%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : COM003-2 : TPTP v8.1.0. Released v1.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n004.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 01:44:11 EDT 2022

% Result   : Unsatisfiable 0.20s 0.44s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   16 (   8 unt;   0 nHn;  16 RR)
%            Number of literals    :   24 (   0 equ;  13 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   1 prp; 0-4 aty)
%            Number of functors    :    8 (   8 usr;   8 con; 0-0 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(11,axiom,
    ( ~ program_halts2(u,v)
    | halts2(u,v) ),
    file('COM003-2.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ halts2(u,v)
    | ~ program_not_halts2(u,v) ),
    file('COM003-2.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ program_halts2_halts3_outputs(u,v,w,x)
    | program_halts2(v,w) ),
    file('COM003-2.p',unknown),
    [] ).

cnf(25,axiom,
    ( ~ program_not_halts2_halts3_outputs(u,v,w,x)
    | program_not_halts2(v,w) ),
    file('COM003-2.p',unknown),
    [] ).

cnf(34,axiom,
    ( ~ algorithm_program_decides(u)
    | program_program_decides(c1) ),
    file('COM003-2.p',unknown),
    [] ).

cnf(35,axiom,
    ( ~ program_program_decides(u)
    | program_halts2_halts3_outputs(u,v,w,good) ),
    file('COM003-2.p',unknown),
    [] ).

cnf(36,axiom,
    ( ~ program_program_decides(u)
    | program_not_halts2_halts3_outputs(u,v,w,bad) ),
    file('COM003-2.p',unknown),
    [] ).

cnf(43,axiom,
    algorithm_program_decides(c4),
    file('COM003-2.p',unknown),
    [] ).

cnf(46,plain,
    program_program_decides(c1),
    inference(res,[status(thm),theory(equality)],[43,34]),
    [iquote('0:Res:43.0,34.0')] ).

cnf(66,plain,
    ( ~ program_program_decides(u)
    | program_not_halts2(v,w) ),
    inference(res,[status(thm),theory(equality)],[36,25]),
    [iquote('0:Res:36.1,25.0')] ).

cnf(68,plain,
    program_not_halts2(u,v),
    inference(ems,[status(thm)],[66,46]),
    [iquote('0:EmS:66.0,46.0')] ).

cnf(70,plain,
    ~ halts2(u,v),
    inference(mrr,[status(thm)],[17,68]),
    [iquote('0:MRR:17.1,68.0')] ).

cnf(80,plain,
    ~ program_halts2(u,v),
    inference(mrr,[status(thm)],[11,70]),
    [iquote('0:MRR:11.1,70.0')] ).

cnf(83,plain,
    ~ program_halts2_halts3_outputs(u,v,w,x),
    inference(mrr,[status(thm)],[22,80]),
    [iquote('0:MRR:22.1,80.0')] ).

cnf(86,plain,
    ~ program_program_decides(u),
    inference(mrr,[status(thm)],[35,83]),
    [iquote('0:MRR:35.1,83.0')] ).

cnf(87,plain,
    $false,
    inference(unc,[status(thm)],[86,46]),
    [iquote('0:UnC:86.0,46.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : COM003-2 : TPTP v8.1.0. Released v1.1.0.
% 0.13/0.14  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n004.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Thu Jun 16 17:59:08 EDT 2022
% 0.20/0.35  % CPUTime  : 
% 0.20/0.44  
% 0.20/0.44  SPASS V 3.9 
% 0.20/0.44  SPASS beiseite: Proof found.
% 0.20/0.44  % SZS status Theorem
% 0.20/0.44  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.44  SPASS derived 26 clauses, backtracked 0 clauses, performed 0 splits and kept 59 clauses.
% 0.20/0.44  SPASS allocated 75663 KBytes.
% 0.20/0.44  SPASS spent	0:00:00.07 on the problem.
% 0.20/0.44  		0:00:00.05 for the input.
% 0.20/0.44  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.44  		0:00:00.00 for inferences.
% 0.20/0.44  		0:00:00.00 for the backtracking.
% 0.20/0.44  		0:00:00.00 for the reduction.
% 0.20/0.44  
% 0.20/0.44  
% 0.20/0.44  Here is a proof with depth 2, length 16 :
% 0.20/0.44  % SZS output start Refutation
% See solution above
% 0.20/0.44  Formulae used in the proof : program_halts3a program_not_halts3a program_halts2_halts3_outputs1 program_not_halts2_halts3_outputs1 axiom1_1 axiom2_1 axiom2_2 prove_algorithm_does_not_exist
% 0.20/0.44  
%------------------------------------------------------------------------------