TSTP Solution File: HEN009-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN009-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 : 600s
% DateTime : Sat Jul 16 13:03:10 EDT 2022
% Result : Unsatisfiable 0.89s 1.10s
% Output : Refutation 0.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 12
% Syntax : Number of clauses : 93 ( 51 unt; 0 nHn; 93 RR)
% Number of literals : 172 ( 0 equ; 82 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 14 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
quotient(identity,a,idQa),
file('HEN009-1.p',unknown),
[] ).
cnf(2,axiom,
quotient(identity,idQa,idQ_idQa),
file('HEN009-1.p',unknown),
[] ).
cnf(3,axiom,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
file('HEN009-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(idQ__idQ_idQa,idQa),
file('HEN009-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ less_equal(u,v)
| quotient(u,v,zero) ),
file('HEN009-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ quotient(u,v,zero)
| less_equal(u,v) ),
file('HEN009-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ quotient(u,v,w)
| less_equal(w,u) ),
file('HEN009-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ quotient(u,v,w)
| ~ quotient(x,y,z)
| ~ quotient(x1,v,x)
| ~ quotient(x2,v,y)
| ~ quotient(x1,x2,u)
| less_equal(z,w) ),
file('HEN009-1.p',unknown),
[] ).
cnf(9,axiom,
less_equal(zero,u),
file('HEN009-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN009-1.p',unknown),
[] ).
cnf(11,axiom,
less_equal(u,identity),
file('HEN009-1.p',unknown),
[] ).
cnf(12,axiom,
quotient(u,v,divide(u,v)),
file('HEN009-1.p',unknown),
[] ).
cnf(14,plain,
( ~ less_equal(idQa,idQ__idQ_idQa)
| ~ less_equal(idQ__idQ_idQa,idQa) ),
inference(res,[status(thm),theory(equality)],[10,4]),
[iquote('0:Res:10.2,4.0')] ).
cnf(22,plain,
less_equal(divide(u,v),u),
inference(res,[status(thm),theory(equality)],[12,7]),
[iquote('0:Res:12.0,7.0')] ).
cnf(25,plain,
( ~ less_equal(u,zero)
| equal(u,zero) ),
inference(res,[status(thm),theory(equality)],[9,10]),
[iquote('0:Res:9.0,10.0')] ).
cnf(29,plain,
equal(divide(zero,u),zero),
inference(res,[status(thm),theory(equality)],[22,25]),
[iquote('0:Res:22.0,25.0')] ).
cnf(54,plain,
( ~ quotient(u,v,w)
| ~ quotient(x,y,u)
| ~ quotient(z,y,v)
| ~ quotient(x,z,x1)
| less_equal(w,divide(x1,y)) ),
inference(res,[status(thm),theory(equality)],[12,8]),
[iquote('0:Res:12.0,8.0')] ).
cnf(55,plain,
( ~ less_equal(u,v)
| ~ quotient(w,x,y)
| ~ quotient(z,v,w)
| ~ quotient(x1,v,x)
| ~ quotient(z,x1,u)
| less_equal(y,zero) ),
inference(res,[status(thm),theory(equality)],[5,8]),
[iquote('0:Res:5.1,8.0')] ).
cnf(154,plain,
( ~ quotient(u,v,w)
| ~ quotient(x,v,y)
| ~ quotient(u,x,z)
| less_equal(divide(w,y),divide(z,v)) ),
inference(res,[status(thm),theory(equality)],[12,54]),
[iquote('0:Res:12.0,54.0')] ).
cnf(160,plain,
( ~ less_equal(u,v)
| ~ quotient(w,v,x)
| ~ quotient(y,v,z)
| ~ quotient(w,y,u)
| less_equal(divide(x,z),zero) ),
inference(res,[status(thm),theory(equality)],[12,55]),
[iquote('0:Res:12.0,55.1')] ).
cnf(280,plain,
( ~ quotient(u,idQa,v)
| ~ quotient(identity,u,w)
| less_equal(divide(idQ_idQa,v),divide(w,idQa)) ),
inference(res,[status(thm),theory(equality)],[2,154]),
[iquote('0:Res:2.0,154.0')] ).
cnf(281,plain,
( ~ quotient(u,a,v)
| ~ quotient(identity,u,w)
| less_equal(divide(idQa,v),divide(w,a)) ),
inference(res,[status(thm),theory(equality)],[1,154]),
[iquote('0:Res:1.0,154.0')] ).
cnf(309,plain,
( ~ less_equal(u,idQ_idQa)
| ~ quotient(v,idQ_idQa,w)
| ~ quotient(identity,v,u)
| less_equal(divide(idQ__idQ_idQa,w),zero) ),
inference(res,[status(thm),theory(equality)],[3,160]),
[iquote('0:Res:3.0,160.1')] ).
cnf(310,plain,
( ~ less_equal(u,idQa)
| ~ quotient(v,idQa,w)
| ~ quotient(identity,v,u)
| less_equal(divide(idQ_idQa,w),zero) ),
inference(res,[status(thm),theory(equality)],[2,160]),
[iquote('0:Res:2.0,160.1')] ).
cnf(312,plain,
( ~ less_equal(u,v)
| ~ quotient(w,v,x)
| ~ quotient(y,w,u)
| less_equal(divide(divide(y,v),x),zero) ),
inference(res,[status(thm),theory(equality)],[12,160]),
[iquote('0:Res:12.0,160.1')] ).
cnf(339,plain,
( ~ quotient(identity,identity,u)
| less_equal(divide(idQ_idQa,idQ_idQa),divide(u,idQa)) ),
inference(res,[status(thm),theory(equality)],[2,280]),
[iquote('0:Res:2.0,280.0')] ).
cnf(361,plain,
( ~ quotient(identity,identity,u)
| less_equal(divide(idQa,idQa),divide(u,a)) ),
inference(res,[status(thm),theory(equality)],[1,281]),
[iquote('0:Res:1.0,281.0')] ).
cnf(363,plain,
( ~ less_equal(u,a)
| ~ quotient(identity,u,v)
| less_equal(divide(idQa,zero),divide(v,a)) ),
inference(res,[status(thm),theory(equality)],[5,281]),
[iquote('0:Res:5.1,281.0')] ).
cnf(406,plain,
( ~ less_equal(u,idQ_idQa)
| ~ quotient(identity,v,u)
| less_equal(divide(idQ__idQ_idQa,divide(v,idQ_idQa)),zero) ),
inference(res,[status(thm),theory(equality)],[12,309]),
[iquote('0:Res:12.0,309.1')] ).
cnf(411,plain,
( ~ quotient(identity,identity,zero)
| less_equal(divide(idQ_idQa,idQ_idQa),zero) ),
inference(spr,[status(thm),theory(equality)],[29,339]),
[iquote('0:SpR:29.0,339.1')] ).
cnf(418,plain,
( ~ quotient(identity,identity,zero)
| equal(divide(idQ_idQa,idQ_idQa),zero) ),
inference(res,[status(thm),theory(equality)],[411,25]),
[iquote('0:Res:411.1,25.0')] ).
cnf(420,plain,
( ~ less_equal(identity,identity)
| equal(divide(idQ_idQa,idQ_idQa),zero) ),
inference(res,[status(thm),theory(equality)],[5,418]),
[iquote('0:Res:5.1,418.0')] ).
cnf(421,plain,
equal(divide(idQ_idQa,idQ_idQa),zero),
inference(mrr,[status(thm)],[420,11]),
[iquote('0:MRR:420.0,11.0')] ).
cnf(429,plain,
( ~ less_equal(u,idQa)
| ~ quotient(identity,v,u)
| less_equal(divide(idQ_idQa,divide(v,idQa)),zero) ),
inference(res,[status(thm),theory(equality)],[12,310]),
[iquote('0:Res:12.0,310.1')] ).
cnf(433,plain,
quotient(idQ_idQa,idQ_idQa,zero),
inference(spr,[status(thm),theory(equality)],[421,12]),
[iquote('0:SpR:421.0,12.0')] ).
cnf(451,plain,
less_equal(idQ_idQa,idQ_idQa),
inference(res,[status(thm),theory(equality)],[433,6]),
[iquote('0:Res:433.0,6.0')] ).
cnf(526,plain,
( ~ less_equal(u,idQ_idQa)
| ~ quotient(v,identity,u)
| less_equal(divide(divide(v,idQ_idQa),idQ__idQ_idQa),zero) ),
inference(res,[status(thm),theory(equality)],[3,312]),
[iquote('0:Res:3.0,312.1')] ).
cnf(527,plain,
( ~ less_equal(u,idQa)
| ~ quotient(v,identity,u)
| less_equal(divide(divide(v,idQa),idQ_idQa),zero) ),
inference(res,[status(thm),theory(equality)],[2,312]),
[iquote('0:Res:2.0,312.1')] ).
cnf(528,plain,
( ~ less_equal(u,a)
| ~ quotient(v,identity,u)
| less_equal(divide(divide(v,a),idQa),zero) ),
inference(res,[status(thm),theory(equality)],[1,312]),
[iquote('0:Res:1.0,312.1')] ).
cnf(530,plain,
( ~ less_equal(u,v)
| ~ less_equal(w,v)
| ~ quotient(x,u,w)
| less_equal(divide(divide(x,v),zero),zero) ),
inference(res,[status(thm),theory(equality)],[5,312]),
[iquote('0:Res:5.1,312.1')] ).
cnf(539,plain,
( ~ quotient(identity,identity,zero)
| less_equal(divide(idQa,idQa),zero) ),
inference(spr,[status(thm),theory(equality)],[29,361]),
[iquote('0:SpR:29.0,361.1')] ).
cnf(546,plain,
( ~ quotient(identity,identity,zero)
| equal(divide(idQa,idQa),zero) ),
inference(res,[status(thm),theory(equality)],[539,25]),
[iquote('0:Res:539.1,25.0')] ).
cnf(554,plain,
( ~ less_equal(identity,identity)
| equal(divide(idQa,idQa),zero) ),
inference(res,[status(thm),theory(equality)],[5,546]),
[iquote('0:Res:5.1,546.0')] ).
cnf(555,plain,
equal(divide(idQa,idQa),zero),
inference(mrr,[status(thm)],[554,11]),
[iquote('0:MRR:554.0,11.0')] ).
cnf(562,plain,
quotient(idQa,idQa,zero),
inference(spr,[status(thm),theory(equality)],[555,12]),
[iquote('0:SpR:555.0,12.0')] ).
cnf(580,plain,
less_equal(idQa,idQa),
inference(res,[status(thm),theory(equality)],[562,6]),
[iquote('0:Res:562.0,6.0')] ).
cnf(975,plain,
( ~ less_equal(idQ_idQa,a)
| less_equal(divide(idQa,zero),divide(idQ__idQ_idQa,a)) ),
inference(res,[status(thm),theory(equality)],[3,363]),
[iquote('0:Res:3.0,363.1')] ).
cnf(1045,plain,
( ~ less_equal(idQ_idQa,idQ_idQa)
| less_equal(divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)),zero) ),
inference(res,[status(thm),theory(equality)],[2,406]),
[iquote('0:Res:2.0,406.1')] ).
cnf(1051,plain,
less_equal(divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)),zero),
inference(mrr,[status(thm)],[1045,451]),
[iquote('0:MRR:1045.0,451.0')] ).
cnf(1058,plain,
equal(divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)),zero),
inference(res,[status(thm),theory(equality)],[1051,25]),
[iquote('0:Res:1051.0,25.0')] ).
cnf(1061,plain,
quotient(idQ__idQ_idQa,divide(idQa,idQ_idQa),zero),
inference(spr,[status(thm),theory(equality)],[1058,12]),
[iquote('0:SpR:1058.0,12.0')] ).
cnf(1074,plain,
less_equal(idQ__idQ_idQa,divide(idQa,idQ_idQa)),
inference(res,[status(thm),theory(equality)],[1061,6]),
[iquote('0:Res:1061.0,6.0')] ).
cnf(1093,plain,
( ~ less_equal(idQa,idQa)
| less_equal(divide(idQ_idQa,divide(a,idQa)),zero) ),
inference(res,[status(thm),theory(equality)],[1,429]),
[iquote('0:Res:1.0,429.1')] ).
cnf(1097,plain,
less_equal(divide(idQ_idQa,divide(a,idQa)),zero),
inference(mrr,[status(thm)],[1093,580]),
[iquote('0:MRR:1093.0,580.0')] ).
cnf(1100,plain,
( ~ less_equal(divide(idQa,idQ_idQa),idQ__idQ_idQa)
| equal(divide(idQa,idQ_idQa),idQ__idQ_idQa) ),
inference(res,[status(thm),theory(equality)],[1074,10]),
[iquote('0:Res:1074.0,10.0')] ).
cnf(1105,plain,
equal(divide(idQ_idQa,divide(a,idQa)),zero),
inference(res,[status(thm),theory(equality)],[1097,25]),
[iquote('0:Res:1097.0,25.0')] ).
cnf(1107,plain,
quotient(idQ_idQa,divide(a,idQa),zero),
inference(spr,[status(thm),theory(equality)],[1105,12]),
[iquote('0:SpR:1105.0,12.0')] ).
cnf(1120,plain,
less_equal(idQ_idQa,divide(a,idQa)),
inference(res,[status(thm),theory(equality)],[1107,6]),
[iquote('0:Res:1107.0,6.0')] ).
cnf(1143,plain,
( ~ less_equal(divide(a,idQa),idQ_idQa)
| equal(divide(a,idQa),idQ_idQa) ),
inference(res,[status(thm),theory(equality)],[1120,10]),
[iquote('0:Res:1120.0,10.0')] ).
cnf(1172,plain,
( ~ less_equal(u,identity)
| ~ less_equal(zero,idQ_idQa)
| less_equal(divide(divide(u,idQ_idQa),idQ__idQ_idQa),zero) ),
inference(res,[status(thm),theory(equality)],[5,526]),
[iquote('0:Res:5.1,526.1')] ).
cnf(1175,plain,
less_equal(divide(divide(u,idQ_idQa),idQ__idQ_idQa),zero),
inference(mrr,[status(thm)],[1172,11,9]),
[iquote('0:MRR:1172.0,1172.1,11.0,9.0')] ).
cnf(1182,plain,
equal(divide(divide(u,idQ_idQa),idQ__idQ_idQa),zero),
inference(res,[status(thm),theory(equality)],[1175,25]),
[iquote('0:Res:1175.0,25.0')] ).
cnf(1193,plain,
quotient(divide(u,idQ_idQa),idQ__idQ_idQa,zero),
inference(spr,[status(thm),theory(equality)],[1182,12]),
[iquote('0:SpR:1182.0,12.0')] ).
cnf(1210,plain,
less_equal(divide(u,idQ_idQa),idQ__idQ_idQa),
inference(res,[status(thm),theory(equality)],[1193,6]),
[iquote('0:Res:1193.0,6.0')] ).
cnf(1225,plain,
equal(divide(idQa,idQ_idQa),idQ__idQ_idQa),
inference(mrr,[status(thm)],[1100,1210]),
[iquote('0:MRR:1100.0,1210.0')] ).
cnf(1239,plain,
less_equal(idQ__idQ_idQa,idQa),
inference(spr,[status(thm),theory(equality)],[1225,22]),
[iquote('0:SpR:1225.0,22.0')] ).
cnf(1256,plain,
~ less_equal(idQa,idQ__idQ_idQa),
inference(mrr,[status(thm)],[14,1239]),
[iquote('0:MRR:14.1,1239.0')] ).
cnf(1345,plain,
( ~ less_equal(u,identity)
| ~ less_equal(zero,idQa)
| less_equal(divide(divide(u,idQa),idQ_idQa),zero) ),
inference(res,[status(thm),theory(equality)],[5,527]),
[iquote('0:Res:5.1,527.1')] ).
cnf(1348,plain,
less_equal(divide(divide(u,idQa),idQ_idQa),zero),
inference(mrr,[status(thm)],[1345,11,9]),
[iquote('0:MRR:1345.0,1345.1,11.0,9.0')] ).
cnf(1404,plain,
equal(divide(divide(u,idQa),idQ_idQa),zero),
inference(res,[status(thm),theory(equality)],[1348,25]),
[iquote('0:Res:1348.0,25.0')] ).
cnf(1420,plain,
( ~ less_equal(u,identity)
| ~ less_equal(zero,a)
| less_equal(divide(divide(u,a),idQa),zero) ),
inference(res,[status(thm),theory(equality)],[5,528]),
[iquote('0:Res:5.1,528.1')] ).
cnf(1423,plain,
less_equal(divide(divide(u,a),idQa),zero),
inference(mrr,[status(thm)],[1420,11,9]),
[iquote('0:MRR:1420.0,1420.1,11.0,9.0')] ).
cnf(1424,plain,
quotient(divide(u,idQa),idQ_idQa,zero),
inference(spr,[status(thm),theory(equality)],[1404,12]),
[iquote('0:SpR:1404.0,12.0')] ).
cnf(1459,plain,
less_equal(divide(u,idQa),idQ_idQa),
inference(res,[status(thm),theory(equality)],[1424,6]),
[iquote('0:Res:1424.0,6.0')] ).
cnf(1478,plain,
equal(divide(a,idQa),idQ_idQa),
inference(mrr,[status(thm)],[1143,1459]),
[iquote('0:MRR:1143.0,1459.0')] ).
cnf(1492,plain,
less_equal(idQ_idQa,a),
inference(spr,[status(thm),theory(equality)],[1478,22]),
[iquote('0:SpR:1478.0,22.0')] ).
cnf(1509,plain,
less_equal(divide(idQa,zero),divide(idQ__idQ_idQa,a)),
inference(mrr,[status(thm)],[975,1492]),
[iquote('0:MRR:975.0,1492.0')] ).
cnf(1734,plain,
equal(divide(divide(u,a),idQa),zero),
inference(res,[status(thm),theory(equality)],[1423,25]),
[iquote('0:Res:1423.0,25.0')] ).
cnf(1757,plain,
quotient(divide(u,a),idQa,zero),
inference(spr,[status(thm),theory(equality)],[1734,12]),
[iquote('0:SpR:1734.0,12.0')] ).
cnf(1794,plain,
less_equal(divide(u,a),idQa),
inference(res,[status(thm),theory(equality)],[1757,6]),
[iquote('0:Res:1757.0,6.0')] ).
cnf(1819,plain,
( ~ less_equal(idQa,divide(u,a))
| equal(divide(u,a),idQa) ),
inference(res,[status(thm),theory(equality)],[1794,10]),
[iquote('0:Res:1794.0,10.0')] ).
cnf(2026,plain,
( ~ less_equal(u,v)
| ~ less_equal(divide(w,u),v)
| less_equal(divide(divide(w,v),zero),zero) ),
inference(res,[status(thm),theory(equality)],[12,530]),
[iquote('0:Res:12.0,530.2')] ).
cnf(5544,plain,
( ~ less_equal(zero,divide(idQ__idQ_idQa,a))
| less_equal(divide(divide(idQa,divide(idQ__idQ_idQa,a)),zero),zero) ),
inference(res,[status(thm),theory(equality)],[1509,2026]),
[iquote('0:Res:1509.0,2026.1')] ).
cnf(5577,plain,
less_equal(divide(divide(idQa,divide(idQ__idQ_idQa,a)),zero),zero),
inference(mrr,[status(thm)],[5544,9]),
[iquote('0:MRR:5544.0,9.0')] ).
cnf(5806,plain,
equal(divide(divide(idQa,divide(idQ__idQ_idQa,a)),zero),zero),
inference(res,[status(thm),theory(equality)],[5577,25]),
[iquote('0:Res:5577.0,25.0')] ).
cnf(6096,plain,
quotient(divide(idQa,divide(idQ__idQ_idQa,a)),zero,zero),
inference(spr,[status(thm),theory(equality)],[5806,12]),
[iquote('0:SpR:5806.0,12.0')] ).
cnf(6142,plain,
less_equal(divide(idQa,divide(idQ__idQ_idQa,a)),zero),
inference(res,[status(thm),theory(equality)],[6096,6]),
[iquote('0:Res:6096.0,6.0')] ).
cnf(6172,plain,
equal(divide(idQa,divide(idQ__idQ_idQa,a)),zero),
inference(res,[status(thm),theory(equality)],[6142,25]),
[iquote('0:Res:6142.0,25.0')] ).
cnf(6190,plain,
quotient(idQa,divide(idQ__idQ_idQa,a),zero),
inference(spr,[status(thm),theory(equality)],[6172,12]),
[iquote('0:SpR:6172.0,12.0')] ).
cnf(6221,plain,
less_equal(idQa,divide(idQ__idQ_idQa,a)),
inference(res,[status(thm),theory(equality)],[6190,6]),
[iquote('0:Res:6190.0,6.0')] ).
cnf(6286,plain,
equal(divide(idQ__idQ_idQa,a),idQa),
inference(res,[status(thm),theory(equality)],[6221,1819]),
[iquote('0:Res:6221.0,1819.0')] ).
cnf(6314,plain,
less_equal(idQa,idQ__idQ_idQa),
inference(spr,[status(thm),theory(equality)],[6286,22]),
[iquote('0:SpR:6286.0,22.0')] ).
cnf(6349,plain,
$false,
inference(mrr,[status(thm)],[6314,1256]),
[iquote('0:MRR:6314.0,1256.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN009-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 1 14:07:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.89/1.10
% 0.89/1.10 SPASS V 3.9
% 0.89/1.10 SPASS beiseite: Proof found.
% 0.89/1.10 % SZS status Theorem
% 0.89/1.10 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.89/1.10 SPASS derived 4854 clauses, backtracked 0 clauses, performed 0 splits and kept 1411 clauses.
% 0.89/1.10 SPASS allocated 67161 KBytes.
% 0.89/1.10 SPASS spent 0:00:00.75 on the problem.
% 0.89/1.10 0:00:00.04 for the input.
% 0.89/1.10 0:00:00.00 for the FLOTTER CNF translation.
% 0.89/1.10 0:00:00.07 for inferences.
% 0.89/1.10 0:00:00.00 for the backtracking.
% 0.89/1.10 0:00:00.61 for the reduction.
% 0.89/1.10
% 0.89/1.10
% 0.89/1.10 Here is a proof with depth 14, length 93 :
% 0.89/1.10 % SZS output start Refutation
% See solution above
% 0.89/1.12 Formulae used in the proof : identity_divide_a identity_divide_idQa identity_divide_idQ_idQa prove_one_inversion_equals_three quotient_less_equal less_equal_quotient divisor_existence quotient_property zero_is_smallest less_equal_and_equal identity_is_largest closure
% 0.89/1.12
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