%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM706+4 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 : Sat Jun 21 05:21:55 AM UTC 2025
% Result : Theorem 40.59s 40.80s
% Output : Proof 40.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 71
% Syntax : Number of formulae : 188 ( 66 unt; 0 typ; 0 def)
% Number of atoms : 1099 ( 86 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 1716 ( 840 ~; 708 |; 22 &)
% ( 137 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 35 ( 35 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 11 con; 0-2 aty)
% Number of variables : 307 ( 285 !; 0 ?; 307 :)
% Comments :
%------------------------------------------------------------------------------
tff(scratc1814191352_is_of_type,type,
scratc1814191352_is_of: ( $i * $i ) > $o ).
tff(aa_TPT43085870d_bool_type,type,
aa_TPT43085870d_bool: ( $i * $i ) > $i ).
tff(tptp_fun_X2_13_type,type,
tptp_fun_X2_13: ( $i * $i ) > $i ).
tff(aTP_Lamm_a_type,type,
aTP_Lamm_a: $i ).
tff(aTP_Lamm_aa_type,type,
aTP_Lamm_aa: $i ).
tff(scratc214101377d_n_is_type,type,
scratc214101377d_n_is: $i ).
tff(aa_TPTP_ind_TPTP_ind_type,type,
aa_TPTP_ind_TPTP_ind: ( $i * $i ) > $i ).
tff(scratc1030418234nd_n_1_type,type,
scratc1030418234nd_n_1: $i ).
tff(scratc214822966d_n_ts_type,type,
scratc214822966d_n_ts: $i > $i ).
tff(gg_TPTP_ind_type,type,
gg_TPTP_ind: $i > $o ).
tff(scratc351358348ptyset_type,type,
scratc351358348ptyset: $i ).
tff(scratc1633262956rdsucc_type,type,
scratc1633262956rdsucc: $i ).
tff(pp_type,type,
pp: $i > $o ).
tff(aa_TPTP_ind_bool_type,type,
aa_TPTP_ind_bool: ( $i * $i ) > $i ).
tff(fequal_TPTP_ind_type,type,
fequal_TPTP_ind: $i ).
tff(scratc695441016d_e_is_type,type,
scratc695441016d_e_is: $i > $i ).
tff(scratc272482122nd_nat_type,type,
scratc272482122nd_nat: $i ).
tff(aa_fun1431113780TP_ind_type,type,
aa_fun1431113780TP_ind: ( $i * $i ) > $i ).
tff(aTP_Lamm_aj_type,type,
aTP_Lamm_aj: $i ).
tff(scratc685395505_d_Sep_type,type,
scratc685395505_d_Sep: $i > $i ).
tff(scratc1593906026_omega_type,type,
scratc1593906026_omega: $i ).
tff(aTP_Lamm_bx_type,type,
aTP_Lamm_bx: $i ).
tff(aa_fun171081125l_bool_type,type,
aa_fun171081125l_bool: ( $i * $i ) > $i ).
tff(scratc403153377all_of_type,type,
scratc403153377all_of: $i > $i ).
tff(1,plain,
( ( scratc1030418234nd_n_1 = aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,scratc351358348ptyset) )
<=> ( scratc1030418234nd_n_1 = aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,scratc351358348ptyset) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
scratc1030418234nd_n_1 = aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,scratc351358348ptyset),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__n__1) ).
tff(3,plain,
scratc1030418234nd_n_1 = aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,scratc351358348ptyset),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,scratc351358348ptyset) = scratc1030418234nd_n_1,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,scratc351358348ptyset)) = aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1) = aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,scratc351358348ptyset)),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1))
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,scratc351358348ptyset))) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,scratc351358348ptyset)))
<=> gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)) ),
inference(symmetry,[status(thm)],[7]) ).
tff(9,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(10,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)],[9]) ).
tff(11,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(12,axiom,
! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_aa_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind) ).
tff(13,plain,
! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [B_1: $i,B_2: $i] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2)),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,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(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,scratc351358348ptyset))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(17,plain,
gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,scratc351358348ptyset))),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),
inference(modus_ponens,[status(thm)],[17,8]) ).
tff(19,plain,
( ( scratc214101377d_n_is = scratc695441016d_e_is(scratc272482122nd_nat) )
<=> ( scratc214101377d_n_is = scratc695441016d_e_is(scratc272482122nd_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
scratc214101377d_n_is = scratc695441016d_e_is(scratc272482122nd_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__n__is) ).
tff(21,plain,
scratc214101377d_n_is = scratc695441016d_e_is(scratc272482122nd_nat),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
scratc695441016d_e_is(scratc272482122nd_nat) = scratc214101377d_n_is,
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
( ( scratc272482122nd_nat = aa_fun1431113780TP_ind(scratc685395505_d_Sep(scratc1593906026_omega),aTP_Lamm_aj) )
<=> ( scratc272482122nd_nat = aa_fun1431113780TP_ind(scratc685395505_d_Sep(scratc1593906026_omega),aTP_Lamm_aj) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
scratc272482122nd_nat = aa_fun1431113780TP_ind(scratc685395505_d_Sep(scratc1593906026_omega),aTP_Lamm_aj),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__nat) ).
tff(25,plain,
scratc272482122nd_nat = aa_fun1431113780TP_ind(scratc685395505_d_Sep(scratc1593906026_omega),aTP_Lamm_aj),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
aa_fun1431113780TP_ind(scratc685395505_d_Sep(scratc1593906026_omega),aTP_Lamm_aj) = scratc272482122nd_nat,
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
scratc695441016d_e_is(aa_fun1431113780TP_ind(scratc685395505_d_Sep(scratc1593906026_omega),aTP_Lamm_aj)) = scratc695441016d_e_is(scratc272482122nd_nat),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
^ [X: $i] :
refl(( ( scratc695441016d_e_is(X) = fequal_TPTP_ind )
<=> ( scratc695441016d_e_is(X) = fequal_TPTP_ind ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [X: $i] : ( scratc695441016d_e_is(X) = fequal_TPTP_ind )
<=> ! [X: $i] : ( scratc695441016d_e_is(X) = fequal_TPTP_ind ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [X: $i] : ( scratc695441016d_e_is(X) = fequal_TPTP_ind )
<=> ! [X: $i] : ( scratc695441016d_e_is(X) = fequal_TPTP_ind ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
! [X: $i] : ( scratc695441016d_e_is(X) = fequal_TPTP_ind ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__e__is) ).
tff(32,plain,
! [X: $i] : ( scratc695441016d_e_is(X) = fequal_TPTP_ind ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [X: $i] : ( scratc695441016d_e_is(X) = fequal_TPTP_ind ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [X: $i] : ( scratc695441016d_e_is(X) = fequal_TPTP_ind ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ~ ! [X: $i] : ( scratc695441016d_e_is(X) = fequal_TPTP_ind )
| ( scratc695441016d_e_is(aa_fun1431113780TP_ind(scratc685395505_d_Sep(scratc1593906026_omega),aTP_Lamm_aj)) = fequal_TPTP_ind ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
scratc695441016d_e_is(aa_fun1431113780TP_ind(scratc685395505_d_Sep(scratc1593906026_omega),aTP_Lamm_aj)) = fequal_TPTP_ind,
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
fequal_TPTP_ind = scratc695441016d_e_is(aa_fun1431113780TP_ind(scratc685395505_d_Sep(scratc1593906026_omega),aTP_Lamm_aj)),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
fequal_TPTP_ind = scratc214101377d_n_is,
inference(transitivity,[status(thm)],[37,27,22]) ).
tff(39,plain,
aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)) = aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
^ [Uu: $i] :
refl(( ( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1)),Uu)) )
<=> ( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1)),Uu)) ) )),
inference(bind,[status(th)],[]) ).
tff(44,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1)),Uu)) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1)),Uu)) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1)),Uu)) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1)),Uu)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,axiom,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1)),Uu)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__4) ).
tff(47,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1)),Uu)) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1)),Uu)) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1)),Uu)) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ~ ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1)),Uu)) )
| ( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
^ [X: $i,Xa: $i] :
refl(( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
^ [X: $i,Xa: $i] :
rewrite(( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) ) ),
inference(transitivity,[status(thm)],[55,53]) ).
tff(57,plain,
^ [X: $i,Xa: $i] :
trans(monotonicity(rewrite(( ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
<=> ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) ) )),
monotonicity(rewrite(( ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) )
<=> ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) )),
( ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) )
<=> ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )),
( ( ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
<=> ( ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) ) )),
rewrite(( ( ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) ) )),
( ( ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(58,plain,
( ! [X: $i,Xa: $i] :
( ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
<=> ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
^ [X: $i,Xa: $i] :
rewrite(( ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
<=> ! [X2: $i] :
( gg_TPTP_ind(X2)
=> ( scratc1814191352_is_of(X2,X)
=> pp(aa_TPTP_ind_bool(Xa,X2)) ) ) )
<=> ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(61,plain,
( ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
<=> ! [X2: $i] :
( gg_TPTP_ind(X2)
=> ( scratc1814191352_is_of(X2,X)
=> pp(aa_TPTP_ind_bool(Xa,X2)) ) ) )
<=> ! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,axiom,
! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
<=> ! [X2: $i] :
( gg_TPTP_ind(X2)
=> ( scratc1814191352_is_of(X2,X)
=> pp(aa_TPTP_ind_bool(Xa,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__all__of) ).
tff(63,plain,
! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [X: $i,Xa: $i] :
( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
<=> ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
! [X: $i,Xa: $i] :
( ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
& ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) ),
inference(modus_ponens,[status(thm)],[65,58]) ).
tff(67,plain,
! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) ),
inference(modus_ponens,[status(thm)],[66,56]) ).
tff(68,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ) ) ) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ) ) ) ),
inference(transitivity,[status(thm)],[70,68]) ).
tff(72,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ) ) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ) ),
inference(unit_resolution,[status(thm)],[73,67]) ).
tff(75,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) )
| pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(76,plain,
( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(unit_resolution,[status(thm)],[75,74]) ).
tff(77,plain,
( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
<=> ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa)) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,axiom,
~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(79,plain,
~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa)),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
( ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) )
| pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(81,plain,
( ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_aa))
| ~ ( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) )
| ~ ( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(unit_resolution,[status(thm)],[80,79]) ).
tff(82,plain,
~ ( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(unit_resolution,[status(thm)],[81,76]) ).
tff(83,plain,
( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)) ),
inference(tautology,[status(thm)],[]) ).
tff(84,plain,
gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),
inference(unit_resolution,[status(thm)],[83,82]) ).
tff(85,plain,
( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ),
inference(tautology,[status(thm)],[]) ).
tff(86,plain,
scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a),
inference(unit_resolution,[status(thm)],[85,82]) ).
tff(87,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ~ ( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a))) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ~ ( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a))) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,plain,
( ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a),aTP_Lamm_a) ) ) )
<=> ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ~ ( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ~ ( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a))) ) ) ) ) ),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a),aTP_Lamm_a) ) ) ) )
<=> ( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ~ ( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a))) ) ) ) ) ),
inference(transitivity,[status(thm)],[89,87]) ).
tff(91,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a),aTP_Lamm_a) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
( ~ ! [X: $i,Xa: $i] :
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(Xa,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,X) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa))
| ~ ( pp(aa_TPTP_ind_bool(Xa,tptp_fun_X2_13(Xa,X)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(Xa,X))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(Xa,X),X) ) ) )
| ~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ~ ( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a))) ) ) ) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
~ ( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ~ ( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a))) ) ) ),
inference(unit_resolution,[status(thm)],[92,67]) ).
tff(94,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) )
| ~ ( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ~ ( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_bx,aTP_Lamm_a))) ) )
| ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],[]) ).
tff(95,plain,
( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[94,93]) ).
tff(96,plain,
( pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
<=> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx)) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,axiom,
pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_satz28a) ).
tff(98,plain,
pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx)),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) )
| ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) ),
inference(tautology,[status(thm)],[]) ).
tff(100,plain,
( ~ ( ~ pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aTP_Lamm_bx))
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) )
| ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ) ),
inference(unit_resolution,[status(thm)],[99,98]) ).
tff(101,plain,
! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) ),
inference(unit_resolution,[status(thm)],[100,95]) ).
tff(102,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) )
| ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) )
| ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(103,plain,
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) )
| ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
( ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) )
<=> ( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) )
| ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(transitivity,[status(thm)],[104,102]) ).
tff(106,plain,
( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(107,plain,
( ~ ! [X2: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,X2))
| ~ gg_TPTP_ind(X2)
| ~ scratc1814191352_is_of(X2,aTP_Lamm_a) )
| ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[107,101,86,84]) ).
tff(109,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) )
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(tautology,[status(thm)],[]) ).
tff(110,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_bx,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(unit_resolution,[status(thm)],[109,108]) ).
tff(111,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[110,51]) ).
tff(112,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),
inference(modus_ponens,[status(thm)],[111,42]) ).
tff(113,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(114,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)],[113]) ).
tff(115,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(116,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)],[115]) ).
tff(117,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(118,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(119,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)],[118]) ).
tff(120,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/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_001t__TPTP____Interpret__Oind_T) ).
tff(121,plain,
! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,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)],[121,117]) ).
tff(123,plain,
! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ ( gg_TPTP_ind(X7)
& gg_TPTP_ind(Y) ) ),
inference(skolemize,[status(sab)],[122]) ).
tff(124,plain,
! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) ),
inference(modus_ponens,[status(thm)],[123,116]) ).
tff(125,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)],[124,114]) ).
tff(126,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(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ( aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1) = tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)) )
<=> ( ~ ! [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(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ( aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1) = tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(127,plain,
( ( ( aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1) = tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)) )
<=> ( ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ( aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1) = tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,plain,
( ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ( aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1) = tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)) )
<=> ( ~ ! [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(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ( aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1) = tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)) ) ),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
( ( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ( aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1) = tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)) )
<=> ( ~ ! [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(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ( aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1) = tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)) ) ),
inference(transitivity,[status(thm)],[128,126]) ).
tff(130,plain,
( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ( aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1) = tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,plain,
( ~ ! [X7: $i,Y: $i] :
( ( X7 = Y )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y))
| ~ gg_TPTP_ind(Y)
| ~ gg_TPTP_ind(X7) )
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| ( aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1) = tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
( ( aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1) = tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1)) ),
inference(unit_resolution,[status(thm)],[131,125,84]) ).
tff(133,plain,
aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1) = tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),
inference(unit_resolution,[status(thm)],[132,112,18]) ).
tff(134,plain,
tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a) = aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1),
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
( scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> scratc1814191352_is_of(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1),aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(monotonicity,[status(thm)],[134]) ).
tff(136,plain,
( scratc1814191352_is_of(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1),aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(symmetry,[status(thm)],[135]) ).
tff(137,plain,
( ~ scratc1814191352_is_of(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1),aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
^ [X: $i,Xa: $i] :
refl(( ( scratc1814191352_is_of(X,Xa)
<=> pp(aa_TPTP_ind_bool(Xa,X)) )
<=> ( scratc1814191352_is_of(X,Xa)
<=> pp(aa_TPTP_ind_bool(Xa,X)) ) )),
inference(bind,[status(th)],[]) ).
tff(139,plain,
( ! [X: $i,Xa: $i] :
( scratc1814191352_is_of(X,Xa)
<=> pp(aa_TPTP_ind_bool(Xa,X)) )
<=> ! [X: $i,Xa: $i] :
( scratc1814191352_is_of(X,Xa)
<=> pp(aa_TPTP_ind_bool(Xa,X)) ) ),
inference(quant_intro,[status(thm)],[138]) ).
tff(140,plain,
( ! [X: $i,Xa: $i] :
( scratc1814191352_is_of(X,Xa)
<=> pp(aa_TPTP_ind_bool(Xa,X)) )
<=> ! [X: $i,Xa: $i] :
( scratc1814191352_is_of(X,Xa)
<=> pp(aa_TPTP_ind_bool(Xa,X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,axiom,
! [X: $i,Xa: $i] :
( scratc1814191352_is_of(X,Xa)
<=> pp(aa_TPTP_ind_bool(Xa,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__is__of) ).
tff(142,plain,
! [X: $i,Xa: $i] :
( scratc1814191352_is_of(X,Xa)
<=> pp(aa_TPTP_ind_bool(Xa,X)) ),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
! [X: $i,Xa: $i] :
( scratc1814191352_is_of(X,Xa)
<=> pp(aa_TPTP_ind_bool(Xa,X)) ),
inference(skolemize,[status(sab)],[142]) ).
tff(144,plain,
! [X: $i,Xa: $i] :
( scratc1814191352_is_of(X,Xa)
<=> pp(aa_TPTP_ind_bool(Xa,X)) ),
inference(modus_ponens,[status(thm)],[143,139]) ).
tff(145,plain,
( ~ ! [X: $i,Xa: $i] :
( scratc1814191352_is_of(X,Xa)
<=> pp(aa_TPTP_ind_bool(Xa,X)) )
| ( scratc1814191352_is_of(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1),aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(146,plain,
( scratc1814191352_is_of(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1),aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1))) ),
inference(unit_resolution,[status(thm)],[145,144]) ).
tff(147,plain,
^ [Uu: $i] :
refl(( ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1))) )
<=> ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1))) ) )),
inference(bind,[status(th)],[]) ).
tff(148,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1))) ) ),
inference(quant_intro,[status(thm)],[147]) ).
tff(149,plain,
( ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1))) )
<=> ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(150,axiom,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__17) ).
tff(151,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1))) ),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1))) ),
inference(skolemize,[status(sab)],[151]) ).
tff(153,plain,
! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1))) ),
inference(modus_ponens,[status(thm)],[152,148]) ).
tff(154,plain,
( ~ ! [Uu: $i] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1))) )
| ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(155,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1))) ),
inference(unit_resolution,[status(thm)],[154,153]) ).
tff(156,plain,
( ~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aTP_Lamm_a)
| ~ gg_TPTP_ind(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(tautology,[status(thm)],[]) ).
tff(157,plain,
~ pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[156,82]) ).
tff(158,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1))) )
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1))) ),
inference(tautology,[status(thm)],[]) ).
tff(159,plain,
( ~ ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1))) )
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1))) ),
inference(unit_resolution,[status(thm)],[158,157]) ).
tff(160,plain,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1))),
inference(unit_resolution,[status(thm)],[159,155]) ).
tff(161,plain,
( ~ ( scratc1814191352_is_of(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1),aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1))) )
| ~ scratc1814191352_is_of(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1),aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1))) ),
inference(tautology,[status(thm)],[]) ).
tff(162,plain,
( ~ ( scratc1814191352_is_of(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1),aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1))) )
| ~ scratc1814191352_is_of(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1),aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(unit_resolution,[status(thm)],[161,160]) ).
tff(163,plain,
~ scratc1814191352_is_of(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),scratc1030418234nd_n_1),aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[162,146]) ).
tff(164,plain,
~ scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),
inference(modus_ponens,[status(thm)],[163,137]) ).
tff(165,plain,
( ~ ! [X: $i,Xa: $i] :
( scratc1814191352_is_of(X,Xa)
<=> pp(aa_TPTP_ind_bool(Xa,X)) )
| ( scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(166,plain,
( scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(unit_resolution,[status(thm)],[165,144]) ).
tff(167,plain,
aa_TPT43085870d_bool(fequal_TPTP_ind,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)) = aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),
inference(monotonicity,[status(thm)],[38]) ).
tff(168,plain,
aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)) = aa_TPT43085870d_bool(fequal_TPTP_ind,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),
inference(monotonicity,[status(thm)],[168]) ).
tff(170,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(symmetry,[status(thm)],[170]) ).
tff(172,plain,
^ [Y: $i] :
refl(( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,Y),Y))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,Y),Y)) )),
inference(bind,[status(th)],[]) ).
tff(173,plain,
( ! [Y: $i] : pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,Y),Y))
<=> ! [Y: $i] : pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,Y),Y)) ),
inference(quant_intro,[status(thm)],[172]) ).
tff(174,plain,
( ! [Y: $i] : pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,Y),Y))
<=> ! [Y: $i] : pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,Y),Y)) ),
inference(rewrite,[status(thm)],[]) ).
tff(175,plain,
( ! [X7: $i,Y: $i] : pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,Y),Y))
<=> ! [Y: $i] : pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,Y),Y)) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(176,plain,
( ! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) )
<=> ! [X7: $i,Y: $i] : pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,Y),Y)) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(177,plain,
( ! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) )
<=> ! [Y: $i] : pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,Y),Y)) ),
inference(transitivity,[status(thm)],[176,175]) ).
tff(178,axiom,
! [X7: $i,Y: $i] :
( ( X7 != Y )
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_001t__TPTP____Interpret__Oind_T) ).
tff(179,plain,
! [Y: $i] : pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,Y),Y)),
inference(modus_ponens,[status(thm)],[178,177]) ).
tff(180,plain,
! [Y: $i] : pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,Y),Y)),
inference(modus_ponens,[status(thm)],[179,174]) ).
tff(181,plain,
! [Y: $i] : pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,Y),Y)),
inference(skolemize,[status(sab)],[180]) ).
tff(182,plain,
! [Y: $i] : pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,Y),Y)),
inference(modus_ponens,[status(thm)],[181,173]) ).
tff(183,plain,
( ~ ! [Y: $i] : pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,Y),Y))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(184,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[183,182]) ).
tff(185,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),
inference(modus_ponens,[status(thm)],[184,171]) ).
tff(186,plain,
( ~ ( scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) )
| scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a)),tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))) ),
inference(tautology,[status(thm)],[]) ).
tff(187,plain,
scratc1814191352_is_of(tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a),aa_TPT43085870d_bool(scratc214101377d_n_is,tptp_fun_X2_13(aTP_Lamm_aa,aTP_Lamm_a))),
inference(unit_resolution,[status(thm)],[186,185,166]) ).
tff(188,plain,
$false,
inference(unit_resolution,[status(thm)],[187,164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM706+4 : TPTP v9.0.0. Released v7.3.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 01:49:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 40.59/40.80 % SZS status Theorem
% 40.59/40.80 % SZS output start Proof
% See solution above
% 40.81/41.02 % E exiting
%------------------------------------------------------------------------------