TSTP Solution File: GRP497-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP497-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 22:27:50 EDT 2022
% Result : Unsatisfiable 0.53s 0.57s
% Output : Proof 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 43
% Syntax : Number of formulae : 206 ( 168 unt; 5 typ; 0 def)
% Number of atoms : 242 ( 237 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 65 ( 28 ~; 24 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 17 ( 3 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 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 : 120 ( 113 !; 0 ?; 120 :)
% Comments :
%------------------------------------------------------------------------------
tff(a2_type,type,
a2: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(identity_type,type,
identity: $i ).
tff(double_divide_type,type,
double_divide: ( $i * $i ) > $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(1,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C )
<=> ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C )
<=> ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C )
<=> ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
tff(5,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C )
| ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),identity)) = a2 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),identity)) = a2,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [A: $i] :
refl(
( ( identity = double_divide(A,inverse(A)) )
<=> ( identity = double_divide(A,inverse(A)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
<=> ! [A: $i] : ( identity = double_divide(A,inverse(A)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
<=> ! [A: $i] : ( identity = double_divide(A,inverse(A)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
tff(14,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
identity = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) = identity,
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C )
| ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
inference(unit_resolution,[status(thm)],[20,7]) ).
tff(22,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C )
| ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity))),identity)) = double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(23,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity))),identity)) = double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),
inference(unit_resolution,[status(thm)],[22,7]) ).
tff(24,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C )
| ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),identity)) = double_divide(a2,identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),identity)) = double_divide(a2,identity),
inference(unit_resolution,[status(thm)],[24,7]) ).
tff(26,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C )
| ( double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(a2,identity))),identity)) = a2 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(a2,identity))),identity)) = a2,
inference(unit_resolution,[status(thm)],[26,7]) ).
tff(28,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(a2,inverse(a2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
identity = double_divide(a2,inverse(a2)),
inference(unit_resolution,[status(thm)],[28,16]) ).
tff(30,plain,
double_divide(a2,inverse(a2)) = identity,
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
^ [A: $i] :
refl(
( ( inverse(A) = double_divide(A,identity) )
<=> ( inverse(A) = double_divide(A,identity) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
<=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
<=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,axiom,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
tff(35,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(a2) = double_divide(a2,identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
inverse(a2) = double_divide(a2,identity),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
double_divide(a2,identity) = inverse(a2),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
double_divide(a2,double_divide(a2,identity)) = double_divide(a2,inverse(a2)),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
double_divide(a2,double_divide(a2,identity)) = identity,
inference(transitivity,[status(thm)],[41,30]) ).
tff(43,plain,
double_divide(a2,double_divide(a2,double_divide(a2,identity))) = double_divide(a2,identity),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
double_divide(double_divide(a2,double_divide(a2,double_divide(a2,identity))),identity) = double_divide(double_divide(a2,identity),identity),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
double_divide(double_divide(a2,identity),identity) = double_divide(double_divide(a2,double_divide(a2,double_divide(a2,identity))),identity),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(a2,identity),identity),
inference(monotonicity,[status(thm)],[19]) ).
tff(47,plain,
double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(a2,double_divide(a2,double_divide(a2,identity))),identity),
inference(transitivity,[status(thm)],[46,45]) ).
tff(48,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(a2,identity))),identity)),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = a2,
inference(transitivity,[status(thm)],[48,27]) ).
tff(50,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),identity) = double_divide(a2,identity),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
double_divide(a2,identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),identity),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C )
| ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity)) = double_divide(a2,identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity)) = double_divide(a2,identity),
inference(unit_resolution,[status(thm)],[52,7]) ).
tff(54,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),
inference(monotonicity,[status(thm)],[19]) ).
tff(55,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity)),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),identity),
inference(transitivity,[status(thm)],[57,53,51]) ).
tff(59,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),identity)),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity))) = double_divide(a2,identity),
inference(transitivity,[status(thm)],[59,25]) ).
tff(61,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity))),identity) = double_divide(double_divide(a2,identity),identity),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
double_divide(double_divide(a2,identity),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity))),identity),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C )
| ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),identity)) = double_divide(a2,identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),identity)) = double_divide(a2,identity),
inference(unit_resolution,[status(thm)],[63,7]) ).
tff(65,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C )
| ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity)) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity)) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),
inference(unit_resolution,[status(thm)],[65,7]) ).
tff(67,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C )
| ( double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity)) = double_divide(a2,identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity)) = double_divide(a2,identity),
inference(unit_resolution,[status(thm)],[67,7]) ).
tff(69,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(a2,identity))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),
inference(monotonicity,[status(thm)],[19]) ).
tff(70,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity)) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity)),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),identity),
inference(transitivity,[status(thm)],[72,68,51]) ).
tff(74,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),identity)),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))) = double_divide(a2,identity),
inference(transitivity,[status(thm)],[74,25]) ).
tff(76,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity) = double_divide(double_divide(a2,identity),identity),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
double_divide(double_divide(a2,identity),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity),
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity),
inference(transitivity,[status(thm)],[46,77]) ).
tff(79,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity)),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),
inference(transitivity,[status(thm)],[79,66]) ).
tff(81,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),identity) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),identity),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),identity)),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),identity),
inference(transitivity,[status(thm)],[83,64,51]) ).
tff(85,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),identity)),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity))) = double_divide(a2,identity),
inference(transitivity,[status(thm)],[85,25]) ).
tff(87,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity))),identity) = double_divide(double_divide(a2,identity),identity),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity))),identity),
inference(transitivity,[status(thm)],[87,62]) ).
tff(89,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity))),identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity))),identity)),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity))),identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity))),identity)),
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C )
| ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity))),identity)) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(92,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity))),identity)) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),
inference(unit_resolution,[status(thm)],[91,7]) ).
tff(93,plain,
double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity))),identity)),
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C )
| ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
inference(unit_resolution,[status(thm)],[94,7]) ).
tff(96,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
identity = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
inference(unit_resolution,[status(thm)],[96,16]) ).
tff(98,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = identity,
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(100,plain,
inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
inference(unit_resolution,[status(thm)],[99,37]) ).
tff(101,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) = inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
inference(monotonicity,[status(thm)],[19]) ).
tff(103,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
inference(transitivity,[status(thm)],[102,101]) ).
tff(104,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
inference(transitivity,[status(thm)],[104,98,18]) ).
tff(106,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),identity) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),identity),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
inference(monotonicity,[status(thm)],[101]) ).
tff(109,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = identity,
inference(transitivity,[status(thm)],[108,98]) ).
tff(110,plain,
double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
inference(monotonicity,[status(thm)],[18,109]) ).
tff(111,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) = double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),identity)),
inference(monotonicity,[status(thm)],[111,107]) ).
tff(113,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity)) = identity,
inference(transitivity,[status(thm)],[112,95,19]) ).
tff(114,plain,
double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
inference(monotonicity,[status(thm)],[18,113]) ).
tff(115,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
inference(monotonicity,[status(thm)],[109]) ).
tff(117,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) = double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),
inference(transitivity,[status(thm)],[116,115,93,90,23]) ).
tff(118,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),identity),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) = double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),
inference(transitivity,[status(thm)],[115,93,90,23]) ).
tff(121,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),identity),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity),
inference(transitivity,[status(thm)],[121,119]) ).
tff(123,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity)),
inference(monotonicity,[status(thm)],[115,122]) ).
tff(124,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),
inference(symmetry,[status(thm)],[121]) ).
tff(125,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
inference(monotonicity,[status(thm)],[113]) ).
tff(126,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) = double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),
inference(transitivity,[status(thm)],[125,115,93,90,23]) ).
tff(127,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),identity),
inference(monotonicity,[status(thm)],[126]) ).
tff(128,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity),
inference(transitivity,[status(thm)],[127,124]) ).
tff(129,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),identity)),
inference(monotonicity,[status(thm)],[114,128]) ).
tff(130,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C )
| ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity)) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(131,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity)) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
inference(unit_resolution,[status(thm)],[130,7]) ).
tff(132,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity)),
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(a2,identity),
inference(monotonicity,[status(thm)],[19]) ).
tff(134,plain,
double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = inverse(a2),
inference(transitivity,[status(thm)],[133,40]) ).
tff(135,plain,
double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(a2,inverse(a2)),
inference(monotonicity,[status(thm)],[134]) ).
tff(136,plain,
double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
inference(transitivity,[status(thm)],[135,30,18]) ).
tff(137,plain,
double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),identity) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),identity) = identity,
inference(transitivity,[status(thm)],[137,132,129,123,21,19]) ).
tff(139,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(a2,identity))),identity),
inference(monotonicity,[status(thm)],[138]) ).
tff(140,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(a2,identity))),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),identity)),
inference(symmetry,[status(thm)],[139]) ).
tff(141,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(a2,identity))) = double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(a2,identity))),
inference(monotonicity,[status(thm)],[19]) ).
tff(142,plain,
double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(a2,identity))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(a2,identity))),
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(a2,identity))),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(a2,identity))),identity),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(a2,identity))),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(a2,identity))),identity),
inference(symmetry,[status(thm)],[143]) ).
tff(145,plain,
^ [B: $i,A: $i] :
refl(
( ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
<=> ( multiply(A,B) = double_divide(double_divide(B,A),identity) ) )),
inference(bind,[status(th)],]) ).
tff(146,plain,
( ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
<=> ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ) ),
inference(quant_intro,[status(thm)],[145]) ).
tff(147,plain,
( ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
<=> ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(148,axiom,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
tff(149,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(skolemize,[status(sab)],[149]) ).
tff(151,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(modus_ponens,[status(thm)],[150,146]) ).
tff(152,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(a2,identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(a2,identity))),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(153,plain,
multiply(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(a2,identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(a2,identity))),identity),
inference(unit_resolution,[status(thm)],[152,151]) ).
tff(154,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
inference(transitivity,[status(thm)],[132,129,123,21]) ).
tff(155,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity)) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(a2,identity)),
inference(monotonicity,[status(thm)],[154]) ).
tff(156,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(a2,identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity)),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
multiply(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(a2,identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = multiply(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
inference(monotonicity,[status(thm)],[156]) ).
tff(158,plain,
multiply(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = multiply(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(a2,identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
inference(symmetry,[status(thm)],[157]) ).
tff(159,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(160,plain,
multiply(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))),identity),
inference(unit_resolution,[status(thm)],[159,151]) ).
tff(161,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))),identity) = multiply(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))),
inference(monotonicity,[status(thm)],[19]) ).
tff(163,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))),identity),
inference(monotonicity,[status(thm)],[162]) ).
tff(164,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))),identity),
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C )
| ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),identity)) = double_divide(a2,identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(166,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),identity)) = double_divide(a2,identity),
inference(unit_resolution,[status(thm)],[165,7]) ).
tff(167,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C )
| ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(168,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
inference(unit_resolution,[status(thm)],[167,7]) ).
tff(169,plain,
double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))) = double_divide(a2,identity),
inference(monotonicity,[status(thm)],[109]) ).
tff(170,plain,
double_divide(double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity) = double_divide(double_divide(a2,identity),identity),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
double_divide(double_divide(a2,identity),identity) = double_divide(double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity),
inference(symmetry,[status(thm)],[170]) ).
tff(172,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),identity)),
inference(monotonicity,[status(thm)],[171]) ).
tff(173,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity)) = identity,
inference(transitivity,[status(thm)],[172,168,19]) ).
tff(174,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
inference(monotonicity,[status(thm)],[173]) ).
tff(175,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity))) = double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),
inference(transitivity,[status(thm)],[174,115,93,90,23]) ).
tff(176,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity))),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),identity),
inference(monotonicity,[status(thm)],[175]) ).
tff(177,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity))),identity),
inference(symmetry,[status(thm)],[176]) ).
tff(178,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(a2,identity)) = double_divide(double_divide(a2,identity),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(179,plain,
inverse(double_divide(a2,identity)) = double_divide(double_divide(a2,identity),identity),
inference(unit_resolution,[status(thm)],[178,37]) ).
tff(180,plain,
double_divide(double_divide(a2,identity),identity) = inverse(double_divide(a2,identity)),
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
inference(monotonicity,[status(thm)],[180]) ).
tff(182,plain,
double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)) = identity,
inference(transitivity,[status(thm)],[181,19]) ).
tff(183,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
inference(monotonicity,[status(thm)],[182]) ).
tff(184,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))) = double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),
inference(transitivity,[status(thm)],[183,115,93,90,23]) ).
tff(185,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(a2,identity),double_divide(a2,identity))),identity))),identity))),identity))),identity),
inference(monotonicity,[status(thm)],[184]) ).
tff(186,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity))),identity),
inference(transitivity,[status(thm)],[185,177]) ).
tff(187,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity))),identity)),
inference(monotonicity,[status(thm)],[186]) ).
tff(188,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity))),identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))),identity)),
inference(symmetry,[status(thm)],[187]) ).
tff(189,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C )
| ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity))),identity)) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(190,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity))),identity)) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))),
inference(unit_resolution,[status(thm)],[189,7]) ).
tff(191,plain,
double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))),double_divide(double_divide(a2,identity),identity))),identity)),
inference(symmetry,[status(thm)],[190]) ).
tff(192,plain,
double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))) = double_divide(a2,identity),
inference(transitivity,[status(thm)],[191,188,166]) ).
tff(193,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))),identity) = double_divide(double_divide(a2,identity),identity),
inference(monotonicity,[status(thm)],[192]) ).
tff(194,plain,
double_divide(double_divide(a2,identity),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),double_divide(a2,identity))),identity),
inference(symmetry,[status(thm)],[193]) ).
tff(195,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(identity,a2) = double_divide(double_divide(a2,identity),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(196,plain,
multiply(identity,a2) = double_divide(double_divide(a2,identity),identity),
inference(unit_resolution,[status(thm)],[195,151]) ).
tff(197,plain,
multiply(identity,a2) = a2,
inference(transitivity,[status(thm)],[196,194,164,161,158,153,144,140,9]) ).
tff(198,plain,
( ( multiply(identity,a2) != a2 )
<=> ( multiply(identity,a2) != a2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(199,axiom,
multiply(identity,a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
tff(200,plain,
multiply(identity,a2) != a2,
inference(modus_ponens,[status(thm)],[199,198]) ).
tff(201,plain,
$false,
inference(unit_resolution,[status(thm)],[200,197]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP497-1 : TPTP v8.1.0. Released v2.6.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n006.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 31 17:15:54 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.53/0.57 % SZS status Unsatisfiable
% 0.53/0.57 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------