%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : COM004-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n016.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 : Fri Jul 15 01:44:13 EDT 2022

% Result   : Unsatisfiable 0.18s 0.40s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   14 (  10 unt;   0 nHn;  14 RR)
%            Number of literals    :   24 (   0 equ;  14 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;  11 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ siblings(u,v)
    | ~ contradictory(w,x)
    | ~ failure_node(v,or__dfg(y,x))
    | ~ failure_node(u,or__dfg(z,w))
    | failure_node(parent_of(u,v),or__dfg(z,y)) ),
    file('COM004-1.p',unknown),
    [] ).

cnf(3,axiom,
    contradictory(u,negate(u)),
    file('COM004-1.p',unknown),
    [] ).

cnf(4,axiom,
    siblings(left_child_of(u),right_child_of(u)),
    file('COM004-1.p',unknown),
    [] ).

cnf(5,axiom,
    failure_node(n_left,or__dfg(empty,atom)),
    file('COM004-1.p',unknown),
    [] ).

cnf(6,axiom,
    failure_node(n_right,or__dfg(empty,negate(atom))),
    file('COM004-1.p',unknown),
    [] ).

cnf(7,axiom,
    equal(left_child_of(n),n_left),
    file('COM004-1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(right_child_of(n),n_right),
    file('COM004-1.p',unknown),
    [] ).

cnf(9,axiom,
    ~ failure_node(u,or__dfg(empty,empty)),
    file('COM004-1.p',unknown),
    [] ).

cnf(10,plain,
    ( ~ siblings(u,v)
    | ~ contradictory(w,x)
    | ~ failure_node(v,or__dfg(empty,x))
    | ~ failure_node(u,or__dfg(empty,w)) ),
    inference(res,[status(thm),theory(equality)],[1,9]),
    [iquote('0:Res:1.4,9.0')] ).

cnf(13,plain,
    siblings(left_child_of(n),n_right),
    inference(spr,[status(thm),theory(equality)],[8,4]),
    [iquote('0:SpR:8.0,4.0')] ).

cnf(15,plain,
    siblings(n_left,n_right),
    inference(rew,[status(thm),theory(equality)],[7,13]),
    [iquote('0:Rew:7.0,13.0')] ).

cnf(20,plain,
    ( ~ siblings(u,n_right)
    | ~ contradictory(v,negate(atom))
    | ~ failure_node(u,or__dfg(empty,v)) ),
    inference(res,[status(thm),theory(equality)],[6,10]),
    [iquote('0:Res:6.0,10.2')] ).

cnf(26,plain,
    ( ~ siblings(n_left,n_right)
    | ~ contradictory(atom,negate(atom)) ),
    inference(res,[status(thm),theory(equality)],[5,20]),
    [iquote('0:Res:5.0,20.2')] ).

cnf(28,plain,
    $false,
    inference(mrr,[status(thm)],[26,15,3]),
    [iquote('0:MRR:26.0,26.1,15.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : COM004-1 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n016.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 : Thu Jun 16 19:58:04 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.40  
% 0.18/0.40  SPASS V 3.9 
% 0.18/0.40  SPASS beiseite: Proof found.
% 0.18/0.40  % SZS status Theorem
% 0.18/0.40  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.40  SPASS derived 15 clauses, backtracked 0 clauses, performed 0 splits and kept 19 clauses.
% 0.18/0.40  SPASS allocated 63111 KBytes.
% 0.18/0.40  SPASS spent	0:00:00.06 on the problem.
% 0.18/0.40  		0:00:00.03 for the input.
% 0.18/0.40  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.40  		0:00:00.00 for inferences.
% 0.18/0.40  		0:00:00.00 for the backtracking.
% 0.18/0.40  		0:00:00.00 for the reduction.
% 0.18/0.40  
% 0.18/0.40  
% 0.18/0.40  Here is a proof with depth 3, length 14 :
% 0.18/0.40  % SZS output start Refutation
% See solution above
% 0.18/0.40  Formulae used in the proof : make_node x_contradicts_not_x n_left_and_n_right_are_siblings n_left_is_atom n_right_is_not_atom n_left_equals_left_child_of_n n_right_equals_right_child_of_n goal_is_there_an_empty_node
% 0.18/0.40  
%------------------------------------------------------------------------------