%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP566-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 : Sat Jun 21 05:08:05 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 32
% Syntax : Number of formulae : 155 ( 128 unt; 0 typ; 0 def)
% Number of atoms : 190 ( 185 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 53 ( 22 ~; 18 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 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 : 95 ( 88 !; 0 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
tff(a2_type,type,
a2: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(identity_type,type,
identity: $i ).
tff(double_divide_type,type,
double_divide: ( $i * $i ) > $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(1,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
<=> ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
<=> ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
<=> ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
tff(5,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(identity,identity)) = a2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(identity,identity)) = a2,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [A: $i] :
refl(( ( identity = double_divide(A,inverse(A)) )
<=> ( identity = double_divide(A,inverse(A)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
<=> ! [A: $i] : ( identity = double_divide(A,inverse(A)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
<=> ! [A: $i] : ( identity = double_divide(A,inverse(A)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
tff(14,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
identity = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = identity,
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
^ [A: $i] :
refl(( ( inverse(A) = double_divide(A,identity) )
<=> ( inverse(A) = double_divide(A,identity) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
<=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
<=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
tff(24,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) = inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(a2,identity)) = double_divide(double_divide(a2,identity),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
inverse(double_divide(a2,identity)) = double_divide(double_divide(a2,identity),identity),
inference(unit_resolution,[status(thm)],[30,26]) ).
tff(32,plain,
double_divide(double_divide(a2,identity),identity) = inverse(double_divide(a2,identity)),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
identity = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
inference(unit_resolution,[status(thm)],[37,16]) ).
tff(39,plain,
double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) = identity,
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
identity = double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),
inference(transitivity,[status(thm)],[38,34]) ).
tff(41,plain,
double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),
inference(monotonicity,[status(thm)],[40,39]) ).
tff(42,plain,
double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
inference(transitivity,[status(thm)],[41,36,29]) ).
tff(43,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(a2,inverse(a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
identity = double_divide(a2,inverse(a2)),
inference(unit_resolution,[status(thm)],[43,16]) ).
tff(45,plain,
double_divide(a2,inverse(a2)) = identity,
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(a2) = double_divide(a2,identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
inverse(a2) = double_divide(a2,identity),
inference(unit_resolution,[status(thm)],[46,26]) ).
tff(48,plain,
double_divide(a2,identity) = inverse(a2),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(a2,identity),
inference(monotonicity,[status(thm)],[39]) ).
tff(50,plain,
double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = inverse(a2),
inference(transitivity,[status(thm)],[49,48]) ).
tff(51,plain,
double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(a2,inverse(a2)),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
inference(transitivity,[status(thm)],[51,45,38]) ).
tff(53,plain,
double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
inference(monotonicity,[status(thm)],[52,42]) ).
tff(54,plain,
double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity) = double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
inference(symmetry,[status(thm)],[41]) ).
tff(55,plain,
double_divide(a2,inverse(a2)) = double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
inference(symmetry,[status(thm)],[51]) ).
tff(56,plain,
identity = double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
inference(transitivity,[status(thm)],[44,55]) ).
tff(57,plain,
double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)) = double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
inference(monotonicity,[status(thm)],[56,54]) ).
tff(58,plain,
double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)) = identity,
inference(transitivity,[status(thm)],[57,53,19]) ).
tff(59,plain,
double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) = double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
inference(transitivity,[status(thm)],[39,44,55]) ).
tff(60,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)) = double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
inference(monotonicity,[status(thm)],[59,54]) ).
tff(61,plain,
double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))) = double_divide(a2,double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
double_divide(double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))) = double_divide(double_divide(a2,double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),identity),
inference(monotonicity,[status(thm)],[61,58]) ).
tff(63,plain,
double_divide(double_divide(a2,double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),identity) = double_divide(double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),
inference(symmetry,[status(thm)],[62]) ).
tff(64,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(65,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)],[64]) ).
tff(66,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(67,axiom,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
tff(68,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),a2) = double_divide(double_divide(a2,double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
multiply(double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),a2) = double_divide(double_divide(a2,double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),identity),
inference(unit_resolution,[status(thm)],[71,70]) ).
tff(73,plain,
double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = identity,
inference(transitivity,[status(thm)],[53,19]) ).
tff(74,plain,
multiply(double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),a2) = multiply(identity,a2),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
multiply(identity,a2) = multiply(double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),a2),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
| ( multiply(identity,a2) = double_divide(double_divide(a2,identity),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
multiply(identity,a2) = double_divide(double_divide(a2,identity),identity),
inference(unit_resolution,[status(thm)],[76,70]) ).
tff(78,plain,
double_divide(double_divide(a2,identity),identity) = multiply(identity,a2),
inference(symmetry,[status(thm)],[77]) ).
tff(79,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(identity,identity)) = double_divide(double_divide(a2,identity),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(identity,identity)) = double_divide(double_divide(a2,identity),identity),
inference(unit_resolution,[status(thm)],[79,7]) ).
tff(81,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),
inference(monotonicity,[status(thm)],[40]) ).
tff(82,plain,
double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity) = double_divide(identity,identity),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[41,82]) ).
tff(84,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(double_divide(a2,identity),identity),inverse(double_divide(double_divide(a2,identity),identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(85,plain,
identity = double_divide(double_divide(double_divide(a2,identity),identity),inverse(double_divide(double_divide(a2,identity),identity))),
inference(unit_resolution,[status(thm)],[84,16]) ).
tff(86,plain,
double_divide(double_divide(double_divide(a2,identity),identity),inverse(double_divide(double_divide(a2,identity),identity))) = identity,
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(double_divide(a2,identity),identity),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(88,plain,
inverse(double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(double_divide(a2,identity),identity),identity),
inference(unit_resolution,[status(thm)],[87,26]) ).
tff(89,plain,
double_divide(double_divide(double_divide(a2,identity),identity),identity) = inverse(double_divide(double_divide(a2,identity),identity)),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(a2,identity),identity),identity),
inference(monotonicity,[status(thm)],[39]) ).
tff(91,plain,
double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = inverse(double_divide(double_divide(a2,identity),identity)),
inference(transitivity,[status(thm)],[90,89]) ).
tff(92,plain,
double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(a2,identity),identity),inverse(double_divide(double_divide(a2,identity),identity))),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
inference(transitivity,[status(thm)],[92,86,44,55]) ).
tff(94,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = identity,
inference(transitivity,[status(thm)],[94,53,19]) ).
tff(96,plain,
double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(double_divide(double_divide(a2,identity),identity),identity),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
double_divide(double_divide(double_divide(a2,identity),identity),identity) = double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a2,identity),identity),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(99,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a2,identity),identity),identity),
inference(unit_resolution,[status(thm)],[98,7]) ).
tff(100,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),
inference(monotonicity,[status(thm)],[34,39]) ).
tff(101,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[100,82]) ).
tff(102,plain,
( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
| ( identity = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),inverse(double_divide(double_divide(double_divide(a2,identity),identity),identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,plain,
identity = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),inverse(double_divide(double_divide(double_divide(a2,identity),identity),identity))),
inference(unit_resolution,[status(thm)],[102,16]) ).
tff(104,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),inverse(double_divide(double_divide(double_divide(a2,identity),identity),identity))) = identity,
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
| ( inverse(double_divide(double_divide(double_divide(a2,identity),identity),identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
inverse(double_divide(double_divide(double_divide(a2,identity),identity),identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),
inference(unit_resolution,[status(thm)],[105,26]) ).
tff(107,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity) = inverse(double_divide(double_divide(double_divide(a2,identity),identity),identity)),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),
inference(monotonicity,[status(thm)],[39]) ).
tff(109,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = inverse(double_divide(double_divide(double_divide(a2,identity),identity),identity)),
inference(transitivity,[status(thm)],[108,107]) ).
tff(110,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),inverse(double_divide(double_divide(double_divide(a2,identity),identity),identity))),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
inference(transitivity,[status(thm)],[110,104,44,55]) ).
tff(112,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = identity,
inference(transitivity,[status(thm)],[112,53,19]) ).
tff(114,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[115,101]) ).
tff(117,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
inference(transitivity,[status(thm)],[116,99,97]) ).
tff(118,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[117,83]) ).
tff(119,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),
inference(transitivity,[status(thm)],[118,80,78,75,72,63]) ).
tff(120,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),
inference(monotonicity,[status(thm)],[119]) ).
tff(121,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
inference(symmetry,[status(thm)],[120]) ).
tff(122,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity))),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity)))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(125,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),
inference(unit_resolution,[status(thm)],[124,7]) ).
tff(126,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(128,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),
inference(unit_resolution,[status(thm)],[127,7]) ).
tff(129,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
inference(transitivity,[status(thm)],[100,54]) ).
tff(130,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
inference(monotonicity,[status(thm)],[59,129]) ).
tff(131,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
inference(transitivity,[status(thm)],[130,53,19,44,55]) ).
tff(132,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
inference(monotonicity,[status(thm)],[131]) ).
tff(133,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = identity,
inference(transitivity,[status(thm)],[132,53,19]) ).
tff(134,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),
inference(monotonicity,[status(thm)],[34,133]) ).
tff(135,plain,
double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B )
| ( double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(identity,identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(identity,identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
inference(unit_resolution,[status(thm)],[136,7]) ).
tff(138,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[135,101]) ).
tff(139,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
inference(transitivity,[status(thm)],[138,137,39,44,55]) ).
tff(140,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = double_divide(double_divide(a2,double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = identity,
inference(transitivity,[status(thm)],[140,53,19]) ).
tff(142,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),
inference(monotonicity,[status(thm)],[34,141]) ).
tff(143,plain,
double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
inference(transitivity,[status(thm)],[142,135]) ).
tff(144,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[143]) ).
tff(145,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[144]) ).
tff(146,plain,
double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[137]) ).
tff(147,plain,
identity = double_divide(identity,identity),
inference(transitivity,[status(thm)],[38,146,145,128,82]) ).
tff(148,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(identity,identity)),
inference(monotonicity,[status(thm)],[97,147]) ).
tff(149,plain,
double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),identity),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
double_divide(double_divide(a2,identity),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[80]) ).
tff(151,plain,
multiply(identity,a2) = a2,
inference(transitivity,[status(thm)],[77,150,149,126,123,9]) ).
tff(152,plain,
( ( multiply(identity,a2) != a2 )
<=> ( multiply(identity,a2) != a2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(153,axiom,
multiply(identity,a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
tff(154,plain,
multiply(identity,a2) != a2,
inference(modus_ponens,[status(thm)],[153,152]) ).
tff(155,plain,
$false,
inference(unit_resolution,[status(thm)],[154,151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP566-1 : TPTP v9.0.0. Released v2.6.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 16:17:56 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------