TSTP Solution File: NUM706+4 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM706+4 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n001.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 : 300s
% DateTime : Wed May 31 12:30:25 EDT 2023
% Result : Theorem 248.17s 31.74s
% Output : CNFRefutation 248.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 52 ( 15 unt; 0 def)
% Number of atoms : 136 ( 15 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 146 ( 62 ~; 62 |; 14 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 69 (; 67 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [B_1,B_2] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,axiom,
scratc214101377d_n_is = scratc695441016d_e_is(scratc272482122nd_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f111,axiom,
! [X] : scratc695441016d_e_is(X) = fequal_TPTP_ind,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f158,axiom,
! [X,Xa] :
( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
<=> ! [X2] :
( gg_TPTP_ind(X2)
=> ( scratc1814191352_is_of(X2,X)
=> pp(aa_TPTP_ind_bool(Xa,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f163,axiom,
pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f323,axiom,
! [Uu] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1)),Uu)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f336,axiom,
! [Uu] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f627,axiom,
! [X7,Y] :
( X7 != Y
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f628,axiom,
! [X7,Y] :
( ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) )
=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| X7 = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f632,conjecture,
pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f633,negated_conjecture,
~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa)),
inference(negated_conjecture,[status(cth)],[f632]) ).
fof(f652,plain,
! [X0,X1] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(X0,X1)),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f769,plain,
scratc214101377d_n_is = scratc695441016d_e_is(scratc272482122nd_nat),
inference(cnf_transformation,[status(esa)],[f64]) ).
fof(f877,plain,
! [X0] : scratc695441016d_e_is(X0) = fequal_TPTP_ind,
inference(cnf_transformation,[status(esa)],[f111]) ).
fof(f1023,plain,
! [X,Xa] :
( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
<=> ! [X2] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X)
| pp(aa_TPTP_ind_bool(Xa,X2)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f158]) ).
fof(f1024,plain,
! [X,Xa] :
( ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X)
| pp(aa_TPTP_ind_bool(Xa,X2)) ) )
& ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ? [X2] :
( gg_TPTP_ind(X2)
& scratc1814191352_is_of(X2,X)
& ~ pp(aa_TPTP_ind_bool(Xa,X2)) ) ) ),
inference(NNF_transformation,[status(esa)],[f1023]) ).
fof(f1025,plain,
( ! [X,Xa] :
( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X)
| pp(aa_TPTP_ind_bool(Xa,X2)) ) )
& ! [X,Xa] :
( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ? [X2] :
( gg_TPTP_ind(X2)
& scratc1814191352_is_of(X2,X)
& ~ pp(aa_TPTP_ind_bool(Xa,X2)) ) ) ),
inference(miniscoping,[status(esa)],[f1024]) ).
fof(f1026,plain,
( ! [X,Xa] :
( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X)
| pp(aa_TPTP_ind_bool(Xa,X2)) ) )
& ! [X,Xa] :
( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ( gg_TPTP_ind(sk0_12(Xa,X))
& scratc1814191352_is_of(sk0_12(Xa,X),X)
& ~ pp(aa_TPTP_ind_bool(Xa,sk0_12(Xa,X))) ) ) ),
inference(skolemization,[status(esa)],[f1025]) ).
fof(f1027,plain,
! [X0,X1,X2] :
( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X0),X1))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X0)
| pp(aa_TPTP_ind_bool(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f1026]) ).
fof(f1028,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc403153377all_of(X0),X1))
| gg_TPTP_ind(sk0_12(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f1026]) ).
fof(f1029,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc403153377all_of(X0),X1))
| scratc1814191352_is_of(sk0_12(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f1026]) ).
fof(f1030,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc403153377all_of(X0),X1))
| ~ pp(aa_TPTP_ind_bool(X1,sk0_12(X1,X0))) ),
inference(cnf_transformation,[status(esa)],[f1026]) ).
fof(f1038,plain,
pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx)),
inference(cnf_transformation,[status(esa)],[f163]) ).
fof(f1307,plain,
! [Uu] :
( ( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1)),Uu)) )
& ( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1)),Uu)) ) ),
inference(NNF_transformation,[status(esa)],[f323]) ).
fof(f1308,plain,
( ! [Uu] :
( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1)),Uu)) )
& ! [Uu] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1)),Uu)) ) ),
inference(miniscoping,[status(esa)],[f1307]) ).
fof(f1309,plain,
! [X0] :
( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X0))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(X0),scratc1030418234nd_n_1)),X0)) ),
inference(cnf_transformation,[status(esa)],[f1308]) ).
fof(f1362,plain,
! [Uu] :
( ( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1))) )
& ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1))) ) ),
inference(NNF_transformation,[status(esa)],[f336]) ).
fof(f1363,plain,
( ! [Uu] :
( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1))) )
& ! [Uu] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1))) ) ),
inference(miniscoping,[status(esa)],[f1362]) ).
fof(f1365,plain,
! [X0] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,X0),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(X0),scratc1030418234nd_n_1))) ),
inference(cnf_transformation,[status(esa)],[f1363]) ).
fof(f2637,plain,
! [X0,X1] :
( X0 != X1
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X0),X1)) ),
inference(cnf_transformation,[status(esa)],[f627]) ).
fof(f2638,plain,
! [X7,Y] :
( ~ gg_TPTP_ind(X7)
| ~ gg_TPTP_ind(Y)
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| X7 = Y ),
inference(pre_NNF_transformation,[status(esa)],[f628]) ).
fof(f2639,plain,
! [X0,X1] :
( ~ gg_TPTP_ind(X0)
| ~ gg_TPTP_ind(X1)
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X0),X1))
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f2638]) ).
fof(f2643,plain,
~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa)),
inference(cnf_transformation,[status(esa)],[f633]) ).
fof(f2709,plain,
scratc214101377d_n_is = fequal_TPTP_ind,
inference(paramodulation,[status(thm)],[f877,f769]) ).
fof(f2711,plain,
! [X0,X1] :
( ~ gg_TPTP_ind(X0)
| ~ gg_TPTP_ind(X1)
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,X0),X1))
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f2709,f2639]) ).
fof(f4263,plain,
! [X0,X1] :
( X0 != X1
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,X0),X1)) ),
inference(paramodulation,[status(thm)],[f2709,f2637]) ).
fof(f9424,plain,
! [X0] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X0))
| X0 != aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(X0),scratc1030418234nd_n_1) ),
inference(resolution,[status(thm)],[f1365,f4263]) ).
fof(f13109,plain,
! [X0] :
( ~ gg_TPTP_ind(X0)
| ~ scratc1814191352_is_of(X0,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X0)) ),
inference(resolution,[status(thm)],[f1027,f1038]) ).
fof(f29572,plain,
! [X0] :
( ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(X0),scratc1030418234nd_n_1))
| ~ gg_TPTP_ind(X0)
| aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(X0),scratc1030418234nd_n_1) = X0
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X0)) ),
inference(resolution,[status(thm)],[f2711,f1309]) ).
fof(f29573,plain,
! [X0] :
( ~ gg_TPTP_ind(X0)
| aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(X0),scratc1030418234nd_n_1) = X0
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f29572,f652]) ).
fof(f37361,plain,
! [X0] :
( ~ gg_TPTP_ind(X0)
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X0))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X0)) ),
inference(resolution,[status(thm)],[f29573,f9424]) ).
fof(f37377,plain,
! [X0] :
( ~ gg_TPTP_ind(sk0_12(aTP_Lamm_aa,X0))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bx,sk0_12(aTP_Lamm_aa,X0)))
| pp(aa_fun171081125l_bool(scratc403153377all_of(X0),aTP_Lamm_aa)) ),
inference(resolution,[status(thm)],[f37361,f1030]) ).
fof(f37378,plain,
! [X0] :
( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bx,sk0_12(aTP_Lamm_aa,X0)))
| pp(aa_fun171081125l_bool(scratc403153377all_of(X0),aTP_Lamm_aa)) ),
inference(forward_subsumption_resolution,[status(thm)],[f37377,f1028]) ).
fof(f37423,plain,
! [X0] :
( pp(aa_fun171081125l_bool(scratc403153377all_of(X0),aTP_Lamm_aa))
| ~ gg_TPTP_ind(sk0_12(aTP_Lamm_aa,X0))
| ~ scratc1814191352_is_of(sk0_12(aTP_Lamm_aa,X0),aTP_Lamm_a) ),
inference(resolution,[status(thm)],[f37378,f13109]) ).
fof(f37424,plain,
! [X0] :
( pp(aa_fun171081125l_bool(scratc403153377all_of(X0),aTP_Lamm_aa))
| ~ scratc1814191352_is_of(sk0_12(aTP_Lamm_aa,X0),aTP_Lamm_a) ),
inference(forward_subsumption_resolution,[status(thm)],[f37423,f1028]) ).
fof(f37779,plain,
( spl0_3725
<=> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa)) ),
introduced(split_symbol_definition) ).
fof(f37780,plain,
( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ spl0_3725 ),
inference(component_clause,[status(thm)],[f37779]) ).
fof(f37782,plain,
( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa)) ),
inference(resolution,[status(thm)],[f37424,f1029]) ).
fof(f37783,plain,
spl0_3725,
inference(split_clause,[status(thm)],[f37782,f37779]) ).
fof(f37786,plain,
( $false
| ~ spl0_3725 ),
inference(forward_subsumption_resolution,[status(thm)],[f37780,f2643]) ).
fof(f37787,plain,
~ spl0_3725,
inference(contradiction_clause,[status(thm)],[f37786]) ).
fof(f37788,plain,
$false,
inference(sat_refutation,[status(thm)],[f37783,f37787]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM706+4 : TPTP v8.1.2. Released v7.3.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n001.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue May 30 10:23:00 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.42 % Drodi V3.5.1
% 248.17/31.74 % Refutation found
% 248.17/31.74 % SZS status Theorem for theBenchmark: Theorem is valid
% 248.17/31.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 250.00/32.02 % Elapsed time: 31.653869 seconds
% 250.00/32.02 % CPU time: 249.957728 seconds
% 250.00/32.02 % Memory used: 1.036 GB
%------------------------------------------------------------------------------