TSTP Solution File: SEU327+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU327+1 : 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 14:36:18 EDT 2022
% Result : Theorem 0.43s 0.58s
% Output : Refutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of clauses : 27 ( 15 unt; 3 nHn; 27 RR)
% Number of literals : 44 ( 0 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(15,axiom,
~ equal(skc3,empty_set),
file('SEU327+1.p',unknown),
[] ).
cnf(16,axiom,
equal(cast_to_subset(u),u),
file('SEU327+1.p',unknown),
[] ).
cnf(19,axiom,
element(skc3,powerset(powerset(skc4))),
file('SEU327+1.p',unknown),
[] ).
cnf(29,axiom,
element(cast_to_subset(u),powerset(u)),
file('SEU327+1.p',unknown),
[] ).
cnf(89,axiom,
~ equal(meet_of_subsets(skc4,complements_of_subsets(skc4,skc3)),subset_complement(skc4,union_of_subsets(skc4,skc3))),
file('SEU327+1.p',unknown),
[] ).
cnf(90,axiom,
( ~ element(u,powerset(v))
| equal(set_difference(v,u),subset_complement(v,u)) ),
file('SEU327+1.p',unknown),
[] ).
cnf(91,axiom,
( ~ element(u,powerset(powerset(v)))
| element(union_of_subsets(v,u),powerset(v)) ),
file('SEU327+1.p',unknown),
[] ).
cnf(94,axiom,
( ~ element(u,powerset(powerset(v)))
| equal(union_of_subsets(v,u),union(u)) ),
file('SEU327+1.p',unknown),
[] ).
cnf(95,axiom,
( ~ element(u,powerset(powerset(v)))
| equal(meet_of_subsets(v,u),set_meet(u)) ),
file('SEU327+1.p',unknown),
[] ).
cnf(98,axiom,
( ~ element(u,powerset(powerset(v)))
| element(complements_of_subsets(v,u),powerset(powerset(v))) ),
file('SEU327+1.p',unknown),
[] ).
cnf(101,axiom,
( ~ element(u,powerset(v))
| ~ element(w,powerset(v))
| equal(subset_difference(v,w,u),set_difference(w,u)) ),
file('SEU327+1.p',unknown),
[] ).
cnf(102,axiom,
( ~ element(u,powerset(powerset(v)))
| equal(subset_difference(v,cast_to_subset(v),union_of_subsets(v,u)),meet_of_subsets(v,complements_of_subsets(v,u)))
| equal(u,empty_set) ),
file('SEU327+1.p',unknown),
[] ).
cnf(103,plain,
element(u,powerset(u)),
inference(rew,[status(thm),theory(equality)],[16,29]),
[iquote('0:Rew:16.0,29.0')] ).
cnf(105,plain,
( ~ element(u,powerset(powerset(v)))
| element(union(u),powerset(v)) ),
inference(rew,[status(thm),theory(equality)],[94,91]),
[iquote('0:Rew:94.1,91.1')] ).
cnf(107,plain,
( ~ element(u,powerset(powerset(v)))
| equal(u,empty_set)
| equal(subset_difference(v,v,union(u)),meet_of_subsets(v,complements_of_subsets(v,u))) ),
inference(rew,[status(thm),theory(equality)],[16,102,94]),
[iquote('0:Rew:16.0,102.1,94.1,102.1')] ).
cnf(153,plain,
( equal(subset_difference(skc4,skc4,union(skc3)),meet_of_subsets(skc4,complements_of_subsets(skc4,skc3)))
| equal(skc3,empty_set) ),
inference(res,[status(thm),theory(equality)],[19,107]),
[iquote('0:Res:19.0,107.0')] ).
cnf(154,plain,
element(complements_of_subsets(skc4,skc3),powerset(powerset(skc4))),
inference(res,[status(thm),theory(equality)],[19,98]),
[iquote('0:Res:19.0,98.0')] ).
cnf(156,plain,
element(union(skc3),powerset(skc4)),
inference(res,[status(thm),theory(equality)],[19,105]),
[iquote('0:Res:19.0,105.0')] ).
cnf(158,plain,
equal(union_of_subsets(skc4,skc3),union(skc3)),
inference(res,[status(thm),theory(equality)],[19,94]),
[iquote('0:Res:19.0,94.0')] ).
cnf(162,plain,
~ equal(meet_of_subsets(skc4,complements_of_subsets(skc4,skc3)),subset_complement(skc4,union(skc3))),
inference(rew,[status(thm),theory(equality)],[158,89]),
[iquote('0:Rew:158.0,89.0')] ).
cnf(164,plain,
equal(subset_difference(skc4,skc4,union(skc3)),meet_of_subsets(skc4,complements_of_subsets(skc4,skc3))),
inference(mrr,[status(thm)],[153,15]),
[iquote('0:MRR:153.1,15.0')] ).
cnf(1012,plain,
equal(meet_of_subsets(skc4,complements_of_subsets(skc4,skc3)),set_meet(complements_of_subsets(skc4,skc3))),
inference(res,[status(thm),theory(equality)],[154,95]),
[iquote('0:Res:154.0,95.0')] ).
cnf(1020,plain,
~ equal(subset_complement(skc4,union(skc3)),set_meet(complements_of_subsets(skc4,skc3))),
inference(rew,[status(thm),theory(equality)],[1012,162]),
[iquote('0:Rew:1012.0,162.0')] ).
cnf(1021,plain,
equal(subset_difference(skc4,skc4,union(skc3)),set_meet(complements_of_subsets(skc4,skc3))),
inference(rew,[status(thm),theory(equality)],[1012,164]),
[iquote('0:Rew:1012.0,164.0')] ).
cnf(2566,plain,
( ~ element(union(skc3),powerset(skc4))
| ~ element(skc4,powerset(skc4))
| equal(set_difference(skc4,union(skc3)),set_meet(complements_of_subsets(skc4,skc3))) ),
inference(spr,[status(thm),theory(equality)],[1021,101]),
[iquote('0:SpR:1021.0,101.2')] ).
cnf(2569,plain,
( ~ element(union(skc3),powerset(skc4))
| ~ element(skc4,powerset(skc4))
| equal(subset_complement(skc4,union(skc3)),set_meet(complements_of_subsets(skc4,skc3))) ),
inference(rew,[status(thm),theory(equality)],[90,2566]),
[iquote('0:Rew:90.1,2566.2')] ).
cnf(2570,plain,
$false,
inference(mrr,[status(thm)],[2569,156,103,1020]),
[iquote('0:MRR:2569.0,2569.1,2569.2,156.0,103.0,1020.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU327+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n023.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 11:06:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.43/0.58
% 0.43/0.58 SPASS V 3.9
% 0.43/0.58 SPASS beiseite: Proof found.
% 0.43/0.58 % SZS status Theorem
% 0.43/0.58 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.43/0.58 SPASS derived 2350 clauses, backtracked 86 clauses, performed 2 splits and kept 1131 clauses.
% 0.43/0.58 SPASS allocated 99015 KBytes.
% 0.43/0.58 SPASS spent 0:00:00.22 on the problem.
% 0.43/0.58 0:00:00.04 for the input.
% 0.43/0.58 0:00:00.03 for the FLOTTER CNF translation.
% 0.43/0.58 0:00:00.02 for inferences.
% 0.43/0.58 0:00:00.00 for the backtracking.
% 0.43/0.58 0:00:00.10 for the reduction.
% 0.43/0.58
% 0.43/0.58
% 0.43/0.58 Here is a proof with depth 2, length 27 :
% 0.43/0.58 % SZS output start Refutation
% See solution above
% 0.43/0.59 Formulae used in the proof : t11_tops_2 d4_subset_1 dt_k2_subset_1 d5_subset_1 dt_k5_setfam_1 redefinition_k5_setfam_1 redefinition_k6_setfam_1 dt_k7_setfam_1 redefinition_k6_subset_1 t47_setfam_1
% 0.43/0.59
%------------------------------------------------------------------------------