TSTP Solution File: NUM386+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM386+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 : Mon Jul 18 14:25:48 EDT 2022
% Result : Theorem 3.73s 3.90s
% Output : Refutation 3.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of clauses : 40 ( 14 unt; 11 nHn; 40 RR)
% Number of literals : 78 ( 0 equ; 37 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(29,axiom,
element(skf5(u),u),
file('NUM386+1.p',unknown),
[] ).
cnf(37,axiom,
equal(set_union2(u,singleton(u)),succ(u)),
file('NUM386+1.p',unknown),
[] ).
cnf(41,axiom,
( ~ empty(u)
| ~ in(v,u) ),
file('NUM386+1.p',unknown),
[] ).
cnf(43,axiom,
( ~ in(skc12,skc13)
| ~ in(skc12,succ(skc13)) ),
file('NUM386+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ equal(skc13,skc12)
| ~ in(skc12,succ(skc13)) ),
file('NUM386+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ element(u,v)
| empty(v)
| in(u,v) ),
file('NUM386+1.p',unknown),
[] ).
cnf(47,axiom,
( equal(skc13,skc12)
| in(skc12,skc13)
| in(skc12,succ(skc13)) ),
file('NUM386+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ in(u,v)
| ~ equal(v,singleton(w))
| equal(u,w) ),
file('NUM386+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ equal(u,v)
| ~ equal(w,singleton(v))
| in(u,w) ),
file('NUM386+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ in(u,v)
| ~ equal(w,set_union2(v,x))
| in(u,w) ),
file('NUM386+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ in(u,v)
| ~ equal(w,set_union2(x,v))
| in(u,w) ),
file('NUM386+1.p',unknown),
[] ).
cnf(56,axiom,
( ~ in(u,v)
| ~ equal(v,set_union2(w,x))
| in(u,x)
| in(u,w) ),
file('NUM386+1.p',unknown),
[] ).
cnf(61,plain,
equal(skc13,skc12),
inference(spt,[spt(split,[position(s1)])],[47]),
[iquote('1:Spt:47.0')] ).
cnf(62,plain,
( ~ equal(skc12,skc12)
| ~ in(skc12,succ(skc13)) ),
inference(rew,[status(thm),theory(equality)],[61,44]),
[iquote('1:Rew:61.0,44.0')] ).
cnf(64,plain,
~ in(skc12,succ(skc13)),
inference(obv,[status(thm),theory(equality)],[62]),
[iquote('1:Obv:62.0')] ).
cnf(65,plain,
~ in(skc12,succ(skc12)),
inference(rew,[status(thm),theory(equality)],[61,64]),
[iquote('1:Rew:61.0,64.0')] ).
cnf(113,plain,
( empty(u)
| in(skf5(u),u) ),
inference(res,[status(thm),theory(equality)],[29,45]),
[iquote('0:Res:29.0,45.0')] ).
cnf(129,plain,
( ~ equal(u,v)
| in(u,singleton(v)) ),
inference(eqr,[status(thm),theory(equality)],[52]),
[iquote('0:EqR:52.1')] ).
cnf(132,plain,
( ~ empty(singleton(u))
| ~ equal(v,u) ),
inference(res,[status(thm),theory(equality)],[129,41]),
[iquote('0:Res:129.1,41.1')] ).
cnf(134,plain,
~ empty(singleton(u)),
inference(aed,[status(thm),theory(equality)],[132]),
[iquote('0:AED:132.1')] ).
cnf(135,plain,
( ~ in(u,singleton(v))
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[51]),
[iquote('0:EqR:51.1')] ).
cnf(141,plain,
( empty(singleton(u))
| equal(skf5(singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[113,135]),
[iquote('0:Res:113.1,135.0')] ).
cnf(144,plain,
equal(skf5(singleton(u)),u),
inference(mrr,[status(thm)],[141,134]),
[iquote('0:MRR:141.0,134.0')] ).
cnf(148,plain,
( ~ in(u,singleton(v))
| ~ equal(w,succ(v))
| in(u,w) ),
inference(spl,[status(thm),theory(equality)],[37,54]),
[iquote('0:SpL:37.0,54.1')] ).
cnf(154,plain,
( empty(singleton(u))
| in(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[144,113]),
[iquote('0:SpR:144.0,113.1')] ).
cnf(158,plain,
in(u,singleton(u)),
inference(mrr,[status(thm)],[154,134]),
[iquote('0:MRR:154.0,134.0')] ).
cnf(166,plain,
( ~ in(u,v)
| in(u,set_union2(v,w)) ),
inference(eqr,[status(thm),theory(equality)],[53]),
[iquote('0:EqR:53.1')] ).
cnf(196,plain,
( ~ in(u,set_union2(v,w))
| in(u,w)
| in(u,v) ),
inference(eqr,[status(thm),theory(equality)],[56]),
[iquote('0:EqR:56.1')] ).
cnf(304,plain,
( ~ in(u,v)
| in(u,succ(v)) ),
inference(spr,[status(thm),theory(equality)],[37,166]),
[iquote('0:SpR:37.0,166.1')] ).
cnf(396,plain,
( ~ in(u,succ(v))
| in(u,singleton(v))
| in(u,v) ),
inference(spl,[status(thm),theory(equality)],[37,196]),
[iquote('0:SpL:37.0,196.0')] ).
cnf(437,plain,
( ~ equal(u,succ(v))
| in(v,u) ),
inference(res,[status(thm),theory(equality)],[158,148]),
[iquote('0:Res:158.0,148.0')] ).
cnf(665,plain,
~ equal(succ(skc12),succ(skc12)),
inference(res,[status(thm),theory(equality)],[437,65]),
[iquote('1:Res:437.1,65.0')] ).
cnf(694,plain,
$false,
inference(obv,[status(thm),theory(equality)],[665]),
[iquote('1:Obv:665.0')] ).
cnf(695,plain,
~ equal(skc13,skc12),
inference(spt,[spt(split,[position(sa)])],[694,61]),
[iquote('1:Spt:694.0,47.0,61.0')] ).
cnf(696,plain,
( in(skc12,skc13)
| in(skc12,succ(skc13)) ),
inference(spt,[spt(split,[position(s2)])],[47]),
[iquote('1:Spt:694.0,47.1,47.2')] ).
cnf(697,plain,
in(skc12,succ(skc13)),
inference(mrr,[status(thm)],[696,304]),
[iquote('1:MRR:696.0,304.0')] ).
cnf(698,plain,
~ in(skc12,skc13),
inference(mrr,[status(thm)],[43,304]),
[iquote('0:MRR:43.1,304.1')] ).
cnf(1815,plain,
( ~ in(u,succ(v))
| in(u,v)
| equal(u,v) ),
inference(res,[status(thm),theory(equality)],[396,135]),
[iquote('0:Res:396.1,135.0')] ).
cnf(13496,plain,
( in(skc12,skc13)
| equal(skc13,skc12) ),
inference(res,[status(thm),theory(equality)],[697,1815]),
[iquote('1:Res:697.0,1815.0')] ).
cnf(13511,plain,
$false,
inference(mrr,[status(thm)],[13496,698,695]),
[iquote('1:MRR:13496.0,13496.1,698.0,695.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM386+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n020.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 : Thu Jul 7 06:44:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.73/3.90
% 3.73/3.90 SPASS V 3.9
% 3.73/3.90 SPASS beiseite: Proof found.
% 3.73/3.90 % SZS status Theorem
% 3.73/3.90 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.73/3.90 SPASS derived 11495 clauses, backtracked 22 clauses, performed 3 splits and kept 3215 clauses.
% 3.73/3.90 SPASS allocated 107763 KBytes.
% 3.73/3.90 SPASS spent 0:00:03.46 on the problem.
% 3.73/3.90 0:00:00.03 for the input.
% 3.73/3.90 0:00:00.04 for the FLOTTER CNF translation.
% 3.73/3.90 0:00:00.16 for inferences.
% 3.73/3.90 0:00:00.07 for the backtracking.
% 3.73/3.90 0:00:03.11 for the reduction.
% 3.73/3.90
% 3.73/3.90
% 3.73/3.90 Here is a proof with depth 5, length 40 :
% 3.73/3.90 % SZS output start Refutation
% See solution above
% 3.73/3.90 Formulae used in the proof : existence_m1_subset_1 d1_ordinal1 t7_boole t13_ordinal1 t2_subset d1_tarski t1_boole d2_xboole_0
% 3.73/3.90
%------------------------------------------------------------------------------