TSTP Solution File: NUM641+4 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM641+4 : TPTP v8.1.0. Released v7.3.0.
% 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 : Mon Jul 18 14:28:30 EDT 2022

% Result   : Theorem 30.92s 31.09s
% Output   : Refutation 30.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   26
% Syntax   : Number of clauses     :   55 (  21 unt;  10 nHn;  55 RR)
%            Number of literals    :  105 (   0 equ;  48 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   26 (  26 usr;  15 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(7,axiom,
    pp(fTrue),
    file('NUM641+4.p',unknown),
    [] ).

cnf(10,axiom,
    gg_bool(scratc546085760_d_not(u)),
    file('NUM641+4.p',unknown),
    [] ).

cnf(13,axiom,
    equal(fimplies,scratc153411835nd_imp),
    file('NUM641+4.p',unknown),
    [] ).

cnf(24,axiom,
    ~ pp(fFalse),
    file('NUM641+4.p',unknown),
    [] ).

cnf(32,axiom,
    gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(u,v)),
    file('NUM641+4.p',unknown),
    [] ).

cnf(41,axiom,
    equal(scratc1564950462d_e_is(scratc193932176nd_nat),scratc1083610823d_n_is),
    file('NUM641+4.p',unknown),
    [] ).

cnf(43,axiom,
    equal(scratc1564950462d_e_is(u),fequal_TPTP_ind),
    file('NUM641+4.p',unknown),
    [] ).

cnf(48,axiom,
    gg_TPTP_ind(skf42(u,v)),
    file('NUM641+4.p',unknown),
    [] ).

cnf(65,axiom,
    pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_bu)),
    file('NUM641+4.p',unknown),
    [] ).

cnf(77,axiom,
    ( ~ scratc268548109nd_wel(u)
    | pp(u) ),
    file('NUM641+4.p',unknown),
    [] ).

cnf(84,axiom,
    ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_aa)),
    file('NUM641+4.p',unknown),
    [] ).

cnf(89,axiom,
    pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,u),u)),
    file('NUM641+4.p',unknown),
    [] ).

cnf(94,axiom,
    ( ~ pp(scratc546085760_d_not(scratc546085760_d_not(u)))
    | scratc268548109nd_wel(u) ),
    file('NUM641+4.p',unknown),
    [] ).

cnf(103,axiom,
    ( ~ scratc1451164978_is_of(u,v)
    | pp(aa_TPTP_ind_bool(v,u)) ),
    file('NUM641+4.p',unknown),
    [] ).

cnf(104,axiom,
    ( ~ pp(aa_TPTP_ind_bool(u,v))
    | scratc1451164978_is_of(v,u) ),
    file('NUM641+4.p',unknown),
    [] ).

cnf(111,axiom,
    ( pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,u),v))
    | pp(u) ),
    file('NUM641+4.p',unknown),
    [] ).

cnf(125,axiom,
    ( ~ gg_bool(u)
    | equal(u,fFalse)
    | equal(u,fTrue) ),
    file('NUM641+4.p',unknown),
    [] ).

cnf(132,axiom,
    ( ~ pp(scratc546085760_d_not(u))
    | pp(aa_bool_bool(aa_boo1142376798l_bool(scratc153411835nd_imp,u),fFalse)) ),
    file('NUM641+4.p',unknown),
    [] ).

cnf(133,axiom,
    ( ~ pp(aa_bool_bool(aa_boo1142376798l_bool(scratc153411835nd_imp,u),fFalse))
    | pp(scratc546085760_d_not(u)) ),
    file('NUM641+4.p',unknown),
    [] ).

cnf(138,axiom,
    ( pp(aa_fun171081125l_bool(scratc1829701671all_of(u),v))
    | scratc1451164978_is_of(skf42(v,u),u) ),
    file('NUM641+4.p',unknown),
    [] ).

cnf(191,axiom,
    ( ~ pp(aa_TPTP_ind_bool(u,skf42(u,v)))
    | pp(aa_fun171081125l_bool(scratc1829701671all_of(v),u)) ),
    file('NUM641+4.p',unknown),
    [] ).

cnf(216,axiom,
    ( ~ pp(u)
    | ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,u),v))
    | pp(v) ),
    file('NUM641+4.p',unknown),
    [] ).

cnf(306,axiom,
    ( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,u))
    | pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(scratc45782132nd_n_1),u)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,u))) ),
    file('NUM641+4.p',unknown),
    [] ).

cnf(313,axiom,
    ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,u)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(scratc45782132nd_n_1),u)))
    | pp(aa_TPTP_ind_bool(aTP_Lamm_aa,u)) ),
    file('NUM641+4.p',unknown),
    [] ).

cnf(324,axiom,
    ( ~ gg_TPTP_ind(u)
    | ~ gg_TPTP_ind(v)
    | ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,u),v))
    | equal(u,v) ),
    file('NUM641+4.p',unknown),
    [] ).

cnf(330,axiom,
    ( ~ gg_TPTP_ind(u)
    | ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(v),w))
    | ~ scratc1451164978_is_of(u,v)
    | pp(aa_TPTP_ind_bool(w,u)) ),
    file('NUM641+4.p',unknown),
    [] ).

cnf(532,plain,
    equal(fequal_TPTP_ind,scratc1083610823d_n_is),
    inference(rew,[status(thm),theory(equality)],[43,41]),
    [iquote('0:Rew:43.0,41.0')] ).

cnf(536,plain,
    pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,u),u)),
    inference(rew,[status(thm),theory(equality)],[532,89]),
    [iquote('0:Rew:532.0,89.0')] ).

cnf(539,plain,
    ( pp(u)
    | pp(aa_bool_bool(aa_boo1142376798l_bool(scratc153411835nd_imp,u),v)) ),
    inference(rew,[status(thm),theory(equality)],[13,111]),
    [iquote('0:Rew:13.0,111.0')] ).

cnf(560,plain,
    ( ~ pp(u)
    | ~ pp(aa_bool_bool(aa_boo1142376798l_bool(scratc153411835nd_imp,u),v))
    | pp(v) ),
    inference(rew,[status(thm),theory(equality)],[13,216]),
    [iquote('0:Rew:13.0,216.1')] ).

cnf(589,plain,
    ( ~ gg_TPTP_ind(u)
    | ~ gg_TPTP_ind(v)
    | ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,v),u))
    | equal(v,u) ),
    inference(rew,[status(thm),theory(equality)],[532,324]),
    [iquote('0:Rew:532.0,324.2')] ).

cnf(727,plain,
    ~ pp(aa_TPTP_ind_bool(aTP_Lamm_aa,skf42(aTP_Lamm_aa,aTP_Lamm_a))),
    inference(res,[status(thm),theory(equality)],[191,84]),
    [iquote('0:Res:191.1,84.0')] ).

cnf(728,plain,
    scratc1451164978_is_of(skf42(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a),
    inference(res,[status(thm),theory(equality)],[138,84]),
    [iquote('0:Res:138.1,84.0')] ).

cnf(760,plain,
    ~ scratc268548109nd_wel(aa_TPTP_ind_bool(aTP_Lamm_aa,skf42(aTP_Lamm_aa,aTP_Lamm_a))),
    inference(res,[status(thm),theory(equality)],[77,727]),
    [iquote('0:Res:77.1,727.0')] ).

cnf(811,plain,
    scratc1451164978_is_of(u,aa_TPT43085870d_bool(scratc1083610823d_n_is,u)),
    inference(res,[status(thm),theory(equality)],[536,104]),
    [iquote('0:Res:536.0,104.0')] ).

cnf(887,plain,
    ( equal(scratc546085760_d_not(u),fFalse)
    | equal(scratc546085760_d_not(u),fTrue) ),
    inference(ems,[status(thm)],[125,10]),
    [iquote('0:EmS:125.0,10.0')] ).

cnf(914,plain,
    ( ~ pp(fTrue)
    | equal(scratc546085760_d_not(scratc546085760_d_not(u)),fFalse)
    | scratc268548109nd_wel(u) ),
    inference(spl,[status(thm),theory(equality)],[887,94]),
    [iquote('0:SpL:887.1,94.0')] ).

cnf(915,plain,
    ( equal(scratc546085760_d_not(scratc546085760_d_not(u)),fFalse)
    | scratc268548109nd_wel(u) ),
    inference(mrr,[status(thm)],[914,7]),
    [iquote('0:MRR:914.0,7.0')] ).

cnf(1057,plain,
    ( pp(u)
    | pp(scratc546085760_d_not(u)) ),
    inference(res,[status(thm),theory(equality)],[539,133]),
    [iquote('0:Res:539.1,133.0')] ).

cnf(1066,plain,
    ( scratc268548109nd_wel(u)
    | pp(scratc546085760_d_not(u))
    | pp(fFalse) ),
    inference(spr,[status(thm),theory(equality)],[915,1057]),
    [iquote('0:SpR:915.0,1057.1')] ).

cnf(1067,plain,
    ( scratc268548109nd_wel(u)
    | pp(scratc546085760_d_not(u)) ),
    inference(mrr,[status(thm)],[1066,24]),
    [iquote('0:MRR:1066.2,24.0')] ).

cnf(3000,plain,
    ( ~ pp(u)
    | ~ pp(scratc546085760_d_not(u))
    | pp(fFalse) ),
    inference(res,[status(thm),theory(equality)],[132,560]),
    [iquote('0:Res:132.1,560.1')] ).

cnf(3002,plain,
    ( ~ pp(u)
    | ~ pp(scratc546085760_d_not(u)) ),
    inference(mrr,[status(thm)],[3000,24]),
    [iquote('0:MRR:3000.2,24.0')] ).

cnf(3016,plain,
    ( ~ pp(u)
    | scratc268548109nd_wel(u) ),
    inference(res,[status(thm),theory(equality)],[1067,3002]),
    [iquote('0:Res:1067.1,3002.1')] ).

cnf(3031,plain,
    ~ pp(aa_TPTP_ind_bool(aTP_Lamm_aa,skf42(aTP_Lamm_aa,aTP_Lamm_a))),
    inference(sor,[status(thm)],[760,3016]),
    [iquote('0:SoR:760.0,3016.1')] ).

cnf(6145,plain,
    ( ~ scratc1451164978_is_of(aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(scratc45782132nd_n_1),u),aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,u)))
    | pp(aa_TPTP_ind_bool(aTP_Lamm_aa,u)) ),
    inference(res,[status(thm),theory(equality)],[103,313]),
    [iquote('0:Res:103.1,313.0')] ).

cnf(6514,plain,
    ( ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,u))
    | ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(scratc45782132nd_n_1),u))
    | ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,u))
    | equal(aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(scratc45782132nd_n_1),u),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,u)) ),
    inference(res,[status(thm),theory(equality)],[306,589]),
    [iquote('0:Res:306.1,589.2')] ).

cnf(6547,plain,
    ( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,u))
    | equal(aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(scratc45782132nd_n_1),u),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,u)) ),
    inference(ssi,[status(thm)],[6514,32]),
    [iquote('0:SSi:6514.1,6514.0,32.0,32.0')] ).

cnf(7912,plain,
    ( ~ gg_TPTP_ind(u)
    | ~ scratc1451164978_is_of(u,aTP_Lamm_a)
    | pp(aa_TPTP_ind_bool(aTP_Lamm_bu,u)) ),
    inference(res,[status(thm),theory(equality)],[65,330]),
    [iquote('0:Res:65.0,330.1')] ).

cnf(45663,plain,
    ( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,u))
    | ~ scratc1451164978_is_of(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,u),aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,u)))
    | pp(aa_TPTP_ind_bool(aTP_Lamm_aa,u)) ),
    inference(spl,[status(thm),theory(equality)],[6547,6145]),
    [iquote('0:SpL:6547.1,6145.0')] ).

cnf(45667,plain,
    ( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,u))
    | pp(aa_TPTP_ind_bool(aTP_Lamm_aa,u)) ),
    inference(mrr,[status(thm)],[45663,811]),
    [iquote('0:MRR:45663.1,811.0')] ).

cnf(45782,plain,
    ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,skf42(aTP_Lamm_aa,aTP_Lamm_a))),
    inference(sor,[status(thm)],[3031,45667]),
    [iquote('0:SoR:3031.0,45667.1')] ).

cnf(45880,plain,
    ( ~ gg_TPTP_ind(skf42(aTP_Lamm_aa,aTP_Lamm_a))
    | ~ scratc1451164978_is_of(skf42(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ),
    inference(res,[status(thm),theory(equality)],[7912,45782]),
    [iquote('0:Res:7912.2,45782.0')] ).

cnf(45889,plain,
    ~ scratc1451164978_is_of(skf42(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a),
    inference(ssi,[status(thm)],[45880,48]),
    [iquote('0:SSi:45880.0,48.0')] ).

cnf(45890,plain,
    $false,
    inference(mrr,[status(thm)],[45889,728]),
    [iquote('0:MRR:45889.0,728.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : NUM641+4 : TPTP v8.1.0. Released v7.3.0.
% 0.08/0.13  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n004.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Tue Jul  5 19:25:22 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 30.92/31.09  
% 30.92/31.09  SPASS V 3.9 
% 30.92/31.09  SPASS beiseite: Proof found.
% 30.92/31.09  % SZS status Theorem
% 30.92/31.09  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 30.92/31.09  SPASS derived 40105 clauses, backtracked 8784 clauses, performed 107 splits and kept 18617 clauses.
% 30.92/31.09  SPASS allocated 132440 KBytes.
% 30.92/31.09  SPASS spent	0:0:28.86 on the problem.
% 30.92/31.09  		0:00:00.04 for the input.
% 30.92/31.09  		0:00:00.26 for the FLOTTER CNF translation.
% 30.92/31.09  		0:00:01.30 for inferences.
% 30.92/31.09  		0:00:00.78 for the backtracking.
% 30.92/31.09  		0:0:25.24 for the reduction.
% 30.92/31.09  
% 30.92/31.09  
% 30.92/31.09  Here is a proof with depth 7, length 55 :
% 30.92/31.09  % SZS output start Refutation
% See solution above
% 30.92/31.09  Formulae used in the proof : help_pp_2_1_U gsy_c_Scratch__tptp__translate__40362__32620_ONUM641__thf__4__p_Obnd__d__not fact_def__imp help_fFalse_1_1_U gsy_c_aa_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind fact_def__n__is fact_def__e__is fact_def__all__of gsy_c_Scratch__tptp__translate__40362__32620_ONUM641__thf__4__p_Obnd__omega fact_satz4c fact_l__et conj_0 help_fequal_2_1_fequal_001t__TPTP____Interpret__Oind_T fact_def__wel fact_def__is__of help_fimplies_1_1_U help_fFalse_1_1_T fact_def__d__not help_fimplies_3_1_U fact_ATP_Olambda__4 fact_ATP_Olambda__8 help_fequal_1_1_fequal_001t__TPTP____Interpret__Oind_T
% 30.92/31.09  
%------------------------------------------------------------------------------