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