TSTP Solution File: SEU230+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU230+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 5.41s 5.66s
% Output : Refutation 5.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 24 ( 21 unt; 1 nHn; 24 RR)
% Number of literals : 27 ( 0 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(42,axiom,
~ in(skc10,succ(skc10)),
file('SEU230+2.p',unknown),
[] ).
cnf(51,axiom,
~ equal(singleton(u),empty_set),
file('SEU230+2.p',unknown),
[] ).
cnf(55,axiom,
equal(set_union2(u,empty_set),u),
file('SEU230+2.p',unknown),
[] ).
cnf(60,axiom,
equal(set_difference(empty_set,u),empty_set),
file('SEU230+2.p',unknown),
[] ).
cnf(78,axiom,
equal(set_union2(u,v),set_union2(v,u)),
file('SEU230+2.p',unknown),
[] ).
cnf(82,axiom,
equal(set_union2(u,singleton(u)),succ(u)),
file('SEU230+2.p',unknown),
[] ).
cnf(91,axiom,
( in(u,v)
| disjoint(singleton(u),v) ),
file('SEU230+2.p',unknown),
[] ).
cnf(150,axiom,
equal(set_union2(u,set_difference(v,u)),set_union2(u,v)),
file('SEU230+2.p',unknown),
[] ).
cnf(152,axiom,
equal(set_difference(set_union2(u,v),v),set_difference(u,v)),
file('SEU230+2.p',unknown),
[] ).
cnf(159,axiom,
( ~ disjoint(u,v)
| equal(set_difference(u,v),u) ),
file('SEU230+2.p',unknown),
[] ).
cnf(657,plain,
equal(set_union2(empty_set,u),u),
inference(spr,[status(thm),theory(equality)],[78,55]),
[iquote('0:SpR:78.0,55.0')] ).
cnf(1197,plain,
equal(set_difference(set_union2(u,v),u),set_difference(v,u)),
inference(spr,[status(thm),theory(equality)],[78,152]),
[iquote('0:SpR:78.0,152.0')] ).
cnf(1199,plain,
equal(set_difference(u,u),set_difference(empty_set,u)),
inference(spr,[status(thm),theory(equality)],[657,152]),
[iquote('0:SpR:657.0,152.0')] ).
cnf(1201,plain,
equal(set_difference(u,u),empty_set),
inference(rew,[status(thm),theory(equality)],[60,1199]),
[iquote('0:Rew:60.0,1199.0')] ).
cnf(1227,plain,
equal(set_union2(u,set_difference(v,u)),set_union2(u,set_union2(v,u))),
inference(spr,[status(thm),theory(equality)],[152,150]),
[iquote('0:SpR:152.0,150.0')] ).
cnf(1234,plain,
equal(set_union2(u,set_union2(v,u)),set_union2(u,v)),
inference(rew,[status(thm),theory(equality)],[150,1227]),
[iquote('0:Rew:150.0,1227.0')] ).
cnf(2758,plain,
equal(set_union2(singleton(u),succ(u)),set_union2(singleton(u),u)),
inference(spr,[status(thm),theory(equality)],[82,1234]),
[iquote('0:SpR:82.0,1234.0')] ).
cnf(2771,plain,
equal(set_union2(succ(u),singleton(u)),succ(u)),
inference(rew,[status(thm),theory(equality)],[78,2758,82]),
[iquote('0:Rew:78.0,2758.0,82.0,2758.0,78.0,2758.0')] ).
cnf(2780,plain,
equal(set_difference(singleton(u),succ(u)),set_difference(succ(u),succ(u))),
inference(spr,[status(thm),theory(equality)],[2771,1197]),
[iquote('0:SpR:2771.0,1197.0')] ).
cnf(2791,plain,
equal(set_difference(singleton(u),succ(u)),empty_set),
inference(rew,[status(thm),theory(equality)],[1201,2780]),
[iquote('0:Rew:1201.0,2780.0')] ).
cnf(2794,plain,
( ~ disjoint(singleton(u),succ(u))
| equal(singleton(u),empty_set) ),
inference(spr,[status(thm),theory(equality)],[2791,159]),
[iquote('0:SpR:2791.0,159.1')] ).
cnf(2804,plain,
~ disjoint(singleton(u),succ(u)),
inference(mrr,[status(thm)],[2794,51]),
[iquote('0:MRR:2794.1,51.0')] ).
cnf(2807,plain,
in(u,succ(u)),
inference(res,[status(thm),theory(equality)],[91,2804]),
[iquote('0:Res:91.1,2804.0')] ).
cnf(2820,plain,
$false,
inference(mrr,[status(thm)],[42,2807]),
[iquote('0:MRR:42.0,2807.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU230+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n023.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 : Mon Jun 20 12:17:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 5.41/5.66
% 5.41/5.66 SPASS V 3.9
% 5.41/5.66 SPASS beiseite: Proof found.
% 5.41/5.66 % SZS status Theorem
% 5.41/5.66 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.41/5.66 SPASS derived 2038 clauses, backtracked 39 clauses, performed 1 splits and kept 1121 clauses.
% 5.41/5.66 SPASS allocated 113458 KBytes.
% 5.41/5.66 SPASS spent 0:00:05.31 on the problem.
% 5.41/5.66 0:00:00.04 for the input.
% 5.41/5.66 0:00:04.92 for the FLOTTER CNF translation.
% 5.41/5.66 0:00:00.02 for inferences.
% 5.41/5.66 0:00:00.00 for the backtracking.
% 5.41/5.66 0:00:00.26 for the reduction.
% 5.41/5.66
% 5.41/5.66
% 5.41/5.66 Here is a proof with depth 5, length 24 :
% 5.41/5.66 % SZS output start Refutation
% See solution above
% 5.41/5.66 Formulae used in the proof : t10_ordinal1 l1_zfmisc_1 t1_boole t4_boole commutativity_k2_xboole_0 d1_ordinal1 l28_zfmisc_1 t39_xboole_1 t40_xboole_1 t83_xboole_1
% 5.41/5.66
%------------------------------------------------------------------------------