%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM639+4 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:16:07 PM UTC 2026
% Result : Theorem 6.48s 2.14s
% Output : Refutation 9.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of formulae : 69 ( 28 unt; 0 def)
% Number of atoms : 158 ( 31 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 152 ( 63 ~; 68 |; 12 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 12 con; 0-2 aty)
% Number of variables : 81 ( 79 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0,X1] : gg_bool(aa_TPTP_ind_bool(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) ).
fof(f18,axiom,
! [X0,X1] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_aa_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind) ).
fof(f25,axiom,
! [X0] : scratc1289955817d_n_pl(X0) = aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__n__pl) ).
fof(f43,axiom,
scratc1289496631d_n_is = scratc1770836270d_e_is(scratc1472361728nd_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__n__is) ).
fof(f90,axiom,
! [X0] : scratc1770836270d_e_is(X0) = fequal_TPTP_ind,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__e__is) ).
fof(f137,axiom,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc1153622423all_of(X0),X1))
<=> ! [X2] :
( gg_TPTP_ind(X2)
=> ( scratc1829621698_is_of(X2,X0)
=> pp(aa_TPTP_ind_bool(X1,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__all__of) ).
fof(f142,axiom,
pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_bu)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_satz4a) ).
fof(f216,axiom,
! [X0] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X0))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(X0),scratc214542084nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ATP_Olambda__3) ).
fof(f220,axiom,
! [X0] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X0))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X0)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(X0),scratc214542084nd_n_1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ATP_Olambda__7) ).
fof(f302,axiom,
pp(fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
fof(f306,axiom,
! [X0] :
( gg_bool(X0)
=> ( X0 = fTrue
| X0 = fFalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
fof(f307,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
fof(f312,axiom,
! [X0,X1] :
( X0 != X1
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_001t__TPTP____Interpret__Oind_T) ).
fof(f313,axiom,
! [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 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_001t__TPTP____Interpret__Oind_T) ).
fof(f317,conjecture,
pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_aa)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f318,negated_conjecture,
~ pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_aa)),
inference(negated_conjecture,[status(cth)],[f317]) ).
fof(f319,plain,
~ pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_aa)),
inference(flattening,[],[f318]) ).
fof(f335,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc1153622423all_of(X0),X1))
<=> ! [X2] :
( pp(aa_TPTP_ind_bool(X1,X2))
| ~ scratc1829621698_is_of(X2,X0)
| ~ gg_TPTP_ind(X2) ) ),
inference(ennf_transformation,[],[f137]) ).
fof(f336,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc1153622423all_of(X0),X1))
<=> ! [X2] :
( pp(aa_TPTP_ind_bool(X1,X2))
| ~ scratc1829621698_is_of(X2,X0)
| ~ gg_TPTP_ind(X2) ) ),
inference(flattening,[],[f335]) ).
fof(f418,plain,
! [X0] :
( X0 = fTrue
| X0 = fFalse
| ~ gg_bool(X0) ),
inference(ennf_transformation,[],[f306]) ).
fof(f419,plain,
! [X0] :
( X0 = fTrue
| X0 = fFalse
| ~ gg_bool(X0) ),
inference(flattening,[],[f418]) ).
fof(f420,plain,
! [X0,X1] :
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X0),X1))
| X0 = X1
| ~ gg_TPTP_ind(X0)
| ~ gg_TPTP_ind(X1) ),
inference(ennf_transformation,[],[f313]) ).
fof(f421,plain,
! [X0,X1] :
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X0),X1))
| X0 = X1
| ~ gg_TPTP_ind(X0)
| ~ gg_TPTP_ind(X1) ),
inference(flattening,[],[f420]) ).
fof(f485,plain,
! [X0,X1] :
( ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X0),X1))
| ? [X2] :
( ~ pp(aa_TPTP_ind_bool(X1,X2))
& scratc1829621698_is_of(X2,X0)
& gg_TPTP_ind(X2) ) )
& ( ! [X2] :
( pp(aa_TPTP_ind_bool(X1,X2))
| ~ scratc1829621698_is_of(X2,X0)
| ~ gg_TPTP_ind(X2) )
| ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X0),X1)) ) ),
inference(nnf_transformation,[],[f336]) ).
fof(f486,plain,
! [X0,X1] :
( ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X0),X1))
| ? [X2] :
( ~ pp(aa_TPTP_ind_bool(X1,X2))
& scratc1829621698_is_of(X2,X0)
& gg_TPTP_ind(X2) ) )
& ( ! [X3] :
( pp(aa_TPTP_ind_bool(X1,X3))
| ~ scratc1829621698_is_of(X3,X0)
| ~ gg_TPTP_ind(X3) )
| ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X0),X1)) ) ),
inference(rectify,[],[f485]) ).
fof(f487,plain,
! [X0,X1] :
( ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X0),X1))
| ( ~ pp(aa_TPTP_ind_bool(X1,sK12(X0,X1)))
& scratc1829621698_is_of(sK12(X0,X1),X0)
& gg_TPTP_ind(sK12(X0,X1)) ) )
& ( ! [X3] :
( pp(aa_TPTP_ind_bool(X1,X3))
| ~ scratc1829621698_is_of(X3,X0)
| ~ gg_TPTP_ind(X3) )
| ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X0),X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X2,sK12(X0,X1))],[f486]) ).
fof(f508,plain,
! [X0] :
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(X0),scratc214542084nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X0))) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(X0),scratc214542084nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X0)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X0)) ) ),
inference(nnf_transformation,[],[f216]) ).
fof(f513,plain,
! [X0] :
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X0)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(X0),scratc214542084nd_n_1))) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X0)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(X0),scratc214542084nd_n_1)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X0)) ) ),
inference(nnf_transformation,[],[f220]) ).
fof(f620,plain,
! [X0,X1] : gg_bool(aa_TPTP_ind_bool(X0,X1)),
inference(cnf_transformation,[],[f17]) ).
fof(f621,plain,
! [X0,X1] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(X0,X1)),
inference(cnf_transformation,[],[f18]) ).
fof(f628,plain,
! [X0] : scratc1289955817d_n_pl(X0) = aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,X0)),
inference(cnf_transformation,[],[f25]) ).
fof(f654,plain,
scratc1289496631d_n_is = scratc1770836270d_e_is(scratc1472361728nd_nat),
inference(cnf_transformation,[],[f43]) ).
fof(f721,plain,
! [X0] : scratc1770836270d_e_is(X0) = fequal_TPTP_ind,
inference(cnf_transformation,[],[f90]) ).
fof(f812,plain,
! [X3,X0,X1] :
( ~ gg_TPTP_ind(X3)
| ~ scratc1829621698_is_of(X3,X0)
| pp(aa_TPTP_ind_bool(X1,X3))
| ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X0),X1)) ),
inference(cnf_transformation,[],[f487]) ).
fof(f813,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc1153622423all_of(X0),X1))
| gg_TPTP_ind(sK12(X0,X1)) ),
inference(cnf_transformation,[],[f487]) ).
fof(f814,plain,
! [X0,X1] :
( scratc1829621698_is_of(sK12(X0,X1),X0)
| pp(aa_fun171081125l_bool(scratc1153622423all_of(X0),X1)) ),
inference(cnf_transformation,[],[f487]) ).
fof(f815,plain,
! [X0,X1] :
( ~ pp(aa_TPTP_ind_bool(X1,sK12(X0,X1)))
| pp(aa_fun171081125l_bool(scratc1153622423all_of(X0),X1)) ),
inference(cnf_transformation,[],[f487]) ).
fof(f821,plain,
pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_bu)),
inference(cnf_transformation,[],[f142]) ).
fof(f925,plain,
! [X0] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(X0),scratc214542084nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X0)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X0)) ),
inference(cnf_transformation,[],[f508]) ).
fof(f936,plain,
! [X0] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X0))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X0)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(X0),scratc214542084nd_n_1))) ),
inference(cnf_transformation,[],[f513]) ).
fof(f1112,plain,
pp(fTrue),
inference(cnf_transformation,[],[f302]) ).
fof(f1116,plain,
! [X0] :
( ~ gg_bool(X0)
| fFalse = X0
| fTrue = X0 ),
inference(cnf_transformation,[],[f419]) ).
fof(f1117,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f307]) ).
fof(f1122,plain,
! [X0,X1] :
( X0 != X1
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X0),X1)) ),
inference(cnf_transformation,[],[f312]) ).
fof(f1123,plain,
! [X0,X1] :
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X0),X1))
| X0 = X1
| ~ gg_TPTP_ind(X0)
| ~ gg_TPTP_ind(X1) ),
inference(cnf_transformation,[],[f421]) ).
fof(f1127,plain,
~ pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_aa)),
inference(cnf_transformation,[],[f319]) ).
fof(f1138,plain,
scratc1289496631d_n_is = fequal_TPTP_ind,
inference(definition_unfolding,[],[f654,f721]) ).
fof(f1179,plain,
! [X0] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,X0)),scratc214542084nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X0)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X0)) ),
inference(definition_unfolding,[],[f925,f628]) ).
fof(f1182,plain,
! [X0] :
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X0)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,X0)),scratc214542084nd_n_1)))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X0)) ),
inference(definition_unfolding,[],[f936,f628]) ).
fof(f1243,plain,
! [X1] : pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X1),X1)),
inference(equality_resolution,[],[f1122]) ).
fof(f1281,plain,
gg_TPTP_ind(sK12(aTP_Lamm_a,aTP_Lamm_aa)),
inference(resolution,[],[f813,f1127]) ).
fof(f1282,plain,
! [X0,X1] :
( ~ scratc1829621698_is_of(sK12(aTP_Lamm_a,aTP_Lamm_aa),X0)
| pp(aa_TPTP_ind_bool(X1,sK12(aTP_Lamm_a,aTP_Lamm_aa)))
| ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X0),X1)) ),
inference(resolution,[],[f1281,f812]) ).
fof(f1285,plain,
! [X0] :
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X0)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,X0)),scratc214542084nd_n_1)))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X0)) ),
inference(superposition,[],[f1182,f1138]) ).
fof(f1288,plain,
! [X0] :
( pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_aa))
| pp(aa_TPTP_ind_bool(X0,sK12(aTP_Lamm_a,aTP_Lamm_aa)))
| ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),X0)) ),
inference(resolution,[],[f814,f1282]) ).
fof(f1289,plain,
! [X0] :
( pp(aa_TPTP_ind_bool(X0,sK12(aTP_Lamm_a,aTP_Lamm_aa)))
| ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),X0)) ),
inference(forward_subsumption_resolution,[],[f1288,f1127]) ).
fof(f1378,plain,
! [X0] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,X0)),scratc214542084nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X0)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X0)) ),
inference(superposition,[],[f1179,f1138]) ).
fof(f1379,plain,
! [X0] :
( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X0))
| aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X0) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,X0)),scratc214542084nd_n_1)
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,X0)),scratc214542084nd_n_1))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X0)) ),
inference(resolution,[],[f1378,f1123]) ).
fof(f1380,plain,
! [X0] :
( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X0))
| aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X0) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,X0)),scratc214542084nd_n_1)
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,X0)),scratc214542084nd_n_1)) ),
inference(forward_subsumption_resolution,[],[f1379,f621]) ).
fof(f1381,plain,
! [X0] :
( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X0))
| aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X0) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,X0)),scratc214542084nd_n_1) ),
inference(forward_subsumption_resolution,[],[f1380,f621]) ).
fof(f1440,plain,
! [X0,X1] :
( aa_TPTP_ind_bool(X0,X1) = fTrue
| aa_TPTP_ind_bool(X0,X1) = fFalse ),
inference(resolution,[],[f620,f1116]) ).
fof(f1531,plain,
! [X0,X1] :
( ~ pp(fTrue)
| pp(aa_fun171081125l_bool(scratc1153622423all_of(X1),X0))
| fFalse = aa_TPTP_ind_bool(X0,sK12(X1,X0)) ),
inference(superposition,[],[f815,f1440]) ).
fof(f1606,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc1153622423all_of(X1),X0))
| fFalse = aa_TPTP_ind_bool(X0,sK12(X1,X0)) ),
inference(forward_subsumption_resolution,[],[f1531,f1112]) ).
fof(f1612,plain,
fFalse = aa_TPTP_ind_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_aa)),
inference(resolution,[],[f1606,f1127]) ).
fof(f1704,plain,
( aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,sK12(aTP_Lamm_a,aTP_Lamm_aa)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,sK12(aTP_Lamm_a,aTP_Lamm_aa))),scratc214542084nd_n_1)
| ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_bu)) ),
inference(resolution,[],[f1381,f1289]) ).
fof(f1710,plain,
aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,sK12(aTP_Lamm_a,aTP_Lamm_aa)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,sK12(aTP_Lamm_a,aTP_Lamm_aa))),scratc214542084nd_n_1),
inference(forward_subsumption_resolution,[],[f1704,f821]) ).
fof(f1714,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,sK12(aTP_Lamm_a,aTP_Lamm_aa))),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,sK12(aTP_Lamm_a,aTP_Lamm_aa))))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_aa))) ),
inference(superposition,[],[f1285,f1710]) ).
fof(f1718,plain,
pp(aa_TPTP_ind_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_aa))),
inference(forward_subsumption_resolution,[],[f1714,f1243]) ).
fof(f1722,plain,
pp(fFalse),
inference(forward_demodulation,[],[f1718,f1612]) ).
fof(f1725,plain,
$false,
inference(forward_subsumption_resolution,[],[f1722,f1117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM639+4 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n003.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 20:55:27 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.48/2.14 % (909918)Detected formulas, will run a generic FOF schedule.
% 6.48/2.14 % (909927)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3939032453:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.48/2.14 % (909927)Refutation not found, incomplete strategy
% 6.48/2.14 % (909927)------------------------------
% 6.48/2.14 % (909927)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/2.14 % (909927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/2.14 % (909927)CaDiCaL version: 2.1.3
% 6.48/2.14 % (909927)Termination reason: Refutation not found, incomplete strategy
% 6.48/2.14 % (909927)Time elapsed: 0.002 s
% 6.48/2.14 % (909927)Peak memory usage: 88 MB
% 6.48/2.14 % (909927)Instructions burned: 3 (million)
% 6.48/2.14 % (909924)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2053095861:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.48/2.14 % (909925)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3081582583:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.48/2.14 % (909923)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1313794570:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.48/2.14 % (909926)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3446426943:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.48/2.14 % (909928)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1460097239:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.48/2.14 % (909926)Refutation not found, incomplete strategy
% 6.48/2.14 % (909926)------------------------------
% 6.48/2.14 % (909926)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/2.14 % (909926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/2.14 % (909926)CaDiCaL version: 2.1.3
% 6.48/2.14 % (909926)Termination reason: Refutation not found, incomplete strategy
% 6.48/2.14 % (909926)Time elapsed: 0.002 s
% 6.48/2.14 % (909926)Peak memory usage: 88 MB
% 6.48/2.14 % (909926)Instructions burned: 1 (million)
% 6.48/2.14 % (909929)dis-21_1_sil=8000:lcm=predicate:random_seed=3974125312:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 6.48/2.14 % (909929)Instruction limit reached!
% 6.48/2.14 % (909929)------------------------------
% 6.48/2.14 % (909929)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/2.14 % (909929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/2.14 % (909929)CaDiCaL version: 2.1.3
% 6.48/2.14 % (909929)Termination reason: Instruction limit
% 6.48/2.14 % (909929)Termination phase: Saturation
% 6.48/2.14 % (909929)Time elapsed: 0.079 s
% 6.48/2.14 % (909929)Peak memory usage: 90 MB
% 6.48/2.14 % (909929)Instructions burned: 129 (million)
% 6.48/2.14 % (909928)Instruction limit reached!
% 6.48/2.14 % (909928)------------------------------
% 6.48/2.14 % (909928)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/2.14 % (909928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/2.14 % (909928)CaDiCaL version: 2.1.3
% 6.48/2.14 % (909928)Termination reason: Instruction limit
% 6.48/2.14 % (909928)Termination phase: Saturation
% 6.48/2.14 % (909928)Time elapsed: 0.094 s
% 6.48/2.14 % (909928)Peak memory usage: 90 MB
% 6.48/2.14 % (909928)Instructions burned: 139 (million)
% 6.48/2.14 % (909927)------------------------------
% 6.48/2.14 % (909927)------------------------------
% 6.48/2.14 % (909939)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1992197149:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.48/2.14 % (909939)Refutation not found, incomplete strategy
% 6.48/2.14 % (909939)------------------------------
% 6.48/2.14 % (909939)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/2.14 % (909939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/2.14 % (909939)CaDiCaL version: 2.1.3
% 6.48/2.14 % (909939)Termination reason: Refutation not found, incomplete strategy
% 6.48/2.14 % (909939)Time elapsed: 0.003 s
% 6.48/2.14 % (909939)Peak memory usage: 89 MB
% 6.48/2.14 % (909939)Instructions burned: 8 (million)
% 6.48/2.14 % (909937)lrs+10_1_sil=8000:sp=occurrence:random_seed=3354013094:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.48/2.14 % (909937)Refutation not found, incomplete strategy
% 6.48/2.14 % (909937)------------------------------
% 6.48/2.14 % (909937)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/2.14 % (909937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/2.14 % (909937)CaDiCaL version: 2.1.3
% 6.48/2.14 % (909937)Termination reason: Refutation not found, incomplete strategy
% 6.48/2.14 % (909937)Time elapsed: 0.006 s
% 6.48/2.14 % (909937)Peak memory usage: 89 MB
% 6.48/2.14 % (909937)Instructions burned: 7 (million)
% 6.48/2.14 % (909938)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3440362672:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.48/2.14 % (909938)Refutation not found, incomplete strategy
% 6.48/2.14 % (909938)------------------------------
% 6.48/2.14 % (909938)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/2.14 % (909938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/2.14 % (909938)CaDiCaL version: 2.1.3
% 6.48/2.14 % (909938)Termination reason: Refutation not found, incomplete strategy
% 6.48/2.14 % (909938)Time elapsed: 0.003 s
% 6.48/2.14 % (909938)Peak memory usage: 88 MB
% 6.48/2.14 % (909938)Instructions burned: 5 (million)
% 6.48/2.14 % (909926)------------------------------
% 6.48/2.14 % (909926)------------------------------
% 6.48/2.14 % (909939)------------------------------
% 6.48/2.14 % (909939)------------------------------
% 6.48/2.14 % (909943)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3862130741:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 6.48/2.14 % (909944)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3615183593:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 6.48/2.14 % (909944)Refutation not found, incomplete strategy
% 6.48/2.14 % (909944)------------------------------
% 6.48/2.14 % (909944)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/2.14 % (909944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/2.14 % (909944)CaDiCaL version: 2.1.3
% 6.48/2.14 % (909944)Termination reason: Refutation not found, incomplete strategy
% 6.48/2.14 % (909944)Time elapsed: 0.003 s
% 6.48/2.14 % (909944)Peak memory usage: 89 MB
% 6.48/2.14 % (909944)Instructions burned: 7 (million)
% 6.48/2.14 % (909937)------------------------------
% 6.48/2.14 % (909937)------------------------------
% 6.48/2.14 % (909938)------------------------------
% 6.48/2.14 % (909938)------------------------------
% 6.48/2.14 % (909943)Instruction limit reached!
% 6.48/2.14 % (909943)------------------------------
% 6.48/2.14 % (909943)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/2.14 % (909943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/2.14 % (909943)CaDiCaL version: 2.1.3
% 6.48/2.14 % (909943)Termination reason: Instruction limit
% 6.48/2.14 % (909943)Termination phase: Saturation
% 6.48/2.14 % (909943)Time elapsed: 0.146 s
% 6.48/2.14 % (909943)Peak memory usage: 94 MB
% 6.48/2.14 % (909943)Instructions burned: 249 (million)
% 6.48/2.14 % (909944)------------------------------
% 6.48/2.14 % (909944)------------------------------
% 6.48/2.14 % (909947)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1516130327:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 6.48/2.14 % (909948)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=493544200:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 6.48/2.14 % (909949)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3158876409:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 6.48/2.14 % (909948)Instruction limit reached!
% 6.48/2.14 % (909948)------------------------------
% 6.48/2.14 % (909948)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/2.14 % (909948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/2.14 % (909948)CaDiCaL version: 2.1.3
% 6.48/2.14 % (909948)Termination reason: Instruction limit
% 6.48/2.14 % (909948)Termination phase: Saturation
% 6.48/2.14 % (909948)Time elapsed: 0.071 s
% 6.48/2.14 % (909948)Peak memory usage: 90 MB
% 6.48/2.14 % (909948)Instructions burned: 113 (million)
% 6.48/2.14 % (909950)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=178214168:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.48/2.14 % (909950)Instruction limit reached!
% 6.48/2.14 % (909950)------------------------------
% 6.48/2.14 % (909950)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/2.14 % (909950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/2.14 % (909950)CaDiCaL version: 2.1.3
% 6.48/2.14 % (909950)Termination reason: Instruction limit
% 6.48/2.14 % (909950)Termination phase: Saturation
% 6.48/2.14 % (909950)Time elapsed: 0.034 s
% 6.48/2.14 % (909950)Peak memory usage: 89 MB
% 6.48/2.14 % (909950)Instructions burned: 117 (million)
% 6.48/2.14 % (909949)Instruction limit reached!
% 6.48/2.14 % (909949)------------------------------
% 6.48/2.14 % (909949)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/2.14 % (909949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/2.14 % (909949)CaDiCaL version: 2.1.3
% 6.48/2.14 % (909949)Termination reason: Instruction limit
% 6.48/2.14 % (909949)Termination phase: Saturation
% 6.48/2.14 % (909949)Time elapsed: 0.063 s
% 6.48/2.14 % (909949)Peak memory usage: 89 MB
% 6.48/2.14 % (909949)Instructions burned: 128 (million)
% 6.48/2.14 % (909956)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3434452713:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 6.48/2.14 % (909956)Refutation not found, incomplete strategy
% 6.48/2.14 % (909956)------------------------------
% 6.48/2.14 % (909956)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/2.14 % (909956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/2.14 % (909956)CaDiCaL version: 2.1.3
% 6.48/2.14 % (909956)Termination reason: Refutation not found, incomplete strategy
% 6.48/2.14 % (909956)Time elapsed: 0.012 s
% 6.48/2.14 % (909956)Peak memory usage: 89 MB
% 6.48/2.14 % (909956)Instructions burned: 41 (million)
% 6.48/2.14 % (909955)lrs+10_1_sil=8000:sp=occurrence:random_seed=2001402242:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 6.48/2.14 % (909924)First to succeed.
% 6.48/2.14 % (909924)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-909918"
% 6.48/2.14 % (909957)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3231949117:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 6.48/2.14 % (909956)------------------------------
% 6.48/2.14 % (909956)------------------------------
% 6.48/2.14 % (909923)Also succeeded, but the first one will report.
% 6.48/2.14 % (909961)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=609197315:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 6.48/2.14 % (909961)Instruction limit reached!
% 6.48/2.14 % (909961)------------------------------
% 6.48/2.14 % (909961)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/2.14 % (909961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/2.14 % (909961)CaDiCaL version: 2.1.3
% 6.48/2.14 % (909961)Termination reason: Instruction limit
% 6.48/2.14 % (909961)Termination phase: Saturation
% 6.48/2.14 % (909961)Time elapsed: 0.040 s
% 6.48/2.14 % (909961)Peak memory usage: 91 MB
% 6.48/2.14 % (909961)Instructions burned: 134 (million)
% 6.48/2.14 % (909924)Refutation found. Thanks to Tanya!
% 6.48/2.14 % SZS status Theorem for theBenchmark
% 6.48/2.14 % SZS output start Proof for theBenchmark
% See solution above
% 9.52/2.33 % (909924)------------------------------
% 9.52/2.33 % (909924)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.52/2.33 % (909924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.52/2.33 % (909924)CaDiCaL version: 2.1.3
% 9.52/2.33 % (909924)Termination reason: Refutation
% 9.52/2.33 % (909924)Time elapsed: 0.864 s
% 9.52/2.33 % (909924)Peak memory usage: 137 MB
% 9.52/2.33 % (909924)Instructions burned: 1326 (million)
% 9.52/2.33 % (909924)------------------------------
% 9.52/2.33 % (909924)------------------------------
% 9.52/2.33 % (909918)Success in time 1.272 s
% 9.52/2.33 % Vampire exiting
%------------------------------------------------------------------------------