%------------------------------------------------------------------------------
% File     : SPASS+T---2.2.22
% Problem  : DAT091_1 : TPTP v8.1.0. Released v6.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : spasst-tptp-script %s %d

% Computer : n008.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 : Sat Jul 16 01:32:11 EDT 2022

% Result   : Theorem 2.00s 1.69s
% Output   : Refutation 2.00s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   13 (   3 unt;   4 nHn;   4 RR)
%            Number of literals    :   36 (   0 equ;  20 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   0 con; 1-2 aty)
%            Number of variables   :   30 (   8 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(7,axiom,
    list(skf6(U,V)),
    file('DAT091=1.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ list(U)
    | list(cons(V,U)) ),
    file('DAT091=1.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ list(U)
    | equal(head(cons(V,U)),V) ),
    file('DAT091=1.p',unknown),
    [] ).

cnf(26,axiom,
    ( ~ list(U)
    | equal(V,W)
    | equal(count(V,cons(W,U)),count(V,U)) ),
    file('DAT091=1.p',unknown),
    [] ).

cnf(30,axiom,
    ( ~ list(U)
    | ~ list(V)
    | ~ equal(count(W,U),count(W,V))
    | equal(U,V) ),
    file('DAT091=1.p',unknown),
    [] ).

cnf(356,plain,
    ( ~ list(U)
    | ~ list(V)
    | ~ list(cons(W,U))
    | ~ equal(count(X,V),count(X,U))
    | equal(X,W)
    | equal(V,cons(W,U)) ),
    inference(spl,[status(thm),theory(equality)],[26,30]),
    [iquote('0:SpL:26.2,30.2')] ).

cnf(358,plain,
    ( ~ list(U)
    | ~ list(V)
    | ~ equal(count(W,V),count(W,U))
    | equal(W,X)
    | equal(V,cons(X,U)) ),
    inference(mrr,[status(thm)],[356,13]),
    [iquote('0:MRR:356.2,13.1')] ).

cnf(4405,plain,
    ( ~ list(U)
    | ~ list(U)
    | equal(V,W)
    | equal(cons(W,U),U) ),
    inference(eqr,[status(thm),theory(equality)],[358]),
    [iquote('0:EqR:358.2')] ).

cnf(4418,plain,
    ( ~ list(U)
    | ~ list(U)
    | equal(cons(V,U),U) ),
    inference(bld,[status(thm)],[4405]),
    [iquote('0:BLD:4405.2')] ).

cnf(4419,plain,
    ( ~ list(U)
    | equal(cons(V,U),U) ),
    inference(obv,[status(thm),theory(equality)],[4418]),
    [iquote('0:Obv:4418.0')] ).

cnf(4444,plain,
    ( ~ list(U)
    | equal(head(U),V) ),
    inference(rew,[status(thm),theory(equality)],[4419,17]),
    [iquote('0:Rew:4419.1,17.1')] ).

cnf(4588,plain,
    ~ list(U),
    inference(bld,[status(thm)],[4444]),
    [iquote('0:BLD:4444.1')] ).

cnf(4589,plain,
    $false,
    inference(unc,[status(thm)],[4588,7]),
    [iquote('0:UnC:4588.0,7.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : DAT091_1 : TPTP v8.1.0. Released v6.1.0.
% 0.03/0.13  % Command  : spasst-tptp-script %s %d
% 0.13/0.34  % Computer : n008.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 : Fri Jul  1 20:30:38 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.48  % Using integer theory
% 2.00/1.69  
% 2.00/1.69  
% 2.00/1.69  % SZS status Theorem for /tmp/SPASST_3965_n008.cluster.edu
% 2.00/1.69  
% 2.00/1.69  SPASS V 2.2.22  in combination with yices.
% 2.00/1.69  SPASS beiseite: Proof found by SPASS.
% 2.00/1.69  Problem: /tmp/SPASST_3965_n008.cluster.edu 
% 2.00/1.69  SPASS derived 2763 clauses, backtracked 0 clauses and kept 830 clauses.
% 2.00/1.69  SPASS backtracked 0 times (0 times due to theory inconsistency).
% 2.00/1.69  SPASS allocated 9577 KBytes.
% 2.00/1.69  SPASS spent	0:00:00.62 on the problem.
% 2.00/1.69  		0:00:00.00 for the input.
% 2.00/1.69  		0:00:00.01 for the FLOTTER CNF translation.
% 2.00/1.69  		0:00:00.04 for inferences.
% 2.00/1.69  		0:00:00.00 for the backtracking.
% 2.00/1.69  		0:00:00.51 for the reduction.
% 2.00/1.69  		0:00:00.04 for interacting with the SMT procedure.
% 2.00/1.69  		
% 2.00/1.69  
% 2.00/1.69  % SZS output start CNFRefutation for /tmp/SPASST_3965_n008.cluster.edu
% See solution above
% 2.00/1.69  
% 2.00/1.69  Formulae used in the proof : fof_l fof_tail_type fof_l2 fof_inRange fof_nil_type fof_t_5 fof_l_6 fof_l_7
% 2.29/1.85  
% 2.29/1.85  SPASS+T ended
%------------------------------------------------------------------------------