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