TSTP Solution File: NUM639+4 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM639+4 : TPTP v8.1.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n006.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 14:28:28 EDT 2022

% Result   : Theorem 27.56s 27.73s
% Output   : Refutation 27.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   27
% Syntax   : Number of clauses     :   56 (  22 unt;  10 nHn;  56 RR)
%            Number of literals    :  106 (   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(2,axiom,
    gg_TPTP_ind(scratc214542084nd_n_1),
    file('NUM639+4.p',unknown),
    [] ).

cnf(7,axiom,
    pp(fTrue),
    file('NUM639+4.p',unknown),
    [] ).

cnf(10,axiom,
    gg_bool(scratc924542480_d_not(u)),
    file('NUM639+4.p',unknown),
    [] ).

cnf(13,axiom,
    equal(fimplies,scratc1431841387nd_imp),
    file('NUM639+4.p',unknown),
    [] ).

cnf(24,axiom,
    ~ pp(fFalse),
    file('NUM639+4.p',unknown),
    [] ).

cnf(32,axiom,
    gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(u,v)),
    file('NUM639+4.p',unknown),
    [] ).

cnf(41,axiom,
    equal(scratc1770836270d_e_is(scratc1472361728nd_nat),scratc1289496631d_n_is),
    file('NUM639+4.p',unknown),
    [] ).

cnf(43,axiom,
    equal(scratc1770836270d_e_is(u),fequal_TPTP_ind),
    file('NUM639+4.p',unknown),
    [] ).

cnf(48,axiom,
    gg_TPTP_ind(skf42(u,v)),
    file('NUM639+4.p',unknown),
    [] ).

cnf(65,axiom,
    pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_bu)),
    file('NUM639+4.p',unknown),
    [] ).

cnf(75,axiom,
    ( ~ scratc1546977661nd_wel(u)
    | pp(u) ),
    file('NUM639+4.p',unknown),
    [] ).

cnf(82,axiom,
    ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_aa)),
    file('NUM639+4.p',unknown),
    [] ).

cnf(87,axiom,
    pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,u),u)),
    file('NUM639+4.p',unknown),
    [] ).

cnf(92,axiom,
    ( ~ pp(scratc924542480_d_not(scratc924542480_d_not(u)))
    | scratc1546977661nd_wel(u) ),
    file('NUM639+4.p',unknown),
    [] ).

cnf(101,axiom,
    ( ~ scratc1829621698_is_of(u,v)
    | pp(aa_TPTP_ind_bool(v,u)) ),
    file('NUM639+4.p',unknown),
    [] ).

cnf(102,axiom,
    ( ~ pp(aa_TPTP_ind_bool(u,v))
    | scratc1829621698_is_of(v,u) ),
    file('NUM639+4.p',unknown),
    [] ).

cnf(109,axiom,
    ( pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,u),v))
    | pp(u) ),
    file('NUM639+4.p',unknown),
    [] ).

cnf(123,axiom,
    ( ~ gg_bool(u)
    | equal(u,fFalse)
    | equal(u,fTrue) ),
    file('NUM639+4.p',unknown),
    [] ).

cnf(130,axiom,
    ( ~ pp(scratc924542480_d_not(u))
    | pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1431841387nd_imp,u),fFalse)) ),
    file('NUM639+4.p',unknown),
    [] ).

cnf(131,axiom,
    ( ~ pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1431841387nd_imp,u),fFalse))
    | pp(scratc924542480_d_not(u)) ),
    file('NUM639+4.p',unknown),
    [] ).

cnf(136,axiom,
    ( pp(aa_fun171081125l_bool(scratc1153622423all_of(u),v))
    | scratc1829621698_is_of(skf42(v,u),u) ),
    file('NUM639+4.p',unknown),
    [] ).

cnf(189,axiom,
    ( ~ pp(aa_TPTP_ind_bool(u,skf42(u,v)))
    | pp(aa_fun171081125l_bool(scratc1153622423all_of(v),u)) ),
    file('NUM639+4.p',unknown),
    [] ).

cnf(212,axiom,
    ( ~ pp(u)
    | ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,u),v))
    | pp(v) ),
    file('NUM639+4.p',unknown),
    [] ).

cnf(300,axiom,
    ( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,u))
    | pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(u),scratc214542084nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,u))) ),
    file('NUM639+4.p',unknown),
    [] ).

cnf(307,axiom,
    ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,u)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(u),scratc214542084nd_n_1)))
    | pp(aa_TPTP_ind_bool(aTP_Lamm_aa,u)) ),
    file('NUM639+4.p',unknown),
    [] ).

cnf(318,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('NUM639+4.p',unknown),
    [] ).

cnf(324,axiom,
    ( ~ gg_TPTP_ind(u)
    | ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(v),w))
    | ~ scratc1829621698_is_of(u,v)
    | pp(aa_TPTP_ind_bool(w,u)) ),
    file('NUM639+4.p',unknown),
    [] ).

cnf(524,plain,
    equal(fequal_TPTP_ind,scratc1289496631d_n_is),
    inference(rew,[status(thm),theory(equality)],[43,41]),
    [iquote('0:Rew:43.0,41.0')] ).

cnf(528,plain,
    pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,u),u)),
    inference(rew,[status(thm),theory(equality)],[524,87]),
    [iquote('0:Rew:524.0,87.0')] ).

cnf(531,plain,
    ( pp(u)
    | pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1431841387nd_imp,u),v)) ),
    inference(rew,[status(thm),theory(equality)],[13,109]),
    [iquote('0:Rew:13.0,109.0')] ).

cnf(552,plain,
    ( ~ pp(u)
    | ~ pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1431841387nd_imp,u),v))
    | pp(v) ),
    inference(rew,[status(thm),theory(equality)],[13,212]),
    [iquote('0:Rew:13.0,212.1')] ).

cnf(581,plain,
    ( ~ gg_TPTP_ind(u)
    | ~ gg_TPTP_ind(v)
    | ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,v),u))
    | equal(v,u) ),
    inference(rew,[status(thm),theory(equality)],[524,318]),
    [iquote('0:Rew:524.0,318.2')] ).

cnf(719,plain,
    ~ pp(aa_TPTP_ind_bool(aTP_Lamm_aa,skf42(aTP_Lamm_aa,aTP_Lamm_a))),
    inference(res,[status(thm),theory(equality)],[189,82]),
    [iquote('0:Res:189.1,82.0')] ).

cnf(720,plain,
    scratc1829621698_is_of(skf42(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a),
    inference(res,[status(thm),theory(equality)],[136,82]),
    [iquote('0:Res:136.1,82.0')] ).

cnf(755,plain,
    ~ scratc1546977661nd_wel(aa_TPTP_ind_bool(aTP_Lamm_aa,skf42(aTP_Lamm_aa,aTP_Lamm_a))),
    inference(res,[status(thm),theory(equality)],[75,719]),
    [iquote('0:Res:75.1,719.0')] ).

cnf(803,plain,
    scratc1829621698_is_of(u,aa_TPT43085870d_bool(scratc1289496631d_n_is,u)),
    inference(res,[status(thm),theory(equality)],[528,102]),
    [iquote('0:Res:528.0,102.0')] ).

cnf(882,plain,
    ( equal(scratc924542480_d_not(u),fFalse)
    | equal(scratc924542480_d_not(u),fTrue) ),
    inference(ems,[status(thm)],[123,10]),
    [iquote('0:EmS:123.0,10.0')] ).

cnf(905,plain,
    ( ~ pp(fTrue)
    | equal(scratc924542480_d_not(scratc924542480_d_not(u)),fFalse)
    | scratc1546977661nd_wel(u) ),
    inference(spl,[status(thm),theory(equality)],[882,92]),
    [iquote('0:SpL:882.1,92.0')] ).

cnf(906,plain,
    ( equal(scratc924542480_d_not(scratc924542480_d_not(u)),fFalse)
    | scratc1546977661nd_wel(u) ),
    inference(mrr,[status(thm)],[905,7]),
    [iquote('0:MRR:905.0,7.0')] ).

cnf(1052,plain,
    ( pp(u)
    | pp(scratc924542480_d_not(u)) ),
    inference(res,[status(thm),theory(equality)],[531,131]),
    [iquote('0:Res:531.1,131.0')] ).

cnf(1058,plain,
    ( scratc1546977661nd_wel(u)
    | pp(scratc924542480_d_not(u))
    | pp(fFalse) ),
    inference(spr,[status(thm),theory(equality)],[906,1052]),
    [iquote('0:SpR:906.0,1052.1')] ).

cnf(1059,plain,
    ( scratc1546977661nd_wel(u)
    | pp(scratc924542480_d_not(u)) ),
    inference(mrr,[status(thm)],[1058,24]),
    [iquote('0:MRR:1058.2,24.0')] ).

cnf(2980,plain,
    ( ~ pp(u)
    | ~ pp(scratc924542480_d_not(u))
    | pp(fFalse) ),
    inference(res,[status(thm),theory(equality)],[130,552]),
    [iquote('0:Res:130.1,552.1')] ).

cnf(2982,plain,
    ( ~ pp(u)
    | ~ pp(scratc924542480_d_not(u)) ),
    inference(mrr,[status(thm)],[2980,24]),
    [iquote('0:MRR:2980.2,24.0')] ).

cnf(2996,plain,
    ( ~ pp(u)
    | scratc1546977661nd_wel(u) ),
    inference(res,[status(thm),theory(equality)],[1059,2982]),
    [iquote('0:Res:1059.1,2982.1')] ).

cnf(3013,plain,
    ~ pp(aa_TPTP_ind_bool(aTP_Lamm_aa,skf42(aTP_Lamm_aa,aTP_Lamm_a))),
    inference(sor,[status(thm)],[755,2996]),
    [iquote('0:SoR:755.0,2996.1')] ).

cnf(6075,plain,
    ( ~ scratc1829621698_is_of(aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(u),scratc214542084nd_n_1),aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,u)))
    | pp(aa_TPTP_ind_bool(aTP_Lamm_aa,u)) ),
    inference(res,[status(thm),theory(equality)],[101,307]),
    [iquote('0:Res:101.1,307.0')] ).

cnf(6550,plain,
    ( ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,u))
    | ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(u),scratc214542084nd_n_1))
    | ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,u))
    | equal(aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(u),scratc214542084nd_n_1),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,u)) ),
    inference(res,[status(thm),theory(equality)],[300,581]),
    [iquote('0:Res:300.1,581.2')] ).

cnf(6569,plain,
    ( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,u))
    | equal(aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(u),scratc214542084nd_n_1),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,u)) ),
    inference(ssi,[status(thm)],[6550,32,2]),
    [iquote('0:SSi:6550.1,6550.0,32.0,2.0,32.0')] ).

cnf(7812,plain,
    ( ~ gg_TPTP_ind(u)
    | ~ scratc1829621698_is_of(u,aTP_Lamm_a)
    | pp(aa_TPTP_ind_bool(aTP_Lamm_bu,u)) ),
    inference(res,[status(thm),theory(equality)],[65,324]),
    [iquote('0:Res:65.0,324.1')] ).

cnf(45213,plain,
    ( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,u))
    | ~ scratc1829621698_is_of(aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,u),aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,u)))
    | pp(aa_TPTP_ind_bool(aTP_Lamm_aa,u)) ),
    inference(spl,[status(thm),theory(equality)],[6569,6075]),
    [iquote('0:SpL:6569.1,6075.0')] ).

cnf(45217,plain,
    ( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,u))
    | pp(aa_TPTP_ind_bool(aTP_Lamm_aa,u)) ),
    inference(mrr,[status(thm)],[45213,803]),
    [iquote('0:MRR:45213.1,803.0')] ).

cnf(45331,plain,
    ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,skf42(aTP_Lamm_aa,aTP_Lamm_a))),
    inference(sor,[status(thm)],[3013,45217]),
    [iquote('0:SoR:3013.0,45217.1')] ).

cnf(45429,plain,
    ( ~ gg_TPTP_ind(skf42(aTP_Lamm_aa,aTP_Lamm_a))
    | ~ scratc1829621698_is_of(skf42(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ),
    inference(res,[status(thm),theory(equality)],[7812,45331]),
    [iquote('0:Res:7812.2,45331.0')] ).

cnf(45438,plain,
    ~ scratc1829621698_is_of(skf42(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a),
    inference(ssi,[status(thm)],[45429,48]),
    [iquote('0:SSi:45429.0,48.0')] ).

cnf(45439,plain,
    $false,
    inference(mrr,[status(thm)],[45438,720]),
    [iquote('0:MRR:45438.0,720.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM639+4 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n006.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Tue Jul  5 05:12:22 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 27.56/27.73  
% 27.56/27.73  SPASS V 3.9 
% 27.56/27.73  SPASS beiseite: Proof found.
% 27.56/27.73  % SZS status Theorem
% 27.56/27.73  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 27.56/27.73  SPASS derived 39723 clauses, backtracked 8759 clauses, performed 103 splits and kept 18438 clauses.
% 27.56/27.73  SPASS allocated 132164 KBytes.
% 27.56/27.73  SPASS spent	0:0:25.68 on the problem.
% 27.56/27.73  		0:00:00.05 for the input.
% 27.56/27.73  		0:00:00.33 for the FLOTTER CNF translation.
% 27.56/27.73  		0:00:01.17 for inferences.
% 27.56/27.73  		0:00:00.69 for the backtracking.
% 27.56/27.73  		0:0:22.30 for the reduction.
% 27.56/27.73  
% 27.56/27.73  
% 27.56/27.73  Here is a proof with depth 7, length 56 :
% 27.56/27.73  % SZS output start Refutation
% See solution above
% 27.56/27.73  Formulae used in the proof : gsy_c_Scratch__tptp__translate__39952__2902_ONUM639__thf__4__p_Obnd__n__1 help_pp_2_1_U gsy_c_Scratch__tptp__translate__39952__2902_ONUM639__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__39952__2902_ONUM639__thf__4__p_Obnd__omega fact_satz4a 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__3 fact_ATP_Olambda__7 help_fequal_1_1_fequal_001t__TPTP____Interpret__Oind_T
% 27.56/27.73  
%------------------------------------------------------------------------------