TSTP Solution File: GRP660-14 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP660-14 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 22:29:17 EDT 2022
% Result : Unsatisfiable 0.66s 0.65s
% Output : Proof 0.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 73
% Syntax : Number of formulae : 309 ( 241 unt; 5 typ; 0 def)
% Number of atoms : 375 ( 370 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 125 ( 58 ~; 54 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 210 ( 201 !; 0 ?; 210 :)
% Comments :
%------------------------------------------------------------------------------
tff(x0_type,type,
x0: $i ).
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(ld_type,type,
ld: ( $i * $i ) > $i ).
tff(x1_type,type,
x1: $i ).
tff(rd_type,type,
rd: ( $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(
( ( rd(mult(A,B),B) = A )
<=> ( rd(mult(A,B),B) = A ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
tff(5,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(x0,x1),x1) = x0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
rd(mult(x0,x1),x1) = x0,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [B: $i,A: $i] :
refl(
( ( ld(A,mult(A,B)) = B )
<=> ( ld(A,mult(A,B)) = B ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
<=> ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
<=> ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
tff(14,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(ld(x1,x1),mult(ld(x1,x1),mult(x0,x1))) = mult(x0,x1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
ld(ld(x1,x1),mult(ld(x1,x1),mult(x0,x1))) = mult(x0,x1),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),mult(mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),ld(x1,x1))) = ld(x1,x1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(20,plain,
ld(mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),mult(mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),ld(x1,x1))) = ld(x1,x1),
inference(unit_resolution,[status(thm)],[19,16]) ).
tff(21,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),ld(x1,x1)))) = mult(mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),ld(x1,x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),ld(x1,x1)))) = mult(mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),ld(x1,x1)),
inference(unit_resolution,[status(thm)],[21,16]) ).
tff(23,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
<=> ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,axiom,
! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
tff(27,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1)),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1)),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))))),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(x1,mult(x1,x1)) = x1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
ld(x1,mult(x1,x1)) = x1,
inference(unit_resolution,[status(thm)],[32,16]) ).
tff(34,plain,
^ [B: $i,A: $i] :
refl(
( ( mult(A,ld(A,B)) = B )
<=> ( mult(A,ld(A,B)) = B ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B )
<=> ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B )
<=> ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
tff(38,plain,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B )
| ( mult(x1,ld(x1,x1)) = x1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
mult(x1,ld(x1,x1)) = x1,
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
mult(mult(x1,ld(x1,x1)),ld(x1,x1)) = mult(x1,ld(x1,x1)),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
mult(x1,ld(x1,x1)) = mult(mult(x1,ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
x1 = mult(x1,ld(x1,x1)),
inference(symmetry,[status(thm)],[42]) ).
tff(46,plain,
x1 = mult(mult(x1,ld(x1,x1)),ld(x1,x1)),
inference(transitivity,[status(thm)],[45,44]) ).
tff(47,plain,
mult(x1,x1) = mult(mult(mult(x1,ld(x1,x1)),ld(x1,x1)),x1),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
mult(mult(mult(x1,ld(x1,x1)),ld(x1,x1)),x1) = mult(x1,x1),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(x1,ld(x1,x1)),ld(x1,x1)),x1) = mult(x1,mult(ld(x1,x1),mult(ld(x1,x1),x1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
mult(mult(mult(x1,ld(x1,x1)),ld(x1,x1)),x1) = mult(x1,mult(ld(x1,x1),mult(ld(x1,x1),x1))),
inference(unit_resolution,[status(thm)],[49,29]) ).
tff(51,plain,
mult(x1,mult(ld(x1,x1),mult(ld(x1,x1),x1))) = mult(mult(mult(x1,ld(x1,x1)),ld(x1,x1)),x1),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
mult(x1,mult(ld(x1,x1),mult(ld(x1,x1),x1))) = mult(x1,x1),
inference(transitivity,[status(thm)],[51,48]) ).
tff(53,plain,
ld(x1,mult(x1,mult(ld(x1,x1),mult(ld(x1,x1),x1)))) = ld(x1,mult(x1,x1)),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(x1,mult(x1,mult(ld(x1,x1),mult(ld(x1,x1),x1)))) = mult(ld(x1,x1),mult(ld(x1,x1),x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
ld(x1,mult(x1,mult(ld(x1,x1),mult(ld(x1,x1),x1)))) = mult(ld(x1,x1),mult(ld(x1,x1),x1)),
inference(unit_resolution,[status(thm)],[54,16]) ).
tff(56,plain,
mult(ld(x1,x1),mult(ld(x1,x1),x1)) = ld(x1,mult(x1,mult(ld(x1,x1),mult(ld(x1,x1),x1)))),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,ld(x1,x1))) = mult(mult(ld(x1,x1),ld(x1,x1)),x1),
inference(monotonicity,[status(thm)],[42]) ).
tff(58,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),x1) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,ld(x1,x1))),
inference(symmetry,[status(thm)],[57]) ).
tff(59,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(ld(x1,x1),ld(x1,x1)),x1),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),ld(x1,x1)),x1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
rd(mult(mult(mult(ld(x1,x1),ld(x1,x1)),x1),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),ld(x1,x1)),x1),
inference(unit_resolution,[status(thm)],[59,7]) ).
tff(61,plain,
mult(ld(x1,x1),mult(x1,ld(x1,x1))) = mult(ld(x1,x1),x1),
inference(monotonicity,[status(thm)],[42]) ).
tff(62,plain,
mult(ld(x1,x1),mult(ld(x1,x1),mult(x1,ld(x1,x1)))) = mult(ld(x1,x1),mult(ld(x1,x1),x1)),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),ld(x1,x1)),x1),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(x1,ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),x1),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(x1,ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[63,29]) ).
tff(65,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),x1),ld(x1,x1)) = mult(x1,ld(x1,x1)),
inference(transitivity,[status(thm)],[64,62,56,53,33,45]) ).
tff(66,plain,
rd(mult(mult(mult(ld(x1,x1),ld(x1,x1)),x1),ld(x1,x1)),ld(x1,x1)) = rd(mult(x1,ld(x1,x1)),ld(x1,x1)),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
rd(mult(x1,ld(x1,x1)),ld(x1,x1)) = rd(mult(mult(mult(ld(x1,x1),ld(x1,x1)),x1),ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(x1,ld(x1,x1)),ld(x1,x1)) = x1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
rd(mult(x1,ld(x1,x1)),ld(x1,x1)) = x1,
inference(unit_resolution,[status(thm)],[68,7]) ).
tff(70,plain,
x1 = rd(mult(x1,ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
x1 = mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,ld(x1,x1))),
inference(transitivity,[status(thm)],[70,67,60,58]) ).
tff(72,plain,
mult(ld(x1,x1),x1) = mult(ld(x1,x1),mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,ld(x1,x1)))),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
mult(ld(x1,x1),mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,ld(x1,x1)))) = mult(ld(x1,x1),x1),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[74,29]) ).
tff(76,plain,
mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),ld(x1,x1)) = mult(ld(x1,x1),x1),
inference(transitivity,[status(thm)],[75,73]) ).
tff(77,plain,
mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),ld(x1,x1))) = mult(ld(x1,x1),mult(ld(x1,x1),x1)),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),ld(x1,x1))) = x1,
inference(transitivity,[status(thm)],[77,56,53,33]) ).
tff(79,plain,
mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),ld(x1,x1)))) = mult(ld(x1,x1),x1),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[80,29]) ).
tff(82,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1)),ld(x1,x1)) = mult(ld(x1,x1),x1),
inference(transitivity,[status(thm)],[81,79]) ).
tff(83,plain,
mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1)),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1))),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1)),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x1,x1),x1))) = mult(ld(x1,x1),x1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x1,x1),x1))) = mult(ld(x1,x1),x1),
inference(unit_resolution,[status(thm)],[85,16]) ).
tff(87,plain,
ld(x1,mult(x1,x1)) = ld(x1,mult(x1,mult(ld(x1,x1),mult(ld(x1,x1),x1)))),
inference(symmetry,[status(thm)],[53]) ).
tff(88,plain,
x1 = ld(x1,mult(x1,x1)),
inference(symmetry,[status(thm)],[33]) ).
tff(89,plain,
mult(ld(x1,x1),mult(ld(x1,x1),x1)) = x1,
inference(transitivity,[status(thm)],[56,53,33]) ).
tff(90,plain,
mult(mult(ld(x1,x1),mult(ld(x1,x1),x1)),ld(x1,x1)) = mult(x1,ld(x1,x1)),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
mult(mult(ld(x1,x1),mult(ld(x1,x1),x1)),ld(x1,x1)) = x1,
inference(transitivity,[status(thm)],[90,42]) ).
tff(92,plain,
mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),x1)),ld(x1,x1)),ld(x1,x1)) = mult(x1,ld(x1,x1)),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),x1)),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),x1)),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[93,29]) ).
tff(95,plain,
mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1)))) = mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),x1)),ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1)))) = mult(ld(x1,x1),mult(ld(x1,x1),x1)),
inference(transitivity,[status(thm)],[95,92,42,88,87,55]) ).
tff(97,plain,
ld(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1))))) = ld(ld(x1,x1),mult(ld(x1,x1),mult(ld(x1,x1),x1))),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1))))) = mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
ld(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1))))) = mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1))),
inference(unit_resolution,[status(thm)],[98,16]) ).
tff(100,plain,
mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1))) = ld(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1))))),
inference(symmetry,[status(thm)],[99]) ).
tff(101,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))))) = mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1)),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))),
inference(symmetry,[status(thm)],[31]) ).
tff(102,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))))) = mult(ld(x1,x1),x1),
inference(transitivity,[status(thm)],[101,83,100,97,86]) ).
tff(103,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))))),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1))),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))))),mult(ld(x1,x1),ld(x1,x1))) = mult(ld(x1,x1),x1),
inference(transitivity,[status(thm)],[103,100,97,86]) ).
tff(105,plain,
mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))))),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1))),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))))),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(107,plain,
mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))))),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))))),
inference(unit_resolution,[status(thm)],[106,29]) ).
tff(108,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))))) = mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))))),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),x1)) = x1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(110,plain,
ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),x1)) = x1,
inference(unit_resolution,[status(thm)],[109,16]) ).
tff(111,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(x1,x1),x1) = x1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(112,plain,
rd(mult(x1,x1),x1) = x1,
inference(unit_resolution,[status(thm)],[111,7]) ).
tff(113,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),x1) = rd(mult(mult(mult(ld(x1,x1),ld(x1,x1)),x1),ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[60]) ).
tff(114,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),x1) = x1,
inference(transitivity,[status(thm)],[113,66,69]) ).
tff(115,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),x1)) = mult(mult(ld(x1,x1),ld(x1,x1)),x1),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),x1)) = x1,
inference(transitivity,[status(thm)],[115,113,66,69]) ).
tff(117,plain,
mult(x1,mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),x1))) = mult(x1,x1),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))),x1) = mult(x1,mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),x1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(119,plain,
mult(mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))),x1) = mult(x1,mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),x1))),
inference(unit_resolution,[status(thm)],[118,29]) ).
tff(120,plain,
mult(mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))),x1) = mult(x1,x1),
inference(transitivity,[status(thm)],[119,117]) ).
tff(121,plain,
rd(mult(mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))),x1),x1) = rd(mult(x1,x1),x1),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))),x1),x1) = mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(123,plain,
rd(mult(mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))),x1),x1) = mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))),
inference(unit_resolution,[status(thm)],[122,7]) ).
tff(124,plain,
mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))) = rd(mult(mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))),x1),x1),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),x1),mult(ld(x1,x1),ld(x1,x1))) = mult(x1,mult(ld(x1,x1),ld(x1,x1))),
inference(monotonicity,[status(thm)],[114]) ).
tff(126,plain,
mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),x1),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),x1),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(128,plain,
mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),x1),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))))),
inference(unit_resolution,[status(thm)],[127,29]) ).
tff(129,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))))) = mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),x1),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))),
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))))) = mult(mult(ld(x1,x1),ld(x1,x1)),x1),
inference(transitivity,[status(thm)],[129,126,124,121,112,70,67,60]) ).
tff(131,plain,
ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))))) = ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),x1)),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))))) = mult(x1,mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(133,plain,
ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))))) = mult(x1,mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[132,16]) ).
tff(134,plain,
mult(x1,mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))) = ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))))),
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
mult(x1,mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))) = x1,
inference(transitivity,[status(thm)],[134,131,110]) ).
tff(136,plain,
ld(x1,mult(x1,mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))))) = ld(x1,x1),
inference(monotonicity,[status(thm)],[135]) ).
tff(137,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(x1,mult(x1,mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
ld(x1,mult(x1,mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))),
inference(unit_resolution,[status(thm)],[137,16]) ).
tff(139,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))) = ld(x1,mult(x1,mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))))),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))) = ld(x1,x1),
inference(transitivity,[status(thm)],[139,136]) ).
tff(141,plain,
mult(mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))) = mult(mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),ld(x1,x1)),
inference(monotonicity,[status(thm)],[140]) ).
tff(142,plain,
mult(mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),ld(x1,x1)) = mult(mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))),
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),ld(x1,x1))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))))),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),ld(x1,x1))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))))),
inference(transitivity,[status(thm)],[143,108,105,84,31]) ).
tff(145,plain,
ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),ld(x1,x1)))) = ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))))),
inference(monotonicity,[status(thm)],[144]) ).
tff(146,plain,
ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))))) = ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),ld(x1,x1)))),
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))),x1) = mult(ld(x1,x1),x1),
inference(monotonicity,[status(thm)],[140]) ).
tff(148,plain,
mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1))),
inference(monotonicity,[status(thm)],[147]) ).
tff(149,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(150,plain,
mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1))))),
inference(unit_resolution,[status(thm)],[149,29]) ).
tff(151,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1))))) = mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),ld(x1,x1))),
inference(symmetry,[status(thm)],[150]) ).
tff(152,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1))))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))))),
inference(transitivity,[status(thm)],[151,148,84,31]) ).
tff(153,plain,
ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))))) = ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))))),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(155,plain,
ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[154,16]) ).
tff(156,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))) = ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))))),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))) = mult(ld(x1,x1),ld(x1,x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(158,plain,
ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))) = mult(ld(x1,x1),ld(x1,x1)),
inference(unit_resolution,[status(thm)],[157,16]) ).
tff(159,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))),ld(x1,x1)) = mult(ld(x1,x1),ld(x1,x1)),
inference(monotonicity,[status(thm)],[140]) ).
tff(160,plain,
mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))),
inference(monotonicity,[status(thm)],[159]) ).
tff(161,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(162,plain,
mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))))),
inference(unit_resolution,[status(thm)],[161,29]) ).
tff(163,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))))) = mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))),
inference(symmetry,[status(thm)],[162]) ).
tff(164,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))),
inference(transitivity,[status(thm)],[163,160]) ).
tff(165,plain,
ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))))) = ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))),
inference(monotonicity,[status(thm)],[164]) ).
tff(166,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(167,plain,
ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[166,16]) ).
tff(168,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))) = ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))))),
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))) = mult(ld(x1,x1),ld(x1,x1)),
inference(transitivity,[status(thm)],[168,165,158]) ).
tff(170,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),mult(x1,mult(ld(x1,x1),ld(x1,x1)))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),mult(x1,mult(ld(x1,x1),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(172,plain,
rd(mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[171,7]) ).
tff(173,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(174,plain,
mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))))),
inference(unit_resolution,[status(thm)],[173,29]) ).
tff(175,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))))) = mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),mult(ld(x1,x1),ld(x1,x1))),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))) = x1,
inference(transitivity,[status(thm)],[124,121,112]) ).
tff(177,plain,
mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1)))) = mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,plain,
mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1) = mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1)))),
inference(symmetry,[status(thm)],[177]) ).
tff(179,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1)) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))))),
inference(monotonicity,[status(thm)],[178]) ).
tff(180,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(181,plain,
rd(mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),
inference(unit_resolution,[status(thm)],[180,7]) ).
tff(182,plain,
mult(ld(x1,x1),mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,ld(x1,x1)))) = mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),ld(x1,x1)),
inference(symmetry,[status(thm)],[75]) ).
tff(183,plain,
mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1)))) = x1,
inference(transitivity,[status(thm)],[95,92,42]) ).
tff(184,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1))))) = mult(mult(ld(x1,x1),ld(x1,x1)),x1),
inference(monotonicity,[status(thm)],[183]) ).
tff(185,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1)),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(186,plain,
mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1)),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1))))),
inference(unit_resolution,[status(thm)],[185,29]) ).
tff(187,plain,
mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1)),mult(ld(x1,x1),ld(x1,x1))) = x1,
inference(transitivity,[status(thm)],[186,184,113,66,69]) ).
tff(188,plain,
mult(ld(x1,x1),mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1)),mult(ld(x1,x1),ld(x1,x1)))) = mult(ld(x1,x1),x1),
inference(monotonicity,[status(thm)],[187]) ).
tff(189,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1))),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1)),mult(ld(x1,x1),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(190,plain,
mult(mult(mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1))),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1)),mult(ld(x1,x1),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[189,29]) ).
tff(191,plain,
mult(mult(mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1))),ld(x1,x1)),ld(x1,x1)) = mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),ld(x1,x1)),
inference(transitivity,[status(thm)],[190,188,72,182]) ).
tff(192,plain,
rd(mult(mult(mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1))),ld(x1,x1)),ld(x1,x1)),ld(x1,x1)) = rd(mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),ld(x1,x1)),ld(x1,x1)),
inference(monotonicity,[status(thm)],[191]) ).
tff(193,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1))),ld(x1,x1)),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1))),ld(x1,x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(194,plain,
rd(mult(mult(mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1))),ld(x1,x1)),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1))),ld(x1,x1)),
inference(unit_resolution,[status(thm)],[193,7]) ).
tff(195,plain,
mult(mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1))),ld(x1,x1)) = rd(mult(mult(mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1))),ld(x1,x1)),ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))),mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1))) = mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1))),
inference(monotonicity,[status(thm)],[140]) ).
tff(197,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))),mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1))),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))),mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(198,plain,
rd(mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))),mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1))),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))),mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1))),
inference(unit_resolution,[status(thm)],[197,7]) ).
tff(199,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))),mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1))),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1)),mult(ld(x1,x1),ld(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(200,plain,
mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))),mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1))),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1)),mult(ld(x1,x1),ld(x1,x1))))),
inference(unit_resolution,[status(thm)],[199,29]) ).
tff(201,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1)),mult(ld(x1,x1),ld(x1,x1))))) = mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))),mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1))),mult(ld(x1,x1),ld(x1,x1))),
inference(symmetry,[status(thm)],[200]) ).
tff(202,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1)),mult(ld(x1,x1),ld(x1,x1)))) = mult(mult(ld(x1,x1),ld(x1,x1)),x1),
inference(monotonicity,[status(thm)],[187]) ).
tff(203,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1)),mult(ld(x1,x1),ld(x1,x1)))) = x1,
inference(transitivity,[status(thm)],[202,113,66,69]) ).
tff(204,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1)),mult(ld(x1,x1),ld(x1,x1))))) = mult(mult(ld(x1,x1),ld(x1,x1)),x1),
inference(monotonicity,[status(thm)],[203]) ).
tff(205,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),x1) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1)),mult(ld(x1,x1),ld(x1,x1))))),
inference(symmetry,[status(thm)],[204]) ).
tff(206,plain,
mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1)),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))),mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1))),mult(ld(x1,x1),ld(x1,x1))),
inference(transitivity,[status(thm)],[186,184,205,201]) ).
tff(207,plain,
rd(mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1)),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))) = rd(mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))),mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1))),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))),
inference(monotonicity,[status(thm)],[206]) ).
tff(208,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1))))) = mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1)),mult(ld(x1,x1),ld(x1,x1))),
inference(symmetry,[status(thm)],[186]) ).
tff(209,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),x1) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(mult(ld(x1,x1),x1),mult(ld(x1,x1),ld(x1,x1))))),
inference(symmetry,[status(thm)],[184]) ).
tff(210,plain,
mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1)),mult(ld(x1,x1),ld(x1,x1))),
inference(transitivity,[status(thm)],[124,121,112,70,67,60,209,208]) ).
tff(211,plain,
rd(mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))) = rd(mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1)),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))),
inference(monotonicity,[status(thm)],[210]) ).
tff(212,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))) = mult(x1,mult(ld(x1,x1),ld(x1,x1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(213,plain,
rd(mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))) = mult(x1,mult(ld(x1,x1),ld(x1,x1))),
inference(unit_resolution,[status(thm)],[212,7]) ).
tff(214,plain,
mult(x1,mult(ld(x1,x1),ld(x1,x1))) = rd(mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))),
inference(symmetry,[status(thm)],[213]) ).
tff(215,plain,
mult(x1,mult(ld(x1,x1),ld(x1,x1))) = mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1))),
inference(transitivity,[status(thm)],[214,211,207,198,196]) ).
tff(216,plain,
mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))) = mult(mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),ld(x1,x1)),ld(x1,x1)),mult(ld(x1,x1),x1))),ld(x1,x1)),
inference(monotonicity,[status(thm)],[215,140]) ).
tff(217,plain,
mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))) = mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),
inference(transitivity,[status(thm)],[216,195,192,181]) ).
tff(218,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1)),
inference(monotonicity,[status(thm)],[217]) ).
tff(219,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(220,plain,
mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(x1,mult(ld(x1,x1),ld(x1,x1))),mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))))),
inference(unit_resolution,[status(thm)],[219,29]) ).
tff(221,plain,
mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),mult(ld(x1,x1),ld(x1,x1))),
inference(transitivity,[status(thm)],[220,218,179,175]) ).
tff(222,plain,
rd(mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))) = rd(mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))),
inference(monotonicity,[status(thm)],[221]) ).
tff(223,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),mult(ld(x1,x1),ld(x1,x1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(224,plain,
rd(mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),mult(ld(x1,x1),ld(x1,x1))),
inference(unit_resolution,[status(thm)],[223,7]) ).
tff(225,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),mult(ld(x1,x1),ld(x1,x1))) = rd(mult(mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))),mult(ld(x1,x1),ld(x1,x1))),
inference(symmetry,[status(thm)],[224]) ).
tff(226,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),ld(x1,x1)),
inference(transitivity,[status(thm)],[225,222,172,170,156,153,146,22]) ).
tff(227,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))))) = mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(228,plain,
ld(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))))) = mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[227,16]) ).
tff(229,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))) = mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),
inference(transitivity,[status(thm)],[156,153,228]) ).
tff(230,plain,
ld(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),mult(ld(x1,x1),ld(x1,x1)))) = ld(mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),mult(mult(mult(mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1))),x1),mult(ld(x1,x1),mult(ld(x1,x1),ld(x1,x1)))),ld(x1,x1))),
inference(monotonicity,[status(thm)],[229,226]) ).
tff(231,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),mult(ld(x1,x1),ld(x1,x1)))) = mult(ld(x1,x1),ld(x1,x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(232,plain,
ld(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),mult(ld(x1,x1),ld(x1,x1)))) = mult(ld(x1,x1),ld(x1,x1)),
inference(unit_resolution,[status(thm)],[231,16]) ).
tff(233,plain,
mult(ld(x1,x1),ld(x1,x1)) = ld(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x1,mult(ld(x1,x1),ld(x1,x1)))),mult(ld(x1,x1),ld(x1,x1)))),
inference(symmetry,[status(thm)],[232]) ).
tff(234,plain,
mult(ld(x1,x1),ld(x1,x1)) = ld(x1,x1),
inference(transitivity,[status(thm)],[233,230,20]) ).
tff(235,plain,
mult(mult(x0,x1),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(x0,x1),ld(x1,x1)),
inference(monotonicity,[status(thm)],[234]) ).
tff(236,plain,
mult(ld(x1,x1),mult(mult(x0,x1),mult(ld(x1,x1),ld(x1,x1)))) = mult(ld(x1,x1),mult(mult(x0,x1),ld(x1,x1))),
inference(monotonicity,[status(thm)],[235]) ).
tff(237,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(x0,x1),mult(ld(x1,x1),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(238,plain,
mult(mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(x0,x1),mult(ld(x1,x1),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[237,29]) ).
tff(239,plain,
mult(mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(x0,x1),ld(x1,x1))),
inference(transitivity,[status(thm)],[238,236]) ).
tff(240,plain,
mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)),ld(x1,x1))) = mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(x0,x1),ld(x1,x1)))),
inference(monotonicity,[status(thm)],[239]) ).
tff(241,plain,
mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(x0,x1),ld(x1,x1)))) = mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)),ld(x1,x1))),
inference(symmetry,[status(thm)],[240]) ).
tff(242,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x0,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(x0,x1),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(243,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x0,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(x0,x1),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[242,29]) ).
tff(244,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(x0,x1)) = mult(ld(x1,x1),mult(x0,x1)),
inference(monotonicity,[status(thm)],[234]) ).
tff(245,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x0,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)),
inference(monotonicity,[status(thm)],[244]) ).
tff(246,plain,
mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)) = mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x0,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[245]) ).
tff(247,plain,
mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)),ld(x1,x1))),
inference(transitivity,[status(thm)],[246,243,241]) ).
tff(248,plain,
mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))) = mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)),ld(x1,x1)))),
inference(monotonicity,[status(thm)],[247]) ).
tff(249,plain,
mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)),ld(x1,x1)))) = mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),
inference(symmetry,[status(thm)],[248]) ).
tff(250,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(251,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),ld(x1,x1)) = mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[250,29]) ).
tff(252,plain,
mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))) = mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),
inference(monotonicity,[status(thm)],[234]) ).
tff(253,plain,
mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),ld(x1,x1)) = mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),
inference(monotonicity,[status(thm)],[252]) ).
tff(254,plain,
mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),ld(x1,x1)) = mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),
inference(symmetry,[status(thm)],[253]) ).
tff(255,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),ld(x1,x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(256,plain,
rd(mult(mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),
inference(unit_resolution,[status(thm)],[255,7]) ).
tff(257,plain,
mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(x0,x1),ld(x1,x1)))) = mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(x0,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[243]) ).
tff(258,plain,
mult(mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))) = mult(mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)),ld(x1,x1)),
inference(monotonicity,[status(thm)],[234]) ).
tff(259,plain,
mult(mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1))) = mult(ld(x1,x1),mult(mult(x0,x1),ld(x1,x1))),
inference(transitivity,[status(thm)],[258,238,236]) ).
tff(260,plain,
mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))) = mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(x0,x1),ld(x1,x1)))),
inference(monotonicity,[status(thm)],[259]) ).
tff(261,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(262,plain,
mult(mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)),mult(ld(x1,x1),ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[261,29]) ).
tff(263,plain,
mult(mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)),
inference(transitivity,[status(thm)],[262,260,257,245]) ).
tff(264,plain,
rd(mult(mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)),ld(x1,x1)) = rd(mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)),ld(x1,x1)),
inference(monotonicity,[status(thm)],[263]) ).
tff(265,plain,
rd(mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)),ld(x1,x1)) = rd(mult(mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[264]) ).
tff(266,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(x0,x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(267,plain,
rd(mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(x0,x1)),
inference(unit_resolution,[status(thm)],[266,7]) ).
tff(268,plain,
mult(ld(x1,x1),mult(x0,x1)) = rd(mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[267]) ).
tff(269,plain,
mult(ld(x1,x1),mult(x0,x1)) = mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),
inference(transitivity,[status(thm)],[268,265,256,254,251,249]) ).
tff(270,plain,
ld(ld(x1,x1),mult(ld(x1,x1),mult(x0,x1))) = ld(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)))),
inference(monotonicity,[status(thm)],[269]) ).
tff(271,plain,
ld(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)))) = ld(ld(x1,x1),mult(ld(x1,x1),mult(x0,x1))),
inference(symmetry,[status(thm)],[270]) ).
tff(272,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)))) = mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(273,plain,
ld(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)))) = mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)),
inference(unit_resolution,[status(thm)],[272,16]) ).
tff(274,plain,
mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)) = ld(ld(x1,x1),mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)))),
inference(symmetry,[status(thm)],[273]) ).
tff(275,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(ld(x1,x1),x0),x1),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),x0),x1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(276,plain,
rd(mult(mult(mult(ld(x1,x1),x0),x1),ld(x1,x1)),ld(x1,x1)) = mult(mult(ld(x1,x1),x0),x1),
inference(unit_resolution,[status(thm)],[275,7]) ).
tff(277,plain,
mult(x0,mult(x1,ld(x1,x1))) = mult(x0,x1),
inference(monotonicity,[status(thm)],[42]) ).
tff(278,plain,
mult(ld(x1,x1),mult(x0,mult(x1,ld(x1,x1)))) = mult(ld(x1,x1),mult(x0,x1)),
inference(monotonicity,[status(thm)],[277]) ).
tff(279,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) )
| ( mult(mult(mult(ld(x1,x1),x0),x1),ld(x1,x1)) = mult(ld(x1,x1),mult(x0,mult(x1,ld(x1,x1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(280,plain,
mult(mult(mult(ld(x1,x1),x0),x1),ld(x1,x1)) = mult(ld(x1,x1),mult(x0,mult(x1,ld(x1,x1)))),
inference(unit_resolution,[status(thm)],[279,29]) ).
tff(281,plain,
mult(mult(mult(ld(x1,x1),x0),x1),ld(x1,x1)) = mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),
inference(transitivity,[status(thm)],[280,278,268,265,256]) ).
tff(282,plain,
rd(mult(mult(mult(ld(x1,x1),x0),x1),ld(x1,x1)),ld(x1,x1)) = rd(mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)),
inference(monotonicity,[status(thm)],[281]) ).
tff(283,plain,
rd(mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)) = rd(mult(mult(mult(ld(x1,x1),x0),x1),ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[282]) ).
tff(284,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(285,plain,
rd(mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)) = mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),
inference(unit_resolution,[status(thm)],[284,7]) ).
tff(286,plain,
mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))) = rd(mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[285]) ).
tff(287,plain,
mult(ld(x1,x1),mult(x0,x1)) = mult(mult(ld(x1,x1),x0),x1),
inference(transitivity,[status(thm)],[268,265,256,254,251,249,286,283,276]) ).
tff(288,plain,
mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)) = mult(mult(mult(ld(x1,x1),x0),x1),ld(x1,x1)),
inference(monotonicity,[status(thm)],[287]) ).
tff(289,plain,
mult(mult(mult(ld(x1,x1),x0),x1),ld(x1,x1)) = mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[288]) ).
tff(290,plain,
mult(ld(x1,x1),mult(x0,mult(x1,ld(x1,x1)))) = mult(mult(mult(ld(x1,x1),x0),x1),ld(x1,x1)),
inference(symmetry,[status(thm)],[280]) ).
tff(291,plain,
mult(ld(x1,x1),mult(x0,x1)) = mult(ld(x1,x1),mult(x0,mult(x1,ld(x1,x1)))),
inference(symmetry,[status(thm)],[278]) ).
tff(292,plain,
mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),ld(x1,x1)) = rd(mult(mult(mult(ld(x1,x1),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[256]) ).
tff(293,plain,
mult(ld(x1,x1),mult(ld(x1,x1),mult(mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1)),ld(x1,x1)))) = mult(mult(mult(ld(x1,x1),ld(x1,x1)),mult(mult(ld(x1,x1),mult(x0,x1)),ld(x1,x1))),ld(x1,x1)),
inference(symmetry,[status(thm)],[251]) ).
tff(294,plain,
mult(mult(ld(x1,x1),x0),x1) = rd(mult(mult(mult(ld(x1,x1),x0),x1),ld(x1,x1)),ld(x1,x1)),
inference(symmetry,[status(thm)],[276]) ).
tff(295,plain,
mult(mult(ld(x1,x1),x0),x1) = mult(x0,x1),
inference(transitivity,[status(thm)],[294,282,285,248,293,253,292,264,267,291,290,289,274,271,18]) ).
tff(296,plain,
rd(mult(mult(ld(x1,x1),x0),x1),x1) = rd(mult(x0,x1),x1),
inference(monotonicity,[status(thm)],[295]) ).
tff(297,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(ld(x1,x1),x0),x1),x1) = mult(ld(x1,x1),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(298,plain,
rd(mult(mult(ld(x1,x1),x0),x1),x1) = mult(ld(x1,x1),x0),
inference(unit_resolution,[status(thm)],[297,7]) ).
tff(299,plain,
mult(ld(x1,x1),x0) = rd(mult(mult(ld(x1,x1),x0),x1),x1),
inference(symmetry,[status(thm)],[298]) ).
tff(300,plain,
mult(ld(x1,x1),x0) = x0,
inference(transitivity,[status(thm)],[299,296,9]) ).
tff(301,plain,
( ( mult(ld(x1,x1),x0) != x0 )
<=> ( mult(ld(x1,x1),x0) != x0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(302,axiom,
mult(ld(x1,x1),x0) != x0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tff(303,plain,
mult(ld(x1,x1),x0) != x0,
inference(modus_ponens,[status(thm)],[302,301]) ).
tff(304,plain,
$false,
inference(unit_resolution,[status(thm)],[303,300]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GRP660-14 : TPTP v8.1.0. Released v8.1.0.
% 0.08/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n016.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 19:58:18 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33 Usage: tptp [options] [-file:]file
% 0.13/0.33 -h, -? prints this message.
% 0.13/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.33 -m, -model generate model.
% 0.13/0.33 -p, -proof generate proof.
% 0.13/0.33 -c, -core generate unsat core of named formulas.
% 0.13/0.33 -st, -statistics display statistics.
% 0.13/0.33 -t:timeout set timeout (in second).
% 0.13/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33 -<param>:<value> configuration parameter and value.
% 0.13/0.33 -o:<output-file> file to place output in.
% 0.66/0.65 % SZS status Unsatisfiable
% 0.66/0.65 % SZS output start Proof
% See solution above
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