TSTP Solution File: NUM641+4 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM641+4 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 13:11:09 EDT 2022
% Result : Theorem 5.75s 3.97s
% Output : Proof 5.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 118
% Syntax : Number of formulae : 250 ( 84 unt; 44 typ; 0 def)
% Number of atoms : 899 ( 159 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 1212 ( 559 ~; 489 |; 22 &)
% ( 133 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of FOOLs : 40 ( 40 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 40 ( 25 >; 15 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 41 ( 41 usr; 19 con; 0-2 aty)
% Number of variables : 300 ( 271 !; 0 ?; 300 :)
% Comments :
%------------------------------------------------------------------------------
tff(gg_TPTP_ind_type,type,
gg_TPTP_ind: $i > $o ).
tff(aa_fun277296641TP_ind_type,type,
aa_fun277296641TP_ind: ( $i * $i ) > $i ).
tff(scratc1146276611_proj1_type,type,
scratc1146276611_proj1: $i ).
tff(scratc407235996eplSep_type,type,
scratc407235996eplSep: ( $i * $i ) > $i ).
tff(aa_TPT43085870d_bool_type,type,
aa_TPT43085870d_bool: ( $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(aTP_Lamm_aa_type,type,
aTP_Lamm_aa: $i ).
tff(aTP_Lamm_bf_type,type,
aTP_Lamm_bf: $i ).
tff(aa_TPTP_ind_TPTP_ind_type,type,
aa_TPTP_ind_TPTP_ind: ( $i * $i ) > $i ).
tff(scratc1745451206ptyset_type,type,
scratc1745451206ptyset: $i ).
tff(scratc854057538d_Sing_type,type,
scratc854057538d_Sing: $i ).
tff(scratc957265209nunion_type,type,
scratc957265209nunion: $i > $i ).
tff(scratc1715799339d_plus_type,type,
scratc1715799339d_plus: $i ).
tff(scratc1084070009d_n_pl_type,type,
scratc1084070009d_n_pl: $i > $i ).
tff(scratc912327602rdsucc_type,type,
scratc912327602rdsucc: $i ).
tff(aa_TPT1424761345TP_ind_type,type,
aa_TPT1424761345TP_ind: ( $i * $i ) > $i ).
tff(scratc1549486784bnd_ap_type,type,
scratc1549486784bnd_ap: $i ).
tff(pp_type,type,
pp: $i > $o ).
tff(aa_TPTP_ind_bool_type,type,
aa_TPTP_ind_bool: ( $i * $i ) > $i ).
tff(fequal_TPTP_ind_type,type,
fequal_TPTP_ind: $i ).
tff(scratc1564950462d_e_is_type,type,
scratc1564950462d_e_is: $i > $i ).
tff(aa_fun1431113780TP_ind_type,type,
aa_fun1431113780TP_ind: ( $i * $i ) > $i ).
tff(aTP_Lamm_ag_type,type,
aTP_Lamm_ag: $i ).
tff(scratc322369131_d_Sep_type,type,
scratc322369131_d_Sep: $i > $i ).
tff(scratc1337809184_nat_p_type,type,
scratc1337809184_nat_p: $i ).
tff(scratc1770865966univof_type,type,
scratc1770865966univof: $i ).
tff(scratc1550011566bnd_if_type,type,
scratc1550011566bnd_if: ( $i * $i ) > $i ).
tff(aa_fun1235454963TP_ind_type,type,
aa_fun1235454963TP_ind: ( $i * $i ) > $i ).
tff(aTP_Lamm_bm_type,type,
aTP_Lamm_bm: $i > $i ).
tff(aa_TPT494704832TP_ind_type,type,
aa_TPT494704832TP_ind: ( $i * $i ) > $i ).
tff(scratc1071331552d_repl_type,type,
scratc1071331552d_repl: $i ).
tff(fEx_TPTP_ind_type,type,
fEx_TPTP_ind: $i > $i ).
tff(cOMBS_2003118649l_bool_type,type,
cOMBS_2003118649l_bool: ( $i * $i ) > $i ).
tff(cOMBB_658106424TP_ind_type,type,
cOMBB_658106424TP_ind: ( $i * $i ) > $i ).
tff(cOMBC_1555011498d_bool_type,type,
cOMBC_1555011498d_bool: $i > $i ).
tff(scratc1550011574bnd_in_type,type,
scratc1550011574bnd_in: $i ).
tff(fconj_type,type,
fconj: $i ).
tff(aTP_Lamm_bu_type,type,
aTP_Lamm_bu: $i ).
tff(scratc45782132nd_n_1_type,type,
scratc45782132nd_n_1: $i ).
tff(scratc1083610823d_n_is_type,type,
scratc1083610823d_n_is: $i ).
tff(scratc1451164978_is_of_type,type,
scratc1451164978_is_of: ( $i * $i ) > $o ).
tff(aa_fun171081125l_bool_type,type,
aa_fun171081125l_bool: ( $i * $i ) > $i ).
tff(scratc1829701671all_of_type,type,
scratc1829701671all_of: $i > $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( scratc1084070009d_n_pl(X) = aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,X)) )
<=> ( scratc1084070009d_n_pl(X) = aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,X)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( scratc1084070009d_n_pl(X) = aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,X)) )
<=> ! [X: $i] : ( scratc1084070009d_n_pl(X) = aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,X)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( scratc1084070009d_n_pl(X) = aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,X)) )
<=> ! [X: $i] : ( scratc1084070009d_n_pl(X) = aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : ( scratc1084070009d_n_pl(X) = aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__n__pl) ).
tff(5,plain,
! [X: $i] : ( scratc1084070009d_n_pl(X) = aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,X)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( scratc1084070009d_n_pl(X) = aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,X)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( scratc1084070009d_n_pl(X) = aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,X)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( scratc1084070009d_n_pl(X) = aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,X)) )
| ( scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))) = aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))) = aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset)))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(
( ( aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(X),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,X)) )
<=> ( aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(X),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,X)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(X),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,X)) )
<=> ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(X),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,X)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(X),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,X)) )
<=> ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(X),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(X),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__ordsucc) ).
tff(14,plain,
! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(X),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,X)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(X),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,X)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(X),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,X)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(X),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,X)) )
| ( aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset)) = aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))) = scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)) = scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)) = aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset)))),
inference(transitivity,[status(thm)],[21,9]) ).
tff(23,plain,
aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset)))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset)))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
^ [X: $i,Xa: $i] :
refl(
( ( aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc407235996eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bf,Xa)),scratc1146276611_proj1) )
<=> ( aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc407235996eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bf,Xa)),scratc1146276611_proj1) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [X: $i,Xa: $i] : ( aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc407235996eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bf,Xa)),scratc1146276611_proj1) )
<=> ! [X: $i,Xa: $i] : ( aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc407235996eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bf,Xa)),scratc1146276611_proj1) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [X: $i,Xa: $i] : ( aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc407235996eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bf,Xa)),scratc1146276611_proj1) )
<=> ! [X: $i,Xa: $i] : ( aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc407235996eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bf,Xa)),scratc1146276611_proj1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,axiom,
! [X: $i,Xa: $i] : ( aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc407235996eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bf,Xa)),scratc1146276611_proj1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__ap) ).
tff(29,plain,
! [X: $i,Xa: $i] : ( aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc407235996eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bf,Xa)),scratc1146276611_proj1) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [X: $i,Xa: $i] : ( aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc407235996eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bf,Xa)),scratc1146276611_proj1) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [X: $i,Xa: $i] : ( aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc407235996eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bf,Xa)),scratc1146276611_proj1) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
( ~ ! [X: $i,Xa: $i] : ( aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc407235996eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bf,Xa)),scratc1146276611_proj1) )
| ( aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset)))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset)))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1),
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,plain,
aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset)))),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1) = aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),
inference(transitivity,[status(thm)],[34,24]) ).
tff(36,plain,
( gg_TPTP_ind(aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1))
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> gg_TPTP_ind(aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)) ),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
^ [B_1: $i,B_2: $i] :
refl(
( gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)) )),
inference(bind,[status(th)],]) ).
tff(39,plain,
( ! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))
<=> ! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))
<=> ! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)) ),
inference(rewrite,[status(thm)],]) ).
tff(41,axiom,
! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_aa_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind) ).
tff(42,plain,
! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
( ~ ! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))
| gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
gg_TPTP_ind(aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)),
inference(modus_ponens,[status(thm)],[46,37]) ).
tff(48,plain,
( ~ ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(X),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,X)) )
| ( aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[48,16]) ).
tff(50,plain,
aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) = aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
^ [X: $i,Xa: $i] :
refl(
( ( aa_fun1431113780TP_ind(scratc322369131_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1550011574bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc1745451206ptyset) )
<=> ( aa_fun1431113780TP_ind(scratc322369131_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1550011574bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc1745451206ptyset) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc322369131_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1550011574bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc1745451206ptyset) )
<=> ! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc322369131_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1550011574bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc1745451206ptyset) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc322369131_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1550011574bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc1745451206ptyset) )
<=> ! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc322369131_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1550011574bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc1745451206ptyset) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,axiom,
! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc322369131_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1550011574bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc1745451206ptyset) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__d__Sep) ).
tff(55,plain,
! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc322369131_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1550011574bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc1745451206ptyset) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc322369131_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1550011574bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc1745451206ptyset) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc322369131_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1550011574bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc1745451206ptyset) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
( ~ ! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc322369131_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1550011574bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc1745451206ptyset) )
| ( aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag) = aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1550011574bnd_in),aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p))),aTP_Lamm_ag)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bm(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag))),scratc1745451206ptyset) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag) = aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1550011574bnd_in),aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p))),aTP_Lamm_ag)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bm(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag))),scratc1745451206ptyset),
inference(unit_resolution,[status(thm)],[58,57]) ).
tff(60,plain,
scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)) = scratc1564950462d_e_is(aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1550011574bnd_in),aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p))),aTP_Lamm_ag)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bm(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag))),scratc1745451206ptyset)),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
scratc1564950462d_e_is(aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1550011574bnd_in),aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p))),aTP_Lamm_ag)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bm(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag))),scratc1745451206ptyset)) = scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
^ [X: $i] :
refl(
( ( scratc1564950462d_e_is(X) = fequal_TPTP_ind )
<=> ( scratc1564950462d_e_is(X) = fequal_TPTP_ind ) )),
inference(bind,[status(th)],]) ).
tff(63,plain,
( ! [X: $i] : ( scratc1564950462d_e_is(X) = fequal_TPTP_ind )
<=> ! [X: $i] : ( scratc1564950462d_e_is(X) = fequal_TPTP_ind ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [X: $i] : ( scratc1564950462d_e_is(X) = fequal_TPTP_ind )
<=> ! [X: $i] : ( scratc1564950462d_e_is(X) = fequal_TPTP_ind ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,axiom,
! [X: $i] : ( scratc1564950462d_e_is(X) = fequal_TPTP_ind ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__e__is) ).
tff(66,plain,
! [X: $i] : ( scratc1564950462d_e_is(X) = fequal_TPTP_ind ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [X: $i] : ( scratc1564950462d_e_is(X) = fequal_TPTP_ind ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [X: $i] : ( scratc1564950462d_e_is(X) = fequal_TPTP_ind ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
( ~ ! [X: $i] : ( scratc1564950462d_e_is(X) = fequal_TPTP_ind )
| ( scratc1564950462d_e_is(aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1550011574bnd_in),aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p))),aTP_Lamm_ag)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bm(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag))),scratc1745451206ptyset)) = fequal_TPTP_ind ) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
scratc1564950462d_e_is(aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1550011574bnd_in),aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p))),aTP_Lamm_ag)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bm(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag))),scratc1745451206ptyset)) = fequal_TPTP_ind,
inference(unit_resolution,[status(thm)],[69,68]) ).
tff(71,plain,
fequal_TPTP_ind = scratc1564950462d_e_is(aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1550011574bnd_in),aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p))),aTP_Lamm_ag)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bm(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag))),scratc1745451206ptyset)),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
fequal_TPTP_ind = scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),
inference(transitivity,[status(thm)],[71,61]) ).
tff(73,plain,
aa_TPT43085870d_bool(fequal_TPTP_ind,aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)) = aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(monotonicity,[status(thm)],[72,35]) ).
tff(74,plain,
aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)),aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(monotonicity,[status(thm)],[73,50]) ).
tff(75,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)),aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)),aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))) ),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
^ [Uu: $i] :
refl(
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),Uu)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu))) )
<=> ( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),Uu)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu))) ) )),
inference(bind,[status(th)],]) ).
tff(78,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),Uu)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),Uu)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu))) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,plain,
^ [Uu: $i] :
rewrite(
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(scratc45782132nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu))) )
<=> ( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),Uu)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu))) ) )),
inference(bind,[status(th)],]) ).
tff(80,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(scratc45782132nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),Uu)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu))) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(scratc45782132nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(scratc45782132nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,axiom,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(scratc45782132nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ATP_Olambda__4) ).
tff(83,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(scratc45782132nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu))) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),Uu)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu))) ),
inference(modus_ponens,[status(thm)],[83,80]) ).
tff(85,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),Uu)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu))) ),
inference(skolemize,[status(sab)],[84]) ).
tff(86,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),Uu)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu))) ),
inference(modus_ponens,[status(thm)],[85,78]) ).
tff(87,plain,
( ~ ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),Uu)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu))) )
| ( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(88,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[87,86]) ).
tff(89,plain,
^ [X: $i,Xa: $i] :
refl(
( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
^ [X: $i,Xa: $i] :
rewrite(
( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(92,plain,
( ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,plain,
( ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) ),
inference(transitivity,[status(thm)],[92,90]) ).
tff(94,plain,
^ [X: $i,Xa: $i] :
trans(
monotonicity(
rewrite(
( ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) )
<=> ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_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))
| ~ scratc1451164978_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))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(Xa,X),X) ) )),
( ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(Xa,X),X) ) )
<=> ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )),
( ( ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ( ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
rewrite(
( ( ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
( ( ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(95,plain,
( ! [X: $i,Xa: $i] :
( ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(97,plain,
^ [X: $i,Xa: $i] :
rewrite(
( ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
<=> ! [X2: $i] :
( gg_TPTP_ind(X2)
=> ( scratc1451164978_is_of(X2,X)
=> pp(aa_TPTP_ind_bool(Xa,X2)) ) ) )
<=> ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) ) )),
inference(bind,[status(th)],]) ).
tff(98,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
<=> ! [X2: $i] :
( gg_TPTP_ind(X2)
=> ( scratc1451164978_is_of(X2,X)
=> pp(aa_TPTP_ind_bool(Xa,X2)) ) ) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,axiom,
! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
<=> ! [X2: $i] :
( gg_TPTP_ind(X2)
=> ( scratc1451164978_is_of(X2,X)
=> pp(aa_TPTP_ind_bool(Xa,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__all__of) ).
tff(100,plain,
! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) ),
inference(modus_ponens,[status(thm)],[100,96]) ).
tff(102,plain,
! [X: $i,Xa: $i] :
( ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ),
inference(skolemize,[status(sab)],[101]) ).
tff(103,plain,
! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ),
inference(modus_ponens,[status(thm)],[102,95]) ).
tff(104,plain,
! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ),
inference(modus_ponens,[status(thm)],[103,93]) ).
tff(105,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(106,plain,
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ) ),
inference(unit_resolution,[status(thm)],[105,104]) ).
tff(107,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) )
| pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(108,plain,
( pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[107,106]) ).
tff(109,plain,
( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_aa))
<=> ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_aa)) ),
inference(rewrite,[status(thm)],]) ).
tff(110,axiom,
~ pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_aa)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(111,plain,
~ pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_aa)),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
( ~ ( pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) )
| pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(113,plain,
( ~ ( pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) )
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[112,111]) ).
tff(114,plain,
~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ),
inference(unit_resolution,[status(thm)],[113,108]) ).
tff(115,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ),
inference(tautology,[status(thm)],]) ).
tff(116,plain,
scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a),
inference(unit_resolution,[status(thm)],[115,114]) ).
tff(117,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) ),
inference(tautology,[status(thm)],]) ).
tff(118,plain,
gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),
inference(unit_resolution,[status(thm)],[117,114]) ).
tff(119,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_bu))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_bu))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,tptp_fun_X2_12(aTP_Lamm_bu,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_bu,aTP_Lamm_a))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_bu,aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(120,plain,
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_bu))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_bu))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,tptp_fun_X2_12(aTP_Lamm_bu,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_bu,aTP_Lamm_a))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_bu,aTP_Lamm_a),aTP_Lamm_a) ) ) ),
inference(unit_resolution,[status(thm)],[119,104]) ).
tff(121,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_bu))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_bu))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,tptp_fun_X2_12(aTP_Lamm_bu,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_bu,aTP_Lamm_a))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_bu,aTP_Lamm_a),aTP_Lamm_a) ) )
| ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_bu))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(122,plain,
( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_bu))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[121,120]) ).
tff(123,plain,
( pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_bu))
<=> pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_bu)) ),
inference(rewrite,[status(thm)],]) ).
tff(124,axiom,
pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_bu)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_satz4c) ).
tff(125,plain,
pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_bu)),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_bu))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,aTP_Lamm_a) ) )
| ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_bu))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(127,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aTP_Lamm_bu))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,aTP_Lamm_a) ) )
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[126,125]) ).
tff(128,plain,
! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,aTP_Lamm_a) ),
inference(unit_resolution,[status(thm)],[127,122]) ).
tff(129,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bu,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bu,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(130,plain,
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bu,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(131,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_bu,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bu,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_bu,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bu,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(transitivity,[status(thm)],[131,129]) ).
tff(133,plain,
( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_bu,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(134,plain,
( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1451164978_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bu,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
pp(aa_TPTP_ind_bool(aTP_Lamm_bu,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[134,128,118,116]) ).
tff(136,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) )
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(tautology,[status(thm)],]) ).
tff(137,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[136,135]) ).
tff(138,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))),
inference(unit_resolution,[status(thm)],[137,88]) ).
tff(139,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)),aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))),
inference(modus_ponens,[status(thm)],[138,76]) ).
tff(140,plain,
( gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(141,plain,
( gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
( ~ ! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))
| gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(143,plain,
gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[142,44]) ).
tff(144,plain,
gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))),
inference(modus_ponens,[status(thm)],[143,141]) ).
tff(145,plain,
( ( aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) )
<=> ( aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) ) ),
inference(commutativity,[status(thm)],]) ).
tff(146,plain,
( ( aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
<=> ( aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) ) ),
inference(monotonicity,[status(thm)],[35,50]) ).
tff(147,plain,
( ( aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
<=> ( aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) ) ),
inference(transitivity,[status(thm)],[146,145]) ).
tff(148,plain,
( ( aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) )
<=> ( aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
( ( aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) != aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) )
<=> ( aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1) != aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(monotonicity,[status(thm)],[148]) ).
tff(150,plain,
aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) = aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(monotonicity,[status(thm)],[72]) ).
tff(151,plain,
aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(monotonicity,[status(thm)],[151]) ).
tff(153,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(symmetry,[status(thm)],[152]) ).
tff(154,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
<=> ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(monotonicity,[status(thm)],[153]) ).
tff(155,plain,
^ [Uu: $i] :
refl(
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),Uu))) )
<=> ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),Uu))) ) )),
inference(bind,[status(th)],]) ).
tff(156,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),Uu))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),Uu))) ) ),
inference(quant_intro,[status(thm)],[155]) ).
tff(157,plain,
^ [Uu: $i] :
rewrite(
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(scratc45782132nd_n_1),Uu))) )
<=> ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),Uu))) ) )),
inference(bind,[status(th)],]) ).
tff(158,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(scratc45782132nd_n_1),Uu))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),Uu))) ) ),
inference(quant_intro,[status(thm)],[157]) ).
tff(159,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(scratc45782132nd_n_1),Uu))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(scratc45782132nd_n_1),Uu))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(160,axiom,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(scratc45782132nd_n_1),Uu))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ATP_Olambda__8) ).
tff(161,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(scratc45782132nd_n_1),Uu))) ),
inference(modus_ponens,[status(thm)],[160,159]) ).
tff(162,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),Uu))) ),
inference(modus_ponens,[status(thm)],[161,158]) ).
tff(163,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),Uu))) ),
inference(skolemize,[status(sab)],[162]) ).
tff(164,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),Uu))) ),
inference(modus_ponens,[status(thm)],[163,156]) ).
tff(165,plain,
( ~ ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),Uu))) )
| ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(166,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[165,164]) ).
tff(167,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1451164978_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(tautology,[status(thm)],]) ).
tff(168,plain,
~ pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[167,114]) ).
tff(169,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(tautology,[status(thm)],]) ).
tff(170,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[169,168]) ).
tff(171,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1770865966univof,scratc1745451206ptyset)),scratc1337809184_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))),
inference(unit_resolution,[status(thm)],[170,166]) ).
tff(172,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))),
inference(modus_ponens,[status(thm)],[171,154]) ).
tff(173,plain,
^ [X7: $i,Y: $i] :
refl(
( ( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) )
<=> ( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) ) )),
inference(bind,[status(th)],]) ).
tff(174,plain,
( ! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) )
<=> ! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) ) ),
inference(quant_intro,[status(thm)],[173]) ).
tff(175,plain,
( ! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) )
<=> ! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(176,axiom,
! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_001t__TPTP____Interpret__Oind_T) ).
tff(177,plain,
! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) ),
inference(modus_ponens,[status(thm)],[176,175]) ).
tff(178,plain,
! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) ),
inference(skolemize,[status(sab)],[177]) ).
tff(179,plain,
! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) ),
inference(modus_ponens,[status(thm)],[178,174]) ).
tff(180,plain,
( ( ~ ! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) )
| ( aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) != aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) )
<=> ( ~ ! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) )
| ( aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) != aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(181,plain,
( ~ ! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) )
| ( aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) != aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(182,plain,
( ~ ! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) )
| ( aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) != aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(modus_ponens,[status(thm)],[181,180]) ).
tff(183,plain,
( ( aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) != aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[182,179]) ).
tff(184,plain,
aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) != aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)),tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),
inference(unit_resolution,[status(thm)],[183,172]) ).
tff(185,plain,
aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1) != aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(modus_ponens,[status(thm)],[184,149]) ).
tff(186,plain,
^ [X7: $i,Y: $i] :
refl(
( ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
<=> ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
inference(bind,[status(th)],]) ).
tff(187,plain,
( ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
<=> ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) ),
inference(quant_intro,[status(thm)],[186]) ).
tff(188,plain,
^ [X7: $i,Y: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) )
<=> ~ ( ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
( ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) )
<=> ~ ~ ( ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
rewrite(
( ~ ~ ( ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
<=> ( ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
( ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) )
<=> ( ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
( ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) )
<=> ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
rewrite(
( ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
<=> ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
( ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) )
<=> ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) )),
inference(bind,[status(th)],]) ).
tff(189,plain,
( ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) )
<=> ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ) ),
inference(quant_intro,[status(thm)],[188]) ).
tff(190,plain,
( ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) )
<=> ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(191,plain,
^ [X7: $i,Y: $i] :
rewrite(
( ( ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) )
=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ( X7 = Y ) ) )
<=> ( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) ) )),
inference(bind,[status(th)],]) ).
tff(192,plain,
( ! [X7: $i,Y: $i] :
( ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) )
=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ( X7 = Y ) ) )
<=> ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) ) ),
inference(quant_intro,[status(thm)],[191]) ).
tff(193,axiom,
! [X7: $i,Y: $i] :
( ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) )
=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ( X7 = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_001t__TPTP____Interpret__Oind_T) ).
tff(194,plain,
! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) ),
inference(modus_ponens,[status(thm)],[193,192]) ).
tff(195,plain,
! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) ),
inference(modus_ponens,[status(thm)],[194,190]) ).
tff(196,plain,
! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) ),
inference(skolemize,[status(sab)],[195]) ).
tff(197,plain,
! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ),
inference(modus_ponens,[status(thm)],[196,189]) ).
tff(198,plain,
! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ),
inference(modus_ponens,[status(thm)],[197,187]) ).
tff(199,plain,
( ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ( aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)),aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)) )
<=> ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ( aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)),aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(200,plain,
( ( ( aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)),aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ gg_TPTP_ind(aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)) )
<=> ( ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ( aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)),aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(201,plain,
( ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ( aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)),aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ gg_TPTP_ind(aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)) )
<=> ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ( aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)),aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)) ) ),
inference(monotonicity,[status(thm)],[200]) ).
tff(202,plain,
( ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ( aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)),aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ gg_TPTP_ind(aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)) )
<=> ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ( aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)),aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)) ) ),
inference(transitivity,[status(thm)],[201,199]) ).
tff(203,plain,
( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ( aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)),aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ gg_TPTP_ind(aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)) ),
inference(quant_inst,[status(thm)],]) ).
tff(204,plain,
( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ( aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)),aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)) ),
inference(modus_ponens,[status(thm)],[203,202]) ).
tff(205,plain,
( ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ( aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)),aa_TPTP_ind_TPTP_ind(scratc957265209nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_fun277296641TP_ind(scratc407235996eplSep(aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,aa_TPTP_ind_TPTP_ind(scratc957265209nunion(scratc1745451206ptyset),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))),aa_TPT43085870d_bool(aTP_Lamm_bf,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),scratc1146276611_proj1)) ),
inference(unit_resolution,[status(thm)],[204,198]) ).
tff(206,plain,
$false,
inference(unit_resolution,[status(thm)],[205,185,144,139,47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM641+4 : TPTP v8.1.0. Released v7.3.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Sep 2 12:50:29 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 5.75/3.97 % SZS status Theorem
% 5.75/3.97 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------