TSTP Solution File: COM003+2 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : COM003+2 : TPTP v8.1.0. Bugfixed v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n014.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 01:44:12 EDT 2022

% Result   : Theorem 0.19s 0.48s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   15
% Syntax   : Number of clauses     :   39 (  11 unt;   3 nHn;  39 RR)
%            Number of literals    :   91 (   0 equ;  54 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   12 (  11 usr;   1 prp; 0-4 aty)
%            Number of functors    :   13 (  13 usr;   9 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    algorithm_program_decides(skc4),
    file('COM003+2.p',unknown),
    [] ).

cnf(2,axiom,
    program(skc6),
    file('COM003+2.p',unknown),
    [] ).

cnf(3,axiom,
    program(skc7),
    file('COM003+2.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ program_program_decides(u)
    | program(u) ),
    file('COM003+2.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ algorithm_program_decides(u)
    | program_program_decides(skc5) ),
    file('COM003+2.p',unknown),
    [] ).

cnf(18,axiom,
    ( ~ halts2_outputs(u,v,w)
    | halts2(u,v) ),
    file('COM003+2.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ program_program_decides(u)
    | program_halts2_halts3_outputs(u,v,w,good) ),
    file('COM003+2.p',unknown),
    [] ).

cnf(23,axiom,
    ( ~ program_program_decides(u)
    | program_not_halts2_halts3_outputs(u,v,w,bad) ),
    file('COM003+2.p',unknown),
    [] ).

cnf(26,axiom,
    ( ~ program(u)
    | program_not_halts2(u,v)
    | halts2(u,v) ),
    file('COM003+2.p',unknown),
    [] ).

cnf(30,axiom,
    ( ~ program(u)
    | ~ halts2(u,v)
    | program_halts2(u,v) ),
    file('COM003+2.p',unknown),
    [] ).

cnf(36,axiom,
    ( ~ program_not_halts2(u,u)
    | ~ program_not_halts2_halts2_outputs(v,u,w)
    | halts2_outputs(v,u,w) ),
    file('COM003+2.p',unknown),
    [] ).

cnf(40,axiom,
    ( ~ program(u)
    | ~ program_not_halts2_halts2_outputs(u,skf11(u),bad)
    | ~ program_halts2_halts2_outputs(u,skf10(u),good)
    | program_not_halts2_halts2_outputs(skc7,v,good) ),
    file('COM003+2.p',unknown),
    [] ).

cnf(41,axiom,
    ( ~ program(u)
    | ~ program_halts2(v,v)
    | ~ halts2(skc7,v)
    | ~ program_not_halts2_halts2_outputs(u,skf11(u),bad)
    | ~ program_halts2_halts2_outputs(u,skf10(u),good) ),
    file('COM003+2.p',unknown),
    [] ).

cnf(42,axiom,
    ( ~ program(u)
    | ~ program_not_halts2_halts3_outputs(u,skf9(u),skf9(u),bad)
    | ~ program_halts2_halts3_outputs(u,skf8(u),skf8(u),good)
    | program_not_halts2_halts2_outputs(skc6,v,bad) ),
    file('COM003+2.p',unknown),
    [] ).

cnf(43,axiom,
    ( ~ program(u)
    | ~ program_not_halts2_halts3_outputs(u,skf9(u),skf9(u),bad)
    | ~ program_halts2_halts3_outputs(u,skf8(u),skf8(u),good)
    | program_halts2_halts2_outputs(skc6,v,good) ),
    file('COM003+2.p',unknown),
    [] ).

cnf(46,plain,
    program_program_decides(skc5),
    inference(res,[status(thm),theory(equality)],[1,9]),
    [iquote('0:Res:1.0,9.0')] ).

cnf(135,plain,
    ( ~ program_program_decides(u)
    | ~ program(u)
    | ~ program_halts2_halts3_outputs(u,skf8(u),skf8(u),good)
    | program_halts2_halts2_outputs(skc6,v,good) ),
    inference(res,[status(thm),theory(equality)],[23,43]),
    [iquote('0:Res:23.1,43.1')] ).

cnf(138,plain,
    ( ~ program_program_decides(u)
    | ~ program_halts2_halts3_outputs(u,skf8(u),skf8(u),good)
    | program_halts2_halts2_outputs(skc6,v,good) ),
    inference(ssi,[status(thm)],[135,5]),
    [iquote('0:SSi:135.1,5.1')] ).

cnf(139,plain,
    ( ~ program_program_decides(u)
    | program_halts2_halts2_outputs(skc6,v,good) ),
    inference(mrr,[status(thm)],[138,22]),
    [iquote('0:MRR:138.1,22.1')] ).

cnf(141,plain,
    program_halts2_halts2_outputs(skc6,u,good),
    inference(ems,[status(thm)],[139,46]),
    [iquote('0:EmS:139.0,46.0')] ).

cnf(205,plain,
    ( ~ program_program_decides(u)
    | ~ program(u)
    | ~ program_halts2_halts3_outputs(u,skf8(u),skf8(u),good)
    | program_not_halts2_halts2_outputs(skc6,v,bad) ),
    inference(res,[status(thm),theory(equality)],[23,42]),
    [iquote('0:Res:23.1,42.1')] ).

cnf(208,plain,
    ( ~ program_program_decides(u)
    | ~ program_halts2_halts3_outputs(u,skf8(u),skf8(u),good)
    | program_not_halts2_halts2_outputs(skc6,v,bad) ),
    inference(ssi,[status(thm)],[205,5]),
    [iquote('0:SSi:205.1,5.1')] ).

cnf(209,plain,
    ( ~ program_program_decides(u)
    | program_not_halts2_halts2_outputs(skc6,v,bad) ),
    inference(mrr,[status(thm)],[208,22]),
    [iquote('0:MRR:208.1,22.1')] ).

cnf(211,plain,
    program_not_halts2_halts2_outputs(skc6,u,bad),
    inference(ems,[status(thm)],[209,46]),
    [iquote('0:EmS:209.0,46.0')] ).

cnf(379,plain,
    ( ~ program(skc6)
    | ~ program_halts2_halts2_outputs(skc6,skf10(skc6),good)
    | program_not_halts2_halts2_outputs(skc7,u,good) ),
    inference(res,[status(thm),theory(equality)],[211,40]),
    [iquote('0:Res:211.0,40.1')] ).

cnf(385,plain,
    ( ~ program_halts2_halts2_outputs(skc6,skf10(skc6),good)
    | program_not_halts2_halts2_outputs(skc7,u,good) ),
    inference(ssi,[status(thm)],[379,2]),
    [iquote('0:SSi:379.0,2.0')] ).

cnf(386,plain,
    program_not_halts2_halts2_outputs(skc7,u,good),
    inference(mrr,[status(thm)],[385,141]),
    [iquote('0:MRR:385.0,141.0')] ).

cnf(387,plain,
    ( ~ program_not_halts2(u,u)
    | halts2_outputs(skc7,u,good) ),
    inference(res,[status(thm),theory(equality)],[386,36]),
    [iquote('0:Res:386.0,36.1')] ).

cnf(393,plain,
    ( ~ program(skc6)
    | ~ program_halts2(u,u)
    | ~ halts2(skc7,u)
    | ~ program_halts2_halts2_outputs(skc6,skf10(skc6),good) ),
    inference(res,[status(thm),theory(equality)],[211,41]),
    [iquote('0:Res:211.0,41.3')] ).

cnf(400,plain,
    ( ~ program_halts2(u,u)
    | ~ halts2(skc7,u)
    | ~ program_halts2_halts2_outputs(skc6,skf10(skc6),good) ),
    inference(ssi,[status(thm)],[393,2]),
    [iquote('0:SSi:393.0,2.0')] ).

cnf(401,plain,
    ( ~ program_halts2(u,u)
    | ~ halts2(skc7,u) ),
    inference(mrr,[status(thm)],[400,141]),
    [iquote('0:MRR:400.2,141.0')] ).

cnf(403,plain,
    ( ~ program(u)
    | halts2(u,u)
    | halts2_outputs(skc7,u,good) ),
    inference(res,[status(thm),theory(equality)],[26,387]),
    [iquote('0:Res:26.1,387.0')] ).

cnf(440,plain,
    ( ~ program(u)
    | halts2(u,u)
    | halts2(skc7,u) ),
    inference(res,[status(thm),theory(equality)],[403,18]),
    [iquote('0:Res:403.2,18.0')] ).

cnf(490,plain,
    ( ~ program(skc7)
    | halts2(skc7,skc7) ),
    inference(fac,[status(thm)],[440]),
    [iquote('0:Fac:440.1,440.2')] ).

cnf(494,plain,
    halts2(skc7,skc7),
    inference(ssi,[status(thm)],[490,3]),
    [iquote('0:SSi:490.0,3.0')] ).

cnf(498,plain,
    ( ~ program(skc7)
    | program_halts2(skc7,skc7) ),
    inference(res,[status(thm),theory(equality)],[494,30]),
    [iquote('0:Res:494.0,30.1')] ).

cnf(500,plain,
    program_halts2(skc7,skc7),
    inference(ssi,[status(thm)],[498,3]),
    [iquote('0:SSi:498.0,3.0')] ).

cnf(503,plain,
    ~ halts2(skc7,skc7),
    inference(res,[status(thm),theory(equality)],[500,401]),
    [iquote('0:Res:500.0,401.0')] ).

cnf(505,plain,
    $false,
    inference(mrr,[status(thm)],[503,494]),
    [iquote('0:MRR:503.0,494.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : COM003+2 : TPTP v8.1.0. Bugfixed v2.2.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n014.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 : Thu Jun 16 20:11:50 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.48  
% 0.19/0.48  SPASS V 3.9 
% 0.19/0.48  SPASS beiseite: Proof found.
% 0.19/0.48  % SZS status Theorem
% 0.19/0.48  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.48  SPASS derived 367 clauses, backtracked 89 clauses, performed 8 splits and kept 303 clauses.
% 0.19/0.48  SPASS allocated 97852 KBytes.
% 0.19/0.48  SPASS spent	0:00:00.12 on the problem.
% 0.19/0.48  		0:00:00.04 for the input.
% 0.19/0.48  		0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.48  		0:00:00.00 for inferences.
% 0.19/0.48  		0:00:00.00 for the backtracking.
% 0.19/0.48  		0:00:00.02 for the reduction.
% 0.19/0.48  
% 0.19/0.48  
% 0.19/0.48  Here is a proof with depth 9, length 39 :
% 0.19/0.48  % SZS output start Refutation
% See solution above
% 0.19/0.48  Formulae used in the proof : prove_this p3 algorithm_program_decides_def p1 program_program_decides_def p4 halts2_outputs_def p2 program_not_halts2_def program_halts2_def program_not_halts2_halts2_outputs_def
% 0.19/0.48  
%------------------------------------------------------------------------------