TSTP Solution File: NUM669+4 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM669+4 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 : Sun Sep 18 13:11:21 EDT 2022
% Result : Theorem 7.89s 5.34s
% Output : Proof 7.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 147
% Syntax : Number of formulae : 318 ( 91 unt; 45 typ; 0 def)
% Number of atoms : 1326 ( 101 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 1893 ( 882 ~; 763 |; 22 &)
% ( 217 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of FOOLs : 42 ( 42 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 25 >; 13 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 42 ( 42 usr; 20 con; 0-2 aty)
% Number of variables : 394 ( 360 !; 0 ?; 394 :)
% Comments :
%------------------------------------------------------------------------------
tff(pp_type,type,
pp: $i > $o ).
tff(aa_TPTP_ind_bool_type,type,
aa_TPTP_ind_bool: ( $i * $i ) > $i ).
tff(aa_TPTP_ind_TPTP_ind_type,type,
aa_TPTP_ind_TPTP_ind: ( $i * $i ) > $i ).
tff(scratc2095348162ptyset_type,type,
scratc2095348162ptyset: $i ).
tff(scratc2018566726d_Sing_type,type,
scratc2018566726d_Sing: $i ).
tff(scratc1307162165nunion_type,type,
scratc1307162165nunion: $i > $i ).
tff(scratc80697981d_n_pl_type,type,
scratc80697981d_n_pl: $i > $i ).
tff(tptp_fun_X2_12_type,type,
tptp_fun_X2_12: ( $i * $i ) > $i ).
tff(aTP_Lamm_a_type,type,
aTP_Lamm_a: $i ).
tff(aTP_Lamm_aa_type,type,
aTP_Lamm_aa: $i ).
tff(aa_TPT43085870d_bool_type,type,
aa_TPT43085870d_bool: ( $i * $i ) > $i ).
tff(scratc2027709436nd_iii_type,type,
scratc2027709436nd_iii: $i ).
tff(scratc2076836790rdsucc_type,type,
scratc2076836790rdsucc: $i ).
tff(gg_TPTP_ind_type,type,
gg_TPTP_ind: $i > $o ).
tff(fequal_TPTP_ind_type,type,
fequal_TPTP_ind: $i ).
tff(scratc561578434d_e_is_type,type,
scratc561578434d_e_is: $i > $i ).
tff(aa_fun1431113780TP_ind_type,type,
aa_fun1431113780TP_ind: ( $i * $i ) > $i ).
tff(aTP_Lamm_ag_type,type,
aTP_Lamm_ag: $i ).
tff(scratc494515559_d_Sep_type,type,
scratc494515559_d_Sep: $i > $i ).
tff(scratc1509955612_nat_p_type,type,
scratc1509955612_nat_p: $i ).
tff(scratc1943012394univof_type,type,
scratc1943012394univof: $i ).
tff(scratc1802667946bnd_if_type,type,
scratc1802667946bnd_if: ( $i * $i ) > $i ).
tff(aa_fun277296641TP_ind_type,type,
aa_fun277296641TP_ind: ( $i * $i ) > $i ).
tff(aa_fun1235454963TP_ind_type,type,
aa_fun1235454963TP_ind: ( $i * $i ) > $i ).
tff(aTP_Lamm_bm_type,type,
aTP_Lamm_bm: $i > $i ).
tff(aa_TPT494704832TP_ind_type,type,
aa_TPT494704832TP_ind: ( $i * $i ) > $i ).
tff(scratc1124382172d_repl_type,type,
scratc1124382172d_repl: $i ).
tff(fEx_TPTP_ind_type,type,
fEx_TPTP_ind: $i > $i ).
tff(cOMBS_2003118649l_bool_type,type,
cOMBS_2003118649l_bool: ( $i * $i ) > $i ).
tff(cOMBB_658106424TP_ind_type,type,
cOMBB_658106424TP_ind: ( $i * $i ) > $i ).
tff(cOMBC_1555011498d_bool_type,type,
cOMBC_1555011498d_bool: $i > $i ).
tff(scratc1802667954bnd_in_type,type,
scratc1802667954bnd_in: $i ).
tff(fconj_type,type,
fconj: $i ).
tff(aTP_Lamm_ex_type,type,
aTP_Lamm_ex: $i ).
tff(scratc98832752nd_n_1_type,type,
scratc98832752nd_n_1: $i ).
tff(scratc80238795d_n_is_type,type,
scratc80238795d_n_is: $i ).
tff(scratc1623311406_is_of_type,type,
scratc1623311406_is_of: ( $i * $i ) > $o ).
tff(aa_fun171081125l_bool_type,type,
aa_fun171081125l_bool: ( $i * $i ) > $i ).
tff(scratc846727211all_of_type,type,
scratc846727211all_of: $i > $i ).
tff(scratc1229761461ffprop_type,type,
scratc1229761461ffprop: $i > $i ).
tff(scratc2104871667l_some_type,type,
scratc2104871667l_some: $i > $i ).
tff(scratc701212661n_some_type,type,
scratc701212661n_some: $i ).
tff(scratc1728063742_29_ii_type,type,
scratc1728063742_29_ii: $i ).
tff(aTP_Lamm_bp_type,type,
aTP_Lamm_bp: $i ).
tff(aTP_Lamm_bq_type,type,
aTP_Lamm_bq: $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(X),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,X)) )
<=> ( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(X),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,X)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(X),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,X)) )
<=> ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(X),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,X)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(X),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,X)) )
<=> ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(X),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(X),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__ordsucc) ).
tff(5,plain,
! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(X),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,X)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(X),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,X)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(X),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,X)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(X),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,X)) )
| ( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) = aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( ~ ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(X),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,X)) )
| ( aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset)),
inference(unit_resolution,[status(thm)],[11,7]) ).
tff(13,plain,
aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset)) = aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset))) = aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
( gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset))))
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))) ),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
^ [B_1: $i,B_2: $i] :
refl(
( gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))
<=> ! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))
<=> ! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_aa_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind) ).
tff(20,plain,
! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
( ~ ! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))
| gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset)))),
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),
inference(modus_ponens,[status(thm)],[24,15]) ).
tff(26,plain,
^ [X: $i,Xa: $i] :
refl(
( ( aa_fun1431113780TP_ind(scratc494515559_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1802667954bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc2095348162ptyset) )
<=> ( aa_fun1431113780TP_ind(scratc494515559_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1802667954bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc2095348162ptyset) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc494515559_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1802667954bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc2095348162ptyset) )
<=> ! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc494515559_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1802667954bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc2095348162ptyset) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc494515559_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1802667954bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc2095348162ptyset) )
<=> ! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc494515559_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1802667954bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc2095348162ptyset) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,axiom,
! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc494515559_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1802667954bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc2095348162ptyset) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__d__Sep) ).
tff(30,plain,
! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc494515559_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1802667954bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc2095348162ptyset) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc494515559_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1802667954bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc2095348162ptyset) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc494515559_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1802667954bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc2095348162ptyset) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ~ ! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc494515559_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1802667954bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc2095348162ptyset) )
| ( aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag) = aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1802667954bnd_in),aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p))),aTP_Lamm_ag)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bm(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag))),scratc2095348162ptyset) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag) = aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1802667954bnd_in),aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p))),aTP_Lamm_ag)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bm(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag))),scratc2095348162ptyset),
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)) = scratc561578434d_e_is(aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1802667954bnd_in),aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p))),aTP_Lamm_ag)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bm(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag))),scratc2095348162ptyset)),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
scratc561578434d_e_is(aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1802667954bnd_in),aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p))),aTP_Lamm_ag)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bm(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag))),scratc2095348162ptyset)) = scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
^ [X: $i] :
refl(
( ( scratc561578434d_e_is(X) = fequal_TPTP_ind )
<=> ( scratc561578434d_e_is(X) = fequal_TPTP_ind ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [X: $i] : ( scratc561578434d_e_is(X) = fequal_TPTP_ind )
<=> ! [X: $i] : ( scratc561578434d_e_is(X) = fequal_TPTP_ind ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [X: $i] : ( scratc561578434d_e_is(X) = fequal_TPTP_ind )
<=> ! [X: $i] : ( scratc561578434d_e_is(X) = fequal_TPTP_ind ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,axiom,
! [X: $i] : ( scratc561578434d_e_is(X) = fequal_TPTP_ind ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__e__is) ).
tff(41,plain,
! [X: $i] : ( scratc561578434d_e_is(X) = fequal_TPTP_ind ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [X: $i] : ( scratc561578434d_e_is(X) = fequal_TPTP_ind ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [X: $i] : ( scratc561578434d_e_is(X) = fequal_TPTP_ind ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
( ~ ! [X: $i] : ( scratc561578434d_e_is(X) = fequal_TPTP_ind )
| ( scratc561578434d_e_is(aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1802667954bnd_in),aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p))),aTP_Lamm_ag)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bm(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag))),scratc2095348162ptyset)) = fequal_TPTP_ind ) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
scratc561578434d_e_is(aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1802667954bnd_in),aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p))),aTP_Lamm_ag)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bm(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag))),scratc2095348162ptyset)) = fequal_TPTP_ind,
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
fequal_TPTP_ind = scratc561578434d_e_is(aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1802667954bnd_in),aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p))),aTP_Lamm_ag)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bm(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag))),scratc2095348162ptyset)),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
fequal_TPTP_ind = scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),
inference(transitivity,[status(thm)],[46,36]) ).
tff(48,plain,
aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))) = aa_TPT43085870d_bool(scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(monotonicity,[status(thm)],[48,10]) ).
tff(50,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))) ),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
^ [Uu: $i] :
refl(
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu))) )
<=> ( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu))) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu))) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
^ [Uu: $i] :
rewrite(
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),scratc98832752nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu))) )
<=> ( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu))) ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),scratc98832752nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu))) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),scratc98832752nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),scratc98832752nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,axiom,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),scratc98832752nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ATP_Olambda__3) ).
tff(58,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),scratc98832752nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu))) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu))) ),
inference(modus_ponens,[status(thm)],[58,55]) ).
tff(60,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu))) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu))) ),
inference(modus_ponens,[status(thm)],[60,53]) ).
tff(62,plain,
( ~ ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu))) )
| ( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
^ [X: $i,Xa: $i] :
refl(
( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(65,plain,
( ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
^ [X: $i,Xa: $i] :
rewrite(
( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(67,plain,
( ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) ),
inference(transitivity,[status(thm)],[67,65]) ).
tff(69,plain,
^ [X: $i,Xa: $i] :
trans(
monotonicity(
rewrite(
( ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
<=> ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) ) )),
monotonicity(
rewrite(
( ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) )
<=> ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) )),
( ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) )
<=> ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )),
( ( ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ( ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
rewrite(
( ( ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
( ( ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(70,plain,
( ! [X: $i,Xa: $i] :
( ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
^ [X: $i,Xa: $i] :
rewrite(
( ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
<=> ! [X2: $i] :
( gg_TPTP_ind(X2)
=> ( scratc1623311406_is_of(X2,X)
=> pp(aa_TPTP_ind_bool(Xa,X2)) ) ) )
<=> ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) ) )),
inference(bind,[status(th)],]) ).
tff(73,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
<=> ! [X2: $i] :
( gg_TPTP_ind(X2)
=> ( scratc1623311406_is_of(X2,X)
=> pp(aa_TPTP_ind_bool(Xa,X2)) ) ) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,axiom,
! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
<=> ! [X2: $i] :
( gg_TPTP_ind(X2)
=> ( scratc1623311406_is_of(X2,X)
=> pp(aa_TPTP_ind_bool(Xa,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__all__of) ).
tff(75,plain,
! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
! [X: $i,Xa: $i] :
( ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ),
inference(modus_ponens,[status(thm)],[77,70]) ).
tff(79,plain,
! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ),
inference(modus_ponens,[status(thm)],[78,68]) ).
tff(80,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ) ),
inference(unit_resolution,[status(thm)],[80,79]) ).
tff(82,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) )
| pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(83,plain,
( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[82,81]) ).
tff(84,plain,
( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
<=> ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa)) ),
inference(rewrite,[status(thm)],]) ).
tff(85,axiom,
~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(86,plain,
~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa)),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
( ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) )
| pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(88,plain,
( ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) )
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[87,86]) ).
tff(89,plain,
~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ),
inference(unit_resolution,[status(thm)],[88,83]) ).
tff(90,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ),
inference(tautology,[status(thm)],]) ).
tff(91,plain,
scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a),
inference(unit_resolution,[status(thm)],[90,89]) ).
tff(92,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) ),
inference(tautology,[status(thm)],]) ).
tff(93,plain,
gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),
inference(unit_resolution,[status(thm)],[92,89]) ).
tff(94,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_ex))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_ex))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,tptp_fun_X2_12(aTP_Lamm_ex,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ex,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_ex,aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_ex))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_ex))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,tptp_fun_X2_12(aTP_Lamm_ex,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ex,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_ex,aTP_Lamm_a),aTP_Lamm_a) ) ) ),
inference(unit_resolution,[status(thm)],[94,79]) ).
tff(96,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_ex))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_ex))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,tptp_fun_X2_12(aTP_Lamm_ex,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ex,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_ex,aTP_Lamm_a),aTP_Lamm_a) ) )
| ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_ex))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(97,plain,
( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_ex))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[96,95]) ).
tff(98,plain,
( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_ex))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_ex)) ),
inference(rewrite,[status(thm)],]) ).
tff(99,axiom,
pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_ex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_satz4a) ).
tff(100,plain,
pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_ex)),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_ex))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_ex))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(102,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_ex))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[101,100]) ).
tff(103,plain,
! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ),
inference(unit_resolution,[status(thm)],[102,97]) ).
tff(104,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_ex,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_ex,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_ex,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(106,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_ex,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_ex,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_ex,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_ex,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(transitivity,[status(thm)],[106,104]) ).
tff(108,plain,
( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_ex,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(109,plain,
( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_ex,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
pp(aa_TPTP_ind_bool(aTP_Lamm_ex,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[109,103,93,91]) ).
tff(111,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) )
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_ex,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(tautology,[status(thm)],]) ).
tff(112,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_ex,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[111,110]) ).
tff(113,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))),
inference(unit_resolution,[status(thm)],[112,63]) ).
tff(114,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))),
inference(modus_ponens,[status(thm)],[113,51]) ).
tff(115,plain,
( gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(116,plain,
( gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
( ~ ! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))
| gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(118,plain,
gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[117,22]) ).
tff(119,plain,
gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))),
inference(modus_ponens,[status(thm)],[118,116]) ).
tff(120,plain,
^ [X7: $i,Y: $i] :
refl(
( ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
<=> ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
inference(bind,[status(th)],]) ).
tff(121,plain,
( ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
<=> ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) ),
inference(quant_intro,[status(thm)],[120]) ).
tff(122,plain,
^ [X7: $i,Y: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) )
<=> ~ ( ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
( ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) )
<=> ~ ~ ( ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
rewrite(
( ~ ~ ( ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
<=> ( ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
( ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) )
<=> ( ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
( ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) )
<=> ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
rewrite(
( ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
<=> ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
( ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) )
<=> ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
inference(bind,[status(th)],]) ).
tff(123,plain,
( ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) )
<=> ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,plain,
( ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) )
<=> ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(125,plain,
^ [X7: $i,Y: $i] :
rewrite(
( ( ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) )
=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ( X7 = Y ) ) )
<=> ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) ) )),
inference(bind,[status(th)],]) ).
tff(126,plain,
( ! [X7: $i,Y: $i] :
( ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) )
=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ( X7 = Y ) ) )
<=> ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) ) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,axiom,
! [X7: $i,Y: $i] :
( ( 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',help_fequal_1_1_fequal_001t__TPTP____Interpret__Oind_T) ).
tff(128,plain,
! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) ),
inference(modus_ponens,[status(thm)],[128,124]) ).
tff(130,plain,
! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) ),
inference(skolemize,[status(sab)],[129]) ).
tff(131,plain,
! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ),
inference(modus_ponens,[status(thm)],[130,123]) ).
tff(132,plain,
! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ),
inference(modus_ponens,[status(thm)],[131,121]) ).
tff(133,plain,
( ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ( aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))) )
<=> ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ( aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(134,plain,
( ( ( aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))) )
<=> ( ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ( aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(135,plain,
( ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ( aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))) )
<=> ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ( aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))) ) ),
inference(monotonicity,[status(thm)],[134]) ).
tff(136,plain,
( ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ( aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))) )
<=> ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ( aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))) ) ),
inference(transitivity,[status(thm)],[135,133]) ).
tff(137,plain,
( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ( aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ( aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))) ),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
( ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ( aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))) ),
inference(unit_resolution,[status(thm)],[138,132]) ).
tff(140,plain,
aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[139,119,114,25]) ).
tff(141,plain,
aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset))) = aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),
inference(transitivity,[status(thm)],[14,140,10]) ).
tff(142,plain,
aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset)))) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset)))))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset))))) ),
inference(symmetry,[status(thm)],[143]) ).
tff(145,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
<=> ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset))))) ),
inference(monotonicity,[status(thm)],[144]) ).
tff(146,plain,
aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(monotonicity,[status(thm)],[10]) ).
tff(147,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(monotonicity,[status(thm)],[146]) ).
tff(148,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
<=> ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(monotonicity,[status(thm)],[147]) ).
tff(149,plain,
^ [X: $i,Xa: $i] :
refl(
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) )
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) ) )),
inference(bind,[status(th)],]) ).
tff(150,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) ) ),
inference(quant_intro,[status(thm)],[149]) ).
tff(151,plain,
^ [X: $i,Xa: $i] :
rewrite(
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) )
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) ) )),
inference(bind,[status(th)],]) ).
tff(152,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) ) ),
inference(quant_intro,[status(thm)],[151]) ).
tff(153,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(154,axiom,
! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__iii) ).
tff(155,plain,
! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) ),
inference(modus_ponens,[status(thm)],[154,153]) ).
tff(156,plain,
! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) ),
inference(modus_ponens,[status(thm)],[155,152]) ).
tff(157,plain,
! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) ),
inference(skolemize,[status(sab)],[156]) ).
tff(158,plain,
! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) ),
inference(modus_ponens,[status(thm)],[157,150]) ).
tff(159,plain,
( ~ ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))) )
| ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(160,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[159,158]) ).
tff(161,plain,
scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) = scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(monotonicity,[status(thm)],[10]) ).
tff(162,plain,
aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),
inference(monotonicity,[status(thm)],[161]) ).
tff(163,plain,
aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) = aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(monotonicity,[status(thm)],[162]) ).
tff(164,plain,
( pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(monotonicity,[status(thm)],[163]) ).
tff(165,plain,
( pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(symmetry,[status(thm)],[164]) ).
tff(166,plain,
( ~ pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
<=> ~ pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(monotonicity,[status(thm)],[165]) ).
tff(167,plain,
^ [X: $i,Xa: $i] :
refl(
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) )
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) ) )),
inference(bind,[status(th)],]) ).
tff(168,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) ) ),
inference(quant_intro,[status(thm)],[167]) ).
tff(169,plain,
^ [X: $i,Xa: $i] :
rewrite(
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) )
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) ) )),
inference(bind,[status(th)],]) ).
tff(170,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) ) ),
inference(quant_intro,[status(thm)],[169]) ).
tff(171,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(172,axiom,
! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__d__29__ii) ).
tff(173,plain,
! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) ),
inference(modus_ponens,[status(thm)],[172,171]) ).
tff(174,plain,
! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) ),
inference(modus_ponens,[status(thm)],[173,170]) ).
tff(175,plain,
! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) ),
inference(skolemize,[status(sab)],[174]) ).
tff(176,plain,
! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) ),
inference(modus_ponens,[status(thm)],[175,168]) ).
tff(177,plain,
( ~ ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))) )
| ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(178,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[177,176]) ).
tff(179,plain,
^ [Uu: $i] :
refl(
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),Uu)) )
<=> ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),Uu)) ) )),
inference(bind,[status(th)],]) ).
tff(180,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),Uu)) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),Uu)) ) ),
inference(quant_intro,[status(thm)],[179]) ).
tff(181,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),Uu)) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),Uu)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(182,axiom,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),Uu)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ATP_Olambda__9) ).
tff(183,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),Uu)) ),
inference(modus_ponens,[status(thm)],[182,181]) ).
tff(184,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),Uu)) ),
inference(skolemize,[status(sab)],[183]) ).
tff(185,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),Uu)) ),
inference(modus_ponens,[status(thm)],[184,180]) ).
tff(186,plain,
( ~ ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),Uu)) )
| ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(187,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(unit_resolution,[status(thm)],[186,185]) ).
tff(188,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(tautology,[status(thm)],]) ).
tff(189,plain,
~ pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[188,89]) ).
tff(190,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(tautology,[status(thm)],]) ).
tff(191,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(unit_resolution,[status(thm)],[190,189]) ).
tff(192,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[191,187]) ).
tff(193,plain,
( ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(tautology,[status(thm)],]) ).
tff(194,plain,
( ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) )
| ~ pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[193,192]) ).
tff(195,plain,
~ pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))),
inference(unit_resolution,[status(thm)],[194,178]) ).
tff(196,plain,
~ pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))),
inference(modus_ponens,[status(thm)],[195,166]) ).
tff(197,plain,
( ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
<=> pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1943012394univof,scratc2095348162ptyset)),scratc1509955612_nat_p)),aTP_Lamm_ag)),aa_TPT43085870d_bool(scratc1229761461ffprop(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(tautology,[status(thm)],]) ).
tff(198,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))),
inference(unit_resolution,[status(thm)],[197,196,160]) ).
tff(199,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))),
inference(modus_ponens,[status(thm)],[198,148]) ).
tff(200,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset))))),
inference(modus_ponens,[status(thm)],[199,145]) ).
tff(201,plain,
^ [Uu: $i,Uua: $i] :
refl(
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua))) )
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua))) ) )),
inference(bind,[status(th)],]) ).
tff(202,plain,
( ! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua))) )
<=> ! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua))) ) ),
inference(quant_intro,[status(thm)],[201]) ).
tff(203,plain,
( ! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua))) )
<=> ! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(204,axiom,
! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ATP_Olambda__91) ).
tff(205,plain,
! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua))) ),
inference(modus_ponens,[status(thm)],[204,203]) ).
tff(206,plain,
! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua))) ),
inference(skolemize,[status(sab)],[205]) ).
tff(207,plain,
! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua))) ),
inference(modus_ponens,[status(thm)],[206,202]) ).
tff(208,plain,
( ~ ! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua))) )
| ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset))))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(209,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset))))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset))))) ),
inference(unit_resolution,[status(thm)],[208,207]) ).
tff(210,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(211,plain,
( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(212,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ) ),
inference(monotonicity,[status(thm)],[211]) ).
tff(213,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ) ),
inference(transitivity,[status(thm)],[212,210]) ).
tff(214,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(215,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(modus_ponens,[status(thm)],[214,213]) ).
tff(216,plain,
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ),
inference(unit_resolution,[status(thm)],[215,79]) ).
tff(217,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) )
| ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) ),
inference(tautology,[status(thm)],]) ).
tff(218,plain,
( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) ),
inference(unit_resolution,[status(thm)],[217,216]) ).
tff(219,plain,
^ [Uu: $i] :
refl(
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) )
<=> ( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) ) )),
inference(bind,[status(th)],]) ).
tff(220,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) ) ),
inference(quant_intro,[status(thm)],[219]) ).
tff(221,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(222,axiom,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ATP_Olambda__52) ).
tff(223,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) ),
inference(modus_ponens,[status(thm)],[222,221]) ).
tff(224,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) ),
inference(skolemize,[status(sab)],[223]) ).
tff(225,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) ),
inference(modus_ponens,[status(thm)],[224,220]) ).
tff(226,plain,
( ~ ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) )
| ( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(227,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[226,225]) ).
tff(228,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_bq,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_bq,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_bq,aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(229,plain,
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_bq,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_bq,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_bq,aTP_Lamm_a),aTP_Lamm_a) ) ) ),
inference(unit_resolution,[status(thm)],[228,79]) ).
tff(230,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_bq,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_bq,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_bq,aTP_Lamm_a),aTP_Lamm_a) ) )
| ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(231,plain,
( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[230,229]) ).
tff(232,plain,
( pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq)) ),
inference(rewrite,[status(thm)],]) ).
tff(233,axiom,
pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_satz18a) ).
tff(234,plain,
pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq)),
inference(modus_ponens,[status(thm)],[233,232]) ).
tff(235,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(236,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) )
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[235,234]) ).
tff(237,plain,
! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) ),
inference(unit_resolution,[status(thm)],[236,231]) ).
tff(238,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(239,plain,
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(240,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(monotonicity,[status(thm)],[239]) ).
tff(241,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(transitivity,[status(thm)],[240,238]) ).
tff(242,plain,
( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(243,plain,
( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1623311406_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(modus_ponens,[status(thm)],[242,241]) ).
tff(244,plain,
pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[243,237,93,91]) ).
tff(245,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) )
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(tautology,[status(thm)],]) ).
tff(246,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) )
| pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[245,244]) ).
tff(247,plain,
pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))),
inference(unit_resolution,[status(thm)],[246,227]) ).
tff(248,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) )
| ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) ),
inference(tautology,[status(thm)],]) ).
tff(249,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) )
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ) ),
inference(unit_resolution,[status(thm)],[248,247]) ).
tff(250,plain,
! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),X2)) ),
inference(unit_resolution,[status(thm)],[249,218]) ).
tff(251,plain,
( scratc1623311406_is_of(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset)),aTP_Lamm_a)
<=> scratc1623311406_is_of(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset),aTP_Lamm_a) ),
inference(monotonicity,[status(thm)],[13]) ).
tff(252,plain,
( scratc1623311406_is_of(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset),aTP_Lamm_a)
<=> scratc1623311406_is_of(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset)),aTP_Lamm_a) ),
inference(symmetry,[status(thm)],[251]) ).
tff(253,plain,
( scratc1623311406_is_of(scratc98832752nd_n_1,aTP_Lamm_a)
<=> scratc1623311406_is_of(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset),aTP_Lamm_a) ),
inference(rewrite,[status(thm)],]) ).
tff(254,plain,
( scratc1623311406_is_of(scratc98832752nd_n_1,aTP_Lamm_a)
<=> scratc1623311406_is_of(scratc98832752nd_n_1,aTP_Lamm_a) ),
inference(rewrite,[status(thm)],]) ).
tff(255,axiom,
scratc1623311406_is_of(scratc98832752nd_n_1,aTP_Lamm_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__1__p) ).
tff(256,plain,
scratc1623311406_is_of(scratc98832752nd_n_1,aTP_Lamm_a),
inference(modus_ponens,[status(thm)],[255,254]) ).
tff(257,plain,
scratc1623311406_is_of(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset),aTP_Lamm_a),
inference(modus_ponens,[status(thm)],[256,253]) ).
tff(258,plain,
scratc1623311406_is_of(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset)),aTP_Lamm_a),
inference(modus_ponens,[status(thm)],[257,252]) ).
tff(259,plain,
( gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset)))
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)) ),
inference(monotonicity,[status(thm)],[13]) ).
tff(260,plain,
( gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset))) ),
inference(symmetry,[status(thm)],[259]) ).
tff(261,plain,
( gg_TPTP_ind(scratc98832752nd_n_1)
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)) ),
inference(rewrite,[status(thm)],]) ).
tff(262,plain,
( gg_TPTP_ind(scratc98832752nd_n_1)
<=> gg_TPTP_ind(scratc98832752nd_n_1) ),
inference(rewrite,[status(thm)],]) ).
tff(263,axiom,
gg_TPTP_ind(scratc98832752nd_n_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Scratch__tptp__translate__45846__17029_ONUM669__thf__4__p_Obnd__n__1) ).
tff(264,plain,
gg_TPTP_ind(scratc98832752nd_n_1),
inference(modus_ponens,[status(thm)],[263,262]) ).
tff(265,plain,
gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)),
inference(modus_ponens,[status(thm)],[264,261]) ).
tff(266,plain,
gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset))),
inference(modus_ponens,[status(thm)],[265,260]) ).
tff(267,plain,
( ( ~ ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),X2)) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset)))
| ~ scratc1623311406_is_of(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset)),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset)))) )
<=> ( ~ ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),X2)) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset)))
| ~ scratc1623311406_is_of(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset)),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(268,plain,
( ~ ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),X2)) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset)))
| ~ scratc1623311406_is_of(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset)),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(269,plain,
( ~ ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1623311406_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),X2)) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset)))
| ~ scratc1623311406_is_of(aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset)),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset)))) ),
inference(modus_ponens,[status(thm)],[268,267]) ).
tff(270,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset)))),
inference(unit_resolution,[status(thm)],[269,266,258,250]) ).
tff(271,plain,
( ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset))))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset))))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset))))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset))))) ),
inference(tautology,[status(thm)],]) ).
tff(272,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(scratc2095348162ptyset),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset))))),
inference(unit_resolution,[status(thm)],[271,270,209]) ).
tff(273,plain,
$false,
inference(unit_resolution,[status(thm)],[272,200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM669+4 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 12:57:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 7.89/5.34 % SZS status Theorem
% 7.89/5.34 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------