%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP521-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:07:59 AM UTC 2025
% Result : Unsatisfiable 0.48s 0.63s
% Output : Proof 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 34
% Syntax : Number of formulae : 129 ( 99 unt; 0 typ; 0 def)
% Number of atoms : 165 ( 161 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 60 ( 27 ~; 23 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of FOOLs : 3 ( 3 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 : 136 ( 128 !; 0 ?; 136 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(b1_type,type,
b1: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(a1_type,type,
a1: $i ).
tff(divide_type,type,
divide: ( $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(( ( inverse(A) = divide(divide(B,B),A) )
<=> ( inverse(A) = divide(divide(B,B),A) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
<=> ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
<=> ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
tff(5,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(b1) = divide(divide(inverse(a1),inverse(a1)),b1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
inverse(b1) = divide(divide(inverse(a1),inverse(a1)),b1),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
multiply(inverse(b1),b1) = multiply(divide(divide(inverse(a1),inverse(a1)),b1),b1),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
multiply(divide(divide(inverse(a1),inverse(a1)),b1),b1) = multiply(inverse(b1),b1),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
<=> ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
<=> ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
<=> ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(divide(inverse(a1),inverse(a1)),b1),b1) = divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
multiply(divide(divide(inverse(a1),inverse(a1)),b1),b1) = divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)) = multiply(divide(divide(inverse(a1),inverse(a1)),b1),b1),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
<=> ( divide(A,divide(B,divide(C,divide(A,B)))) = C ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
<=> ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
<=> ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
tff(26,plain,
! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))))) = divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))))) = divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))) = divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
multiply(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))) = divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),
inference(unit_resolution,[status(thm)],[31,18]) ).
tff(33,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))) = divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
multiply(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))) = divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),
inference(unit_resolution,[status(thm)],[33,18]) ).
tff(35,plain,
divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))) = multiply(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))) = divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),
inference(transitivity,[status(thm)],[35,32]) ).
tff(37,plain,
divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))))) = divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))))),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))))) = divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))))),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))))) = divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))))) = divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),
inference(unit_resolution,[status(thm)],[39,28]) ).
tff(41,plain,
divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))) = divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))))),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))))))) = divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))))))) = divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),
inference(unit_resolution,[status(thm)],[42,28]) ).
tff(44,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))))) = divide(a1,divide(inverse(a1),inverse(a1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))))) = divide(a1,divide(inverse(a1),inverse(a1))),
inference(unit_resolution,[status(thm)],[44,28]) ).
tff(46,plain,
divide(divide(inverse(a1),inverse(a1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))))) = divide(divide(inverse(a1),inverse(a1)),divide(a1,divide(inverse(a1),inverse(a1)))),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
divide(divide(inverse(a1),inverse(a1)),divide(a1,divide(inverse(a1),inverse(a1)))) = divide(divide(inverse(a1),inverse(a1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))))),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(a1,divide(inverse(a1),inverse(a1)))) = divide(divide(inverse(a1),inverse(a1)),divide(a1,divide(inverse(a1),inverse(a1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
inverse(divide(a1,divide(inverse(a1),inverse(a1)))) = divide(divide(inverse(a1),inverse(a1)),divide(a1,divide(inverse(a1),inverse(a1)))),
inference(unit_resolution,[status(thm)],[48,7]) ).
tff(50,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(a1,divide(inverse(a1),inverse(a1)))) = divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(a1,divide(inverse(a1),inverse(a1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
inverse(divide(a1,divide(inverse(a1),inverse(a1)))) = divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(a1,divide(inverse(a1),inverse(a1)))),
inference(unit_resolution,[status(thm)],[50,7]) ).
tff(52,plain,
divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(a1,divide(inverse(a1),inverse(a1)))) = inverse(divide(a1,divide(inverse(a1),inverse(a1)))),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))))) = divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(a1,divide(inverse(a1),inverse(a1)))),
inference(monotonicity,[status(thm)],[45]) ).
tff(54,plain,
divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))))) = divide(divide(inverse(a1),inverse(a1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))))),
inference(transitivity,[status(thm)],[53,52,49,47]) ).
tff(55,plain,
divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))))))) = divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),divide(divide(inverse(a1),inverse(a1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))))))),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),divide(divide(inverse(a1),inverse(a1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))))))) = divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))))))),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),divide(divide(inverse(a1),inverse(a1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))))))) = divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))))))),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),divide(divide(inverse(a1),inverse(a1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))))))) = divide(inverse(a1),inverse(a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),divide(divide(inverse(a1),inverse(a1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))))))) = divide(inverse(a1),inverse(a1)),
inference(unit_resolution,[status(thm)],[58,28]) ).
tff(60,plain,
divide(inverse(a1),inverse(a1)) = divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),divide(divide(inverse(a1),inverse(a1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))))))),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))) = divide(divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(a1,divide(inverse(a1),inverse(a1)))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
inverse(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))) = divide(divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(a1,divide(inverse(a1),inverse(a1)))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),
inference(unit_resolution,[status(thm)],[61,7]) ).
tff(63,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))) = divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
inverse(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))) = divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),
inference(unit_resolution,[status(thm)],[63,7]) ).
tff(65,plain,
divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))) = inverse(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
divide(inverse(a1),inverse(a1)) = divide(divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(a1,divide(inverse(a1),inverse(a1)))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),
inference(transitivity,[status(thm)],[60,57,43,65,62]) ).
tff(67,plain,
divide(a1,divide(inverse(a1),inverse(a1))) = divide(a1,divide(divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(a1,divide(inverse(a1),inverse(a1)))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
divide(a1,divide(divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(a1,divide(inverse(a1),inverse(a1)))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))) = divide(a1,divide(inverse(a1),inverse(a1))),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(a1,divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))) = divide(a1,divide(divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(a1,divide(inverse(a1),inverse(a1)))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
multiply(a1,divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))) = divide(a1,divide(divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(a1,divide(inverse(a1),inverse(a1)))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),
inference(unit_resolution,[status(thm)],[69,18]) ).
tff(71,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(a1,divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))) = divide(a1,divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
multiply(a1,divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))) = divide(a1,divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),
inference(unit_resolution,[status(thm)],[71,18]) ).
tff(73,plain,
divide(a1,divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))) = multiply(a1,divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(inverse(a1),divide(inverse(a1),divide(divide(a1,divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),divide(inverse(a1),inverse(a1))))) = divide(a1,divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(75,plain,
divide(inverse(a1),divide(inverse(a1),divide(divide(a1,divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),divide(inverse(a1),inverse(a1))))) = divide(a1,divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),
inference(unit_resolution,[status(thm)],[74,28]) ).
tff(76,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(a1,divide(inverse(a1),inverse(a1))))))) = divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(a1,divide(inverse(a1),inverse(a1))))))) = divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),
inference(unit_resolution,[status(thm)],[76,28]) ).
tff(78,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(a1,divide(inverse(a1),inverse(a1))))) = divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(a1,divide(inverse(a1),inverse(a1)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
multiply(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(a1,divide(inverse(a1),inverse(a1))))) = divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(a1,divide(inverse(a1),inverse(a1)))))),
inference(unit_resolution,[status(thm)],[78,18]) ).
tff(80,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(a1,divide(inverse(a1),inverse(a1))))) = divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1))))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(a1,divide(inverse(a1),inverse(a1)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(81,plain,
multiply(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(a1,divide(inverse(a1),inverse(a1))))) = divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1))))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(a1,divide(inverse(a1),inverse(a1)))))),
inference(unit_resolution,[status(thm)],[80,18]) ).
tff(82,plain,
divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1))))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(a1,divide(inverse(a1),inverse(a1)))))) = multiply(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(a1,divide(inverse(a1),inverse(a1))))),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1))))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(a1,divide(inverse(a1),inverse(a1)))))) = divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(a1,divide(inverse(a1),inverse(a1)))))),
inference(transitivity,[status(thm)],[82,79]) ).
tff(84,plain,
divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1))))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(a1,divide(inverse(a1),inverse(a1))))))) = divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(a1,divide(inverse(a1),inverse(a1))))))),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1))))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(a1,divide(inverse(a1),inverse(a1))))))) = divide(divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1))))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(a1,divide(inverse(a1),inverse(a1))))))) = divide(divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1))))),
inference(unit_resolution,[status(thm)],[85,28]) ).
tff(87,plain,
divide(divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1))))) = divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1))))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(a1,divide(inverse(a1),inverse(a1))))))),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
divide(divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1))))) = divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),
inference(transitivity,[status(thm)],[87,84,77]) ).
tff(89,plain,
divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))))) = divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))) = divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))))),
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
divide(inverse(a1),inverse(a1)) = divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),
inference(transitivity,[status(thm)],[60,57,43,41,38,30]) ).
tff(92,plain,
divide(a1,divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))) = divide(a1,divide(inverse(a1),inverse(a1))),
inference(transitivity,[status(thm)],[73,70,68]) ).
tff(93,plain,
divide(divide(a1,divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),divide(inverse(a1),inverse(a1))) = divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),
inference(monotonicity,[status(thm)],[92,91]) ).
tff(94,plain,
divide(divide(a1,divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),divide(inverse(a1),inverse(a1))) = divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))))),
inference(transitivity,[status(thm)],[93,90]) ).
tff(95,plain,
divide(inverse(a1),divide(divide(a1,divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),divide(inverse(a1),inverse(a1)))) = divide(inverse(a1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1))))))),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
divide(inverse(a1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1))))))) = divide(inverse(a1),divide(divide(a1,divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),divide(inverse(a1),inverse(a1)))),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(inverse(a1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1))))))) = divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
divide(inverse(a1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1))))))) = divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))),
inference(unit_resolution,[status(thm)],[97,28]) ).
tff(99,plain,
divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))) = divide(inverse(a1),divide(divide(a1,divide(inverse(a1),inverse(a1))),divide(divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1))))))),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))) = divide(inverse(a1),divide(divide(a1,divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),divide(inverse(a1),inverse(a1)))),
inference(transitivity,[status(thm)],[99,96]) ).
tff(101,plain,
divide(inverse(a1),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1))))) = divide(inverse(a1),divide(inverse(a1),divide(divide(a1,divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),divide(inverse(a1),inverse(a1))))),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(inverse(a1),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1))))) = a1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,plain,
divide(inverse(a1),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1))))) = a1,
inference(unit_resolution,[status(thm)],[102,28]) ).
tff(104,plain,
a1 = divide(inverse(a1),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1))))),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
a1 = divide(a1,divide(inverse(a1),inverse(a1))),
inference(transitivity,[status(thm)],[104,101,75,73,70,68]) ).
tff(106,plain,
inverse(a1) = inverse(divide(a1,divide(inverse(a1),inverse(a1)))),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
inverse(divide(a1,divide(inverse(a1),inverse(a1)))) = inverse(a1),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))))) = divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),
inference(monotonicity,[status(thm)],[88]) ).
tff(109,plain,
divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))))) = divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),
inference(transitivity,[status(thm)],[108,41,38,30]) ).
tff(110,plain,
divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))) = divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),
inference(transitivity,[status(thm)],[41,38,30]) ).
tff(111,plain,
divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1))))))) = divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),
inference(monotonicity,[status(thm)],[110,109]) ).
tff(112,plain,
divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))) = divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))))),
inference(symmetry,[status(thm)],[108]) ).
tff(113,plain,
divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))) = divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1)))),divide(inverse(a1),divide(a1,divide(inverse(a1),inverse(a1))))))),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))) = divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),
inference(transitivity,[status(thm)],[113,111]) ).
tff(115,plain,
divide(divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),divide(a1,divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))))) = divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(a1,divide(inverse(a1),inverse(a1)))),
inference(monotonicity,[status(thm)],[114,92]) ).
tff(116,plain,
divide(divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),divide(a1,divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))))) = inverse(a1),
inference(transitivity,[status(thm)],[115,52,107]) ).
tff(117,plain,
divide(divide(inverse(a1),inverse(a1)),divide(a1,divide(inverse(a1),inverse(a1)))) = inverse(divide(a1,divide(inverse(a1),inverse(a1)))),
inference(symmetry,[status(thm)],[49]) ).
tff(118,plain,
divide(divide(inverse(a1),inverse(a1)),divide(a1,divide(inverse(a1),inverse(a1)))) = inverse(a1),
inference(transitivity,[status(thm)],[117,107]) ).
tff(119,plain,
divide(divide(divide(inverse(a1),inverse(a1)),divide(a1,divide(inverse(a1),inverse(a1)))),divide(divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),divide(a1,divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))))) = divide(inverse(a1),inverse(a1)),
inference(monotonicity,[status(thm)],[118,116]) ).
tff(120,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(divide(inverse(a1),inverse(a1)),divide(a1,divide(inverse(a1),inverse(a1)))),divide(a1,divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))))) = divide(divide(divide(inverse(a1),inverse(a1)),divide(a1,divide(inverse(a1),inverse(a1)))),divide(divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),divide(a1,divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(121,plain,
multiply(divide(divide(inverse(a1),inverse(a1)),divide(a1,divide(inverse(a1),inverse(a1)))),divide(a1,divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))))) = divide(divide(divide(inverse(a1),inverse(a1)),divide(a1,divide(inverse(a1),inverse(a1)))),divide(divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),divide(a1,divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))))),
inference(unit_resolution,[status(thm)],[120,18]) ).
tff(122,plain,
a1 = divide(a1,divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)))),
inference(transitivity,[status(thm)],[104,101,75]) ).
tff(123,plain,
inverse(a1) = divide(divide(inverse(a1),inverse(a1)),divide(a1,divide(inverse(a1),inverse(a1)))),
inference(transitivity,[status(thm)],[106,49]) ).
tff(124,plain,
multiply(inverse(a1),a1) = multiply(divide(divide(inverse(a1),inverse(a1)),divide(a1,divide(inverse(a1),inverse(a1)))),divide(a1,divide(divide(divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1)),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))),divide(divide(divide(inverse(a1),inverse(a1)),b1),divide(divide(inverse(a1),inverse(a1)),b1))))),
inference(monotonicity,[status(thm)],[123,122]) ).
tff(125,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(transitivity,[status(thm)],[124,121,119,60,57,43,41,38,30,21,11]) ).
tff(126,plain,
( ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1) )
<=> ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(127,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_1) ).
tff(128,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
$false,
inference(unit_resolution,[status(thm)],[128,125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : GRP521-1 : TPTP v9.0.0. Released v2.6.0.
% 0.09/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 16:13:53 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.48/0.63 % SZS status Unsatisfiable
% 0.48/0.63 % SZS output start Proof
% See solution above
% 0.48/0.67 % E exiting
%------------------------------------------------------------------------------