TSTP Solution File: HEN009-6 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN009-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 13:03:11 EDT 2022
% Result : Unsatisfiable 0.20s 0.53s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of clauses : 42 ( 27 unt; 0 nHn; 42 RR)
% Number of literals : 58 ( 0 equ; 19 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 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(3,axiom,
equal(divide(u,u),zero),
file('HEN009-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ less_equal(divide(u,v),w)
| less_equal(divide(u,w),v) ),
file('HEN009-6.p',unknown),
[] ).
cnf(5,axiom,
( ~ less_equal(u,v)
| less_equal(divide(u,w),divide(v,w)) ),
file('HEN009-6.p',unknown),
[] ).
cnf(7,axiom,
equal(divide(identity,a),b),
file('HEN009-6.p',unknown),
[] ).
cnf(8,axiom,
equal(divide(identity,b),c),
file('HEN009-6.p',unknown),
[] ).
cnf(9,axiom,
equal(divide(identity,c),d),
file('HEN009-6.p',unknown),
[] ).
cnf(10,axiom,
~ equal(d,b),
file('HEN009-6.p',unknown),
[] ).
cnf(11,axiom,
( ~ less_equal(u,v)
| equal(divide(u,v),zero) ),
file('HEN009-6.p',unknown),
[] ).
cnf(12,axiom,
( ~ equal(divide(u,v),zero)
| less_equal(u,v) ),
file('HEN009-6.p',unknown),
[] ).
cnf(13,axiom,
less_equal(divide(u,v),u),
file('HEN009-6.p',unknown),
[] ).
cnf(14,axiom,
less_equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),
file('HEN009-6.p',unknown),
[] ).
cnf(15,axiom,
less_equal(zero,u),
file('HEN009-6.p',unknown),
[] ).
cnf(16,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN009-6.p',unknown),
[] ).
cnf(17,axiom,
less_equal(u,identity),
file('HEN009-6.p',unknown),
[] ).
cnf(19,plain,
( ~ less_equal(b,d)
| ~ less_equal(d,b) ),
inference(res,[status(thm),theory(equality)],[16,10]),
[iquote('0:Res:16.2,10.0')] ).
cnf(49,plain,
( ~ equal(zero,zero)
| less_equal(u,u) ),
inference(spl,[status(thm),theory(equality)],[3,12]),
[iquote('0:SpL:3.0,12.0')] ).
cnf(53,plain,
less_equal(u,u),
inference(obv,[status(thm),theory(equality)],[49]),
[iquote('0:Obv:49.0')] ).
cnf(56,plain,
( ~ less_equal(u,zero)
| equal(u,zero) ),
inference(res,[status(thm),theory(equality)],[15,16]),
[iquote('0:Res:15.0,16.0')] ).
cnf(71,plain,
( ~ less_equal(u,identity)
| less_equal(divide(u,b),c) ),
inference(spr,[status(thm),theory(equality)],[8,5]),
[iquote('0:SpR:8.0,5.1')] ).
cnf(72,plain,
( ~ less_equal(u,identity)
| less_equal(divide(u,a),b) ),
inference(spr,[status(thm),theory(equality)],[7,5]),
[iquote('0:SpR:7.0,5.1')] ).
cnf(86,plain,
less_equal(divide(u,b),c),
inference(mrr,[status(thm)],[71,17]),
[iquote('0:MRR:71.0,17.0')] ).
cnf(87,plain,
less_equal(divide(u,a),b),
inference(mrr,[status(thm)],[72,17]),
[iquote('0:MRR:72.0,17.0')] ).
cnf(117,plain,
less_equal(divide(u,divide(u,v)),v),
inference(res,[status(thm),theory(equality)],[53,4]),
[iquote('0:Res:53.0,4.0')] ).
cnf(120,plain,
less_equal(divide(u,c),b),
inference(res,[status(thm),theory(equality)],[86,4]),
[iquote('0:Res:86.0,4.0')] ).
cnf(121,plain,
less_equal(divide(u,b),a),
inference(res,[status(thm),theory(equality)],[87,4]),
[iquote('0:Res:87.0,4.0')] ).
cnf(131,plain,
less_equal(d,b),
inference(spr,[status(thm),theory(equality)],[9,120]),
[iquote('0:SpR:9.0,120.0')] ).
cnf(137,plain,
~ less_equal(b,d),
inference(mrr,[status(thm)],[19,131]),
[iquote('0:MRR:19.1,131.0')] ).
cnf(158,plain,
less_equal(divide(b,divide(u,a)),divide(divide(identity,u),a)),
inference(spr,[status(thm),theory(equality)],[7,14]),
[iquote('0:SpR:7.0,14.0')] ).
cnf(179,plain,
less_equal(c,a),
inference(spr,[status(thm),theory(equality)],[8,121]),
[iquote('0:SpR:8.0,121.0')] ).
cnf(341,plain,
equal(divide(u,divide(u,zero)),zero),
inference(res,[status(thm),theory(equality)],[117,56]),
[iquote('0:Res:117.0,56.0')] ).
cnf(375,plain,
( ~ equal(zero,zero)
| less_equal(u,divide(u,zero)) ),
inference(spl,[status(thm),theory(equality)],[341,12]),
[iquote('0:SpL:341.0,12.0')] ).
cnf(377,plain,
less_equal(u,divide(u,zero)),
inference(obv,[status(thm),theory(equality)],[375]),
[iquote('0:Obv:375.0')] ).
cnf(383,plain,
( ~ less_equal(divide(u,zero),u)
| equal(divide(u,zero),u) ),
inference(res,[status(thm),theory(equality)],[377,16]),
[iquote('0:Res:377.0,16.0')] ).
cnf(386,plain,
equal(divide(u,zero),u),
inference(mrr,[status(thm)],[383,13]),
[iquote('0:MRR:383.0,13.0')] ).
cnf(955,plain,
less_equal(divide(b,divide(c,a)),divide(d,a)),
inference(spr,[status(thm),theory(equality)],[9,158]),
[iquote('0:SpR:9.0,158.0')] ).
cnf(1922,plain,
( ~ less_equal(c,a)
| less_equal(divide(b,zero),divide(d,a)) ),
inference(spr,[status(thm),theory(equality)],[11,955]),
[iquote('0:SpR:11.1,955.0')] ).
cnf(1927,plain,
( ~ less_equal(c,a)
| less_equal(b,divide(d,a)) ),
inference(rew,[status(thm),theory(equality)],[386,1922]),
[iquote('0:Rew:386.0,1922.1')] ).
cnf(1928,plain,
less_equal(b,divide(d,a)),
inference(mrr,[status(thm)],[1927,179]),
[iquote('0:MRR:1927.0,179.0')] ).
cnf(1931,plain,
( ~ less_equal(divide(d,a),b)
| equal(divide(d,a),b) ),
inference(res,[status(thm),theory(equality)],[1928,16]),
[iquote('0:Res:1928.0,16.0')] ).
cnf(1932,plain,
equal(divide(d,a),b),
inference(mrr,[status(thm)],[1931,87]),
[iquote('0:MRR:1931.0,87.0')] ).
cnf(2062,plain,
less_equal(b,d),
inference(spr,[status(thm),theory(equality)],[1932,13]),
[iquote('0:SpR:1932.0,13.0')] ).
cnf(2090,plain,
$false,
inference(mrr,[status(thm)],[2062,137]),
[iquote('0:MRR:2062.0,137.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN009-6 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n025.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 14:22:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.53
% 0.20/0.53 SPASS V 3.9
% 0.20/0.53 SPASS beiseite: Proof found.
% 0.20/0.53 % SZS status Theorem
% 0.20/0.53 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.53 SPASS derived 1556 clauses, backtracked 0 clauses, performed 0 splits and kept 427 clauses.
% 0.20/0.53 SPASS allocated 64320 KBytes.
% 0.20/0.53 SPASS spent 0:00:00.17 on the problem.
% 0.20/0.53 0:00:00.04 for the input.
% 0.20/0.53 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.53 0:00:00.01 for inferences.
% 0.20/0.53 0:00:00.00 for the backtracking.
% 0.20/0.53 0:00:00.10 for the reduction.
% 0.20/0.53
% 0.20/0.53
% 0.20/0.53 Here is a proof with depth 5, length 42 :
% 0.20/0.53 % SZS output start Refutation
% See solution above
% 0.20/0.53 Formulae used in the proof : x_divide_x_is_zero property_of_divide1 property_of_divide3 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
% 0.20/0.53
%------------------------------------------------------------------------------