TSTP Solution File: GRP705-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP705-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 22:29:34 EDT 2022
% Result : Unsatisfiable 6.54s 4.54s
% Output : Proof 6.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 70
% Syntax : Number of formulae : 276 ( 213 unt; 7 typ; 0 def)
% Number of atoms : 339 ( 331 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 108 ( 45 ~; 41 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of FOOLs : 7 ( 7 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 190 ( 179 !; 0 ?; 190 :)
% Comments :
%------------------------------------------------------------------------------
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(op_b_type,type,
op_b: $i ).
tff(op_a_type,type,
op_a: $i ).
tff(unit_type,type,
unit: $i ).
tff(rd_type,type,
rd: ( $i * $i ) > $i ).
tff(ld_type,type,
ld: ( $i * $i ) > $i ).
tff(1,plain,
^ [A: $i] :
refl(
( ( mult(A,mult(op_a,mult(op_a,mult(op_a,op_a)))) = A )
<=> ( mult(A,mult(op_a,mult(op_a,mult(op_a,op_a)))) = A ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [A: $i] : ( mult(A,mult(op_a,mult(op_a,mult(op_a,op_a)))) = A )
<=> ! [A: $i] : ( mult(A,mult(op_a,mult(op_a,mult(op_a,op_a)))) = A ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [A: $i] :
rewrite(
( ( mult(A,unit) = A )
<=> ( mult(A,mult(op_a,mult(op_a,mult(op_a,op_a)))) = A ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [A: $i] : ( mult(A,unit) = A )
<=> ! [A: $i] : ( mult(A,mult(op_a,mult(op_a,mult(op_a,op_a)))) = A ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [A: $i] : ( mult(A,unit) = A )
<=> ! [A: $i] : ( mult(A,unit) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
! [A: $i] : ( mult(A,unit) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
tff(7,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [A: $i] : ( mult(A,mult(op_a,mult(op_a,mult(op_a,op_a)))) = A ),
inference(modus_ponens,[status(thm)],[7,4]) ).
tff(9,plain,
! [A: $i] : ( mult(A,mult(op_a,mult(op_a,mult(op_a,op_a)))) = A ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [A: $i] : ( mult(A,mult(op_a,mult(op_a,mult(op_a,op_a)))) = A ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ ! [A: $i] : ( mult(A,mult(op_a,mult(op_a,mult(op_a,op_a)))) = A )
| ( mult(op_b,mult(op_a,mult(op_a,mult(op_a,op_a)))) = op_b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
mult(op_b,mult(op_a,mult(op_a,mult(op_a,op_a)))) = op_b,
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
( ( mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = unit )
<=> ( mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = mult(op_a,mult(op_a,mult(op_a,op_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( ( mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = unit )
<=> ( mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = unit ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c09) ).
tff(16,plain,
mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = unit,
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = mult(op_a,mult(op_a,mult(op_a,op_a))),
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
<=> ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c07) ).
tff(22,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(26,plain,
mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))),
inference(unit_resolution,[status(thm)],[28,24]) ).
tff(30,plain,
mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b)))) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b)))) = mult(op_a,mult(op_a,mult(op_a,op_a))),
inference(transitivity,[status(thm)],[31,27,17]) ).
tff(33,plain,
mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))))) = mult(op_b,mult(op_a,mult(op_a,mult(op_a,op_a)))),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))))) = mult(mult(mult(op_b,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))))) = mult(mult(mult(op_b,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))),
inference(unit_resolution,[status(thm)],[34,24]) ).
tff(36,plain,
mult(mult(mult(op_b,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))) = mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))))),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
^ [B: $i,A: $i] :
refl(
( ( rd(mult(A,B),B) = A )
<=> ( rd(mult(A,B),B) = A ) )),
inference(bind,[status(th)],]) ).
tff(38,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)],[37]) ).
tff(39,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(40,axiom,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
tff(41,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(op_b,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),op_b),op_b) = mult(mult(op_b,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
rd(mult(mult(mult(op_b,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),op_b),op_b) = mult(mult(op_b,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),mult(op_b,mult(op_b,op_b))) = mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),op_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),mult(op_b,mult(op_b,op_b))) = mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),op_b),
inference(unit_resolution,[status(thm)],[46,24]) ).
tff(48,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))) = mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),mult(op_b,mult(op_b,op_b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))) = mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),mult(op_b,mult(op_b,op_b))),
inference(unit_resolution,[status(thm)],[48,24]) ).
tff(50,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))))) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))))) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))),
inference(unit_resolution,[status(thm)],[50,24]) ).
tff(52,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b)))),
inference(unit_resolution,[status(thm)],[52,24]) ).
tff(54,plain,
mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b)))) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_b,mult(op_b,mult(op_b,op_b))) = mult(mult(mult(op_b,op_b),op_b),op_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
mult(op_b,mult(op_b,mult(op_b,op_b))) = mult(mult(mult(op_b,op_b),op_b),op_b),
inference(unit_resolution,[status(thm)],[55,24]) ).
tff(57,plain,
mult(mult(mult(op_b,op_b),op_b),op_b) = mult(op_b,mult(op_b,mult(op_b,op_b))),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b)) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b)))),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b)) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))),
inference(transitivity,[status(thm)],[58,54]) ).
tff(60,plain,
mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b))) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))))),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b))) = mult(mult(mult(op_b,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),op_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b))) = mult(mult(mult(op_b,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),op_b),
inference(unit_resolution,[status(thm)],[61,24]) ).
tff(63,plain,
mult(mult(mult(op_b,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),op_b) = mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b))),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
mult(mult(mult(op_b,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),op_b) = mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),op_b),
inference(transitivity,[status(thm)],[63,60,51,49,47]) ).
tff(65,plain,
rd(mult(mult(mult(op_b,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),op_b),op_b) = rd(mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),op_b),op_b),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
rd(mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),op_b),op_b) = rd(mult(mult(mult(op_b,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),op_b),op_b),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),op_b),op_b) = mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
rd(mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),op_b),op_b) = mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),
inference(unit_resolution,[status(thm)],[67,43]) ).
tff(69,plain,
mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b) = rd(mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),op_b),op_b),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(mult(mult(mult(op_b,op_b),op_b),op_b),mult(op_b,mult(op_b,op_b))) = mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
mult(mult(mult(mult(op_b,op_b),op_b),op_b),mult(op_b,mult(op_b,op_b))) = mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),
inference(unit_resolution,[status(thm)],[70,24]) ).
tff(72,plain,
mult(mult(mult(mult(op_b,op_b),op_b),op_b),mult(op_b,mult(op_b,op_b))) = mult(mult(op_b,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),
inference(transitivity,[status(thm)],[71,69,66,45]) ).
tff(73,plain,
mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))) = mult(mult(mult(op_b,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))) = op_b,
inference(transitivity,[status(thm)],[73,36,33,12]) ).
tff(75,plain,
mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))),mult(op_b,op_b)) = mult(op_b,mult(op_b,op_b)),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(mult(mult(mult(op_b,op_b),op_b),op_b),mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(op_b,op_b)))) = mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))),mult(op_b,op_b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(77,plain,
mult(mult(mult(mult(op_b,op_b),op_b),op_b),mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(op_b,op_b)))) = mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))),mult(op_b,op_b)),
inference(unit_resolution,[status(thm)],[76,24]) ).
tff(78,plain,
^ [B: $i,A: $i] :
refl(
( ( ld(A,mult(A,B)) = B )
<=> ( ld(A,mult(A,B)) = B ) )),
inference(bind,[status(th)],]) ).
tff(79,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)],[78]) ).
tff(80,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(81,axiom,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
tff(82,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[83,79]) ).
tff(85,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(op_b,mult(op_b,mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(op_b,op_b))))) = mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(op_b,op_b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
ld(op_b,mult(op_b,mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(op_b,op_b))))) = mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(op_b,op_b))),
inference(unit_resolution,[status(thm)],[85,84]) ).
tff(87,plain,
mult(op_b,mult(mult(mult(op_b,op_b),op_b),op_b)) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))),
inference(monotonicity,[status(thm)],[57]) ).
tff(88,plain,
mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),op_b))) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),op_b)))) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),op_b)))) = mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),op_b)))) = mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b)),
inference(unit_resolution,[status(thm)],[90,24]) ).
tff(92,plain,
mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b)) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),op_b)))),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b)))) = mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b)),
inference(monotonicity,[status(thm)],[56]) ).
tff(94,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b)))) = mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),mult(op_b,op_b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b)))) = mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),mult(op_b,op_b)),
inference(unit_resolution,[status(thm)],[94,24]) ).
tff(96,plain,
mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),mult(op_b,op_b)) = mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b)))),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
mult(mult(op_b,mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))) = mult(mult(mult(mult(op_b,op_b),op_b),op_b),mult(op_b,mult(op_b,op_b))),
inference(monotonicity,[status(thm)],[56]) ).
tff(98,plain,
mult(mult(op_b,mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))) = mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),
inference(transitivity,[status(thm)],[97,71]) ).
tff(99,plain,
mult(mult(mult(op_b,mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))),mult(op_b,op_b)) = mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),mult(op_b,op_b)),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_b,mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(op_b,op_b)))) = mult(mult(mult(op_b,mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))),mult(op_b,op_b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
mult(op_b,mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(op_b,op_b)))) = mult(mult(mult(op_b,mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))),mult(op_b,op_b)),
inference(unit_resolution,[status(thm)],[100,24]) ).
tff(102,plain,
mult(op_b,mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(op_b,op_b)))) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))),
inference(transitivity,[status(thm)],[101,99,96,93,92,89,27]) ).
tff(103,plain,
ld(op_b,mult(op_b,mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(op_b,op_b))))) = ld(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))))))),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
ld(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))))))) = ld(op_b,mult(op_b,mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(op_b,op_b))))),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))))))) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(106,plain,
ld(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))))))) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))))),
inference(unit_resolution,[status(thm)],[105,84]) ).
tff(107,plain,
mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))))) = ld(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))))))),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))))),
inference(symmetry,[status(thm)],[51]) ).
tff(109,plain,
mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))) = mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(op_b,op_b))),
inference(transitivity,[status(thm)],[108,107,104,86]) ).
tff(110,plain,
mult(mult(mult(mult(op_b,op_b),op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))) = mult(mult(mult(mult(op_b,op_b),op_b),op_b),mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(op_b,op_b)))),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(mult(op_b,op_b),mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = mult(mult(mult(mult(op_b,op_b),op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(112,plain,
mult(mult(op_b,op_b),mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = mult(mult(mult(mult(op_b,op_b),op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))),
inference(unit_resolution,[status(thm)],[111,24]) ).
tff(113,plain,
mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))),
inference(monotonicity,[status(thm)],[108]) ).
tff(114,plain,
mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))) = mult(op_a,mult(op_a,mult(op_a,op_a))),
inference(transitivity,[status(thm)],[113,17]) ).
tff(115,plain,
mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))))) = mult(op_b,mult(op_a,mult(op_a,mult(op_a,op_a)))),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
mult(op_b,mult(op_a,mult(op_a,mult(op_a,op_a)))) = mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))))),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
op_b = mult(op_b,mult(op_a,mult(op_a,mult(op_a,op_a)))),
inference(symmetry,[status(thm)],[12]) ).
tff(118,plain,
op_b = mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))))),
inference(transitivity,[status(thm)],[117,116]) ).
tff(119,plain,
mult(mult(op_b,op_b),op_b) = mult(mult(op_b,op_b),mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
mult(mult(op_b,op_b),op_b) = mult(op_b,mult(op_b,op_b)),
inference(transitivity,[status(thm)],[119,112,110,77,75]) ).
tff(121,plain,
mult(mult(mult(op_b,op_b),op_b),op_b) = mult(mult(op_b,mult(op_b,op_b)),op_b),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
mult(mult(op_b,mult(op_b,op_b)),op_b) = mult(mult(mult(op_b,op_b),op_b),op_b),
inference(symmetry,[status(thm)],[121]) ).
tff(123,plain,
mult(mult(op_b,op_b),mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = mult(mult(op_b,op_b),op_b),
inference(symmetry,[status(thm)],[119]) ).
tff(124,plain,
mult(mult(mult(mult(op_b,op_b),op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))) = mult(mult(op_b,op_b),mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))),
inference(symmetry,[status(thm)],[112]) ).
tff(125,plain,
mult(mult(mult(mult(op_b,op_b),op_b),op_b),mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(op_b,op_b)))) = mult(mult(mult(mult(op_b,op_b),op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))),
inference(symmetry,[status(thm)],[110]) ).
tff(126,plain,
mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))),mult(op_b,op_b)) = mult(mult(mult(mult(op_b,op_b),op_b),op_b),mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(op_b,op_b)))),
inference(symmetry,[status(thm)],[77]) ).
tff(127,plain,
mult(op_b,mult(op_b,op_b)) = mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))),mult(op_b,op_b)),
inference(symmetry,[status(thm)],[75]) ).
tff(128,plain,
mult(op_b,mult(op_b,op_b)) = mult(mult(op_b,op_b),op_b),
inference(transitivity,[status(thm)],[127,126,125,124,123]) ).
tff(129,plain,
mult(mult(op_b,mult(op_b,op_b)),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b)))) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))),
inference(monotonicity,[status(thm)],[128,30]) ).
tff(130,plain,
mult(mult(op_b,mult(op_b,op_b)),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b)))) = mult(op_a,mult(op_a,mult(op_a,op_a))),
inference(transitivity,[status(thm)],[129,27,17]) ).
tff(131,plain,
mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))))) = mult(mult(op_b,mult(op_b,op_b)),mult(op_a,mult(op_a,mult(op_a,op_a)))),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
mult(mult(op_b,mult(op_b,op_b)),mult(op_a,mult(op_a,mult(op_a,op_a)))) = mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))))),
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
( ~ ! [A: $i] : ( mult(A,mult(op_a,mult(op_a,mult(op_a,op_a)))) = A )
| ( mult(mult(op_b,mult(op_b,op_b)),mult(op_a,mult(op_a,mult(op_a,op_a)))) = mult(op_b,mult(op_b,op_b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(134,plain,
mult(mult(op_b,mult(op_b,op_b)),mult(op_a,mult(op_a,mult(op_a,op_a)))) = mult(op_b,mult(op_b,op_b)),
inference(unit_resolution,[status(thm)],[133,10]) ).
tff(135,plain,
mult(op_b,mult(op_b,op_b)) = mult(mult(op_b,mult(op_b,op_b)),mult(op_a,mult(op_a,mult(op_a,op_a)))),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
mult(mult(op_b,op_b),op_b) = mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))))),
inference(transitivity,[status(thm)],[119,112,110,77,75,135,132]) ).
tff(137,plain,
mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)) = mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b)))))),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b)))))) = mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b)))))) = mult(mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(140,plain,
mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b)))))) = mult(mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b)))),
inference(unit_resolution,[status(thm)],[139,24]) ).
tff(141,plain,
mult(mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b)))) = mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b)))))),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
( ~ ! [A: $i] : ( mult(A,mult(op_a,mult(op_a,mult(op_a,op_a)))) = A )
| ( mult(op_a,mult(op_a,mult(op_a,mult(op_a,op_a)))) = op_a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(143,plain,
mult(op_a,mult(op_a,mult(op_a,mult(op_a,op_a)))) = op_a,
inference(unit_resolution,[status(thm)],[142,10]) ).
tff(144,plain,
mult(op_a,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))))) = mult(op_a,mult(op_a,mult(op_a,mult(op_a,op_a)))),
inference(monotonicity,[status(thm)],[32]) ).
tff(145,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_a,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))))) = mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(146,plain,
mult(op_a,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))))) = mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))),
inference(unit_resolution,[status(thm)],[145,24]) ).
tff(147,plain,
mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))) = mult(op_a,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))))),
inference(symmetry,[status(thm)],[146]) ).
tff(148,plain,
mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))) = mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),
inference(monotonicity,[status(thm)],[128]) ).
tff(149,plain,
mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))) = mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))),
inference(monotonicity,[status(thm)],[148]) ).
tff(150,plain,
mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))) = op_a,
inference(transitivity,[status(thm)],[149,147,144,143]) ).
tff(151,plain,
mult(mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b)))) = mult(op_a,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b)))),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
mult(op_a,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b)))) = mult(mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b)))),
inference(symmetry,[status(thm)],[151]) ).
tff(153,plain,
mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),op_b))) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))),
inference(transitivity,[status(thm)],[88,29]) ).
tff(154,plain,
mult(op_a,mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),op_b)))) = mult(op_a,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b)))),
inference(monotonicity,[status(thm)],[153]) ).
tff(155,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_a,mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),op_b)))) = mult(mult(mult(op_a,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(156,plain,
mult(op_a,mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),op_b)))) = mult(mult(mult(op_a,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b)),
inference(unit_resolution,[status(thm)],[155,24]) ).
tff(157,plain,
mult(mult(mult(op_a,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b)) = mult(op_a,mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),op_b)))),
inference(symmetry,[status(thm)],[156]) ).
tff(158,plain,
mult(mult(mult(op_a,op_b),op_b),mult(mult(op_b,mult(op_b,op_b)),op_b)) = mult(mult(mult(op_a,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b)),
inference(monotonicity,[status(thm)],[122]) ).
tff(159,plain,
mult(mult(mult(op_a,op_b),op_b),mult(mult(op_b,mult(op_b,op_b)),op_b)) = mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),
inference(transitivity,[status(thm)],[158,157,154,152,141,138]) ).
tff(160,plain,
mult(mult(mult(mult(op_a,op_b),op_b),mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b)) = mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),op_b)),
inference(monotonicity,[status(thm)],[159,122]) ).
tff(161,plain,
mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),op_b)) = mult(mult(mult(mult(op_a,op_b),op_b),mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b)),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_a,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b)))) = mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),op_b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(163,plain,
mult(op_a,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b)))) = mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),op_b)),
inference(unit_resolution,[status(thm)],[162,24]) ).
tff(164,plain,
mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))))),
inference(monotonicity,[status(thm)],[54]) ).
tff(165,plain,
mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b)))))) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))),
inference(monotonicity,[status(thm)],[164]) ).
tff(166,plain,
mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b)))))) = mult(op_a,mult(op_a,mult(op_a,op_a))),
inference(transitivity,[status(thm)],[165,17]) ).
tff(167,plain,
mult(op_b,mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))))) = mult(op_b,mult(op_a,mult(op_a,mult(op_a,op_a)))),
inference(monotonicity,[status(thm)],[166]) ).
tff(168,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_b,mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))))) = mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(169,plain,
mult(op_b,mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))))) = mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))),
inference(unit_resolution,[status(thm)],[168,24]) ).
tff(170,plain,
mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))) = mult(op_b,mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))))),
inference(symmetry,[status(thm)],[169]) ).
tff(171,plain,
mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b))) = mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))),
inference(monotonicity,[status(thm)],[58]) ).
tff(172,plain,
mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b))) = op_b,
inference(transitivity,[status(thm)],[171,170,167,12]) ).
tff(173,plain,
mult(op_a,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b)))) = mult(op_a,op_b),
inference(monotonicity,[status(thm)],[172]) ).
tff(174,plain,
mult(op_a,op_b) = mult(op_a,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b)))),
inference(symmetry,[status(thm)],[173]) ).
tff(175,plain,
mult(op_a,op_b) = mult(mult(mult(mult(op_a,op_b),op_b),mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b)),
inference(transitivity,[status(thm)],[174,163,161]) ).
tff(176,plain,
mult(mult(op_a,op_b),a) = mult(mult(mult(mult(mult(op_a,op_b),op_b),mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b)),a),
inference(monotonicity,[status(thm)],[175]) ).
tff(177,plain,
mult(mult(mult(mult(mult(op_a,op_b),op_b),mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b)),a) = mult(mult(op_a,op_b),a),
inference(symmetry,[status(thm)],[176]) ).
tff(178,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(mult(mult(op_a,op_b),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),a))) = mult(mult(mult(mult(mult(op_a,op_b),op_b),mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b)),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(179,plain,
mult(mult(mult(op_a,op_b),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),a))) = mult(mult(mult(mult(mult(op_a,op_b),op_b),mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b)),a),
inference(unit_resolution,[status(thm)],[178,24]) ).
tff(180,plain,
^ [A: $i] :
refl(
( ( mult(mult(op_a,mult(op_a,mult(op_a,op_a))),A) = A )
<=> ( mult(mult(op_a,mult(op_a,mult(op_a,op_a))),A) = A ) )),
inference(bind,[status(th)],]) ).
tff(181,plain,
( ! [A: $i] : ( mult(mult(op_a,mult(op_a,mult(op_a,op_a))),A) = A )
<=> ! [A: $i] : ( mult(mult(op_a,mult(op_a,mult(op_a,op_a))),A) = A ) ),
inference(quant_intro,[status(thm)],[180]) ).
tff(182,plain,
^ [A: $i] :
rewrite(
( ( mult(unit,A) = A )
<=> ( mult(mult(op_a,mult(op_a,mult(op_a,op_a))),A) = A ) )),
inference(bind,[status(th)],]) ).
tff(183,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(mult(op_a,mult(op_a,mult(op_a,op_a))),A) = A ) ),
inference(quant_intro,[status(thm)],[182]) ).
tff(184,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(185,axiom,
! [A: $i] : ( mult(unit,A) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c06) ).
tff(186,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[185,184]) ).
tff(187,plain,
! [A: $i] : ( mult(mult(op_a,mult(op_a,mult(op_a,op_a))),A) = A ),
inference(modus_ponens,[status(thm)],[186,183]) ).
tff(188,plain,
! [A: $i] : ( mult(mult(op_a,mult(op_a,mult(op_a,op_a))),A) = A ),
inference(skolemize,[status(sab)],[187]) ).
tff(189,plain,
! [A: $i] : ( mult(mult(op_a,mult(op_a,mult(op_a,op_a))),A) = A ),
inference(modus_ponens,[status(thm)],[188,181]) ).
tff(190,plain,
( ~ ! [A: $i] : ( mult(mult(op_a,mult(op_a,mult(op_a,op_a))),A) = A )
| ( mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(191,plain,
mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a) = a,
inference(unit_resolution,[status(thm)],[190,189]) ).
tff(192,plain,
( ~ ! [A: $i] : ( mult(mult(op_a,mult(op_a,mult(op_a,op_a))),A) = A )
| ( mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a)) = mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(193,plain,
mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a)) = mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a),
inference(unit_resolution,[status(thm)],[192,189]) ).
tff(194,plain,
mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a)) = a,
inference(transitivity,[status(thm)],[193,191]) ).
tff(195,plain,
mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a))) = mult(mult(mult(op_b,mult(op_b,op_b)),op_b),a),
inference(monotonicity,[status(thm)],[194]) ).
tff(196,plain,
mult(mult(mult(op_b,mult(op_b,op_b)),op_b),a) = mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a))),
inference(symmetry,[status(thm)],[195]) ).
tff(197,plain,
mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),a)) = mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a)))),
inference(monotonicity,[status(thm)],[196]) ).
tff(198,plain,
mult(mult(mult(op_a,op_b),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),a))) = mult(mult(mult(op_a,op_b),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a))))),
inference(monotonicity,[status(thm)],[197]) ).
tff(199,plain,
mult(mult(mult(op_a,op_b),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a))))) = mult(mult(mult(op_a,op_b),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),a))),
inference(symmetry,[status(thm)],[198]) ).
tff(200,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_a,mult(op_b,mult(op_b,mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a))))))) = mult(mult(mult(op_a,op_b),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(201,plain,
mult(op_a,mult(op_b,mult(op_b,mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a))))))) = mult(mult(mult(op_a,op_b),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a))))),
inference(unit_resolution,[status(thm)],[200,24]) ).
tff(202,plain,
mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b) = mult(mult(op_b,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),
inference(transitivity,[status(thm)],[69,66,45]) ).
tff(203,plain,
mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),mult(op_b,mult(op_b,op_b))) = mult(mult(mult(op_b,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))),
inference(monotonicity,[status(thm)],[202]) ).
tff(204,plain,
mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),mult(op_b,mult(op_b,op_b))) = op_b,
inference(transitivity,[status(thm)],[203,36,33,12]) ).
tff(205,plain,
mult(mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))) = mult(op_b,mult(op_b,mult(op_b,op_b))),
inference(monotonicity,[status(thm)],[204]) ).
tff(206,plain,
mult(op_b,mult(op_b,mult(op_b,op_b))) = mult(mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))),
inference(symmetry,[status(thm)],[205]) ).
tff(207,plain,
mult(mult(mult(op_b,op_b),op_b),op_b) = mult(mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))),
inference(transitivity,[status(thm)],[57,206]) ).
tff(208,plain,
mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b) = mult(mult(mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))),op_b),
inference(monotonicity,[status(thm)],[207]) ).
tff(209,plain,
mult(mult(mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))),op_b) = mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),
inference(symmetry,[status(thm)],[208]) ).
tff(210,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b))) = mult(mult(mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))),op_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(211,plain,
mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b))) = mult(mult(mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))),op_b),
inference(unit_resolution,[status(thm)],[210,24]) ).
tff(212,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(213,plain,
ld(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))),
inference(unit_resolution,[status(thm)],[212,84]) ).
tff(214,plain,
mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),mult(op_b,mult(op_b,op_b))) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))),
inference(symmetry,[status(thm)],[49]) ).
tff(215,plain,
mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),op_b) = mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),mult(op_b,mult(op_b,op_b))),
inference(symmetry,[status(thm)],[47]) ).
tff(216,plain,
mult(mult(mult(op_b,mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))),op_b) = mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),op_b),
inference(monotonicity,[status(thm)],[98]) ).
tff(217,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_b,mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b))) = mult(mult(mult(op_b,mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))),op_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(218,plain,
mult(op_b,mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b))) = mult(mult(mult(op_b,mult(op_b,mult(op_b,op_b))),mult(op_b,mult(op_b,op_b))),op_b),
inference(unit_resolution,[status(thm)],[217,24]) ).
tff(219,plain,
mult(op_b,mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b))) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))))),
inference(transitivity,[status(thm)],[218,216,215,214,108]) ).
tff(220,plain,
ld(op_b,mult(op_b,mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b)))) = ld(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))),
inference(monotonicity,[status(thm)],[219]) ).
tff(221,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(op_b,mult(op_b,mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b)))) = mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(222,plain,
ld(op_b,mult(op_b,mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b)))) = mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b)),
inference(unit_resolution,[status(thm)],[221,84]) ).
tff(223,plain,
mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b)) = ld(op_b,mult(op_b,mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b)))),
inference(symmetry,[status(thm)],[222]) ).
tff(224,plain,
mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b)) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b)))),
inference(transitivity,[status(thm)],[223,220,213,53]) ).
tff(225,plain,
mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b))) = mult(mult(mult(op_b,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))),
inference(monotonicity,[status(thm)],[202,224]) ).
tff(226,plain,
mult(mult(mult(op_b,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))) = mult(mult(mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),op_b),op_b),mult(mult(op_b,mult(op_b,op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b))),
inference(symmetry,[status(thm)],[225]) ).
tff(227,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))))) = mult(mult(mult(op_b,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(228,plain,
mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))))) = mult(mult(mult(op_b,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))),
inference(unit_resolution,[status(thm)],[227,24]) ).
tff(229,plain,
mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))) = op_b,
inference(transitivity,[status(thm)],[170,167,12]) ).
tff(230,plain,
mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b)))))) = mult(mult(mult(op_b,op_b),op_b),op_b),
inference(monotonicity,[status(thm)],[229]) ).
tff(231,plain,
mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b)))))) = mult(op_b,mult(op_b,mult(op_b,op_b))),
inference(transitivity,[status(thm)],[230,57]) ).
tff(232,plain,
mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))))) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))),
inference(monotonicity,[status(thm)],[231]) ).
tff(233,plain,
mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))) = mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))))),
inference(symmetry,[status(thm)],[232]) ).
tff(234,plain,
mult(op_b,mult(op_b,mult(op_b,op_b))) = mult(mult(op_b,mult(op_b,op_b)),op_b),
inference(transitivity,[status(thm)],[56,121]) ).
tff(235,plain,
mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))) = mult(op_b,mult(mult(op_b,mult(op_b,op_b)),op_b)),
inference(monotonicity,[status(thm)],[234]) ).
tff(236,plain,
mult(op_b,mult(mult(op_b,mult(op_b,op_b)),op_b)) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))),
inference(symmetry,[status(thm)],[235]) ).
tff(237,plain,
( ~ ! [A: $i] : ( mult(A,mult(op_a,mult(op_a,mult(op_a,op_a)))) = A )
| ( mult(mult(op_b,mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(op_a,mult(op_a,mult(op_a,op_a)))) = mult(op_b,mult(mult(op_b,mult(op_b,op_b)),op_b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(238,plain,
mult(mult(op_b,mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(op_a,mult(op_a,mult(op_a,op_a)))) = mult(op_b,mult(mult(op_b,mult(op_b,op_b)),op_b)),
inference(unit_resolution,[status(thm)],[237,10]) ).
tff(239,plain,
( ~ ! [A: $i] : ( mult(A,mult(op_a,mult(op_a,mult(op_a,op_a)))) = A )
| ( mult(mult(mult(op_b,mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(op_a,mult(op_a,mult(op_a,op_a)))),mult(op_a,mult(op_a,mult(op_a,op_a)))) = mult(mult(op_b,mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(op_a,mult(op_a,mult(op_a,op_a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(240,plain,
mult(mult(mult(op_b,mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(op_a,mult(op_a,mult(op_a,op_a)))),mult(op_a,mult(op_a,mult(op_a,op_a)))) = mult(mult(op_b,mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(op_a,mult(op_a,mult(op_a,op_a)))),
inference(unit_resolution,[status(thm)],[239,10]) ).
tff(241,plain,
mult(mult(mult(op_b,mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(op_a,mult(op_a,mult(op_a,op_a)))),mult(op_a,mult(op_a,mult(op_a,op_a)))) = mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),
inference(transitivity,[status(thm)],[240,238,236,233,228,226,211,209]) ).
tff(242,plain,
mult(mult(mult(mult(op_b,mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(op_a,mult(op_a,mult(op_a,op_a)))),mult(op_a,mult(op_a,mult(op_a,op_a)))),mult(mult(op_b,mult(op_b,op_b)),op_b)) = mult(mult(mult(mult(mult(op_b,op_b),op_b),op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b)),
inference(monotonicity,[status(thm)],[241,122]) ).
tff(243,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(mult(op_b,mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_b,mult(op_b,op_b)),op_b)))) = mult(mult(mult(mult(op_b,mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(op_a,mult(op_a,mult(op_a,op_a)))),mult(op_a,mult(op_a,mult(op_a,op_a)))),mult(mult(op_b,mult(op_b,op_b)),op_b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(244,plain,
mult(mult(op_b,mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_b,mult(op_b,op_b)),op_b)))) = mult(mult(mult(mult(op_b,mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(op_a,mult(op_a,mult(op_a,op_a)))),mult(op_a,mult(op_a,mult(op_a,op_a)))),mult(mult(op_b,mult(op_b,op_b)),op_b)),
inference(unit_resolution,[status(thm)],[243,24]) ).
tff(245,plain,
( ~ ! [A: $i] : ( mult(mult(op_a,mult(op_a,mult(op_a,op_a))),A) = A )
| ( mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_b,mult(op_b,op_b)),op_b)) = mult(mult(op_b,mult(op_b,op_b)),op_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(246,plain,
mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_b,mult(op_b,op_b)),op_b)) = mult(mult(op_b,mult(op_b,op_b)),op_b),
inference(unit_resolution,[status(thm)],[245,189]) ).
tff(247,plain,
mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_b,mult(op_b,op_b)),op_b))) = mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_b,mult(op_b,op_b)),op_b)),
inference(monotonicity,[status(thm)],[246]) ).
tff(248,plain,
mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_b,mult(op_b,op_b)),op_b)) = mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_b,mult(op_b,op_b)),op_b))),
inference(symmetry,[status(thm)],[247]) ).
tff(249,plain,
mult(mult(op_b,mult(op_b,op_b)),op_b) = mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_b,mult(op_b,op_b)),op_b)),
inference(symmetry,[status(thm)],[246]) ).
tff(250,plain,
mult(mult(op_b,mult(op_b,op_b)),op_b) = mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_b,mult(op_b,op_b)),op_b))),
inference(transitivity,[status(thm)],[249,248]) ).
tff(251,plain,
mult(mult(op_b,mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b)) = mult(mult(op_b,mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_b,mult(op_b,op_b)),op_b)))),
inference(monotonicity,[status(thm)],[250]) ).
tff(252,plain,
mult(mult(op_b,mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b)) = mult(op_a,mult(op_a,mult(op_a,op_a))),
inference(transitivity,[status(thm)],[251,244,242,92,89,27,17]) ).
tff(253,plain,
mult(mult(mult(op_b,mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a)) = mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a)),
inference(monotonicity,[status(thm)],[252]) ).
tff(254,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_b,mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a)))) = mult(mult(mult(op_b,mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(255,plain,
mult(op_b,mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a)))) = mult(mult(mult(op_b,mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(mult(op_b,mult(op_b,op_b)),op_b)),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a)),
inference(unit_resolution,[status(thm)],[254,24]) ).
tff(256,plain,
mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a) = mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a)),
inference(symmetry,[status(thm)],[193]) ).
tff(257,plain,
mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a)) = mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a))),
inference(monotonicity,[status(thm)],[256]) ).
tff(258,plain,
mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a))) = mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a)))),
inference(monotonicity,[status(thm)],[257]) ).
tff(259,plain,
mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a)))) = mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a))),
inference(symmetry,[status(thm)],[258]) ).
tff(260,plain,
mult(op_b,mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a))))) = mult(op_b,mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a)))),
inference(monotonicity,[status(thm)],[259]) ).
tff(261,plain,
mult(op_b,mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a))))) = a,
inference(transitivity,[status(thm)],[260,255,253,193,191]) ).
tff(262,plain,
mult(op_b,mult(op_b,mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a)))))) = mult(op_b,a),
inference(monotonicity,[status(thm)],[261]) ).
tff(263,plain,
mult(op_a,mult(op_b,mult(op_b,mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a))))))) = mult(op_a,mult(op_b,a)),
inference(monotonicity,[status(thm)],[262]) ).
tff(264,plain,
mult(op_a,mult(op_b,a)) = mult(op_a,mult(op_b,mult(op_b,mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(mult(op_b,mult(op_b,op_b)),op_b),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),mult(mult(op_a,mult(op_a,mult(op_a,op_a))),a))))))),
inference(symmetry,[status(thm)],[263]) ).
tff(265,plain,
mult(op_a,mult(op_b,a)) = mult(mult(op_a,op_b),a),
inference(transitivity,[status(thm)],[264,201,199,179,177]) ).
tff(266,plain,
( ( mult(op_a,mult(op_b,a)) != mult(mult(op_a,op_b),a) )
<=> ( mult(op_a,mult(op_b,a)) != mult(mult(op_a,op_b),a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(267,axiom,
mult(op_a,mult(op_b,a)) != mult(mult(op_a,op_b),a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(268,plain,
mult(op_a,mult(op_b,a)) != mult(mult(op_a,op_b),a),
inference(modus_ponens,[status(thm)],[267,266]) ).
tff(269,plain,
$false,
inference(unit_resolution,[status(thm)],[268,265]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP705-1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n009.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 20:15:05 EDT 2022
% 0.13/0.34 % 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.
% 6.54/4.54 % SZS status Unsatisfiable
% 6.54/4.54 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------