TSTP Solution File: RNG128-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG128-1 : TPTP v8.1.0. Released v5.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 03:18:34 EDT 2022
% Result : Unsatisfiable 3.96s 2.72s
% Output : Proof 3.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 159
% Syntax : Number of formulae : 731 ( 580 unt; 6 typ; 0 def)
% Number of atoms : 884 ( 876 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 286 ( 134 ~; 130 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 7 ( 7 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 439 ( 426 !; 0 ?; 439 :)
% Comments :
%------------------------------------------------------------------------------
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(x1_type,type,
x1: $i ).
tff(x0_type,type,
x0: $i ).
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(unit_type,type,
unit: $i ).
tff(zero_type,type,
zero: $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(
( ( mult(A,B) = mult(B,A) )
<=> ( mult(A,B) = mult(B,A) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,A: $i] : ( mult(A,B) = mult(B,A) )
<=> ! [B: $i,A: $i] : ( mult(A,B) = mult(B,A) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i] : ( mult(A,B) = mult(B,A) )
<=> ! [B: $i,A: $i] : ( mult(A,B) = mult(B,A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [B: $i,A: $i] : ( mult(A,B) = mult(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_002) ).
tff(5,plain,
! [B: $i,A: $i] : ( mult(A,B) = mult(B,A) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( mult(A,B) = mult(B,A) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( mult(A,B) = mult(B,A) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,B) = mult(B,A) )
| ( mult(x0,x1) = mult(x1,x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
mult(x0,x1) = mult(x1,x0),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
mult(x1,x0) = mult(x0,x1),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [A: $i] :
refl(
( ( add(unit,add(A,mult(A,A))) = A )
<=> ( add(unit,add(A,mult(A,A))) = A ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [A: $i] : ( add(unit,add(A,mult(A,A))) = A )
<=> ! [A: $i] : ( add(unit,add(A,mult(A,A))) = A ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [A: $i] : ( add(unit,add(A,mult(A,A))) = A )
<=> ! [A: $i] : ( add(unit,add(A,mult(A,A))) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
! [A: $i] : ( add(unit,add(A,mult(A,A))) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_006) ).
tff(15,plain,
! [A: $i] : ( add(unit,add(A,mult(A,A))) = A ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [A: $i] : ( add(unit,add(A,mult(A,A))) = A ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [A: $i] : ( add(unit,add(A,mult(A,A))) = A ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [A: $i] : ( add(unit,add(A,mult(A,A))) = A )
| ( add(unit,add(x0,mult(x0,x0))) = x0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
add(unit,add(x0,mult(x0,x0))) = x0,
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
mult(x1,add(unit,add(x0,mult(x0,x0)))) = mult(x1,x0),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
<=> ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_003) ).
tff(25,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(x1,add(unit,add(x0,mult(x0,x0)))) = add(mult(x1,unit),mult(x1,add(x0,mult(x0,x0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
mult(x1,add(unit,add(x0,mult(x0,x0)))) = add(mult(x1,unit),mult(x1,add(x0,mult(x0,x0)))),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
add(mult(x1,unit),mult(x1,add(x0,mult(x0,x0)))) = mult(x1,add(unit,add(x0,mult(x0,x0)))),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
^ [A: $i] :
refl(
( ( mult(A,unit) = A )
<=> ( mult(A,unit) = A ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [A: $i] : ( mult(A,unit) = A )
<=> ! [A: $i] : ( mult(A,unit) = A ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [A: $i] : ( mult(A,unit) = A )
<=> ! [A: $i] : ( mult(A,unit) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,axiom,
! [A: $i] : ( mult(A,unit) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_005) ).
tff(35,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(x1,unit) = x1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
mult(x1,unit) = x1,
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
x1 = mult(x1,unit),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
( ~ ! [A: $i] : ( add(unit,add(A,mult(A,A))) = A )
| ( add(unit,add(x1,mult(x1,x1))) = x1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
add(unit,add(x1,mult(x1,x1))) = x1,
inference(unit_resolution,[status(thm)],[41,17]) ).
tff(43,plain,
add(add(unit,add(x1,mult(x1,x1))),mult(x1,x1)) = add(x1,mult(x1,x1)),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( add(A,add(B,C)) = add(add(A,B),C) )
<=> ( add(A,add(B,C)) = add(add(A,B),C) ) )),
inference(bind,[status(th)],]) ).
tff(45,plain,
( ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,axiom,
! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos) ).
tff(48,plain,
! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(unit,add(add(x1,mult(x1,x1)),mult(x1,x1))) = add(add(unit,add(x1,mult(x1,x1))),mult(x1,x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
add(unit,add(add(x1,mult(x1,x1)),mult(x1,x1))) = add(add(unit,add(x1,mult(x1,x1))),mult(x1,x1)),
inference(unit_resolution,[status(thm)],[51,50]) ).
tff(53,plain,
add(unit,add(add(x1,mult(x1,x1)),mult(x1,x1))) = add(x1,mult(x1,x1)),
inference(transitivity,[status(thm)],[52,43]) ).
tff(54,plain,
add(unit,add(unit,add(add(x1,mult(x1,x1)),mult(x1,x1)))) = add(unit,add(x1,mult(x1,x1))),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(unit,add(unit,add(add(x1,mult(x1,x1)),mult(x1,x1)))) = add(add(unit,unit),add(add(x1,mult(x1,x1)),mult(x1,x1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
add(unit,add(unit,add(add(x1,mult(x1,x1)),mult(x1,x1)))) = add(add(unit,unit),add(add(x1,mult(x1,x1)),mult(x1,x1))),
inference(unit_resolution,[status(thm)],[55,50]) ).
tff(57,plain,
add(add(unit,unit),add(add(x1,mult(x1,x1)),mult(x1,x1))) = add(unit,add(unit,add(add(x1,mult(x1,x1)),mult(x1,x1)))),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
mult(x1,add(unit,add(x1,mult(x1,x1)))) = mult(x1,x1),
inference(monotonicity,[status(thm)],[42]) ).
tff(59,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(x1,add(unit,add(x1,mult(x1,x1)))) = add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
mult(x1,add(unit,add(x1,mult(x1,x1)))) = add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),
inference(unit_resolution,[status(thm)],[59,27]) ).
tff(61,plain,
add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))) = mult(x1,add(unit,add(x1,mult(x1,x1)))),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))) = mult(x1,x1),
inference(transitivity,[status(thm)],[61,58]) ).
tff(63,plain,
add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))) = add(add(x1,mult(x1,x1)),mult(x1,x1)),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
add(add(unit,unit),add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = add(add(unit,unit),add(add(x1,mult(x1,x1)),mult(x1,x1))),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
add(add(unit,unit),add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = mult(x1,unit),
inference(transitivity,[status(thm)],[64,57,54,42,40]) ).
tff(66,plain,
add(add(add(unit,unit),add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))),mult(x1,add(x0,mult(x0,x0)))) = add(mult(x1,unit),mult(x1,add(x0,mult(x0,x0)))),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(add(unit,unit),add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),mult(x1,add(x0,mult(x0,x0))))) = add(add(add(unit,unit),add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))),mult(x1,add(x0,mult(x0,x0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
add(add(unit,unit),add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),mult(x1,add(x0,mult(x0,x0))))) = add(add(add(unit,unit),add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))),mult(x1,add(x0,mult(x0,x0)))),
inference(unit_resolution,[status(thm)],[67,50]) ).
tff(69,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(unit,add(x1,mult(x1,x1))) = add(add(unit,x1),mult(x1,x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
add(unit,add(x1,mult(x1,x1))) = add(add(unit,x1),mult(x1,x1)),
inference(unit_resolution,[status(thm)],[69,50]) ).
tff(71,plain,
add(add(unit,x1),mult(x1,x1)) = add(unit,add(x1,mult(x1,x1))),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
^ [B: $i,A: $i] :
refl(
( ( add(A,B) = add(B,A) )
<=> ( add(A,B) = add(B,A) ) )),
inference(bind,[status(th)],]) ).
tff(73,plain,
( ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
<=> ! [B: $i,A: $i] : ( add(A,B) = add(B,A) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
( ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
<=> ! [B: $i,A: $i] : ( add(A,B) = add(B,A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,axiom,
! [B: $i,A: $i] : ( add(A,B) = add(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_001) ).
tff(76,plain,
! [B: $i,A: $i] : ( add(A,B) = add(B,A) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
! [B: $i,A: $i] : ( add(A,B) = add(B,A) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [B: $i,A: $i] : ( add(A,B) = add(B,A) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(unit,x1) = add(x1,unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
add(unit,x1) = add(x1,unit),
inference(unit_resolution,[status(thm)],[79,78]) ).
tff(81,plain,
add(x1,unit) = add(unit,x1),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
add(add(x1,unit),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))) = add(add(unit,x1),mult(x1,x1)),
inference(monotonicity,[status(thm)],[81,62]) ).
tff(83,plain,
mult(x1,x1) = mult(x1,add(unit,add(x1,mult(x1,x1)))),
inference(symmetry,[status(thm)],[58]) ).
tff(84,plain,
mult(x1,x1) = add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),
inference(transitivity,[status(thm)],[83,60]) ).
tff(85,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(add(x1,mult(x1,x1)),unit) = add(unit,add(x1,mult(x1,x1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
add(add(x1,mult(x1,x1)),unit) = add(unit,add(x1,mult(x1,x1))),
inference(unit_resolution,[status(thm)],[85,78]) ).
tff(87,plain,
add(unit,add(x1,mult(x1,x1))) = add(add(x1,mult(x1,x1)),unit),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
x1 = add(unit,add(x1,mult(x1,x1))),
inference(symmetry,[status(thm)],[42]) ).
tff(89,plain,
x1 = add(add(x1,mult(x1,x1)),unit),
inference(transitivity,[status(thm)],[88,87]) ).
tff(90,plain,
add(x1,unit) = add(add(add(x1,mult(x1,x1)),unit),unit),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
add(add(add(x1,mult(x1,x1)),unit),unit) = add(x1,unit),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(add(x1,mult(x1,x1)),add(unit,unit)) = add(add(add(x1,mult(x1,x1)),unit),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
add(add(x1,mult(x1,x1)),add(unit,unit)) = add(add(add(x1,mult(x1,x1)),unit),unit),
inference(unit_resolution,[status(thm)],[92,50]) ).
tff(94,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(add(x1,mult(x1,x1)),add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit)) = add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
add(add(x1,mult(x1,x1)),add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit)) = add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),unit),
inference(unit_resolution,[status(thm)],[94,50]) ).
tff(96,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(add(x1,mult(x1,x1)),add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit)) = add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit),add(x1,mult(x1,x1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
add(add(x1,mult(x1,x1)),add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit)) = add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit),add(x1,mult(x1,x1))),
inference(unit_resolution,[status(thm)],[96,78]) ).
tff(98,plain,
add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit),add(x1,mult(x1,x1))) = add(add(x1,mult(x1,x1)),add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit)),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(unit,add(x1,mult(x1,x1)))) = add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit),add(x1,mult(x1,x1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(100,plain,
add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(unit,add(x1,mult(x1,x1)))) = add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit),add(x1,mult(x1,x1))),
inference(unit_resolution,[status(thm)],[99,50]) ).
tff(101,plain,
add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(unit,add(x1,mult(x1,x1)))) = add(mult(x1,x1),x1),
inference(monotonicity,[status(thm)],[62,42]) ).
tff(102,plain,
add(mult(x1,x1),x1) = add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(unit,add(x1,mult(x1,x1)))),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(mult(x1,x1),x1) = add(x1,mult(x1,x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
add(mult(x1,x1),x1) = add(x1,mult(x1,x1)),
inference(unit_resolution,[status(thm)],[103,78]) ).
tff(105,plain,
add(x1,mult(x1,x1)) = add(mult(x1,x1),x1),
inference(symmetry,[status(thm)],[104]) ).
tff(106,plain,
add(x1,mult(x1,x1)) = add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),unit),
inference(transitivity,[status(thm)],[105,102,100,98,95]) ).
tff(107,plain,
add(add(x1,mult(x1,x1)),add(unit,unit)) = add(add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),unit),add(unit,unit)),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
add(add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),unit),add(unit,unit)) = add(add(x1,mult(x1,x1)),add(unit,unit)),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),add(unit,add(unit,unit))) = add(add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),unit),add(unit,unit)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(110,plain,
add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),add(unit,add(unit,unit))) = add(add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),unit),add(unit,unit)),
inference(unit_resolution,[status(thm)],[109,50]) ).
tff(111,plain,
( ~ ! [A: $i] : ( add(unit,add(A,mult(A,A))) = A )
| ( add(unit,add(unit,mult(unit,unit))) = unit ) ),
inference(quant_inst,[status(thm)],]) ).
tff(112,plain,
add(unit,add(unit,mult(unit,unit))) = unit,
inference(unit_resolution,[status(thm)],[111,17]) ).
tff(113,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(unit,unit) = unit ) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,plain,
mult(unit,unit) = unit,
inference(unit_resolution,[status(thm)],[113,37]) ).
tff(115,plain,
add(unit,mult(unit,unit)) = add(unit,unit),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
add(unit,add(unit,mult(unit,unit))) = add(unit,add(unit,unit)),
inference(monotonicity,[status(thm)],[115]) ).
tff(117,plain,
add(unit,add(unit,unit)) = add(unit,add(unit,mult(unit,unit))),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
add(unit,add(unit,unit)) = unit,
inference(transitivity,[status(thm)],[117,112]) ).
tff(119,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(x1,mult(x1,x1))) = add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(120,plain,
add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(x1,mult(x1,x1))) = add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),
inference(unit_resolution,[status(thm)],[119,78]) ).
tff(121,plain,
add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))) = add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(x1,mult(x1,x1))),
inference(symmetry,[status(thm)],[120]) ).
tff(122,plain,
add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),add(unit,add(unit,unit))) = add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(x1,mult(x1,x1))),unit),
inference(monotonicity,[status(thm)],[121,118]) ).
tff(123,plain,
add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(x1,mult(x1,x1))),unit) = add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),add(unit,add(unit,unit))),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(add(x1,mult(x1,x1)),unit)) = add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(x1,mult(x1,x1))),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(125,plain,
add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(add(x1,mult(x1,x1)),unit)) = add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(x1,mult(x1,x1))),unit),
inference(unit_resolution,[status(thm)],[124,50]) ).
tff(126,plain,
add(add(x1,mult(x1,x1)),unit) = x1,
inference(transitivity,[status(thm)],[86,42]) ).
tff(127,plain,
add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(add(x1,mult(x1,x1)),unit)) = add(mult(x1,x1),x1),
inference(monotonicity,[status(thm)],[62,126]) ).
tff(128,plain,
add(mult(x1,x1),x1) = add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(add(x1,mult(x1,x1)),unit)),
inference(symmetry,[status(thm)],[127]) ).
tff(129,plain,
add(x1,mult(x1,x1)) = add(x1,unit),
inference(transitivity,[status(thm)],[105,128,125,123,110,108,93,91]) ).
tff(130,plain,
add(add(x1,mult(x1,x1)),mult(x1,x1)) = add(add(x1,unit),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),
inference(monotonicity,[status(thm)],[129,84]) ).
tff(131,plain,
add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))) = mult(x1,unit),
inference(transitivity,[status(thm)],[63,130,82,71,42,40]) ).
tff(132,plain,
add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),mult(x1,add(x0,mult(x0,x0)))) = add(mult(x1,unit),mult(x1,add(x0,mult(x0,x0)))),
inference(monotonicity,[status(thm)],[131]) ).
tff(133,plain,
add(mult(x1,unit),mult(x1,add(x0,mult(x0,x0)))) = add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),mult(x1,add(x0,mult(x0,x0)))),
inference(symmetry,[status(thm)],[132]) ).
tff(134,plain,
mult(x1,x0) = mult(x1,add(unit,add(x0,mult(x0,x0)))),
inference(symmetry,[status(thm)],[20]) ).
tff(135,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,B) = mult(B,A) )
| ( mult(unit,add(x1,mult(x1,x1))) = mult(add(x1,mult(x1,x1)),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(136,plain,
mult(unit,add(x1,mult(x1,x1))) = mult(add(x1,mult(x1,x1)),unit),
inference(unit_resolution,[status(thm)],[135,7]) ).
tff(137,plain,
add(x1,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))) = add(x1,mult(x1,x1)),
inference(monotonicity,[status(thm)],[62]) ).
tff(138,plain,
add(x1,mult(x1,x1)) = add(x1,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
mult(unit,add(x1,mult(x1,x1))) = mult(unit,add(x1,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))),
inference(monotonicity,[status(thm)],[138]) ).
tff(140,plain,
mult(unit,add(x1,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = mult(unit,add(x1,mult(x1,x1))),
inference(symmetry,[status(thm)],[139]) ).
tff(141,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(unit,add(x1,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = add(mult(unit,x1),mult(unit,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(142,plain,
mult(unit,add(x1,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = add(mult(unit,x1),mult(unit,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))),
inference(unit_resolution,[status(thm)],[141,27]) ).
tff(143,plain,
add(mult(unit,x1),mult(unit,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = mult(unit,add(x1,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,B) = mult(B,A) )
| ( mult(x1,unit) = mult(unit,x1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(145,plain,
mult(x1,unit) = mult(unit,x1),
inference(unit_resolution,[status(thm)],[144,7]) ).
tff(146,plain,
mult(unit,x1) = mult(x1,unit),
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
mult(unit,x1) = x1,
inference(transitivity,[status(thm)],[146,39]) ).
tff(148,plain,
add(mult(unit,unit),mult(unit,x1)) = add(unit,x1),
inference(monotonicity,[status(thm)],[114,147]) ).
tff(149,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(unit,add(unit,x1)) = add(mult(unit,unit),mult(unit,x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(150,plain,
mult(unit,add(unit,x1)) = add(mult(unit,unit),mult(unit,x1)),
inference(unit_resolution,[status(thm)],[149,27]) ).
tff(151,plain,
mult(unit,add(unit,x1)) = add(x1,unit),
inference(transitivity,[status(thm)],[150,148,80]) ).
tff(152,plain,
add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),mult(unit,add(unit,x1))) = add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(x1,unit)),
inference(monotonicity,[status(thm)],[151]) ).
tff(153,plain,
add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(x1,unit)) = add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),mult(unit,add(unit,x1))),
inference(symmetry,[status(thm)],[152]) ).
tff(154,plain,
add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(x1,unit)) = add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(unit,x1)),
inference(monotonicity,[status(thm)],[81]) ).
tff(155,plain,
add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(unit,x1)) = add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(x1,unit)),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(unit,x1)) = add(add(unit,x1),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(157,plain,
add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(unit,x1)) = add(add(unit,x1),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),
inference(unit_resolution,[status(thm)],[156,78]) ).
tff(158,plain,
add(add(unit,x1),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))) = add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(unit,x1)),
inference(symmetry,[status(thm)],[157]) ).
tff(159,plain,
add(add(unit,x1),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))) = add(add(unit,x1),mult(x1,x1)),
inference(monotonicity,[status(thm)],[62]) ).
tff(160,plain,
add(add(unit,x1),mult(x1,x1)) = add(add(unit,x1),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
mult(unit,x1) = add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),mult(unit,add(unit,x1))),
inference(transitivity,[status(thm)],[146,39,88,70,160,158,155,153]) ).
tff(162,plain,
add(mult(unit,x1),mult(unit,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),mult(unit,add(unit,x1))),mult(unit,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))),
inference(monotonicity,[status(thm)],[161]) ).
tff(163,plain,
add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),mult(unit,add(unit,x1))),mult(unit,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = add(mult(unit,x1),mult(unit,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))),
inference(symmetry,[status(thm)],[162]) ).
tff(164,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(mult(unit,add(unit,x1)),mult(unit,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))))) = add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),mult(unit,add(unit,x1))),mult(unit,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(165,plain,
add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(mult(unit,add(unit,x1)),mult(unit,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))))) = add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),mult(unit,add(unit,x1))),mult(unit,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))),
inference(unit_resolution,[status(thm)],[164,50]) ).
tff(166,plain,
add(add(unit,x1),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))) = x1,
inference(transitivity,[status(thm)],[159,71,42]) ).
tff(167,plain,
mult(unit,add(add(unit,x1),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = mult(unit,x1),
inference(monotonicity,[status(thm)],[166]) ).
tff(168,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(unit,add(add(unit,x1),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = add(mult(unit,add(unit,x1)),mult(unit,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(169,plain,
mult(unit,add(add(unit,x1),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = add(mult(unit,add(unit,x1)),mult(unit,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))),
inference(unit_resolution,[status(thm)],[168,27]) ).
tff(170,plain,
add(mult(unit,add(unit,x1)),mult(unit,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = mult(unit,add(add(unit,x1),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))),
inference(symmetry,[status(thm)],[169]) ).
tff(171,plain,
add(mult(unit,add(unit,x1)),mult(unit,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = x1,
inference(transitivity,[status(thm)],[170,167,146,39]) ).
tff(172,plain,
add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(mult(unit,add(unit,x1)),mult(unit,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))))) = add(mult(x1,x1),x1),
inference(monotonicity,[status(thm)],[62,171]) ).
tff(173,plain,
add(mult(x1,x1),x1) = add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(mult(unit,add(unit,x1)),mult(unit,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))))),
inference(symmetry,[status(thm)],[172]) ).
tff(174,plain,
add(x1,mult(x1,x1)) = mult(add(x1,mult(x1,x1)),unit),
inference(transitivity,[status(thm)],[105,173,165,163,143,140,136]) ).
tff(175,plain,
add(add(x1,mult(x1,x1)),mult(add(x1,mult(x1,x1)),add(x1,mult(x1,x1)))) = add(mult(add(x1,mult(x1,x1)),unit),mult(add(x1,mult(x1,x1)),add(x1,mult(x1,x1)))),
inference(monotonicity,[status(thm)],[174]) ).
tff(176,plain,
add(mult(add(x1,mult(x1,x1)),unit),mult(add(x1,mult(x1,x1)),add(x1,mult(x1,x1)))) = add(add(x1,mult(x1,x1)),mult(add(x1,mult(x1,x1)),add(x1,mult(x1,x1)))),
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(add(x1,mult(x1,x1)),add(unit,add(x1,mult(x1,x1)))) = add(mult(add(x1,mult(x1,x1)),unit),mult(add(x1,mult(x1,x1)),add(x1,mult(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(178,plain,
mult(add(x1,mult(x1,x1)),add(unit,add(x1,mult(x1,x1)))) = add(mult(add(x1,mult(x1,x1)),unit),mult(add(x1,mult(x1,x1)),add(x1,mult(x1,x1)))),
inference(unit_resolution,[status(thm)],[177,27]) ).
tff(179,plain,
mult(add(x1,mult(x1,x1)),add(unit,add(x1,mult(x1,x1)))) = mult(add(x1,mult(x1,x1)),x1),
inference(monotonicity,[status(thm)],[42]) ).
tff(180,plain,
mult(add(x1,mult(x1,x1)),x1) = mult(add(x1,mult(x1,x1)),add(unit,add(x1,mult(x1,x1)))),
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,B) = mult(B,A) )
| ( mult(x1,add(x1,mult(x1,x1))) = mult(add(x1,mult(x1,x1)),x1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(182,plain,
mult(x1,add(x1,mult(x1,x1))) = mult(add(x1,mult(x1,x1)),x1),
inference(unit_resolution,[status(thm)],[181,7]) ).
tff(183,plain,
mult(x1,add(x1,mult(x1,x1))) = mult(x1,add(x1,unit)),
inference(monotonicity,[status(thm)],[129]) ).
tff(184,plain,
mult(x1,add(x1,unit)) = mult(x1,add(x1,mult(x1,x1))),
inference(symmetry,[status(thm)],[183]) ).
tff(185,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(x1,add(x1,unit)) = add(mult(x1,x1),mult(x1,unit)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(186,plain,
mult(x1,add(x1,unit)) = add(mult(x1,x1),mult(x1,unit)),
inference(unit_resolution,[status(thm)],[185,27]) ).
tff(187,plain,
add(mult(x1,x1),mult(x1,unit)) = mult(x1,add(x1,unit)),
inference(symmetry,[status(thm)],[186]) ).
tff(188,plain,
add(mult(x1,x1),mult(x1,unit)) = add(mult(x1,x1),x1),
inference(monotonicity,[status(thm)],[39]) ).
tff(189,plain,
add(mult(x1,x1),x1) = add(mult(x1,x1),mult(x1,unit)),
inference(symmetry,[status(thm)],[188]) ).
tff(190,plain,
add(x1,mult(x1,x1)) = add(add(x1,mult(x1,x1)),mult(add(x1,mult(x1,x1)),add(x1,mult(x1,x1)))),
inference(transitivity,[status(thm)],[105,189,187,184,182,180,178,176]) ).
tff(191,plain,
add(unit,add(x1,mult(x1,x1))) = add(unit,add(add(x1,mult(x1,x1)),mult(add(x1,mult(x1,x1)),add(x1,mult(x1,x1))))),
inference(monotonicity,[status(thm)],[190]) ).
tff(192,plain,
add(unit,add(add(x1,mult(x1,x1)),mult(add(x1,mult(x1,x1)),add(x1,mult(x1,x1))))) = add(unit,add(x1,mult(x1,x1))),
inference(symmetry,[status(thm)],[191]) ).
tff(193,plain,
( ~ ! [A: $i] : ( add(unit,add(A,mult(A,A))) = A )
| ( add(unit,add(add(x1,mult(x1,x1)),mult(add(x1,mult(x1,x1)),add(x1,mult(x1,x1))))) = add(x1,mult(x1,x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(194,plain,
add(unit,add(add(x1,mult(x1,x1)),mult(add(x1,mult(x1,x1)),add(x1,mult(x1,x1))))) = add(x1,mult(x1,x1)),
inference(unit_resolution,[status(thm)],[193,17]) ).
tff(195,plain,
add(x1,mult(x1,x1)) = add(unit,add(add(x1,mult(x1,x1)),mult(add(x1,mult(x1,x1)),add(x1,mult(x1,x1))))),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
add(x1,mult(x1,x1)) = x1,
inference(transitivity,[status(thm)],[195,192,42]) ).
tff(197,plain,
mult(x0,add(x1,mult(x1,x1))) = mult(x0,x1),
inference(monotonicity,[status(thm)],[196]) ).
tff(198,plain,
add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(x1,mult(x1,x1))),unit) = add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(add(x1,mult(x1,x1)),unit)),
inference(symmetry,[status(thm)],[125]) ).
tff(199,plain,
add(add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),unit),add(unit,unit)) = add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),add(unit,add(unit,unit))),
inference(symmetry,[status(thm)],[110]) ).
tff(200,plain,
add(add(add(x1,mult(x1,x1)),unit),unit) = add(add(x1,mult(x1,x1)),add(unit,unit)),
inference(symmetry,[status(thm)],[93]) ).
tff(201,plain,
add(unit,x1) = add(x1,mult(x1,x1)),
inference(transitivity,[status(thm)],[80,90,200,107,199,122,198,127,104]) ).
tff(202,plain,
mult(x0,add(unit,x1)) = mult(x0,add(x1,mult(x1,x1))),
inference(monotonicity,[status(thm)],[201]) ).
tff(203,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(x0,add(unit,x1)) = add(mult(x0,unit),mult(x0,x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(204,plain,
mult(x0,add(unit,x1)) = add(mult(x0,unit),mult(x0,x1)),
inference(unit_resolution,[status(thm)],[203,27]) ).
tff(205,plain,
add(mult(x0,unit),mult(x0,x1)) = mult(x0,add(unit,x1)),
inference(symmetry,[status(thm)],[204]) ).
tff(206,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(x0,unit) = x0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(207,plain,
mult(x0,unit) = x0,
inference(unit_resolution,[status(thm)],[206,37]) ).
tff(208,plain,
x0 = mult(x0,unit),
inference(symmetry,[status(thm)],[207]) ).
tff(209,plain,
add(x0,mult(x1,x0)) = add(mult(x0,unit),mult(x0,x1)),
inference(monotonicity,[status(thm)],[208,10]) ).
tff(210,plain,
add(x1,mult(x1,add(x0,mult(x0,x0)))) = add(mult(x1,unit),mult(x1,add(x0,mult(x0,x0)))),
inference(monotonicity,[status(thm)],[40]) ).
tff(211,plain,
add(x1,mult(x1,add(x0,mult(x0,x0)))) = mult(x1,x0),
inference(transitivity,[status(thm)],[210,30,20]) ).
tff(212,plain,
add(x0,add(x1,mult(x1,add(x0,mult(x0,x0))))) = add(x0,mult(x1,x0)),
inference(monotonicity,[status(thm)],[211]) ).
tff(213,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(x0,add(x1,mult(x1,add(x0,mult(x0,x0))))) = add(add(x0,x1),mult(x1,add(x0,mult(x0,x0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(214,plain,
add(x0,add(x1,mult(x1,add(x0,mult(x0,x0))))) = add(add(x0,x1),mult(x1,add(x0,mult(x0,x0)))),
inference(unit_resolution,[status(thm)],[213,50]) ).
tff(215,plain,
add(add(x0,x1),mult(x1,add(x0,mult(x0,x0)))) = add(x0,add(x1,mult(x1,add(x0,mult(x0,x0))))),
inference(symmetry,[status(thm)],[214]) ).
tff(216,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,B) = mult(B,A) )
| ( mult(x1,add(x0,mult(x0,x0))) = mult(add(x0,mult(x0,x0)),x1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(217,plain,
mult(x1,add(x0,mult(x0,x0))) = mult(add(x0,mult(x0,x0)),x1),
inference(unit_resolution,[status(thm)],[216,7]) ).
tff(218,plain,
mult(add(x0,mult(x0,x0)),x1) = mult(x1,add(x0,mult(x0,x0))),
inference(symmetry,[status(thm)],[217]) ).
tff(219,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(x1,x0) = add(x0,x1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(220,plain,
add(x1,x0) = add(x0,x1),
inference(unit_resolution,[status(thm)],[219,78]) ).
tff(221,plain,
add(x1,add(unit,add(x0,mult(x0,x0)))) = add(x1,x0),
inference(monotonicity,[status(thm)],[19]) ).
tff(222,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(x1,add(unit,add(x0,mult(x0,x0)))) = add(add(x1,unit),add(x0,mult(x0,x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(223,plain,
add(x1,add(unit,add(x0,mult(x0,x0)))) = add(add(x1,unit),add(x0,mult(x0,x0))),
inference(unit_resolution,[status(thm)],[222,50]) ).
tff(224,plain,
add(add(x1,unit),add(x0,mult(x0,x0))) = add(x1,add(unit,add(x0,mult(x0,x0)))),
inference(symmetry,[status(thm)],[223]) ).
tff(225,plain,
add(add(x1,mult(x1,x1)),add(x0,mult(x0,x0))) = add(add(x1,unit),add(x0,mult(x0,x0))),
inference(monotonicity,[status(thm)],[129]) ).
tff(226,plain,
add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit),add(x1,mult(x1,x1))) = add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(unit,add(x1,mult(x1,x1)))),
inference(symmetry,[status(thm)],[100]) ).
tff(227,plain,
add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),unit) = add(add(x1,mult(x1,x1)),add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit)),
inference(symmetry,[status(thm)],[95]) ).
tff(228,plain,
add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),unit) = add(x1,mult(x1,x1)),
inference(transitivity,[status(thm)],[227,97,226,101,104]) ).
tff(229,plain,
add(add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),unit),add(x0,mult(x0,x0))) = add(add(x1,mult(x1,x1)),add(x0,mult(x0,x0))),
inference(monotonicity,[status(thm)],[228]) ).
tff(230,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),add(unit,add(x0,mult(x0,x0)))) = add(add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),unit),add(x0,mult(x0,x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(231,plain,
add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),add(unit,add(x0,mult(x0,x0)))) = add(add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),unit),add(x0,mult(x0,x0))),
inference(unit_resolution,[status(thm)],[230,50]) ).
tff(232,plain,
x0 = add(unit,add(x0,mult(x0,x0))),
inference(symmetry,[status(thm)],[19]) ).
tff(233,plain,
add(add(x1,mult(x1,x1)),mult(x1,x1)) = add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),
inference(symmetry,[status(thm)],[63]) ).
tff(234,plain,
add(add(add(x1,mult(x1,x1)),mult(x1,x1)),x0) = add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),add(unit,add(x0,mult(x0,x0)))),
inference(monotonicity,[status(thm)],[233,232]) ).
tff(235,plain,
add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),x0) = add(add(add(x1,mult(x1,x1)),mult(x1,x1)),x0),
inference(monotonicity,[status(thm)],[63]) ).
tff(236,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(add(x1,mult(x1,x1)),add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),x0)) = add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(237,plain,
add(add(x1,mult(x1,x1)),add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),x0)) = add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),x0),
inference(unit_resolution,[status(thm)],[236,50]) ).
tff(238,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(zero,x0) = add(x0,zero) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(239,plain,
add(zero,x0) = add(x0,zero),
inference(unit_resolution,[status(thm)],[238,78]) ).
tff(240,plain,
^ [A: $i] :
refl(
( ( add(zero,A) = A )
<=> ( add(zero,A) = A ) )),
inference(bind,[status(th)],]) ).
tff(241,plain,
( ! [A: $i] : ( add(zero,A) = A )
<=> ! [A: $i] : ( add(zero,A) = A ) ),
inference(quant_intro,[status(thm)],[240]) ).
tff(242,plain,
( ! [A: $i] : ( add(zero,A) = A )
<=> ! [A: $i] : ( add(zero,A) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(243,axiom,
! [A: $i] : ( add(zero,A) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_004) ).
tff(244,plain,
! [A: $i] : ( add(zero,A) = A ),
inference(modus_ponens,[status(thm)],[243,242]) ).
tff(245,plain,
! [A: $i] : ( add(zero,A) = A ),
inference(skolemize,[status(sab)],[244]) ).
tff(246,plain,
! [A: $i] : ( add(zero,A) = A ),
inference(modus_ponens,[status(thm)],[245,241]) ).
tff(247,plain,
( ~ ! [A: $i] : ( add(zero,A) = A )
| ( add(zero,x0) = x0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(248,plain,
add(zero,x0) = x0,
inference(unit_resolution,[status(thm)],[247,246]) ).
tff(249,plain,
x0 = add(zero,x0),
inference(symmetry,[status(thm)],[248]) ).
tff(250,plain,
x0 = add(x0,zero),
inference(transitivity,[status(thm)],[249,239]) ).
tff(251,plain,
add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),x0) = add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(x0,zero)),
inference(monotonicity,[status(thm)],[250]) ).
tff(252,plain,
add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(x0,zero)) = add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),x0),
inference(symmetry,[status(thm)],[251]) ).
tff(253,plain,
add(x0,zero) = add(zero,x0),
inference(symmetry,[status(thm)],[239]) ).
tff(254,plain,
add(x0,zero) = x0,
inference(transitivity,[status(thm)],[253,248]) ).
tff(255,plain,
mult(add(x1,mult(x1,x1)),x1) = mult(x1,add(x1,mult(x1,x1))),
inference(symmetry,[status(thm)],[182]) ).
tff(256,plain,
add(mult(add(x1,mult(x1,x1)),x1),x1) = add(mult(x1,add(x1,mult(x1,x1))),x1),
inference(monotonicity,[status(thm)],[255]) ).
tff(257,plain,
add(mult(x1,add(x1,mult(x1,x1))),x1) = add(mult(add(x1,mult(x1,x1)),x1),x1),
inference(symmetry,[status(thm)],[256]) ).
tff(258,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(mult(x1,add(x1,mult(x1,x1))),x1) = add(x1,mult(x1,add(x1,mult(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(259,plain,
add(mult(x1,add(x1,mult(x1,x1))),x1) = add(x1,mult(x1,add(x1,mult(x1,x1)))),
inference(unit_resolution,[status(thm)],[258,78]) ).
tff(260,plain,
add(x1,mult(x1,add(x1,mult(x1,x1)))) = add(mult(x1,add(x1,mult(x1,x1))),x1),
inference(symmetry,[status(thm)],[259]) ).
tff(261,plain,
add(x1,mult(x1,add(x1,mult(x1,x1)))) = add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),
inference(monotonicity,[status(thm)],[40]) ).
tff(262,plain,
add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))) = add(x1,mult(x1,add(x1,mult(x1,x1)))),
inference(symmetry,[status(thm)],[261]) ).
tff(263,plain,
add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))) = add(mult(add(x1,mult(x1,x1)),x1),x1),
inference(transitivity,[status(thm)],[262,260,257]) ).
tff(264,plain,
add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(x0,zero)) = add(add(mult(add(x1,mult(x1,x1)),x1),x1),x0),
inference(monotonicity,[status(thm)],[263,254]) ).
tff(265,plain,
add(add(mult(add(x1,mult(x1,x1)),x1),x1),x0) = add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(x0,zero)),
inference(symmetry,[status(thm)],[264]) ).
tff(266,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(mult(add(x1,mult(x1,x1)),x1),add(x1,x0)) = add(add(mult(add(x1,mult(x1,x1)),x1),x1),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(267,plain,
add(mult(add(x1,mult(x1,x1)),x1),add(x1,x0)) = add(add(mult(add(x1,mult(x1,x1)),x1),x1),x0),
inference(unit_resolution,[status(thm)],[266,50]) ).
tff(268,plain,
add(mult(add(x1,mult(x1,x1)),x1),add(x1,x0)) = add(mult(add(x1,mult(x1,x1)),x1),add(x0,x1)),
inference(monotonicity,[status(thm)],[220]) ).
tff(269,plain,
add(mult(add(x1,mult(x1,x1)),x1),add(x0,x1)) = add(mult(add(x1,mult(x1,x1)),x1),add(x1,x0)),
inference(symmetry,[status(thm)],[268]) ).
tff(270,plain,
mult(add(x1,mult(x1,x1)),x1) = add(x1,mult(x1,x1)),
inference(transitivity,[status(thm)],[255,183,186,188,104]) ).
tff(271,plain,
add(mult(add(x1,mult(x1,x1)),x1),add(x0,x1)) = add(add(x1,mult(x1,x1)),add(x0,x1)),
inference(monotonicity,[status(thm)],[270]) ).
tff(272,plain,
add(add(x1,mult(x1,x1)),add(x0,x1)) = add(mult(add(x1,mult(x1,x1)),x1),add(x0,x1)),
inference(symmetry,[status(thm)],[271]) ).
tff(273,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(add(x0,x1),add(x1,mult(x1,x1))) = add(add(x1,mult(x1,x1)),add(x0,x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(274,plain,
add(add(x0,x1),add(x1,mult(x1,x1))) = add(add(x1,mult(x1,x1)),add(x0,x1)),
inference(unit_resolution,[status(thm)],[273,78]) ).
tff(275,plain,
add(add(x0,x1),add(x1,mult(x1,x1))) = add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),x0),
inference(transitivity,[status(thm)],[274,272,269,267,265,252]) ).
tff(276,plain,
add(add(x1,mult(x1,x1)),add(add(x0,x1),add(x1,mult(x1,x1)))) = add(add(x1,mult(x1,x1)),add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),x0)),
inference(monotonicity,[status(thm)],[275]) ).
tff(277,plain,
add(add(x1,mult(x1,x1)),add(add(x0,x1),add(x1,mult(x1,x1)))) = add(x0,x1),
inference(transitivity,[status(thm)],[276,237,235,234,231,229,225,224,221,220]) ).
tff(278,plain,
add(add(add(x1,mult(x1,x1)),add(add(x0,x1),add(x1,mult(x1,x1)))),mult(add(x0,mult(x0,x0)),x1)) = add(add(x0,x1),mult(x1,add(x0,mult(x0,x0)))),
inference(monotonicity,[status(thm)],[277,218]) ).
tff(279,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(add(x1,mult(x1,x1)),add(add(add(x0,x1),add(x1,mult(x1,x1))),mult(add(x0,mult(x0,x0)),x1))) = add(add(add(x1,mult(x1,x1)),add(add(x0,x1),add(x1,mult(x1,x1)))),mult(add(x0,mult(x0,x0)),x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(280,plain,
add(add(x1,mult(x1,x1)),add(add(add(x0,x1),add(x1,mult(x1,x1))),mult(add(x0,mult(x0,x0)),x1))) = add(add(add(x1,mult(x1,x1)),add(add(x0,x1),add(x1,mult(x1,x1)))),mult(add(x0,mult(x0,x0)),x1)),
inference(unit_resolution,[status(thm)],[279,50]) ).
tff(281,plain,
x1 = add(x1,mult(x1,x1)),
inference(transitivity,[status(thm)],[88,191,194]) ).
tff(282,plain,
add(x1,add(add(add(x0,x1),add(x1,mult(x1,x1))),mult(add(x0,mult(x0,x0)),x1))) = add(add(x1,mult(x1,x1)),add(add(add(x0,x1),add(x1,mult(x1,x1))),mult(add(x0,mult(x0,x0)),x1))),
inference(monotonicity,[status(thm)],[281]) ).
tff(283,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(x1,add(add(add(x0,x1),add(x1,mult(x1,x1))),mult(add(x0,mult(x0,x0)),x1))) = add(add(x1,add(add(x0,x1),add(x1,mult(x1,x1)))),mult(add(x0,mult(x0,x0)),x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(284,plain,
add(x1,add(add(add(x0,x1),add(x1,mult(x1,x1))),mult(add(x0,mult(x0,x0)),x1))) = add(add(x1,add(add(x0,x1),add(x1,mult(x1,x1)))),mult(add(x0,mult(x0,x0)),x1)),
inference(unit_resolution,[status(thm)],[283,50]) ).
tff(285,plain,
add(add(x1,add(add(x0,x1),add(x1,mult(x1,x1)))),mult(add(x0,mult(x0,x0)),x1)) = add(x1,add(add(add(x0,x1),add(x1,mult(x1,x1))),mult(add(x0,mult(x0,x0)),x1))),
inference(symmetry,[status(thm)],[284]) ).
tff(286,plain,
add(x1,add(add(x0,x1),add(x1,mult(x1,x1)))) = add(x1,add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),x0)),
inference(monotonicity,[status(thm)],[275]) ).
tff(287,plain,
add(x1,add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),x0)) = add(x1,add(add(x0,x1),add(x1,mult(x1,x1)))),
inference(symmetry,[status(thm)],[286]) ).
tff(288,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(x1,add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),x0)) = add(add(x1,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(289,plain,
add(x1,add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),x0)) = add(add(x1,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),x0),
inference(unit_resolution,[status(thm)],[288,50]) ).
tff(290,plain,
add(add(x1,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),x0) = add(x1,add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),x0)),
inference(symmetry,[status(thm)],[289]) ).
tff(291,plain,
add(add(x1,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),x0) = add(add(x1,mult(x1,x1)),x0),
inference(monotonicity,[status(thm)],[137]) ).
tff(292,plain,
add(add(x1,mult(x1,x1)),x0) = add(add(x1,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),x0),
inference(symmetry,[status(thm)],[291]) ).
tff(293,plain,
add(add(x1,mult(x1,x1)),add(unit,add(x0,mult(x0,x0)))) = add(add(x1,mult(x1,x1)),x0),
inference(monotonicity,[status(thm)],[19]) ).
tff(294,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(add(x1,mult(x1,x1)),add(unit,add(x0,mult(x0,x0)))) = add(add(add(x1,mult(x1,x1)),unit),add(x0,mult(x0,x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(295,plain,
add(add(x1,mult(x1,x1)),add(unit,add(x0,mult(x0,x0)))) = add(add(add(x1,mult(x1,x1)),unit),add(x0,mult(x0,x0))),
inference(unit_resolution,[status(thm)],[294,50]) ).
tff(296,plain,
add(add(add(x1,mult(x1,x1)),unit),add(x0,mult(x0,x0))) = add(add(x1,mult(x1,x1)),add(unit,add(x0,mult(x0,x0)))),
inference(symmetry,[status(thm)],[295]) ).
tff(297,plain,
add(x1,add(x0,mult(x0,x0))) = add(add(add(x1,mult(x1,x1)),unit),add(x0,mult(x0,x0))),
inference(monotonicity,[status(thm)],[89]) ).
tff(298,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(add(x0,mult(x0,x0)),x1) = add(x1,add(x0,mult(x0,x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(299,plain,
add(add(x0,mult(x0,x0)),x1) = add(x1,add(x0,mult(x0,x0))),
inference(unit_resolution,[status(thm)],[298,78]) ).
tff(300,plain,
add(add(x0,mult(x0,x0)),x1) = add(x1,add(add(x0,x1),add(x1,mult(x1,x1)))),
inference(transitivity,[status(thm)],[299,297,296,293,292,290,287]) ).
tff(301,plain,
add(add(add(x0,mult(x0,x0)),x1),mult(x1,add(x0,mult(x0,x0)))) = add(add(x1,add(add(x0,x1),add(x1,mult(x1,x1)))),mult(add(x0,mult(x0,x0)),x1)),
inference(monotonicity,[status(thm)],[300,217]) ).
tff(302,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(add(x0,mult(x0,x0)),add(x1,mult(x1,add(x0,mult(x0,x0))))) = add(add(add(x0,mult(x0,x0)),x1),mult(x1,add(x0,mult(x0,x0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(303,plain,
add(add(x0,mult(x0,x0)),add(x1,mult(x1,add(x0,mult(x0,x0))))) = add(add(add(x0,mult(x0,x0)),x1),mult(x1,add(x0,mult(x0,x0)))),
inference(unit_resolution,[status(thm)],[302,50]) ).
tff(304,plain,
add(mult(x1,unit),mult(x1,add(x0,mult(x0,x0)))) = add(x1,mult(x1,add(x0,mult(x0,x0)))),
inference(symmetry,[status(thm)],[210]) ).
tff(305,plain,
mult(x1,x0) = add(x1,mult(x1,add(x0,mult(x0,x0)))),
inference(transitivity,[status(thm)],[134,29,304]) ).
tff(306,plain,
add(add(x0,mult(x0,x0)),mult(x1,x0)) = add(add(x0,mult(x0,x0)),add(x1,mult(x1,add(x0,mult(x0,x0))))),
inference(monotonicity,[status(thm)],[305]) ).
tff(307,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(mult(x0,x0),x0) = add(x0,mult(x0,x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(308,plain,
add(mult(x0,x0),x0) = add(x0,mult(x0,x0)),
inference(unit_resolution,[status(thm)],[307,78]) ).
tff(309,plain,
mult(x0,add(unit,add(x0,mult(x0,x0)))) = mult(x0,x0),
inference(monotonicity,[status(thm)],[19]) ).
tff(310,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(x0,add(unit,add(x0,mult(x0,x0)))) = add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(311,plain,
mult(x0,add(unit,add(x0,mult(x0,x0)))) = add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))),
inference(unit_resolution,[status(thm)],[310,27]) ).
tff(312,plain,
add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))) = mult(x0,add(unit,add(x0,mult(x0,x0)))),
inference(symmetry,[status(thm)],[311]) ).
tff(313,plain,
add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))) = mult(x0,x0),
inference(transitivity,[status(thm)],[312,309]) ).
tff(314,plain,
add(add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))),x0) = add(mult(x0,x0),x0),
inference(monotonicity,[status(thm)],[313]) ).
tff(315,plain,
add(add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))),x0) = add(x0,mult(x0,x0)),
inference(transitivity,[status(thm)],[314,308]) ).
tff(316,plain,
add(add(add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))),x0),mult(x1,x0)) = add(add(x0,mult(x0,x0)),mult(x1,x0)),
inference(monotonicity,[status(thm)],[315]) ).
tff(317,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))),add(x0,mult(x1,x0))) = add(add(add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))),x0),mult(x1,x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(318,plain,
add(add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))),add(x0,mult(x1,x0))) = add(add(add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))),x0),mult(x1,x0)),
inference(unit_resolution,[status(thm)],[317,50]) ).
tff(319,plain,
add(mult(x0,unit),mult(x0,x1)) = add(x0,mult(x1,x0)),
inference(symmetry,[status(thm)],[209]) ).
tff(320,plain,
mult(x0,add(x1,mult(x1,x1))) = mult(x0,add(unit,x1)),
inference(symmetry,[status(thm)],[202]) ).
tff(321,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,B) = mult(B,A) )
| ( mult(x0,add(x1,mult(x1,x1))) = mult(add(x1,mult(x1,x1)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(322,plain,
mult(x0,add(x1,mult(x1,x1))) = mult(add(x1,mult(x1,x1)),x0),
inference(unit_resolution,[status(thm)],[321,7]) ).
tff(323,plain,
mult(add(x1,mult(x1,x1)),x0) = mult(x0,add(x1,mult(x1,x1))),
inference(symmetry,[status(thm)],[322]) ).
tff(324,plain,
mult(add(x1,mult(x1,x1)),x0) = add(x0,mult(x1,x0)),
inference(transitivity,[status(thm)],[323,320,204,319]) ).
tff(325,plain,
add(add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))),mult(add(x1,mult(x1,x1)),x0)) = add(add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))),add(x0,mult(x1,x0))),
inference(monotonicity,[status(thm)],[324]) ).
tff(326,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))),mult(add(x1,mult(x1,x1)),x0)) = add(mult(add(x1,mult(x1,x1)),x0),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(327,plain,
add(add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))),mult(add(x1,mult(x1,x1)),x0)) = add(mult(add(x1,mult(x1,x1)),x0),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))),
inference(unit_resolution,[status(thm)],[326,78]) ).
tff(328,plain,
add(mult(add(x1,mult(x1,x1)),x0),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))) = add(add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))),mult(add(x1,mult(x1,x1)),x0)),
inference(symmetry,[status(thm)],[327]) ).
tff(329,plain,
mult(x0,x0) = mult(x0,add(unit,add(x0,mult(x0,x0)))),
inference(symmetry,[status(thm)],[309]) ).
tff(330,plain,
mult(x0,x0) = add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))),
inference(transitivity,[status(thm)],[329,311]) ).
tff(331,plain,
add(mult(x0,add(x1,mult(x1,x1))),mult(x0,x0)) = add(mult(add(x1,mult(x1,x1)),x0),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))),
inference(monotonicity,[status(thm)],[322,330]) ).
tff(332,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(x0,add(add(x1,mult(x1,x1)),x0)) = add(mult(x0,add(x1,mult(x1,x1))),mult(x0,x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(333,plain,
mult(x0,add(add(x1,mult(x1,x1)),x0)) = add(mult(x0,add(x1,mult(x1,x1))),mult(x0,x0)),
inference(unit_resolution,[status(thm)],[332,27]) ).
tff(334,plain,
add(x1,add(x0,mult(x0,x0))) = add(add(x1,mult(x1,x1)),x0),
inference(transitivity,[status(thm)],[297,296,293]) ).
tff(335,plain,
mult(x0,add(x1,add(x0,mult(x0,x0)))) = mult(x0,add(add(x1,mult(x1,x1)),x0)),
inference(monotonicity,[status(thm)],[334]) ).
tff(336,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(x0,add(x1,add(x0,mult(x0,x0)))) = add(mult(x0,x1),mult(x0,add(x0,mult(x0,x0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(337,plain,
mult(x0,add(x1,add(x0,mult(x0,x0)))) = add(mult(x0,x1),mult(x0,add(x0,mult(x0,x0)))),
inference(unit_resolution,[status(thm)],[336,27]) ).
tff(338,plain,
add(mult(x0,x1),mult(x0,add(x0,mult(x0,x0)))) = mult(x0,add(x1,add(x0,mult(x0,x0)))),
inference(symmetry,[status(thm)],[337]) ).
tff(339,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,B) = mult(B,A) )
| ( mult(x0,add(x0,mult(x0,x0))) = mult(add(x0,mult(x0,x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(340,plain,
mult(x0,add(x0,mult(x0,x0))) = mult(add(x0,mult(x0,x0)),x0),
inference(unit_resolution,[status(thm)],[339,7]) ).
tff(341,plain,
mult(add(x0,mult(x0,x0)),x0) = mult(x0,add(x0,mult(x0,x0))),
inference(symmetry,[status(thm)],[340]) ).
tff(342,plain,
add(x1,mult(add(x0,mult(x0,x0)),x1)) = add(mult(x1,unit),mult(x1,add(x0,mult(x0,x0)))),
inference(monotonicity,[status(thm)],[40,218]) ).
tff(343,plain,
add(x1,mult(add(x0,mult(x0,x0)),x1)) = mult(x0,x1),
inference(transitivity,[status(thm)],[342,30,20,10]) ).
tff(344,plain,
add(add(x1,mult(add(x0,mult(x0,x0)),x1)),mult(add(x0,mult(x0,x0)),x0)) = add(mult(x0,x1),mult(x0,add(x0,mult(x0,x0)))),
inference(monotonicity,[status(thm)],[343,341]) ).
tff(345,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(x1,add(mult(add(x0,mult(x0,x0)),x1),mult(add(x0,mult(x0,x0)),x0))) = add(add(x1,mult(add(x0,mult(x0,x0)),x1)),mult(add(x0,mult(x0,x0)),x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(346,plain,
add(x1,add(mult(add(x0,mult(x0,x0)),x1),mult(add(x0,mult(x0,x0)),x0))) = add(add(x1,mult(add(x0,mult(x0,x0)),x1)),mult(add(x0,mult(x0,x0)),x0)),
inference(unit_resolution,[status(thm)],[345,50]) ).
tff(347,plain,
mult(add(x0,mult(x0,x0)),add(x0,zero)) = mult(add(x0,mult(x0,x0)),x0),
inference(monotonicity,[status(thm)],[254]) ).
tff(348,plain,
mult(add(x0,mult(x0,x0)),x0) = mult(add(x0,mult(x0,x0)),add(x0,zero)),
inference(symmetry,[status(thm)],[347]) ).
tff(349,plain,
add(mult(add(x0,mult(x0,x0)),x1),mult(add(x0,mult(x0,x0)),x0)) = add(mult(add(x0,mult(x0,x0)),x1),mult(add(x0,mult(x0,x0)),add(x0,zero))),
inference(monotonicity,[status(thm)],[348]) ).
tff(350,plain,
add(mult(add(x0,mult(x0,x0)),x1),mult(add(x0,mult(x0,x0)),add(x0,zero))) = add(mult(add(x0,mult(x0,x0)),x1),mult(add(x0,mult(x0,x0)),x0)),
inference(symmetry,[status(thm)],[349]) ).
tff(351,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(add(x0,mult(x0,x0)),add(x1,add(x0,zero))) = add(mult(add(x0,mult(x0,x0)),x1),mult(add(x0,mult(x0,x0)),add(x0,zero))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(352,plain,
mult(add(x0,mult(x0,x0)),add(x1,add(x0,zero))) = add(mult(add(x0,mult(x0,x0)),x1),mult(add(x0,mult(x0,x0)),add(x0,zero))),
inference(unit_resolution,[status(thm)],[351,27]) ).
tff(353,plain,
( ~ ! [A: $i] : ( add(zero,A) = A )
| ( add(zero,x1) = x1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(354,plain,
add(zero,x1) = x1,
inference(unit_resolution,[status(thm)],[353,246]) ).
tff(355,plain,
add(x0,add(zero,x1)) = add(x0,x1),
inference(monotonicity,[status(thm)],[354]) ).
tff(356,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(x0,add(zero,x1)) = add(add(x0,zero),x1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(357,plain,
add(x0,add(zero,x1)) = add(add(x0,zero),x1),
inference(unit_resolution,[status(thm)],[356,50]) ).
tff(358,plain,
add(add(x0,zero),x1) = add(x0,add(zero,x1)),
inference(symmetry,[status(thm)],[357]) ).
tff(359,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(x1,add(x0,zero)) = add(add(x0,zero),x1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(360,plain,
add(x1,add(x0,zero)) = add(add(x0,zero),x1),
inference(unit_resolution,[status(thm)],[359,78]) ).
tff(361,plain,
add(x1,add(x0,zero)) = add(x0,x1),
inference(transitivity,[status(thm)],[360,358,355]) ).
tff(362,plain,
mult(add(x0,mult(x0,x0)),add(x1,add(x0,zero))) = mult(add(x0,mult(x0,x0)),add(x0,x1)),
inference(monotonicity,[status(thm)],[361]) ).
tff(363,plain,
mult(add(x0,mult(x0,x0)),add(x0,x1)) = mult(add(x0,mult(x0,x0)),add(x1,add(x0,zero))),
inference(symmetry,[status(thm)],[362]) ).
tff(364,plain,
mult(add(x0,mult(x0,x0)),add(x0,x1)) = add(mult(add(x0,mult(x0,x0)),x1),mult(add(x0,mult(x0,x0)),x0)),
inference(transitivity,[status(thm)],[363,352,350]) ).
tff(365,plain,
add(add(x1,mult(x1,x1)),mult(add(x0,mult(x0,x0)),add(x0,x1))) = add(x1,add(mult(add(x0,mult(x0,x0)),x1),mult(add(x0,mult(x0,x0)),x0))),
inference(monotonicity,[status(thm)],[196,364]) ).
tff(366,plain,
mult(add(x1,mult(x1,x1)),add(x1,mult(x1,x1))) = mult(x1,add(x1,mult(x1,x1))),
inference(monotonicity,[status(thm)],[196]) ).
tff(367,plain,
mult(add(x1,mult(x1,x1)),add(x1,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = mult(add(x1,mult(x1,x1)),add(x1,mult(x1,x1))),
inference(monotonicity,[status(thm)],[137]) ).
tff(368,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(add(x1,mult(x1,x1)),add(x1,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = add(mult(add(x1,mult(x1,x1)),x1),mult(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(369,plain,
mult(add(x1,mult(x1,x1)),add(x1,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = add(mult(add(x1,mult(x1,x1)),x1),mult(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))),
inference(unit_resolution,[status(thm)],[368,27]) ).
tff(370,plain,
add(mult(add(x1,mult(x1,x1)),x1),mult(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = mult(add(x1,mult(x1,x1)),add(x1,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))),
inference(symmetry,[status(thm)],[369]) ).
tff(371,plain,
add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),mult(unit,add(unit,x1))),mult(unit,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(mult(unit,add(unit,x1)),mult(unit,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))))),
inference(symmetry,[status(thm)],[165]) ).
tff(372,plain,
mult(add(x1,mult(x1,x1)),unit) = mult(unit,add(x1,mult(x1,x1))),
inference(symmetry,[status(thm)],[136]) ).
tff(373,plain,
mult(add(x1,mult(x1,x1)),unit) = mult(add(x1,mult(x1,x1)),x1),
inference(transitivity,[status(thm)],[372,139,142,162,371,172,189,187,184,182]) ).
tff(374,plain,
add(mult(add(x1,mult(x1,x1)),unit),mult(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = add(mult(add(x1,mult(x1,x1)),x1),mult(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))),
inference(monotonicity,[status(thm)],[373]) ).
tff(375,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(add(x1,mult(x1,x1)),add(unit,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = add(mult(add(x1,mult(x1,x1)),unit),mult(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(376,plain,
mult(add(x1,mult(x1,x1)),add(unit,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = add(mult(add(x1,mult(x1,x1)),unit),mult(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))),
inference(unit_resolution,[status(thm)],[375,27]) ).
tff(377,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(unit,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))) = add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(378,plain,
add(unit,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))) = add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit),
inference(unit_resolution,[status(thm)],[377,78]) ).
tff(379,plain,
add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit) = add(unit,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),
inference(symmetry,[status(thm)],[378]) ).
tff(380,plain,
mult(add(x1,mult(x1,x1)),add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit)) = mult(add(x1,mult(x1,x1)),add(unit,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))),
inference(monotonicity,[status(thm)],[379]) ).
tff(381,plain,
add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit) = add(add(mult(add(x1,mult(x1,x1)),x1),x1),unit),
inference(monotonicity,[status(thm)],[263]) ).
tff(382,plain,
add(add(mult(add(x1,mult(x1,x1)),x1),x1),unit) = add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit),
inference(symmetry,[status(thm)],[381]) ).
tff(383,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(mult(add(x1,mult(x1,x1)),x1),add(x1,unit)) = add(add(mult(add(x1,mult(x1,x1)),x1),x1),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(384,plain,
add(mult(add(x1,mult(x1,x1)),x1),add(x1,unit)) = add(add(mult(add(x1,mult(x1,x1)),x1),x1),unit),
inference(unit_resolution,[status(thm)],[383,50]) ).
tff(385,plain,
add(x1,unit) = add(x1,mult(x1,x1)),
inference(transitivity,[status(thm)],[90,200,107,199,122,198,127,104]) ).
tff(386,plain,
add(mult(add(x1,mult(x1,x1)),x1),add(x1,unit)) = add(mult(add(x1,mult(x1,x1)),x1),add(x1,mult(x1,x1))),
inference(monotonicity,[status(thm)],[385]) ).
tff(387,plain,
add(mult(add(x1,mult(x1,x1)),x1),add(x1,mult(x1,x1))) = add(mult(add(x1,mult(x1,x1)),x1),add(x1,unit)),
inference(symmetry,[status(thm)],[386]) ).
tff(388,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(mult(add(x1,mult(x1,x1)),x1),add(x1,mult(x1,x1))) = add(add(x1,mult(x1,x1)),mult(add(x1,mult(x1,x1)),x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(389,plain,
add(mult(add(x1,mult(x1,x1)),x1),add(x1,mult(x1,x1))) = add(add(x1,mult(x1,x1)),mult(add(x1,mult(x1,x1)),x1)),
inference(unit_resolution,[status(thm)],[388,78]) ).
tff(390,plain,
add(add(x1,mult(x1,x1)),mult(add(x1,mult(x1,x1)),x1)) = add(mult(add(x1,mult(x1,x1)),x1),add(x1,mult(x1,x1))),
inference(symmetry,[status(thm)],[389]) ).
tff(391,plain,
add(add(x1,mult(x1,x1)),mult(add(x1,mult(x1,x1)),x1)) = add(add(x1,mult(x1,x1)),mult(x1,add(x1,mult(x1,x1)))),
inference(monotonicity,[status(thm)],[255]) ).
tff(392,plain,
add(add(x1,mult(x1,x1)),mult(x1,add(x1,mult(x1,x1)))) = add(add(x1,mult(x1,x1)),mult(add(x1,mult(x1,x1)),x1)),
inference(symmetry,[status(thm)],[391]) ).
tff(393,plain,
mult(x1,add(x1,mult(x1,x1))) = add(x1,mult(x1,x1)),
inference(transitivity,[status(thm)],[183,186,188,104]) ).
tff(394,plain,
add(add(x1,mult(x1,x1)),mult(x1,add(x1,mult(x1,x1)))) = add(add(x1,mult(x1,x1)),add(x1,mult(x1,x1))),
inference(monotonicity,[status(thm)],[393]) ).
tff(395,plain,
add(add(x1,mult(x1,x1)),add(x1,mult(x1,x1))) = add(add(x1,mult(x1,x1)),mult(x1,add(x1,mult(x1,x1)))),
inference(symmetry,[status(thm)],[394]) ).
tff(396,plain,
add(add(x1,unit),add(x1,mult(x1,x1))) = add(add(x1,mult(x1,x1)),add(x1,mult(x1,x1))),
inference(monotonicity,[status(thm)],[385]) ).
tff(397,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(x1,add(unit,add(x1,mult(x1,x1)))) = add(add(x1,unit),add(x1,mult(x1,x1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(398,plain,
add(x1,add(unit,add(x1,mult(x1,x1)))) = add(add(x1,unit),add(x1,mult(x1,x1))),
inference(unit_resolution,[status(thm)],[397,50]) ).
tff(399,plain,
add(x1,x1) = add(x1,add(unit,add(x1,mult(x1,x1)))),
inference(monotonicity,[status(thm)],[88]) ).
tff(400,plain,
add(x1,x1) = add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit),
inference(transitivity,[status(thm)],[399,398,396,395,392,390,387,384,382]) ).
tff(401,plain,
mult(add(x1,unit),add(x1,x1)) = mult(add(x1,mult(x1,x1)),add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit)),
inference(monotonicity,[status(thm)],[385,400]) ).
tff(402,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(add(x1,unit),add(x1,x1)) = add(mult(add(x1,unit),x1),mult(add(x1,unit),x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(403,plain,
mult(add(x1,unit),add(x1,x1)) = add(mult(add(x1,unit),x1),mult(add(x1,unit),x1)),
inference(unit_resolution,[status(thm)],[402,27]) ).
tff(404,plain,
add(mult(add(x1,unit),x1),mult(add(x1,unit),x1)) = mult(add(x1,unit),add(x1,x1)),
inference(symmetry,[status(thm)],[403]) ).
tff(405,plain,
mult(add(x1,unit),x1) = mult(add(unit,x1),x1),
inference(monotonicity,[status(thm)],[81]) ).
tff(406,plain,
mult(add(unit,x1),x1) = mult(add(x1,unit),x1),
inference(symmetry,[status(thm)],[405]) ).
tff(407,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,B) = mult(B,A) )
| ( mult(x1,add(unit,x1)) = mult(add(unit,x1),x1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(408,plain,
mult(x1,add(unit,x1)) = mult(add(unit,x1),x1),
inference(unit_resolution,[status(thm)],[407,7]) ).
tff(409,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(x1,add(unit,x1)) = add(mult(x1,unit),mult(x1,x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(410,plain,
mult(x1,add(unit,x1)) = add(mult(x1,unit),mult(x1,x1)),
inference(unit_resolution,[status(thm)],[409,27]) ).
tff(411,plain,
add(mult(x1,unit),mult(x1,x1)) = mult(x1,add(unit,x1)),
inference(symmetry,[status(thm)],[410]) ).
tff(412,plain,
add(mult(x1,unit),mult(x1,x1)) = add(x1,mult(x1,x1)),
inference(monotonicity,[status(thm)],[39]) ).
tff(413,plain,
add(x1,mult(x1,x1)) = add(mult(x1,unit),mult(x1,x1)),
inference(symmetry,[status(thm)],[412]) ).
tff(414,plain,
add(x1,mult(x1,x1)) = mult(add(x1,unit),x1),
inference(transitivity,[status(thm)],[413,411,408,406]) ).
tff(415,plain,
add(add(x1,mult(x1,x1)),add(x1,mult(x1,x1))) = add(mult(add(x1,unit),x1),mult(add(x1,unit),x1)),
inference(monotonicity,[status(thm)],[414,414]) ).
tff(416,plain,
add(add(x1,unit),add(x1,mult(x1,x1))) = add(x1,mult(x1,x1)),
inference(transitivity,[status(thm)],[396,415,404,401,380,376,374,370,367,366,183,186,188,104]) ).
tff(417,plain,
add(add(add(x1,unit),add(x1,mult(x1,x1))),mult(add(x0,mult(x0,x0)),add(x0,x1))) = add(add(x1,mult(x1,x1)),mult(add(x0,mult(x0,x0)),add(x0,x1))),
inference(monotonicity,[status(thm)],[416]) ).
tff(418,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,B) = mult(B,A) )
| ( mult(add(x0,x1),add(x0,mult(x0,x0))) = mult(add(x0,mult(x0,x0)),add(x0,x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(419,plain,
mult(add(x0,x1),add(x0,mult(x0,x0))) = mult(add(x0,mult(x0,x0)),add(x0,x1)),
inference(unit_resolution,[status(thm)],[418,7]) ).
tff(420,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(unit,add(add(x0,mult(x0,x0)),mult(x0,x0))) = add(add(unit,add(x0,mult(x0,x0))),mult(x0,x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(421,plain,
add(unit,add(add(x0,mult(x0,x0)),mult(x0,x0))) = add(add(unit,add(x0,mult(x0,x0))),mult(x0,x0)),
inference(unit_resolution,[status(thm)],[420,50]) ).
tff(422,plain,
add(add(unit,add(x0,mult(x0,x0))),mult(x0,x0)) = add(unit,add(add(x0,mult(x0,x0)),mult(x0,x0))),
inference(symmetry,[status(thm)],[421]) ).
tff(423,plain,
add(add(unit,add(x0,mult(x0,x0))),mult(x0,x0)) = add(x0,mult(x0,x0)),
inference(monotonicity,[status(thm)],[19]) ).
tff(424,plain,
add(x0,mult(x0,x0)) = add(add(unit,add(x0,mult(x0,x0))),mult(x0,x0)),
inference(symmetry,[status(thm)],[423]) ).
tff(425,plain,
add(x0,mult(x0,x0)) = add(unit,add(add(x0,mult(x0,x0)),mult(x0,x0))),
inference(transitivity,[status(thm)],[424,422]) ).
tff(426,plain,
mult(add(x0,x1),add(x0,mult(x0,x0))) = mult(add(x0,x1),add(unit,add(add(x0,mult(x0,x0)),mult(x0,x0)))),
inference(monotonicity,[status(thm)],[425]) ).
tff(427,plain,
mult(add(x0,x1),add(unit,add(add(x0,mult(x0,x0)),mult(x0,x0)))) = mult(add(x0,x1),add(x0,mult(x0,x0))),
inference(symmetry,[status(thm)],[426]) ).
tff(428,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(add(x0,x1),add(unit,add(add(x0,mult(x0,x0)),mult(x0,x0)))) = add(mult(add(x0,x1),unit),mult(add(x0,x1),add(add(x0,mult(x0,x0)),mult(x0,x0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(429,plain,
mult(add(x0,x1),add(unit,add(add(x0,mult(x0,x0)),mult(x0,x0)))) = add(mult(add(x0,x1),unit),mult(add(x0,x1),add(add(x0,mult(x0,x0)),mult(x0,x0)))),
inference(unit_resolution,[status(thm)],[428,27]) ).
tff(430,plain,
add(mult(add(x0,x1),unit),mult(add(x0,x1),add(add(x0,mult(x0,x0)),mult(x0,x0)))) = mult(add(x0,x1),add(unit,add(add(x0,mult(x0,x0)),mult(x0,x0)))),
inference(symmetry,[status(thm)],[429]) ).
tff(431,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(add(x0,x1),unit) = add(x0,x1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(432,plain,
mult(add(x0,x1),unit) = add(x0,x1),
inference(unit_resolution,[status(thm)],[431,37]) ).
tff(433,plain,
add(x0,x1) = mult(add(x0,x1),unit),
inference(symmetry,[status(thm)],[432]) ).
tff(434,plain,
add(add(x0,x1),mult(add(x0,x1),add(add(x0,mult(x0,x0)),mult(x0,x0)))) = add(mult(add(x0,x1),unit),mult(add(x0,x1),add(add(x0,mult(x0,x0)),mult(x0,x0)))),
inference(monotonicity,[status(thm)],[433]) ).
tff(435,plain,
add(add(x0,x1),mult(add(x0,x1),add(add(x0,mult(x0,x0)),mult(x0,x0)))) = mult(add(x0,mult(x0,x0)),add(x0,x1)),
inference(transitivity,[status(thm)],[434,430,427,419]) ).
tff(436,plain,
add(add(add(x1,unit),add(x1,mult(x1,x1))),add(add(x0,x1),mult(add(x0,x1),add(add(x0,mult(x0,x0)),mult(x0,x0))))) = add(add(add(x1,unit),add(x1,mult(x1,x1))),mult(add(x0,mult(x0,x0)),add(x0,x1))),
inference(monotonicity,[status(thm)],[435]) ).
tff(437,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(add(add(x1,unit),add(x1,mult(x1,x1))),add(add(x0,x1),mult(add(x0,x1),add(add(x0,mult(x0,x0)),mult(x0,x0))))) = add(add(add(add(x1,unit),add(x1,mult(x1,x1))),add(x0,x1)),mult(add(x0,x1),add(add(x0,mult(x0,x0)),mult(x0,x0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(438,plain,
add(add(add(x1,unit),add(x1,mult(x1,x1))),add(add(x0,x1),mult(add(x0,x1),add(add(x0,mult(x0,x0)),mult(x0,x0))))) = add(add(add(add(x1,unit),add(x1,mult(x1,x1))),add(x0,x1)),mult(add(x0,x1),add(add(x0,mult(x0,x0)),mult(x0,x0)))),
inference(unit_resolution,[status(thm)],[437,50]) ).
tff(439,plain,
add(add(add(add(x1,unit),add(x1,mult(x1,x1))),add(x0,x1)),mult(add(x0,x1),add(add(x0,mult(x0,x0)),mult(x0,x0)))) = add(add(add(x1,unit),add(x1,mult(x1,x1))),add(add(x0,x1),mult(add(x0,x1),add(add(x0,mult(x0,x0)),mult(x0,x0))))),
inference(symmetry,[status(thm)],[438]) ).
tff(440,plain,
add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))) = add(mult(x1,x1),mult(x1,x1)),
inference(monotonicity,[status(thm)],[62,62]) ).
tff(441,plain,
add(mult(x1,x1),mult(x1,x1)) = add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),
inference(symmetry,[status(thm)],[440]) ).
tff(442,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(x1,add(x1,x1)) = add(mult(x1,x1),mult(x1,x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(443,plain,
mult(x1,add(x1,x1)) = add(mult(x1,x1),mult(x1,x1)),
inference(unit_resolution,[status(thm)],[442,27]) ).
tff(444,plain,
add(x1,x1) = add(add(x1,unit),add(x1,mult(x1,x1))),
inference(transitivity,[status(thm)],[399,398]) ).
tff(445,plain,
mult(x1,add(x1,x1)) = mult(x1,add(add(x1,unit),add(x1,mult(x1,x1)))),
inference(monotonicity,[status(thm)],[444]) ).
tff(446,plain,
mult(x1,add(add(x1,unit),add(x1,mult(x1,x1)))) = mult(x1,add(x1,x1)),
inference(symmetry,[status(thm)],[445]) ).
tff(447,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(x1,add(add(x1,unit),add(x1,mult(x1,x1)))) = add(mult(x1,add(x1,unit)),mult(x1,add(x1,mult(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(448,plain,
mult(x1,add(add(x1,unit),add(x1,mult(x1,x1)))) = add(mult(x1,add(x1,unit)),mult(x1,add(x1,mult(x1,x1)))),
inference(unit_resolution,[status(thm)],[447,27]) ).
tff(449,plain,
add(mult(x1,add(x1,unit)),mult(x1,add(x1,mult(x1,x1)))) = mult(x1,add(add(x1,unit),add(x1,mult(x1,x1)))),
inference(symmetry,[status(thm)],[448]) ).
tff(450,plain,
mult(x1,add(x1,unit)) = add(x1,mult(x1,x1)),
inference(transitivity,[status(thm)],[186,188,104]) ).
tff(451,plain,
add(mult(x1,add(x1,unit)),mult(x1,add(x1,mult(x1,x1)))) = add(add(x1,mult(x1,x1)),mult(x1,add(x1,mult(x1,x1)))),
inference(monotonicity,[status(thm)],[450]) ).
tff(452,plain,
add(add(x1,mult(x1,x1)),mult(x1,add(x1,mult(x1,x1)))) = add(mult(x1,add(x1,unit)),mult(x1,add(x1,mult(x1,x1)))),
inference(symmetry,[status(thm)],[451]) ).
tff(453,plain,
add(add(x1,unit),add(x1,mult(x1,x1))) = add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),
inference(transitivity,[status(thm)],[396,395,452,449,446,443,441]) ).
tff(454,plain,
add(add(add(x1,unit),add(x1,mult(x1,x1))),add(x0,x1)) = add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),add(x0,x1)),
inference(monotonicity,[status(thm)],[453]) ).
tff(455,plain,
add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),add(x0,x1)) = add(add(add(x1,unit),add(x1,mult(x1,x1))),add(x0,x1)),
inference(symmetry,[status(thm)],[454]) ).
tff(456,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(add(x1,mult(x1,x1)),add(x0,unit)) = add(add(x0,unit),add(x1,mult(x1,x1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(457,plain,
add(add(x1,mult(x1,x1)),add(x0,unit)) = add(add(x0,unit),add(x1,mult(x1,x1))),
inference(unit_resolution,[status(thm)],[456,78]) ).
tff(458,plain,
add(add(x0,unit),add(x1,mult(x1,x1))) = add(add(x1,mult(x1,x1)),add(x0,unit)),
inference(symmetry,[status(thm)],[457]) ).
tff(459,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(x0,add(unit,add(x1,mult(x1,x1)))) = add(add(x0,unit),add(x1,mult(x1,x1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(460,plain,
add(x0,add(unit,add(x1,mult(x1,x1)))) = add(add(x0,unit),add(x1,mult(x1,x1))),
inference(unit_resolution,[status(thm)],[459,50]) ).
tff(461,plain,
add(x0,add(unit,add(x1,mult(x1,x1)))) = add(x0,x1),
inference(monotonicity,[status(thm)],[42]) ).
tff(462,plain,
add(x0,x1) = add(x0,add(unit,add(x1,mult(x1,x1)))),
inference(symmetry,[status(thm)],[461]) ).
tff(463,plain,
add(x0,x1) = add(add(x1,mult(x1,x1)),add(x0,unit)),
inference(transitivity,[status(thm)],[462,460,458]) ).
tff(464,plain,
add(mult(x1,x1),mult(x1,x1)) = mult(x1,add(x1,x1)),
inference(symmetry,[status(thm)],[443]) ).
tff(465,plain,
add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))) = add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit),
inference(transitivity,[status(thm)],[440,464,445,448,451,392,390,387,384,382]) ).
tff(466,plain,
add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),add(x0,x1)) = add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit),add(add(x1,mult(x1,x1)),add(x0,unit))),
inference(monotonicity,[status(thm)],[465,463]) ).
tff(467,plain,
add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit),add(add(x1,mult(x1,x1)),add(x0,unit))) = add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),add(x0,x1)),
inference(symmetry,[status(thm)],[466]) ).
tff(468,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit),add(add(x1,mult(x1,x1)),add(x0,unit))) = add(add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit),add(x1,mult(x1,x1))),add(x0,unit)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(469,plain,
add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit),add(add(x1,mult(x1,x1)),add(x0,unit))) = add(add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit),add(x1,mult(x1,x1))),add(x0,unit)),
inference(unit_resolution,[status(thm)],[468,50]) ).
tff(470,plain,
add(add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit),add(x1,mult(x1,x1))),add(x0,unit)) = add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit),add(add(x1,mult(x1,x1)),add(x0,unit))),
inference(symmetry,[status(thm)],[469]) ).
tff(471,plain,
add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit),add(x1,mult(x1,x1))) = add(x1,mult(x1,x1)),
inference(transitivity,[status(thm)],[226,101,104]) ).
tff(472,plain,
add(add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit),add(x1,mult(x1,x1))),add(x0,unit)) = add(add(x1,mult(x1,x1)),add(x0,unit)),
inference(monotonicity,[status(thm)],[471]) ).
tff(473,plain,
add(add(x1,mult(x1,x1)),add(x0,unit)) = add(add(add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),unit),add(x1,mult(x1,x1))),add(x0,unit)),
inference(symmetry,[status(thm)],[472]) ).
tff(474,plain,
mult(add(x0,x1),unit) = add(add(add(x1,unit),add(x1,mult(x1,x1))),add(x0,x1)),
inference(transitivity,[status(thm)],[432,462,460,458,473,470,467,455]) ).
tff(475,plain,
add(mult(add(x0,x1),unit),mult(add(x0,x1),add(add(x0,mult(x0,x0)),mult(x0,x0)))) = add(add(add(add(x1,unit),add(x1,mult(x1,x1))),add(x0,x1)),mult(add(x0,x1),add(add(x0,mult(x0,x0)),mult(x0,x0)))),
inference(monotonicity,[status(thm)],[474]) ).
tff(476,plain,
( ~ ! [A: $i] : ( add(zero,A) = A )
| ( add(zero,unit) = unit ) ),
inference(quant_inst,[status(thm)],]) ).
tff(477,plain,
add(zero,unit) = unit,
inference(unit_resolution,[status(thm)],[476,246]) ).
tff(478,plain,
add(add(zero,unit),add(add(x0,mult(x0,x0)),mult(x0,x0))) = add(unit,add(add(x0,mult(x0,x0)),mult(x0,x0))),
inference(monotonicity,[status(thm)],[477]) ).
tff(479,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(zero,add(unit,add(add(x0,mult(x0,x0)),mult(x0,x0)))) = add(add(zero,unit),add(add(x0,mult(x0,x0)),mult(x0,x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(480,plain,
add(zero,add(unit,add(add(x0,mult(x0,x0)),mult(x0,x0)))) = add(add(zero,unit),add(add(x0,mult(x0,x0)),mult(x0,x0))),
inference(unit_resolution,[status(thm)],[479,50]) ).
tff(481,plain,
add(zero,add(x0,mult(x0,x0))) = add(zero,add(unit,add(add(x0,mult(x0,x0)),mult(x0,x0)))),
inference(monotonicity,[status(thm)],[425]) ).
tff(482,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(zero,add(x0,mult(x0,x0))) = add(add(x0,mult(x0,x0)),zero) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(483,plain,
add(zero,add(x0,mult(x0,x0))) = add(add(x0,mult(x0,x0)),zero),
inference(unit_resolution,[status(thm)],[482,78]) ).
tff(484,plain,
add(add(x0,mult(x0,x0)),zero) = add(zero,add(x0,mult(x0,x0))),
inference(symmetry,[status(thm)],[483]) ).
tff(485,plain,
add(unit,add(add(x0,mult(x0,x0)),mult(x0,x0))) = add(x0,mult(x0,x0)),
inference(transitivity,[status(thm)],[421,423]) ).
tff(486,plain,
add(add(unit,add(add(x0,mult(x0,x0)),mult(x0,x0))),zero) = add(add(x0,mult(x0,x0)),zero),
inference(monotonicity,[status(thm)],[485]) ).
tff(487,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(unit,add(add(add(x0,mult(x0,x0)),mult(x0,x0)),zero)) = add(add(unit,add(add(x0,mult(x0,x0)),mult(x0,x0))),zero) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(488,plain,
add(unit,add(add(add(x0,mult(x0,x0)),mult(x0,x0)),zero)) = add(add(unit,add(add(x0,mult(x0,x0)),mult(x0,x0))),zero),
inference(unit_resolution,[status(thm)],[487,50]) ).
tff(489,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(unit,add(unit,unit)) = add(add(unit,unit),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(490,plain,
add(unit,add(unit,unit)) = add(add(unit,unit),unit),
inference(unit_resolution,[status(thm)],[489,78]) ).
tff(491,plain,
add(add(unit,unit),unit) = add(unit,add(unit,unit)),
inference(symmetry,[status(thm)],[490]) ).
tff(492,plain,
add(add(unit,unit),unit) = unit,
inference(transitivity,[status(thm)],[491,117,112]) ).
tff(493,plain,
add(add(add(unit,unit),unit),add(add(add(x0,mult(x0,x0)),mult(x0,x0)),zero)) = add(unit,add(add(add(x0,mult(x0,x0)),mult(x0,x0)),zero)),
inference(monotonicity,[status(thm)],[492]) ).
tff(494,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(add(unit,unit),add(unit,add(add(add(x0,mult(x0,x0)),mult(x0,x0)),zero))) = add(add(add(unit,unit),unit),add(add(add(x0,mult(x0,x0)),mult(x0,x0)),zero)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(495,plain,
add(add(unit,unit),add(unit,add(add(add(x0,mult(x0,x0)),mult(x0,x0)),zero))) = add(add(add(unit,unit),unit),add(add(add(x0,mult(x0,x0)),mult(x0,x0)),zero)),
inference(unit_resolution,[status(thm)],[494,50]) ).
tff(496,plain,
add(add(unit,add(add(x0,mult(x0,x0)),mult(x0,x0))),zero) = add(unit,add(add(add(x0,mult(x0,x0)),mult(x0,x0)),zero)),
inference(symmetry,[status(thm)],[488]) ).
tff(497,plain,
add(add(x0,mult(x0,x0)),zero) = add(add(unit,add(add(x0,mult(x0,x0)),mult(x0,x0))),zero),
inference(symmetry,[status(thm)],[486]) ).
tff(498,plain,
add(zero,add(unit,add(add(x0,mult(x0,x0)),mult(x0,x0)))) = add(zero,add(x0,mult(x0,x0))),
inference(symmetry,[status(thm)],[481]) ).
tff(499,plain,
add(add(zero,unit),add(add(x0,mult(x0,x0)),mult(x0,x0))) = add(zero,add(unit,add(add(x0,mult(x0,x0)),mult(x0,x0)))),
inference(symmetry,[status(thm)],[480]) ).
tff(500,plain,
add(unit,add(add(x0,mult(x0,x0)),mult(x0,x0))) = add(add(zero,unit),add(add(x0,mult(x0,x0)),mult(x0,x0))),
inference(symmetry,[status(thm)],[478]) ).
tff(501,plain,
add(x0,mult(x0,x0)) = add(unit,add(add(add(x0,mult(x0,x0)),mult(x0,x0)),zero)),
inference(transitivity,[status(thm)],[424,422,500,499,498,483,497,496]) ).
tff(502,plain,
add(add(unit,unit),add(x0,mult(x0,x0))) = add(add(unit,unit),add(unit,add(add(add(x0,mult(x0,x0)),mult(x0,x0)),zero))),
inference(monotonicity,[status(thm)],[501]) ).
tff(503,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(unit,add(unit,add(x0,mult(x0,x0)))) = add(add(unit,unit),add(x0,mult(x0,x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(504,plain,
add(unit,add(unit,add(x0,mult(x0,x0)))) = add(add(unit,unit),add(x0,mult(x0,x0))),
inference(unit_resolution,[status(thm)],[503,50]) ).
tff(505,plain,
add(unit,x0) = add(unit,add(unit,add(x0,mult(x0,x0)))),
inference(monotonicity,[status(thm)],[232]) ).
tff(506,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(unit,x0) = add(x0,unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(507,plain,
add(unit,x0) = add(x0,unit),
inference(unit_resolution,[status(thm)],[506,78]) ).
tff(508,plain,
add(x0,unit) = add(unit,x0),
inference(symmetry,[status(thm)],[507]) ).
tff(509,plain,
add(x0,unit) = add(x0,mult(x0,x0)),
inference(transitivity,[status(thm)],[508,505,504,502,495,493,488,486,484,481,480,478,421,423]) ).
tff(510,plain,
mult(add(x0,x1),add(x0,unit)) = mult(add(x0,x1),add(x0,mult(x0,x0))),
inference(monotonicity,[status(thm)],[509]) ).
tff(511,plain,
add(x0,add(zero,unit)) = add(x0,unit),
inference(monotonicity,[status(thm)],[477]) ).
tff(512,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(x0,add(zero,unit)) = add(add(x0,zero),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(513,plain,
add(x0,add(zero,unit)) = add(add(x0,zero),unit),
inference(unit_resolution,[status(thm)],[512,50]) ).
tff(514,plain,
add(add(x0,zero),unit) = add(x0,add(zero,unit)),
inference(symmetry,[status(thm)],[513]) ).
tff(515,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(unit,add(x0,zero)) = add(add(x0,zero),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(516,plain,
add(unit,add(x0,zero)) = add(add(x0,zero),unit),
inference(unit_resolution,[status(thm)],[515,78]) ).
tff(517,plain,
add(unit,add(x0,zero)) = add(x0,unit),
inference(transitivity,[status(thm)],[516,514,511]) ).
tff(518,plain,
mult(add(x0,x1),add(unit,add(x0,zero))) = mult(add(x0,x1),add(x0,unit)),
inference(monotonicity,[status(thm)],[517]) ).
tff(519,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(add(x0,x1),add(unit,add(x0,zero))) = add(mult(add(x0,x1),unit),mult(add(x0,x1),add(x0,zero))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(520,plain,
mult(add(x0,x1),add(unit,add(x0,zero))) = add(mult(add(x0,x1),unit),mult(add(x0,x1),add(x0,zero))),
inference(unit_resolution,[status(thm)],[519,27]) ).
tff(521,plain,
add(mult(add(x0,x1),unit),mult(add(x0,x1),add(x0,zero))) = mult(add(x0,x1),add(unit,add(x0,zero))),
inference(symmetry,[status(thm)],[520]) ).
tff(522,plain,
mult(add(x0,x1),add(x0,zero)) = mult(add(x0,x1),x0),
inference(monotonicity,[status(thm)],[254]) ).
tff(523,plain,
mult(add(x0,x1),x0) = mult(add(x0,x1),add(x0,zero)),
inference(symmetry,[status(thm)],[522]) ).
tff(524,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,B) = mult(B,A) )
| ( mult(add(x0,x1),x0) = mult(x0,add(x0,x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(525,plain,
mult(add(x0,x1),x0) = mult(x0,add(x0,x1)),
inference(unit_resolution,[status(thm)],[524,7]) ).
tff(526,plain,
mult(x0,add(x0,x1)) = mult(add(x0,x1),x0),
inference(symmetry,[status(thm)],[525]) ).
tff(527,plain,
mult(x0,add(x0,x1)) = mult(add(x0,x1),add(x0,zero)),
inference(transitivity,[status(thm)],[526,523]) ).
tff(528,plain,
add(add(x0,x1),mult(x0,add(x0,x1))) = add(mult(add(x0,x1),unit),mult(add(x0,x1),add(x0,zero))),
inference(monotonicity,[status(thm)],[433,527]) ).
tff(529,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(x0,add(x0,x1)) = add(mult(x0,x0),mult(x0,x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(530,plain,
mult(x0,add(x0,x1)) = add(mult(x0,x0),mult(x0,x1)),
inference(unit_resolution,[status(thm)],[529,27]) ).
tff(531,plain,
add(mult(x0,x0),mult(x0,x1)) = mult(x0,add(x0,x1)),
inference(symmetry,[status(thm)],[530]) ).
tff(532,plain,
add(mult(x0,x0),mult(x0,x1)) = add(mult(x0,x0),mult(x1,x0)),
inference(monotonicity,[status(thm)],[9]) ).
tff(533,plain,
add(mult(x0,x0),mult(x1,x0)) = add(mult(x0,x0),mult(x0,x1)),
inference(symmetry,[status(thm)],[532]) ).
tff(534,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(mult(x1,x0),mult(x0,x0)) = add(mult(x0,x0),mult(x1,x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(535,plain,
add(mult(x1,x0),mult(x0,x0)) = add(mult(x0,x0),mult(x1,x0)),
inference(unit_resolution,[status(thm)],[534,78]) ).
tff(536,plain,
add(mult(x1,x0),mult(x0,x0)) = add(add(x1,mult(x1,add(x0,mult(x0,x0)))),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))),
inference(monotonicity,[status(thm)],[305,330]) ).
tff(537,plain,
add(add(x1,mult(x1,add(x0,mult(x0,x0)))),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))) = add(mult(x1,x0),mult(x0,x0)),
inference(symmetry,[status(thm)],[536]) ).
tff(538,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(x1,add(mult(x1,add(x0,mult(x0,x0))),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))))) = add(add(x1,mult(x1,add(x0,mult(x0,x0)))),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(539,plain,
add(x1,add(mult(x1,add(x0,mult(x0,x0))),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))))) = add(add(x1,mult(x1,add(x0,mult(x0,x0)))),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))),
inference(unit_resolution,[status(thm)],[538,50]) ).
tff(540,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(unit,add(unit,x1)) = add(add(unit,unit),x1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(541,plain,
add(unit,add(unit,x1)) = add(add(unit,unit),x1),
inference(unit_resolution,[status(thm)],[540,50]) ).
tff(542,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(unit,add(unit,add(x1,mult(x1,x1)))) = add(add(unit,unit),add(x1,mult(x1,x1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(543,plain,
add(unit,add(unit,add(x1,mult(x1,x1)))) = add(add(unit,unit),add(x1,mult(x1,x1))),
inference(unit_resolution,[status(thm)],[542,50]) ).
tff(544,plain,
add(unit,add(unit,add(x1,mult(x1,x1)))) = add(unit,x1),
inference(monotonicity,[status(thm)],[42]) ).
tff(545,plain,
add(unit,x1) = add(unit,add(unit,add(x1,mult(x1,x1)))),
inference(symmetry,[status(thm)],[544]) ).
tff(546,plain,
add(unit,x1) = add(add(unit,unit),add(x1,mult(x1,x1))),
inference(transitivity,[status(thm)],[545,543]) ).
tff(547,plain,
add(unit,add(unit,x1)) = add(unit,add(add(unit,unit),add(x1,mult(x1,x1)))),
inference(monotonicity,[status(thm)],[546]) ).
tff(548,plain,
add(unit,add(add(unit,unit),add(x1,mult(x1,x1)))) = add(unit,add(unit,x1)),
inference(symmetry,[status(thm)],[547]) ).
tff(549,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(unit,add(add(unit,unit),add(x1,mult(x1,x1)))) = add(add(unit,add(unit,unit)),add(x1,mult(x1,x1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(550,plain,
add(unit,add(add(unit,unit),add(x1,mult(x1,x1)))) = add(add(unit,add(unit,unit)),add(x1,mult(x1,x1))),
inference(unit_resolution,[status(thm)],[549,50]) ).
tff(551,plain,
add(add(unit,add(unit,unit)),add(x1,mult(x1,x1))) = add(unit,add(add(unit,unit),add(x1,mult(x1,x1)))),
inference(symmetry,[status(thm)],[550]) ).
tff(552,plain,
add(add(unit,add(unit,unit)),add(x1,mult(x1,x1))) = add(unit,add(x1,mult(x1,x1))),
inference(monotonicity,[status(thm)],[118]) ).
tff(553,plain,
add(unit,add(x1,mult(x1,x1))) = add(add(unit,add(unit,unit)),add(x1,mult(x1,x1))),
inference(symmetry,[status(thm)],[552]) ).
tff(554,plain,
x1 = add(add(unit,unit),x1),
inference(transitivity,[status(thm)],[88,553,551,548,541]) ).
tff(555,plain,
add(x1,add(mult(x1,add(x0,mult(x0,x0))),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))))) = add(add(add(unit,unit),x1),add(mult(x1,add(x0,mult(x0,x0))),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))))),
inference(monotonicity,[status(thm)],[554]) ).
tff(556,plain,
add(add(add(unit,unit),x1),add(mult(x1,add(x0,mult(x0,x0))),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))))) = add(x1,add(mult(x1,add(x0,mult(x0,x0))),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))))),
inference(symmetry,[status(thm)],[555]) ).
tff(557,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(add(unit,unit),add(x1,add(mult(x1,add(x0,mult(x0,x0))),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))))) = add(add(add(unit,unit),x1),add(mult(x1,add(x0,mult(x0,x0))),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(558,plain,
add(add(unit,unit),add(x1,add(mult(x1,add(x0,mult(x0,x0))),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))))) = add(add(add(unit,unit),x1),add(mult(x1,add(x0,mult(x0,x0))),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))))),
inference(unit_resolution,[status(thm)],[557,50]) ).
tff(559,plain,
add(x1,add(mult(x1,add(x0,mult(x0,x0))),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))))) = mult(x0,add(x0,x1)),
inference(transitivity,[status(thm)],[539,537,535,533,531]) ).
tff(560,plain,
add(add(unit,unit),add(x1,add(mult(x1,add(x0,mult(x0,x0))),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))))) = add(add(unit,unit),mult(x0,add(x0,x1))),
inference(monotonicity,[status(thm)],[559]) ).
tff(561,plain,
add(add(unit,unit),mult(x0,add(x0,x1))) = add(add(unit,unit),add(x1,add(mult(x1,add(x0,mult(x0,x0))),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))))),
inference(symmetry,[status(thm)],[560]) ).
tff(562,plain,
add(mult(x1,x0),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))) = add(mult(x1,x0),mult(x0,x0)),
inference(monotonicity,[status(thm)],[313]) ).
tff(563,plain,
add(mult(x1,x0),mult(x0,x0)) = add(mult(x1,x0),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))),
inference(symmetry,[status(thm)],[562]) ).
tff(564,plain,
add(mult(x0,x0),mult(x1,x0)) = add(mult(x1,x0),mult(x0,x0)),
inference(symmetry,[status(thm)],[535]) ).
tff(565,plain,
mult(x0,add(x0,x1)) = add(mult(x1,x0),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))),
inference(transitivity,[status(thm)],[530,532,564,563]) ).
tff(566,plain,
add(add(unit,unit),mult(x0,add(x0,x1))) = add(add(unit,unit),add(mult(x1,x0),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))))),
inference(monotonicity,[status(thm)],[565]) ).
tff(567,plain,
add(add(unit,unit),add(mult(x1,x0),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))))) = add(add(unit,unit),mult(x0,add(x0,x1))),
inference(symmetry,[status(thm)],[566]) ).
tff(568,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(add(unit,unit),add(mult(x1,x0),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))))) = add(add(add(unit,unit),mult(x1,x0)),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(569,plain,
add(add(unit,unit),add(mult(x1,x0),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))))) = add(add(add(unit,unit),mult(x1,x0)),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))),
inference(unit_resolution,[status(thm)],[568,50]) ).
tff(570,plain,
add(add(add(unit,unit),mult(x1,x0)),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))) = add(add(unit,unit),add(mult(x1,x0),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))))),
inference(symmetry,[status(thm)],[569]) ).
tff(571,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(mult(x1,x0),add(unit,unit)) = add(add(mult(x1,x0),unit),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(572,plain,
add(mult(x1,x0),add(unit,unit)) = add(add(mult(x1,x0),unit),unit),
inference(unit_resolution,[status(thm)],[571,50]) ).
tff(573,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(mult(x1,x0),add(unit,unit)) = add(add(unit,unit),mult(x1,x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(574,plain,
add(mult(x1,x0),add(unit,unit)) = add(add(unit,unit),mult(x1,x0)),
inference(unit_resolution,[status(thm)],[573,78]) ).
tff(575,plain,
add(add(unit,unit),mult(x1,x0)) = add(mult(x1,x0),add(unit,unit)),
inference(symmetry,[status(thm)],[574]) ).
tff(576,plain,
add(add(unit,unit),mult(x1,x0)) = add(add(mult(x1,x0),unit),unit),
inference(transitivity,[status(thm)],[575,572]) ).
tff(577,plain,
add(add(add(unit,unit),mult(x1,x0)),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))) = add(add(add(mult(x1,x0),unit),unit),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))),
inference(monotonicity,[status(thm)],[576]) ).
tff(578,plain,
add(add(add(mult(x1,x0),unit),unit),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))) = add(add(add(unit,unit),mult(x1,x0)),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))),
inference(symmetry,[status(thm)],[577]) ).
tff(579,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(unit,add(mult(x1,x0),unit)) = add(add(mult(x1,x0),unit),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(580,plain,
add(unit,add(mult(x1,x0),unit)) = add(add(mult(x1,x0),unit),unit),
inference(unit_resolution,[status(thm)],[579,78]) ).
tff(581,plain,
add(add(mult(x1,x0),unit),unit) = add(unit,add(mult(x1,x0),unit)),
inference(symmetry,[status(thm)],[580]) ).
tff(582,plain,
add(add(add(mult(x1,x0),unit),unit),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))) = add(add(unit,add(mult(x1,x0),unit)),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))),
inference(monotonicity,[status(thm)],[581]) ).
tff(583,plain,
add(add(unit,add(mult(x1,x0),unit)),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))) = add(add(add(mult(x1,x0),unit),unit),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))),
inference(symmetry,[status(thm)],[582]) ).
tff(584,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(unit,add(add(mult(x1,x0),unit),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))))) = add(add(unit,add(mult(x1,x0),unit)),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(585,plain,
add(unit,add(add(mult(x1,x0),unit),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))))) = add(add(unit,add(mult(x1,x0),unit)),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))),
inference(unit_resolution,[status(thm)],[584,50]) ).
tff(586,plain,
mult(x0,add(unit,add(x1,mult(x1,x1)))) = mult(x0,x1),
inference(monotonicity,[status(thm)],[42]) ).
tff(587,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(x0,add(unit,add(x1,mult(x1,x1)))) = add(mult(x0,unit),mult(x0,add(x1,mult(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(588,plain,
mult(x0,add(unit,add(x1,mult(x1,x1)))) = add(mult(x0,unit),mult(x0,add(x1,mult(x1,x1)))),
inference(unit_resolution,[status(thm)],[587,27]) ).
tff(589,plain,
add(mult(x0,unit),mult(x0,add(x1,mult(x1,x1)))) = mult(x0,add(unit,add(x1,mult(x1,x1)))),
inference(symmetry,[status(thm)],[588]) ).
tff(590,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(mult(x0,add(x1,mult(x1,x1))),mult(x0,unit)) = add(mult(x0,unit),mult(x0,add(x1,mult(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(591,plain,
add(mult(x0,add(x1,mult(x1,x1))),mult(x0,unit)) = add(mult(x0,unit),mult(x0,add(x1,mult(x1,x1)))),
inference(unit_resolution,[status(thm)],[590,78]) ).
tff(592,plain,
add(mult(x0,add(x1,mult(x1,x1))),x0) = add(mult(x0,add(x1,mult(x1,x1))),mult(x0,unit)),
inference(monotonicity,[status(thm)],[208]) ).
tff(593,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(unit,add(x0,mult(x0,x0))) = add(add(unit,x0),mult(x0,x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(594,plain,
add(unit,add(x0,mult(x0,x0))) = add(add(unit,x0),mult(x0,x0)),
inference(unit_resolution,[status(thm)],[593,50]) ).
tff(595,plain,
add(add(unit,x0),mult(x0,x0)) = add(unit,add(x0,mult(x0,x0))),
inference(symmetry,[status(thm)],[594]) ).
tff(596,plain,
add(add(x0,unit),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))) = add(add(unit,x0),mult(x0,x0)),
inference(monotonicity,[status(thm)],[508,313]) ).
tff(597,plain,
add(add(x0,unit),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))) = x0,
inference(transitivity,[status(thm)],[596,595,19]) ).
tff(598,plain,
add(mult(add(x1,mult(x1,x1)),x0),add(add(x0,unit),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))))) = add(mult(x0,add(x1,mult(x1,x1))),x0),
inference(monotonicity,[status(thm)],[323,597]) ).
tff(599,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(mult(add(x1,mult(x1,x1)),x0),add(add(x0,unit),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))))) = add(add(mult(add(x1,mult(x1,x1)),x0),add(x0,unit)),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(600,plain,
add(mult(add(x1,mult(x1,x1)),x0),add(add(x0,unit),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))))) = add(add(mult(add(x1,mult(x1,x1)),x0),add(x0,unit)),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))),
inference(unit_resolution,[status(thm)],[599,50]) ).
tff(601,plain,
add(add(mult(add(x1,mult(x1,x1)),x0),add(x0,unit)),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))) = add(mult(add(x1,mult(x1,x1)),x0),add(add(x0,unit),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))))),
inference(symmetry,[status(thm)],[600]) ).
tff(602,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(mult(add(x1,mult(x1,x1)),x0),add(x0,unit)) = add(add(mult(add(x1,mult(x1,x1)),x0),x0),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(603,plain,
add(mult(add(x1,mult(x1,x1)),x0),add(x0,unit)) = add(add(mult(add(x1,mult(x1,x1)),x0),x0),unit),
inference(unit_resolution,[status(thm)],[602,50]) ).
tff(604,plain,
add(add(mult(add(x1,mult(x1,x1)),x0),x0),unit) = add(mult(add(x1,mult(x1,x1)),x0),add(x0,unit)),
inference(symmetry,[status(thm)],[603]) ).
tff(605,plain,
add(mult(add(x1,mult(x1,x1)),x0),x0) = add(mult(x0,add(x1,mult(x1,x1))),x0),
inference(monotonicity,[status(thm)],[323]) ).
tff(606,plain,
add(mult(add(x1,mult(x1,x1)),x0),x0) = mult(x1,x0),
inference(transitivity,[status(thm)],[605,592,591,589,586,9]) ).
tff(607,plain,
add(add(mult(add(x1,mult(x1,x1)),x0),x0),unit) = add(mult(x1,x0),unit),
inference(monotonicity,[status(thm)],[606]) ).
tff(608,plain,
add(mult(x1,x0),unit) = add(add(mult(add(x1,mult(x1,x1)),x0),x0),unit),
inference(symmetry,[status(thm)],[607]) ).
tff(609,plain,
add(mult(x1,x0),unit) = add(mult(add(x1,mult(x1,x1)),x0),add(x0,unit)),
inference(transitivity,[status(thm)],[608,604]) ).
tff(610,plain,
add(add(mult(x1,x0),unit),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))) = add(add(mult(add(x1,mult(x1,x1)),x0),add(x0,unit)),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))),
inference(monotonicity,[status(thm)],[609]) ).
tff(611,plain,
add(add(mult(x1,x0),unit),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0))))) = mult(x1,x0),
inference(transitivity,[status(thm)],[610,601,598,592,591,589,586,9]) ).
tff(612,plain,
add(unit,add(add(mult(x1,x0),unit),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))))) = add(unit,mult(x1,x0)),
inference(monotonicity,[status(thm)],[611]) ).
tff(613,plain,
add(unit,mult(x1,x0)) = add(unit,add(add(mult(x1,x0),unit),add(mult(x0,unit),mult(x0,add(x0,mult(x0,x0)))))),
inference(symmetry,[status(thm)],[612]) ).
tff(614,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(unit,mult(x1,x0)) = add(mult(x1,x0),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(615,plain,
add(unit,mult(x1,x0)) = add(mult(x1,x0),unit),
inference(unit_resolution,[status(thm)],[614,78]) ).
tff(616,plain,
add(mult(x1,x0),unit) = add(unit,mult(x1,x0)),
inference(symmetry,[status(thm)],[615]) ).
tff(617,plain,
add(mult(add(x0,mult(x0,x0)),x1),x1) = add(mult(x1,add(x0,mult(x0,x0))),x1),
inference(monotonicity,[status(thm)],[218]) ).
tff(618,plain,
add(mult(x1,add(x0,mult(x0,x0))),x1) = add(mult(add(x0,mult(x0,x0)),x1),x1),
inference(symmetry,[status(thm)],[617]) ).
tff(619,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(mult(x1,add(x0,mult(x0,x0))),x1) = add(x1,mult(x1,add(x0,mult(x0,x0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(620,plain,
add(mult(x1,add(x0,mult(x0,x0))),x1) = add(x1,mult(x1,add(x0,mult(x0,x0)))),
inference(unit_resolution,[status(thm)],[619,78]) ).
tff(621,plain,
add(x1,mult(x1,add(x0,mult(x0,x0)))) = add(mult(x1,add(x0,mult(x0,x0))),x1),
inference(symmetry,[status(thm)],[620]) ).
tff(622,plain,
mult(x1,x0) = add(mult(add(x0,mult(x0,x0)),x1),x1),
inference(transitivity,[status(thm)],[134,29,304,621,618]) ).
tff(623,plain,
add(mult(x1,x0),unit) = add(add(mult(add(x0,mult(x0,x0)),x1),x1),unit),
inference(monotonicity,[status(thm)],[622]) ).
tff(624,plain,
add(add(mult(add(x0,mult(x0,x0)),x1),x1),unit) = add(mult(x1,x0),unit),
inference(symmetry,[status(thm)],[623]) ).
tff(625,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(mult(add(x0,mult(x0,x0)),x1),add(x1,unit)) = add(add(mult(add(x0,mult(x0,x0)),x1),x1),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(626,plain,
add(mult(add(x0,mult(x0,x0)),x1),add(x1,unit)) = add(add(mult(add(x0,mult(x0,x0)),x1),x1),unit),
inference(unit_resolution,[status(thm)],[625,50]) ).
tff(627,plain,
add(mult(add(x0,mult(x0,x0)),x1),add(x1,unit)) = add(mult(add(x0,mult(x0,x0)),x1),add(x1,mult(x1,x1))),
inference(monotonicity,[status(thm)],[385]) ).
tff(628,plain,
add(mult(add(x0,mult(x0,x0)),x1),add(x1,mult(x1,x1))) = add(mult(add(x0,mult(x0,x0)),x1),add(x1,unit)),
inference(symmetry,[status(thm)],[627]) ).
tff(629,plain,
( ~ ! [B: $i,A: $i] : ( add(A,B) = add(B,A) )
| ( add(mult(add(x0,mult(x0,x0)),x1),add(x1,mult(x1,x1))) = add(add(x1,mult(x1,x1)),mult(add(x0,mult(x0,x0)),x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(630,plain,
add(mult(add(x0,mult(x0,x0)),x1),add(x1,mult(x1,x1))) = add(add(x1,mult(x1,x1)),mult(add(x0,mult(x0,x0)),x1)),
inference(unit_resolution,[status(thm)],[629,78]) ).
tff(631,plain,
add(add(x1,mult(x1,x1)),mult(add(x0,mult(x0,x0)),x1)) = add(mult(add(x0,mult(x0,x0)),x1),add(x1,mult(x1,x1))),
inference(symmetry,[status(thm)],[630]) ).
tff(632,plain,
add(add(x1,mult(x1,x1)),mult(add(x0,mult(x0,x0)),x1)) = add(add(x1,mult(x1,x1)),mult(x1,add(x0,mult(x0,x0)))),
inference(monotonicity,[status(thm)],[218]) ).
tff(633,plain,
add(add(x1,mult(x1,x1)),mult(x1,add(x0,mult(x0,x0)))) = add(add(x1,mult(x1,x1)),mult(add(x0,mult(x0,x0)),x1)),
inference(symmetry,[status(thm)],[632]) ).
tff(634,plain,
add(x1,mult(x1,x1)) = mult(x1,unit),
inference(transitivity,[status(thm)],[195,192,42,40]) ).
tff(635,plain,
add(add(x1,mult(x1,x1)),mult(x1,add(x0,mult(x0,x0)))) = add(mult(x1,unit),mult(x1,add(x0,mult(x0,x0)))),
inference(monotonicity,[status(thm)],[634]) ).
tff(636,plain,
add(mult(x1,unit),mult(x1,add(x0,mult(x0,x0)))) = add(add(x1,mult(x1,x1)),mult(x1,add(x0,mult(x0,x0)))),
inference(symmetry,[status(thm)],[635]) ).
tff(637,plain,
mult(x1,x0) = mult(x0,add(x0,x1)),
inference(transitivity,[status(thm)],[134,29,636,633,631,628,626,624,616,613,585,583,578,570,567,561,558,556,539,537,535,533,531]) ).
tff(638,plain,
add(add(x0,x1),mult(x1,x0)) = add(add(x0,x1),mult(x0,add(x0,x1))),
inference(monotonicity,[status(thm)],[637]) ).
tff(639,plain,
mult(x0,add(add(x1,unit),add(x1,mult(x1,x1)))) = mult(x0,add(x1,mult(x1,x1))),
inference(monotonicity,[status(thm)],[416]) ).
tff(640,plain,
add(add(x1,mult(x1,x1)),add(x1,mult(x1,x1))) = add(add(x1,unit),add(x1,mult(x1,x1))),
inference(symmetry,[status(thm)],[396]) ).
tff(641,plain,
add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))) = add(add(x1,unit),add(x1,mult(x1,x1))),
inference(transitivity,[status(thm)],[440,464,445,448,451,394,640]) ).
tff(642,plain,
mult(add(x0,zero),add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = mult(x0,add(add(x1,unit),add(x1,mult(x1,x1)))),
inference(monotonicity,[status(thm)],[254,641]) ).
tff(643,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(add(x0,zero),add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = add(mult(add(x0,zero),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),mult(add(x0,zero),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(644,plain,
mult(add(x0,zero),add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = add(mult(add(x0,zero),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),mult(add(x0,zero),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))),
inference(unit_resolution,[status(thm)],[643,27]) ).
tff(645,plain,
add(mult(add(x0,zero),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),mult(add(x0,zero),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = mult(add(x0,zero),add(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))),
inference(symmetry,[status(thm)],[644]) ).
tff(646,plain,
mult(add(x0,zero),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))) = mult(x0,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),
inference(monotonicity,[status(thm)],[254]) ).
tff(647,plain,
mult(x0,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))) = mult(add(x0,zero),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),
inference(symmetry,[status(thm)],[646]) ).
tff(648,plain,
add(mult(x0,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),mult(x0,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = add(mult(add(x0,zero),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),mult(add(x0,zero),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))),
inference(monotonicity,[status(thm)],[647,647]) ).
tff(649,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,B) = mult(B,A) )
| ( mult(x0,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))) = mult(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(650,plain,
mult(x0,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))) = mult(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),x0),
inference(unit_resolution,[status(thm)],[649,7]) ).
tff(651,plain,
mult(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),x0) = mult(x0,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),
inference(symmetry,[status(thm)],[650]) ).
tff(652,plain,
add(x1,mult(add(x1,mult(x1,x1)),x1)) = add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),
inference(monotonicity,[status(thm)],[40,255]) ).
tff(653,plain,
add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))) = add(x1,mult(add(x1,mult(x1,x1)),x1)),
inference(symmetry,[status(thm)],[652]) ).
tff(654,plain,
mult(x0,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))) = mult(x0,add(x1,mult(add(x1,mult(x1,x1)),x1))),
inference(monotonicity,[status(thm)],[653]) ).
tff(655,plain,
mult(x0,add(x1,mult(add(x1,mult(x1,x1)),x1))) = mult(x0,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),
inference(symmetry,[status(thm)],[654]) ).
tff(656,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(x0,add(x1,mult(add(x1,mult(x1,x1)),x1))) = add(mult(x0,x1),mult(x0,mult(add(x1,mult(x1,x1)),x1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(657,plain,
mult(x0,add(x1,mult(add(x1,mult(x1,x1)),x1))) = add(mult(x0,x1),mult(x0,mult(add(x1,mult(x1,x1)),x1))),
inference(unit_resolution,[status(thm)],[656,27]) ).
tff(658,plain,
add(mult(x0,x1),mult(x0,mult(add(x1,mult(x1,x1)),x1))) = mult(x0,add(x1,mult(add(x1,mult(x1,x1)),x1))),
inference(symmetry,[status(thm)],[657]) ).
tff(659,plain,
mult(x0,mult(add(x1,mult(x1,x1)),x1)) = mult(x0,add(x1,mult(x1,x1))),
inference(monotonicity,[status(thm)],[270]) ).
tff(660,plain,
mult(x0,add(x1,mult(x1,x1))) = mult(x0,mult(add(x1,mult(x1,x1)),x1)),
inference(symmetry,[status(thm)],[659]) ).
tff(661,plain,
add(x0,mult(x1,x0)) = mult(x0,mult(add(x1,mult(x1,x1)),x1)),
inference(transitivity,[status(thm)],[209,205,202,660]) ).
tff(662,plain,
add(mult(x1,x0),add(x0,mult(x1,x0))) = add(mult(x0,x1),mult(x0,mult(add(x1,mult(x1,x1)),x1))),
inference(monotonicity,[status(thm)],[10,661]) ).
tff(663,plain,
add(mult(x1,x0),add(x0,mult(x1,x0))) = mult(x0,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),
inference(transitivity,[status(thm)],[662,658,655]) ).
tff(664,plain,
add(add(mult(x1,x0),add(x0,mult(x1,x0))),mult(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),x0)) = add(mult(x0,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),mult(x0,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))),
inference(monotonicity,[status(thm)],[663,651]) ).
tff(665,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(mult(x1,x0),add(add(x0,mult(x1,x0)),mult(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),x0))) = add(add(mult(x1,x0),add(x0,mult(x1,x0))),mult(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(666,plain,
add(mult(x1,x0),add(add(x0,mult(x1,x0)),mult(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),x0))) = add(add(mult(x1,x0),add(x0,mult(x1,x0))),mult(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),x0)),
inference(unit_resolution,[status(thm)],[665,50]) ).
tff(667,plain,
add(add(x0,mult(x1,x0)),mult(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),x0)) = add(add(x0,mult(x1,x0)),mult(x0,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))),
inference(monotonicity,[status(thm)],[651]) ).
tff(668,plain,
add(add(x0,mult(x1,x0)),mult(x0,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = add(add(x0,mult(x1,x0)),mult(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),x0)),
inference(symmetry,[status(thm)],[667]) ).
tff(669,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( add(A,add(B,C)) = add(add(A,B),C) )
| ( add(x0,add(mult(x1,x0),mult(x0,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))))) = add(add(x0,mult(x1,x0)),mult(x0,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(670,plain,
add(x0,add(mult(x1,x0),mult(x0,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))))) = add(add(x0,mult(x1,x0)),mult(x0,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))),
inference(unit_resolution,[status(thm)],[669,50]) ).
tff(671,plain,
mult(x0,add(x1,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = mult(x0,add(x1,mult(x1,x1))),
inference(monotonicity,[status(thm)],[137]) ).
tff(672,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(x0,add(x1,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = add(mult(x0,x1),mult(x0,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(673,plain,
mult(x0,add(x1,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = add(mult(x0,x1),mult(x0,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))),
inference(unit_resolution,[status(thm)],[672,27]) ).
tff(674,plain,
add(mult(x0,x1),mult(x0,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = mult(x0,add(x1,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))),
inference(symmetry,[status(thm)],[673]) ).
tff(675,plain,
add(mult(x1,x0),mult(x0,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = add(mult(x0,x1),mult(x0,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))),
inference(monotonicity,[status(thm)],[10]) ).
tff(676,plain,
add(mult(x1,x0),mult(x0,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))))) = mult(x0,add(x1,mult(x1,x1))),
inference(transitivity,[status(thm)],[675,674,671]) ).
tff(677,plain,
add(x0,add(mult(x1,x0),mult(x0,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))))) = add(mult(x0,unit),mult(x0,add(x1,mult(x1,x1)))),
inference(monotonicity,[status(thm)],[208,676]) ).
tff(678,plain,
add(mult(x0,unit),mult(x0,add(x1,mult(x1,x1)))) = add(x0,add(mult(x1,x0),mult(x0,add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))))),
inference(symmetry,[status(thm)],[677]) ).
tff(679,plain,
mult(x0,x1) = mult(x0,add(unit,add(x1,mult(x1,x1)))),
inference(symmetry,[status(thm)],[586]) ).
tff(680,plain,
mult(x1,x0) = add(add(x0,mult(x1,x0)),mult(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),x0)),
inference(transitivity,[status(thm)],[10,679,588,678,670,668]) ).
tff(681,plain,
add(mult(x1,x0),mult(x1,x0)) = add(mult(x1,x0),add(add(x0,mult(x1,x0)),mult(add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1)))),x0))),
inference(monotonicity,[status(thm)],[680]) ).
tff(682,plain,
mult(add(x0,x1),add(x0,mult(x0,x0))) = mult(x1,x0),
inference(transitivity,[status(thm)],[426,429,475,439,436,417,365,346,344,338,335,333,331,328,325,318,316,306,303,301,285,282,280,278,215,212,209,205,202,197,9]) ).
tff(683,plain,
add(mult(x1,add(x1,mult(x1,x1))),mult(x1,add(x0,mult(x0,x0)))) = add(add(x1,mult(x1,x1)),mult(x1,add(x0,mult(x0,x0)))),
inference(monotonicity,[status(thm)],[393]) ).
tff(684,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(x1,add(add(x1,mult(x1,x1)),add(x0,mult(x0,x0)))) = add(mult(x1,add(x1,mult(x1,x1))),mult(x1,add(x0,mult(x0,x0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(685,plain,
mult(x1,add(add(x1,mult(x1,x1)),add(x0,mult(x0,x0)))) = add(mult(x1,add(x1,mult(x1,x1))),mult(x1,add(x0,mult(x0,x0)))),
inference(unit_resolution,[status(thm)],[684,27]) ).
tff(686,plain,
add(add(x1,unit),add(x0,mult(x0,x0))) = add(add(x1,mult(x1,x1)),add(x0,mult(x0,x0))),
inference(symmetry,[status(thm)],[225]) ).
tff(687,plain,
add(x1,x0) = add(x1,add(unit,add(x0,mult(x0,x0)))),
inference(symmetry,[status(thm)],[221]) ).
tff(688,plain,
add(x0,x1) = add(x1,x0),
inference(symmetry,[status(thm)],[220]) ).
tff(689,plain,
add(x0,x1) = add(add(x1,mult(x1,x1)),add(x0,mult(x0,x0))),
inference(transitivity,[status(thm)],[688,687,223,686]) ).
tff(690,plain,
mult(add(x1,mult(x1,x1)),add(x0,x1)) = mult(x1,add(add(x1,mult(x1,x1)),add(x0,mult(x0,x0)))),
inference(monotonicity,[status(thm)],[196,689]) ).
tff(691,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,B) = mult(B,A) )
| ( mult(add(x1,mult(x1,x1)),add(x0,x1)) = mult(add(x0,x1),add(x1,mult(x1,x1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(692,plain,
mult(add(x1,mult(x1,x1)),add(x0,x1)) = mult(add(x0,x1),add(x1,mult(x1,x1))),
inference(unit_resolution,[status(thm)],[691,7]) ).
tff(693,plain,
mult(add(x0,x1),add(x1,mult(x1,x1))) = mult(add(x1,mult(x1,x1)),add(x0,x1)),
inference(symmetry,[status(thm)],[692]) ).
tff(694,plain,
mult(add(x0,x1),add(x1,mult(x1,x1))) = mult(x1,x0),
inference(transitivity,[status(thm)],[693,690,685,683,635,30,20]) ).
tff(695,plain,
add(mult(add(x0,x1),add(x1,mult(x1,x1))),mult(add(x0,x1),add(x0,mult(x0,x0)))) = add(mult(x1,x0),mult(x1,x0)),
inference(monotonicity,[status(thm)],[694,682]) ).
tff(696,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(add(x0,x1),add(add(x1,mult(x1,x1)),add(x0,mult(x0,x0)))) = add(mult(add(x0,x1),add(x1,mult(x1,x1))),mult(add(x0,x1),add(x0,mult(x0,x0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(697,plain,
mult(add(x0,x1),add(add(x1,mult(x1,x1)),add(x0,mult(x0,x0)))) = add(mult(add(x0,x1),add(x1,mult(x1,x1))),mult(add(x0,x1),add(x0,mult(x0,x0)))),
inference(unit_resolution,[status(thm)],[696,27]) ).
tff(698,plain,
mult(add(x0,x1),add(x0,x1)) = mult(add(x0,x1),add(add(x1,mult(x1,x1)),add(x0,mult(x0,x0)))),
inference(monotonicity,[status(thm)],[689]) ).
tff(699,plain,
mult(add(x0,x1),add(x0,x1)) = mult(x1,x0),
inference(transitivity,[status(thm)],[698,697,695,681,666,664,648,645,642,639,197,9]) ).
tff(700,plain,
add(add(x0,x1),mult(add(x0,x1),add(x0,x1))) = add(add(x0,x1),mult(x1,x0)),
inference(monotonicity,[status(thm)],[699]) ).
tff(701,plain,
add(add(x0,x1),mult(add(x0,x1),add(x0,x1))) = add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),mult(x1,add(x0,mult(x0,x0)))),
inference(transitivity,[status(thm)],[700,638,528,521,518,510,426,429,475,439,436,417,365,346,344,338,335,333,331,328,325,318,316,306,303,301,285,282,280,278,215,212,209,205,202,197,9,134,29,133]) ).
tff(702,plain,
( ~ ! [A: $i] : ( add(unit,add(A,mult(A,A))) = A )
| ( add(unit,add(add(unit,unit),mult(add(unit,unit),add(unit,unit)))) = add(unit,unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(703,plain,
add(unit,add(add(unit,unit),mult(add(unit,unit),add(unit,unit)))) = add(unit,unit),
inference(unit_resolution,[status(thm)],[702,17]) ).
tff(704,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(add(unit,unit),unit) = add(unit,unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(705,plain,
mult(add(unit,unit),unit) = add(unit,unit),
inference(unit_resolution,[status(thm)],[704,37]) ).
tff(706,plain,
add(unit,unit) = mult(add(unit,unit),unit),
inference(symmetry,[status(thm)],[705]) ).
tff(707,plain,
add(add(unit,unit),mult(add(unit,unit),add(unit,unit))) = add(mult(add(unit,unit),unit),mult(add(unit,unit),add(unit,unit))),
inference(monotonicity,[status(thm)],[706]) ).
tff(708,plain,
add(mult(add(unit,unit),unit),mult(add(unit,unit),add(unit,unit))) = add(add(unit,unit),mult(add(unit,unit),add(unit,unit))),
inference(symmetry,[status(thm)],[707]) ).
tff(709,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,add(B,C)) = add(mult(A,B),mult(A,C)) )
| ( mult(add(unit,unit),add(unit,add(unit,unit))) = add(mult(add(unit,unit),unit),mult(add(unit,unit),add(unit,unit))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(710,plain,
mult(add(unit,unit),add(unit,add(unit,unit))) = add(mult(add(unit,unit),unit),mult(add(unit,unit),add(unit,unit))),
inference(unit_resolution,[status(thm)],[709,27]) ).
tff(711,plain,
mult(add(unit,unit),add(unit,add(unit,unit))) = mult(add(unit,unit),unit),
inference(monotonicity,[status(thm)],[118]) ).
tff(712,plain,
mult(add(unit,unit),unit) = mult(add(unit,unit),add(unit,add(unit,unit))),
inference(symmetry,[status(thm)],[711]) ).
tff(713,plain,
add(unit,unit) = add(add(unit,unit),mult(add(unit,unit),add(unit,unit))),
inference(transitivity,[status(thm)],[706,712,710,708]) ).
tff(714,plain,
add(unit,add(unit,unit)) = add(unit,add(add(unit,unit),mult(add(unit,unit),add(unit,unit)))),
inference(monotonicity,[status(thm)],[713]) ).
tff(715,plain,
unit = add(unit,add(unit,mult(unit,unit))),
inference(symmetry,[status(thm)],[112]) ).
tff(716,plain,
unit = add(unit,unit),
inference(transitivity,[status(thm)],[715,116,714,703]) ).
tff(717,plain,
add(unit,add(add(x0,x1),mult(add(x0,x1),add(x0,x1)))) = add(add(unit,unit),add(add(add(x1,mult(x1,x1)),add(mult(x1,unit),mult(x1,add(x1,mult(x1,x1))))),mult(x1,add(x0,mult(x0,x0))))),
inference(monotonicity,[status(thm)],[716,701]) ).
tff(718,plain,
( ~ ! [A: $i] : ( add(unit,add(A,mult(A,A))) = A )
| ( add(unit,add(add(x0,x1),mult(add(x0,x1),add(x0,x1)))) = add(x0,x1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(719,plain,
add(unit,add(add(x0,x1),mult(add(x0,x1),add(x0,x1)))) = add(x0,x1),
inference(unit_resolution,[status(thm)],[718,17]) ).
tff(720,plain,
add(x0,x1) = add(unit,add(add(x0,x1),mult(add(x0,x1),add(x0,x1)))),
inference(symmetry,[status(thm)],[719]) ).
tff(721,plain,
add(x0,x1) = mult(x0,x1),
inference(transitivity,[status(thm)],[720,717,68,66,30,20,10]) ).
tff(722,plain,
( ( add(x0,x1) != mult(x0,x1) )
<=> ( add(x0,x1) != mult(x0,x1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(723,axiom,
add(x0,x1) != mult(x0,x1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
tff(724,plain,
add(x0,x1) != mult(x0,x1),
inference(modus_ponens,[status(thm)],[723,722]) ).
tff(725,plain,
$false,
inference(unit_resolution,[status(thm)],[724,721]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : RNG128-1 : TPTP v8.1.0. Released v5.4.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Sep 2 22:51:03 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 3.96/2.72 % SZS status Unsatisfiable
% 3.96/2.72 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------