TSTP Solution File: SET241-6 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET241-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n006.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 05:25:13 EDT 2022

% Result   : Unsatisfiable 1.06s 1.24s
% Output   : Refutation 1.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   16 (   8 unt;   3 nHn;  16 RR)
%            Number of literals    :   25 (   0 equ;   8 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   9 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    member(ordered_pair(u__dfg,v__dfg),restrict(xr,x__dfg,y__dfg)),
    file('SET241-6.p',unknown),
    [] ).

cnf(2,axiom,
    ~ member(v__dfg,y__dfg),
    file('SET241-6.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ member(u,v)
    | ~ subclass(v,w)
    | member(u,w) ),
    file('SET241-6.p',unknown),
    [] ).

cnf(4,axiom,
    ( subclass(u,v)
    | member(not_subclass_element(u,v),u) ),
    file('SET241-6.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ member(not_subclass_element(u,v),v)
    | subclass(u,v) ),
    file('SET241-6.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ member(ordered_pair(u,v),cross_product(w,x))
    | member(v,x) ),
    file('SET241-6.p',unknown),
    [] ).

cnf(24,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,w) ),
    file('SET241-6.p',unknown),
    [] ).

cnf(30,axiom,
    equal(intersection(u,cross_product(v,w)),restrict(u,v,w)),
    file('SET241-6.p',unknown),
    [] ).

cnf(123,plain,
    ~ member(ordered_pair(u,v__dfg),cross_product(v,y__dfg)),
    inference(res,[status(thm),theory(equality)],[17,2]),
    [iquote('0:Res:17.1,2.0')] ).

cnf(124,plain,
    ( ~ subclass(restrict(xr,x__dfg,y__dfg),u)
    | member(ordered_pair(u__dfg,v__dfg),u) ),
    inference(res,[status(thm),theory(equality)],[1,3]),
    [iquote('0:Res:1.0,3.1')] ).

cnf(182,plain,
    ( subclass(intersection(u,v),w)
    | member(not_subclass_element(intersection(u,v),w),v) ),
    inference(res,[status(thm),theory(equality)],[4,24]),
    [iquote('0:Res:4.1,24.0')] ).

cnf(4132,plain,
    ( subclass(intersection(u,v),v)
    | subclass(intersection(u,v),v) ),
    inference(res,[status(thm),theory(equality)],[182,5]),
    [iquote('0:Res:182.1,5.0')] ).

cnf(4134,plain,
    subclass(intersection(u,v),v),
    inference(obv,[status(thm),theory(equality)],[4132]),
    [iquote('0:Obv:4132.0')] ).

cnf(4153,plain,
    subclass(restrict(u,v,w),cross_product(v,w)),
    inference(spr,[status(thm),theory(equality)],[30,4134]),
    [iquote('0:SpR:30.0,4134.0')] ).

cnf(5107,plain,
    member(ordered_pair(u__dfg,v__dfg),cross_product(x__dfg,y__dfg)),
    inference(res,[status(thm),theory(equality)],[4153,124]),
    [iquote('0:Res:4153.0,124.0')] ).

cnf(5108,plain,
    $false,
    inference(mrr,[status(thm)],[5107,123]),
    [iquote('0:MRR:5107.0,123.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET241-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n006.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 : Mon Jul 11 10:35:50 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.06/1.24  
% 1.06/1.24  SPASS V 3.9 
% 1.06/1.24  SPASS beiseite: Proof found.
% 1.06/1.24  % SZS status Theorem
% 1.06/1.24  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 1.06/1.24  SPASS derived 4479 clauses, backtracked 138 clauses, performed 4 splits and kept 2127 clauses.
% 1.06/1.24  SPASS allocated 80307 KBytes.
% 1.06/1.24  SPASS spent	0:00:00.86 on the problem.
% 1.06/1.24  		0:00:00.04 for the input.
% 1.06/1.24  		0:00:00.00 for the FLOTTER CNF translation.
% 1.06/1.24  		0:00:00.07 for inferences.
% 1.06/1.24  		0:00:00.02 for the backtracking.
% 1.06/1.24  		0:00:00.68 for the reduction.
% 1.06/1.24  
% 1.06/1.24  
% 1.06/1.24  Here is a proof with depth 4, length 16 :
% 1.06/1.24  % SZS output start Refutation
% See solution above
% 1.06/1.24  Formulae used in the proof : prove_restriction_alternate_defn4_1 prove_restriction_alternate_defn4_2 subclass_members not_subclass_members1 not_subclass_members2 cartesian_product2 intersection2 restriction1
% 1.06/1.24  
%------------------------------------------------------------------------------