TSTP Solution File: GRP487-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP487-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 22:27:46 EDT 2022
% Result : Unsatisfiable 0.16s 0.37s
% Output : Proof 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 36
% Syntax : Number of formulae : 162 ( 131 unt; 5 typ; 0 def)
% Number of atoms : 191 ( 186 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 51 ( 21 ~; 17 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 20 ( 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 : 99 ( 92 !; 0 ?; 99 :)
% Comments :
%------------------------------------------------------------------------------
tff(identity_type,type,
identity: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(a1_type,type,
a1: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(double_divide_type,type,
double_divide: ( $i * $i ) > $i ).
tff(1,plain,
^ [A: $i] :
refl(
( ( identity = double_divide(A,inverse(A)) )
<=> ( identity = double_divide(A,inverse(A)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
<=> ! [A: $i] : ( identity = double_divide(A,inverse(A)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
<=> ! [A: $i] : ( identity = double_divide(A,inverse(A)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
tff(5,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(a1,inverse(a1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
identity = double_divide(a1,inverse(a1)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
double_divide(a1,inverse(a1)) = identity,
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
<=> ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
<=> ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
<=> ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
| ( double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(a1,inverse(a1))))),double_divide(a1,inverse(a1))),identity)) = double_divide(a1,inverse(a1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(a1,inverse(a1))))),double_divide(a1,inverse(a1))),identity)) = double_divide(a1,inverse(a1)),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
double_divide(double_divide(a1,inverse(a1)),double_divide(a1,inverse(a1))) = double_divide(double_divide(a1,inverse(a1)),identity),
inference(monotonicity,[status(thm)],[10]) ).
tff(21,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(double_divide(a1,inverse(a1)),identity),inverse(double_divide(double_divide(a1,inverse(a1)),identity))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
identity = double_divide(double_divide(double_divide(a1,inverse(a1)),identity),inverse(double_divide(double_divide(a1,inverse(a1)),identity))),
inference(unit_resolution,[status(thm)],[21,7]) ).
tff(23,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),inverse(double_divide(double_divide(a1,inverse(a1)),identity))) = identity,
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
^ [A: $i] :
refl(
( ( inverse(A) = double_divide(A,identity) )
<=> ( inverse(A) = double_divide(A,identity) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
<=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
<=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
tff(28,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(double_divide(a1,inverse(a1)),identity)) = double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
inverse(double_divide(double_divide(a1,inverse(a1)),identity)) = double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity) = inverse(double_divide(double_divide(a1,inverse(a1)),identity)),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))) = double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity),
inference(monotonicity,[status(thm)],[10]) ).
tff(35,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))) = inverse(double_divide(double_divide(a1,inverse(a1)),identity)),
inference(transitivity,[status(thm)],[34,33]) ).
tff(36,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1)))) = double_divide(double_divide(double_divide(a1,inverse(a1)),identity),inverse(double_divide(double_divide(a1,inverse(a1)),identity))),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1)))) = identity,
inference(transitivity,[status(thm)],[36,23]) ).
tff(38,plain,
double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))) = double_divide(double_divide(a1,inverse(a1)),identity),
inference(monotonicity,[status(thm)],[9,37]) ).
tff(39,plain,
double_divide(double_divide(a1,inverse(a1)),identity) = double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(a1,inverse(a1)))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))),double_divide(double_divide(a1,inverse(a1)),identity)),
inference(monotonicity,[status(thm)],[39,20]) ).
tff(41,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))),double_divide(double_divide(a1,inverse(a1)),identity)) = double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(a1,inverse(a1)))),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
| ( double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),identity)) = double_divide(double_divide(a1,inverse(a1)),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),identity)) = double_divide(double_divide(a1,inverse(a1)),identity),
inference(unit_resolution,[status(thm)],[42,17]) ).
tff(44,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),identity))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))),double_divide(double_divide(a1,inverse(a1)),identity)),
inference(monotonicity,[status(thm)],[39,43]) ).
tff(45,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),identity))) = double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(a1,inverse(a1)))),
inference(transitivity,[status(thm)],[44,41]) ).
tff(46,plain,
double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(a1,inverse(a1))))),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),identity)))),double_divide(a1,inverse(a1))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(a1,inverse(a1))))),double_divide(a1,inverse(a1))),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),identity)))),double_divide(a1,inverse(a1))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(a1,inverse(a1))))),double_divide(a1,inverse(a1))),identity),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(a1,inverse(a1))))),double_divide(a1,inverse(a1))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),identity)))),double_divide(a1,inverse(a1))),identity),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(a1,inverse(a1))))),double_divide(a1,inverse(a1))),identity)) = double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),identity)))),double_divide(a1,inverse(a1))),identity)),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),identity)))),double_divide(a1,inverse(a1))),identity)) = double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(a1,inverse(a1))))),double_divide(a1,inverse(a1))),identity)),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
| ( double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),identity)))),double_divide(a1,inverse(a1))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),identity)))),double_divide(a1,inverse(a1))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),identity),
inference(unit_resolution,[status(thm)],[52,17]) ).
tff(54,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),identity) = double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),identity)))),double_divide(a1,inverse(a1))),identity)),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(a1) = double_divide(a1,identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
inverse(a1) = double_divide(a1,identity),
inference(unit_resolution,[status(thm)],[55,30]) ).
tff(57,plain,
double_divide(a1,identity) = inverse(a1),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
double_divide(a1,double_divide(a1,identity)) = double_divide(a1,inverse(a1)),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
double_divide(a1,inverse(a1)) = double_divide(a1,double_divide(a1,identity)),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
identity = double_divide(a1,double_divide(a1,identity)),
inference(transitivity,[status(thm)],[9,59]) ).
tff(61,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),
inference(monotonicity,[status(thm)],[9]) ).
tff(62,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(a1,double_divide(a1,identity))),
inference(monotonicity,[status(thm)],[62,60]) ).
tff(64,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(a1,double_divide(a1,identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),identity),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
double_divide(a1,double_divide(a1,identity)) = identity,
inference(transitivity,[status(thm)],[58,10]) ).
tff(66,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
| ( double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)) = double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)) = double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity),
inference(unit_resolution,[status(thm)],[66,17]) ).
tff(68,plain,
double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)) = inverse(double_divide(double_divide(a1,inverse(a1)),identity)),
inference(transitivity,[status(thm)],[67,33]) ).
tff(69,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity))) = double_divide(double_divide(double_divide(a1,inverse(a1)),identity),inverse(double_divide(double_divide(a1,inverse(a1)),identity))),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity))) = identity,
inference(transitivity,[status(thm)],[69,23]) ).
tff(71,plain,
double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)))) = double_divide(double_divide(a1,inverse(a1)),identity),
inference(monotonicity,[status(thm)],[9,70]) ).
tff(72,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)))),double_divide(a1,inverse(a1))) = double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity),
inference(monotonicity,[status(thm)],[71,10]) ).
tff(73,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)))),double_divide(a1,inverse(a1))),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(a1,double_divide(a1,identity)))) = double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),identity)),
inference(monotonicity,[status(thm)],[9,64]) ).
tff(75,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)) = double_divide(double_divide(double_divide(a1,inverse(a1)),identity),inverse(double_divide(double_divide(a1,inverse(a1)),identity))),
inference(monotonicity,[status(thm)],[33]) ).
tff(76,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)) = double_divide(a1,double_divide(a1,identity)),
inference(transitivity,[status(thm)],[75,23,9,59]) ).
tff(77,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(a1,double_divide(a1,identity))),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(a1,double_divide(a1,identity)))),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))),
inference(transitivity,[status(thm)],[78,74,43,39]) ).
tff(80,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))),double_divide(double_divide(a1,inverse(a1)),identity)),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))),double_divide(double_divide(a1,inverse(a1)),identity)),identity),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))),double_divide(double_divide(a1,inverse(a1)),identity)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
| ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)))),double_divide(a1,inverse(a1))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))),double_divide(double_divide(a1,inverse(a1)),identity)),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)))),double_divide(a1,inverse(a1))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))),double_divide(double_divide(a1,inverse(a1)),identity)),identity),
inference(unit_resolution,[status(thm)],[83,17]) ).
tff(85,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
| ( double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)) = double_divide(a1,inverse(a1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)) = double_divide(a1,inverse(a1)),
inference(unit_resolution,[status(thm)],[85,17]) ).
tff(87,plain,
double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)) = double_divide(a1,double_divide(a1,identity)),
inference(transitivity,[status(thm)],[86,59]) ).
tff(88,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))),double_divide(double_divide(a1,inverse(a1)),identity)),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(a1,double_divide(a1,identity))),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(a1,double_divide(a1,identity)))),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(a1,double_divide(a1,identity)))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)))),
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(92,plain,
identity = double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1)))),
inference(unit_resolution,[status(thm)],[91,7]) ).
tff(93,plain,
double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1)))) = identity,
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(a1,inverse(a1))) = double_divide(double_divide(a1,inverse(a1)),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
inverse(double_divide(a1,inverse(a1))) = double_divide(double_divide(a1,inverse(a1)),identity),
inference(unit_resolution,[status(thm)],[94,30]) ).
tff(96,plain,
double_divide(double_divide(a1,inverse(a1)),identity) = inverse(double_divide(a1,inverse(a1))),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)) = double_divide(double_divide(a1,inverse(a1)),inverse(double_divide(a1,inverse(a1)))),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)) = double_divide(a1,double_divide(a1,identity)),
inference(transitivity,[status(thm)],[97,93,9,59]) ).
tff(99,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(a1,double_divide(a1,identity))),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(a1,double_divide(a1,identity)))),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)))),
inference(transitivity,[status(thm)],[100,90]) ).
tff(102,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)))),double_divide(a1,inverse(a1))),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)))),double_divide(a1,inverse(a1))),identity),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)))),double_divide(a1,inverse(a1))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),identity),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)))),double_divide(a1,inverse(a1))),identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),identity)),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(a1,inverse(a1))))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)))),double_divide(a1,inverse(a1))),identity)),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
| ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),identity)) = double_divide(double_divide(a1,inverse(a1)),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),identity)) = double_divide(double_divide(a1,inverse(a1)),identity),
inference(unit_resolution,[status(thm)],[107,17]) ).
tff(109,plain,
double_divide(double_divide(a1,inverse(a1)),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(a1,identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,identity),a1))),double_divide(a1,identity)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))),identity)),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
double_divide(double_divide(a1,inverse(a1)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity),
inference(transitivity,[status(thm)],[109,106,84,82]) ).
tff(111,plain,
double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)) = identity,
inference(transitivity,[status(thm)],[97,93]) ).
tff(112,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity))) = double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity) = double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity))),
inference(symmetry,[status(thm)],[112]) ).
tff(114,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)) = identity,
inference(transitivity,[status(thm)],[75,23]) ).
tff(115,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity))) = double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity))) = double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity))),
inference(transitivity,[status(thm)],[115,113]) ).
tff(117,plain,
double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)),
inference(monotonicity,[status(thm)],[117,110]) ).
tff(119,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
| ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)) = double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(121,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)) = double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity),
inference(unit_resolution,[status(thm)],[120,17]) ).
tff(122,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)),
inference(symmetry,[status(thm)],[121]) ).
tff(123,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)))),double_divide(a1,inverse(a1))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),
inference(transitivity,[status(thm)],[72,122,119]) ).
tff(124,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)))),double_divide(a1,inverse(a1))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)))),double_divide(a1,inverse(a1))),identity)) = double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)),
inference(monotonicity,[status(thm)],[124]) ).
tff(126,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C )
| ( double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)))),double_divide(a1,inverse(a1))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(127,plain,
double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)))),double_divide(a1,inverse(a1))),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity),
inference(unit_resolution,[status(thm)],[126,17]) ).
tff(128,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity) = double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)))),double_divide(a1,inverse(a1))),identity)),
inference(symmetry,[status(thm)],[127]) ).
tff(129,plain,
double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)) = double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)))),double_divide(a1,inverse(a1))),identity)),
inference(symmetry,[status(thm)],[125]) ).
tff(130,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity) = double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)),
inference(symmetry,[status(thm)],[67]) ).
tff(131,plain,
double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity),
inference(transitivity,[status(thm)],[112,130,129,127]) ).
tff(132,plain,
double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))) = double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)),
inference(monotonicity,[status(thm)],[9,131]) ).
tff(133,plain,
double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)))),double_divide(a1,inverse(a1))),
inference(transitivity,[status(thm)],[132,67,73]) ).
tff(134,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),double_divide(a1,inverse(a1))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)))),double_divide(a1,inverse(a1))),identity),
inference(monotonicity,[status(thm)],[133,10]) ).
tff(135,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)))),double_divide(a1,inverse(a1))),
inference(transitivity,[status(thm)],[61,134,124,128,125,67,73]) ).
tff(136,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(a1,double_divide(a1,identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)))),double_divide(a1,inverse(a1))),identity),
inference(monotonicity,[status(thm)],[135,65]) ).
tff(137,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)))),double_divide(a1,inverse(a1))),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(a1,inverse(a1)),identity)))),identity),double_divide(a1,double_divide(a1,identity))),
inference(symmetry,[status(thm)],[136]) ).
tff(138,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity)))),double_divide(a1,inverse(a1))),identity),
inference(symmetry,[status(thm)],[124]) ).
tff(139,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(140,plain,
inverse(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),identity),
inference(unit_resolution,[status(thm)],[139,30]) ).
tff(141,plain,
double_divide(a1,inverse(a1)) = double_divide(double_divide(a1,inverse(a1)),double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(a1,inverse(a1)),double_divide(a1,inverse(a1))))),double_divide(a1,inverse(a1))),identity)),
inference(symmetry,[status(thm)],[19]) ).
tff(142,plain,
double_divide(a1,inverse(a1)) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity)),
inference(transitivity,[status(thm)],[141,50,53,63,136,124,128,125,67,122,119]) ).
tff(143,plain,
inverse(double_divide(a1,inverse(a1))) = inverse(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),double_divide(double_divide(double_divide(a1,inverse(a1)),identity),identity)))),double_divide(double_divide(a1,inverse(a1)),identity))),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,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(145,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)],[144]) ).
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(rewrite,[status(thm)],]) ).
tff(147,axiom,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
tff(148,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(skolemize,[status(sab)],[148]) ).
tff(150,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(modus_ponens,[status(thm)],[149,145]) ).
tff(151,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(inverse(a1),a1) = double_divide(double_divide(a1,inverse(a1)),identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(152,plain,
multiply(inverse(a1),a1) = double_divide(double_divide(a1,inverse(a1)),identity),
inference(unit_resolution,[status(thm)],[151,150]) ).
tff(153,plain,
multiply(inverse(a1),a1) = identity,
inference(transitivity,[status(thm)],[152,96,143,140,138,137,64,54,51,19,10]) ).
tff(154,plain,
( ( multiply(inverse(a1),a1) != identity )
<=> ( multiply(inverse(a1),a1) != identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(155,axiom,
multiply(inverse(a1),a1) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_1) ).
tff(156,plain,
multiply(inverse(a1),a1) != identity,
inference(modus_ponens,[status(thm)],[155,154]) ).
tff(157,plain,
$false,
inference(unit_resolution,[status(thm)],[156,153]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP487-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.31 % Computer : n022.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Wed Aug 31 17:15:10 EDT 2022
% 0.12/0.31 % CPUTime :
% 0.16/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.32 Usage: tptp [options] [-file:]file
% 0.16/0.32 -h, -? prints this message.
% 0.16/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.32 -m, -model generate model.
% 0.16/0.32 -p, -proof generate proof.
% 0.16/0.32 -c, -core generate unsat core of named formulas.
% 0.16/0.32 -st, -statistics display statistics.
% 0.16/0.32 -t:timeout set timeout (in second).
% 0.16/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.32 -<param>:<value> configuration parameter and value.
% 0.16/0.32 -o:<output-file> file to place output in.
% 0.16/0.37 % SZS status Unsatisfiable
% 0.16/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------