%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU308+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n026.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 14:36:07 EDT 2022

% Result   : Theorem 114.60s 114.83s
% Output   : Refutation 114.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   15 (   9 unt;   0 nHn;  15 RR)
%            Number of literals    :   24 (   0 equ;  14 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   5 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    one_sorted_str(skc30),
    file('SEU308+2.p',unknown),
    [] ).

cnf(130,axiom,
    equal(cast_to_subset(u),u),
    file('SEU308+2.p',unknown),
    [] ).

cnf(153,axiom,
    element(skc31,powerset(the_carrier(skc30))),
    file('SEU308+2.p',unknown),
    [] ).

cnf(180,axiom,
    element(cast_to_subset(u),powerset(u)),
    file('SEU308+2.p',unknown),
    [] ).

cnf(405,axiom,
    ( ~ one_sorted_str(u)
    | equal(cast_as_carrier_subset(u),the_carrier(u)) ),
    file('SEU308+2.p',unknown),
    [] ).

cnf(656,axiom,
    ~ equal(subset_difference(the_carrier(skc30),cast_as_carrier_subset(skc30),skc31),subset_complement(the_carrier(skc30),skc31)),
    file('SEU308+2.p',unknown),
    [] ).

cnf(667,axiom,
    ( ~ element(u,powerset(v))
    | equal(set_difference(v,u),subset_complement(v,u)) ),
    file('SEU308+2.p',unknown),
    [] ).

cnf(911,axiom,
    ( ~ element(u,powerset(v))
    | ~ element(w,powerset(v))
    | equal(subset_difference(v,w,u),set_difference(w,u)) ),
    file('SEU308+2.p',unknown),
    [] ).

cnf(1198,plain,
    element(u,powerset(u)),
    inference(rew,[status(thm),theory(equality)],[130,180]),
    [iquote('0:Rew:130.0,180.0')] ).

cnf(1325,plain,
    equal(cast_as_carrier_subset(skc30),the_carrier(skc30)),
    inference(res,[status(thm),theory(equality)],[1,405]),
    [iquote('0:Res:1.0,405.0')] ).

cnf(1457,plain,
    ~ equal(subset_difference(the_carrier(skc30),the_carrier(skc30),skc31),subset_complement(the_carrier(skc30),skc31)),
    inference(rew,[status(thm),theory(equality)],[1325,656]),
    [iquote('0:Rew:1325.0,656.0')] ).

cnf(29118,plain,
    ( ~ element(skc31,powerset(the_carrier(skc30)))
    | ~ element(the_carrier(skc30),powerset(the_carrier(skc30)))
    | ~ equal(set_difference(the_carrier(skc30),skc31),subset_complement(the_carrier(skc30),skc31)) ),
    inference(spl,[status(thm),theory(equality)],[911,1457]),
    [iquote('0:SpL:911.2,1457.0')] ).

cnf(29120,plain,
    ( ~ element(skc31,powerset(the_carrier(skc30)))
    | ~ element(the_carrier(skc30),powerset(the_carrier(skc30)))
    | ~ equal(subset_complement(the_carrier(skc30),skc31),subset_complement(the_carrier(skc30),skc31)) ),
    inference(rew,[status(thm),theory(equality)],[667,29118]),
    [iquote('0:Rew:667.1,29118.2')] ).

cnf(29121,plain,
    ( ~ element(skc31,powerset(the_carrier(skc30)))
    | ~ element(the_carrier(skc30),powerset(the_carrier(skc30))) ),
    inference(obv,[status(thm),theory(equality)],[29120]),
    [iquote('0:Obv:29120.2')] ).

cnf(29122,plain,
    $false,
    inference(mrr,[status(thm)],[29121,153,1198]),
    [iquote('0:MRR:29121.0,29121.1,153.0,1198.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SEU308+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n026.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Sun Jun 19 18:33:40 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 114.60/114.83  
% 114.60/114.83  SPASS V 3.9 
% 114.60/114.83  SPASS beiseite: Proof found.
% 114.60/114.83  % SZS status Theorem
% 114.60/114.83  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 114.60/114.83  SPASS derived 22455 clauses, backtracked 1558 clauses, performed 61 splits and kept 13985 clauses.
% 114.60/114.83  SPASS allocated 159962 KBytes.
% 114.60/114.83  SPASS spent	0:1:53.74 on the problem.
% 114.60/114.83  		0:00:00.04 for the input.
% 114.60/114.83  		0:1:29.51 for the FLOTTER CNF translation.
% 114.60/114.83  		0:00:00.44 for inferences.
% 114.60/114.83  		0:00:00.12 for the backtracking.
% 114.60/114.83  		0:0:22.74 for the reduction.
% 114.60/114.83  
% 114.60/114.83  
% 114.60/114.83  Here is a proof with depth 1, length 15 :
% 114.60/114.83  % SZS output start Refutation
% See solution above
% 114.60/114.83  Formulae used in the proof : t17_pre_topc d4_subset_1 dt_k2_subset_1 t12_pre_topc d5_subset_1 redefinition_k6_subset_1
% 114.60/114.83  
%------------------------------------------------------------------------------