TSTP Solution File: NUM639+4 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM639+4 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 13:11:08 EDT 2022
% Result : Theorem 5.29s 3.69s
% Output : Proof 5.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 104
% Syntax : Number of formulae : 221 ( 67 unt; 38 typ; 0 def)
% Number of atoms : 866 ( 128 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 1202 ( 557 ~; 487 |; 22 &)
% ( 127 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of FOOLs : 38 ( 38 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 23 >; 13 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 35 ( 35 usr; 15 con; 0-2 aty)
% Number of variables : 270 ( 244 !; 0 ?; 270 :)
% Comments :
%------------------------------------------------------------------------------
tff(gg_TPTP_ind_type,type,
gg_TPTP_ind: $i > $o ).
tff(aa_TPTP_ind_TPTP_ind_type,type,
aa_TPTP_ind_TPTP_ind: ( $i * $i ) > $i ).
tff(scratc1455160150ptyset_type,type,
scratc1455160150ptyset: $i ).
tff(scratc236248354rdsucc_type,type,
scratc236248354rdsucc: $i ).
tff(scratc1289955817d_n_pl_type,type,
scratc1289955817d_n_pl: $i > $i ).
tff(tptp_fun_X2_12_type,type,
tptp_fun_X2_12: ( $i * $i ) > $i ).
tff(aTP_Lamm_a_type,type,
aTP_Lamm_a: $i ).
tff(aTP_Lamm_aa_type,type,
aTP_Lamm_aa: $i ).
tff(scratc177978290d_Sing_type,type,
scratc177978290d_Sing: $i ).
tff(scratc666974153nunion_type,type,
scratc666974153nunion: $i > $i ).
tff(pp_type,type,
pp: $i > $o ).
tff(aa_TPTP_ind_bool_type,type,
aa_TPTP_ind_bool: ( $i * $i ) > $i ).
tff(aa_TPT43085870d_bool_type,type,
aa_TPT43085870d_bool: ( $i * $i ) > $i ).
tff(fequal_TPTP_ind_type,type,
fequal_TPTP_ind: $i ).
tff(scratc1770836270d_e_is_type,type,
scratc1770836270d_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(scratc700825851_d_Sep_type,type,
scratc700825851_d_Sep: $i > $i ).
tff(scratc1716265904_nat_p_type,type,
scratc1716265904_nat_p: $i ).
tff(scratc1839038univof_type,type,
scratc1839038univof: $i ).
tff(scratc932620094bnd_if_type,type,
scratc932620094bnd_if: ( $i * $i ) > $i ).
tff(aa_fun277296641TP_ind_type,type,
aa_fun277296641TP_ind: ( $i * $i ) > $i ).
tff(aa_fun1235454963TP_ind_type,type,
aa_fun1235454963TP_ind: ( $i * $i ) > $i ).
tff(aTP_Lamm_bm_type,type,
aTP_Lamm_bm: $i > $i ).
tff(aa_TPT494704832TP_ind_type,type,
aa_TPT494704832TP_ind: ( $i * $i ) > $i ).
tff(scratc1240091504d_repl_type,type,
scratc1240091504d_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(scratc932620102bnd_in_type,type,
scratc932620102bnd_in: $i ).
tff(fconj_type,type,
fconj: $i ).
tff(aTP_Lamm_bu_type,type,
aTP_Lamm_bu: $i ).
tff(scratc214542084nd_n_1_type,type,
scratc214542084nd_n_1: $i ).
tff(scratc1289496631d_n_is_type,type,
scratc1289496631d_n_is: $i ).
tff(scratc1829621698_is_of_type,type,
scratc1829621698_is_of: ( $i * $i ) > $o ).
tff(aa_fun171081125l_bool_type,type,
aa_fun171081125l_bool: ( $i * $i ) > $i ).
tff(scratc1153622423all_of_type,type,
scratc1153622423all_of: $i > $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(X),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,X)) )
<=> ( aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(X),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,X)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(X),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,X)) )
<=> ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(X),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,X)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(X),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,X)) )
<=> ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(X),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(X),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__ordsucc) ).
tff(5,plain,
! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(X),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,X)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(X),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,X)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(X),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,X)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(X),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,X)) )
| ( aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(scratc1455160150ptyset),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,scratc1455160150ptyset)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(scratc1455160150ptyset),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,scratc1455160150ptyset)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
aa_TPTP_ind_TPTP_ind(scratc666974153nunion(scratc1455160150ptyset),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,scratc1455160150ptyset)) = aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc666974153nunion(scratc1455160150ptyset),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,scratc1455160150ptyset))) = aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) = aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc666974153nunion(scratc1455160150ptyset),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,scratc1455160150ptyset))),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc666974153nunion(scratc1455160150ptyset),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,scratc1455160150ptyset)))) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc666974153nunion(scratc1455160150ptyset),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,scratc1455160150ptyset))))
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))) ),
inference(symmetry,[status(thm)],[13]) ).
tff(15,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(16,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)],[15]) ).
tff(17,plain,
( ! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))
<=> ! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)) ),
inference(rewrite,[status(thm)],]) ).
tff(18,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(19,plain,
! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,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(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc666974153nunion(scratc1455160150ptyset),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,scratc1455160150ptyset)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(23,plain,
gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc666974153nunion(scratc1455160150ptyset),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,scratc1455160150ptyset)))),
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),
inference(modus_ponens,[status(thm)],[23,14]) ).
tff(25,plain,
( ~ ! [X: $i] : ( aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(X),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,X)) )
| ( aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(26,plain,
aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[25,7]) ).
tff(27,plain,
aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) = aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
^ [X: $i,Xa: $i] :
refl(
( ( aa_fun1431113780TP_ind(scratc700825851_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc932620094bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc932620102bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1240091504d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc1455160150ptyset) )
<=> ( aa_fun1431113780TP_ind(scratc700825851_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc932620094bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc932620102bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1240091504d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc1455160150ptyset) ) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc700825851_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc932620094bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc932620102bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1240091504d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc1455160150ptyset) )
<=> ! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc700825851_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc932620094bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc932620102bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1240091504d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc1455160150ptyset) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc700825851_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc932620094bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc932620102bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1240091504d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc1455160150ptyset) )
<=> ! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc700825851_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc932620094bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc932620102bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1240091504d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc1455160150ptyset) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,axiom,
! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc700825851_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc932620094bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc932620102bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1240091504d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc1455160150ptyset) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__d__Sep) ).
tff(32,plain,
! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc700825851_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc932620094bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc932620102bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1240091504d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc1455160150ptyset) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc700825851_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc932620094bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc932620102bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1240091504d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc1455160150ptyset) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc700825851_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc932620094bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc932620102bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1240091504d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc1455160150ptyset) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ~ ! [X: $i,Xa: $i] : ( aa_fun1431113780TP_ind(scratc700825851_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc932620094bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc932620102bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1240091504d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc1455160150ptyset) )
| ( aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag) = aa_TPTP_ind_TPTP_ind(scratc932620094bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc932620102bnd_in),aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p))),aTP_Lamm_ag)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1240091504d_repl,aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bm(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag))),scratc1455160150ptyset) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag) = aa_TPTP_ind_TPTP_ind(scratc932620094bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc932620102bnd_in),aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p))),aTP_Lamm_ag)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1240091504d_repl,aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bm(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag))),scratc1455160150ptyset),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)) = scratc1770836270d_e_is(aa_TPTP_ind_TPTP_ind(scratc932620094bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc932620102bnd_in),aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p))),aTP_Lamm_ag)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1240091504d_repl,aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bm(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag))),scratc1455160150ptyset)),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
scratc1770836270d_e_is(aa_TPTP_ind_TPTP_ind(scratc932620094bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc932620102bnd_in),aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p))),aTP_Lamm_ag)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1240091504d_repl,aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bm(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag))),scratc1455160150ptyset)) = scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
^ [X: $i] :
refl(
( ( scratc1770836270d_e_is(X) = fequal_TPTP_ind )
<=> ( scratc1770836270d_e_is(X) = fequal_TPTP_ind ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [X: $i] : ( scratc1770836270d_e_is(X) = fequal_TPTP_ind )
<=> ! [X: $i] : ( scratc1770836270d_e_is(X) = fequal_TPTP_ind ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [X: $i] : ( scratc1770836270d_e_is(X) = fequal_TPTP_ind )
<=> ! [X: $i] : ( scratc1770836270d_e_is(X) = fequal_TPTP_ind ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,axiom,
! [X: $i] : ( scratc1770836270d_e_is(X) = fequal_TPTP_ind ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__e__is) ).
tff(43,plain,
! [X: $i] : ( scratc1770836270d_e_is(X) = fequal_TPTP_ind ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [X: $i] : ( scratc1770836270d_e_is(X) = fequal_TPTP_ind ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [X: $i] : ( scratc1770836270d_e_is(X) = fequal_TPTP_ind ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
( ~ ! [X: $i] : ( scratc1770836270d_e_is(X) = fequal_TPTP_ind )
| ( scratc1770836270d_e_is(aa_TPTP_ind_TPTP_ind(scratc932620094bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc932620102bnd_in),aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p))),aTP_Lamm_ag)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1240091504d_repl,aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bm(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag))),scratc1455160150ptyset)) = fequal_TPTP_ind ) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
scratc1770836270d_e_is(aa_TPTP_ind_TPTP_ind(scratc932620094bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc932620102bnd_in),aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p))),aTP_Lamm_ag)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1240091504d_repl,aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bm(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag))),scratc1455160150ptyset)) = fequal_TPTP_ind,
inference(unit_resolution,[status(thm)],[46,45]) ).
tff(48,plain,
fequal_TPTP_ind = scratc1770836270d_e_is(aa_TPTP_ind_TPTP_ind(scratc932620094bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc932620102bnd_in),aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p))),aTP_Lamm_ag)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1240091504d_repl,aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aa_fun1235454963TP_ind(aTP_Lamm_bm(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag))),scratc1455160150ptyset)),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
fequal_TPTP_ind = scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),
inference(transitivity,[status(thm)],[48,38]) ).
tff(50,plain,
aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))) = aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(monotonicity,[status(thm)],[50,27]) ).
tff(52,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,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(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))) ),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
^ [Uu: $i] :
refl(
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu))) )
<=> ( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu))) ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu))) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
^ [Uu: $i] :
rewrite(
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),scratc214542084nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu))) )
<=> ( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu))) ) )),
inference(bind,[status(th)],]) ).
tff(57,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),scratc214542084nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu))) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),scratc214542084nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),scratc214542084nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,axiom,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),scratc214542084nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ATP_Olambda__3) ).
tff(60,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),scratc214542084nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu))) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu))) ),
inference(modus_ponens,[status(thm)],[60,57]) ).
tff(62,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu))) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu))) ),
inference(modus_ponens,[status(thm)],[62,55]) ).
tff(64,plain,
( ~ ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,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(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(65,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(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
^ [X: $i,Xa: $i] :
refl(
( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(67,plain,
( ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
^ [X: $i,Xa: $i] :
rewrite(
( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(69,plain,
( ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) ),
inference(transitivity,[status(thm)],[69,67]) ).
tff(71,plain,
^ [X: $i,Xa: $i] :
trans(
monotonicity(
rewrite(
( ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) )
<=> ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_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))
| ~ scratc1829621698_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))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(Xa,X),X) ) )),
( ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(Xa,X),X) ) )
<=> ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )),
( ( ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ( ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
rewrite(
( ( ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
( ( ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(72,plain,
( ! [X: $i,Xa: $i] :
( ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
^ [X: $i,Xa: $i] :
rewrite(
( ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
<=> ! [X2: $i] :
( gg_TPTP_ind(X2)
=> ( scratc1829621698_is_of(X2,X)
=> pp(aa_TPTP_ind_bool(Xa,X2)) ) ) )
<=> ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) ) )),
inference(bind,[status(th)],]) ).
tff(75,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
<=> ! [X2: $i] :
( gg_TPTP_ind(X2)
=> ( scratc1829621698_is_of(X2,X)
=> pp(aa_TPTP_ind_bool(Xa,X2)) ) ) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,axiom,
! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
<=> ! [X2: $i] :
( gg_TPTP_ind(X2)
=> ( scratc1829621698_is_of(X2,X)
=> pp(aa_TPTP_ind_bool(Xa,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__all__of) ).
tff(77,plain,
! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
! [X: $i,Xa: $i] :
( ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ),
inference(modus_ponens,[status(thm)],[79,72]) ).
tff(81,plain,
! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(Xa,X),X) ) ) ),
inference(modus_ponens,[status(thm)],[80,70]) ).
tff(82,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1153622423all_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))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(83,plain,
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1153622423all_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))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ) ),
inference(unit_resolution,[status(thm)],[82,81]) ).
tff(84,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1153622423all_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))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) )
| pp(aa_fun171081125l_bool(scratc1153622423all_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))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(85,plain,
( pp(aa_fun171081125l_bool(scratc1153622423all_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))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[84,83]) ).
tff(86,plain,
( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_aa))
<=> ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_aa)) ),
inference(rewrite,[status(thm)],]) ).
tff(87,axiom,
~ pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_aa)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(88,plain,
~ pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_aa)),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
( ~ ( pp(aa_fun171081125l_bool(scratc1153622423all_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))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) )
| pp(aa_fun171081125l_bool(scratc1153622423all_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))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(90,plain,
( ~ ( pp(aa_fun171081125l_bool(scratc1153622423all_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))
| ~ scratc1829621698_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))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[89,88]) ).
tff(91,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))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ),
inference(unit_resolution,[status(thm)],[90,85]) ).
tff(92,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| scratc1829621698_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ),
inference(tautology,[status(thm)],]) ).
tff(93,plain,
scratc1829621698_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a),
inference(unit_resolution,[status(thm)],[92,91]) ).
tff(94,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))
| ~ scratc1829621698_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(95,plain,
gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),
inference(unit_resolution,[status(thm)],[94,91]) ).
tff(96,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_12(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_12(Xa,X))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_bu))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1153622423all_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))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(aTP_Lamm_bu,aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_bu))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1153622423all_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))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(aTP_Lamm_bu,aTP_Lamm_a),aTP_Lamm_a) ) ) ),
inference(unit_resolution,[status(thm)],[96,81]) ).
tff(98,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_bu))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc1153622423all_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))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(aTP_Lamm_bu,aTP_Lamm_a),aTP_Lamm_a) ) )
| ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_bu))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(99,plain,
( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_bu))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[98,97]) ).
tff(100,plain,
( pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_bu))
<=> pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_bu)) ),
inference(rewrite,[status(thm)],]) ).
tff(101,axiom,
pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_bu)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_satz4a) ).
tff(102,plain,
pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_bu)),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_bu))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,aTP_Lamm_a) ) )
| ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_bu))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],]) ).
tff(104,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_bu))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,aTP_Lamm_a) ) )
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[103,102]) ).
tff(105,plain,
! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,aTP_Lamm_a) ),
inference(unit_resolution,[status(thm)],[104,99]) ).
tff(106,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1829621698_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)
| ~ scratc1829621698_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1829621698_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(107,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))
| ~ scratc1829621698_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))
| ~ scratc1829621698_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(108,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_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))
| ~ scratc1829621698_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)
| ~ scratc1829621698_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1829621698_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)],[107]) ).
tff(109,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_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))
| ~ scratc1829621698_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)
| ~ scratc1829621698_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1829621698_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)],[108,106]) ).
tff(110,plain,
( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_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))
| ~ scratc1829621698_is_of(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(111,plain,
( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1829621698_is_of(X2,aTP_Lamm_a) )
| ~ gg_TPTP_ind(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1829621698_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)],[110,109]) ).
tff(112,plain,
pp(aa_TPTP_ind_bool(aTP_Lamm_bu,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[111,105,95,93]) ).
tff(113,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(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,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(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(tautology,[status(thm)],]) ).
tff(114,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(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(unit_resolution,[status(thm)],[113,112]) ).
tff(115,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))),
inference(unit_resolution,[status(thm)],[114,65]) ).
tff(116,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))),
inference(modus_ponens,[status(thm)],[115,53]) ).
tff(117,plain,
( gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(118,plain,
( gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))) ),
inference(symmetry,[status(thm)],[117]) ).
tff(119,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(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(120,plain,
gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[119,21]) ).
tff(121,plain,
gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))),
inference(modus_ponens,[status(thm)],[120,118]) ).
tff(122,plain,
( ( aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) = aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) )
<=> ( aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) ) ),
inference(commutativity,[status(thm)],]) ).
tff(123,plain,
( ( aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
<=> ( aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) = aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) ) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(124,plain,
( ( aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
<=> ( aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) ) ),
inference(transitivity,[status(thm)],[123,122]) ).
tff(125,plain,
( ( aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) = aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) )
<=> ( aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(symmetry,[status(thm)],[124]) ).
tff(126,plain,
( ( aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) != aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) )
<=> ( aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) != aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,plain,
aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) = aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(monotonicity,[status(thm)],[49]) ).
tff(128,plain,
aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))) ),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))) ),
inference(symmetry,[status(thm)],[129]) ).
tff(131,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))))
<=> ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))) ),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
^ [Uu: $i] :
refl(
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))) )
<=> ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))) ) )),
inference(bind,[status(th)],]) ).
tff(133,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))) ) ),
inference(quant_intro,[status(thm)],[132]) ).
tff(134,plain,
^ [Uu: $i] :
rewrite(
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),scratc214542084nd_n_1))) )
<=> ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))) ) )),
inference(bind,[status(th)],]) ).
tff(135,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),scratc214542084nd_n_1))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))) ) ),
inference(quant_intro,[status(thm)],[134]) ).
tff(136,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),scratc214542084nd_n_1))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),scratc214542084nd_n_1))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(137,axiom,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),scratc214542084nd_n_1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ATP_Olambda__7) ).
tff(138,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),scratc214542084nd_n_1))) ),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))) ),
inference(modus_ponens,[status(thm)],[138,135]) ).
tff(140,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))) ),
inference(skolemize,[status(sab)],[139]) ).
tff(141,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))) ),
inference(modus_ponens,[status(thm)],[140,133]) ).
tff(142,plain,
( ~ ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))) )
| ( 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(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(143,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(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))) ),
inference(unit_resolution,[status(thm)],[142,141]) ).
tff(144,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))
| ~ scratc1829621698_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(145,plain,
~ pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[144,91]) ).
tff(146,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(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))) )
| 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(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))) ),
inference(tautology,[status(thm)],]) ).
tff(147,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(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))) ),
inference(unit_resolution,[status(thm)],[146,145]) ).
tff(148,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1770836270d_e_is(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_fun1431113780TP_ind(scratc700825851_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1839038univof,scratc1455160150ptyset)),scratc1716265904_nat_p)),aTP_Lamm_ag)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))),
inference(unit_resolution,[status(thm)],[147,143]) ).
tff(149,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))),
inference(modus_ponens,[status(thm)],[148,131]) ).
tff(150,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(151,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)],[150]) ).
tff(152,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(153,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(154,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)],[153,152]) ).
tff(155,plain,
! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) ),
inference(skolemize,[status(sab)],[154]) ).
tff(156,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)],[155,151]) ).
tff(157,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(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) != aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))) )
<=> ( ~ ! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) )
| ( aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) != aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(158,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(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) != aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(159,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(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) != aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
( ( aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) != aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)))) ),
inference(unit_resolution,[status(thm)],[159,156]) ).
tff(161,plain,
aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)) != aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)),
inference(unit_resolution,[status(thm)],[160,149]) ).
tff(162,plain,
aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) != aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))),
inference(modus_ponens,[status(thm)],[161,126]) ).
tff(163,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(164,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)],[163]) ).
tff(165,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(166,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)],[165]) ).
tff(167,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(168,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(169,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)],[168]) ).
tff(170,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(171,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)],[170,169]) ).
tff(172,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)],[171,167]) ).
tff(173,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)],[172]) ).
tff(174,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)],[173,166]) ).
tff(175,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)],[174,164]) ).
tff(176,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(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ( aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))) )
<=> ( ~ ! [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(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ( aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(177,plain,
( ( ( aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))) )
<=> ( ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ( aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(178,plain,
( ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ( aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))) )
<=> ( ~ ! [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(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ( aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))) ) ),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
( ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ( aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))) )
<=> ( ~ ! [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(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ( aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))) ) ),
inference(transitivity,[status(thm)],[178,176]) ).
tff(180,plain,
( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ( aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))) ),
inference(quant_inst,[status(thm)],]) ).
tff(181,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(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ( aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))) ),
inference(modus_ponens,[status(thm)],[180,179]) ).
tff(182,plain,
( ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))))
| ( aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset)) = aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))),aa_TPTP_ind_TPTP_ind(scratc666974153nunion(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc177978290d_Sing,tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)))))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(tptp_fun_X2_12(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,scratc1455160150ptyset))) ),
inference(unit_resolution,[status(thm)],[181,175]) ).
tff(183,plain,
$false,
inference(unit_resolution,[status(thm)],[182,162,121,116,24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM639+4 : TPTP v8.1.0. Released v7.3.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n008.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 12:42:10 EDT 2022
% 0.13/0.34 % 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.
% 5.29/3.69 % SZS status Theorem
% 5.29/3.69 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------