%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU307+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n007.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 14:36:06 EDT 2022

% Result   : Theorem 0.20s 0.51s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   20 (  12 unt;   0 nHn;  20 RR)
%            Number of literals    :   30 (   0 equ;  16 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    one_sorted_str(skc4),
    file('SEU307+1.p',unknown),
    [] ).

cnf(19,axiom,
    element(skc5,powerset(the_carrier(skc4))),
    file('SEU307+1.p',unknown),
    [] ).

cnf(69,axiom,
    ( ~ element(u,powerset(v))
    | subset(u,v) ),
    file('SEU307+1.p',unknown),
    [] ).

cnf(71,axiom,
    ( ~ one_sorted_str(u)
    | equal(the_carrier(u),cast_as_carrier_subset(u)) ),
    file('SEU307+1.p',unknown),
    [] ).

cnf(72,axiom,
    ~ equal(subset_intersection2(the_carrier(skc4),skc5,cast_as_carrier_subset(skc4)),skc5),
    file('SEU307+1.p',unknown),
    [] ).

cnf(90,axiom,
    ( ~ one_sorted_str(u)
    | element(cast_as_carrier_subset(u),powerset(the_carrier(u))) ),
    file('SEU307+1.p',unknown),
    [] ).

cnf(91,axiom,
    ( ~ subset(u,v)
    | equal(set_intersection2(u,v),u) ),
    file('SEU307+1.p',unknown),
    [] ).

cnf(111,axiom,
    ( ~ element(u,powerset(v))
    | ~ element(w,powerset(v))
    | equal(subset_intersection2(v,w,u),set_intersection2(w,u)) ),
    file('SEU307+1.p',unknown),
    [] ).

cnf(113,plain,
    ( ~ one_sorted_str(u)
    | element(cast_as_carrier_subset(u),powerset(cast_as_carrier_subset(u))) ),
    inference(rew,[status(thm),theory(equality)],[71,90]),
    [iquote('0:Rew:71.1,90.1')] ).

cnf(116,plain,
    element(cast_as_carrier_subset(skc4),powerset(cast_as_carrier_subset(skc4))),
    inference(res,[status(thm),theory(equality)],[1,113]),
    [iquote('0:Res:1.0,113.0')] ).

cnf(117,plain,
    equal(the_carrier(skc4),cast_as_carrier_subset(skc4)),
    inference(res,[status(thm),theory(equality)],[1,71]),
    [iquote('0:Res:1.0,71.0')] ).

cnf(152,plain,
    subset(skc5,the_carrier(skc4)),
    inference(res,[status(thm),theory(equality)],[19,69]),
    [iquote('0:Res:19.0,69.0')] ).

cnf(159,plain,
    element(skc5,powerset(cast_as_carrier_subset(skc4))),
    inference(rew,[status(thm),theory(equality)],[117,19]),
    [iquote('0:Rew:117.0,19.0')] ).

cnf(160,plain,
    ~ equal(subset_intersection2(cast_as_carrier_subset(skc4),skc5,cast_as_carrier_subset(skc4)),skc5),
    inference(rew,[status(thm),theory(equality)],[117,72]),
    [iquote('0:Rew:117.0,72.0')] ).

cnf(161,plain,
    subset(skc5,cast_as_carrier_subset(skc4)),
    inference(rew,[status(thm),theory(equality)],[117,152]),
    [iquote('0:Rew:117.0,152.0')] ).

cnf(1034,plain,
    ( ~ element(cast_as_carrier_subset(skc4),powerset(cast_as_carrier_subset(skc4)))
    | ~ element(skc5,powerset(cast_as_carrier_subset(skc4)))
    | ~ equal(set_intersection2(skc5,cast_as_carrier_subset(skc4)),skc5) ),
    inference(spl,[status(thm),theory(equality)],[111,160]),
    [iquote('0:SpL:111.2,160.0')] ).

cnf(1036,plain,
    ~ equal(set_intersection2(skc5,cast_as_carrier_subset(skc4)),skc5),
    inference(mrr,[status(thm)],[1034,116,159]),
    [iquote('0:MRR:1034.0,1034.1,116.0,159.0')] ).

cnf(1038,plain,
    ( ~ subset(skc5,cast_as_carrier_subset(skc4))
    | ~ equal(skc5,skc5) ),
    inference(spl,[status(thm),theory(equality)],[91,1036]),
    [iquote('0:SpL:91.1,1036.0')] ).

cnf(1039,plain,
    ~ subset(skc5,cast_as_carrier_subset(skc4)),
    inference(obv,[status(thm),theory(equality)],[1038]),
    [iquote('0:Obv:1038.1')] ).

cnf(1040,plain,
    $false,
    inference(mrr,[status(thm)],[1039,161]),
    [iquote('0:MRR:1039.0,161.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SEU307+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n007.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 10:35:29 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.51  
% 0.20/0.51  SPASS V 3.9 
% 0.20/0.51  SPASS beiseite: Proof found.
% 0.20/0.51  % SZS status Theorem
% 0.20/0.51  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.51  SPASS derived 907 clauses, backtracked 0 clauses, performed 0 splits and kept 470 clauses.
% 0.20/0.51  SPASS allocated 98212 KBytes.
% 0.20/0.51  SPASS spent	0:00:00.15 on the problem.
% 0.20/0.51  		0:00:00.04 for the input.
% 0.20/0.51  		0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.51  		0:00:00.01 for inferences.
% 0.20/0.51  		0:00:00.00 for the backtracking.
% 0.20/0.51  		0:00:00.04 for the reduction.
% 0.20/0.51  
% 0.20/0.51  
% 0.20/0.51  Here is a proof with depth 2, length 20 :
% 0.20/0.51  % SZS output start Refutation
% See solution above
% 0.20/0.51  Formulae used in the proof : t15_pre_topc t3_subset d3_pre_topc dt_k2_pre_topc t28_xboole_1 redefinition_k5_subset_1
% 0.20/0.51  
%------------------------------------------------------------------------------