%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP522-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:08:00 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 39
% Syntax : Number of formulae : 183 ( 148 unt; 0 typ; 0 def)
% Number of atoms : 224 ( 220 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 70 ( 32 ~; 28 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 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 : 148 ( 140 !; 0 ?; 148 :)
% Comments :
%------------------------------------------------------------------------------
tff(a2_type,type,
a2: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(b2_type,type,
b2: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(divide_type,type,
divide: ( $i * $i ) > $i ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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(5,plain,
! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(a2,divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)))))) = a2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(a2,divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)))))) = a2,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,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(14,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(a2,divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) = divide(a2,divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
multiply(a2,divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) = divide(a2,divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)))),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(a2,divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) = divide(a2,divide(divide(inverse(b2),inverse(b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
multiply(a2,divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) = divide(a2,divide(divide(inverse(b2),inverse(b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)))),
inference(unit_resolution,[status(thm)],[19,16]) ).
tff(21,plain,
divide(a2,divide(divide(inverse(b2),inverse(b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)))) = multiply(a2,divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))) = divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))) = divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),
inference(unit_resolution,[status(thm)],[22,7]) ).
tff(24,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))) = a2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))) = a2,
inference(unit_resolution,[status(thm)],[24,7]) ).
tff(26,plain,
divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))),
inference(symmetry,[status(thm)],[26]) ).
tff(28,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(29,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)],[28]) ).
tff(30,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(31,axiom,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
tff(32,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(a2) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
inverse(a2) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(a2) = divide(divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))),a2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
inverse(a2) = divide(divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))),a2),
inference(unit_resolution,[status(thm)],[37,34]) ).
tff(39,plain,
divide(divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))),a2) = inverse(a2),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
divide(divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))) = divide(divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))),a2),
inference(monotonicity,[status(thm)],[25]) ).
tff(41,plain,
divide(divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))),
inference(transitivity,[status(thm)],[40,39,36,27]) ).
tff(42,plain,
divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))))) = divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))))),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))) = divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))) = divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))) = divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))),
inference(unit_resolution,[status(thm)],[44,7]) ).
tff(46,plain,
divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))) = divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))) = divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),
inference(transitivity,[status(thm)],[46,43,23]) ).
tff(48,plain,
divide(divide(inverse(b2),inverse(b2)),divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2))))) = divide(divide(inverse(b2),inverse(b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
divide(a2,divide(divide(inverse(b2),inverse(b2)),divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))))) = divide(a2,divide(divide(inverse(b2),inverse(b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)))),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(a2,divide(divide(inverse(b2),inverse(b2)),divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))))) = divide(a2,divide(inverse(b2),inverse(b2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
divide(a2,divide(divide(inverse(b2),inverse(b2)),divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))))) = divide(a2,divide(inverse(b2),inverse(b2))),
inference(unit_resolution,[status(thm)],[50,7]) ).
tff(52,plain,
divide(a2,divide(inverse(b2),inverse(b2))) = divide(a2,divide(divide(inverse(b2),inverse(b2)),divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))))),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(a2,divide(a2,divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2)))) = divide(a2,divide(inverse(b2),inverse(b2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
divide(a2,divide(a2,divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2)))) = divide(a2,divide(inverse(b2),inverse(b2))),
inference(unit_resolution,[status(thm)],[53,7]) ).
tff(55,plain,
divide(a2,divide(a2,divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2)))) = divide(a2,divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)))),
inference(transitivity,[status(thm)],[54,52,49,21,18]) ).
tff(56,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(a2) = divide(divide(a2,a2),a2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
inverse(a2) = divide(divide(a2,a2),a2),
inference(unit_resolution,[status(thm)],[56,34]) ).
tff(58,plain,
divide(divide(a2,a2),a2) = inverse(a2),
inference(symmetry,[status(thm)],[57]) ).
tff(59,plain,
divide(divide(a2,a2),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))) = divide(divide(a2,a2),a2),
inference(monotonicity,[status(thm)],[25]) ).
tff(60,plain,
divide(divide(a2,a2),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))),
inference(transitivity,[status(thm)],[59,58,36,27]) ).
tff(61,plain,
divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(a2,a2),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))))) = divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))))),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(a2,a2),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))) = divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(a2,a2),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))) = divide(a2,a2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(a2,a2),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))) = divide(a2,a2),
inference(unit_resolution,[status(thm)],[63,7]) ).
tff(65,plain,
divide(a2,a2) = divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(a2,a2),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
divide(a2,a2) = divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),
inference(transitivity,[status(thm)],[65,62,23]) ).
tff(67,plain,
divide(divide(a2,a2),divide(a2,divide(a2,divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2))))) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(a2,divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))))),
inference(monotonicity,[status(thm)],[66,55]) ).
tff(68,plain,
divide(a2,divide(inverse(b2),inverse(b2))) = divide(a2,divide(a2,divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2)))),
inference(symmetry,[status(thm)],[54]) ).
tff(69,plain,
divide(divide(a2,a2),divide(a2,divide(inverse(b2),inverse(b2)))) = divide(divide(a2,a2),divide(a2,divide(a2,divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2))))),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
divide(divide(a2,a2),divide(a2,divide(inverse(b2),inverse(b2)))) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(a2,divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))))),
inference(transitivity,[status(thm)],[69,67]) ).
tff(71,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2))))))) = a2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2))))))) = a2,
inference(unit_resolution,[status(thm)],[71,7]) ).
tff(73,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(inverse(b2),inverse(b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))) = divide(inverse(b2),inverse(b2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(inverse(b2),inverse(b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))) = divide(inverse(b2),inverse(b2)),
inference(unit_resolution,[status(thm)],[73,7]) ).
tff(75,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(a2) = divide(divide(inverse(b2),inverse(b2)),a2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
inverse(a2) = divide(divide(inverse(b2),inverse(b2)),a2),
inference(unit_resolution,[status(thm)],[75,34]) ).
tff(77,plain,
divide(divide(inverse(b2),inverse(b2)),a2) = inverse(a2),
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
divide(divide(inverse(b2),inverse(b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))) = divide(divide(inverse(b2),inverse(b2)),a2),
inference(monotonicity,[status(thm)],[25]) ).
tff(79,plain,
divide(divide(inverse(b2),inverse(b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))),
inference(transitivity,[status(thm)],[78,77,36,27]) ).
tff(80,plain,
divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(inverse(b2),inverse(b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))))) = divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))))),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(inverse(b2),inverse(b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))) = divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))) = divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(inverse(b2),inverse(b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))) = divide(inverse(b2),inverse(b2)),
inference(transitivity,[status(thm)],[46,43,82,74]) ).
tff(84,plain,
divide(a2,divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2))))) = divide(a2,divide(inverse(b2),inverse(b2))),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))))) = divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))) = divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))))),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))) = divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))),
inference(symmetry,[status(thm)],[43]) ).
tff(88,plain,
divide(a2,a2) = divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))))),
inference(transitivity,[status(thm)],[65,62,87,45,86]) ).
tff(89,plain,
divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2)) = divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2))))))),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2)) = a2,
inference(transitivity,[status(thm)],[89,72]) ).
tff(91,plain,
divide(a2,divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2))) = divide(a2,a2),
inference(monotonicity,[status(thm)],[90]) ).
tff(92,plain,
divide(a2,divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2))) = divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),
inference(transitivity,[status(thm)],[91,65,62,23]) ).
tff(93,plain,
divide(divide(a2,divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2))),divide(divide(a2,a2),divide(a2,divide(inverse(b2),inverse(b2))))) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(a2,divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)))))),
inference(monotonicity,[status(thm)],[92,70]) ).
tff(94,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(a2,divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2))),divide(a2,divide(inverse(b2),inverse(b2)))) = divide(divide(a2,divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2))),divide(divide(a2,a2),divide(a2,divide(inverse(b2),inverse(b2))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(95,plain,
multiply(divide(a2,divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2))),divide(a2,divide(inverse(b2),inverse(b2)))) = divide(divide(a2,divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2))),divide(divide(a2,a2),divide(a2,divide(inverse(b2),inverse(b2))))),
inference(unit_resolution,[status(thm)],[94,16]) ).
tff(96,plain,
divide(a2,divide(divide(inverse(b2),inverse(b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)))) = divide(a2,divide(divide(inverse(b2),inverse(b2)),divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))))),
inference(symmetry,[status(thm)],[49]) ).
tff(97,plain,
divide(divide(inverse(b2),inverse(b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) = divide(divide(inverse(b2),inverse(b2)),divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2))))),
inference(symmetry,[status(thm)],[48]) ).
tff(98,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) = divide(divide(inverse(b2),inverse(b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(99,plain,
inverse(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) = divide(divide(inverse(b2),inverse(b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),
inference(unit_resolution,[status(thm)],[98,34]) ).
tff(100,plain,
divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)) = divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))),
inference(symmetry,[status(thm)],[23]) ).
tff(101,plain,
divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)) = divide(inverse(b2),inverse(b2)),
inference(transitivity,[status(thm)],[100,82,74]) ).
tff(102,plain,
inverse(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) = inverse(divide(inverse(b2),inverse(b2))),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
inverse(divide(inverse(b2),inverse(b2))) = inverse(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(divide(inverse(b2),inverse(b2))) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),inverse(b2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
inverse(divide(inverse(b2),inverse(b2))) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),inverse(b2))),
inference(unit_resolution,[status(thm)],[104,34]) ).
tff(106,plain,
divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),inverse(b2))) = inverse(divide(inverse(b2),inverse(b2))),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
divide(a2,a2) = divide(inverse(b2),inverse(b2)),
inference(transitivity,[status(thm)],[65,62,82,74]) ).
tff(108,plain,
divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(a2,a2)) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),inverse(b2))),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(a2,a2)) = divide(divide(inverse(b2),inverse(b2)),divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2))))),
inference(transitivity,[status(thm)],[108,106,103,99,97]) ).
tff(110,plain,
divide(a2,divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(a2,a2))) = divide(a2,divide(divide(inverse(b2),inverse(b2)),divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))))),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
divide(a2,divide(divide(inverse(b2),inverse(b2)),divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2)))))) = divide(a2,divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(a2,a2))),
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
divide(a2,divide(inverse(b2),inverse(b2))) = divide(a2,divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(a2,a2))),
inference(transitivity,[status(thm)],[52,111]) ).
tff(113,plain,
divide(divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2)),divide(a2,divide(inverse(b2),inverse(b2)))) = divide(a2,divide(a2,divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(a2,a2)))),
inference(monotonicity,[status(thm)],[90,112]) ).
tff(114,plain,
divide(a2,divide(a2,divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(a2,a2)))) = divide(divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2)),divide(a2,divide(inverse(b2),inverse(b2)))),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(a2,divide(a2,divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(a2,a2)))) = divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(116,plain,
divide(a2,divide(a2,divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(a2,a2)))) = divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),
inference(unit_resolution,[status(thm)],[115,7]) ).
tff(117,plain,
divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)) = divide(a2,divide(a2,divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(a2,a2)))),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)) = divide(divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2)),divide(a2,divide(inverse(b2),inverse(b2)))),
inference(transitivity,[status(thm)],[117,114]) ).
tff(119,plain,
multiply(a2,divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) = multiply(a2,divide(divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2)),divide(a2,divide(inverse(b2),inverse(b2))))),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
multiply(a2,divide(divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2)),divide(a2,divide(inverse(b2),inverse(b2))))) = multiply(a2,divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(a2,divide(divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2)),divide(a2,divide(inverse(b2),inverse(b2))))) = divide(a2,divide(divide(inverse(b2),inverse(b2)),divide(divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2)),divide(a2,divide(inverse(b2),inverse(b2)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(122,plain,
multiply(a2,divide(divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2)),divide(a2,divide(inverse(b2),inverse(b2))))) = divide(a2,divide(divide(inverse(b2),inverse(b2)),divide(divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2)),divide(a2,divide(inverse(b2),inverse(b2)))))),
inference(unit_resolution,[status(thm)],[121,16]) ).
tff(123,plain,
divide(a2,divide(divide(inverse(b2),inverse(b2)),divide(divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2)),divide(a2,divide(inverse(b2),inverse(b2)))))) = multiply(a2,divide(divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2)),divide(a2,divide(inverse(b2),inverse(b2))))),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(a2,divide(divide(inverse(b2),inverse(b2)),divide(divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2)),divide(a2,divide(inverse(b2),inverse(b2)))))) = divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(125,plain,
divide(a2,divide(divide(inverse(b2),inverse(b2)),divide(divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2)),divide(a2,divide(inverse(b2),inverse(b2)))))) = divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2)),
inference(unit_resolution,[status(thm)],[124,7]) ).
tff(126,plain,
divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2)) = divide(a2,divide(divide(inverse(b2),inverse(b2)),divide(divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2)),divide(a2,divide(inverse(b2),inverse(b2)))))),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2))))))) = divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2)),
inference(symmetry,[status(thm)],[89]) ).
tff(128,plain,
a2 = divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,divide(inverse(b2),inverse(b2))))))),
inference(symmetry,[status(thm)],[72]) ).
tff(129,plain,
a2 = divide(a2,divide(inverse(b2),inverse(b2))),
inference(transitivity,[status(thm)],[128,127,126,123,120,20,96,51]) ).
tff(130,plain,
divide(a2,a2) = divide(a2,divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2))),
inference(symmetry,[status(thm)],[91]) ).
tff(131,plain,
divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))) = divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(a2,a2),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))),
inference(symmetry,[status(thm)],[62]) ).
tff(132,plain,
divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)) = divide(a2,divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2))),
inference(transitivity,[status(thm)],[100,131,64,130]) ).
tff(133,plain,
multiply(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2) = multiply(divide(a2,divide(divide(a2,divide(inverse(b2),inverse(b2))),divide(a2,a2))),divide(a2,divide(inverse(b2),inverse(b2)))),
inference(monotonicity,[status(thm)],[132,129]) ).
tff(134,plain,
divide(inverse(b2),inverse(b2)) = divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(inverse(b2),inverse(b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))),
inference(symmetry,[status(thm)],[74]) ).
tff(135,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(b2) = divide(divide(divide(divide(inverse(b2),inverse(b2)),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))),divide(divide(inverse(b2),inverse(b2)),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))),b2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(136,plain,
inverse(b2) = divide(divide(divide(divide(inverse(b2),inverse(b2)),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))),divide(divide(inverse(b2),inverse(b2)),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))),b2),
inference(unit_resolution,[status(thm)],[135,34]) ).
tff(137,plain,
divide(divide(divide(divide(inverse(b2),inverse(b2)),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))),divide(divide(inverse(b2),inverse(b2)),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))),b2) = inverse(b2),
inference(symmetry,[status(thm)],[136]) ).
tff(138,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))) = inverse(b2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(139,plain,
divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))) = inverse(b2),
inference(unit_resolution,[status(thm)],[138,7]) ).
tff(140,plain,
divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),inverse(b2))),
inference(monotonicity,[status(thm)],[101]) ).
tff(141,plain,
divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),inverse(b2))) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(143,plain,
multiply(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2)),
inference(unit_resolution,[status(thm)],[142,16]) ).
tff(144,plain,
divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2)) = multiply(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2),
inference(symmetry,[status(thm)],[143]) ).
tff(145,plain,
divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2)) = a2,
inference(transitivity,[status(thm)],[144,133,95,93,9]) ).
tff(146,plain,
divide(a2,divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2))) = divide(a2,a2),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
divide(a2,a2) = divide(a2,divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2))),
inference(symmetry,[status(thm)],[146]) ).
tff(148,plain,
divide(inverse(b2),inverse(b2)) = divide(a2,divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2))),
inference(transitivity,[status(thm)],[134,81,131,64,147]) ).
tff(149,plain,
divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),inverse(b2))) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(a2,divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2)))),
inference(monotonicity,[status(thm)],[148]) ).
tff(150,plain,
divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(a2,divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2)))) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),inverse(b2))),
inference(symmetry,[status(thm)],[149]) ).
tff(151,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(a2,divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2)))) = divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(152,plain,
divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(a2,divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2)))) = divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),
inference(unit_resolution,[status(thm)],[151,7]) ).
tff(153,plain,
divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(a2,divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2)))),
inference(symmetry,[status(thm)],[152]) ).
tff(154,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(a2) = divide(divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))),a2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(155,plain,
inverse(a2) = divide(divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))),a2),
inference(unit_resolution,[status(thm)],[154,34]) ).
tff(156,plain,
divide(divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))),a2) = inverse(a2),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
divide(divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))) = divide(divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))),a2),
inference(monotonicity,[status(thm)],[25]) ).
tff(158,plain,
divide(divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))),
inference(transitivity,[status(thm)],[157,156,36,27]) ).
tff(159,plain,
divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))))) = divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))))),
inference(monotonicity,[status(thm)],[158]) ).
tff(160,plain,
divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))) = divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))),
inference(monotonicity,[status(thm)],[159]) ).
tff(161,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
| ( divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))) = divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(162,plain,
divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))) = divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))),
inference(unit_resolution,[status(thm)],[161,7]) ).
tff(163,plain,
divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))) = divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))),
inference(symmetry,[status(thm)],[162]) ).
tff(164,plain,
divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))) = divide(a2,divide(inverse(b2),inverse(b2))),
inference(transitivity,[status(thm)],[25,128,127,126,123,120,20,96,51]) ).
tff(165,plain,
divide(inverse(b2),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))) = divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),
inference(monotonicity,[status(thm)],[164]) ).
tff(166,plain,
divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))))) = divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))),
inference(monotonicity,[status(thm)],[165]) ).
tff(167,plain,
divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))))) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2))),
inference(transitivity,[status(thm)],[166,163,160,23,153,150,141]) ).
tff(168,plain,
divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))) = divide(inverse(b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)))),
inference(monotonicity,[status(thm)],[167]) ).
tff(169,plain,
divide(inverse(b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)))) = divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))),
inference(symmetry,[status(thm)],[168]) ).
tff(170,plain,
divide(inverse(b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)))) = inverse(b2),
inference(transitivity,[status(thm)],[169,139]) ).
tff(171,plain,
divide(divide(inverse(b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)))),divide(divide(divide(divide(inverse(b2),inverse(b2)),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))),divide(divide(inverse(b2),inverse(b2)),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))),b2)) = divide(inverse(b2),inverse(b2)),
inference(monotonicity,[status(thm)],[170,137]) ).
tff(172,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(inverse(b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)))),b2) = divide(divide(inverse(b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)))),divide(divide(divide(divide(inverse(b2),inverse(b2)),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))),divide(divide(inverse(b2),inverse(b2)),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))),b2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(173,plain,
multiply(divide(inverse(b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)))),b2) = divide(divide(inverse(b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)))),divide(divide(divide(divide(inverse(b2),inverse(b2)),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2))))),divide(divide(inverse(b2),inverse(b2)),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))),b2)),
inference(unit_resolution,[status(thm)],[172,16]) ).
tff(174,plain,
inverse(b2) = divide(inverse(b2),divide(divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))),divide(inverse(b2),divide(inverse(b2),divide(inverse(b2),divide(a2,divide(inverse(b2),inverse(b2)))))))),
inference(symmetry,[status(thm)],[139]) ).
tff(175,plain,
inverse(b2) = divide(inverse(b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)))),
inference(transitivity,[status(thm)],[174,168]) ).
tff(176,plain,
multiply(inverse(b2),b2) = multiply(divide(inverse(b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)))),b2),
inference(monotonicity,[status(thm)],[175]) ).
tff(177,plain,
multiply(inverse(b2),b2) = divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),
inference(transitivity,[status(thm)],[176,173,171,134,81,23]) ).
tff(178,plain,
multiply(multiply(inverse(b2),b2),a2) = multiply(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(transitivity,[status(thm)],[178,133,95,93,9]) ).
tff(180,plain,
( ( multiply(multiply(inverse(b2),b2),a2) != a2 )
<=> ( multiply(multiply(inverse(b2),b2),a2) != a2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(181,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
tff(182,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(modus_ponens,[status(thm)],[181,180]) ).
tff(183,plain,
$false,
inference(unit_resolution,[status(thm)],[182,179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP522-1 : TPTP v9.0.0. Released v2.6.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n006.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 16:13:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.46 % SZS status Unsatisfiable
% 0.19/0.46 % SZS output start Proof
% See solution above
% 0.19/0.49 % E exiting
%------------------------------------------------------------------------------