TSTP Solution File: SET993+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET993+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n028.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 05:30:17 EDT 2022

% Result   : Theorem 3.54s 3.76s
% Output   : Refutation 3.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   14
% Syntax   : Number of clauses     :   39 (   9 unt;  12 nHn;  39 RR)
%            Number of literals    :  104 (   0 equ;  56 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(19,axiom,
    ~ equal(skc8,empty_set),
    file('SET993+1.p',unknown),
    [] ).

cnf(20,axiom,
    element(skf13(u),u),
    file('SET993+1.p',unknown),
    [] ).

cnf(23,axiom,
    relation(skf16(u,v)),
    file('SET993+1.p',unknown),
    [] ).

cnf(24,axiom,
    function(skf16(u,v)),
    file('SET993+1.p',unknown),
    [] ).

cnf(34,axiom,
    equal(relation_dom(skf16(u,v)),v),
    file('SET993+1.p',unknown),
    [] ).

cnf(35,axiom,
    ( ~ empty(u)
    | equal(u,empty_set) ),
    file('SET993+1.p',unknown),
    [] ).

cnf(43,axiom,
    ( ~ element(u,v)
    | empty(v)
    | in(u,v) ),
    file('SET993+1.p',unknown),
    [] ).

cnf(45,axiom,
    ( ~ in(u,v)
    | equal(apply(skf16(w,v),u),w) ),
    file('SET993+1.p',unknown),
    [] ).

cnf(47,axiom,
    ( ~ in(u,v)
    | ~ equal(v,singleton(w))
    | equal(u,w) ),
    file('SET993+1.p',unknown),
    [] ).

cnf(48,axiom,
    ( ~ equal(u,v)
    | ~ equal(w,singleton(v))
    | in(u,w) ),
    file('SET993+1.p',unknown),
    [] ).

cnf(52,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | ~ equal(relation_dom(u),skc8)
    | ~ equal(relation_rng(u),singleton(skc9)) ),
    file('SET993+1.p',unknown),
    [] ).

cnf(53,axiom,
    ( ~ in(u,relation_dom(v))
    | ~ in(skf11(v,w),w)
    | ~ equal(skf11(v,w),apply(v,u)) ),
    file('SET993+1.p',unknown),
    [] ).

cnf(54,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | equal(v,relation_rng(u))
    | in(skf11(u,v),v)
    | in(skf12(u,w),relation_dom(u)) ),
    file('SET993+1.p',unknown),
    [] ).

cnf(57,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | equal(v,relation_rng(u))
    | in(skf11(u,v),v)
    | equal(apply(u,skf12(u,v)),skf11(u,v)) ),
    file('SET993+1.p',unknown),
    [] ).

cnf(59,plain,
    ~ empty(skc8),
    inference(res,[status(thm),theory(equality)],[35,19]),
    [iquote('0:Res:35.1,19.0')] ).

cnf(72,plain,
    ( ~ relation(skf16(u,skc8))
    | ~ function(skf16(u,skc8))
    | ~ equal(relation_rng(skf16(u,skc8)),singleton(skc9)) ),
    inference(res,[status(thm),theory(equality)],[34,52]),
    [iquote('0:Res:34.0,52.2')] ).

cnf(74,plain,
    ~ equal(relation_rng(skf16(u,skc8)),singleton(skc9)),
    inference(mrr,[status(thm)],[72,23,24]),
    [iquote('0:MRR:72.0,72.1,23.0,24.0')] ).

cnf(127,plain,
    ( empty(u)
    | in(skf13(u),u) ),
    inference(res,[status(thm),theory(equality)],[20,43]),
    [iquote('0:Res:20.0,43.0')] ).

cnf(176,plain,
    ( ~ in(u,singleton(v))
    | equal(u,v) ),
    inference(eqr,[status(thm),theory(equality)],[47]),
    [iquote('0:EqR:47.1')] ).

cnf(211,plain,
    ( ~ equal(u,v)
    | in(u,singleton(v)) ),
    inference(eqr,[status(thm),theory(equality)],[48]),
    [iquote('0:EqR:48.1')] ).

cnf(267,plain,
    ( ~ in(u,v)
    | ~ in(u,relation_dom(skf16(w,v)))
    | ~ in(skf11(skf16(w,v),x),x)
    | ~ equal(skf11(skf16(w,v),x),w) ),
    inference(spl,[status(thm),theory(equality)],[45,53]),
    [iquote('0:SpL:45.1,53.2')] ).

cnf(268,plain,
    ( ~ in(u,v)
    | ~ in(u,v)
    | ~ in(skf11(skf16(w,v),x),x)
    | ~ equal(skf11(skf16(w,v),x),w) ),
    inference(rew,[status(thm),theory(equality)],[34,267]),
    [iquote('0:Rew:34.0,267.1')] ).

cnf(269,plain,
    ( ~ in(u,v)
    | ~ in(skf11(skf16(w,v),x),x)
    | ~ equal(skf11(skf16(w,v),x),w) ),
    inference(obv,[status(thm),theory(equality)],[268]),
    [iquote('0:Obv:268.0')] ).

cnf(320,plain,
    ( ~ function(skf16(u,v))
    | ~ relation(skf16(u,v))
    | equal(w,relation_rng(skf16(u,v)))
    | in(skf11(skf16(u,v),w),w)
    | in(skf12(skf16(u,v),x),v) ),
    inference(spr,[status(thm),theory(equality)],[34,54]),
    [iquote('0:SpR:34.0,54.4')] ).

cnf(337,plain,
    ( equal(u,relation_rng(skf16(v,w)))
    | in(skf11(skf16(v,w),u),u)
    | in(skf12(skf16(v,w),x),w) ),
    inference(ssi,[status(thm)],[320,24,23]),
    [iquote('0:SSi:320.1,320.0,24.0,23.0,24.0,23.0')] ).

cnf(379,plain,
    ( ~ function(skf16(u,v))
    | ~ relation(skf16(u,v))
    | ~ in(skf12(skf16(u,v),w),v)
    | equal(w,relation_rng(skf16(u,v)))
    | in(skf11(skf16(u,v),w),w)
    | equal(skf11(skf16(u,v),w),u) ),
    inference(spr,[status(thm),theory(equality)],[57,45]),
    [iquote('0:SpR:57.4,45.1')] ).

cnf(389,plain,
    ( ~ in(skf12(skf16(u,v),w),v)
    | equal(w,relation_rng(skf16(u,v)))
    | in(skf11(skf16(u,v),w),w)
    | equal(skf11(skf16(u,v),w),u) ),
    inference(ssi,[status(thm)],[379,24,23]),
    [iquote('0:SSi:379.1,379.0,24.0,23.0,24.0,23.0')] ).

cnf(390,plain,
    ( equal(u,relation_rng(skf16(v,w)))
    | in(skf11(skf16(v,w),u),u)
    | equal(skf11(skf16(v,w),u),v) ),
    inference(mrr,[status(thm)],[389,337]),
    [iquote('0:MRR:389.0,337.2')] ).

cnf(849,plain,
    ( ~ equal(skf11(skf16(u,v),singleton(w)),w)
    | ~ in(x,v)
    | ~ equal(skf11(skf16(u,v),singleton(w)),u) ),
    inference(res,[status(thm),theory(equality)],[211,269]),
    [iquote('0:Res:211.1,269.1')] ).

cnf(939,plain,
    ( equal(singleton(u),relation_rng(skf16(v,w)))
    | equal(skf11(skf16(v,w),singleton(u)),v)
    | equal(skf11(skf16(v,w),singleton(u)),u) ),
    inference(res,[status(thm),theory(equality)],[390,176]),
    [iquote('0:Res:390.1,176.0')] ).

cnf(3243,plain,
    ( equal(relation_rng(skf16(u,v)),singleton(u))
    | equal(skf11(skf16(u,v),singleton(u)),u) ),
    inference(fac,[status(thm)],[939]),
    [iquote('0:Fac:939.1,939.2')] ).

cnf(9450,plain,
    ( ~ equal(u,u)
    | ~ in(v,w)
    | ~ equal(skf11(skf16(u,w),singleton(u)),u)
    | equal(relation_rng(skf16(u,w)),singleton(u)) ),
    inference(spl,[status(thm),theory(equality)],[3243,849]),
    [iquote('0:SpL:3243.1,849.0')] ).

cnf(9453,plain,
    ( ~ in(u,v)
    | ~ equal(skf11(skf16(w,v),singleton(w)),w)
    | equal(relation_rng(skf16(w,v)),singleton(w)) ),
    inference(obv,[status(thm),theory(equality)],[9450]),
    [iquote('0:Obv:9450.0')] ).

cnf(9454,plain,
    ( ~ in(u,v)
    | ~ equal(w,w)
    | equal(relation_rng(skf16(w,v)),singleton(w)) ),
    inference(rew,[status(thm),theory(equality)],[3243,9453]),
    [iquote('0:Rew:3243.1,9453.1')] ).

cnf(9455,plain,
    ( ~ in(u,v)
    | equal(relation_rng(skf16(w,v)),singleton(w)) ),
    inference(obv,[status(thm),theory(equality)],[9454]),
    [iquote('0:Obv:9454.1')] ).

cnf(9777,plain,
    ( empty(u)
    | equal(relation_rng(skf16(v,u)),singleton(v)) ),
    inference(res,[status(thm),theory(equality)],[127,9455]),
    [iquote('0:Res:127.1,9455.0')] ).

cnf(10455,plain,
    ( ~ equal(singleton(u),singleton(skc9))
    | empty(skc8) ),
    inference(spl,[status(thm),theory(equality)],[9777,74]),
    [iquote('0:SpL:9777.1,74.0')] ).

cnf(10457,plain,
    ~ equal(singleton(u),singleton(skc9)),
    inference(mrr,[status(thm)],[10455,59]),
    [iquote('0:MRR:10455.1,59.0')] ).

cnf(10470,plain,
    $false,
    inference(eqr,[status(thm),theory(equality)],[10457]),
    [iquote('0:EqR:10457.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : SET993+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.15  % Command  : run_spass %d %s
% 0.16/0.36  % Computer : n028.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 600
% 0.16/0.36  % DateTime : Sun Jul 10 03:25:57 EDT 2022
% 0.16/0.36  % CPUTime  : 
% 3.54/3.76  
% 3.54/3.76  SPASS V 3.9 
% 3.54/3.76  SPASS beiseite: Proof found.
% 3.54/3.76  % SZS status Theorem
% 3.54/3.76  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 3.54/3.76  SPASS derived 8032 clauses, backtracked 0 clauses, performed 3 splits and kept 2927 clauses.
% 3.54/3.76  SPASS allocated 107012 KBytes.
% 3.54/3.76  SPASS spent	0:00:03.28 on the problem.
% 3.54/3.76  		0:00:00.03 for the input.
% 3.54/3.76  		0:00:00.04 for the FLOTTER CNF translation.
% 3.54/3.76  		0:00:00.15 for inferences.
% 3.54/3.76  		0:00:00.13 for the backtracking.
% 3.54/3.76  		0:00:02.85 for the reduction.
% 3.54/3.76  
% 3.54/3.76  
% 3.54/3.76  Here is a proof with depth 7, length 39 :
% 3.54/3.76  % SZS output start Refutation
% See solution above
% 3.54/3.76  Formulae used in the proof : t15_funct_1 existence_m1_subset_1 s3_funct_1__e2_13__funct_1 t6_boole t2_subset d1_tarski antisymmetry_r2_hidden d5_funct_1
% 3.54/3.76  
%------------------------------------------------------------------------------