%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWV371+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n029.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 : Wed Jul 20 21:42:33 EDT 2022

% Result   : Theorem 0.20s 0.46s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   13 (   7 unt;   0 nHn;  13 RR)
%            Number of literals    :   20 (   0 equ;  10 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(13,axiom,
    equal(findmin_cpq_res(u),removemin_cpq_res(u)),
    file('SWV371+1.p',unknown),
    [] ).

cnf(14,axiom,
    phi(findmin_cpq_eff(triple(skc3,skc4,skc5))),
    file('SWV371+1.p',unknown),
    [] ).

cnf(59,axiom,
    ( ~ issmallestelement_pq(u,v)
    | ~ contains_pq(u,v)
    | pi_sharp_find_min(u,v) ),
    file('SWV371+1.p',unknown),
    [] ).

cnf(61,axiom,
    ~ pi_sharp_find_min(i(triple(skc3,skc4,skc5)),findmin_cpq_res(triple(skc3,skc4,skc5))),
    file('SWV371+1.p',unknown),
    [] ).

cnf(77,axiom,
    ( ~ phi(findmin_cpq_eff(triple(u,v,w)))
    | contains_pq(i(triple(u,v,w)),findmin_cpq_res(triple(u,v,w))) ),
    file('SWV371+1.p',unknown),
    [] ).

cnf(78,axiom,
    ( ~ phi(findmin_cpq_eff(triple(u,v,w)))
    | issmallestelement_pq(i(triple(u,v,w)),findmin_cpq_res(triple(u,v,w))) ),
    file('SWV371+1.p',unknown),
    [] ).

cnf(94,plain,
    ~ pi_sharp_find_min(i(triple(skc3,skc4,skc5)),removemin_cpq_res(triple(skc3,skc4,skc5))),
    inference(rew,[status(thm),theory(equality)],[13,61]),
    [iquote('0:Rew:13.0,61.0')] ).

cnf(95,plain,
    ( ~ phi(findmin_cpq_eff(triple(u,v,w)))
    | issmallestelement_pq(i(triple(u,v,w)),removemin_cpq_res(triple(u,v,w))) ),
    inference(rew,[status(thm),theory(equality)],[13,78]),
    [iquote('0:Rew:13.0,78.1')] ).

cnf(96,plain,
    ( ~ phi(findmin_cpq_eff(triple(u,v,w)))
    | contains_pq(i(triple(u,v,w)),removemin_cpq_res(triple(u,v,w))) ),
    inference(rew,[status(thm),theory(equality)],[13,77]),
    [iquote('0:Rew:13.0,77.1')] ).

cnf(101,plain,
    contains_pq(i(triple(skc3,skc4,skc5)),removemin_cpq_res(triple(skc3,skc4,skc5))),
    inference(res,[status(thm),theory(equality)],[14,96]),
    [iquote('0:Res:14.0,96.0')] ).

cnf(102,plain,
    issmallestelement_pq(i(triple(skc3,skc4,skc5)),removemin_cpq_res(triple(skc3,skc4,skc5))),
    inference(res,[status(thm),theory(equality)],[14,95]),
    [iquote('0:Res:14.0,95.0')] ).

cnf(103,plain,
    ( ~ contains_pq(i(triple(skc3,skc4,skc5)),removemin_cpq_res(triple(skc3,skc4,skc5)))
    | ~ issmallestelement_pq(i(triple(skc3,skc4,skc5)),removemin_cpq_res(triple(skc3,skc4,skc5))) ),
    inference(res,[status(thm),theory(equality)],[59,94]),
    [iquote('0:Res:59.2,94.0')] ).

cnf(104,plain,
    $false,
    inference(mrr,[status(thm)],[103,101,102]),
    [iquote('0:MRR:103.0,103.1,101.0,102.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV371+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n029.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 : Tue Jun 14 15:44:56 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.46  
% 0.20/0.46  SPASS V 3.9 
% 0.20/0.46  SPASS beiseite: Proof found.
% 0.20/0.46  % SZS status Theorem
% 0.20/0.46  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.46  SPASS derived 3 clauses, backtracked 0 clauses, performed 0 splits and kept 92 clauses.
% 0.20/0.46  SPASS allocated 98078 KBytes.
% 0.20/0.46  SPASS spent	0:00:00.11 on the problem.
% 0.20/0.46  		0:00:00.04 for the input.
% 0.20/0.46  		0:00:00.05 for the FLOTTER CNF translation.
% 0.20/0.46  		0:00:00.00 for inferences.
% 0.20/0.46  		0:00:00.00 for the backtracking.
% 0.20/0.46  		0:00:00.00 for the reduction.
% 0.20/0.46  
% 0.20/0.46  
% 0.20/0.46  Here is a proof with depth 1, length 13 :
% 0.20/0.46  % SZS output start Refutation
% See solution above
% 0.20/0.46  Formulae used in the proof : ax53 l7_co ax58 l7_l8 l7_lX
% 0.20/0.46  
%------------------------------------------------------------------------------