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  
%------------------------------------------------------------------------------