TSTP Solution File: GRP458-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP458-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Fri Sep 16 22:27:36 EDT 2022
% Result : Unsatisfiable 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 31
% Syntax : Number of formulae : 147 ( 120 unt; 4 typ; 0 def)
% Number of atoms : 172 ( 168 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 46 ( 20 ~; 16 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 95 ( 89 !; 0 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
tff(a2_type,type,
a2: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(identity_type,type,
identity: $i ).
tff(divide_type,type,
divide: ( $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C) = B )
<=> ( divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C) = B ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C) = B ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [B: $i,A: $i,C: $i] : ( divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
tff(5,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C) = B ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C) = B ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C) = B ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C) = B )
| ( divide(divide(divide(divide(identity,divide(identity,a2)),divide(identity,divide(identity,a2))),divide(divide(identity,divide(identity,a2)),divide(a2,divide(divide(identity,divide(identity,divide(identity,a2))),divide(divide(identity,a2),divide(identity,divide(identity,a2))))))),divide(divide(identity,a2),divide(identity,divide(identity,a2)))) = a2 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
divide(divide(divide(divide(identity,divide(identity,a2)),divide(identity,divide(identity,a2))),divide(divide(identity,divide(identity,a2)),divide(a2,divide(divide(identity,divide(identity,divide(identity,a2))),divide(divide(identity,a2),divide(identity,divide(identity,a2))))))),divide(divide(identity,a2),divide(identity,divide(identity,a2)))) = a2,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C) = B )
| ( divide(divide(divide(identity,identity),divide(identity,divide(a2,divide(divide(identity,identity),divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))))),divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))) = a2 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(11,plain,
divide(divide(divide(identity,identity),divide(identity,divide(a2,divide(divide(identity,identity),divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))))),divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))) = a2,
inference(unit_resolution,[status(thm)],[10,7]) ).
tff(12,plain,
^ [A: $i] :
refl(
( ( identity = divide(A,A) )
<=> ( identity = divide(A,A) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [A: $i] : ( identity = divide(A,A) )
<=> ! [A: $i] : ( identity = divide(A,A) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [A: $i] : ( identity = divide(A,A) )
<=> ! [A: $i] : ( identity = divide(A,A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
! [A: $i] : ( identity = divide(A,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
tff(16,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
( ~ ! [A: $i] : ( identity = divide(A,A) )
| ( identity = divide(identity,identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(20,plain,
identity = divide(identity,identity),
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
divide(identity,identity) = identity,
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
divide(divide(identity,identity),divide(identity,a2)) = divide(identity,divide(identity,a2)),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))) = divide(divide(identity,a2),divide(identity,divide(identity,a2))),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
divide(divide(identity,a2),divide(identity,divide(identity,a2))) = divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
divide(divide(identity,identity),a2) = divide(identity,a2),
inference(monotonicity,[status(thm)],[21]) ).
tff(26,plain,
divide(identity,divide(divide(identity,identity),a2)) = divide(identity,divide(identity,a2)),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
divide(identity,divide(identity,a2)) = divide(identity,divide(divide(identity,identity),a2)),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C) = B )
| ( divide(divide(divide(a2,a2),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))))),divide(divide(identity,identity),divide(identity,a2))) = identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
divide(divide(divide(a2,a2),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))))),divide(divide(identity,identity),divide(identity,a2))) = identity,
inference(unit_resolution,[status(thm)],[28,7]) ).
tff(30,plain,
divide(identity,divide(divide(divide(a2,a2),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))))),divide(divide(identity,identity),divide(identity,a2)))) = divide(identity,identity),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
divide(identity,divide(divide(divide(a2,a2),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))))),divide(divide(identity,identity),divide(identity,a2)))) = identity,
inference(transitivity,[status(thm)],[30,21]) ).
tff(32,plain,
divide(divide(identity,identity),divide(identity,divide(divide(divide(a2,a2),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))))),divide(divide(identity,identity),divide(identity,a2))))) = divide(identity,identity),
inference(monotonicity,[status(thm)],[21,31]) ).
tff(33,plain,
divide(divide(identity,identity),divide(identity,divide(divide(divide(a2,a2),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))))),divide(divide(identity,identity),divide(identity,a2))))) = identity,
inference(transitivity,[status(thm)],[32,21]) ).
tff(34,plain,
divide(divide(divide(identity,identity),divide(identity,divide(divide(divide(a2,a2),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))))),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2)) = divide(identity,divide(identity,a2)),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C) = B )
| ( divide(divide(divide(identity,identity),divide(identity,divide(divide(divide(a2,a2),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))))),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2)) = divide(divide(a2,a2),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
divide(divide(divide(identity,identity),divide(identity,divide(divide(divide(a2,a2),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))))),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2)) = divide(divide(a2,a2),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))))),
inference(unit_resolution,[status(thm)],[35,7]) ).
tff(37,plain,
divide(divide(a2,a2),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))))) = divide(divide(divide(identity,identity),divide(identity,divide(divide(divide(a2,a2),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))))),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2)),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
divide(divide(identity,identity),divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))) = divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),
inference(monotonicity,[status(thm)],[21]) ).
tff(39,plain,
divide(a2,divide(divide(identity,identity),divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))) = divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( ~ ! [A: $i] : ( identity = divide(A,A) )
| ( identity = divide(a2,a2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
identity = divide(a2,a2),
inference(unit_resolution,[status(thm)],[40,18]) ).
tff(42,plain,
divide(identity,divide(a2,divide(divide(identity,identity),divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))))) = divide(divide(a2,a2),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))))),
inference(monotonicity,[status(thm)],[41,39]) ).
tff(43,plain,
divide(identity,divide(a2,divide(divide(identity,identity),divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))))) = divide(identity,divide(divide(identity,identity),a2)),
inference(transitivity,[status(thm)],[42,37,34,27]) ).
tff(44,plain,
divide(divide(identity,identity),divide(identity,divide(a2,divide(divide(identity,identity),divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))))) = divide(identity,divide(identity,divide(divide(identity,identity),a2))),
inference(monotonicity,[status(thm)],[21,43]) ).
tff(45,plain,
divide(identity,divide(identity,divide(divide(identity,identity),a2))) = divide(divide(identity,identity),divide(identity,divide(a2,divide(divide(identity,identity),divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))))),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
divide(identity,divide(identity,divide(identity,a2))) = divide(identity,divide(identity,divide(divide(identity,identity),a2))),
inference(monotonicity,[status(thm)],[27]) ).
tff(47,plain,
divide(identity,divide(identity,divide(identity,a2))) = divide(divide(identity,identity),divide(identity,divide(a2,divide(divide(identity,identity),divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))))),
inference(transitivity,[status(thm)],[46,45]) ).
tff(48,plain,
divide(divide(identity,divide(identity,divide(identity,a2))),divide(divide(identity,a2),divide(identity,divide(identity,a2)))) = divide(divide(divide(identity,identity),divide(identity,divide(a2,divide(divide(identity,identity),divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))))),divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),
inference(monotonicity,[status(thm)],[47,24]) ).
tff(49,plain,
divide(divide(identity,divide(identity,divide(identity,a2))),divide(divide(identity,a2),divide(identity,divide(identity,a2)))) = a2,
inference(transitivity,[status(thm)],[48,11]) ).
tff(50,plain,
divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),divide(divide(identity,divide(identity,divide(identity,a2))),divide(divide(identity,a2),divide(identity,divide(identity,a2))))) = divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),a2),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),a2) = divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),divide(divide(identity,divide(identity,divide(identity,a2))),divide(divide(identity,a2),divide(identity,divide(identity,a2))))),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C) = B )
| ( divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),a2) = identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),a2) = identity,
inference(unit_resolution,[status(thm)],[52,7]) ).
tff(54,plain,
identity = divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),a2),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
divide(a2,a2) = identity,
inference(symmetry,[status(thm)],[41]) ).
tff(56,plain,
divide(a2,divide(divide(identity,divide(identity,divide(identity,a2))),divide(divide(identity,a2),divide(identity,divide(identity,a2))))) = divide(a2,a2),
inference(monotonicity,[status(thm)],[49]) ).
tff(57,plain,
divide(a2,divide(divide(identity,divide(identity,divide(identity,a2))),divide(divide(identity,a2),divide(identity,divide(identity,a2))))) = divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),divide(divide(identity,divide(identity,divide(identity,a2))),divide(divide(identity,a2),divide(identity,divide(identity,a2))))),
inference(transitivity,[status(thm)],[56,55,54,51]) ).
tff(58,plain,
divide(divide(identity,divide(identity,a2)),divide(a2,divide(divide(identity,divide(identity,divide(identity,a2))),divide(divide(identity,a2),divide(identity,divide(identity,a2)))))) = divide(divide(identity,divide(identity,a2)),divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),divide(divide(identity,divide(identity,divide(identity,a2))),divide(divide(identity,a2),divide(identity,divide(identity,a2)))))),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
divide(divide(divide(identity,divide(identity,a2)),divide(identity,divide(identity,a2))),divide(divide(identity,divide(identity,a2)),divide(a2,divide(divide(identity,divide(identity,divide(identity,a2))),divide(divide(identity,a2),divide(identity,divide(identity,a2))))))) = divide(divide(divide(identity,divide(identity,a2)),divide(identity,divide(identity,a2))),divide(divide(identity,divide(identity,a2)),divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),divide(divide(identity,divide(identity,divide(identity,a2))),divide(divide(identity,a2),divide(identity,divide(identity,a2))))))),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
divide(divide(divide(divide(identity,divide(identity,a2)),divide(identity,divide(identity,a2))),divide(divide(identity,divide(identity,a2)),divide(a2,divide(divide(identity,divide(identity,divide(identity,a2))),divide(divide(identity,a2),divide(identity,divide(identity,a2))))))),divide(divide(identity,a2),divide(identity,divide(identity,a2)))) = divide(divide(divide(divide(identity,divide(identity,a2)),divide(identity,divide(identity,a2))),divide(divide(identity,divide(identity,a2)),divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),divide(divide(identity,divide(identity,divide(identity,a2))),divide(divide(identity,a2),divide(identity,divide(identity,a2))))))),divide(divide(identity,a2),divide(identity,divide(identity,a2)))),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
divide(divide(divide(divide(identity,divide(identity,a2)),divide(identity,divide(identity,a2))),divide(divide(identity,divide(identity,a2)),divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),divide(divide(identity,divide(identity,divide(identity,a2))),divide(divide(identity,a2),divide(identity,divide(identity,a2))))))),divide(divide(identity,a2),divide(identity,divide(identity,a2)))) = divide(divide(divide(divide(identity,divide(identity,a2)),divide(identity,divide(identity,a2))),divide(divide(identity,divide(identity,a2)),divide(a2,divide(divide(identity,divide(identity,divide(identity,a2))),divide(divide(identity,a2),divide(identity,divide(identity,a2))))))),divide(divide(identity,a2),divide(identity,divide(identity,a2)))),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C) = B )
| ( divide(divide(divide(divide(identity,divide(identity,a2)),divide(identity,divide(identity,a2))),divide(divide(identity,divide(identity,a2)),divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),divide(divide(identity,divide(identity,divide(identity,a2))),divide(divide(identity,a2),divide(identity,divide(identity,a2))))))),divide(divide(identity,a2),divide(identity,divide(identity,a2)))) = divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
divide(divide(divide(divide(identity,divide(identity,a2)),divide(identity,divide(identity,a2))),divide(divide(identity,divide(identity,a2)),divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),divide(divide(identity,divide(identity,divide(identity,a2))),divide(divide(identity,a2),divide(identity,divide(identity,a2))))))),divide(divide(identity,a2),divide(identity,divide(identity,a2)))) = divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),
inference(unit_resolution,[status(thm)],[62,7]) ).
tff(64,plain,
divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))) = divide(divide(divide(divide(identity,divide(identity,a2)),divide(identity,divide(identity,a2))),divide(divide(identity,divide(identity,a2)),divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),divide(divide(identity,divide(identity,divide(identity,a2))),divide(divide(identity,a2),divide(identity,divide(identity,a2))))))),divide(divide(identity,a2),divide(identity,divide(identity,a2)))),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C) = B )
| ( divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),divide(divide(identity,divide(identity,a2)),divide(identity,a2))))),divide(identity,a2)) = divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),divide(divide(identity,divide(identity,a2)),divide(identity,a2))))),divide(identity,a2)) = divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),
inference(unit_resolution,[status(thm)],[65,7]) ).
tff(67,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C) = B )
| ( divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))))))),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))))) = identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))))))),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))))) = identity,
inference(unit_resolution,[status(thm)],[67,7]) ).
tff(69,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C) = B )
| ( divide(divide(divide(identity,identity),divide(identity,divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2)) = divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
divide(divide(divide(identity,identity),divide(identity,divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2)) = divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),
inference(unit_resolution,[status(thm)],[69,7]) ).
tff(71,plain,
divide(identity,divide(divide(identity,divide(identity,divide(identity,a2))),divide(divide(identity,a2),divide(identity,divide(identity,a2))))) = divide(identity,a2),
inference(monotonicity,[status(thm)],[49]) ).
tff(72,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C) = B )
| ( divide(divide(divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2))))),divide(identity,a2)) = identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
divide(divide(divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2))))),divide(identity,a2)) = identity,
inference(unit_resolution,[status(thm)],[72,7]) ).
tff(74,plain,
divide(divide(divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2))))),divide(divide(identity,identity),a2)) = divide(divide(divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2))))),divide(identity,a2)),
inference(monotonicity,[status(thm)],[25]) ).
tff(75,plain,
divide(divide(divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2))))),divide(divide(identity,identity),a2)) = identity,
inference(transitivity,[status(thm)],[74,73]) ).
tff(76,plain,
divide(identity,divide(divide(divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2))))),divide(divide(identity,identity),a2))) = divide(identity,identity),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
divide(identity,divide(divide(divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2))))),divide(divide(identity,identity),a2))) = identity,
inference(transitivity,[status(thm)],[76,21]) ).
tff(78,plain,
divide(divide(identity,identity),divide(identity,divide(divide(divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2))))),divide(divide(identity,identity),a2)))) = divide(identity,identity),
inference(monotonicity,[status(thm)],[21,77]) ).
tff(79,plain,
divide(divide(identity,identity),divide(identity,divide(divide(divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2))))),divide(divide(identity,identity),a2)))) = identity,
inference(transitivity,[status(thm)],[78,21]) ).
tff(80,plain,
divide(divide(divide(identity,identity),divide(identity,divide(divide(divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2))))),divide(divide(identity,identity),a2)))),a2) = divide(identity,a2),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C) = B )
| ( divide(divide(divide(identity,identity),divide(identity,divide(divide(divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2))))),divide(divide(identity,identity),a2)))),a2) = divide(divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
divide(divide(divide(identity,identity),divide(identity,divide(divide(divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2))))),divide(divide(identity,identity),a2)))),a2) = divide(divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2))))),
inference(unit_resolution,[status(thm)],[81,7]) ).
tff(83,plain,
divide(divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2))))) = divide(divide(divide(identity,identity),divide(identity,divide(divide(divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2))))),divide(divide(identity,identity),a2)))),a2),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C) = B )
| ( divide(divide(divide(identity,identity),divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2)) = divide(identity,a2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
divide(divide(divide(identity,identity),divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2)) = divide(identity,a2),
inference(unit_resolution,[status(thm)],[84,7]) ).
tff(86,plain,
divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))) = divide(divide(identity,identity),divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),
inference(monotonicity,[status(thm)],[20]) ).
tff(87,plain,
divide(divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2)) = divide(divide(divide(identity,identity),divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2)),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
divide(divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2)) = divide(identity,a2),
inference(transitivity,[status(thm)],[87,85]) ).
tff(89,plain,
divide(identity,divide(divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2))) = divide(identity,divide(identity,a2)),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
divide(identity,divide(identity,a2)) = divide(identity,divide(divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2))),
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
divide(divide(identity,identity),divide(identity,a2)) = divide(identity,divide(divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2))),
inference(transitivity,[status(thm)],[22,90]) ).
tff(92,plain,
divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(divide(identity,identity),divide(identity,a2))) = divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2)))),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
( ~ ! [A: $i] : ( identity = divide(A,A) )
| ( identity = divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
identity = divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),
inference(unit_resolution,[status(thm)],[93,18]) ).
tff(95,plain,
divide(identity,divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(divide(identity,identity),divide(identity,a2)))) = divide(divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2))))),
inference(monotonicity,[status(thm)],[94,92]) ).
tff(96,plain,
divide(identity,divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(divide(identity,identity),divide(identity,a2)))) = divide(identity,a2),
inference(transitivity,[status(thm)],[95,83,80]) ).
tff(97,plain,
divide(divide(identity,identity),divide(identity,divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(divide(identity,identity),divide(identity,a2))))) = divide(identity,divide(identity,a2)),
inference(monotonicity,[status(thm)],[21,96]) ).
tff(98,plain,
divide(identity,divide(identity,a2)) = divide(divide(identity,identity),divide(identity,divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(divide(identity,identity),divide(identity,a2))))),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
divide(divide(identity,divide(identity,a2)),divide(identity,divide(divide(identity,divide(identity,divide(identity,a2))),divide(divide(identity,a2),divide(identity,divide(identity,a2)))))) = divide(divide(divide(identity,identity),divide(identity,divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2)),
inference(monotonicity,[status(thm)],[98,71]) ).
tff(100,plain,
divide(identity,a2) = divide(identity,divide(divide(identity,divide(identity,divide(identity,a2))),divide(divide(identity,a2),divide(identity,divide(identity,a2))))),
inference(symmetry,[status(thm)],[71]) ).
tff(101,plain,
divide(divide(identity,divide(identity,a2)),divide(identity,a2)) = divide(divide(identity,divide(identity,a2)),divide(identity,divide(divide(identity,divide(identity,divide(identity,a2))),divide(divide(identity,a2),divide(identity,divide(identity,a2)))))),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
divide(divide(identity,divide(identity,a2)),divide(identity,a2)) = divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),
inference(transitivity,[status(thm)],[101,99,70]) ).
tff(103,plain,
divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))) = a2,
inference(transitivity,[status(thm)],[64,61,9]) ).
tff(104,plain,
divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),divide(divide(identity,divide(identity,a2)),divide(identity,a2))) = divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),
inference(monotonicity,[status(thm)],[103,102]) ).
tff(105,plain,
divide(divide(identity,identity),divide(identity,divide(identity,a2))) = divide(identity,divide(identity,divide(divide(identity,identity),a2))),
inference(monotonicity,[status(thm)],[21,27]) ).
tff(106,plain,
divide(identity,divide(divide(identity,identity),divide(identity,divide(identity,a2)))) = divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),
inference(monotonicity,[status(thm)],[20,105]) ).
tff(107,plain,
divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))) = divide(identity,divide(divide(identity,identity),divide(identity,divide(identity,a2)))),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
divide(identity,identity) = divide(a2,a2),
inference(transitivity,[status(thm)],[21,41]) ).
tff(109,plain,
divide(divide(identity,identity),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))))) = divide(divide(a2,a2),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))))),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
divide(divide(identity,identity),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))))) = divide(identity,divide(divide(identity,identity),a2)),
inference(transitivity,[status(thm)],[109,37,34,27]) ).
tff(111,plain,
divide(identity,divide(divide(identity,identity),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))))) = divide(identity,divide(identity,divide(divide(identity,identity),a2))),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
divide(identity,divide(identity,divide(divide(identity,identity),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))))))) = divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),
inference(monotonicity,[status(thm)],[20,111]) ).
tff(113,plain,
divide(identity,divide(identity,divide(divide(identity,identity),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))))))) = divide(identity,divide(divide(identity,identity),divide(identity,divide(identity,a2)))),
inference(transitivity,[status(thm)],[112,107]) ).
tff(114,plain,
divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))))))) = divide(identity,divide(identity,divide(divide(identity,identity),divide(identity,divide(identity,a2))))),
inference(monotonicity,[status(thm)],[21,113]) ).
tff(115,plain,
divide(identity,divide(identity,divide(divide(identity,identity),divide(identity,divide(identity,a2))))) = divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))))))),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
divide(identity,divide(divide(identity,identity),divide(identity,divide(identity,a2)))) = a2,
inference(transitivity,[status(thm)],[106,64,61,9]) ).
tff(117,plain,
divide(identity,divide(identity,divide(divide(identity,identity),divide(identity,divide(identity,a2))))) = divide(identity,a2),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
divide(identity,a2) = divide(identity,divide(identity,divide(divide(identity,identity),divide(identity,divide(identity,a2))))),
inference(symmetry,[status(thm)],[117]) ).
tff(119,plain,
divide(identity,a2) = divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))))))),
inference(transitivity,[status(thm)],[118,115]) ).
tff(120,plain,
divide(divide(identity,a2),divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),divide(divide(identity,divide(identity,a2)),divide(identity,a2)))) = divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))))))),divide(a2,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))))),
inference(monotonicity,[status(thm)],[119,104]) ).
tff(121,plain,
divide(divide(identity,a2),divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),divide(divide(identity,divide(identity,a2)),divide(identity,a2)))) = identity,
inference(transitivity,[status(thm)],[120,68]) ).
tff(122,plain,
divide(identity,a2) = divide(divide(divide(identity,identity),divide(identity,divide(divide(divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2))))),divide(divide(identity,identity),a2)))),a2),
inference(symmetry,[status(thm)],[80]) ).
tff(123,plain,
divide(identity,a2) = divide(divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2))))),
inference(transitivity,[status(thm)],[122,82]) ).
tff(124,plain,
divide(divide(identity,a2),divide(identity,a2)) = divide(divide(divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2)))),divide(identity,divide(divide(identity,divide(identity,divide(divide(identity,a2),divide(divide(identity,identity),divide(identity,a2))))),divide(identity,a2))))),divide(identity,a2)),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
divide(divide(identity,a2),divide(identity,a2)) = identity,
inference(transitivity,[status(thm)],[124,73]) ).
tff(126,plain,
divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),divide(divide(identity,divide(identity,a2)),divide(identity,a2))))) = divide(identity,identity),
inference(monotonicity,[status(thm)],[125,121]) ).
tff(127,plain,
divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),divide(divide(identity,divide(identity,a2)),divide(identity,a2))))) = identity,
inference(transitivity,[status(thm)],[126,21]) ).
tff(128,plain,
divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),divide(divide(identity,divide(identity,a2)),divide(identity,a2))))),divide(identity,a2)) = divide(identity,divide(identity,a2)),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
divide(identity,divide(identity,a2)) = divide(divide(divide(divide(identity,a2),divide(identity,a2)),divide(divide(identity,a2),divide(divide(divide(identity,identity),divide(identity,divide(identity,divide(divide(identity,identity),a2)))),divide(divide(identity,divide(identity,a2)),divide(identity,a2))))),divide(identity,a2)),
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
^ [B: $i,A: $i] :
refl(
( ( multiply(A,B) = divide(A,divide(identity,B)) )
<=> ( multiply(A,B) = divide(A,divide(identity,B)) ) )),
inference(bind,[status(th)],]) ).
tff(131,plain,
( ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) )
<=> ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ) ),
inference(quant_intro,[status(thm)],[130]) ).
tff(132,plain,
( ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) )
<=> ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(133,axiom,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
tff(134,plain,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
inference(skolemize,[status(sab)],[134]) ).
tff(136,plain,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
inference(modus_ponens,[status(thm)],[135,131]) ).
tff(137,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) )
| ( multiply(identity,a2) = divide(identity,divide(identity,a2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
multiply(identity,a2) = divide(identity,divide(identity,a2)),
inference(unit_resolution,[status(thm)],[137,136]) ).
tff(139,plain,
multiply(identity,a2) = a2,
inference(transitivity,[status(thm)],[138,129,66,64,61,9]) ).
tff(140,plain,
( ( multiply(identity,a2) != a2 )
<=> ( multiply(identity,a2) != a2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(141,axiom,
multiply(identity,a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
tff(142,plain,
multiply(identity,a2) != a2,
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
$false,
inference(unit_resolution,[status(thm)],[142,139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP458-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 16:59:32 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.44 % SZS status Unsatisfiable
% 0.19/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------