TSTP Solution File: GRP544-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP544-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 22:28:11 EDT 2022
% Result : Unsatisfiable 0.16s 0.42s
% Output : Proof 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 31
% Syntax : Number of formulae : 146 ( 119 unt; 5 typ; 0 def)
% Number of atoms : 169 ( 165 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 44 ( 19 ~; 15 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 10 ( 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 91 ( 85 !; 0 ?; 91 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(divide_type,type,
divide: ( $i * $i ) > $i ).
tff(identity_type,type,
identity: $i ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,axiom,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
tff(5,plain,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) )
| ( multiply(b,a) = divide(b,divide(identity,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
multiply(b,a) = divide(b,divide(identity,a)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
divide(b,divide(identity,a)) = multiply(b,a),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
<=> ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)),identity)),divide(identity,b)) = divide(b,divide(identity,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
divide(divide(identity,divide(divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)),identity)),divide(identity,b)) = divide(b,divide(identity,a)),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(identity,a),divide(divide(identity,a),divide(identity,identity))),identity)),divide(divide(identity,a),divide(identity,identity))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
divide(divide(identity,divide(divide(divide(identity,a),divide(divide(identity,a),divide(identity,identity))),identity)),divide(divide(identity,a),divide(identity,identity))) = a,
inference(unit_resolution,[status(thm)],[20,17]) ).
tff(22,plain,
^ [A: $i] :
refl(
( ( identity = divide(A,A) )
<=> ( identity = divide(A,A) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [A: $i] : ( identity = divide(A,A) )
<=> ! [A: $i] : ( identity = divide(A,A) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [A: $i] : ( identity = divide(A,A) )
<=> ! [A: $i] : ( identity = divide(A,A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,axiom,
! [A: $i] : ( identity = divide(A,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
tff(26,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
( ~ ! [A: $i] : ( identity = divide(A,A) )
| ( identity = divide(identity,identity) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
identity = divide(identity,identity),
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,plain,
divide(identity,identity) = identity,
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
divide(divide(identity,identity),a) = divide(identity,a),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
divide(divide(divide(identity,identity),a),identity) = divide(divide(identity,a),identity),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
divide(divide(identity,a),identity) = divide(divide(divide(identity,identity),a),identity),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
divide(divide(identity,a),identity) = divide(divide(identity,a),divide(identity,identity)),
inference(monotonicity,[status(thm)],[30]) ).
tff(36,plain,
divide(divide(identity,a),divide(identity,identity)) = divide(divide(identity,a),identity),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
divide(divide(identity,a),divide(identity,identity)) = divide(divide(divide(identity,identity),a),identity),
inference(transitivity,[status(thm)],[36,34]) ).
tff(38,plain,
( ~ ! [A: $i] : ( identity = divide(A,A) )
| ( identity = divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
identity = divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),
inference(unit_resolution,[status(thm)],[38,28]) ).
tff(40,plain,
divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))) = identity,
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))) = divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
divide(divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))) = divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
divide(divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))) = identity,
inference(transitivity,[status(thm)],[42,40]) ).
tff(44,plain,
divide(identity,divide(divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))))) = divide(identity,identity),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))) = divide(divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),
inference(symmetry,[status(thm)],[42]) ).
tff(46,plain,
identity = divide(divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),
inference(transitivity,[status(thm)],[39,45]) ).
tff(47,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(identity,identity),divide(divide(identity,a),divide(identity,identity))),identity)),divide(divide(identity,a),divide(identity,identity))) = identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
divide(divide(identity,divide(divide(divide(identity,identity),divide(divide(identity,a),divide(identity,identity))),identity)),divide(divide(identity,a),divide(identity,identity))) = identity,
inference(unit_resolution,[status(thm)],[47,17]) ).
tff(49,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(identity,a),identity),identity)),identity) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
divide(divide(identity,divide(divide(divide(identity,a),identity),identity)),identity) = a,
inference(unit_resolution,[status(thm)],[49,17]) ).
tff(51,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(identity,identity),a),identity)),a) = identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
divide(divide(identity,divide(divide(divide(identity,identity),a),identity)),a) = identity,
inference(unit_resolution,[status(thm)],[51,17]) ).
tff(53,plain,
divide(divide(divide(identity,identity),a),identity) = divide(divide(identity,a),divide(identity,identity)),
inference(transitivity,[status(thm)],[33,35]) ).
tff(54,plain,
divide(identity,divide(divide(divide(identity,identity),a),identity)) = divide(identity,divide(divide(identity,a),divide(identity,identity))),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
divide(identity,divide(divide(identity,a),divide(identity,identity))) = divide(identity,divide(divide(divide(identity,identity),a),identity)),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
divide(divide(identity,divide(divide(identity,a),divide(identity,identity))),a) = divide(divide(identity,divide(divide(divide(identity,identity),a),identity)),a),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
divide(divide(identity,divide(divide(identity,a),divide(identity,identity))),a) = identity,
inference(transitivity,[status(thm)],[56,52]) ).
tff(58,plain,
divide(divide(divide(identity,divide(divide(identity,a),divide(identity,identity))),a),identity) = divide(identity,divide(divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))))),
inference(monotonicity,[status(thm)],[57,46]) ).
tff(59,plain,
divide(divide(divide(identity,divide(divide(identity,a),divide(identity,identity))),a),identity) = divide(divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),
inference(transitivity,[status(thm)],[58,44,31,39,45]) ).
tff(60,plain,
divide(identity,divide(divide(divide(identity,divide(divide(identity,a),divide(identity,identity))),a),identity)) = divide(identity,divide(divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))))),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
divide(identity,divide(divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))))) = divide(identity,divide(divide(divide(identity,divide(divide(identity,a),divide(identity,identity))),a),identity)),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
divide(identity,identity) = divide(identity,divide(divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))))),
inference(symmetry,[status(thm)],[44]) ).
tff(63,plain,
identity = divide(identity,divide(divide(divide(identity,divide(divide(identity,a),divide(identity,identity))),a),identity)),
inference(transitivity,[status(thm)],[30,62,61]) ).
tff(64,plain,
divide(identity,a) = divide(divide(identity,divide(divide(divide(identity,divide(divide(identity,a),divide(identity,identity))),a),identity)),a),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
divide(divide(identity,divide(divide(divide(identity,divide(divide(identity,a),divide(identity,identity))),a),identity)),a) = divide(identity,a),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(identity,divide(divide(identity,a),divide(identity,identity))),a),identity)),a) = divide(divide(identity,a),divide(identity,identity)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
divide(divide(identity,divide(divide(divide(identity,divide(divide(identity,a),divide(identity,identity))),a),identity)),a) = divide(divide(identity,a),divide(identity,identity)),
inference(unit_resolution,[status(thm)],[66,17]) ).
tff(68,plain,
divide(divide(identity,a),divide(identity,identity)) = divide(divide(identity,divide(divide(divide(identity,divide(divide(identity,a),divide(identity,identity))),a),identity)),a),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
divide(divide(identity,a),identity) = divide(identity,a),
inference(transitivity,[status(thm)],[35,68,65]) ).
tff(70,plain,
divide(divide(divide(identity,a),identity),identity) = divide(divide(identity,a),identity),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
divide(divide(divide(identity,a),identity),identity) = divide(divide(divide(identity,identity),a),identity),
inference(transitivity,[status(thm)],[70,34]) ).
tff(72,plain,
divide(identity,divide(divide(divide(identity,a),identity),identity)) = divide(identity,divide(divide(divide(identity,identity),a),identity)),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
divide(identity,divide(divide(divide(identity,identity),a),identity)) = divide(identity,divide(divide(divide(identity,a),identity),identity)),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
divide(divide(identity,identity),divide(divide(identity,a),divide(identity,identity))) = divide(identity,divide(divide(divide(identity,identity),a),identity)),
inference(monotonicity,[status(thm)],[31,37]) ).
tff(75,plain,
divide(divide(identity,identity),divide(divide(identity,a),divide(identity,identity))) = divide(identity,divide(divide(divide(identity,a),identity),identity)),
inference(transitivity,[status(thm)],[74,73]) ).
tff(76,plain,
divide(divide(divide(identity,identity),divide(divide(identity,a),divide(identity,identity))),identity) = divide(divide(identity,divide(divide(divide(identity,a),identity),identity)),identity),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
divide(divide(divide(identity,identity),divide(divide(identity,a),divide(identity,identity))),identity) = a,
inference(transitivity,[status(thm)],[76,50]) ).
tff(78,plain,
divide(identity,divide(divide(divide(identity,identity),divide(divide(identity,a),divide(identity,identity))),identity)) = divide(identity,a),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
divide(identity,a) = divide(identity,divide(divide(divide(identity,identity),divide(divide(identity,a),divide(identity,identity))),identity)),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
divide(divide(identity,a),divide(divide(identity,a),divide(identity,identity))) = divide(divide(identity,divide(divide(divide(identity,identity),divide(divide(identity,a),divide(identity,identity))),identity)),divide(divide(identity,a),divide(identity,identity))),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
divide(divide(identity,a),divide(divide(identity,a),divide(identity,identity))) = identity,
inference(transitivity,[status(thm)],[80,48]) ).
tff(82,plain,
divide(divide(divide(identity,a),divide(divide(identity,a),divide(identity,identity))),identity) = divide(identity,divide(divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))))),
inference(monotonicity,[status(thm)],[81,46]) ).
tff(83,plain,
divide(divide(divide(identity,a),divide(divide(identity,a),divide(identity,identity))),identity) = divide(divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),
inference(transitivity,[status(thm)],[82,44,31,39,45]) ).
tff(84,plain,
divide(identity,divide(divide(divide(identity,a),divide(divide(identity,a),divide(identity,identity))),identity)) = divide(identity,divide(divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))))),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
divide(identity,divide(divide(divide(identity,a),divide(divide(identity,a),divide(identity,identity))),identity)) = identity,
inference(transitivity,[status(thm)],[84,44,31]) ).
tff(86,plain,
divide(divide(identity,divide(divide(divide(identity,a),divide(divide(identity,a),divide(identity,identity))),identity)),divide(divide(identity,a),divide(identity,identity))) = divide(identity,divide(divide(divide(identity,identity),a),identity)),
inference(monotonicity,[status(thm)],[85,37]) ).
tff(87,plain,
divide(identity,divide(divide(divide(identity,identity),a),identity)) = divide(divide(identity,divide(divide(divide(identity,a),divide(divide(identity,a),divide(identity,identity))),identity)),divide(divide(identity,a),divide(identity,identity))),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(divide(divide(identity,a),divide(identity,identity)),divide(divide(identity,a),divide(identity,identity))),divide(identity,b)),divide(divide(identity,a),divide(identity,identity)))),divide(identity,b)) = divide(divide(identity,a),divide(identity,identity)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(89,plain,
divide(divide(identity,divide(divide(divide(divide(divide(identity,a),divide(identity,identity)),divide(divide(identity,a),divide(identity,identity))),divide(identity,b)),divide(divide(identity,a),divide(identity,identity)))),divide(identity,b)) = divide(divide(identity,a),divide(identity,identity)),
inference(unit_resolution,[status(thm)],[88,17]) ).
tff(90,plain,
divide(divide(identity,a),divide(identity,identity)) = divide(identity,a),
inference(transitivity,[status(thm)],[68,65]) ).
tff(91,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(identity,b),divide(identity,b)),identity)),divide(identity,b)) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(92,plain,
divide(divide(identity,divide(divide(divide(identity,b),divide(identity,b)),identity)),divide(identity,b)) = b,
inference(unit_resolution,[status(thm)],[91,17]) ).
tff(93,plain,
( ~ ! [A: $i] : ( identity = divide(A,A) )
| ( identity = divide(divide(identity,b),divide(identity,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
identity = divide(divide(identity,b),divide(identity,b)),
inference(unit_resolution,[status(thm)],[93,28]) ).
tff(95,plain,
divide(divide(identity,b),divide(identity,b)) = identity,
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
divide(divide(divide(identity,b),divide(identity,b)),identity) = divide(identity,divide(divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))))),
inference(monotonicity,[status(thm)],[95,46]) ).
tff(97,plain,
divide(divide(divide(identity,b),divide(identity,b)),identity) = divide(divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),
inference(transitivity,[status(thm)],[96,44,31,39,45]) ).
tff(98,plain,
divide(identity,divide(divide(divide(identity,b),divide(identity,b)),identity)) = divide(identity,divide(divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))))),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
divide(identity,divide(divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))))) = divide(identity,divide(divide(divide(identity,b),divide(identity,b)),identity)),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,b)) = identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,b)) = identity,
inference(unit_resolution,[status(thm)],[100,17]) ).
tff(102,plain,
divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,b)),identity) = divide(identity,divide(divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))))),
inference(monotonicity,[status(thm)],[101,46]) ).
tff(103,plain,
divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,b)),identity) = divide(divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),
inference(transitivity,[status(thm)],[102,44,31,39,45]) ).
tff(104,plain,
divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,b)),identity)) = divide(identity,divide(divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)))),divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))))),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,b)),identity)) = divide(identity,divide(divide(divide(identity,b),divide(identity,b)),identity)),
inference(transitivity,[status(thm)],[104,99]) ).
tff(106,plain,
divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,b)),identity)),divide(identity,b)) = divide(divide(identity,divide(divide(divide(identity,b),divide(identity,b)),identity)),divide(identity,b)),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B )
| ( divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,b)),identity)),divide(identity,b)) = divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,b)),identity)),divide(identity,b)) = divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)),
inference(unit_resolution,[status(thm)],[107,17]) ).
tff(109,plain,
divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)) = divide(divide(identity,divide(divide(divide(identity,divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a))),divide(identity,b)),identity)),divide(identity,b)),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
divide(divide(divide(identity,a),divide(identity,identity)),divide(identity,b)) = divide(divide(divide(identity,a),identity),divide(identity,b)),
inference(monotonicity,[status(thm)],[36]) ).
tff(111,plain,
divide(divide(divide(divide(identity,a),divide(identity,identity)),divide(identity,b)),divide(divide(identity,a),divide(identity,identity))) = divide(divide(divide(divide(identity,a),identity),divide(identity,b)),divide(identity,a)),
inference(monotonicity,[status(thm)],[110,90]) ).
tff(112,plain,
divide(divide(divide(divide(identity,a),divide(identity,identity)),divide(identity,b)),divide(divide(identity,a),divide(identity,identity))) = b,
inference(transitivity,[status(thm)],[111,109,106,92]) ).
tff(113,plain,
divide(divide(divide(divide(divide(identity,a),divide(identity,identity)),divide(identity,b)),divide(divide(identity,a),divide(identity,identity))),divide(divide(identity,a),divide(identity,identity))) = divide(b,divide(identity,a)),
inference(monotonicity,[status(thm)],[112,90]) ).
tff(114,plain,
divide(b,divide(identity,a)) = divide(divide(divide(divide(divide(identity,a),divide(identity,identity)),divide(identity,b)),divide(divide(identity,a),divide(identity,identity))),divide(divide(identity,a),divide(identity,identity))),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
divide(divide(identity,a),divide(identity,identity)) = divide(identity,divide(divide(divide(identity,identity),divide(divide(identity,a),divide(identity,identity))),identity)),
inference(transitivity,[status(thm)],[68,65,79]) ).
tff(116,plain,
divide(divide(divide(identity,a),divide(identity,identity)),divide(divide(identity,a),divide(identity,identity))) = divide(divide(identity,divide(divide(divide(identity,identity),divide(divide(identity,a),divide(identity,identity))),identity)),divide(divide(identity,a),divide(identity,identity))),
inference(monotonicity,[status(thm)],[115]) ).
tff(117,plain,
divide(divide(divide(identity,a),divide(identity,identity)),divide(divide(identity,a),divide(identity,identity))) = divide(identity,divide(divide(divide(identity,b),divide(identity,b)),identity)),
inference(transitivity,[status(thm)],[116,48,30,62,99]) ).
tff(118,plain,
divide(divide(divide(divide(identity,a),divide(identity,identity)),divide(divide(identity,a),divide(identity,identity))),divide(identity,b)) = divide(divide(identity,divide(divide(divide(identity,b),divide(identity,b)),identity)),divide(identity,b)),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
divide(divide(divide(divide(identity,a),divide(identity,identity)),divide(divide(identity,a),divide(identity,identity))),divide(identity,b)) = b,
inference(transitivity,[status(thm)],[118,92]) ).
tff(120,plain,
divide(divide(divide(divide(divide(identity,a),divide(identity,identity)),divide(divide(identity,a),divide(identity,identity))),divide(identity,b)),divide(divide(identity,a),divide(identity,identity))) = divide(b,divide(identity,a)),
inference(monotonicity,[status(thm)],[119,90]) ).
tff(121,plain,
divide(divide(divide(divide(divide(identity,a),divide(identity,identity)),divide(divide(identity,a),divide(identity,identity))),divide(identity,b)),divide(divide(identity,a),divide(identity,identity))) = divide(divide(divide(divide(divide(identity,a),divide(identity,identity)),divide(identity,b)),divide(divide(identity,a),divide(identity,identity))),divide(divide(identity,a),divide(identity,identity))),
inference(transitivity,[status(thm)],[120,114]) ).
tff(122,plain,
divide(identity,divide(divide(divide(divide(divide(identity,a),divide(identity,identity)),divide(divide(identity,a),divide(identity,identity))),divide(identity,b)),divide(divide(identity,a),divide(identity,identity)))) = divide(identity,divide(divide(divide(divide(divide(identity,a),divide(identity,identity)),divide(identity,b)),divide(divide(identity,a),divide(identity,identity))),divide(divide(identity,a),divide(identity,identity)))),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
divide(identity,divide(divide(divide(divide(divide(identity,a),divide(identity,identity)),divide(identity,b)),divide(divide(identity,a),divide(identity,identity))),divide(divide(identity,a),divide(identity,identity)))) = divide(identity,divide(divide(divide(divide(divide(identity,a),divide(identity,identity)),divide(divide(identity,a),divide(identity,identity))),divide(identity,b)),divide(divide(identity,a),divide(identity,identity)))),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
divide(identity,divide(divide(divide(divide(divide(identity,a),divide(identity,identity)),divide(identity,b)),divide(divide(identity,a),divide(identity,identity))),divide(divide(identity,a),divide(identity,identity)))) = divide(identity,divide(b,divide(identity,a))),
inference(monotonicity,[status(thm)],[113]) ).
tff(125,plain,
divide(identity,divide(b,divide(identity,a))) = divide(identity,divide(divide(divide(divide(divide(identity,a),divide(identity,identity)),divide(identity,b)),divide(divide(identity,a),divide(identity,identity))),divide(divide(identity,a),divide(identity,identity)))),
inference(symmetry,[status(thm)],[124]) ).
tff(126,plain,
divide(identity,divide(b,divide(identity,a))) = divide(identity,divide(divide(divide(divide(divide(identity,a),divide(identity,identity)),divide(divide(identity,a),divide(identity,identity))),divide(identity,b)),divide(divide(identity,a),divide(identity,identity)))),
inference(transitivity,[status(thm)],[125,123]) ).
tff(127,plain,
divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)) = divide(divide(identity,divide(divide(divide(divide(divide(identity,a),divide(identity,identity)),divide(divide(identity,a),divide(identity,identity))),divide(identity,b)),divide(divide(identity,a),divide(identity,identity)))),divide(identity,b)),
inference(monotonicity,[status(thm)],[126]) ).
tff(128,plain,
divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)) = divide(identity,a),
inference(transitivity,[status(thm)],[127,89,68,65]) ).
tff(129,plain,
divide(divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)),identity) = divide(divide(identity,a),identity),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,plain,
divide(divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)),identity) = divide(divide(divide(identity,identity),a),identity),
inference(transitivity,[status(thm)],[129,34]) ).
tff(131,plain,
divide(identity,divide(divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)),identity)) = divide(identity,divide(divide(divide(identity,identity),a),identity)),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
divide(identity,divide(divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)),identity)) = a,
inference(transitivity,[status(thm)],[131,87,21]) ).
tff(133,plain,
divide(divide(identity,divide(divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)),identity)),divide(identity,b)) = divide(a,divide(identity,b)),
inference(monotonicity,[status(thm)],[132]) ).
tff(134,plain,
divide(a,divide(identity,b)) = divide(divide(identity,divide(divide(divide(identity,divide(b,divide(identity,a))),divide(identity,b)),identity)),divide(identity,b)),
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
( ~ ! [B: $i,A: $i] : ( multiply(A,B) = divide(A,divide(identity,B)) )
| ( multiply(a,b) = divide(a,divide(identity,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(136,plain,
multiply(a,b) = divide(a,divide(identity,b)),
inference(unit_resolution,[status(thm)],[135,7]) ).
tff(137,plain,
multiply(a,b) = multiply(b,a),
inference(transitivity,[status(thm)],[136,134,19,10]) ).
tff(138,plain,
( ( multiply(a,b) != multiply(b,a) )
<=> ( multiply(a,b) != multiply(b,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(139,axiom,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_4) ).
tff(140,plain,
multiply(a,b) != multiply(b,a),
inference(modus_ponens,[status(thm)],[139,138]) ).
tff(141,plain,
$false,
inference(unit_resolution,[status(thm)],[140,137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : GRP544-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.02/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n026.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Wed Aug 31 17:48:37 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.10/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.31 Usage: tptp [options] [-file:]file
% 0.10/0.31 -h, -? prints this message.
% 0.10/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.31 -m, -model generate model.
% 0.10/0.31 -p, -proof generate proof.
% 0.10/0.31 -c, -core generate unsat core of named formulas.
% 0.10/0.31 -st, -statistics display statistics.
% 0.10/0.31 -t:timeout set timeout (in second).
% 0.10/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.31 -<param>:<value> configuration parameter and value.
% 0.10/0.31 -o:<output-file> file to place output in.
% 0.16/0.42 % SZS status Unsatisfiable
% 0.16/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------