%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWV417+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n015.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 21:42:43 EDT 2022

% Result   : Theorem 0.42s 0.59s
% Output   : Refutation 0.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   14 (   4 unt;   0 nHn;  14 RR)
%            Number of literals    :   27 (   0 equ;  19 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(14,axiom,
    equal(findmin_cpq_res(u),removemin_cpq_res(u)),
    file('SWV417+1.p',unknown),
    [] ).

cnf(15,axiom,
    phi(findmin_cpq_eff(triple(skc3,skc4,skc5))),
    file('SWV417+1.p',unknown),
    [] ).

cnf(27,axiom,
    ( ~ pi_sharp_find_min(u,v)
    | contains_pq(u,v) ),
    file('SWV417+1.p',unknown),
    [] ).

cnf(28,axiom,
    ( ~ pi_sharp_find_min(u,v)
    | issmallestelement_pq(u,v) ),
    file('SWV417+1.p',unknown),
    [] ).

cnf(65,axiom,
    ( ~ issmallestelement_pq(u,v)
    | ~ contains_pq(u,v)
    | equal(findmin_pq_res(u,v),v) ),
    file('SWV417+1.p',unknown),
    [] ).

cnf(77,axiom,
    ( ~ phi(findmin_cpq_eff(triple(u,v,w)))
    | pi_sharp_find_min(i(triple(u,v,w)),findmin_cpq_res(triple(u,v,w))) ),
    file('SWV417+1.p',unknown),
    [] ).

cnf(86,axiom,
    ( ~ pi_sharp_find_min(i(triple(skc3,skc4,skc5)),u)
    | ~ equal(findmin_pq_res(i(triple(skc3,skc4,skc5)),u),findmin_cpq_res(triple(skc3,skc4,skc5))) ),
    file('SWV417+1.p',unknown),
    [] ).

cnf(94,plain,
    ( ~ phi(findmin_cpq_eff(triple(u,v,w)))
    | pi_sharp_find_min(i(triple(u,v,w)),removemin_cpq_res(triple(u,v,w))) ),
    inference(rew,[status(thm),theory(equality)],[14,77]),
    [iquote('0:Rew:14.0,77.1')] ).

cnf(96,plain,
    ( ~ pi_sharp_find_min(i(triple(skc3,skc4,skc5)),u)
    | ~ equal(findmin_pq_res(i(triple(skc3,skc4,skc5)),u),removemin_cpq_res(triple(skc3,skc4,skc5))) ),
    inference(rew,[status(thm),theory(equality)],[14,86]),
    [iquote('0:Rew:14.0,86.1')] ).

cnf(1140,plain,
    ( ~ issmallestelement_pq(i(triple(skc3,skc4,skc5)),u)
    | ~ contains_pq(i(triple(skc3,skc4,skc5)),u)
    | ~ pi_sharp_find_min(i(triple(skc3,skc4,skc5)),u)
    | ~ equal(u,removemin_cpq_res(triple(skc3,skc4,skc5))) ),
    inference(spl,[status(thm),theory(equality)],[65,96]),
    [iquote('0:SpL:65.2,96.1')] ).

cnf(1141,plain,
    ( ~ pi_sharp_find_min(i(triple(skc3,skc4,skc5)),u)
    | ~ equal(u,removemin_cpq_res(triple(skc3,skc4,skc5))) ),
    inference(mrr,[status(thm)],[1140,28,27]),
    [iquote('0:MRR:1140.0,1140.1,28.1,27.1')] ).

cnf(1148,plain,
    ( ~ phi(findmin_cpq_eff(triple(skc3,skc4,skc5)))
    | ~ equal(removemin_cpq_res(triple(skc3,skc4,skc5)),removemin_cpq_res(triple(skc3,skc4,skc5))) ),
    inference(res,[status(thm),theory(equality)],[94,1141]),
    [iquote('0:Res:94.1,1141.0')] ).

cnf(1153,plain,
    ~ phi(findmin_cpq_eff(triple(skc3,skc4,skc5))),
    inference(obv,[status(thm),theory(equality)],[1148]),
    [iquote('0:Obv:1148.1')] ).

cnf(1154,plain,
    $false,
    inference(mrr,[status(thm)],[1153,15]),
    [iquote('0:MRR:1153.0,15.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SWV417+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n015.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Wed Jun 15 09:45:40 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.42/0.59  
% 0.42/0.59  SPASS V 3.9 
% 0.42/0.59  SPASS beiseite: Proof found.
% 0.42/0.59  % SZS status Theorem
% 0.42/0.59  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.42/0.59  SPASS derived 970 clauses, backtracked 9 clauses, performed 1 splits and kept 419 clauses.
% 0.42/0.59  SPASS allocated 98742 KBytes.
% 0.42/0.59  SPASS spent	0:00:00.24 on the problem.
% 0.42/0.59  		0:00:00.03 for the input.
% 0.42/0.59  		0:00:00.05 for the FLOTTER CNF translation.
% 0.42/0.59  		0:00:00.02 for inferences.
% 0.42/0.59  		0:00:00.00 for the backtracking.
% 0.42/0.59  		0:00:00.12 for the reduction.
% 0.42/0.59  
% 0.42/0.59  
% 0.42/0.59  Here is a proof with depth 2, length 14 :
% 0.42/0.59  % SZS output start Refutation
% See solution above
% 0.42/0.59  Formulae used in the proof : ax53 co4 ax58 ax14 main4_l7
% 0.42/0.59  
%------------------------------------------------------------------------------