TSTP Solution File: NUM635+4 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM635+4 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 13:11:06 EDT 2022
% Result : Theorem 101.11s 65.30s
% Output : Proof 101.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 129
% Syntax : Number of formulae : 277 ( 64 unt; 32 typ; 0 def)
% Number of atoms : 1372 ( 26 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 2082 ( 990 ~; 859 |; 6 &)
% ( 215 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of FOOLs : 35 ( 35 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 16 >; 9 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 29 ( 29 usr; 16 con; 0-2 aty)
% Number of variables : 386 ( 353 !; 0 ?; 386 :)
% 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(tptp_fun_X2_12_type,type,
tptp_fun_X2_12: ( $i * $i ) > $i ).
tff(aTP_Lamm_a_type,type,
aTP_Lamm_a: $i ).
tff(aa_TPT43085870d_bool_type,type,
aa_TPT43085870d_bool: ( $i * $i ) > $i ).
tff(aTP_Lamm_ab_type,type,
aTP_Lamm_ab: $i ).
tff(aTP_Lamm_aa_type,type,
aTP_Lamm_aa: $i ).
tff(scratc528047725rdsucc_type,type,
scratc528047725rdsucc: $i ).
tff(scratc469777661d_Sing_type,type,
scratc469777661d_Sing: $i ).
tff(scratc1892157758nunion_type,type,
scratc1892157758nunion: $i > $i ).
tff(scratc1144391673d_e_is_type,type,
scratc1144391673d_e_is: $i > $i ).
tff(aa_fun1431113780TP_ind_type,type,
aa_fun1431113780TP_ind: ( $i * $i ) > $i ).
tff(aTP_Lamm_ad_type,type,
aTP_Lamm_ad: $i ).
tff(scratc808795376_d_Sep_type,type,
scratc808795376_d_Sep: $i > $i ).
tff(scratc1824235429_nat_p_type,type,
scratc1824235429_nat_p: $i ).
tff(scratc532860107ptyset_type,type,
scratc532860107ptyset: $i ).
tff(scratc109808563univof_type,type,
scratc109808563univof: $i ).
tff(aTP_Lamm_bp_type,type,
aTP_Lamm_bp: $i ).
tff(scratc663052034d_n_is_type,type,
scratc663052034d_n_is: $i ).
tff(scratc1937591223_is_of_type,type,
scratc1937591223_is_of: ( $i * $i ) > $o ).
tff(gg_TPTP_ind_type,type,
gg_TPTP_ind: $i > $o ).
tff(aa_fun171081125l_bool_type,type,
aa_fun171081125l_bool: ( $i * $i ) > $i ).
tff(scratc1445421794all_of_type,type,
scratc1445421794all_of: $i > $i ).
tff(aTP_Lamm_bq_type,type,
aTP_Lamm_bq: $i ).
tff(aa_bool_bool_type,type,
aa_bool_bool: ( $i * $i ) > $i ).
tff(fFalse_type,type,
fFalse: $i ).
tff(aa_boo1142376798l_bool_type,type,
aa_boo1142376798l_bool: ( $i * $i ) > $i ).
tff(fimplies_type,type,
fimplies: $i ).
tff(scratc1032512005_d_not_type,type,
scratc1032512005_d_not: $i > $i ).
tff(scratc11065014nd_imp_type,type,
scratc11065014nd_imp: $i ).
tff(scratc52110146nd_nis_type,type,
scratc52110146nd_nis: $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(X),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,X)) )
<=> ( aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(X),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,X)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(X),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,X)) )
<=> ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(X),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,X)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(X),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,X)) )
<=> ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(X),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(X),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__ordsucc) ).
tff(5,plain,
! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(X),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,X)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(X),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,X)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(X),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,X)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(X),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,X)) )
| ( aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)) = aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)) = aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))) = aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( ~ ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(X),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,X)) )
| ( aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)) = aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)) = aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[11,7]) ).
tff(13,plain,
aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))) = aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))) = aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))) = aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))),
inference(monotonicity,[status(thm)],[15,10]) ).
tff(17,plain,
aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) ),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))))
<=> ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) ),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))),
inference(monotonicity,[status(thm)],[15]) ).
tff(22,plain,
aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))),
inference(transitivity,[status(thm)],[21,17]) ).
tff(23,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))) ),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))
<=> ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))) ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,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(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),Uu),Uua))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) )
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),Uu),Uua))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) ) )),
inference(bind,[status(th)],]) ).
tff(26,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(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),Uu),Uua))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,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(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),Uu),Uua))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
^ [Uu: $i,Uua: $i] :
rewrite(
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc663052034d_n_is,Uu),Uua))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc663052034d_n_is,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) )
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),Uu),Uua))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) ) )),
inference(bind,[status(th)],]) ).
tff(28,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(scratc663052034d_n_is,Uu),Uua))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc663052034d_n_is,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,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(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),Uu),Uua))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,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(scratc663052034d_n_is,Uu),Uua))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc663052034d_n_is,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,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(scratc663052034d_n_is,Uu),Uua))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc663052034d_n_is,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
^ [Uu: $i,Uua: $i] :
rewrite(
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc663052034d_n_is,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua)))
=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc663052034d_n_is,Uu),Uua)) ) )
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc663052034d_n_is,Uu),Uua))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc663052034d_n_is,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) ) )),
inference(bind,[status(th)],]) ).
tff(31,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(scratc663052034d_n_is,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua)))
=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc663052034d_n_is,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(scratc663052034d_n_is,Uu),Uua))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc663052034d_n_is,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,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(scratc663052034d_n_is,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua)))
=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc663052034d_n_is,Uu),Uua)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__13) ).
tff(33,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(scratc663052034d_n_is,Uu),Uua))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc663052034d_n_is,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,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(scratc663052034d_n_is,Uu),Uua))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc663052034d_n_is,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,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(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),Uu),Uua))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) ),
inference(modus_ponens,[status(thm)],[34,28]) ).
tff(36,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(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),Uu),Uua))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,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(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),Uu),Uua))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) ),
inference(modus_ponens,[status(thm)],[36,26]) ).
tff(38,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(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),Uu),Uua))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) )
| ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) ) ),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
^ [X: $i,Xa: $i] :
refl(
( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
^ [X: $i,Xa: $i] :
rewrite(
( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) ),
inference(transitivity,[status(thm)],[43,41]) ).
tff(45,plain,
^ [X: $i,Xa: $i] :
trans(
monotonicity(
rewrite(
( ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
<=> ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_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))
| ~ scratc1937591223_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))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) )),
( ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) )
<=> ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )),
( ( ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ( ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
rewrite(
( ( ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
( ( ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [X: $i,Xa: $i] :
( ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
^ [X: $i,Xa: $i] :
rewrite(
( ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
<=> ! [X2: $i] :
( gg_TPTP_ind(X2)
=> ( scratc1937591223_is_of(X2,X)
=> pp(aa_TPTP_ind_bool(Xa,X2)) ) ) )
<=> ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
<=> ! [X2: $i] :
( gg_TPTP_ind(X2)
=> ( scratc1937591223_is_of(X2,X)
=> pp(aa_TPTP_ind_bool(Xa,X2)) ) ) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,axiom,
! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
<=> ! [X2: $i] :
( gg_TPTP_ind(X2)
=> ( scratc1937591223_is_of(X2,X)
=> pp(aa_TPTP_ind_bool(Xa,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__all__of) ).
tff(51,plain,
! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
! [X: $i,Xa: $i] :
( ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ),
inference(modus_ponens,[status(thm)],[53,46]) ).
tff(55,plain,
! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ),
inference(modus_ponens,[status(thm)],[54,44]) ).
tff(56,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,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_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,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_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,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_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,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_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,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_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,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_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ) ),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,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_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,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_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ) ),
inference(transitivity,[status(thm)],[58,56]) ).
tff(60,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,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_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,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_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,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_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ),
inference(unit_resolution,[status(thm)],[61,55]) ).
tff(63,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,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_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) )
| ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) ) ),
inference(tautology,[status(thm)],]) ).
tff(64,plain,
( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) ) ),
inference(unit_resolution,[status(thm)],[63,62]) ).
tff(65,plain,
^ [Uu: $i] :
refl(
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) )
<=> ( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) ) )),
inference(bind,[status(th)],]) ).
tff(66,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_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(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_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(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,axiom,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__6) ).
tff(69,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))) ),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
( ~ ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_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_ab,aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[72,71]) ).
tff(74,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_ab))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_ab))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_ab))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_ab))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a),aTP_Lamm_a) ) ) ),
inference(unit_resolution,[status(thm)],[74,55]) ).
tff(76,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_ab))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_ab))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a),aTP_Lamm_a) ) )
| pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_ab))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(77,plain,
( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_ab))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[76,75]) ).
tff(78,plain,
( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_ab))
<=> ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_ab)) ),
inference(rewrite,[status(thm)],]) ).
tff(79,axiom,
~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_ab)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(80,plain,
~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_ab)),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
( ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_ab))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a),aTP_Lamm_a) ) )
| pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_ab))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(82,plain,
( ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_ab))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a),aTP_Lamm_a) ) )
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[81,80]) ).
tff(83,plain,
~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a),aTP_Lamm_a) ),
inference(unit_resolution,[status(thm)],[82,77]) ).
tff(84,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a),aTP_Lamm_a)
| scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a),aTP_Lamm_a) ),
inference(tautology,[status(thm)],]) ).
tff(85,plain,
scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a),aTP_Lamm_a),
inference(unit_resolution,[status(thm)],[84,83]) ).
tff(86,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a),aTP_Lamm_a)
| gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)) ),
inference(tautology,[status(thm)],]) ).
tff(87,plain,
gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),
inference(unit_resolution,[status(thm)],[86,83]) ).
tff(88,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_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))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_bq,aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(89,plain,
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_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))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_bq,aTP_Lamm_a),aTP_Lamm_a) ) ) ),
inference(unit_resolution,[status(thm)],[88,55]) ).
tff(90,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_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))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_bq,aTP_Lamm_a),aTP_Lamm_a) ) )
| ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(91,plain,
( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[90,89]) ).
tff(92,plain,
( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_bq))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_bq)) ),
inference(rewrite,[status(thm)],]) ).
tff(93,axiom,
pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_bq)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__ax4) ).
tff(94,plain,
pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_bq)),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) ) )
| ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(96,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aTP_Lamm_bq))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) ) )
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[95,94]) ).
tff(97,plain,
! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) ),
inference(unit_resolution,[status(thm)],[96,91]) ).
tff(98,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(99,plain,
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))) ) ),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))) ) ),
inference(transitivity,[status(thm)],[100,98]) ).
tff(102,plain,
( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a),aTP_Lamm_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(103,plain,
( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[103,97,87,85]) ).
tff(105,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))) )
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))
| pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))) ),
inference(tautology,[status(thm)],]) ).
tff(106,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bq,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))) )
| pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[105,104]) ).
tff(107,plain,
pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),
inference(unit_resolution,[status(thm)],[106,73]) ).
tff(108,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) ) )
| ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) ) ),
inference(tautology,[status(thm)],]) ).
tff(109,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) ) )
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) ) ),
inference(unit_resolution,[status(thm)],[108,107]) ).
tff(110,plain,
! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) ),
inference(unit_resolution,[status(thm)],[109,64]) ).
tff(111,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(112,plain,
( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ) ),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ) ),
inference(transitivity,[status(thm)],[113,111]) ).
tff(115,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(116,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ) ),
inference(unit_resolution,[status(thm)],[116,55]) ).
tff(118,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) )
| pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(119,plain,
( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[118,117]) ).
tff(120,plain,
^ [Uu: $i] :
refl(
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,Uu))) )
<=> ( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,Uu))) ) )),
inference(bind,[status(th)],]) ).
tff(121,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,Uu))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,Uu))) ) ),
inference(quant_intro,[status(thm)],[120]) ).
tff(122,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,Uu))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,Uu))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(123,axiom,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,Uu))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__7) ).
tff(124,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,Uu))) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,Uu))) ),
inference(skolemize,[status(sab)],[124]) ).
tff(126,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,Uu))) ),
inference(modus_ponens,[status(thm)],[125,121]) ).
tff(127,plain,
( ~ ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,Uu))) )
| ( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(128,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[127,126]) ).
tff(129,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a),aTP_Lamm_a)
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_ab,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))) ),
inference(tautology,[status(thm)],]) ).
tff(130,plain,
~ pp(aa_TPTP_ind_bool(aTP_Lamm_ab,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[129,83]) ).
tff(131,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_ab,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))
| ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))) ),
inference(tautology,[status(thm)],]) ).
tff(132,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))
<=> pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))) )
| ~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[131,130]) ).
tff(133,plain,
~ pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),
inference(unit_resolution,[status(thm)],[132,128]) ).
tff(134,plain,
( ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) )
| pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(135,plain,
( ~ ( pp(aa_fun171081125l_bool(scratc1445421794all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))))
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) )
| ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[134,133]) ).
tff(136,plain,
~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ),
inference(unit_resolution,[status(thm)],[135,119]) ).
tff(137,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a)
| scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a) ),
inference(tautology,[status(thm)],]) ).
tff(138,plain,
scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a),
inference(unit_resolution,[status(thm)],[137,136]) ).
tff(139,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a)
| gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)) ),
inference(tautology,[status(thm)],]) ).
tff(140,plain,
gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)),
inference(unit_resolution,[status(thm)],[139,136]) ).
tff(141,plain,
( ( ~ ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))) )
<=> ( ~ ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(142,plain,
( ~ ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(143,plain,
( ~ ! [X2: $i] :
( ~ gg_TPTP_ind(X2)
| ~ scratc1937591223_is_of(X2,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),X2)) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))) ),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[143,140,138,110]) ).
tff(145,plain,
( ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) ) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) ),
inference(tautology,[status(thm)],]) ).
tff(146,plain,
( ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) ) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[145,144]) ).
tff(147,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[146,39]) ).
tff(148,plain,
^ [X: $i] :
refl(
( ( pp(scratc1032512005_d_not(X))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X),fFalse)) )
<=> ( pp(scratc1032512005_d_not(X))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X),fFalse)) ) )),
inference(bind,[status(th)],]) ).
tff(149,plain,
( ! [X: $i] :
( pp(scratc1032512005_d_not(X))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X),fFalse)) )
<=> ! [X: $i] :
( pp(scratc1032512005_d_not(X))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X),fFalse)) ) ),
inference(quant_intro,[status(thm)],[148]) ).
tff(150,plain,
^ [X: $i] :
rewrite(
( ( pp(scratc1032512005_d_not(X))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc11065014nd_imp,X),fFalse)) )
<=> ( pp(scratc1032512005_d_not(X))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X),fFalse)) ) )),
inference(bind,[status(th)],]) ).
tff(151,plain,
( ! [X: $i] :
( pp(scratc1032512005_d_not(X))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc11065014nd_imp,X),fFalse)) )
<=> ! [X: $i] :
( pp(scratc1032512005_d_not(X))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X),fFalse)) ) ),
inference(quant_intro,[status(thm)],[150]) ).
tff(152,plain,
( ! [X: $i] :
( pp(scratc1032512005_d_not(X))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc11065014nd_imp,X),fFalse)) )
<=> ! [X: $i] :
( pp(scratc1032512005_d_not(X))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc11065014nd_imp,X),fFalse)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(153,axiom,
! [X: $i] :
( pp(scratc1032512005_d_not(X))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc11065014nd_imp,X),fFalse)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__d__not) ).
tff(154,plain,
! [X: $i] :
( pp(scratc1032512005_d_not(X))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc11065014nd_imp,X),fFalse)) ),
inference(modus_ponens,[status(thm)],[153,152]) ).
tff(155,plain,
! [X: $i] :
( pp(scratc1032512005_d_not(X))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X),fFalse)) ),
inference(modus_ponens,[status(thm)],[154,151]) ).
tff(156,plain,
! [X: $i] :
( pp(scratc1032512005_d_not(X))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X),fFalse)) ),
inference(skolemize,[status(sab)],[155]) ).
tff(157,plain,
! [X: $i] :
( pp(scratc1032512005_d_not(X))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X),fFalse)) ),
inference(modus_ponens,[status(thm)],[156,149]) ).
tff(158,plain,
( ~ ! [X: $i] :
( pp(scratc1032512005_d_not(X))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X),fFalse)) )
| ( pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))),fFalse)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(159,plain,
( pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))),fFalse)) ),
inference(unit_resolution,[status(thm)],[158,157]) ).
tff(160,plain,
^ [X: $i,Xa: $i] :
refl(
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,X),Xa))
<=> pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),X),Xa))) )
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,X),Xa))
<=> pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),X),Xa))) ) )),
inference(bind,[status(th)],]) ).
tff(161,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,X),Xa))
<=> pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),X),Xa))) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,X),Xa))
<=> pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),X),Xa))) ) ),
inference(quant_intro,[status(thm)],[160]) ).
tff(162,plain,
^ [X: $i,Xa: $i] :
rewrite(
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,X),Xa))
<=> pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc663052034d_n_is,X),Xa))) )
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,X),Xa))
<=> pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),X),Xa))) ) )),
inference(bind,[status(th)],]) ).
tff(163,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,X),Xa))
<=> pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc663052034d_n_is,X),Xa))) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,X),Xa))
<=> pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),X),Xa))) ) ),
inference(quant_intro,[status(thm)],[162]) ).
tff(164,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,X),Xa))
<=> pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc663052034d_n_is,X),Xa))) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,X),Xa))
<=> pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc663052034d_n_is,X),Xa))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(165,axiom,
! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,X),Xa))
<=> pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc663052034d_n_is,X),Xa))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__nis) ).
tff(166,plain,
! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,X),Xa))
<=> pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc663052034d_n_is,X),Xa))) ),
inference(modus_ponens,[status(thm)],[165,164]) ).
tff(167,plain,
! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,X),Xa))
<=> pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),X),Xa))) ),
inference(modus_ponens,[status(thm)],[166,163]) ).
tff(168,plain,
! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,X),Xa))
<=> pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),X),Xa))) ),
inference(skolemize,[status(sab)],[167]) ).
tff(169,plain,
! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,X),Xa))
<=> pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),X),Xa))) ),
inference(modus_ponens,[status(thm)],[168,161]) ).
tff(170,plain,
( ~ ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,X),Xa))
<=> pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),X),Xa))) )
| ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
<=> pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(171,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
<=> pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[170,169]) ).
tff(172,plain,
^ [Uu: $i,Uua: $i] :
refl(
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua))
<=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,Uu),Uua))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) )
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua))
<=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,Uu),Uua))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) ) )),
inference(bind,[status(th)],]) ).
tff(173,plain,
( ! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua))
<=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,Uu),Uua))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) )
<=> ! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua))
<=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,Uu),Uua))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) ) ),
inference(quant_intro,[status(thm)],[172]) ).
tff(174,plain,
( ! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua))
<=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,Uu),Uua))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) )
<=> ! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua))
<=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,Uu),Uua))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(175,plain,
^ [Uu: $i,Uua: $i] :
rewrite(
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,Uu),Uua))
=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) )
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua))
<=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,Uu),Uua))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) ) )),
inference(bind,[status(th)],]) ).
tff(176,plain,
( ! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,Uu),Uua))
=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) )
<=> ! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua))
<=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,Uu),Uua))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) ) ),
inference(quant_intro,[status(thm)],[175]) ).
tff(177,axiom,
! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,Uu),Uua))
=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__14) ).
tff(178,plain,
! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua))
<=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,Uu),Uua))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) ),
inference(modus_ponens,[status(thm)],[177,176]) ).
tff(179,plain,
! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua))
<=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,Uu),Uua))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) ),
inference(modus_ponens,[status(thm)],[178,174]) ).
tff(180,plain,
! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua))
<=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,Uu),Uua))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) ),
inference(skolemize,[status(sab)],[179]) ).
tff(181,plain,
! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua))
<=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,Uu),Uua))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) ),
inference(modus_ponens,[status(thm)],[180,173]) ).
tff(182,plain,
( ~ ! [Uu: $i,Uua: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua))
<=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,Uu),Uua))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,Uua))) ) )
| ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
<=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(183,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
<=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) ) ),
inference(unit_resolution,[status(thm)],[182,181]) ).
tff(184,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))
| ~ scratc1937591223_is_of(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a),aTP_Lamm_a)
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))) ),
inference(tautology,[status(thm)],]) ).
tff(185,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[184,136]) ).
tff(186,plain,
( ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
<=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) ) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) ) ),
inference(tautology,[status(thm)],]) ).
tff(187,plain,
( ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
<=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) ) )
| ~ ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) ) ),
inference(unit_resolution,[status(thm)],[186,185]) ).
tff(188,plain,
~ ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[187,183]) ).
tff(189,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))) ),
inference(tautology,[status(thm)],]) ).
tff(190,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[189,188]) ).
tff(191,plain,
( ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
<=> pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) ),
inference(tautology,[status(thm)],]) ).
tff(192,plain,
( ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
<=> pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) )
| pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[191,190]) ).
tff(193,plain,
pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))),
inference(unit_resolution,[status(thm)],[192,171]) ).
tff(194,plain,
( ~ ( pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))),fFalse)) )
| ~ pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))
| pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))),fFalse)) ),
inference(tautology,[status(thm)],]) ).
tff(195,plain,
( ~ ( pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))),fFalse)) )
| pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))),fFalse)) ),
inference(unit_resolution,[status(thm)],[194,193]) ).
tff(196,plain,
pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))),fFalse)),
inference(unit_resolution,[status(thm)],[195,159]) ).
tff(197,plain,
^ [P: $i,Q: $i] :
refl(
( ( pp(Q)
| ~ pp(P)
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) )
<=> ( pp(Q)
| ~ pp(P)
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) ) )),
inference(bind,[status(th)],]) ).
tff(198,plain,
( ! [P: $i,Q: $i] :
( pp(Q)
| ~ pp(P)
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) )
<=> ! [P: $i,Q: $i] :
( pp(Q)
| ~ pp(P)
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) ) ),
inference(quant_intro,[status(thm)],[197]) ).
tff(199,plain,
( ! [P: $i,Q: $i] :
( pp(Q)
| ~ pp(P)
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) )
<=> ! [P: $i,Q: $i] :
( pp(Q)
| ~ pp(P)
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(200,plain,
^ [P: $i,Q: $i] :
trans(
monotonicity(
rewrite(
( ( ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q))
| ~ pp(P) )
<=> ( ~ pp(P)
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) ) )),
( ( ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q))
| ~ pp(P)
| pp(Q) )
<=> ( ~ pp(P)
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q))
| pp(Q) ) )),
rewrite(
( ( ~ pp(P)
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q))
| pp(Q) )
<=> ( pp(Q)
| ~ pp(P)
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) ) )),
( ( ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q))
| ~ pp(P)
| pp(Q) )
<=> ( pp(Q)
| ~ pp(P)
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) ) )),
inference(bind,[status(th)],]) ).
tff(201,plain,
( ! [P: $i,Q: $i] :
( ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q))
| ~ pp(P)
| pp(Q) )
<=> ! [P: $i,Q: $i] :
( pp(Q)
| ~ pp(P)
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) ) ),
inference(quant_intro,[status(thm)],[200]) ).
tff(202,axiom,
! [P: $i,Q: $i] :
( ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q))
| ~ pp(P)
| pp(Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
tff(203,plain,
! [P: $i,Q: $i] :
( pp(Q)
| ~ pp(P)
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) ),
inference(modus_ponens,[status(thm)],[202,201]) ).
tff(204,plain,
! [P: $i,Q: $i] :
( pp(Q)
| ~ pp(P)
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) ),
inference(modus_ponens,[status(thm)],[203,199]) ).
tff(205,plain,
! [P: $i,Q: $i] :
( pp(Q)
| ~ pp(P)
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) ),
inference(skolemize,[status(sab)],[204]) ).
tff(206,plain,
! [P: $i,Q: $i] :
( pp(Q)
| ~ pp(P)
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) ),
inference(modus_ponens,[status(thm)],[205,198]) ).
tff(207,plain,
( ~ pp(fFalse)
<=> ~ pp(fFalse) ),
inference(rewrite,[status(thm)],]) ).
tff(208,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
tff(209,plain,
~ pp(fFalse),
inference(modus_ponens,[status(thm)],[208,207]) ).
tff(210,plain,
( ( ~ ! [P: $i,Q: $i] :
( pp(Q)
| ~ pp(P)
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) )
| pp(fFalse)
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))),fFalse)) )
<=> ( ~ ! [P: $i,Q: $i] :
( pp(Q)
| ~ pp(P)
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) )
| pp(fFalse)
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))),fFalse)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(211,plain,
( ~ ! [P: $i,Q: $i] :
( pp(Q)
| ~ pp(P)
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) )
| pp(fFalse)
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))),fFalse)) ),
inference(quant_inst,[status(thm)],]) ).
tff(212,plain,
( ~ ! [P: $i,Q: $i] :
( pp(Q)
| ~ pp(P)
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) )
| pp(fFalse)
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))),fFalse)) ),
inference(modus_ponens,[status(thm)],[211,210]) ).
tff(213,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[212,209,206,196]) ).
tff(214,plain,
( ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) ),
inference(tautology,[status(thm)],]) ).
tff(215,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))),
inference(unit_resolution,[status(thm)],[214,213,147]) ).
tff(216,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))),
inference(modus_ponens,[status(thm)],[215,24]) ).
tff(217,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))),
inference(modus_ponens,[status(thm)],[216,20]) ).
tff(218,plain,
( ~ ! [X: $i] :
( pp(scratc1032512005_d_not(X))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X),fFalse)) )
| ( pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))),fFalse)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(219,plain,
( pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))),fFalse)) ),
inference(unit_resolution,[status(thm)],[218,157]) ).
tff(220,plain,
( ~ ! [X: $i,Xa: $i] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,X),Xa))
<=> pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),X),Xa))) )
| ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))
<=> pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(221,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))
<=> pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))) ),
inference(unit_resolution,[status(thm)],[220,169]) ).
tff(222,plain,
aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))) = aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),
inference(monotonicity,[status(thm)],[13]) ).
tff(223,plain,
aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))),
inference(monotonicity,[status(thm)],[222]) ).
tff(224,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) ),
inference(monotonicity,[status(thm)],[223]) ).
tff(225,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) ),
inference(symmetry,[status(thm)],[224]) ).
tff(226,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))
<=> ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) ),
inference(monotonicity,[status(thm)],[225]) ).
tff(227,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))) ),
inference(tautology,[status(thm)],]) ).
tff(228,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))),
inference(unit_resolution,[status(thm)],[227,188]) ).
tff(229,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))),
inference(modus_ponens,[status(thm)],[228,226]) ).
tff(230,plain,
( ~ ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))
<=> pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52110146nd_nis,aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))
| ~ pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))) ),
inference(tautology,[status(thm)],]) ).
tff(231,plain,
~ pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))),
inference(unit_resolution,[status(thm)],[230,229,221]) ).
tff(232,plain,
( ~ ( pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))),fFalse)) )
| pp(scratc1032512005_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))))
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))),fFalse)) ),
inference(tautology,[status(thm)],]) ).
tff(233,plain,
~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))),fFalse)),
inference(unit_resolution,[status(thm)],[232,231,219]) ).
tff(234,plain,
^ [P: $i,Q: $i] :
refl(
( ( pp(P)
| pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) )
<=> ( pp(P)
| pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) ) )),
inference(bind,[status(th)],]) ).
tff(235,plain,
( ! [P: $i,Q: $i] :
( pp(P)
| pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) )
<=> ! [P: $i,Q: $i] :
( pp(P)
| pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) ) ),
inference(quant_intro,[status(thm)],[234]) ).
tff(236,plain,
( ! [P: $i,Q: $i] :
( pp(P)
| pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) )
<=> ! [P: $i,Q: $i] :
( pp(P)
| pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(237,axiom,
! [P: $i,Q: $i] :
( pp(P)
| pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
tff(238,plain,
! [P: $i,Q: $i] :
( pp(P)
| pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) ),
inference(modus_ponens,[status(thm)],[237,236]) ).
tff(239,plain,
! [P: $i,Q: $i] :
( pp(P)
| pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) ),
inference(skolemize,[status(sab)],[238]) ).
tff(240,plain,
! [P: $i,Q: $i] :
( pp(P)
| pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) ),
inference(modus_ponens,[status(thm)],[239,235]) ).
tff(241,plain,
( ( ~ ! [P: $i,Q: $i] :
( pp(P)
| pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))
| pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))),fFalse)) )
<=> ( ~ ! [P: $i,Q: $i] :
( pp(P)
| pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))
| pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))),fFalse)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(242,plain,
( ~ ! [P: $i,Q: $i] :
( pp(P)
| pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))
| pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))),fFalse)) ),
inference(quant_inst,[status(thm)],]) ).
tff(243,plain,
( ~ ! [P: $i,Q: $i] :
( pp(P)
| pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a))))
| pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))),fFalse)) ),
inference(modus_ponens,[status(thm)],[242,241]) ).
tff(244,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1144391673d_e_is(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_fun1431113780TP_ind(scratc808795376_d_Sep(aa_TPTP_ind_TPTP_ind(scratc109808563univof,scratc532860107ptyset)),scratc1824235429_nat_p)),aTP_Lamm_ad)),aa_TPTP_ind_TPTP_ind(scratc1892157758nunion(tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc469777661d_Sing,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)))),aa_TPTP_ind_TPTP_ind(scratc528047725rdsucc,tptp_fun_X2_12(aa_TPT43085870d_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_ab,aTP_Lamm_a)),aTP_Lamm_a)))),
inference(unit_resolution,[status(thm)],[243,240,233]) ).
tff(245,plain,
$false,
inference(unit_resolution,[status(thm)],[244,217]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM635+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 : n018.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 12:37:13 EDT 2022
% 0.13/0.35 % 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.
% 101.11/65.30 % SZS status Theorem
% 101.11/65.30 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------