TSTP Solution File: SEU174+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU174+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 14:34:43 EDT 2022
% Result : Theorem 67.22s 67.41s
% Output : Refutation 67.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 27 ( 20 unt; 3 nHn; 27 RR)
% Number of literals : 40 ( 0 equ; 14 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
empty(skc64),
file('SEU174+2.p',unknown),
[] ).
cnf(3,axiom,
empty(skf44(u)),
file('SEU174+2.p',unknown),
[] ).
cnf(7,axiom,
~ equal(empty_set,skc4),
file('SEU174+2.p',unknown),
[] ).
cnf(13,axiom,
element(skc4,powerset(powerset(skc5))),
file('SEU174+2.p',unknown),
[] ).
cnf(14,axiom,
equal(complements_of_subsets(skc5,skc4),empty_set),
file('SEU174+2.p',unknown),
[] ).
cnf(21,axiom,
element(skf44(u),powerset(u)),
file('SEU174+2.p',unknown),
[] ).
cnf(33,axiom,
( ~ empty(u)
| equal(u,empty_set) ),
file('SEU174+2.p',unknown),
[] ).
cnf(52,axiom,
( ~ in(u,v)
| ~ equal(v,empty_set) ),
file('SEU174+2.p',unknown),
[] ).
cnf(146,axiom,
( ~ element(u,powerset(powerset(v)))
| equal(complements_of_subsets(v,complements_of_subsets(v,u)),u) ),
file('SEU174+2.p',unknown),
[] ).
cnf(197,axiom,
( ~ element(u,powerset(powerset(v)))
| ~ element(w,powerset(powerset(v)))
| equal(u,complements_of_subsets(v,w))
| in(subset_complement(v,skf40(w,u,v)),w)
| in(skf40(w,u,v),u) ),
file('SEU174+2.p',unknown),
[] ).
cnf(241,plain,
~ in(u,complements_of_subsets(skc5,skc4)),
inference(res,[status(thm),theory(equality)],[14,52]),
[iquote('0:Res:14.0,52.0')] ).
cnf(277,plain,
equal(complements_of_subsets(skc5,complements_of_subsets(skc5,skc4)),skc4),
inference(res,[status(thm),theory(equality)],[13,146]),
[iquote('0:Res:13.0,146.0')] ).
cnf(281,plain,
~ in(u,empty_set),
inference(rew,[status(thm),theory(equality)],[14,241]),
[iquote('0:Rew:14.0,241.0')] ).
cnf(288,plain,
equal(complements_of_subsets(skc5,empty_set),skc4),
inference(rew,[status(thm),theory(equality)],[14,277]),
[iquote('0:Rew:14.0,277.0')] ).
cnf(391,plain,
equal(skf44(u),empty_set),
inference(ems,[status(thm)],[33,3]),
[iquote('0:EmS:33.0,3.0')] ).
cnf(393,plain,
equal(empty_set,skc64),
inference(ems,[status(thm)],[33,2]),
[iquote('0:EmS:33.0,2.0')] ).
cnf(396,plain,
~ equal(skc64,skc4),
inference(rew,[status(thm),theory(equality)],[393,7]),
[iquote('0:Rew:393.0,7.0')] ).
cnf(397,plain,
~ in(u,skc64),
inference(rew,[status(thm),theory(equality)],[393,281]),
[iquote('0:Rew:393.0,281.0')] ).
cnf(400,plain,
equal(complements_of_subsets(skc5,skc64),skc4),
inference(rew,[status(thm),theory(equality)],[393,288]),
[iquote('0:Rew:393.0,288.0')] ).
cnf(445,plain,
equal(skf44(u),skc64),
inference(rew,[status(thm),theory(equality)],[393,391]),
[iquote('0:Rew:393.0,391.0')] ).
cnf(447,plain,
element(skc64,powerset(u)),
inference(rew,[status(thm),theory(equality)],[445,21]),
[iquote('0:Rew:445.0,21.0')] ).
cnf(7292,plain,
( ~ element(u,powerset(powerset(v)))
| equal(complements_of_subsets(v,u),skc64)
| in(subset_complement(v,skf40(u,skc64,v)),u)
| in(skf40(u,skc64,v),skc64) ),
inference(res,[status(thm),theory(equality)],[447,197]),
[iquote('0:Res:447.0,197.0')] ).
cnf(7304,plain,
( ~ element(u,powerset(powerset(v)))
| equal(complements_of_subsets(v,u),skc64)
| in(subset_complement(v,skf40(u,skc64,v)),u) ),
inference(mrr,[status(thm)],[7292,397]),
[iquote('0:MRR:7292.3,397.0')] ).
cnf(44431,plain,
( ~ element(skc64,powerset(powerset(u)))
| equal(complements_of_subsets(u,skc64),skc64) ),
inference(res,[status(thm),theory(equality)],[7304,397]),
[iquote('0:Res:7304.2,397.0')] ).
cnf(44494,plain,
equal(complements_of_subsets(u,skc64),skc64),
inference(mrr,[status(thm)],[44431,447]),
[iquote('0:MRR:44431.0,447.0')] ).
cnf(44495,plain,
equal(skc64,skc4),
inference(rew,[status(thm),theory(equality)],[44494,400]),
[iquote('0:Rew:44494.0,400.0')] ).
cnf(44499,plain,
$false,
inference(mrr,[status(thm)],[44495,396]),
[iquote('0:MRR:44495.0,396.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SEU174+2 : TPTP v8.1.0. Released v3.3.0.
% 0.09/0.11 % Command : run_spass %d %s
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Mon Jun 20 00:48:03 EDT 2022
% 0.11/0.31 % CPUTime :
% 67.22/67.41
% 67.22/67.41 SPASS V 3.9
% 67.22/67.41 SPASS beiseite: Proof found.
% 67.22/67.41 % SZS status Theorem
% 67.22/67.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 67.22/67.41 SPASS derived 38718 clauses, backtracked 429 clauses, performed 3 splits and kept 19840 clauses.
% 67.22/67.41 SPASS allocated 131517 KBytes.
% 67.22/67.41 SPASS spent 0:01:06.46 on the problem.
% 67.22/67.41 0:00:00.03 for the input.
% 67.22/67.41 0:00:00.27 for the FLOTTER CNF translation.
% 67.22/67.41 0:00:00.75 for inferences.
% 67.22/67.41 0:00:00.27 for the backtracking.
% 67.22/67.41 0:01:04.38 for the reduction.
% 67.22/67.41
% 67.22/67.41
% 67.22/67.41 Here is a proof with depth 2, length 27 :
% 67.22/67.41 % SZS output start Refutation
% See solution above
% 67.22/67.41 Formulae used in the proof : rc1_xboole_0 rc2_subset_1 t46_setfam_1 t6_boole d1_xboole_0 involutiveness_k7_setfam_1 d8_setfam_1 existence_m1_subset_1
% 67.22/67.41
%------------------------------------------------------------------------------