TSTP Solution File: SET825-1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET825-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n020.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 05:28:56 EDT 2022

% Result   : Unsatisfiable 2.98s 3.19s
% Output   : Refutation 2.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   14 (   7 unt;   3 nHn;  14 RR)
%            Number of literals    :   24 (   0 equ;   9 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   8 con; 0-4 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    v_Q(v_n),
    file('SET825-1.p',unknown),
    [] ).

cnf(2,axiom,
    ~ v_Q(v_m),
    file('SET825-1.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),u,tc_prod(tc_nat,tc_nat))
    | c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),u,tc_prod(tc_nat,tc_nat))
    | c_in(c_Pair(v_x(u),v_xa(u),tc_nat,tc_nat),u,tc_prod(tc_nat,tc_nat)) ),
    file('SET825-1.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),u,tc_prod(tc_nat,tc_nat))
    | ~ c_in(c_Pair(c_Suc(v_x(u)),c_Suc(v_xa(u)),tc_nat,tc_nat),u,tc_prod(tc_nat,tc_nat))
    | c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),u,tc_prod(tc_nat,tc_nat)) ),
    file('SET825-1.p',unknown),
    [] ).

cnf(130,axiom,
    c_in(c_Pair(u,u,v,v),c_Relation_OId,tc_prod(v,v)),
    file('SET825-1.p',unknown),
    [] ).

cnf(135,axiom,
    ( ~ c_in(c_Pair(u,v,w,w),c_Relation_OId,tc_prod(w,w))
    | equal(u,v) ),
    file('SET825-1.p',unknown),
    [] ).

cnf(1374,plain,
    ( ~ c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_xa(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
    | c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
    inference(res,[status(thm),theory(equality)],[130,4]),
    [iquote('0:Res:130.0,4.1')] ).

cnf(5010,plain,
    ( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
    | c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
    | equal(v_xa(c_Relation_OId),v_x(c_Relation_OId)) ),
    inference(res,[status(thm),theory(equality)],[3,135]),
    [iquote('0:Res:3.2,135.0')] ).

cnf(5026,plain,
    ( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
    | equal(v_xa(c_Relation_OId),v_x(c_Relation_OId)) ),
    inference(mrr,[status(thm)],[5010,130]),
    [iquote('0:MRR:5010.0,130.0')] ).

cnf(5028,plain,
    ( ~ c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_x(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
    | c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
    inference(rew,[status(thm),theory(equality)],[5026,1374]),
    [iquote('0:Rew:5026.1,1374.0')] ).

cnf(5029,plain,
    c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)),
    inference(mrr,[status(thm)],[5028,130]),
    [iquote('0:MRR:5028.0,130.0')] ).

cnf(5034,plain,
    equal(v_m,v_n),
    inference(res,[status(thm),theory(equality)],[5029,135]),
    [iquote('0:Res:5029.0,135.0')] ).

cnf(5040,plain,
    ~ v_Q(v_n),
    inference(rew,[status(thm),theory(equality)],[5034,2]),
    [iquote('0:Rew:5034.0,2.0')] ).

cnf(5075,plain,
    $false,
    inference(mrr,[status(thm)],[5040,1]),
    [iquote('0:MRR:5040.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET825-1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n020.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 03:52:58 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 2.98/3.19  
% 2.98/3.19  SPASS V 3.9 
% 2.98/3.19  SPASS beiseite: Proof found.
% 2.98/3.19  % SZS status Theorem
% 2.98/3.19  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 2.98/3.19  SPASS derived 3090 clauses, backtracked 24 clauses, performed 1 splits and kept 2945 clauses.
% 2.98/3.19  SPASS allocated 82836 KBytes.
% 2.98/3.19  SPASS spent	0:00:02.73 on the problem.
% 2.98/3.19  		0:00:00.09 for the input.
% 2.98/3.19  		0:00:00.00 for the FLOTTER CNF translation.
% 2.98/3.19  		0:00:00.19 for inferences.
% 2.98/3.19  		0:00:00.00 for the backtracking.
% 2.98/3.19  		0:00:02.15 for the reduction.
% 2.98/3.19  
% 2.98/3.19  
% 2.98/3.19  Here is a proof with depth 2, length 14 :
% 2.98/3.19  % SZS output start Refutation
% See solution above
% 2.98/3.19  Formulae used in the proof : cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3 cls_Relation_OIdI_0 cls_Relation_Opair__in__Id__conv__iff1_0
% 2.98/3.19  
%------------------------------------------------------------------------------