TSTP Solution File: HEN009-3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN009-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 0.70s 0.87s
% Output : Refutation 0.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of clauses : 79 ( 51 unt; 0 nHn; 79 RR)
% Number of literals : 108 ( 0 equ; 32 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
equal(divide(identity,a),b),
file('HEN009-3.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(identity,b),c),
file('HEN009-3.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(identity,c),d),
file('HEN009-3.p',unknown),
[] ).
cnf(5,axiom,
~ equal(d,b),
file('HEN009-3.p',unknown),
[] ).
cnf(6,axiom,
( ~ less_equal(u,v)
| equal(divide(u,v),zero) ),
file('HEN009-3.p',unknown),
[] ).
cnf(7,axiom,
( ~ equal(divide(u,v),zero)
| less_equal(u,v) ),
file('HEN009-3.p',unknown),
[] ).
cnf(8,axiom,
less_equal(divide(u,v),u),
file('HEN009-3.p',unknown),
[] ).
cnf(9,axiom,
less_equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),
file('HEN009-3.p',unknown),
[] ).
cnf(10,axiom,
less_equal(zero,u),
file('HEN009-3.p',unknown),
[] ).
cnf(11,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN009-3.p',unknown),
[] ).
cnf(12,axiom,
less_equal(u,identity),
file('HEN009-3.p',unknown),
[] ).
cnf(14,plain,
( ~ less_equal(b,d)
| ~ less_equal(d,b) ),
inference(res,[status(thm),theory(equality)],[11,5]),
[iquote('0:Res:11.2,5.0')] ).
cnf(32,plain,
( ~ less_equal(u,zero)
| equal(u,zero) ),
inference(res,[status(thm),theory(equality)],[10,11]),
[iquote('0:Res:10.0,11.0')] ).
cnf(33,plain,
( ~ less_equal(u,divide(u,v))
| equal(divide(u,v),u) ),
inference(res,[status(thm),theory(equality)],[8,11]),
[iquote('0:Res:8.0,11.0')] ).
cnf(51,plain,
less_equal(divide(divide(u,c),d),divide(divide(u,identity),c)),
inference(spr,[status(thm),theory(equality)],[4,9]),
[iquote('0:SpR:4.0,9.0')] ).
cnf(52,plain,
less_equal(divide(divide(u,b),c),divide(divide(u,identity),b)),
inference(spr,[status(thm),theory(equality)],[3,9]),
[iquote('0:SpR:3.0,9.0')] ).
cnf(53,plain,
less_equal(divide(divide(u,a),b),divide(divide(u,identity),a)),
inference(spr,[status(thm),theory(equality)],[2,9]),
[iquote('0:SpR:2.0,9.0')] ).
cnf(55,plain,
less_equal(divide(d,divide(u,c)),divide(divide(identity,u),c)),
inference(spr,[status(thm),theory(equality)],[4,9]),
[iquote('0:SpR:4.0,9.0')] ).
cnf(56,plain,
less_equal(divide(c,divide(u,b)),divide(divide(identity,u),b)),
inference(spr,[status(thm),theory(equality)],[3,9]),
[iquote('0:SpR:3.0,9.0')] ).
cnf(57,plain,
less_equal(divide(b,divide(u,a)),divide(divide(identity,u),a)),
inference(spr,[status(thm),theory(equality)],[2,9]),
[iquote('0:SpR:2.0,9.0')] ).
cnf(60,plain,
( ~ less_equal(divide(divide(u,v),w),divide(divide(u,w),divide(v,w)))
| equal(divide(divide(u,w),divide(v,w)),divide(divide(u,v),w)) ),
inference(res,[status(thm),theory(equality)],[9,11]),
[iquote('0:Res:9.0,11.0')] ).
cnf(62,plain,
equal(divide(zero,u),zero),
inference(res,[status(thm),theory(equality)],[8,32]),
[iquote('0:Res:8.0,32.0')] ).
cnf(69,plain,
less_equal(divide(divide(u,v),zero),divide(divide(u,zero),v)),
inference(spr,[status(thm),theory(equality)],[62,9]),
[iquote('0:SpR:62.0,9.0')] ).
cnf(75,plain,
( ~ less_equal(u,identity)
| less_equal(divide(divide(u,c),d),divide(zero,c)) ),
inference(spr,[status(thm),theory(equality)],[6,51]),
[iquote('0:SpR:6.1,51.0')] ).
cnf(84,plain,
( ~ less_equal(u,identity)
| less_equal(divide(divide(u,c),d),zero) ),
inference(rew,[status(thm),theory(equality)],[62,75]),
[iquote('0:Rew:62.0,75.1')] ).
cnf(85,plain,
less_equal(divide(divide(u,c),d),zero),
inference(mrr,[status(thm)],[84,12]),
[iquote('0:MRR:84.0,12.0')] ).
cnf(92,plain,
equal(divide(divide(u,c),d),zero),
inference(res,[status(thm),theory(equality)],[85,32]),
[iquote('0:Res:85.0,32.0')] ).
cnf(113,plain,
( ~ less_equal(u,identity)
| less_equal(divide(divide(u,b),c),divide(zero,b)) ),
inference(spr,[status(thm),theory(equality)],[6,52]),
[iquote('0:SpR:6.1,52.0')] ).
cnf(122,plain,
( ~ less_equal(u,identity)
| less_equal(divide(divide(u,b),c),zero) ),
inference(rew,[status(thm),theory(equality)],[62,113]),
[iquote('0:Rew:62.0,113.1')] ).
cnf(123,plain,
less_equal(divide(divide(u,b),c),zero),
inference(mrr,[status(thm)],[122,12]),
[iquote('0:MRR:122.0,12.0')] ).
cnf(135,plain,
( ~ equal(zero,zero)
| less_equal(divide(u,c),d) ),
inference(spl,[status(thm),theory(equality)],[92,7]),
[iquote('0:SpL:92.0,7.0')] ).
cnf(136,plain,
less_equal(divide(u,c),d),
inference(obv,[status(thm),theory(equality)],[135]),
[iquote('0:Obv:135.0')] ).
cnf(148,plain,
equal(divide(divide(u,b),c),zero),
inference(res,[status(thm),theory(equality)],[123,32]),
[iquote('0:Res:123.0,32.0')] ).
cnf(158,plain,
( ~ less_equal(u,identity)
| less_equal(divide(divide(u,a),b),divide(zero,a)) ),
inference(spr,[status(thm),theory(equality)],[6,53]),
[iquote('0:SpR:6.1,53.0')] ).
cnf(167,plain,
( ~ less_equal(u,identity)
| less_equal(divide(divide(u,a),b),zero) ),
inference(rew,[status(thm),theory(equality)],[62,158]),
[iquote('0:Rew:62.0,158.1')] ).
cnf(168,plain,
less_equal(divide(divide(u,a),b),zero),
inference(mrr,[status(thm)],[167,12]),
[iquote('0:MRR:167.0,12.0')] ).
cnf(195,plain,
( ~ equal(zero,zero)
| less_equal(divide(u,b),c) ),
inference(spl,[status(thm),theory(equality)],[148,7]),
[iquote('0:SpL:148.0,7.0')] ).
cnf(196,plain,
less_equal(divide(u,b),c),
inference(obv,[status(thm),theory(equality)],[195]),
[iquote('0:Obv:195.0')] ).
cnf(208,plain,
less_equal(divide(d,divide(b,c)),zero),
inference(spr,[status(thm),theory(equality)],[148,55]),
[iquote('0:SpR:148.0,55.0')] ).
cnf(224,plain,
equal(divide(d,divide(b,c)),zero),
inference(res,[status(thm),theory(equality)],[208,32]),
[iquote('0:Res:208.0,32.0')] ).
cnf(237,plain,
( ~ equal(zero,zero)
| less_equal(d,divide(b,c)) ),
inference(spl,[status(thm),theory(equality)],[224,7]),
[iquote('0:SpL:224.0,7.0')] ).
cnf(239,plain,
less_equal(d,divide(b,c)),
inference(obv,[status(thm),theory(equality)],[237]),
[iquote('0:Obv:237.0')] ).
cnf(243,plain,
( ~ less_equal(divide(b,c),d)
| equal(divide(b,c),d) ),
inference(res,[status(thm),theory(equality)],[239,11]),
[iquote('0:Res:239.0,11.0')] ).
cnf(244,plain,
equal(divide(b,c),d),
inference(mrr,[status(thm)],[243,136]),
[iquote('0:MRR:243.0,136.0')] ).
cnf(254,plain,
less_equal(divide(c,divide(a,b)),divide(b,b)),
inference(spr,[status(thm),theory(equality)],[2,56]),
[iquote('0:SpR:2.0,56.0')] ).
cnf(264,plain,
less_equal(d,b),
inference(spr,[status(thm),theory(equality)],[244,8]),
[iquote('0:SpR:244.0,8.0')] ).
cnf(274,plain,
~ less_equal(b,d),
inference(mrr,[status(thm)],[14,264]),
[iquote('0:MRR:14.1,264.0')] ).
cnf(282,plain,
less_equal(divide(b,divide(c,a)),divide(d,a)),
inference(spr,[status(thm),theory(equality)],[4,57]),
[iquote('0:SpR:4.0,57.0')] ).
cnf(293,plain,
less_equal(divide(b,b),zero),
inference(spr,[status(thm),theory(equality)],[2,168]),
[iquote('0:SpR:2.0,168.0')] ).
cnf(298,plain,
equal(divide(divide(u,a),b),zero),
inference(res,[status(thm),theory(equality)],[168,32]),
[iquote('0:Res:168.0,32.0')] ).
cnf(305,plain,
equal(divide(b,b),zero),
inference(res,[status(thm),theory(equality)],[293,32]),
[iquote('0:Res:293.0,32.0')] ).
cnf(309,plain,
less_equal(divide(c,divide(a,b)),zero),
inference(rew,[status(thm),theory(equality)],[305,254]),
[iquote('0:Rew:305.0,254.0')] ).
cnf(344,plain,
equal(divide(c,divide(a,b)),zero),
inference(res,[status(thm),theory(equality)],[309,32]),
[iquote('0:Res:309.0,32.0')] ).
cnf(355,plain,
( ~ equal(zero,zero)
| less_equal(c,divide(a,b)) ),
inference(spl,[status(thm),theory(equality)],[344,7]),
[iquote('0:SpL:344.0,7.0')] ).
cnf(357,plain,
less_equal(c,divide(a,b)),
inference(obv,[status(thm),theory(equality)],[355]),
[iquote('0:Obv:355.0')] ).
cnf(361,plain,
( ~ less_equal(divide(a,b),c)
| equal(divide(a,b),c) ),
inference(res,[status(thm),theory(equality)],[357,11]),
[iquote('0:Res:357.0,11.0')] ).
cnf(362,plain,
equal(divide(a,b),c),
inference(mrr,[status(thm)],[361,196]),
[iquote('0:MRR:361.0,196.0')] ).
cnf(386,plain,
less_equal(c,a),
inference(spr,[status(thm),theory(equality)],[362,8]),
[iquote('0:SpR:362.0,8.0')] ).
cnf(434,plain,
( ~ equal(zero,zero)
| less_equal(divide(u,a),b) ),
inference(spl,[status(thm),theory(equality)],[298,7]),
[iquote('0:SpL:298.0,7.0')] ).
cnf(437,plain,
less_equal(divide(u,a),b),
inference(obv,[status(thm),theory(equality)],[434]),
[iquote('0:Obv:434.0')] ).
cnf(589,plain,
( ~ less_equal(c,a)
| less_equal(divide(b,zero),divide(d,a)) ),
inference(spr,[status(thm),theory(equality)],[6,282]),
[iquote('0:SpR:6.1,282.0')] ).
cnf(592,plain,
less_equal(divide(b,zero),divide(d,a)),
inference(mrr,[status(thm)],[589,386]),
[iquote('0:MRR:589.0,386.0')] ).
cnf(633,plain,
( ~ less_equal(divide(d,a),divide(b,zero))
| equal(divide(d,a),divide(b,zero)) ),
inference(res,[status(thm),theory(equality)],[592,11]),
[iquote('0:Res:592.0,11.0')] ).
cnf(803,plain,
( ~ less_equal(divide(zero,u),divide(divide(b,u),divide(b,u)))
| equal(divide(divide(b,u),divide(b,u)),divide(divide(b,b),u)) ),
inference(spl,[status(thm),theory(equality)],[305,60]),
[iquote('0:SpL:305.0,60.0')] ).
cnf(820,plain,
( ~ less_equal(zero,divide(divide(b,u),divide(b,u)))
| equal(divide(divide(b,u),divide(b,u)),zero) ),
inference(rew,[status(thm),theory(equality)],[62,803,305]),
[iquote('0:Rew:62.0,803.1,305.0,803.1,62.0,803.0')] ).
cnf(821,plain,
equal(divide(divide(b,u),divide(b,u)),zero),
inference(mrr,[status(thm)],[820,10]),
[iquote('0:MRR:820.0,10.0')] ).
cnf(4401,plain,
less_equal(divide(divide(b,divide(b,zero)),zero),zero),
inference(spr,[status(thm),theory(equality)],[821,69]),
[iquote('0:SpR:821.0,69.0')] ).
cnf(4476,plain,
equal(divide(divide(b,divide(b,zero)),zero),zero),
inference(res,[status(thm),theory(equality)],[4401,32]),
[iquote('0:Res:4401.0,32.0')] ).
cnf(4621,plain,
( ~ equal(zero,zero)
| less_equal(divide(b,divide(b,zero)),zero) ),
inference(spl,[status(thm),theory(equality)],[4476,7]),
[iquote('0:SpL:4476.0,7.0')] ).
cnf(4631,plain,
less_equal(divide(b,divide(b,zero)),zero),
inference(obv,[status(thm),theory(equality)],[4621]),
[iquote('0:Obv:4621.0')] ).
cnf(4654,plain,
equal(divide(b,divide(b,zero)),zero),
inference(res,[status(thm),theory(equality)],[4631,32]),
[iquote('0:Res:4631.0,32.0')] ).
cnf(4755,plain,
( ~ equal(zero,zero)
| less_equal(b,divide(b,zero)) ),
inference(spl,[status(thm),theory(equality)],[4654,7]),
[iquote('0:SpL:4654.0,7.0')] ).
cnf(4764,plain,
less_equal(b,divide(b,zero)),
inference(obv,[status(thm),theory(equality)],[4755]),
[iquote('0:Obv:4755.0')] ).
cnf(4785,plain,
equal(divide(b,zero),b),
inference(res,[status(thm),theory(equality)],[4764,33]),
[iquote('0:Res:4764.0,33.0')] ).
cnf(4795,plain,
( ~ less_equal(divide(d,a),b)
| equal(divide(d,a),divide(b,zero)) ),
inference(rew,[status(thm),theory(equality)],[4785,633]),
[iquote('0:Rew:4785.0,633.0')] ).
cnf(4823,plain,
( ~ less_equal(divide(d,a),b)
| equal(divide(d,a),b) ),
inference(rew,[status(thm),theory(equality)],[4785,4795]),
[iquote('0:Rew:4785.0,4795.1')] ).
cnf(4824,plain,
equal(divide(d,a),b),
inference(mrr,[status(thm)],[4823,437]),
[iquote('0:MRR:4823.0,437.0')] ).
cnf(4919,plain,
less_equal(b,d),
inference(spr,[status(thm),theory(equality)],[4824,8]),
[iquote('0:SpR:4824.0,8.0')] ).
cnf(4954,plain,
$false,
inference(mrr,[status(thm)],[4919,274]),
[iquote('0:MRR:4919.0,274.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN009-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n029.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 13:43:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.70/0.87
% 0.70/0.87 SPASS V 3.9
% 0.70/0.87 SPASS beiseite: Proof found.
% 0.70/0.87 % SZS status Theorem
% 0.70/0.87 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.70/0.87 SPASS derived 3412 clauses, backtracked 0 clauses, performed 0 splits and kept 894 clauses.
% 0.70/0.87 SPASS allocated 66540 KBytes.
% 0.70/0.87 SPASS spent 0:00:00.50 on the problem.
% 0.70/0.87 0:00:00.04 for the input.
% 0.70/0.87 0:00:00.00 for the FLOTTER CNF translation.
% 0.70/0.87 0:00:00.04 for inferences.
% 0.70/0.87 0:00:00.00 for the backtracking.
% 0.70/0.87 0:00:00.40 for the reduction.
% 0.70/0.87
% 0.70/0.87
% 0.70/0.87 Here is a proof with depth 11, length 79 :
% 0.70/0.87 % SZS output start Refutation
% See solution above
% 0.70/0.87 Formulae used in the proof : id_divide_a_is_b id_divide_b_is_c id_divide_c_is_d prove_b_equals_d quotient_less_equal1 quotient_less_equal2 quotient_smaller_than_numerator quotient_property zero_is_smallest less_equal_and_equal identity_is_largest
% 0.70/0.87
%------------------------------------------------------------------------------