TSTP Solution File: SEU230+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU230+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : Tue Jul 19 14:35:17 EDT 2022
% Result : Theorem 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 24 ( 9 unt; 4 nHn; 24 RR)
% Number of literals : 44 ( 0 equ; 23 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(26,axiom,
element(skf5(u),u),
file('SEU230+1.p',unknown),
[] ).
cnf(28,axiom,
~ in(skc10,succ(skc10)),
file('SEU230+1.p',unknown),
[] ).
cnf(31,axiom,
equal(set_union2(u,u),u),
file('SEU230+1.p',unknown),
[] ).
cnf(35,axiom,
equal(set_union2(u,singleton(u)),succ(u)),
file('SEU230+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ empty(u)
| ~ in(v,u) ),
file('SEU230+1.p',unknown),
[] ).
cnf(41,axiom,
( ~ element(u,v)
| empty(v)
| in(u,v) ),
file('SEU230+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ in(u,v)
| ~ equal(v,singleton(w))
| equal(u,w) ),
file('SEU230+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ equal(u,v)
| ~ equal(w,singleton(v))
| in(u,w) ),
file('SEU230+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ in(u,v)
| ~ equal(w,set_union2(x,v))
| in(u,w) ),
file('SEU230+1.p',unknown),
[] ).
cnf(59,plain,
( ~ in(skc10,u)
| ~ equal(set_union2(v,u),succ(skc10)) ),
inference(res,[status(thm),theory(equality)],[49,28]),
[iquote('0:Res:49.2,28.0')] ).
cnf(110,plain,
( empty(u)
| in(skf5(u),u) ),
inference(res,[status(thm),theory(equality)],[26,41]),
[iquote('0:Res:26.0,41.0')] ).
cnf(127,plain,
( ~ in(skc10,u)
| ~ equal(u,succ(skc10)) ),
inference(spl,[status(thm),theory(equality)],[31,59]),
[iquote('0:SpL:31.0,59.1')] ).
cnf(133,plain,
( ~ equal(u,v)
| in(u,singleton(v)) ),
inference(eqr,[status(thm),theory(equality)],[47]),
[iquote('0:EqR:47.1')] ).
cnf(136,plain,
( ~ empty(singleton(u))
| ~ equal(v,u) ),
inference(res,[status(thm),theory(equality)],[133,39]),
[iquote('0:Res:133.1,39.1')] ).
cnf(139,plain,
~ empty(singleton(u)),
inference(aed,[status(thm),theory(equality)],[136]),
[iquote('0:AED:136.1')] ).
cnf(144,plain,
( ~ in(u,singleton(v))
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[46]),
[iquote('0:EqR:46.1')] ).
cnf(147,plain,
( empty(singleton(u))
| equal(skf5(singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[110,144]),
[iquote('0:Res:110.1,144.0')] ).
cnf(150,plain,
equal(skf5(singleton(u)),u),
inference(mrr,[status(thm)],[147,139]),
[iquote('0:MRR:147.0,139.0')] ).
cnf(152,plain,
( empty(singleton(u))
| in(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[150,110]),
[iquote('0:SpR:150.0,110.1')] ).
cnf(156,plain,
in(u,singleton(u)),
inference(mrr,[status(thm)],[152,139]),
[iquote('0:MRR:152.0,139.0')] ).
cnf(165,plain,
( ~ in(u,singleton(v))
| ~ equal(w,succ(v))
| in(u,w) ),
inference(spl,[status(thm),theory(equality)],[35,49]),
[iquote('0:SpL:35.0,49.1')] ).
cnf(534,plain,
( ~ equal(u,succ(v))
| in(v,u) ),
inference(res,[status(thm),theory(equality)],[156,165]),
[iquote('0:Res:156.0,165.0')] ).
cnf(538,plain,
~ equal(u,succ(skc10)),
inference(mrr,[status(thm)],[127,534]),
[iquote('0:MRR:127.0,534.1')] ).
cnf(539,plain,
$false,
inference(obv,[status(thm),theory(equality)],[538]),
[iquote('0:Obv:538.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU230+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 20:03:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.49
% 0.20/0.49 SPASS V 3.9
% 0.20/0.49 SPASS beiseite: Proof found.
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.49 SPASS derived 450 clauses, backtracked 5 clauses, performed 1 splits and kept 273 clauses.
% 0.20/0.49 SPASS allocated 98029 KBytes.
% 0.20/0.49 SPASS spent 0:00:00.14 on the problem.
% 0.20/0.49 0:00:00.03 for the input.
% 0.20/0.49 0:00:00.04 for the FLOTTER CNF translation.
% 0.20/0.49 0:00:00.01 for inferences.
% 0.20/0.49 0:00:00.00 for the backtracking.
% 0.20/0.49 0:00:00.04 for the reduction.
% 0.20/0.49
% 0.20/0.49
% 0.20/0.49 Here is a proof with depth 4, length 24 :
% 0.20/0.49 % SZS output start Refutation
% See solution above
% 0.20/0.49 Formulae used in the proof : existence_m1_subset_1 t10_ordinal1 idempotence_k2_xboole_0 d1_ordinal1 t7_boole t2_subset d1_tarski t1_boole d2_xboole_0
% 0.20/0.49
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