TSTP Solution File: SYN074-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SYN074-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 : Thu Jul 21 12:18:21 EDT 2022
% Result : Unsatisfiable 0.18s 0.42s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of clauses : 63 ( 16 unt; 23 nHn; 63 RR)
% Number of literals : 127 ( 0 equ; 62 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ big(u,v)
| equal(u,a) ),
file('SYN074-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ big(u,v)
| equal(v,b) ),
file('SYN074-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ equal(u,b)
| ~ equal(v,a)
| big(v,u) ),
file('SYN074-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ equal(u,g(v))
| equal(f(v),v)
| big(f(v),u) ),
file('SYN074-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ equal(f(u),u)
| big(f(u),h(u,v))
| equal(h(u,v),v) ),
file('SYN074-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ equal(f(u),u)
| ~ big(f(u),h(u,v))
| ~ equal(h(u,v),v) ),
file('SYN074-1.p',unknown),
[] ).
cnf(18,plain,
( ~ equal(u,g(v))
| equal(f(v),v)
| equal(f(v),a) ),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.2,1.0')] ).
cnf(20,plain,
( equal(f(u),u)
| equal(f(u),a) ),
inference(aed,[status(thm),theory(equality)],[18]),
[iquote('0:AED:18.0')] ).
cnf(21,plain,
( ~ equal(u,g(v))
| equal(f(v),v)
| big(a,u) ),
inference(rew,[status(thm),theory(equality)],[20,8]),
[iquote('0:Rew:20.1,8.2')] ).
cnf(23,plain,
( equal(f(u),u)
| big(a,g(u)) ),
inference(eqr,[status(thm),theory(equality)],[21]),
[iquote('0:EqR:21.0')] ).
cnf(24,plain,
( ~ equal(u,a)
| equal(f(u),a) ),
inference(eqf,[status(thm),theory(equality)],[20]),
[iquote('0:EqF:20.0,20.1')] ).
cnf(26,plain,
equal(f(a),a),
inference(fac,[status(thm)],[20]),
[iquote('0:Fac:20.0,20.1')] ).
cnf(38,plain,
( equal(f(u),u)
| equal(g(u),b) ),
inference(res,[status(thm),theory(equality)],[23,2]),
[iquote('0:Res:23.1,2.0')] ).
cnf(39,plain,
( equal(f(u),u)
| big(a,b) ),
inference(rew,[status(thm),theory(equality)],[38,23]),
[iquote('0:Rew:38.1,23.1')] ).
cnf(40,plain,
( ~ equal(u,b)
| equal(f(v),v)
| big(a,u) ),
inference(rew,[status(thm),theory(equality)],[38,21]),
[iquote('0:Rew:38.1,21.0')] ).
cnf(43,plain,
equal(f(u),u),
inference(spt,[spt(split,[position(s1)])],[40]),
[iquote('1:Spt:40.1')] ).
cnf(46,plain,
( ~ equal(u,u)
| ~ big(f(u),h(u,v))
| ~ equal(h(u,v),v) ),
inference(rew,[status(thm),theory(equality)],[43,11]),
[iquote('1:Rew:43.0,11.0')] ).
cnf(47,plain,
( ~ equal(u,u)
| big(f(u),h(u,v))
| equal(h(u,v),v) ),
inference(rew,[status(thm),theory(equality)],[43,10]),
[iquote('1:Rew:43.0,10.0')] ).
cnf(51,plain,
( big(f(u),h(u,v))
| equal(h(u,v),v) ),
inference(obv,[status(thm),theory(equality)],[47]),
[iquote('1:Obv:47.0')] ).
cnf(52,plain,
( big(u,h(u,v))
| equal(h(u,v),v) ),
inference(rew,[status(thm),theory(equality)],[43,51]),
[iquote('1:Rew:43.0,51.0')] ).
cnf(53,plain,
( ~ big(f(u),h(u,v))
| ~ equal(h(u,v),v) ),
inference(obv,[status(thm),theory(equality)],[46]),
[iquote('1:Obv:46.0')] ).
cnf(54,plain,
( ~ big(u,h(u,v))
| ~ equal(h(u,v),v) ),
inference(rew,[status(thm),theory(equality)],[43,53]),
[iquote('1:Rew:43.0,53.0')] ).
cnf(57,plain,
( equal(h(u,v),v)
| equal(h(u,v),b) ),
inference(res,[status(thm),theory(equality)],[52,2]),
[iquote('1:Res:52.0,2.0')] ).
cnf(58,plain,
( big(u,b)
| equal(h(u,v),v) ),
inference(rew,[status(thm),theory(equality)],[57,52]),
[iquote('1:Rew:57.1,52.0')] ).
cnf(64,plain,
equal(h(u,b),b),
inference(fac,[status(thm)],[57]),
[iquote('1:Fac:57.0,57.1')] ).
cnf(76,plain,
( ~ big(u,v)
| ~ equal(h(u,v),v)
| big(u,b) ),
inference(spl,[status(thm),theory(equality)],[58,54]),
[iquote('1:SpL:58.1,54.0')] ).
cnf(79,plain,
( ~ big(u,v)
| ~ equal(v,v)
| big(u,b) ),
inference(rew,[status(thm),theory(equality)],[58,76]),
[iquote('1:Rew:58.1,76.1')] ).
cnf(80,plain,
( ~ big(u,v)
| big(u,b) ),
inference(obv,[status(thm),theory(equality)],[79]),
[iquote('1:Obv:79.1')] ).
cnf(86,plain,
( ~ big(u,b)
| ~ equal(h(u,b),b) ),
inference(spl,[status(thm),theory(equality)],[64,54]),
[iquote('1:SpL:64.0,54.0')] ).
cnf(87,plain,
( ~ big(u,b)
| ~ equal(b,b) ),
inference(rew,[status(thm),theory(equality)],[64,86]),
[iquote('1:Rew:64.0,86.1')] ).
cnf(88,plain,
~ big(u,b),
inference(obv,[status(thm),theory(equality)],[87]),
[iquote('1:Obv:87.1')] ).
cnf(90,plain,
~ big(u,v),
inference(mrr,[status(thm)],[80,88]),
[iquote('1:MRR:80.1,88.0')] ).
cnf(91,plain,
( ~ equal(u,b)
| ~ equal(v,a) ),
inference(mrr,[status(thm)],[3,90]),
[iquote('1:MRR:3.2,90.0')] ).
cnf(94,plain,
$false,
inference(aed,[status(thm),theory(equality)],[91]),
[iquote('1:AED:91.1')] ).
cnf(97,plain,
( ~ equal(u,b)
| big(a,u) ),
inference(spt,[spt(split,[position(s2)])],[40]),
[iquote('1:Spt:94.0,40.0,40.2')] ).
cnf(99,plain,
equal(f(u),u),
inference(spt,[spt(split,[position(s2s1)])],[39]),
[iquote('2:Spt:39.0')] ).
cnf(102,plain,
( ~ equal(u,u)
| ~ big(f(u),h(u,v))
| ~ equal(h(u,v),v) ),
inference(rew,[status(thm),theory(equality)],[99,11]),
[iquote('2:Rew:99.0,11.0')] ).
cnf(103,plain,
( ~ equal(u,u)
| big(f(u),h(u,v))
| equal(h(u,v),v) ),
inference(rew,[status(thm),theory(equality)],[99,10]),
[iquote('2:Rew:99.0,10.0')] ).
cnf(107,plain,
( big(f(u),h(u,v))
| equal(h(u,v),v) ),
inference(obv,[status(thm),theory(equality)],[103]),
[iquote('2:Obv:103.0')] ).
cnf(108,plain,
( big(u,h(u,v))
| equal(h(u,v),v) ),
inference(rew,[status(thm),theory(equality)],[99,107]),
[iquote('2:Rew:99.0,107.0')] ).
cnf(109,plain,
( ~ big(f(u),h(u,v))
| ~ equal(h(u,v),v) ),
inference(obv,[status(thm),theory(equality)],[102]),
[iquote('2:Obv:102.0')] ).
cnf(110,plain,
( ~ big(u,h(u,v))
| ~ equal(h(u,v),v) ),
inference(rew,[status(thm),theory(equality)],[99,109]),
[iquote('2:Rew:99.0,109.0')] ).
cnf(115,plain,
( equal(h(u,v),v)
| equal(h(u,v),b) ),
inference(res,[status(thm),theory(equality)],[108,2]),
[iquote('2:Res:108.0,2.0')] ).
cnf(116,plain,
( big(u,b)
| equal(h(u,v),v) ),
inference(rew,[status(thm),theory(equality)],[115,108]),
[iquote('2:Rew:115.1,108.0')] ).
cnf(122,plain,
equal(h(u,b),b),
inference(fac,[status(thm)],[115]),
[iquote('2:Fac:115.0,115.1')] ).
cnf(200,plain,
( ~ big(u,b)
| ~ equal(h(u,b),b) ),
inference(spl,[status(thm),theory(equality)],[122,110]),
[iquote('2:SpL:122.0,110.0')] ).
cnf(206,plain,
( ~ equal(h(a,u),b)
| ~ equal(h(a,u),u) ),
inference(res,[status(thm),theory(equality)],[97,110]),
[iquote('2:Res:97.1,110.0')] ).
cnf(208,plain,
( ~ big(u,b)
| ~ equal(b,b) ),
inference(rew,[status(thm),theory(equality)],[122,200]),
[iquote('2:Rew:122.0,200.1')] ).
cnf(209,plain,
~ big(u,b),
inference(obv,[status(thm),theory(equality)],[208]),
[iquote('2:Obv:208.1')] ).
cnf(210,plain,
equal(h(u,v),v),
inference(mrr,[status(thm)],[116,209]),
[iquote('2:MRR:116.0,209.0')] ).
cnf(219,plain,
( ~ equal(u,b)
| ~ equal(u,u) ),
inference(rew,[status(thm),theory(equality)],[210,206]),
[iquote('2:Rew:210.0,206.1,210.0,206.0')] ).
cnf(220,plain,
~ equal(u,b),
inference(obv,[status(thm),theory(equality)],[219]),
[iquote('2:Obv:219.1')] ).
cnf(221,plain,
$false,
inference(unc,[status(thm)],[220,99]),
[iquote('2:UnC:220.0,99.0')] ).
cnf(224,plain,
big(a,b),
inference(spt,[spt(split,[position(s2s2)])],[39]),
[iquote('2:Spt:221.0,39.1')] ).
cnf(245,plain,
( ~ equal(f(a),a)
| big(a,h(a,u))
| equal(h(a,u),u) ),
inference(spr,[status(thm),theory(equality)],[26,10]),
[iquote('0:SpR:26.0,10.1')] ).
cnf(256,plain,
( ~ equal(a,a)
| big(a,h(a,u))
| equal(h(a,u),u) ),
inference(rew,[status(thm),theory(equality)],[26,245]),
[iquote('0:Rew:26.0,245.0')] ).
cnf(257,plain,
( big(a,h(a,u))
| equal(h(a,u),u) ),
inference(obv,[status(thm),theory(equality)],[256]),
[iquote('0:Obv:256.0')] ).
cnf(266,plain,
( equal(h(a,u),u)
| equal(h(a,u),b) ),
inference(res,[status(thm),theory(equality)],[257,2]),
[iquote('0:Res:257.0,2.0')] ).
cnf(271,plain,
equal(h(a,b),b),
inference(fac,[status(thm)],[266]),
[iquote('0:Fac:266.0,266.1')] ).
cnf(299,plain,
( ~ equal(f(a),a)
| ~ big(f(a),b)
| ~ equal(h(a,b),b) ),
inference(spl,[status(thm),theory(equality)],[271,11]),
[iquote('0:SpL:271.0,11.1')] ).
cnf(300,plain,
( ~ equal(a,a)
| ~ big(a,b)
| ~ equal(b,b) ),
inference(rew,[status(thm),theory(equality)],[271,299,24,26]),
[iquote('0:Rew:271.0,299.2,24.1,299.1,26.0,299.0')] ).
cnf(301,plain,
~ big(a,b),
inference(obv,[status(thm),theory(equality)],[300]),
[iquote('0:Obv:300.2')] ).
cnf(302,plain,
$false,
inference(mrr,[status(thm)],[301,224]),
[iquote('2:MRR:301.0,224.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN074-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jul 12 05:55:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.42
% 0.18/0.42 SPASS V 3.9
% 0.18/0.42 SPASS beiseite: Proof found.
% 0.18/0.42 % SZS status Theorem
% 0.18/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.42 SPASS derived 222 clauses, backtracked 43 clauses, performed 3 splits and kept 123 clauses.
% 0.18/0.42 SPASS allocated 63235 KBytes.
% 0.18/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.18/0.42 0:00:00.03 for the input.
% 0.18/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.42 0:00:00.00 for inferences.
% 0.18/0.42 0:00:00.00 for the backtracking.
% 0.18/0.42 0:00:00.01 for the reduction.
% 0.18/0.42
% 0.18/0.42
% 0.18/0.42 Here is a proof with depth 6, length 63 :
% 0.18/0.42 % SZS output start Refutation
% See solution above
% 0.18/0.42 Formulae used in the proof : clause_1 clause_2 clause_3 clause_8 clause_10 clause_11
% 0.18/0.42
%------------------------------------------------------------------------------