%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN010-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 13:03:12 EDT 2022
% Result : Unsatisfiable 0.98s 1.16s
% Output : Refutation 0.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 12
% Syntax : Number of clauses : 87 ( 42 unt; 0 nHn; 87 RR)
% Number of literals : 167 ( 0 equ; 81 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('HEN010-1.p',unknown),
[] ).
cnf(2,axiom,
quotient(identity,idQa,idQ_idQa),
file('HEN010-1.p',unknown),
[] ).
cnf(3,axiom,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
file('HEN010-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(idQa_Q__idQ_idQa,idQa),
file('HEN010-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ less_equal(u,v)
| quotient(u,v,zero) ),
file('HEN010-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ quotient(u,v,zero)
| less_equal(u,v) ),
file('HEN010-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ quotient(u,v,w)
| less_equal(w,u) ),
file('HEN010-1.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('HEN010-1.p',unknown),
[] ).
cnf(9,axiom,
less_equal(zero,u),
file('HEN010-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN010-1.p',unknown),
[] ).
cnf(11,axiom,
less_equal(u,identity),
file('HEN010-1.p',unknown),
[] ).
cnf(12,axiom,
quotient(u,v,divide(u,v)),
file('HEN010-1.p',unknown),
[] ).
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(26,plain,
( ~ less_equal(u,divide(u,v))
| equal(divide(u,v),u) ),
inference(res,[status(thm),theory(equality)],[22,10]),
[iquote('0:Res:22.0,10.0')] ).
cnf(30,plain,
equal(divide(zero,u),zero),
inference(res,[status(thm),theory(equality)],[22,25]),
[iquote('0:Res:22.0,25.0')] ).
cnf(55,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(56,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(128,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)],[12,55]),
[iquote('0:Res:12.0,55.0')] ).
cnf(162,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)],[12,56]),
[iquote('0:Res:12.0,56.1')] ).
cnf(292,plain,
( ~ quotient(u,idQ_idQa,v)
| ~ quotient(idQa,u,w)
| less_equal(divide(idQa_Q__idQ_idQa,v),divide(w,idQ_idQa)) ),
inference(res,[status(thm),theory(equality)],[3,128]),
[iquote('0:Res:3.0,128.0')] ).
cnf(294,plain,
( ~ quotient(u,a,v)
| ~ quotient(identity,u,w)
| less_equal(divide(idQa,v),divide(w,a)) ),
inference(res,[status(thm),theory(equality)],[1,128]),
[iquote('0:Res:1.0,128.0')] ).
cnf(301,plain,
( ~ quotient(idQa,u,v)
| less_equal(divide(idQa_Q__idQ_idQa,divide(u,idQ_idQa)),divide(v,idQ_idQa)) ),
inference(res,[status(thm),theory(equality)],[12,292]),
[iquote('0:Res:12.0,292.0')] ).
cnf(316,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)],[2,162]),
[iquote('0:Res:2.0,162.1')] ).
cnf(318,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)],[12,162]),
[iquote('0:Res:12.0,162.1')] ).
cnf(379,plain,
( ~ quotient(identity,identity,u)
| less_equal(divide(idQa,idQa),divide(u,a)) ),
inference(res,[status(thm),theory(equality)],[1,294]),
[iquote('0:Res:1.0,294.0')] ).
cnf(381,plain,
( ~ less_equal(u,a)
| ~ quotient(identity,u,v)
| less_equal(divide(idQa,zero),divide(v,a)) ),
inference(res,[status(thm),theory(equality)],[5,294]),
[iquote('0:Res:5.1,294.0')] ).
cnf(430,plain,
( ~ less_equal(u,idQa)
| ~ quotient(identity,v,u)
| less_equal(divide(idQ_idQa,divide(v,idQa)),zero) ),
inference(res,[status(thm),theory(equality)],[12,316]),
[iquote('0:Res:12.0,316.1')] ).
cnf(521,plain,
( ~ less_equal(u,idQ_idQa)
| ~ quotient(v,idQa,u)
| less_equal(divide(divide(v,idQ_idQa),idQa_Q__idQ_idQa),zero) ),
inference(res,[status(thm),theory(equality)],[3,318]),
[iquote('0:Res:3.0,318.1')] ).
cnf(522,plain,
( ~ less_equal(u,idQa)
| ~ quotient(v,identity,u)
| less_equal(divide(divide(v,idQa),idQ_idQa),zero) ),
inference(res,[status(thm),theory(equality)],[2,318]),
[iquote('0:Res:2.0,318.1')] ).
cnf(523,plain,
( ~ less_equal(u,a)
| ~ quotient(v,identity,u)
| less_equal(divide(divide(v,a),idQa),zero) ),
inference(res,[status(thm),theory(equality)],[1,318]),
[iquote('0:Res:1.0,318.1')] ).
cnf(525,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)],[5,318]),
[iquote('0:Res:5.1,318.1')] ).
cnf(568,plain,
( ~ quotient(identity,identity,zero)
| less_equal(divide(idQa,idQa),zero) ),
inference(spr,[status(thm),theory(equality)],[30,379]),
[iquote('0:SpR:30.0,379.1')] ).
cnf(599,plain,
( ~ quotient(identity,identity,zero)
| equal(divide(idQa,idQa),zero) ),
inference(res,[status(thm),theory(equality)],[568,25]),
[iquote('0:Res:568.1,25.0')] ).
cnf(601,plain,
( ~ less_equal(identity,identity)
| equal(divide(idQa,idQa),zero) ),
inference(res,[status(thm),theory(equality)],[5,599]),
[iquote('0:Res:5.1,599.0')] ).
cnf(602,plain,
equal(divide(idQa,idQa),zero),
inference(mrr,[status(thm)],[601,11]),
[iquote('0:MRR:601.0,11.0')] ).
cnf(615,plain,
quotient(idQa,idQa,zero),
inference(spr,[status(thm),theory(equality)],[602,12]),
[iquote('0:SpR:602.0,12.0')] ).
cnf(643,plain,
less_equal(idQa,idQa),
inference(res,[status(thm),theory(equality)],[615,6]),
[iquote('0:Res:615.0,6.0')] ).
cnf(732,plain,
( ~ quotient(idQa,u,zero)
| less_equal(divide(idQa_Q__idQ_idQa,divide(u,idQ_idQa)),zero) ),
inference(spr,[status(thm),theory(equality)],[30,301]),
[iquote('0:SpR:30.0,301.1')] ).
cnf(847,plain,
( ~ quotient(idQa,u,zero)
| equal(divide(idQa_Q__idQ_idQa,divide(u,idQ_idQa)),zero) ),
inference(res,[status(thm),theory(equality)],[732,25]),
[iquote('0:Res:732.1,25.0')] ).
cnf(939,plain,
( ~ quotient(idQa,u,zero)
| quotient(idQa_Q__idQ_idQa,divide(u,idQ_idQa),zero) ),
inference(spr,[status(thm),theory(equality)],[847,12]),
[iquote('0:SpR:847.1,12.0')] ).
cnf(955,plain,
( ~ quotient(idQa,u,zero)
| less_equal(idQa_Q__idQ_idQa,divide(u,idQ_idQa)) ),
inference(res,[status(thm),theory(equality)],[939,6]),
[iquote('0:Res:939.1,6.0')] ).
cnf(1208,plain,
( ~ less_equal(idQa,idQa)
| less_equal(divide(idQ_idQa,divide(a,idQa)),zero) ),
inference(res,[status(thm),theory(equality)],[1,430]),
[iquote('0:Res:1.0,430.1')] ).
cnf(1213,plain,
less_equal(divide(idQ_idQa,divide(a,idQa)),zero),
inference(mrr,[status(thm)],[1208,643]),
[iquote('0:MRR:1208.0,643.0')] ).
cnf(1218,plain,
equal(divide(idQ_idQa,divide(a,idQa)),zero),
inference(res,[status(thm),theory(equality)],[1213,25]),
[iquote('0:Res:1213.0,25.0')] ).
cnf(1221,plain,
quotient(idQ_idQa,divide(a,idQa),zero),
inference(spr,[status(thm),theory(equality)],[1218,12]),
[iquote('0:SpR:1218.0,12.0')] ).
cnf(1234,plain,
less_equal(idQ_idQa,divide(a,idQa)),
inference(res,[status(thm),theory(equality)],[1221,6]),
[iquote('0:Res:1221.0,6.0')] ).
cnf(1252,plain,
( ~ less_equal(divide(a,idQa),idQ_idQa)
| equal(divide(a,idQa),idQ_idQa) ),
inference(res,[status(thm),theory(equality)],[1234,10]),
[iquote('0:Res:1234.0,10.0')] ).
cnf(1303,plain,
( ~ less_equal(divide(u,idQa),idQ_idQa)
| less_equal(divide(divide(u,idQ_idQa),idQa_Q__idQ_idQa),zero) ),
inference(res,[status(thm),theory(equality)],[12,521]),
[iquote('0:Res:12.0,521.1')] ).
cnf(1350,plain,
( ~ less_equal(u,identity)
| ~ less_equal(zero,idQa)
| less_equal(divide(divide(u,idQa),idQ_idQa),zero) ),
inference(res,[status(thm),theory(equality)],[5,522]),
[iquote('0:Res:5.1,522.1')] ).
cnf(1353,plain,
less_equal(divide(divide(u,idQa),idQ_idQa),zero),
inference(mrr,[status(thm)],[1350,11,9]),
[iquote('0:MRR:1350.0,1350.1,11.0,9.0')] ).
cnf(1360,plain,
equal(divide(divide(u,idQa),idQ_idQa),zero),
inference(res,[status(thm),theory(equality)],[1353,25]),
[iquote('0:Res:1353.0,25.0')] ).
cnf(1371,plain,
quotient(divide(u,idQa),idQ_idQa,zero),
inference(spr,[status(thm),theory(equality)],[1360,12]),
[iquote('0:SpR:1360.0,12.0')] ).
cnf(1414,plain,
less_equal(divide(u,idQa),idQ_idQa),
inference(res,[status(thm),theory(equality)],[1371,6]),
[iquote('0:Res:1371.0,6.0')] ).
cnf(1429,plain,
equal(divide(a,idQa),idQ_idQa),
inference(mrr,[status(thm)],[1252,1414]),
[iquote('0:MRR:1252.0,1414.0')] ).
cnf(1430,plain,
less_equal(divide(divide(u,idQ_idQa),idQa_Q__idQ_idQa),zero),
inference(mrr,[status(thm)],[1303,1414]),
[iquote('0:MRR:1303.0,1414.0')] ).
cnf(1444,plain,
less_equal(idQ_idQa,a),
inference(spr,[status(thm),theory(equality)],[1429,22]),
[iquote('0:SpR:1429.0,22.0')] ).
cnf(1473,plain,
( ~ less_equal(u,identity)
| ~ less_equal(zero,a)
| less_equal(divide(divide(u,a),idQa),zero) ),
inference(res,[status(thm),theory(equality)],[5,523]),
[iquote('0:Res:5.1,523.1')] ).
cnf(1476,plain,
less_equal(divide(divide(u,a),idQa),zero),
inference(mrr,[status(thm)],[1473,11,9]),
[iquote('0:MRR:1473.0,1473.1,11.0,9.0')] ).
cnf(1685,plain,
equal(divide(divide(u,idQ_idQa),idQa_Q__idQ_idQa),zero),
inference(res,[status(thm),theory(equality)],[1430,25]),
[iquote('0:Res:1430.0,25.0')] ).
cnf(1710,plain,
equal(divide(divide(u,a),idQa),zero),
inference(res,[status(thm),theory(equality)],[1476,25]),
[iquote('0:Res:1476.0,25.0')] ).
cnf(1724,plain,
quotient(divide(u,idQ_idQa),idQa_Q__idQ_idQa,zero),
inference(spr,[status(thm),theory(equality)],[1685,12]),
[iquote('0:SpR:1685.0,12.0')] ).
cnf(1747,plain,
less_equal(divide(u,idQ_idQa),idQa_Q__idQ_idQa),
inference(res,[status(thm),theory(equality)],[1724,6]),
[iquote('0:Res:1724.0,6.0')] ).
cnf(1775,plain,
quotient(divide(u,a),idQa,zero),
inference(spr,[status(thm),theory(equality)],[1710,12]),
[iquote('0:SpR:1710.0,12.0')] ).
cnf(1812,plain,
less_equal(divide(u,a),idQa),
inference(res,[status(thm),theory(equality)],[1775,6]),
[iquote('0:Res:1775.0,6.0')] ).
cnf(1837,plain,
( ~ less_equal(idQa,divide(u,a))
| equal(divide(u,a),idQa) ),
inference(res,[status(thm),theory(equality)],[1812,10]),
[iquote('0:Res:1812.0,10.0')] ).
cnf(1880,plain,
( ~ quotient(idQa,u,zero)
| ~ less_equal(divide(u,idQ_idQa),idQa_Q__idQ_idQa)
| equal(divide(u,idQ_idQa),idQa_Q__idQ_idQa) ),
inference(res,[status(thm),theory(equality)],[955,10]),
[iquote('0:Res:955.1,10.0')] ).
cnf(1882,plain,
( ~ quotient(idQa,u,zero)
| equal(divide(u,idQ_idQa),idQa_Q__idQ_idQa) ),
inference(mrr,[status(thm)],[1880,1747]),
[iquote('0:MRR:1880.1,1747.0')] ).
cnf(1938,plain,
( ~ less_equal(idQa,u)
| equal(divide(u,idQ_idQa),idQa_Q__idQ_idQa) ),
inference(res,[status(thm),theory(equality)],[5,1882]),
[iquote('0:Res:5.1,1882.0')] ).
cnf(1942,plain,
( ~ less_equal(idQa,u)
| quotient(u,idQ_idQa,idQa_Q__idQ_idQa) ),
inference(spr,[status(thm),theory(equality)],[1938,12]),
[iquote('0:SpR:1938.1,12.0')] ).
cnf(1943,plain,
( ~ less_equal(idQa,u)
| less_equal(idQa_Q__idQ_idQa,u) ),
inference(spr,[status(thm),theory(equality)],[1938,22]),
[iquote('0:SpR:1938.1,22.0')] ).
cnf(2009,plain,
( ~ less_equal(idQa,divide(idQa_Q__idQ_idQa,u))
| equal(divide(idQa_Q__idQ_idQa,u),idQa_Q__idQ_idQa) ),
inference(res,[status(thm),theory(equality)],[1943,26]),
[iquote('0:Res:1943.1,26.0')] ).
cnf(2032,plain,
( ~ less_equal(idQa,identity)
| ~ less_equal(idQ_idQa,a)
| less_equal(divide(idQa,zero),divide(idQa_Q__idQ_idQa,a)) ),
inference(res,[status(thm),theory(equality)],[1942,381]),
[iquote('0:Res:1942.1,381.1')] ).
cnf(2047,plain,
less_equal(divide(idQa,zero),divide(idQa_Q__idQ_idQa,a)),
inference(mrr,[status(thm)],[2032,11,1444]),
[iquote('0:MRR:2032.0,2032.1,11.0,1444.0')] ).
cnf(2070,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)],[12,525]),
[iquote('0:Res:12.0,525.2')] ).
cnf(5596,plain,
( ~ less_equal(zero,divide(idQa_Q__idQ_idQa,a))
| less_equal(divide(divide(idQa,divide(idQa_Q__idQ_idQa,a)),zero),zero) ),
inference(res,[status(thm),theory(equality)],[2047,2070]),
[iquote('0:Res:2047.0,2070.1')] ).
cnf(5623,plain,
less_equal(divide(divide(idQa,divide(idQa_Q__idQ_idQa,a)),zero),zero),
inference(mrr,[status(thm)],[5596,9]),
[iquote('0:MRR:5596.0,9.0')] ).
cnf(5952,plain,
equal(divide(divide(idQa,divide(idQa_Q__idQ_idQa,a)),zero),zero),
inference(res,[status(thm),theory(equality)],[5623,25]),
[iquote('0:Res:5623.0,25.0')] ).
cnf(6295,plain,
quotient(divide(idQa,divide(idQa_Q__idQ_idQa,a)),zero,zero),
inference(spr,[status(thm),theory(equality)],[5952,12]),
[iquote('0:SpR:5952.0,12.0')] ).
cnf(6329,plain,
less_equal(divide(idQa,divide(idQa_Q__idQ_idQa,a)),zero),
inference(res,[status(thm),theory(equality)],[6295,6]),
[iquote('0:Res:6295.0,6.0')] ).
cnf(6396,plain,
equal(divide(idQa,divide(idQa_Q__idQ_idQa,a)),zero),
inference(res,[status(thm),theory(equality)],[6329,25]),
[iquote('0:Res:6329.0,25.0')] ).
cnf(6413,plain,
quotient(idQa,divide(idQa_Q__idQ_idQa,a),zero),
inference(spr,[status(thm),theory(equality)],[6396,12]),
[iquote('0:SpR:6396.0,12.0')] ).
cnf(6450,plain,
less_equal(idQa,divide(idQa_Q__idQ_idQa,a)),
inference(res,[status(thm),theory(equality)],[6413,6]),
[iquote('0:Res:6413.0,6.0')] ).
cnf(6487,plain,
equal(divide(idQa_Q__idQ_idQa,a),idQa),
inference(res,[status(thm),theory(equality)],[6450,1837]),
[iquote('0:Res:6450.0,1837.0')] ).
cnf(6488,plain,
equal(divide(idQa_Q__idQ_idQa,a),idQa_Q__idQ_idQa),
inference(res,[status(thm),theory(equality)],[6450,2009]),
[iquote('0:Res:6450.0,2009.0')] ).
cnf(6507,plain,
equal(idQa_Q__idQ_idQa,idQa),
inference(rew,[status(thm),theory(equality)],[6487,6488]),
[iquote('0:Rew:6487.0,6488.0')] ).
cnf(6508,plain,
$false,
inference(mrr,[status(thm)],[6507,4]),
[iquote('0:MRR:6507.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN010-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n015.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 14:46:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.98/1.16
% 0.98/1.16 SPASS V 3.9
% 0.98/1.16 SPASS beiseite: Proof found.
% 0.98/1.16 % SZS status Theorem
% 0.98/1.16 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.98/1.16 SPASS derived 5219 clauses, backtracked 0 clauses, performed 0 splits and kept 1348 clauses.
% 0.98/1.16 SPASS allocated 67182 KBytes.
% 0.98/1.16 SPASS spent 0:00:00.80 on the problem.
% 0.98/1.16 0:00:00.04 for the input.
% 0.98/1.16 0:00:00.00 for the FLOTTER CNF translation.
% 0.98/1.16 0:00:00.07 for inferences.
% 0.98/1.16 0:00:00.00 for the backtracking.
% 0.98/1.16 0:00:00.67 for the reduction.
% 0.98/1.16
% 0.98/1.16
% 0.98/1.16 Here is a proof with depth 20, length 87 :
% 0.98/1.16 % SZS output start Refutation
% See solution above
% 0.98/1.18 Formulae used in the proof : identity_divide_a identity_divide_idQa identity_divide_idQ_idQa prove_idQa_equals_idQa_Q__idQ_idQa quotient_less_equal less_equal_quotient divisor_existence quotient_property zero_is_smallest less_equal_and_equal identity_is_largest closure
% 0.98/1.18
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