(a),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(107,plain,
multiply(additive_inverse(additive_inverse(a)),b) = additive_inverse(multiply(additive_inverse(a),b)),
inference(unit_resolution,[status(thm)],[106,90]) ).
tff(108,plain,
multiply(additive_inverse(additive_inverse(a)),b) = multiply(a,b),
inference(monotonicity,[status(thm)],[60]) ).
tff(109,plain,
multiply(a,b) = multiply(additive_inverse(additive_inverse(a)),b),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
additive_inverse(add(additive_identity,additive_inverse(b))) = additive_inverse(additive_inverse(b)),
inference(symmetry,[status(thm)],[44]) ).
tff(111,plain,
add(additive_inverse(additive_identity),additive_inverse(additive_inverse(b))) = additive_inverse(add(additive_identity,additive_inverse(b))),
inference(symmetry,[status(thm)],[33]) ).
tff(112,plain,
add(additive_identity,b) = add(additive_inverse(additive_identity),additive_inverse(additive_inverse(b))),
inference(symmetry,[status(thm)],[24]) ).
tff(113,plain,
add(b,additive_identity) = add(additive_identity,b),
inference(symmetry,[status(thm)],[12]) ).
tff(114,plain,
add(b,additive_identity) = b,
inference(transitivity,[status(thm)],[113,112,111,110,20]) ).
tff(115,plain,
additive_inverse(add(additive_identity,additive_inverse(a))) = additive_inverse(additive_inverse(a)),
inference(symmetry,[status(thm)],[67]) ).
tff(116,plain,
add(additive_inverse(additive_identity),additive_inverse(additive_inverse(a))) = additive_inverse(add(additive_identity,additive_inverse(a))),
inference(symmetry,[status(thm)],[63]) ).
tff(117,plain,
add(additive_identity,a) = add(additive_inverse(additive_identity),additive_inverse(additive_inverse(a))),
inference(symmetry,[status(thm)],[61]) ).
tff(118,plain,
add(a,additive_identity) = add(additive_identity,a),
inference(symmetry,[status(thm)],[58]) ).
tff(119,plain,
add(a,additive_identity) = a,
inference(transitivity,[status(thm)],[118,117,116,115,60]) ).
tff(120,plain,
multiply(add(a,additive_identity),add(b,additive_identity)) = multiply(a,b),
inference(monotonicity,[status(thm)],[119,114]) ).
tff(121,plain,
multiply(add(a,additive_identity),add(b,additive_identity)) = add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity),
inference(transitivity,[status(thm)],[120,109,107,105,100,98,83]) ).
tff(122,plain,
multiply(add(a,additive_identity),multiply(add(a,additive_identity),add(b,additive_identity))) = multiply(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
multiply(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)) = multiply(add(a,additive_identity),multiply(add(a,additive_identity),add(b,additive_identity))),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
add(additive_inverse(additive_identity),additive_inverse(additive_inverse(multiply(a,b)))) = additive_inverse(add(additive_identity,additive_inverse(multiply(a,b)))),
inference(symmetry,[status(thm)],[100]) ).
tff(125,plain,
add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity) = add(additive_identity,additive_inverse(multiply(additive_inverse(a),b))),
inference(symmetry,[status(thm)],[83]) ).
tff(126,plain,
add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity) = additive_inverse(additive_inverse(multiply(a,b))),
inference(transitivity,[status(thm)],[125,97,124,104,95]) ).
tff(127,plain,
multiply(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)) = multiply(add(a,additive_identity),additive_inverse(additive_inverse(multiply(a,b)))),
inference(monotonicity,[status(thm)],[126]) ).
tff(128,plain,
multiply(add(a,additive_identity),additive_inverse(additive_inverse(multiply(a,b)))) = multiply(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)),
inference(symmetry,[status(thm)],[127]) ).
tff(129,plain,
^ [Y: $i,X: $i] :
refl(( ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) )
<=> ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(130,plain,
( ! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) )
<=> ! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) ) ),
inference(quant_intro,[status(thm)],[129]) ).
tff(131,plain,
( ! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) )
<=> ! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(132,axiom,
! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',multiply_additive_inverse1) ).
tff(133,plain,
! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) ),
inference(skolemize,[status(sab)],[133]) ).
tff(135,plain,
! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) ),
inference(modus_ponens,[status(thm)],[134,130]) ).
tff(136,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) )
| ( multiply(add(a,additive_identity),additive_inverse(additive_inverse(multiply(a,b)))) = additive_inverse(multiply(add(a,additive_identity),additive_inverse(multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
multiply(add(a,additive_identity),additive_inverse(additive_inverse(multiply(a,b)))) = additive_inverse(multiply(add(a,additive_identity),additive_inverse(multiply(a,b)))),
inference(unit_resolution,[status(thm)],[136,135]) ).
tff(138,plain,
additive_inverse(multiply(add(a,additive_identity),additive_inverse(multiply(a,b)))) = multiply(add(a,additive_identity),additive_inverse(additive_inverse(multiply(a,b)))),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) )
| ( multiply(additive_inverse(add(a,additive_identity)),additive_inverse(multiply(a,b))) = additive_inverse(multiply(add(a,additive_identity),additive_inverse(multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(140,plain,
multiply(additive_inverse(add(a,additive_identity)),additive_inverse(multiply(a,b))) = additive_inverse(multiply(add(a,additive_identity),additive_inverse(multiply(a,b)))),
inference(unit_resolution,[status(thm)],[139,90]) ).
tff(141,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(additive_inverse(a),additive_identity) = add(additive_identity,additive_inverse(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(142,plain,
add(additive_inverse(a),additive_identity) = add(additive_identity,additive_inverse(a)),
inference(unit_resolution,[status(thm)],[141,10]) ).
tff(143,plain,
add(additive_inverse(a),additive_inverse(additive_identity)) = add(additive_inverse(a),additive_identity),
inference(monotonicity,[status(thm)],[23]) ).
tff(144,plain,
( ~ ! [Y: $i,X: $i] : ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) )
| ( additive_inverse(add(a,additive_identity)) = add(additive_inverse(a),additive_inverse(additive_identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
additive_inverse(add(a,additive_identity)) = add(additive_inverse(a),additive_inverse(additive_identity)),
inference(unit_resolution,[status(thm)],[144,31]) ).
tff(146,plain,
additive_inverse(add(a,additive_identity)) = add(additive_identity,additive_inverse(a)),
inference(transitivity,[status(thm)],[145,143,142]) ).
tff(147,plain,
multiply(additive_inverse(add(a,additive_identity)),additive_inverse(multiply(a,b))) = multiply(add(additive_identity,additive_inverse(a)),additive_inverse(multiply(a,b))),
inference(monotonicity,[status(thm)],[146]) ).
tff(148,plain,
multiply(add(additive_identity,additive_inverse(a)),additive_inverse(multiply(a,b))) = multiply(additive_inverse(add(a,additive_identity)),additive_inverse(multiply(a,b))),
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
multiply(add(additive_identity,additive_inverse(a)),add(b,additive_identity)) = multiply(additive_inverse(a),b),
inference(monotonicity,[status(thm)],[65,114]) ).
tff(150,plain,
multiply(additive_inverse(a),b) = multiply(add(additive_identity,additive_inverse(a)),add(b,additive_identity)),
inference(symmetry,[status(thm)],[149]) ).
tff(151,plain,
additive_inverse(multiply(a,b)) = multiply(add(additive_identity,additive_inverse(a)),add(b,additive_identity)),
inference(transitivity,[status(thm)],[93,150]) ).
tff(152,plain,
multiply(add(additive_identity,additive_inverse(a)),additive_inverse(multiply(a,b))) = multiply(add(additive_identity,additive_inverse(a)),multiply(add(additive_identity,additive_inverse(a)),add(b,additive_identity))),
inference(monotonicity,[status(thm)],[151]) ).
tff(153,plain,
multiply(add(additive_identity,additive_inverse(a)),multiply(add(additive_identity,additive_inverse(a)),add(b,additive_identity))) = multiply(add(additive_identity,additive_inverse(a)),additive_inverse(multiply(a,b))),
inference(symmetry,[status(thm)],[152]) ).
tff(154,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(add(additive_identity,additive_inverse(a)),add(additive_identity,additive_inverse(a))),add(b,additive_identity)) = multiply(add(additive_identity,additive_inverse(a)),multiply(add(additive_identity,additive_inverse(a)),add(b,additive_identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(155,plain,
multiply(multiply(add(additive_identity,additive_inverse(a)),add(additive_identity,additive_inverse(a))),add(b,additive_identity)) = multiply(add(additive_identity,additive_inverse(a)),multiply(add(additive_identity,additive_inverse(a)),add(b,additive_identity))),
inference(unit_resolution,[status(thm)],[154,78]) ).
tff(156,plain,
( ~ ! [X: $i] : ( multiply(X,X) = X )
| ( multiply(add(additive_identity,additive_inverse(a)),add(additive_identity,additive_inverse(a))) = add(additive_identity,additive_inverse(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(157,plain,
multiply(add(additive_identity,additive_inverse(a)),add(additive_identity,additive_inverse(a))) = add(additive_identity,additive_inverse(a)),
inference(unit_resolution,[status(thm)],[156,53]) ).
tff(158,plain,
multiply(add(additive_identity,additive_inverse(a)),add(additive_identity,additive_inverse(a))) = additive_inverse(a),
inference(transitivity,[status(thm)],[157,65]) ).
tff(159,plain,
multiply(multiply(add(additive_identity,additive_inverse(a)),add(additive_identity,additive_inverse(a))),add(b,additive_identity)) = multiply(additive_inverse(a),b),
inference(monotonicity,[status(thm)],[158,114]) ).
tff(160,plain,
multiply(additive_inverse(a),b) = multiply(multiply(add(additive_identity,additive_inverse(a)),add(additive_identity,additive_inverse(a))),add(b,additive_identity)),
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(b,additive_inverse(b)) = add(additive_inverse(b),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(162,plain,
add(b,additive_inverse(b)) = add(additive_inverse(b),b),
inference(unit_resolution,[status(thm)],[161,10]) ).
tff(163,plain,
add(additive_inverse(b),b) = add(b,additive_inverse(b)),
inference(symmetry,[status(thm)],[162]) ).
tff(164,plain,
^ [X: $i] :
refl(( ( add(additive_inverse(X),X) = additive_identity )
<=> ( add(additive_inverse(X),X) = additive_identity ) )),
inference(bind,[status(th)],[]) ).
tff(165,plain,
( ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
<=> ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ) ),
inference(quant_intro,[status(thm)],[164]) ).
tff(166,plain,
( ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
<=> ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(167,axiom,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',left_additive_inverse) ).
tff(168,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(skolemize,[status(sab)],[168]) ).
tff(170,plain,
! [X: $i] : ( add(additive_inverse(X),X) = additive_identity ),
inference(modus_ponens,[status(thm)],[169,165]) ).
tff(171,plain,
( ~ ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
| ( add(additive_inverse(b),b) = additive_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(172,plain,
add(additive_inverse(b),b) = additive_identity,
inference(unit_resolution,[status(thm)],[171,170]) ).
tff(173,plain,
additive_identity = add(additive_inverse(b),b),
inference(symmetry,[status(thm)],[172]) ).
tff(174,plain,
additive_identity = add(b,additive_inverse(b)),
inference(transitivity,[status(thm)],[173,163]) ).
tff(175,plain,
add(additive_identity,additive_inverse(multiply(a,b))) = add(add(b,additive_inverse(b)),additive_inverse(multiply(a,b))),
inference(monotonicity,[status(thm)],[174]) ).
tff(176,plain,
add(add(b,additive_inverse(b)),additive_inverse(multiply(a,b))) = add(additive_identity,additive_inverse(multiply(a,b))),
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
<=> ( add(add(X,Y),Z) = add(X,add(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(178,plain,
( ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[177]) ).
tff(179,plain,
( ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(180,axiom,
! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',associative_addition) ).
tff(181,plain,
! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ),
inference(modus_ponens,[status(thm)],[180,179]) ).
tff(182,plain,
! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ),
inference(skolemize,[status(sab)],[181]) ).
tff(183,plain,
! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) ),
inference(modus_ponens,[status(thm)],[182,178]) ).
tff(184,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(b,additive_inverse(b)),additive_inverse(multiply(a,b))) = add(b,add(additive_inverse(b),additive_inverse(multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(185,plain,
add(add(b,additive_inverse(b)),additive_inverse(multiply(a,b))) = add(b,add(additive_inverse(b),additive_inverse(multiply(a,b)))),
inference(unit_resolution,[status(thm)],[184,183]) ).
tff(186,plain,
add(b,add(additive_inverse(b),additive_inverse(multiply(a,b)))) = add(add(b,additive_inverse(b)),additive_inverse(multiply(a,b))),
inference(symmetry,[status(thm)],[185]) ).
tff(187,plain,
add(b,add(additive_inverse(b),additive_inverse(multiply(a,b)))) = add(add(b,additive_identity),add(additive_inverse(b),additive_inverse(multiply(a,b)))),
inference(monotonicity,[status(thm)],[46]) ).
tff(188,plain,
add(add(b,additive_identity),add(additive_inverse(b),additive_inverse(multiply(a,b)))) = add(b,add(additive_inverse(b),additive_inverse(multiply(a,b)))),
inference(symmetry,[status(thm)],[187]) ).
tff(189,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(add(additive_inverse(b),additive_inverse(multiply(a,b))),add(b,additive_identity)) = add(add(b,additive_identity),add(additive_inverse(b),additive_inverse(multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(190,plain,
add(add(additive_inverse(b),additive_inverse(multiply(a,b))),add(b,additive_identity)) = add(add(b,additive_identity),add(additive_inverse(b),additive_inverse(multiply(a,b)))),
inference(unit_resolution,[status(thm)],[189,10]) ).
tff(191,plain,
( ~ ! [X: $i] : ( multiply(X,X) = X )
| ( multiply(add(additive_identity,additive_inverse(b)),add(additive_identity,additive_inverse(b))) = add(additive_identity,additive_inverse(b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(192,plain,
multiply(add(additive_identity,additive_inverse(b)),add(additive_identity,additive_inverse(b))) = add(additive_identity,additive_inverse(b)),
inference(unit_resolution,[status(thm)],[191,53]) ).
tff(193,plain,
( ~ ! [Y: $i,X: $i] : ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) )
| ( additive_inverse(add(b,additive_identity)) = add(additive_inverse(b),additive_inverse(additive_identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(194,plain,
additive_inverse(add(b,additive_identity)) = add(additive_inverse(b),additive_inverse(additive_identity)),
inference(unit_resolution,[status(thm)],[193,31]) ).
tff(195,plain,
add(additive_inverse(b),additive_inverse(additive_identity)) = additive_inverse(add(b,additive_identity)),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
add(additive_inverse(b),additive_inverse(additive_identity)) = add(additive_inverse(b),additive_identity),
inference(monotonicity,[status(thm)],[23]) ).
tff(197,plain,
add(additive_inverse(b),additive_identity) = add(additive_inverse(b),additive_inverse(additive_identity)),
inference(symmetry,[status(thm)],[196]) ).
tff(198,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(additive_inverse(b),additive_identity) = add(additive_identity,additive_inverse(b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(199,plain,
add(additive_inverse(b),additive_identity) = add(additive_identity,additive_inverse(b)),
inference(unit_resolution,[status(thm)],[198,10]) ).
tff(200,plain,
add(additive_identity,additive_inverse(b)) = add(additive_inverse(b),additive_identity),
inference(symmetry,[status(thm)],[199]) ).
tff(201,plain,
add(additive_identity,additive_inverse(b)) = additive_inverse(add(b,additive_identity)),
inference(transitivity,[status(thm)],[200,197,195]) ).
tff(202,plain,
multiply(add(additive_identity,additive_inverse(b)),add(additive_identity,additive_inverse(b))) = multiply(additive_inverse(add(b,additive_identity)),add(additive_identity,additive_inverse(b))),
inference(monotonicity,[status(thm)],[201]) ).
tff(203,plain,
multiply(additive_inverse(add(b,additive_identity)),add(additive_identity,additive_inverse(b))) = multiply(add(additive_identity,additive_inverse(b)),add(additive_identity,additive_inverse(b))),
inference(symmetry,[status(thm)],[202]) ).
tff(204,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) )
| ( multiply(additive_inverse(add(b,additive_identity)),add(additive_identity,additive_inverse(b))) = additive_inverse(multiply(add(b,additive_identity),add(additive_identity,additive_inverse(b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(205,plain,
multiply(additive_inverse(add(b,additive_identity)),add(additive_identity,additive_inverse(b))) = additive_inverse(multiply(add(b,additive_identity),add(additive_identity,additive_inverse(b)))),
inference(unit_resolution,[status(thm)],[204,90]) ).
tff(206,plain,
additive_inverse(multiply(add(b,additive_identity),add(additive_identity,additive_inverse(b)))) = multiply(additive_inverse(add(b,additive_identity)),add(additive_identity,additive_inverse(b))),
inference(symmetry,[status(thm)],[205]) ).
tff(207,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) )
| ( multiply(add(b,additive_identity),additive_inverse(add(additive_identity,additive_inverse(b)))) = additive_inverse(multiply(add(b,additive_identity),add(additive_identity,additive_inverse(b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(208,plain,
multiply(add(b,additive_identity),additive_inverse(add(additive_identity,additive_inverse(b)))) = additive_inverse(multiply(add(b,additive_identity),add(additive_identity,additive_inverse(b)))),
inference(unit_resolution,[status(thm)],[207,135]) ).
tff(209,plain,
additive_inverse(add(additive_identity,additive_inverse(b))) = add(b,additive_identity),
inference(transitivity,[status(thm)],[33,24,12]) ).
tff(210,plain,
multiply(add(b,additive_identity),additive_inverse(add(additive_identity,additive_inverse(b)))) = multiply(add(b,additive_identity),add(b,additive_identity)),
inference(monotonicity,[status(thm)],[209]) ).
tff(211,plain,
multiply(add(b,additive_identity),add(b,additive_identity)) = multiply(add(b,additive_identity),additive_inverse(add(additive_identity,additive_inverse(b)))),
inference(symmetry,[status(thm)],[210]) ).
tff(212,plain,
( ~ ! [X: $i] : ( multiply(X,X) = X )
| ( multiply(add(b,additive_identity),add(b,additive_identity)) = add(b,additive_identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(213,plain,
multiply(add(b,additive_identity),add(b,additive_identity)) = add(b,additive_identity),
inference(unit_resolution,[status(thm)],[212,53]) ).
tff(214,plain,
add(b,additive_identity) = multiply(add(b,additive_identity),add(b,additive_identity)),
inference(symmetry,[status(thm)],[213]) ).
tff(215,plain,
add(b,additive_identity) = add(additive_identity,additive_inverse(b)),
inference(transitivity,[status(thm)],[214,211,208,206,203,192]) ).
tff(216,plain,
add(add(additive_inverse(b),additive_inverse(multiply(a,b))),add(b,additive_identity)) = add(add(additive_inverse(b),additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(b))),
inference(monotonicity,[status(thm)],[215]) ).
tff(217,plain,
add(add(additive_inverse(b),additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(b))) = add(add(additive_inverse(b),additive_inverse(multiply(a,b))),add(b,additive_identity)),
inference(symmetry,[status(thm)],[216]) ).
tff(218,plain,
add(add(additive_identity,additive_inverse(b)),add(additive_identity,additive_inverse(b))) = add(additive_inverse(b),additive_inverse(b)),
inference(monotonicity,[status(thm)],[42,42]) ).
tff(219,plain,
add(additive_inverse(b),additive_inverse(b)) = add(add(additive_identity,additive_inverse(b)),add(additive_identity,additive_inverse(b))),
inference(symmetry,[status(thm)],[218]) ).
tff(220,plain,
add(add(additive_inverse(b),additive_inverse(b)),add(b,additive_inverse(multiply(a,b)))) = add(add(add(additive_identity,additive_inverse(b)),add(additive_identity,additive_inverse(b))),add(b,additive_inverse(multiply(a,b)))),
inference(monotonicity,[status(thm)],[219]) ).
tff(221,plain,
add(add(add(additive_identity,additive_inverse(b)),add(additive_identity,additive_inverse(b))),add(b,additive_inverse(multiply(a,b)))) = add(add(additive_inverse(b),additive_inverse(b)),add(b,additive_inverse(multiply(a,b)))),
inference(symmetry,[status(thm)],[220]) ).
tff(222,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(add(additive_identity,additive_inverse(b)),add(additive_identity,additive_inverse(b))),add(b,additive_inverse(multiply(a,b)))) = add(add(additive_identity,additive_inverse(b)),add(add(additive_identity,additive_inverse(b)),add(b,additive_inverse(multiply(a,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(223,plain,
add(add(add(additive_identity,additive_inverse(b)),add(additive_identity,additive_inverse(b))),add(b,additive_inverse(multiply(a,b)))) = add(add(additive_identity,additive_inverse(b)),add(add(additive_identity,additive_inverse(b)),add(b,additive_inverse(multiply(a,b))))),
inference(unit_resolution,[status(thm)],[222,183]) ).
tff(224,plain,
add(add(additive_identity,additive_inverse(b)),add(add(additive_identity,additive_inverse(b)),add(b,additive_inverse(multiply(a,b))))) = add(add(add(additive_identity,additive_inverse(b)),add(additive_identity,additive_inverse(b))),add(b,additive_inverse(multiply(a,b)))),
inference(symmetry,[status(thm)],[223]) ).
tff(225,plain,
( ~ ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
| ( add(additive_inverse(additive_identity),additive_identity) = additive_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(226,plain,
add(additive_inverse(additive_identity),additive_identity) = additive_identity,
inference(unit_resolution,[status(thm)],[225,170]) ).
tff(227,plain,
add(additive_identity,add(additive_inverse(b),b)) = add(additive_inverse(additive_identity),additive_identity),
inference(monotonicity,[status(thm)],[96,172]) ).
tff(228,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(additive_identity,additive_inverse(b)),b) = add(additive_identity,add(additive_inverse(b),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(229,plain,
add(add(additive_identity,additive_inverse(b)),b) = add(additive_identity,add(additive_inverse(b),b)),
inference(unit_resolution,[status(thm)],[228,183]) ).
tff(230,plain,
add(add(additive_identity,additive_inverse(b)),b) = additive_identity,
inference(transitivity,[status(thm)],[229,227,226]) ).
tff(231,plain,
add(add(add(additive_identity,additive_inverse(b)),b),additive_inverse(multiply(a,b))) = add(additive_identity,additive_inverse(multiply(a,b))),
inference(monotonicity,[status(thm)],[230]) ).
tff(232,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(add(additive_identity,additive_inverse(b)),b),additive_inverse(multiply(a,b))) = add(add(additive_identity,additive_inverse(b)),add(b,additive_inverse(multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(233,plain,
add(add(add(additive_identity,additive_inverse(b)),b),additive_inverse(multiply(a,b))) = add(add(additive_identity,additive_inverse(b)),add(b,additive_inverse(multiply(a,b)))),
inference(unit_resolution,[status(thm)],[232,183]) ).
tff(234,plain,
add(add(additive_identity,additive_inverse(b)),add(b,additive_inverse(multiply(a,b)))) = add(add(add(additive_identity,additive_inverse(b)),b),additive_inverse(multiply(a,b))),
inference(symmetry,[status(thm)],[233]) ).
tff(235,plain,
add(add(additive_identity,additive_inverse(b)),add(b,additive_inverse(multiply(a,b)))) = additive_inverse(multiply(a,b)),
inference(transitivity,[status(thm)],[234,231,102]) ).
tff(236,plain,
add(add(additive_identity,additive_inverse(b)),add(add(additive_identity,additive_inverse(b)),add(b,additive_inverse(multiply(a,b))))) = add(additive_inverse(b),additive_inverse(multiply(a,b))),
inference(monotonicity,[status(thm)],[42,235]) ).
tff(237,plain,
add(additive_inverse(b),additive_inverse(multiply(a,b))) = add(add(additive_identity,additive_inverse(b)),add(add(additive_identity,additive_inverse(b)),add(b,additive_inverse(multiply(a,b))))),
inference(symmetry,[status(thm)],[236]) ).
tff(238,plain,
add(additive_inverse(b),additive_inverse(multiply(a,b))) = add(add(additive_inverse(b),additive_inverse(b)),add(b,additive_inverse(multiply(a,b)))),
inference(transitivity,[status(thm)],[237,224,221]) ).
tff(239,plain,
add(add(additive_inverse(b),additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(b))) = add(add(add(additive_inverse(b),additive_inverse(b)),add(b,additive_inverse(multiply(a,b)))),add(additive_identity,additive_inverse(b))),
inference(monotonicity,[status(thm)],[238]) ).
tff(240,plain,
add(add(add(additive_inverse(b),additive_inverse(b)),add(b,additive_inverse(multiply(a,b)))),add(additive_identity,additive_inverse(b))) = add(add(additive_inverse(b),additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(b))),
inference(symmetry,[status(thm)],[239]) ).
tff(241,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(add(additive_inverse(b),additive_inverse(b)),add(b,additive_inverse(multiply(a,b)))),add(additive_identity,additive_inverse(b))) = add(add(additive_inverse(b),additive_inverse(b)),add(add(b,additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(242,plain,
add(add(add(additive_inverse(b),additive_inverse(b)),add(b,additive_inverse(multiply(a,b)))),add(additive_identity,additive_inverse(b))) = add(add(additive_inverse(b),additive_inverse(b)),add(add(b,additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(b)))),
inference(unit_resolution,[status(thm)],[241,183]) ).
tff(243,plain,
add(add(additive_inverse(b),additive_inverse(b)),add(add(b,additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(b)))) = add(add(add(additive_inverse(b),additive_inverse(b)),add(b,additive_inverse(multiply(a,b)))),add(additive_identity,additive_inverse(b))),
inference(symmetry,[status(thm)],[242]) ).
tff(244,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(add(b,additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(b))) = add(add(additive_identity,additive_inverse(b)),add(b,additive_inverse(multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(245,plain,
add(add(b,additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(b))) = add(add(additive_identity,additive_inverse(b)),add(b,additive_inverse(multiply(a,b)))),
inference(unit_resolution,[status(thm)],[244,10]) ).
tff(246,plain,
add(add(b,additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(b))) = additive_inverse(multiply(a,b)),
inference(transitivity,[status(thm)],[245,234,231,102]) ).
tff(247,plain,
add(add(additive_inverse(b),additive_inverse(b)),add(add(b,additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(b)))) = add(add(additive_inverse(b),additive_inverse(b)),additive_inverse(multiply(a,b))),
inference(monotonicity,[status(thm)],[246]) ).
tff(248,plain,
add(add(additive_inverse(b),additive_inverse(b)),additive_inverse(multiply(a,b))) = add(add(additive_inverse(b),additive_inverse(b)),add(add(b,additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(b)))),
inference(symmetry,[status(thm)],[247]) ).
tff(249,plain,
add(add(a,additive_identity),add(b,additive_identity)) = add(a,b),
inference(monotonicity,[status(thm)],[119,114]) ).
tff(250,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(add(a,additive_identity),add(b,additive_identity)) = add(add(b,additive_identity),add(a,additive_identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(251,plain,
add(add(a,additive_identity),add(b,additive_identity)) = add(add(b,additive_identity),add(a,additive_identity)),
inference(unit_resolution,[status(thm)],[250,10]) ).
tff(252,plain,
add(add(b,additive_identity),add(a,additive_identity)) = add(add(a,additive_identity),add(b,additive_identity)),
inference(symmetry,[status(thm)],[251]) ).
tff(253,plain,
add(add(b,additive_identity),add(a,additive_identity)) = add(a,b),
inference(transitivity,[status(thm)],[252,249]) ).
tff(254,plain,
add(add(add(b,additive_identity),add(a,additive_identity)),add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b))))) = add(add(a,b),add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b))))),
inference(monotonicity,[status(thm)],[253]) ).
tff(255,plain,
add(add(a,b),add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b))))) = add(add(add(b,additive_identity),add(a,additive_identity)),add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b))))),
inference(symmetry,[status(thm)],[254]) ).
tff(256,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(add(a,b),add(additive_identity,additive_inverse(b))),add(additive_inverse(a),additive_inverse(multiply(a,b)))) = add(add(a,b),add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(257,plain,
add(add(add(a,b),add(additive_identity,additive_inverse(b))),add(additive_inverse(a),additive_inverse(multiply(a,b)))) = add(add(a,b),add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b))))),
inference(unit_resolution,[status(thm)],[256,183]) ).
tff(258,plain,
add(b,additive_inverse(b)) = additive_identity,
inference(transitivity,[status(thm)],[162,172]) ).
tff(259,plain,
add(a,add(b,additive_inverse(b))) = add(a,additive_identity),
inference(monotonicity,[status(thm)],[258]) ).
tff(260,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(a,b),additive_inverse(b)) = add(a,add(b,additive_inverse(b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(261,plain,
add(add(a,b),additive_inverse(b)) = add(a,add(b,additive_inverse(b))),
inference(unit_resolution,[status(thm)],[260,183]) ).
tff(262,plain,
add(add(a,b),add(additive_identity,additive_inverse(b))) = add(add(a,b),additive_inverse(b)),
inference(monotonicity,[status(thm)],[42]) ).
tff(263,plain,
add(add(a,b),add(additive_identity,additive_inverse(b))) = a,
inference(transitivity,[status(thm)],[262,261,259,118,117,116,115,60]) ).
tff(264,plain,
add(add(add(a,b),add(additive_identity,additive_inverse(b))),add(additive_inverse(a),additive_inverse(multiply(a,b)))) = add(a,add(additive_inverse(a),additive_inverse(multiply(a,b)))),
inference(monotonicity,[status(thm)],[263]) ).
tff(265,plain,
add(a,add(additive_inverse(a),additive_inverse(multiply(a,b)))) = add(add(add(a,b),add(additive_identity,additive_inverse(b))),add(additive_inverse(a),additive_inverse(multiply(a,b)))),
inference(symmetry,[status(thm)],[264]) ).
tff(266,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(a,additive_inverse(a)),additive_inverse(multiply(a,b))) = add(a,add(additive_inverse(a),additive_inverse(multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(267,plain,
add(add(a,additive_inverse(a)),additive_inverse(multiply(a,b))) = add(a,add(additive_inverse(a),additive_inverse(multiply(a,b)))),
inference(unit_resolution,[status(thm)],[266,183]) ).
tff(268,plain,
( ~ ! [X: $i] : ( add(additive_inverse(X),X) = additive_identity )
| ( add(additive_inverse(a),a) = additive_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(269,plain,
add(additive_inverse(a),a) = additive_identity,
inference(unit_resolution,[status(thm)],[268,170]) ).
tff(270,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(a,additive_inverse(a)) = add(additive_inverse(a),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(271,plain,
add(a,additive_inverse(a)) = add(additive_inverse(a),a),
inference(unit_resolution,[status(thm)],[270,10]) ).
tff(272,plain,
add(a,additive_inverse(a)) = additive_identity,
inference(transitivity,[status(thm)],[271,269]) ).
tff(273,plain,
add(add(a,additive_inverse(a)),additive_inverse(multiply(a,b))) = add(additive_identity,additive_inverse(multiply(a,b))),
inference(monotonicity,[status(thm)],[272]) ).
tff(274,plain,
add(additive_identity,additive_inverse(multiply(a,b))) = add(add(a,additive_inverse(a)),additive_inverse(multiply(a,b))),
inference(symmetry,[status(thm)],[273]) ).
tff(275,plain,
additive_inverse(multiply(a,b)) = add(additive_identity,additive_inverse(multiply(a,b))),
inference(symmetry,[status(thm)],[102]) ).
tff(276,plain,
additive_inverse(multiply(a,b)) = add(add(add(b,additive_identity),add(a,additive_identity)),add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b))))),
inference(transitivity,[status(thm)],[275,274,267,265,257,255]) ).
tff(277,plain,
add(add(additive_inverse(b),additive_inverse(b)),additive_inverse(multiply(a,b))) = add(add(additive_inverse(b),additive_inverse(b)),add(add(add(b,additive_identity),add(a,additive_identity)),add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b)))))),
inference(monotonicity,[status(thm)],[276]) ).
tff(278,plain,
add(add(additive_inverse(b),additive_inverse(b)),add(add(add(b,additive_identity),add(a,additive_identity)),add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b)))))) = add(add(additive_inverse(b),additive_inverse(b)),additive_inverse(multiply(a,b))),
inference(symmetry,[status(thm)],[277]) ).
tff(279,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(add(additive_inverse(b),additive_inverse(b)),add(add(b,additive_identity),add(a,additive_identity))),add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b))))) = add(add(additive_inverse(b),additive_inverse(b)),add(add(add(b,additive_identity),add(a,additive_identity)),add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(280,plain,
add(add(add(additive_inverse(b),additive_inverse(b)),add(add(b,additive_identity),add(a,additive_identity))),add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b))))) = add(add(additive_inverse(b),additive_inverse(b)),add(add(add(b,additive_identity),add(a,additive_identity)),add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b)))))),
inference(unit_resolution,[status(thm)],[279,183]) ).
tff(281,plain,
a = add(a,additive_identity),
inference(transitivity,[status(thm)],[68,67,63,61,58]) ).
tff(282,plain,
add(a,add(additive_identity,additive_inverse(b))) = add(add(a,additive_identity),additive_inverse(b)),
inference(monotonicity,[status(thm)],[281,42]) ).
tff(283,plain,
add(add(a,additive_identity),additive_inverse(b)) = add(a,add(additive_identity,additive_inverse(b))),
inference(symmetry,[status(thm)],[282]) ).
tff(284,plain,
add(add(b,additive_inverse(b)),additive_inverse(b)) = add(additive_identity,additive_inverse(b)),
inference(monotonicity,[status(thm)],[258]) ).
tff(285,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(b,additive_inverse(b)),additive_inverse(b)) = add(b,add(additive_inverse(b),additive_inverse(b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(286,plain,
add(add(b,additive_inverse(b)),additive_inverse(b)) = add(b,add(additive_inverse(b),additive_inverse(b))),
inference(unit_resolution,[status(thm)],[285,183]) ).
tff(287,plain,
add(b,add(additive_inverse(b),additive_inverse(b))) = add(add(b,additive_inverse(b)),additive_inverse(b)),
inference(symmetry,[status(thm)],[286]) ).
tff(288,plain,
add(add(b,additive_identity),add(additive_inverse(b),additive_inverse(b))) = add(b,add(additive_inverse(b),additive_inverse(b))),
inference(monotonicity,[status(thm)],[114]) ).
tff(289,plain,
add(add(b,additive_identity),add(additive_inverse(b),additive_inverse(b))) = additive_inverse(b),
inference(transitivity,[status(thm)],[288,287,284,42]) ).
tff(290,plain,
add(add(a,additive_identity),add(add(b,additive_identity),add(additive_inverse(b),additive_inverse(b)))) = add(add(a,additive_identity),additive_inverse(b)),
inference(monotonicity,[status(thm)],[289]) ).
tff(291,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(add(a,additive_identity),add(b,additive_identity)),add(additive_inverse(b),additive_inverse(b))) = add(add(a,additive_identity),add(add(b,additive_identity),add(additive_inverse(b),additive_inverse(b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(292,plain,
add(add(add(a,additive_identity),add(b,additive_identity)),add(additive_inverse(b),additive_inverse(b))) = add(add(a,additive_identity),add(add(b,additive_identity),add(additive_inverse(b),additive_inverse(b)))),
inference(unit_resolution,[status(thm)],[291,183]) ).
tff(293,plain,
add(add(add(b,additive_identity),add(a,additive_identity)),add(additive_inverse(b),additive_inverse(b))) = add(add(add(a,additive_identity),add(b,additive_identity)),add(additive_inverse(b),additive_inverse(b))),
inference(monotonicity,[status(thm)],[252]) ).
tff(294,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(add(additive_inverse(b),additive_inverse(b)),add(add(b,additive_identity),add(a,additive_identity))) = add(add(add(b,additive_identity),add(a,additive_identity)),add(additive_inverse(b),additive_inverse(b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(295,plain,
add(add(additive_inverse(b),additive_inverse(b)),add(add(b,additive_identity),add(a,additive_identity))) = add(add(add(b,additive_identity),add(a,additive_identity)),add(additive_inverse(b),additive_inverse(b))),
inference(unit_resolution,[status(thm)],[294,10]) ).
tff(296,plain,
add(add(additive_inverse(b),additive_inverse(b)),add(add(b,additive_identity),add(a,additive_identity))) = add(a,add(additive_identity,additive_inverse(b))),
inference(transitivity,[status(thm)],[295,293,292,290,283]) ).
tff(297,plain,
add(add(add(additive_inverse(b),additive_inverse(b)),add(add(b,additive_identity),add(a,additive_identity))),add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b))))) = add(add(a,add(additive_identity,additive_inverse(b))),add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b))))),
inference(monotonicity,[status(thm)],[296]) ).
tff(298,plain,
add(add(a,add(additive_identity,additive_inverse(b))),add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b))))) = add(add(add(additive_inverse(b),additive_inverse(b)),add(add(b,additive_identity),add(a,additive_identity))),add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b))))),
inference(symmetry,[status(thm)],[297]) ).
tff(299,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(additive_inverse(multiply(a,b)),additive_identity) = add(additive_identity,additive_inverse(multiply(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(300,plain,
add(additive_inverse(multiply(a,b)),additive_identity) = add(additive_identity,additive_inverse(multiply(a,b))),
inference(unit_resolution,[status(thm)],[299,10]) ).
tff(301,plain,
additive_inverse(multiply(additive_inverse(a),b)) = multiply(additive_inverse(additive_inverse(a)),b),
inference(symmetry,[status(thm)],[107]) ).
tff(302,plain,
additive_inverse(multiply(additive_inverse(a),b)) = multiply(a,b),
inference(transitivity,[status(thm)],[301,108]) ).
tff(303,plain,
additive_inverse(additive_inverse(multiply(additive_inverse(a),b))) = additive_inverse(multiply(a,b)),
inference(monotonicity,[status(thm)],[302]) ).
tff(304,plain,
add(additive_inverse(additive_inverse(multiply(additive_inverse(a),b))),additive_inverse(additive_identity)) = add(additive_inverse(multiply(a,b)),additive_identity),
inference(monotonicity,[status(thm)],[303,23]) ).
tff(305,plain,
( ~ ! [Y: $i,X: $i] : ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) )
| ( additive_inverse(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)) = add(additive_inverse(additive_inverse(multiply(additive_inverse(a),b))),additive_inverse(additive_identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(306,plain,
additive_inverse(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)) = add(additive_inverse(additive_inverse(multiply(additive_inverse(a),b))),additive_inverse(additive_identity)),
inference(unit_resolution,[status(thm)],[305,31]) ).
tff(307,plain,
additive_inverse(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)) = additive_inverse(multiply(a,b)),
inference(transitivity,[status(thm)],[306,304,300,102]) ).
tff(308,plain,
additive_inverse(add(a,additive_identity)) = additive_inverse(a),
inference(transitivity,[status(thm)],[145,143,142,65]) ).
tff(309,plain,
add(additive_inverse(add(a,additive_identity)),additive_inverse(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity))) = add(additive_inverse(a),additive_inverse(multiply(a,b))),
inference(monotonicity,[status(thm)],[308,307]) ).
tff(310,plain,
add(additive_inverse(a),additive_inverse(multiply(a,b))) = add(additive_inverse(add(a,additive_identity)),additive_inverse(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity))),
inference(symmetry,[status(thm)],[309]) ).
tff(311,plain,
add(add(additive_inverse(a),additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(b))) = add(add(additive_inverse(add(a,additive_identity)),additive_inverse(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity))),add(additive_identity,additive_inverse(b))),
inference(monotonicity,[status(thm)],[310]) ).
tff(312,plain,
add(add(additive_inverse(add(a,additive_identity)),additive_inverse(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity))),add(additive_identity,additive_inverse(b))) = add(add(additive_inverse(a),additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(b))),
inference(symmetry,[status(thm)],[311]) ).
tff(313,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(add(additive_identity,additive_inverse(b)),add(additive_inverse(add(a,additive_identity)),additive_inverse(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)))) = add(add(additive_inverse(add(a,additive_identity)),additive_inverse(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity))),add(additive_identity,additive_inverse(b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(314,plain,
add(add(additive_identity,additive_inverse(b)),add(additive_inverse(add(a,additive_identity)),additive_inverse(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)))) = add(add(additive_inverse(add(a,additive_identity)),additive_inverse(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity))),add(additive_identity,additive_inverse(b))),
inference(unit_resolution,[status(thm)],[313,10]) ).
tff(315,plain,
add(add(additive_identity,additive_inverse(b)),add(additive_inverse(add(a,additive_identity)),additive_inverse(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)))) = add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b)))),
inference(monotonicity,[status(thm)],[309]) ).
tff(316,plain,
add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b)))) = add(add(additive_identity,additive_inverse(b)),add(additive_inverse(add(a,additive_identity)),additive_inverse(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)))),
inference(symmetry,[status(thm)],[315]) ).
tff(317,plain,
add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b)))) = add(add(additive_inverse(a),additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(b))),
inference(transitivity,[status(thm)],[316,314,312]) ).
tff(318,plain,
add(additive_inverse(a),additive_inverse(additive_identity)) = additive_inverse(add(a,additive_identity)),
inference(symmetry,[status(thm)],[145]) ).
tff(319,plain,
add(additive_inverse(a),additive_identity) = add(additive_inverse(a),additive_inverse(additive_identity)),
inference(symmetry,[status(thm)],[143]) ).
tff(320,plain,
add(additive_identity,additive_inverse(a)) = add(additive_inverse(a),additive_identity),
inference(symmetry,[status(thm)],[142]) ).
tff(321,plain,
additive_inverse(a) = additive_inverse(add(a,additive_identity)),
inference(transitivity,[status(thm)],[66,320,319,318]) ).
tff(322,plain,
additive_inverse(b) = additive_inverse(add(b,additive_identity)),
inference(transitivity,[status(thm)],[43,200,197,195]) ).
tff(323,plain,
add(additive_inverse(b),additive_inverse(a)) = add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),
inference(monotonicity,[status(thm)],[322,321]) ).
tff(324,plain,
add(add(additive_identity,additive_inverse(b)),add(additive_identity,additive_inverse(a))) = add(additive_inverse(b),additive_inverse(a)),
inference(monotonicity,[status(thm)],[42,65]) ).
tff(325,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(add(additive_identity,additive_inverse(b)),add(additive_identity,additive_inverse(a))) = add(add(additive_identity,additive_inverse(a)),add(additive_identity,additive_inverse(b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(326,plain,
add(add(additive_identity,additive_inverse(b)),add(additive_identity,additive_inverse(a))) = add(add(additive_identity,additive_inverse(a)),add(additive_identity,additive_inverse(b))),
inference(unit_resolution,[status(thm)],[325,10]) ).
tff(327,plain,
add(add(additive_identity,additive_inverse(a)),add(additive_identity,additive_inverse(b))) = add(add(additive_identity,additive_inverse(b)),add(additive_identity,additive_inverse(a))),
inference(symmetry,[status(thm)],[326]) ).
tff(328,plain,
add(additive_inverse(a),additive_inverse(b)) = add(add(additive_identity,additive_inverse(a)),add(additive_identity,additive_inverse(b))),
inference(monotonicity,[status(thm)],[66,43]) ).
tff(329,plain,
add(additive_identity,additive_inverse(a)) = additive_inverse(add(a,additive_identity)),
inference(transitivity,[status(thm)],[320,319,318]) ).
tff(330,plain,
multiply(add(additive_identity,additive_inverse(a)),add(additive_identity,additive_inverse(a))) = multiply(additive_inverse(add(a,additive_identity)),add(additive_identity,additive_inverse(a))),
inference(monotonicity,[status(thm)],[329]) ).
tff(331,plain,
multiply(additive_inverse(add(a,additive_identity)),add(additive_identity,additive_inverse(a))) = multiply(add(additive_identity,additive_inverse(a)),add(additive_identity,additive_inverse(a))),
inference(symmetry,[status(thm)],[330]) ).
tff(332,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) )
| ( multiply(additive_inverse(add(a,additive_identity)),add(additive_identity,additive_inverse(a))) = additive_inverse(multiply(add(a,additive_identity),add(additive_identity,additive_inverse(a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(333,plain,
multiply(additive_inverse(add(a,additive_identity)),add(additive_identity,additive_inverse(a))) = additive_inverse(multiply(add(a,additive_identity),add(additive_identity,additive_inverse(a)))),
inference(unit_resolution,[status(thm)],[332,90]) ).
tff(334,plain,
additive_inverse(multiply(add(a,additive_identity),add(additive_identity,additive_inverse(a)))) = multiply(additive_inverse(add(a,additive_identity)),add(additive_identity,additive_inverse(a))),
inference(symmetry,[status(thm)],[333]) ).
tff(335,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) )
| ( multiply(add(a,additive_identity),additive_inverse(add(additive_identity,additive_inverse(a)))) = additive_inverse(multiply(add(a,additive_identity),add(additive_identity,additive_inverse(a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(336,plain,
multiply(add(a,additive_identity),additive_inverse(add(additive_identity,additive_inverse(a)))) = additive_inverse(multiply(add(a,additive_identity),add(additive_identity,additive_inverse(a)))),
inference(unit_resolution,[status(thm)],[335,135]) ).
tff(337,plain,
additive_inverse(add(additive_identity,additive_inverse(a))) = add(a,additive_identity),
inference(transitivity,[status(thm)],[63,61,58]) ).
tff(338,plain,
multiply(add(a,additive_identity),additive_inverse(add(additive_identity,additive_inverse(a)))) = multiply(add(a,additive_identity),add(a,additive_identity)),
inference(monotonicity,[status(thm)],[337]) ).
tff(339,plain,
multiply(add(a,additive_identity),add(a,additive_identity)) = multiply(add(a,additive_identity),additive_inverse(add(additive_identity,additive_inverse(a)))),
inference(symmetry,[status(thm)],[338]) ).
tff(340,plain,
add(a,additive_identity) = additive_inverse(a),
inference(transitivity,[status(thm)],[56,339,336,334,331,157,65]) ).
tff(341,plain,
add(add(a,additive_identity),additive_inverse(b)) = add(additive_inverse(a),additive_inverse(b)),
inference(monotonicity,[status(thm)],[340]) ).
tff(342,plain,
add(a,add(additive_identity,additive_inverse(b))) = add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),
inference(transitivity,[status(thm)],[282,341,328,327,324,323]) ).
tff(343,plain,
add(add(a,add(additive_identity,additive_inverse(b))),add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b))))) = add(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(add(additive_inverse(a),additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(b)))),
inference(monotonicity,[status(thm)],[342,317]) ).
tff(344,plain,
add(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(add(additive_inverse(a),additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(b)))) = add(add(a,add(additive_identity,additive_inverse(b))),add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b))))),
inference(symmetry,[status(thm)],[343]) ).
tff(345,plain,
add(add(additive_inverse(add(a,additive_identity)),additive_inverse(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity))),add(additive_identity,additive_inverse(b))) = add(add(additive_identity,additive_inverse(b)),add(additive_inverse(add(a,additive_identity)),additive_inverse(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)))),
inference(symmetry,[status(thm)],[314]) ).
tff(346,plain,
add(add(additive_inverse(a),additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(b))) = add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b)))),
inference(transitivity,[status(thm)],[311,345,315]) ).
tff(347,plain,
( ~ ! [X: $i] : ( multiply(X,X) = X )
| ( multiply(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))) = add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(348,plain,
multiply(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))) = add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),
inference(unit_resolution,[status(thm)],[347,53]) ).
tff(349,plain,
add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))) = multiply(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))),
inference(symmetry,[status(thm)],[348]) ).
tff(350,plain,
add(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(add(additive_inverse(a),additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(b)))) = add(multiply(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))),add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b))))),
inference(monotonicity,[status(thm)],[349,346]) ).
tff(351,plain,
add(multiply(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))),add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b))))) = add(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(add(additive_inverse(a),additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(b)))),
inference(symmetry,[status(thm)],[350]) ).
tff(352,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(add(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)),add(b,additive_identity)) = add(add(b,additive_identity),add(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(353,plain,
add(add(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)),add(b,additive_identity)) = add(add(b,additive_identity),add(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity))),
inference(unit_resolution,[status(thm)],[352,10]) ).
tff(354,plain,
add(add(b,additive_identity),add(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity))) = add(add(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)),add(b,additive_identity)),
inference(symmetry,[status(thm)],[353]) ).
tff(355,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(add(b,additive_identity),add(a,additive_identity)),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)) = add(add(b,additive_identity),add(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(356,plain,
add(add(add(b,additive_identity),add(a,additive_identity)),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)) = add(add(b,additive_identity),add(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity))),
inference(unit_resolution,[status(thm)],[355,183]) ).
tff(357,plain,
add(add(add(b,additive_identity),add(a,additive_identity)),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)) = add(add(a,b),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)),
inference(monotonicity,[status(thm)],[253]) ).
tff(358,plain,
add(add(a,b),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)) = add(add(add(b,additive_identity),add(a,additive_identity)),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)),
inference(symmetry,[status(thm)],[357]) ).
tff(359,plain,
multiply(add(additive_identity,additive_inverse(a)),multiply(add(additive_identity,additive_inverse(a)),add(b,additive_identity))) = multiply(multiply(add(additive_identity,additive_inverse(a)),add(additive_identity,additive_inverse(a))),add(b,additive_identity)),
inference(symmetry,[status(thm)],[155]) ).
tff(360,plain,
additive_inverse(multiply(add(a,additive_identity),additive_inverse(multiply(a,b)))) = multiply(additive_inverse(add(a,additive_identity)),additive_inverse(multiply(a,b))),
inference(symmetry,[status(thm)],[140]) ).
tff(361,plain,
add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity) = additive_inverse(multiply(a,b)),
inference(transitivity,[status(thm)],[125,97,124,104,301,108,70,80,122,127,137,360,147,152,359,159,92]) ).
tff(362,plain,
add(add(a,b),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)) = add(add(a,b),additive_inverse(multiply(a,b))),
inference(monotonicity,[status(thm)],[361]) ).
tff(363,plain,
add(add(a,b),additive_inverse(multiply(a,b))) = add(add(a,b),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)),
inference(symmetry,[status(thm)],[362]) ).
tff(364,plain,
add(a,b) = add(add(a,additive_identity),add(b,additive_identity)),
inference(symmetry,[status(thm)],[249]) ).
tff(365,plain,
add(a,b) = add(add(b,additive_identity),add(a,additive_identity)),
inference(transitivity,[status(thm)],[364,251]) ).
tff(366,plain,
add(add(a,b),additive_inverse(multiply(a,b))) = add(add(add(b,additive_identity),add(a,additive_identity)),additive_inverse(multiply(a,b))),
inference(monotonicity,[status(thm)],[365]) ).
tff(367,plain,
add(add(add(b,additive_identity),add(a,additive_identity)),additive_inverse(multiply(a,b))) = add(add(a,b),additive_inverse(multiply(a,b))),
inference(symmetry,[status(thm)],[366]) ).
tff(368,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(add(b,additive_identity),add(a,additive_identity)),additive_inverse(multiply(a,b))) = add(add(b,additive_identity),add(add(a,additive_identity),additive_inverse(multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(369,plain,
add(add(add(b,additive_identity),add(a,additive_identity)),additive_inverse(multiply(a,b))) = add(add(b,additive_identity),add(add(a,additive_identity),additive_inverse(multiply(a,b)))),
inference(unit_resolution,[status(thm)],[368,183]) ).
tff(370,plain,
add(add(b,additive_identity),add(add(a,additive_identity),additive_inverse(multiply(a,b)))) = add(add(add(b,additive_identity),add(a,additive_identity)),additive_inverse(multiply(a,b))),
inference(symmetry,[status(thm)],[369]) ).
tff(371,plain,
add(a,additive_inverse(multiply(a,b))) = add(add(a,additive_identity),additive_inverse(multiply(a,b))),
inference(monotonicity,[status(thm)],[281]) ).
tff(372,plain,
add(add(a,additive_identity),additive_inverse(multiply(a,b))) = add(a,additive_inverse(multiply(a,b))),
inference(symmetry,[status(thm)],[371]) ).
tff(373,plain,
add(add(b,additive_identity),add(add(a,additive_identity),additive_inverse(multiply(a,b)))) = add(add(b,additive_identity),add(a,additive_inverse(multiply(a,b)))),
inference(monotonicity,[status(thm)],[372]) ).
tff(374,plain,
add(add(b,additive_identity),add(a,additive_inverse(multiply(a,b)))) = add(add(b,additive_identity),add(add(a,additive_identity),additive_inverse(multiply(a,b)))),
inference(symmetry,[status(thm)],[373]) ).
tff(375,plain,
add(b,additive_inverse(multiply(a,b))) = add(add(b,additive_identity),additive_inverse(multiply(a,b))),
inference(monotonicity,[status(thm)],[46]) ).
tff(376,plain,
add(add(a,add(additive_identity,additive_inverse(b))),add(b,additive_inverse(multiply(a,b)))) = add(add(a,add(additive_identity,additive_inverse(b))),add(add(b,additive_identity),additive_inverse(multiply(a,b)))),
inference(monotonicity,[status(thm)],[375]) ).
tff(377,plain,
add(add(a,add(additive_identity,additive_inverse(b))),add(add(b,additive_identity),additive_inverse(multiply(a,b)))) = add(add(a,add(additive_identity,additive_inverse(b))),add(b,additive_inverse(multiply(a,b)))),
inference(symmetry,[status(thm)],[376]) ).
tff(378,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(add(a,add(additive_identity,additive_inverse(b))),add(b,additive_identity)),additive_inverse(multiply(a,b))) = add(add(a,add(additive_identity,additive_inverse(b))),add(add(b,additive_identity),additive_inverse(multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(379,plain,
add(add(add(a,add(additive_identity,additive_inverse(b))),add(b,additive_identity)),additive_inverse(multiply(a,b))) = add(add(a,add(additive_identity,additive_inverse(b))),add(add(b,additive_identity),additive_inverse(multiply(a,b)))),
inference(unit_resolution,[status(thm)],[378,183]) ).
tff(380,plain,
add(a,add(add(additive_identity,additive_inverse(b)),b)) = add(a,additive_identity),
inference(monotonicity,[status(thm)],[230]) ).
tff(381,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(a,add(additive_identity,additive_inverse(b))),b) = add(a,add(add(additive_identity,additive_inverse(b)),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(382,plain,
add(add(a,add(additive_identity,additive_inverse(b))),b) = add(a,add(add(additive_identity,additive_inverse(b)),b)),
inference(unit_resolution,[status(thm)],[381,183]) ).
tff(383,plain,
add(add(a,add(additive_identity,additive_inverse(b))),add(b,additive_identity)) = add(add(a,add(additive_identity,additive_inverse(b))),b),
inference(monotonicity,[status(thm)],[114]) ).
tff(384,plain,
add(add(a,add(additive_identity,additive_inverse(b))),add(b,additive_identity)) = add(a,additive_identity),
inference(transitivity,[status(thm)],[383,382,380]) ).
tff(385,plain,
add(add(add(a,add(additive_identity,additive_inverse(b))),add(b,additive_identity)),additive_inverse(multiply(a,b))) = add(add(a,additive_identity),additive_inverse(multiply(a,b))),
inference(monotonicity,[status(thm)],[384]) ).
tff(386,plain,
add(add(a,additive_identity),additive_inverse(multiply(a,b))) = add(add(add(a,add(additive_identity,additive_inverse(b))),add(b,additive_identity)),additive_inverse(multiply(a,b))),
inference(symmetry,[status(thm)],[385]) ).
tff(387,plain,
add(a,additive_inverse(multiply(a,b))) = add(add(a,add(additive_identity,additive_inverse(b))),add(b,additive_inverse(multiply(a,b)))),
inference(transitivity,[status(thm)],[371,386,379,377]) ).
tff(388,plain,
add(add(b,additive_identity),add(a,additive_inverse(multiply(a,b)))) = add(add(b,additive_identity),add(add(a,add(additive_identity,additive_inverse(b))),add(b,additive_inverse(multiply(a,b))))),
inference(monotonicity,[status(thm)],[387]) ).
tff(389,plain,
add(add(b,additive_identity),add(add(a,add(additive_identity,additive_inverse(b))),add(b,additive_inverse(multiply(a,b))))) = add(add(b,additive_identity),add(a,additive_inverse(multiply(a,b)))),
inference(symmetry,[status(thm)],[388]) ).
tff(390,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(add(b,additive_identity),add(a,add(additive_identity,additive_inverse(b)))),add(b,additive_inverse(multiply(a,b)))) = add(add(b,additive_identity),add(add(a,add(additive_identity,additive_inverse(b))),add(b,additive_inverse(multiply(a,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(391,plain,
add(add(add(b,additive_identity),add(a,add(additive_identity,additive_inverse(b)))),add(b,additive_inverse(multiply(a,b)))) = add(add(b,additive_identity),add(add(a,add(additive_identity,additive_inverse(b))),add(b,additive_inverse(multiply(a,b))))),
inference(unit_resolution,[status(thm)],[390,183]) ).
tff(392,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(add(b,additive_identity),add(a,add(additive_identity,additive_inverse(b)))) = add(add(a,add(additive_identity,additive_inverse(b))),add(b,additive_identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(393,plain,
add(add(b,additive_identity),add(a,add(additive_identity,additive_inverse(b)))) = add(add(a,add(additive_identity,additive_inverse(b))),add(b,additive_identity)),
inference(unit_resolution,[status(thm)],[392,10]) ).
tff(394,plain,
add(add(b,additive_identity),add(a,add(additive_identity,additive_inverse(b)))) = add(a,additive_identity),
inference(transitivity,[status(thm)],[393,383,382,380]) ).
tff(395,plain,
add(add(add(b,additive_identity),add(a,add(additive_identity,additive_inverse(b)))),add(b,additive_inverse(multiply(a,b)))) = add(add(a,additive_identity),add(b,additive_inverse(multiply(a,b)))),
inference(monotonicity,[status(thm)],[394]) ).
tff(396,plain,
add(add(a,additive_identity),add(b,additive_inverse(multiply(a,b)))) = add(add(add(b,additive_identity),add(a,add(additive_identity,additive_inverse(b)))),add(b,additive_inverse(multiply(a,b)))),
inference(symmetry,[status(thm)],[395]) ).
tff(397,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(add(b,additive_inverse(multiply(a,b))),add(a,additive_identity)) = add(add(a,additive_identity),add(b,additive_inverse(multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(398,plain,
add(add(b,additive_inverse(multiply(a,b))),add(a,additive_identity)) = add(add(a,additive_identity),add(b,additive_inverse(multiply(a,b)))),
inference(unit_resolution,[status(thm)],[397,10]) ).
tff(399,plain,
add(a,additive_identity) = add(additive_identity,additive_inverse(a)),
inference(transitivity,[status(thm)],[56,339,336,334,331,157]) ).
tff(400,plain,
add(add(b,additive_inverse(multiply(a,b))),add(a,additive_identity)) = add(add(b,additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(a))),
inference(monotonicity,[status(thm)],[399]) ).
tff(401,plain,
add(add(b,additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(a))) = add(add(b,additive_inverse(multiply(a,b))),add(a,additive_identity)),
inference(symmetry,[status(thm)],[400]) ).
tff(402,plain,
add(add(b,additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(a))) = add(add(add(b,additive_identity),additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(a))),
inference(monotonicity,[status(thm)],[375]) ).
tff(403,plain,
add(add(add(b,additive_identity),additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(a))) = add(add(b,additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(a))),
inference(symmetry,[status(thm)],[402]) ).
tff(404,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(add(b,additive_identity),additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(a))) = add(add(b,additive_identity),add(additive_inverse(multiply(a,b)),add(additive_identity,additive_inverse(a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(405,plain,
add(add(add(b,additive_identity),additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(a))) = add(add(b,additive_identity),add(additive_inverse(multiply(a,b)),add(additive_identity,additive_inverse(a)))),
inference(unit_resolution,[status(thm)],[404,183]) ).
tff(406,plain,
add(add(b,additive_identity),add(additive_inverse(multiply(a,b)),add(additive_identity,additive_inverse(a)))) = add(add(add(b,additive_identity),additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(a))),
inference(symmetry,[status(thm)],[405]) ).
tff(407,plain,
add(additive_inverse(a),additive_inverse(multiply(a,b))) = add(add(additive_identity,additive_inverse(a)),additive_inverse(multiply(a,b))),
inference(monotonicity,[status(thm)],[66]) ).
tff(408,plain,
add(add(additive_identity,additive_inverse(a)),additive_inverse(multiply(a,b))) = add(additive_inverse(a),additive_inverse(multiply(a,b))),
inference(symmetry,[status(thm)],[407]) ).
tff(409,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(add(additive_identity,additive_inverse(a)),additive_inverse(multiply(a,b))) = add(additive_inverse(multiply(a,b)),add(additive_identity,additive_inverse(a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(410,plain,
add(add(additive_identity,additive_inverse(a)),additive_inverse(multiply(a,b))) = add(additive_inverse(multiply(a,b)),add(additive_identity,additive_inverse(a))),
inference(unit_resolution,[status(thm)],[409,10]) ).
tff(411,plain,
add(additive_inverse(multiply(a,b)),add(additive_identity,additive_inverse(a))) = add(add(additive_identity,additive_inverse(a)),additive_inverse(multiply(a,b))),
inference(symmetry,[status(thm)],[410]) ).
tff(412,plain,
add(additive_inverse(multiply(a,b)),add(additive_identity,additive_inverse(a))) = add(additive_inverse(a),additive_inverse(multiply(a,b))),
inference(transitivity,[status(thm)],[411,408]) ).
tff(413,plain,
add(add(b,additive_identity),add(additive_inverse(multiply(a,b)),add(additive_identity,additive_inverse(a)))) = add(add(b,additive_identity),add(additive_inverse(a),additive_inverse(multiply(a,b)))),
inference(monotonicity,[status(thm)],[412]) ).
tff(414,plain,
add(add(b,additive_identity),add(additive_inverse(a),additive_inverse(multiply(a,b)))) = add(add(b,additive_identity),add(additive_inverse(multiply(a,b)),add(additive_identity,additive_inverse(a)))),
inference(symmetry,[status(thm)],[413]) ).
tff(415,plain,
add(add(b,additive_identity),add(additive_inverse(a),additive_inverse(multiply(a,b)))) = add(add(b,additive_identity),add(additive_inverse(add(a,additive_identity)),additive_inverse(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)))),
inference(monotonicity,[status(thm)],[310]) ).
tff(416,plain,
add(add(b,additive_identity),add(additive_inverse(add(a,additive_identity)),additive_inverse(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)))) = add(add(b,additive_identity),add(additive_inverse(a),additive_inverse(multiply(a,b)))),
inference(symmetry,[status(thm)],[415]) ).
tff(417,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(add(additive_inverse(add(a,additive_identity)),additive_inverse(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity))),add(b,additive_identity)) = add(add(b,additive_identity),add(additive_inverse(add(a,additive_identity)),additive_inverse(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(418,plain,
add(add(additive_inverse(add(a,additive_identity)),additive_inverse(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity))),add(b,additive_identity)) = add(add(b,additive_identity),add(additive_inverse(add(a,additive_identity)),additive_inverse(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)))),
inference(unit_resolution,[status(thm)],[417,10]) ).
tff(419,plain,
add(add(additive_inverse(add(a,additive_identity)),additive_inverse(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity))),add(b,additive_identity)) = add(add(additive_inverse(a),additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(b))),
inference(monotonicity,[status(thm)],[309,215]) ).
tff(420,plain,
add(add(additive_inverse(a),additive_inverse(multiply(a,b))),add(additive_identity,additive_inverse(b))) = add(add(additive_inverse(add(a,additive_identity)),additive_inverse(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity))),add(b,additive_identity)),
inference(symmetry,[status(thm)],[419]) ).
tff(421,plain,
add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b)))) = add(add(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)),add(b,additive_identity)),
inference(transitivity,[status(thm)],[316,314,312,420,418,416,414,406,403,401,398,396,391,389,374,370,367,363,358,356,354]) ).
tff(422,plain,
add(multiply(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))),add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b))))) = add(multiply(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))),add(add(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)),add(b,additive_identity))),
inference(monotonicity,[status(thm)],[421]) ).
tff(423,plain,
add(multiply(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))),add(add(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)),add(b,additive_identity))) = add(multiply(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))),add(add(additive_identity,additive_inverse(b)),add(additive_inverse(a),additive_inverse(multiply(a,b))))),
inference(symmetry,[status(thm)],[422]) ).
tff(424,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(multiply(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))),add(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity))),add(b,additive_identity)) = add(multiply(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))),add(add(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)),add(b,additive_identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(425,plain,
add(add(multiply(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))),add(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity))),add(b,additive_identity)) = add(multiply(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))),add(add(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)),add(b,additive_identity))),
inference(unit_resolution,[status(thm)],[424,183]) ).
tff(426,plain,
multiply(add(b,additive_identity),add(b,additive_identity)) = b,
inference(transitivity,[status(thm)],[213,113,112,111,110,20]) ).
tff(427,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) )
| ( multiply(additive_inverse(b),a) = additive_inverse(multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(428,plain,
multiply(additive_inverse(b),a) = additive_inverse(multiply(b,a)),
inference(unit_resolution,[status(thm)],[427,90]) ).
tff(429,plain,
additive_inverse(multiply(additive_inverse(b),a)) = additive_inverse(additive_inverse(multiply(b,a))),
inference(monotonicity,[status(thm)],[428]) ).
tff(430,plain,
additive_inverse(additive_inverse(multiply(b,a))) = additive_inverse(multiply(additive_inverse(b),a)),
inference(symmetry,[status(thm)],[429]) ).
tff(431,plain,
( ~ ! [X: $i] : ( additive_inverse(additive_inverse(X)) = X )
| ( additive_inverse(additive_inverse(multiply(b,a))) = multiply(b,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(432,plain,
additive_inverse(additive_inverse(multiply(b,a))) = multiply(b,a),
inference(unit_resolution,[status(thm)],[431,18]) ).
tff(433,plain,
multiply(b,a) = additive_inverse(additive_inverse(multiply(b,a))),
inference(symmetry,[status(thm)],[432]) ).
tff(434,plain,
multiply(add(b,additive_identity),add(a,additive_identity)) = multiply(b,a),
inference(monotonicity,[status(thm)],[114,119]) ).
tff(435,plain,
multiply(add(b,additive_identity),add(a,additive_identity)) = additive_inverse(multiply(additive_inverse(b),a)),
inference(transitivity,[status(thm)],[434,433,430]) ).
tff(436,plain,
add(multiply(add(b,additive_identity),add(a,additive_identity)),multiply(add(b,additive_identity),add(b,additive_identity))) = add(additive_inverse(multiply(additive_inverse(b),a)),b),
inference(monotonicity,[status(thm)],[435,426]) ).
tff(437,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
<=> ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(438,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ) ),
inference(quant_intro,[status(thm)],[437]) ).
tff(439,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(440,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',distribute1) ).
tff(441,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[440,439]) ).
tff(442,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(skolemize,[status(sab)],[441]) ).
tff(443,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[442,438]) ).
tff(444,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
| ( multiply(add(b,additive_identity),add(add(a,additive_identity),add(b,additive_identity))) = add(multiply(add(b,additive_identity),add(a,additive_identity)),multiply(add(b,additive_identity),add(b,additive_identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(445,plain,
multiply(add(b,additive_identity),add(add(a,additive_identity),add(b,additive_identity))) = add(multiply(add(b,additive_identity),add(a,additive_identity)),multiply(add(b,additive_identity),add(b,additive_identity))),
inference(unit_resolution,[status(thm)],[444,443]) ).
tff(446,plain,
multiply(add(b,additive_identity),add(a,b)) = multiply(add(b,additive_identity),add(add(a,additive_identity),add(b,additive_identity))),
inference(monotonicity,[status(thm)],[364]) ).
tff(447,plain,
multiply(additive_inverse(add(additive_identity,additive_inverse(b))),add(add(b,additive_identity),add(a,additive_identity))) = multiply(add(b,additive_identity),add(a,b)),
inference(monotonicity,[status(thm)],[209,253]) ).
tff(448,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) )
| ( multiply(additive_inverse(add(additive_identity,additive_inverse(b))),add(add(b,additive_identity),add(a,additive_identity))) = additive_inverse(multiply(add(additive_identity,additive_inverse(b)),add(add(b,additive_identity),add(a,additive_identity)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(449,plain,
multiply(additive_inverse(add(additive_identity,additive_inverse(b))),add(add(b,additive_identity),add(a,additive_identity))) = additive_inverse(multiply(add(additive_identity,additive_inverse(b)),add(add(b,additive_identity),add(a,additive_identity)))),
inference(unit_resolution,[status(thm)],[448,90]) ).
tff(450,plain,
additive_inverse(multiply(add(additive_identity,additive_inverse(b)),add(add(b,additive_identity),add(a,additive_identity)))) = multiply(additive_inverse(add(additive_identity,additive_inverse(b))),add(add(b,additive_identity),add(a,additive_identity))),
inference(symmetry,[status(thm)],[449]) ).
tff(451,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) )
| ( multiply(add(additive_identity,additive_inverse(b)),additive_inverse(add(add(b,additive_identity),add(a,additive_identity)))) = additive_inverse(multiply(add(additive_identity,additive_inverse(b)),add(add(b,additive_identity),add(a,additive_identity)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(452,plain,
multiply(add(additive_identity,additive_inverse(b)),additive_inverse(add(add(b,additive_identity),add(a,additive_identity)))) = additive_inverse(multiply(add(additive_identity,additive_inverse(b)),add(add(b,additive_identity),add(a,additive_identity)))),
inference(unit_resolution,[status(thm)],[451,135]) ).
tff(453,plain,
( ~ ! [Y: $i,X: $i] : ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) )
| ( additive_inverse(add(add(b,additive_identity),add(a,additive_identity))) = add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(454,plain,
additive_inverse(add(add(b,additive_identity),add(a,additive_identity))) = add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),
inference(unit_resolution,[status(thm)],[453,31]) ).
tff(455,plain,
add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))) = additive_inverse(add(add(b,additive_identity),add(a,additive_identity))),
inference(symmetry,[status(thm)],[454]) ).
tff(456,plain,
add(additive_inverse(b),additive_inverse(a)) = additive_inverse(add(add(b,additive_identity),add(a,additive_identity))),
inference(transitivity,[status(thm)],[323,455]) ).
tff(457,plain,
multiply(add(additive_identity,additive_inverse(b)),add(additive_inverse(b),additive_inverse(a))) = multiply(add(additive_identity,additive_inverse(b)),additive_inverse(add(add(b,additive_identity),add(a,additive_identity)))),
inference(monotonicity,[status(thm)],[456]) ).
tff(458,plain,
add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))) = add(additive_inverse(b),additive_inverse(a)),
inference(symmetry,[status(thm)],[323]) ).
tff(459,plain,
add(add(add(additive_identity,additive_inverse(b)),b),additive_inverse(b)) = add(additive_identity,additive_inverse(b)),
inference(monotonicity,[status(thm)],[230]) ).
tff(460,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(add(additive_identity,additive_inverse(b)),b),additive_inverse(b)) = add(add(additive_identity,additive_inverse(b)),add(b,additive_inverse(b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(461,plain,
add(add(add(additive_identity,additive_inverse(b)),b),additive_inverse(b)) = add(add(additive_identity,additive_inverse(b)),add(b,additive_inverse(b))),
inference(unit_resolution,[status(thm)],[460,183]) ).
tff(462,plain,
add(add(additive_identity,additive_inverse(b)),add(b,additive_inverse(b))) = add(add(add(additive_identity,additive_inverse(b)),b),additive_inverse(b)),
inference(symmetry,[status(thm)],[461]) ).
tff(463,plain,
add(additive_identity,add(additive_inverse(a),a)) = add(additive_inverse(additive_identity),additive_identity),
inference(monotonicity,[status(thm)],[96,269]) ).
tff(464,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(additive_identity,additive_inverse(a)),a) = add(additive_identity,add(additive_inverse(a),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(465,plain,
add(add(additive_identity,additive_inverse(a)),a) = add(additive_identity,add(additive_inverse(a),a)),
inference(unit_resolution,[status(thm)],[464,183]) ).
tff(466,plain,
add(add(additive_identity,additive_inverse(a)),a) = additive_inverse(additive_identity),
inference(transitivity,[status(thm)],[465,463,226,96]) ).
tff(467,plain,
add(add(add(additive_identity,additive_inverse(a)),a),additive_identity) = add(additive_inverse(additive_identity),additive_identity),
inference(monotonicity,[status(thm)],[466]) ).
tff(468,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(add(additive_identity,additive_inverse(a)),a),additive_identity) = add(add(additive_identity,additive_inverse(a)),add(a,additive_identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(469,plain,
add(add(add(additive_identity,additive_inverse(a)),a),additive_identity) = add(add(additive_identity,additive_inverse(a)),add(a,additive_identity)),
inference(unit_resolution,[status(thm)],[468,183]) ).
tff(470,plain,
add(add(additive_identity,additive_inverse(a)),add(a,additive_identity)) = add(add(add(additive_identity,additive_inverse(a)),a),additive_identity),
inference(symmetry,[status(thm)],[469]) ).
tff(471,plain,
add(add(additive_identity,additive_inverse(a)),add(a,additive_identity)) = add(b,additive_inverse(b)),
inference(transitivity,[status(thm)],[470,467,226,173,163]) ).
tff(472,plain,
add(add(additive_identity,additive_inverse(b)),add(add(additive_identity,additive_inverse(a)),add(a,additive_identity))) = add(add(additive_identity,additive_inverse(b)),add(b,additive_inverse(b))),
inference(monotonicity,[status(thm)],[471]) ).
tff(473,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(add(additive_identity,additive_inverse(b)),add(additive_identity,additive_inverse(a))),add(a,additive_identity)) = add(add(additive_identity,additive_inverse(b)),add(add(additive_identity,additive_inverse(a)),add(a,additive_identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(474,plain,
add(add(add(additive_identity,additive_inverse(b)),add(additive_identity,additive_inverse(a))),add(a,additive_identity)) = add(add(additive_identity,additive_inverse(b)),add(add(additive_identity,additive_inverse(a)),add(a,additive_identity))),
inference(unit_resolution,[status(thm)],[473,183]) ).
tff(475,plain,
add(additive_inverse(b),additive_inverse(a)) = add(add(additive_identity,additive_inverse(b)),add(additive_identity,additive_inverse(a))),
inference(symmetry,[status(thm)],[324]) ).
tff(476,plain,
add(add(additive_inverse(b),additive_inverse(a)),add(a,additive_identity)) = add(add(add(additive_identity,additive_inverse(b)),add(additive_identity,additive_inverse(a))),add(a,additive_identity)),
inference(monotonicity,[status(thm)],[475]) ).
tff(477,plain,
add(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(a,additive_identity)) = add(add(additive_inverse(b),additive_inverse(a)),add(a,additive_identity)),
inference(monotonicity,[status(thm)],[458]) ).
tff(478,plain,
add(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(a,additive_identity)) = add(additive_identity,additive_inverse(b)),
inference(transitivity,[status(thm)],[477,476,474,472,462,459]) ).
tff(479,plain,
multiply(add(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(a,additive_identity)),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))) = multiply(add(additive_identity,additive_inverse(b)),add(additive_inverse(b),additive_inverse(a))),
inference(monotonicity,[status(thm)],[478,458]) ).
tff(480,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
<=> ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(481,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[480]) ).
tff(482,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(483,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',distribute2) ).
tff(484,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[483,482]) ).
tff(485,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[484]) ).
tff(486,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[485,481]) ).
tff(487,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
| ( multiply(add(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(a,additive_identity)),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))) = add(multiply(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))),multiply(add(a,additive_identity),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(488,plain,
multiply(add(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(a,additive_identity)),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))) = add(multiply(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))),multiply(add(a,additive_identity),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))))),
inference(unit_resolution,[status(thm)],[487,486]) ).
tff(489,plain,
add(multiply(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))),multiply(add(a,additive_identity),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))))) = multiply(add(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(a,additive_identity)),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))),
inference(symmetry,[status(thm)],[488]) ).
tff(490,plain,
add(add(additive_identity,additive_inverse(a)),add(additive_identity,additive_inverse(b))) = add(additive_inverse(a),additive_inverse(b)),
inference(symmetry,[status(thm)],[328]) ).
tff(491,plain,
add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))) = add(additive_inverse(a),additive_inverse(b)),
inference(transitivity,[status(thm)],[458,475,326,490]) ).
tff(492,plain,
multiply(add(a,additive_identity),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))) = multiply(add(a,additive_identity),add(additive_inverse(a),additive_inverse(b))),
inference(monotonicity,[status(thm)],[491]) ).
tff(493,plain,
multiply(add(a,additive_identity),add(additive_inverse(a),additive_inverse(b))) = multiply(add(a,additive_identity),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))),
inference(symmetry,[status(thm)],[492]) ).
tff(494,plain,
multiply(add(a,additive_identity),add(additive_inverse(a),additive_inverse(b))) = multiply(add(additive_identity,additive_inverse(a)),add(additive_inverse(a),additive_inverse(b))),
inference(monotonicity,[status(thm)],[399]) ).
tff(495,plain,
multiply(add(additive_identity,additive_inverse(a)),add(additive_inverse(a),additive_inverse(b))) = multiply(add(a,additive_identity),add(additive_inverse(a),additive_inverse(b))),
inference(symmetry,[status(thm)],[494]) ).
tff(496,plain,
additive_inverse(add(add(b,additive_identity),add(a,additive_identity))) = add(additive_inverse(a),additive_inverse(b)),
inference(transitivity,[status(thm)],[454,458,475,326,490]) ).
tff(497,plain,
multiply(add(additive_identity,additive_inverse(a)),additive_inverse(add(add(b,additive_identity),add(a,additive_identity)))) = multiply(add(additive_identity,additive_inverse(a)),add(additive_inverse(a),additive_inverse(b))),
inference(monotonicity,[status(thm)],[496]) ).
tff(498,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) )
| ( multiply(add(additive_identity,additive_inverse(a)),additive_inverse(add(add(b,additive_identity),add(a,additive_identity)))) = additive_inverse(multiply(add(additive_identity,additive_inverse(a)),add(add(b,additive_identity),add(a,additive_identity)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(499,plain,
multiply(add(additive_identity,additive_inverse(a)),additive_inverse(add(add(b,additive_identity),add(a,additive_identity)))) = additive_inverse(multiply(add(additive_identity,additive_inverse(a)),add(add(b,additive_identity),add(a,additive_identity)))),
inference(unit_resolution,[status(thm)],[498,135]) ).
tff(500,plain,
additive_inverse(multiply(add(additive_identity,additive_inverse(a)),add(add(b,additive_identity),add(a,additive_identity)))) = multiply(add(additive_identity,additive_inverse(a)),additive_inverse(add(add(b,additive_identity),add(a,additive_identity)))),
inference(symmetry,[status(thm)],[499]) ).
tff(501,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) )
| ( multiply(additive_inverse(add(additive_identity,additive_inverse(a))),add(add(b,additive_identity),add(a,additive_identity))) = additive_inverse(multiply(add(additive_identity,additive_inverse(a)),add(add(b,additive_identity),add(a,additive_identity)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(502,plain,
multiply(additive_inverse(add(additive_identity,additive_inverse(a))),add(add(b,additive_identity),add(a,additive_identity))) = additive_inverse(multiply(add(additive_identity,additive_inverse(a)),add(add(b,additive_identity),add(a,additive_identity)))),
inference(unit_resolution,[status(thm)],[501,90]) ).
tff(503,plain,
add(b,a) = add(add(b,additive_identity),add(a,additive_identity)),
inference(monotonicity,[status(thm)],[46,281]) ).
tff(504,plain,
add(a,additive_identity) = additive_inverse(add(additive_identity,additive_inverse(a))),
inference(transitivity,[status(thm)],[118,117,116]) ).
tff(505,plain,
multiply(add(a,additive_identity),add(b,a)) = multiply(additive_inverse(add(additive_identity,additive_inverse(a))),add(add(b,additive_identity),add(a,additive_identity))),
inference(monotonicity,[status(thm)],[504,503]) ).
tff(506,plain,
add(add(b,additive_identity),add(a,additive_identity)) = add(b,a),
inference(symmetry,[status(thm)],[503]) ).
tff(507,plain,
multiply(add(a,additive_identity),add(add(b,additive_identity),add(a,additive_identity))) = multiply(add(a,additive_identity),add(b,a)),
inference(monotonicity,[status(thm)],[506]) ).
tff(508,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
| ( multiply(add(a,additive_identity),add(add(b,additive_identity),add(a,additive_identity))) = add(multiply(add(a,additive_identity),add(b,additive_identity)),multiply(add(a,additive_identity),add(a,additive_identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(509,plain,
multiply(add(a,additive_identity),add(add(b,additive_identity),add(a,additive_identity))) = add(multiply(add(a,additive_identity),add(b,additive_identity)),multiply(add(a,additive_identity),add(a,additive_identity))),
inference(unit_resolution,[status(thm)],[508,443]) ).
tff(510,plain,
add(multiply(add(a,additive_identity),add(b,additive_identity)),multiply(add(a,additive_identity),add(a,additive_identity))) = multiply(add(a,additive_identity),add(add(b,additive_identity),add(a,additive_identity))),
inference(symmetry,[status(thm)],[509]) ).
tff(511,plain,
multiply(a,b) = multiply(add(a,additive_identity),add(b,additive_identity)),
inference(symmetry,[status(thm)],[120]) ).
tff(512,plain,
additive_inverse(multiply(additive_inverse(a),b)) = multiply(add(a,additive_identity),add(b,additive_identity)),
inference(transitivity,[status(thm)],[301,108,511]) ).
tff(513,plain,
add(additive_inverse(multiply(additive_inverse(a),b)),a) = add(multiply(add(a,additive_identity),add(b,additive_identity)),multiply(add(a,additive_identity),add(a,additive_identity))),
inference(monotonicity,[status(thm)],[512,69]) ).
tff(514,plain,
add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity) = additive_inverse(multiply(additive_inverse(a),b)),
inference(transitivity,[status(thm)],[125,97,124,104]) ).
tff(515,plain,
add(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity),add(a,additive_identity)) = add(additive_inverse(multiply(additive_inverse(a),b)),a),
inference(monotonicity,[status(thm)],[514,119]) ).
tff(516,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity),add(a,additive_identity)) = add(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(517,plain,
add(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity),add(a,additive_identity)) = add(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)),
inference(unit_resolution,[status(thm)],[516,10]) ).
tff(518,plain,
add(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)) = add(add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity),add(a,additive_identity)),
inference(symmetry,[status(thm)],[517]) ).
tff(519,plain,
add(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity)) = multiply(add(a,additive_identity),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))),
inference(transitivity,[status(thm)],[518,515,513,510,507,505,502,500,497,495,493]) ).
tff(520,plain,
add(multiply(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))),add(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity))) = add(multiply(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))),multiply(add(a,additive_identity),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))))),
inference(monotonicity,[status(thm)],[519]) ).
tff(521,plain,
add(multiply(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))),add(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity))) = add(additive_inverse(multiply(additive_inverse(b),a)),b),
inference(transitivity,[status(thm)],[520,489,479,457,452,450,447,446,445,436]) ).
tff(522,plain,
add(add(multiply(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))),add(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity))),add(b,additive_identity)) = add(add(additive_inverse(multiply(additive_inverse(b),a)),b),add(b,additive_identity)),
inference(monotonicity,[status(thm)],[521]) ).
tff(523,plain,
add(add(additive_inverse(multiply(additive_inverse(b),a)),b),add(b,additive_identity)) = add(add(multiply(add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity))),add(additive_inverse(add(b,additive_identity)),additive_inverse(add(a,additive_identity)))),add(add(a,additive_identity),add(additive_inverse(multiply(additive_inverse(a),b)),additive_identity))),add(b,additive_identity)),
inference(symmetry,[status(thm)],[522]) ).
tff(524,plain,
add(b,additive_identity) = additive_inverse(b),
inference(transitivity,[status(thm)],[214,211,208,206,203,192,42]) ).
tff(525,plain,
add(add(additive_inverse(multiply(additive_inverse(b),a)),b),add(b,additive_identity)) = add(add(additive_inverse(multiply(additive_inverse(b),a)),b),additive_inverse(b)),
inference(monotonicity,[status(thm)],[524]) ).
tff(526,plain,
add(add(additive_inverse(multiply(additive_inverse(b),a)),b),additive_inverse(b)) = add(add(additive_inverse(multiply(additive_inverse(b),a)),b),add(b,additive_identity)),
inference(symmetry,[status(thm)],[525]) ).
tff(527,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(add(X,Y),Z) = add(X,add(Y,Z)) )
| ( add(add(additive_inverse(multiply(additive_inverse(b),a)),b),additive_inverse(b)) = add(additive_inverse(multiply(additive_inverse(b),a)),add(b,additive_inverse(b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(528,plain,
add(add(additive_inverse(multiply(additive_inverse(b),a)),b),additive_inverse(b)) = add(additive_inverse(multiply(additive_inverse(b),a)),add(b,additive_inverse(b))),
inference(unit_resolution,[status(thm)],[527,183]) ).
tff(529,plain,
add(additive_inverse(multiply(additive_inverse(b),a)),add(b,additive_inverse(b))) = add(add(additive_inverse(multiply(additive_inverse(b),a)),b),additive_inverse(b)),
inference(symmetry,[status(thm)],[528]) ).
tff(530,plain,
add(additive_inverse(multiply(additive_inverse(b),a)),add(b,additive_inverse(b))) = add(additive_inverse(multiply(additive_inverse(b),a)),additive_identity),
inference(monotonicity,[status(thm)],[258]) ).
tff(531,plain,
add(additive_inverse(multiply(additive_inverse(b),a)),additive_identity) = add(additive_inverse(multiply(additive_inverse(b),a)),add(b,additive_inverse(b))),
inference(symmetry,[status(thm)],[530]) ).
tff(532,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(additive_identity,additive_inverse(multiply(additive_inverse(b),a))) = add(additive_inverse(multiply(additive_inverse(b),a)),additive_identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(533,plain,
add(additive_identity,additive_inverse(multiply(additive_inverse(b),a))) = add(additive_inverse(multiply(additive_inverse(b),a)),additive_identity),
inference(unit_resolution,[status(thm)],[532,10]) ).
tff(534,plain,
add(additive_identity,additive_inverse(multiply(additive_inverse(b),a))) = add(additive_inverse(additive_identity),additive_inverse(additive_inverse(multiply(b,a)))),
inference(monotonicity,[status(thm)],[96,429]) ).
tff(535,plain,
add(additive_inverse(additive_identity),additive_inverse(additive_inverse(multiply(b,a)))) = add(additive_identity,additive_inverse(multiply(additive_inverse(b),a))),
inference(symmetry,[status(thm)],[534]) ).
tff(536,plain,
( ~ ! [Y: $i,X: $i] : ( additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) )
| ( additive_inverse(add(additive_identity,additive_inverse(multiply(b,a)))) = add(additive_inverse(additive_identity),additive_inverse(additive_inverse(multiply(b,a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(537,plain,
additive_inverse(add(additive_identity,additive_inverse(multiply(b,a)))) = add(additive_inverse(additive_identity),additive_inverse(additive_inverse(multiply(b,a)))),
inference(unit_resolution,[status(thm)],[536,31]) ).
tff(538,plain,
( ~ ! [X: $i] : ( add(additive_identity,X) = X )
| ( add(additive_identity,additive_inverse(multiply(b,a))) = additive_inverse(multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(539,plain,
add(additive_identity,additive_inverse(multiply(b,a))) = additive_inverse(multiply(b,a)),
inference(unit_resolution,[status(thm)],[538,40]) ).
tff(540,plain,
additive_inverse(add(additive_identity,additive_inverse(multiply(b,a)))) = additive_inverse(additive_inverse(multiply(b,a))),
inference(monotonicity,[status(thm)],[539]) ).
tff(541,plain,
additive_inverse(additive_inverse(multiply(b,a))) = additive_inverse(add(additive_identity,additive_inverse(multiply(b,a)))),
inference(symmetry,[status(thm)],[540]) ).
tff(542,plain,
multiply(b,a) = c,
inference(transitivity,[status(thm)],[433,541,537,535,533,531,529,526,523,425,423,351,344,298,280,278,248,243,240,217,190,188,186,176,102,93,160,155,153,148,140,138,128,123,81,71,3]) ).
tff(543,plain,
( ( multiply(b,a) != c )
<=> ( multiply(b,a) != c ) ),
inference(rewrite,[status(thm)],[]) ).
tff(544,axiom,
multiply(b,a) != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity) ).
tff(545,plain,
multiply(b,a) != c,
inference(modus_ponens,[status(thm)],[544,543]) ).
tff(546,plain,
$false,
inference(unit_resolution,[status(thm)],[545,542]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG008-4 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n005.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 : Fri Jun 20 03:05:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 58.58/58.81 % SZS status Unsatisfiable
% 58.58/58.81 % SZS output start Proof
% See solution above
% 58.67/58.87 % E exiting
%------------------------------------------------------------------------------