TSTP Solution File: SEU108+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU108+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 14:34:00 EDT 2022
% Result : Theorem 0.80s 1.02s
% Output : Refutation 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 21
% Syntax : Number of clauses : 46 ( 12 unt; 8 nHn; 46 RR)
% Number of literals : 100 ( 0 equ; 53 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(10,axiom,
empty(skf10(u)),
file('SEU108+1.p',unknown),
[] ).
cnf(22,axiom,
~ preboolean(powerset(skc5)),
file('SEU108+1.p',unknown),
[] ).
cnf(24,axiom,
~ empty(powerset(u)),
file('SEU108+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ preboolean(u)
| cup_closed(u) ),
file('SEU108+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ preboolean(u)
| diff_closed(u) ),
file('SEU108+1.p',unknown),
[] ).
cnf(30,axiom,
element(skf10(u),powerset(u)),
file('SEU108+1.p',unknown),
[] ).
cnf(42,axiom,
( preboolean(u)
| in(skf15(u),u) ),
file('SEU108+1.p',unknown),
[] ).
cnf(43,axiom,
( preboolean(u)
| in(skf14(u),u) ),
file('SEU108+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ empty(u)
| equal(u,empty_set) ),
file('SEU108+1.p',unknown),
[] ).
cnf(45,axiom,
equal(set_union2(u,v),set_union2(v,u)),
file('SEU108+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ in(u,v)
| element(u,v) ),
file('SEU108+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ empty(u)
| ~ in(v,u) ),
file('SEU108+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ diff_closed(u)
| ~ cup_closed(u)
| preboolean(u) ),
file('SEU108+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ element(u,powerset(v))
| subset(u,v) ),
file('SEU108+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ subset(u,v)
| element(u,powerset(v)) ),
file('SEU108+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ element(u,v)
| empty(v)
| in(u,v) ),
file('SEU108+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ element(u,powerset(v))
| ~ element(w,powerset(v))
| element(subset_union2(v,u,w),powerset(v)) ),
file('SEU108+1.p',unknown),
[] ).
cnf(65,axiom,
( ~ element(u,powerset(v))
| ~ element(w,powerset(v))
| element(subset_difference(v,u,w),powerset(v)) ),
file('SEU108+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ element(u,powerset(v))
| ~ element(w,powerset(v))
| equal(subset_union2(v,w,u),set_union2(w,u)) ),
file('SEU108+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ element(u,powerset(v))
| ~ element(w,powerset(v))
| equal(subset_difference(v,w,u),set_difference(w,u)) ),
file('SEU108+1.p',unknown),
[] ).
cnf(68,axiom,
( ~ in(set_union2(skf15(u),skf14(u)),u)
| ~ in(set_difference(skf15(u),skf14(u)),u)
| preboolean(u) ),
file('SEU108+1.p',unknown),
[] ).
cnf(70,plain,
( ~ in(set_difference(skf15(u),skf14(u)),u)
| ~ in(set_union2(skf14(u),skf15(u)),u)
| preboolean(u) ),
inference(rew,[status(thm),theory(equality)],[45,68]),
[iquote('0:Rew:45.0,68.0')] ).
cnf(71,plain,
( ~ element(u,powerset(v))
| ~ element(w,powerset(v))
| element(set_difference(w,u),powerset(v)) ),
inference(rew,[status(thm),theory(equality)],[67,65]),
[iquote('0:Rew:67.2,65.2')] ).
cnf(72,plain,
( ~ element(u,powerset(v))
| ~ element(w,powerset(v))
| element(set_union2(w,u),powerset(v)) ),
inference(rew,[status(thm),theory(equality)],[66,64]),
[iquote('0:Rew:66.2,64.2')] ).
cnf(75,plain,
( ~ diff_closed(powerset(skc5))
| ~ cup_closed(powerset(skc5)) ),
inference(res,[status(thm),theory(equality)],[52,22]),
[iquote('0:Res:52.2,22.0')] ).
cnf(84,plain,
equal(skf10(u),empty_set),
inference(ems,[status(thm)],[44,10]),
[iquote('0:EmS:44.0,10.0')] ).
cnf(98,plain,
element(empty_set,powerset(u)),
inference(rew,[status(thm),theory(equality)],[84,30]),
[iquote('0:Rew:84.0,30.0')] ).
cnf(132,plain,
( ~ preboolean(powerset(skc5))
| ~ preboolean(powerset(skc5)) ),
inference(sor,[status(thm)],[75,27,26]),
[iquote('0:SoR:75.0,75.1,27.1,26.1')] ).
cnf(133,plain,
~ preboolean(powerset(skc5)),
inference(obv,[status(thm),theory(equality)],[132]),
[iquote('0:Obv:132.0')] ).
cnf(142,plain,
( ~ in(u,powerset(v))
| subset(u,v) ),
inference(res,[status(thm),theory(equality)],[49,53]),
[iquote('0:Res:49.1,53.0')] ).
cnf(146,plain,
( preboolean(powerset(u))
| subset(skf14(powerset(u)),u) ),
inference(res,[status(thm),theory(equality)],[43,142]),
[iquote('0:Res:43.1,142.0')] ).
cnf(147,plain,
( preboolean(powerset(u))
| subset(skf15(powerset(u)),u) ),
inference(res,[status(thm),theory(equality)],[42,142]),
[iquote('0:Res:42.1,142.0')] ).
cnf(153,plain,
( empty(powerset(u))
| in(empty_set,powerset(u)) ),
inference(res,[status(thm),theory(equality)],[98,55]),
[iquote('0:Res:98.0,55.0')] ).
cnf(156,plain,
in(empty_set,powerset(u)),
inference(mrr,[status(thm)],[153,24]),
[iquote('0:MRR:153.0,24.0')] ).
cnf(161,plain,
~ empty(powerset(u)),
inference(res,[status(thm),theory(equality)],[156,50]),
[iquote('0:Res:156.0,50.1')] ).
cnf(226,plain,
( ~ element(u,powerset(v))
| ~ element(w,powerset(v))
| empty(powerset(v))
| in(set_difference(w,u),powerset(v)) ),
inference(res,[status(thm),theory(equality)],[71,55]),
[iquote('0:Res:71.2,55.0')] ).
cnf(228,plain,
( ~ element(u,powerset(v))
| ~ element(w,powerset(v))
| in(set_difference(w,u),powerset(v)) ),
inference(mrr,[status(thm)],[226,161]),
[iquote('0:MRR:226.2,161.0')] ).
cnf(259,plain,
( ~ element(u,powerset(v))
| ~ element(w,powerset(v))
| empty(powerset(v))
| in(set_union2(w,u),powerset(v)) ),
inference(res,[status(thm),theory(equality)],[72,55]),
[iquote('0:Res:72.2,55.0')] ).
cnf(261,plain,
( ~ element(u,powerset(v))
| ~ element(w,powerset(v))
| in(set_union2(w,u),powerset(v)) ),
inference(mrr,[status(thm)],[259,161]),
[iquote('0:MRR:259.2,161.0')] ).
cnf(806,plain,
( ~ element(skf14(powerset(u)),powerset(u))
| ~ element(skf15(powerset(u)),powerset(u))
| ~ in(set_union2(skf14(powerset(u)),skf15(powerset(u))),powerset(u))
| preboolean(powerset(u)) ),
inference(res,[status(thm),theory(equality)],[228,70]),
[iquote('0:Res:228.2,70.0')] ).
cnf(815,plain,
( ~ element(skf14(powerset(u)),powerset(u))
| ~ element(skf15(powerset(u)),powerset(u))
| preboolean(powerset(u)) ),
inference(mrr,[status(thm)],[806,261]),
[iquote('0:MRR:806.2,261.2')] ).
cnf(1736,plain,
( ~ subset(skf15(powerset(u)),u)
| ~ element(skf14(powerset(u)),powerset(u))
| preboolean(powerset(u)) ),
inference(res,[status(thm),theory(equality)],[54,815]),
[iquote('0:Res:54.1,815.1')] ).
cnf(1737,plain,
( ~ element(skf14(powerset(u)),powerset(u))
| preboolean(powerset(u)) ),
inference(mrr,[status(thm)],[1736,147]),
[iquote('0:MRR:1736.0,147.1')] ).
cnf(3330,plain,
( ~ subset(skf14(powerset(u)),u)
| preboolean(powerset(u)) ),
inference(res,[status(thm),theory(equality)],[54,1737]),
[iquote('0:Res:54.1,1737.0')] ).
cnf(3331,plain,
preboolean(powerset(u)),
inference(mrr,[status(thm)],[3330,146]),
[iquote('0:MRR:3330.0,146.1')] ).
cnf(3332,plain,
$false,
inference(unc,[status(thm)],[3331,133]),
[iquote('0:UnC:3331.0,133.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU108+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n028.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 : Sun Jun 19 08:07:00 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.80/1.02
% 0.80/1.02 SPASS V 3.9
% 0.80/1.02 SPASS beiseite: Proof found.
% 0.80/1.02 % SZS status Theorem
% 0.80/1.02 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.80/1.02 SPASS derived 2768 clauses, backtracked 0 clauses, performed 0 splits and kept 1645 clauses.
% 0.80/1.02 SPASS allocated 100543 KBytes.
% 0.80/1.02 SPASS spent 0:00:00.65 on the problem.
% 0.80/1.02 0:00:00.04 for the input.
% 0.80/1.02 0:00:00.04 for the FLOTTER CNF translation.
% 0.80/1.02 0:00:00.04 for inferences.
% 0.80/1.02 0:00:00.00 for the backtracking.
% 0.80/1.02 0:00:00.49 for the reduction.
% 0.80/1.02
% 0.80/1.02
% 0.80/1.02 Here is a proof with depth 4, length 46 :
% 0.80/1.02 % SZS output start Refutation
% See solution above
% 0.80/1.02 Formulae used in the proof : rc2_finset_1 t20_finsub_1 fc1_subset_1 cc1_finsub_1 t10_finsub_1 t6_boole commutativity_k2_xboole_0 t1_subset t7_boole cc2_finsub_1 t3_subset t2_subset dt_k4_subset_1 dt_k6_subset_1 redefinition_k4_subset_1 redefinition_k6_subset_1
% 0.80/1.02
%------------------------------------------------------------------------------