TSTP Solution File: ITP388_1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n019.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 : Thu Aug 31 03:33:39 EDT 2023
% Result : Theorem 15.85s 16.44s
% Output : Proof 15.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.21/0.22 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% 0.21/0.23 % Command : do_cvc5 %s %d
% 0.24/0.44 % Computer : n019.cluster.edu
% 0.24/0.44 % Model : x86_64 x86_64
% 0.24/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.44 % Memory : 8042.1875MB
% 0.24/0.44 % OS : Linux 3.10.0-693.el7.x86_64
% 0.24/0.44 % CPULimit : 300
% 0.24/0.44 % WCLimit : 300
% 0.24/0.44 % DateTime : Sun Aug 27 10:09:58 EDT 2023
% 0.24/0.44 % CPUTime :
% 0.30/0.67 %----Proving TF0_ARI
% 15.85/16.44 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.peiHDoWDWK/cvc5---1.0.5_31541.p...
% 15.85/16.44 ------- get file name : TPTP file name is ITP001_1
% 15.85/16.44 ------- cvc5-tfa : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_31541.smt2...
% 15.85/16.44 --- Run --finite-model-find --decision=internal at 15...
% 15.85/16.44 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 15.85/16.44 % SZS status Theorem for ITP001_1
% 15.85/16.44 % SZS output start Proof for ITP001_1
% 15.85/16.44 (
% 15.85/16.44 (let ((_let_1 (= 1 1))) (let ((_let_2 (|tptp.'uminus$c'| |tptp.'one$'|))) (let ((_let_3 (not (= |tptp.'zero$'| |tptp.'one$'|)))) (let ((_let_4 (<= 0 1))) (let ((_let_5 (|tptp.'fun_app$x'| |tptp.'less_eq$d'| |tptp.'zero$e'|))) (let ((_let_6 (|tptp.'fun_app$w'| _let_5 |tptp.'one$b'|))) (let ((_let_7 (|tptp.'fun_app$x'| |tptp.'less_eq$d'| |tptp.'one$b'|))) (let ((_let_8 (|tptp.'member$e'| 1 |tptp.'top$g'|))) (let ((_let_9 (= 0 0))) (let ((_let_10 (= (|tptp.'uminus$c'| |tptp.'zero$'|) |tptp.'zero$'|))) (let ((_let_11 (|tptp.'member$e'| 0 |tptp.'top$g'|))) (let ((_let_12 (|tptp.'member$c'| |tptp.'zero$'| |tptp.'top$e'|))) (let ((_let_13 (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|)) (= (= (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) |tptp.'top$a'|) |tptp.'top$b'|) (forall ((A__questionmark_v1 |tptp.'A_b_prod_ell2$'|)) (exists ((A__questionmark_v2 |tptp.'B_ell2$'|)) (= A__questionmark_v1 (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v2)))))))) (let ((_let_14 (|tptp.'tensor_ell2$'| |tptp.'psi$'|))) (let ((_let_15 (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2$'|)) (exists ((A__questionmark_v1 |tptp.'B_ell2$'|)) (= (|tptp.'fun_app$e'| (|tptp.'tensor_ell2$'| |tptp.'psi$'|) A__questionmark_v1) A__questionmark_v0))))) (let ((_let_16 (|tptp.'fun_app$n'| (|tptp.'image$'| _let_14) |tptp.'top$a'|))) (let ((_let_17 (not (= _let_16 |tptp.'top$b'|)))) (let ((_let_18 (= |tptp.'top$b'| _let_16))) (let ((_let_19 (forall ((A__questionmark_v1 |tptp.'A_b_prod_ell2$'|)) (not (forall ((A__questionmark_v2 |tptp.'B_ell2$'|)) (not (= A__questionmark_v1 (|tptp.'fun_app$e'| (|tptp.'tensor_ell2$'| |tptp.'psi$'|) A__questionmark_v2)))))))) (let ((_let_20 (= _let_18 _let_19))) (let ((_let_21 (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2$'|)) (not (forall ((A__questionmark_v1 |tptp.'B_ell2$'|)) (not (= A__questionmark_v0 (|tptp.'fun_app$e'| (|tptp.'tensor_ell2$'| |tptp.'psi$'|) A__questionmark_v1)))))))) (let ((_let_22 (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|)) (= (= |tptp.'top$b'| (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) |tptp.'top$a'|)) (forall ((A__questionmark_v1 |tptp.'A_b_prod_ell2$'|)) (not (forall ((A__questionmark_v2 |tptp.'B_ell2$'|)) (not (= A__questionmark_v1 (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v2)))))))))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_20)) :args ((or _let_18 (not _let_19) (not _let_20)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (_let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((|tptp.'image$'| A__questionmark_v0)))) :args (_let_22))) _let_23 :args (_let_20 false _let_22)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_21 (= A__questionmark_v1 A__questionmark_v2) (= A__questionmark_v0 A__questionmark_v1)))) (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))) :args (_let_19 false _let_21)) (SYMM (ASSUME :args (_let_17))) :args (false false _let_20 false _let_19 true _let_18)) :args ((forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|)) (= (|tptp.'fun_app$'| |tptp.'uuv$'| A__questionmark_v0) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) |tptp.'top$'|))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (|tptp.'fun_app$b'| (|tptp.'uun$'| A__questionmark_v0) A__questionmark_v1) (= (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'B_ell2$'|) (A__questionmark_v1 |tptp.'A_ell2$'|)) (= (|tptp.'fun_app$d'| (|tptp.'uuf$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$e'| (|tptp.'tensor_ell2$'| A__questionmark_v1) A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_ell2$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2$'|)) (= (|tptp.'fun_app$f'| (|tptp.'uue$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'tensor_ell2$a'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_ell2$'|) (A__questionmark_v1 |tptp.'B_ell2$'|)) (= (|tptp.'fun_app$g'| (|tptp.'uud$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'tensor_ell2$b'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (|tptp.'fun_app$h'| (|tptp.'uuo$'| A__questionmark_v0) A__questionmark_v1) (- A__questionmark_v0 A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2$'|)) (= (|tptp.'fun_app$i'| (|tptp.'uuq$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$i'| (|tptp.'minus$'| A__questionmark_v1) A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'B_ell2$'|) (A__questionmark_v1 |tptp.'B_ell2$'|)) (= (|tptp.'fun_app$j'| (|tptp.'uup$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$j'| (|tptp.'minus$a'| A__questionmark_v1) A__questionmark_v0))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (|tptp.'fun_app$h'| (|tptp.'uur$'| A__questionmark_v0) A__questionmark_v1) (- A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (|tptp.'fun_app$b'| (|tptp.'uug$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v1) A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'of_nat$'| A__questionmark_v1))) (let ((_let_3 (|tptp.'fun_app$c'| (|tptp.'uuw$'| A__questionmark_v0) A__questionmark_v1))) (let ((_let_4 (< _let_2 _let_1))) (and (=> _let_4 (= _let_3 (|tptp.'nat$'| 0))) (=> (not _let_4) (= _let_3 (|tptp.'nat$'| (- _let_2 _let_1)))))))))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (|tptp.'fun_app$b'| (|tptp.'uuu$'| A__questionmark_v0) A__questionmark_v1) (not (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v1) A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|) (A__questionmark_v1 |tptp.'Nat_bool_fun$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (|tptp.'fun_app$b'| (|tptp.'uut$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (and (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v2) A__questionmark_v0) (|tptp.'fun_app$b'| A__questionmark_v1 A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'member$'| A__questionmark_v2))) (= (|tptp.'fun_app$b'| (|tptp.'uus$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (and (|tptp.'fun_app$a'| _let_1 A__questionmark_v0) (not (|tptp.'fun_app$a'| _let_1 A__questionmark_v1)))))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v2 |tptp.'B_ell2$'|)) (= (|tptp.'fun_app$e'| (|tptp.'uu$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$i'| A__questionmark_v0 (|tptp.'fun_app$e'| A__questionmark_v1 A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2_b_ell2_fun$'|) (A__questionmark_v2 |tptp.'A_b_prod_ell2$'|)) (= (|tptp.'fun_app$i'| (|tptp.'uub$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$e'| A__questionmark_v0 (|tptp.'fun_app$k'| A__questionmark_v1 A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_b_ell2_fun$'|) (A__questionmark_v2 |tptp.'B_ell2$'|)) (= (|tptp.'fun_app$e'| (|tptp.'uua$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$e'| A__questionmark_v0 (|tptp.'fun_app$j'| A__questionmark_v1 A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'A_b_prod_ell2_bool_fun$'|) (A__questionmark_v3 |tptp.'A_b_prod_ell2$'|)) (= (|tptp.'fun_app$l'| (|tptp.'uuj$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (and (|tptp.'fun_app$m'| (|tptp.'member$a'| A__questionmark_v3) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$l'| A__questionmark_v2 A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_bool_fun$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (= (|tptp.'fun_app$b'| (|tptp.'uul$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (and (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v3) (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$b'| A__questionmark_v2 A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'A_b_prod_ell2_bool_fun$'|) (A__questionmark_v3 |tptp.'B_ell2$'|)) (= (|tptp.'fun_app$p'| (|tptp.'uuk$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (and (|tptp.'member$b'| A__questionmark_v3 A__questionmark_v1) (|tptp.'fun_app$l'| A__questionmark_v2 (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v3))))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_bool_fun$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (= (|tptp.'fun_app$b'| (|tptp.'uum$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (and (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v3) A__questionmark_v1) (|tptp.'fun_app$b'| A__questionmark_v2 (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v3))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (|tptp.'fun_app$c'| |tptp.'uuc$'| A__questionmark_v0) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2$'|)) (= (|tptp.'fun_app$l'| |tptp.'uui$'| A__questionmark_v0) true)) (forall ((A__questionmark_v0 |tptp.'B_ell2$'|)) (= (|tptp.'fun_app$p'| |tptp.'uuh$'| A__questionmark_v0) true)) _let_17 _let_15 (not (= |tptp.'psi$'| |tptp.'zero$'|)) (|tptp.'inj_on$a'| _let_14 |tptp.'top$a'|) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v2 |tptp.'B_ell2$'|) (A__questionmark_v3 |tptp.'B_ell2_set$'|)) (=> (and (= A__questionmark_v0 (|tptp.'fun_app$e'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'member$b'| A__questionmark_v2 A__questionmark_v3)) (|tptp.'fun_app$m'| (|tptp.'member$a'| A__questionmark_v0) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v1) A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat_nat_fun$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat_set$'|)) (=> (and (= A__questionmark_v0 (|tptp.'fun_app$c'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v2) A__questionmark_v3)) (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v0) (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v1) A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v0) |tptp.'top$'|)) (forall ((A__questionmark_v0 |tptp.'B_ell2$'|)) (|tptp.'member$b'| A__questionmark_v0 |tptp.'top$a'|)) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2$'|)) (|tptp.'fun_app$m'| (|tptp.'member$a'| A__questionmark_v0) |tptp.'top$b'|)) (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v0) |tptp.'top$'|) true)) (forall ((A__questionmark_v0 |tptp.'B_ell2$'|)) (= (|tptp.'member$b'| A__questionmark_v0 |tptp.'top$a'|) true)) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2$'|)) (= (|tptp.'fun_app$m'| (|tptp.'member$a'| A__questionmark_v0) |tptp.'top$b'|) true)) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|)) (=> (and (|tptp.'fun_app$m'| (|tptp.'member$a'| A__questionmark_v0) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v1) |tptp.'top$a'|)) (forall ((A__questionmark_v2 |tptp.'B_ell2$'|)) (=> (= A__questionmark_v0 (|tptp.'fun_app$e'| A__questionmark_v1 A__questionmark_v2)) false))) false)) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'B_ell2_nat_fun$'|)) (=> (and (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v0) (|tptp.'image$b'| A__questionmark_v1 |tptp.'top$a'|)) (forall ((A__questionmark_v2 |tptp.'B_ell2$'|)) (=> (= A__questionmark_v0 (|tptp.'fun_app$q'| A__questionmark_v1 A__questionmark_v2)) false))) false)) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2_nat_fun$'|)) (=> (and (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v0) (|tptp.'image$c'| A__questionmark_v1 |tptp.'top$b'|)) (forall ((A__questionmark_v2 |tptp.'A_b_prod_ell2$'|)) (=> (= A__questionmark_v0 (|tptp.'fun_app$r'| A__questionmark_v1 A__questionmark_v2)) false))) false)) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|)) (= (|tptp.'fun_app$n'| (|tptp.'image$'| (|tptp.'uu$'| A__questionmark_v0 A__questionmark_v1)) |tptp.'top$a'|) (|tptp.'image$d'| A__questionmark_v0 (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v1) |tptp.'top$a'|)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_b_ell2_fun$'|)) (= (|tptp.'fun_app$n'| (|tptp.'image$'| (|tptp.'uua$'| A__questionmark_v0 A__questionmark_v1)) |tptp.'top$a'|) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) (|tptp.'image$e'| A__questionmark_v1 |tptp.'top$a'|)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2_b_ell2_fun$'|)) (= (|tptp.'image$d'| (|tptp.'uub$'| A__questionmark_v0 A__questionmark_v1) |tptp.'top$b'|) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) (|tptp.'image$f'| A__questionmark_v1 |tptp.'top$b'|)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_b_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2$'|)) (=> (= (|tptp.'image$e'| A__questionmark_v0 |tptp.'top$a'|) |tptp.'top$a'|) (exists ((A__questionmark_v2 |tptp.'B_ell2$'|)) (= A__questionmark_v1 (|tptp.'fun_app$j'| A__questionmark_v0 A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2$'|)) (=> (= (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) |tptp.'top$a'|) |tptp.'top$b'|) (exists ((A__questionmark_v2 |tptp.'B_ell2$'|)) (= A__questionmark_v1 (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_b_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2$'|)) (=> (= (|tptp.'image$f'| A__questionmark_v0 |tptp.'top$b'|) |tptp.'top$a'|) (exists ((A__questionmark_v2 |tptp.'A_b_prod_ell2$'|)) (= A__questionmark_v1 (|tptp.'fun_app$k'| A__questionmark_v0 A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2$'|)) (=> (= (|tptp.'image$d'| A__questionmark_v0 |tptp.'top$b'|) |tptp.'top$b'|) (exists ((A__questionmark_v2 |tptp.'A_b_prod_ell2$'|)) (= A__questionmark_v1 (|tptp.'fun_app$i'| A__questionmark_v0 A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'B_ell2_b_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2$'|)) (=> (and (= (|tptp.'image$e'| A__questionmark_v0 |tptp.'top$a'|) |tptp.'top$a'|) (forall ((A__questionmark_v2 |tptp.'B_ell2$'|)) (=> (= A__questionmark_v1 (|tptp.'fun_app$j'| A__questionmark_v0 A__questionmark_v2)) false))) false)) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2$'|)) (=> (and (= (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) |tptp.'top$a'|) |tptp.'top$b'|) (forall ((A__questionmark_v2 |tptp.'B_ell2$'|)) (=> (= A__questionmark_v1 (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v2)) false))) false)) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_b_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2$'|)) (=> (and (= (|tptp.'image$f'| A__questionmark_v0 |tptp.'top$b'|) |tptp.'top$a'|) (forall ((A__questionmark_v2 |tptp.'A_b_prod_ell2$'|)) (=> (= A__questionmark_v1 (|tptp.'fun_app$k'| A__questionmark_v0 A__questionmark_v2)) false))) false)) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2$'|)) (=> (and (= (|tptp.'image$d'| A__questionmark_v0 |tptp.'top$b'|) |tptp.'top$b'|) (forall ((A__questionmark_v2 |tptp.'A_b_prod_ell2$'|)) (=> (= A__questionmark_v1 (|tptp.'fun_app$i'| A__questionmark_v0 A__questionmark_v2)) false))) false)) (forall ((A__questionmark_v0 |tptp.'B_ell2_b_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_b_ell2_fun$'|)) (=> (forall ((A__questionmark_v2 |tptp.'B_ell2$'|)) (= (|tptp.'fun_app$j'| A__questionmark_v0 (|tptp.'fun_app$j'| A__questionmark_v1 A__questionmark_v2)) A__questionmark_v2)) (= (|tptp.'image$e'| A__questionmark_v0 |tptp.'top$a'|) |tptp.'top$a'|))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2_b_ell2_fun$'|)) (=> (forall ((A__questionmark_v2 |tptp.'A_b_prod_ell2$'|)) (= (|tptp.'fun_app$e'| A__questionmark_v0 (|tptp.'fun_app$k'| A__questionmark_v1 A__questionmark_v2)) A__questionmark_v2)) (= (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) |tptp.'top$a'|) |tptp.'top$b'|))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_b_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|)) (=> (forall ((A__questionmark_v2 |tptp.'B_ell2$'|)) (= (|tptp.'fun_app$k'| A__questionmark_v0 (|tptp.'fun_app$e'| A__questionmark_v1 A__questionmark_v2)) A__questionmark_v2)) (= (|tptp.'image$f'| A__questionmark_v0 |tptp.'top$b'|) |tptp.'top$a'|))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|)) (=> (forall ((A__questionmark_v2 |tptp.'A_b_prod_ell2$'|)) (= (|tptp.'fun_app$i'| A__questionmark_v0 (|tptp.'fun_app$i'| A__questionmark_v1 A__questionmark_v2)) A__questionmark_v2)) (= (|tptp.'image$d'| A__questionmark_v0 |tptp.'top$b'|) |tptp.'top$b'|))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2$'|)) (|tptp.'fun_app$m'| (|tptp.'member$a'| (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) |tptp.'top$a'|))) (forall ((A__questionmark_v0 |tptp.'B_ell2_nat_fun$'|) (A__questionmark_v1 |tptp.'B_ell2$'|)) (|tptp.'fun_app$a'| (|tptp.'member$'| (|tptp.'fun_app$q'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'image$b'| A__questionmark_v0 |tptp.'top$a'|))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_nat_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2$'|)) (|tptp.'fun_app$a'| (|tptp.'member$'| (|tptp.'fun_app$r'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'image$c'| A__questionmark_v0 |tptp.'top$b'|))) (forall ((A__questionmark_v0 |tptp.'A_ell2$'|)) (= (|tptp.'fun_app$e'| (|tptp.'tensor_ell2$'| A__questionmark_v0) |tptp.'zero$a'|) |tptp.'zero$b'|)) (forall ((A__questionmark_v0 |tptp.'B_ell2$'|)) (= (|tptp.'fun_app$e'| (|tptp.'tensor_ell2$'| |tptp.'zero$'|) A__questionmark_v0) |tptp.'zero$b'|)) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'B_ell2$'|) (A__questionmark_v3 |tptp.'B_ell2$'|)) (=> (and (|tptp.'inj_on$a'| A__questionmark_v0 A__questionmark_v1) (= (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v2) (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v3)) (|tptp.'member$b'| A__questionmark_v2 A__questionmark_v1) (|tptp.'member$b'| A__questionmark_v3 A__questionmark_v1)) (= A__questionmark_v2 A__questionmark_v3))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) A__questionmark_v1) (= (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v2) (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v3)) (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v2) A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v3) A__questionmark_v1)) (= A__questionmark_v2 A__questionmark_v3))) (forall ((A__questionmark_v0 |tptp.'B_ell2_set$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|)) (=> (forall ((A__questionmark_v2 |tptp.'B_ell2$'|) (A__questionmark_v3 |tptp.'B_ell2$'|)) (=> (and (|tptp.'member$b'| A__questionmark_v2 A__questionmark_v0) (|tptp.'member$b'| A__questionmark_v3 A__questionmark_v0) (= (|tptp.'fun_app$e'| A__questionmark_v1 A__questionmark_v2) (|tptp.'fun_app$e'| A__questionmark_v1 A__questionmark_v3))) (= A__questionmark_v2 A__questionmark_v3))) (|tptp.'inj_on$a'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|) (A__questionmark_v1 |tptp.'Nat_nat_fun$'|)) (=> (forall ((A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v2) A__questionmark_v0) (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v3) A__questionmark_v0) (= (|tptp.'fun_app$c'| A__questionmark_v1 A__questionmark_v2) (|tptp.'fun_app$c'| A__questionmark_v1 A__questionmark_v3))) (= A__questionmark_v2 A__questionmark_v3))) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v1) A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|)) (= (|tptp.'inj_on$a'| A__questionmark_v0 A__questionmark_v1) (forall ((A__questionmark_v2 |tptp.'B_ell2$'|)) (=> (|tptp.'member$b'| A__questionmark_v2 A__questionmark_v1) (forall ((A__questionmark_v3 |tptp.'B_ell2$'|)) (=> (and (|tptp.'member$b'| A__questionmark_v3 A__questionmark_v1) (= (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v2) (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v3))) (= A__questionmark_v2 A__questionmark_v3))))))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|)) (= (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) A__questionmark_v1) (forall ((A__questionmark_v2 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v2) A__questionmark_v1) (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v3) A__questionmark_v1) (= (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v2) (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v3))) (= A__questionmark_v2 A__questionmark_v3))))))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|)) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| |tptp.'uuc$'|) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'B_ell2_set$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v2 |tptp.'B_ell2_a_b_prod_ell2_fun$'|)) (=> (forall ((A__questionmark_v3 |tptp.'B_ell2$'|)) (=> (|tptp.'member$b'| A__questionmark_v3 A__questionmark_v0) (= (|tptp.'fun_app$e'| A__questionmark_v1 A__questionmark_v3) (|tptp.'fun_app$e'| A__questionmark_v2 A__questionmark_v3)))) (= (|tptp.'inj_on$a'| A__questionmark_v1 A__questionmark_v0) (|tptp.'inj_on$a'| A__questionmark_v2 A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|) (A__questionmark_v1 |tptp.'Nat_nat_fun$'|) (A__questionmark_v2 |tptp.'Nat_nat_fun$'|)) (=> (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v3) A__questionmark_v0) (= (|tptp.'fun_app$c'| A__questionmark_v1 A__questionmark_v3) (|tptp.'fun_app$c'| A__questionmark_v2 A__questionmark_v3)))) (= (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v1) A__questionmark_v0) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v2) A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'B_ell2$'|) (A__questionmark_v3 |tptp.'B_ell2$'|)) (=> (and (|tptp.'inj_on$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'member$b'| A__questionmark_v2 A__questionmark_v1) (|tptp.'member$b'| A__questionmark_v3 A__questionmark_v1)) (= (= (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v2) (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v3)) (= A__questionmark_v2 A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v2) A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v3) A__questionmark_v1)) (= (= (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v2) (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v3)) (= A__questionmark_v2 A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'B_ell2$'|) (A__questionmark_v3 |tptp.'B_ell2$'|)) (=> (and (|tptp.'inj_on$a'| A__questionmark_v0 A__questionmark_v1) (not (= A__questionmark_v2 A__questionmark_v3)) (|tptp.'member$b'| A__questionmark_v2 A__questionmark_v1) (|tptp.'member$b'| A__questionmark_v3 A__questionmark_v1)) (not (= (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v2) (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v3))))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) A__questionmark_v1) (not (= A__questionmark_v2 A__questionmark_v3)) (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v2) A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v3) A__questionmark_v1)) (not (= (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v2) (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v3))))) (forall ((A__questionmark_v0 |tptp.'B_ell2_set$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2_b_ell2_fun$'|) (A__questionmark_v2 |tptp.'B_ell2_a_b_prod_ell2_fun$'|)) (=> (forall ((A__questionmark_v3 |tptp.'B_ell2$'|)) (=> (|tptp.'member$b'| A__questionmark_v3 A__questionmark_v0) (= (|tptp.'fun_app$k'| A__questionmark_v1 (|tptp.'fun_app$e'| A__questionmark_v2 A__questionmark_v3)) A__questionmark_v3))) (|tptp.'inj_on$a'| A__questionmark_v2 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|) (A__questionmark_v1 |tptp.'Nat_nat_fun$'|) (A__questionmark_v2 |tptp.'Nat_nat_fun$'|)) (=> (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v3) A__questionmark_v0) (= (|tptp.'fun_app$c'| A__questionmark_v1 (|tptp.'fun_app$c'| A__questionmark_v2 A__questionmark_v3)) A__questionmark_v3))) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v2) A__questionmark_v0))) (= |tptp.'top$a'| (|tptp.'collect$'| |tptp.'top$c'|)) (= |tptp.'top$b'| (|tptp.'collect$a'| |tptp.'top$d'|)) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|)) (= (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) |tptp.'top$'|) (forall ((A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (= (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v2)) (= A__questionmark_v1 A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|)) (= (|tptp.'inj_on$a'| A__questionmark_v0 |tptp.'top$a'|) (forall ((A__questionmark_v1 |tptp.'B_ell2$'|) (A__questionmark_v2 |tptp.'B_ell2$'|)) (=> (= (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v2)) (= A__questionmark_v1 A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) |tptp.'top$'|) (= (= (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v2)) (= A__questionmark_v1 A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2$'|) (A__questionmark_v2 |tptp.'B_ell2$'|)) (=> (|tptp.'inj_on$a'| A__questionmark_v0 |tptp.'top$a'|) (= (= (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v2)) (= A__questionmark_v1 A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|)) (=> (forall ((A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (= (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v2)) (= A__questionmark_v1 A__questionmark_v2))) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) |tptp.'top$'|))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|)) (=> (forall ((A__questionmark_v1 |tptp.'B_ell2$'|) (A__questionmark_v2 |tptp.'B_ell2$'|)) (=> (= (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v2)) (= A__questionmark_v1 A__questionmark_v2))) (|tptp.'inj_on$a'| A__questionmark_v0 |tptp.'top$a'|))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) |tptp.'top$'|) (= (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v2))) (= A__questionmark_v1 A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2$'|) (A__questionmark_v2 |tptp.'B_ell2$'|)) (=> (and (|tptp.'inj_on$a'| A__questionmark_v0 |tptp.'top$a'|) (= (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v2))) (= A__questionmark_v1 A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'B_ell2_set$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v2 |tptp.'B_ell2_b_ell2_fun$'|)) (=> (and (forall ((A__questionmark_v3 |tptp.'B_ell2$'|)) (=> (|tptp.'member$b'| A__questionmark_v3 A__questionmark_v0) (forall ((A__questionmark_v4 |tptp.'B_ell2$'|)) (=> (|tptp.'member$b'| A__questionmark_v4 A__questionmark_v0) (= (= (|tptp.'fun_app$e'| A__questionmark_v1 (|tptp.'fun_app$j'| A__questionmark_v2 A__questionmark_v3)) (|tptp.'fun_app$e'| A__questionmark_v1 (|tptp.'fun_app$j'| A__questionmark_v2 A__questionmark_v4))) (= (|tptp.'fun_app$e'| A__questionmark_v1 A__questionmark_v3) (|tptp.'fun_app$e'| A__questionmark_v1 A__questionmark_v4))))))) (|tptp.'inj_on$b'| A__questionmark_v2 A__questionmark_v0)) (= (|tptp.'inj_on$a'| A__questionmark_v1 (|tptp.'image$e'| A__questionmark_v2 A__questionmark_v0)) (|tptp.'inj_on$a'| A__questionmark_v1 A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|) (A__questionmark_v1 |tptp.'Nat_nat_fun$'|) (A__questionmark_v2 |tptp.'Nat_nat_fun$'|)) (let ((_let_1 (|tptp.'inj_on$'| A__questionmark_v1))) (=> (and (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v3) A__questionmark_v0) (forall ((A__questionmark_v4 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v4) A__questionmark_v0) (= (= (|tptp.'fun_app$c'| A__questionmark_v1 (|tptp.'fun_app$c'| A__questionmark_v2 A__questionmark_v3)) (|tptp.'fun_app$c'| A__questionmark_v1 (|tptp.'fun_app$c'| A__questionmark_v2 A__questionmark_v4))) (= (|tptp.'fun_app$c'| A__questionmark_v1 A__questionmark_v3) (|tptp.'fun_app$c'| A__questionmark_v1 A__questionmark_v4))))))) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v2) A__questionmark_v0)) (= (|tptp.'fun_app$a'| _let_1 (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v2) A__questionmark_v0)) (|tptp.'fun_app$a'| _let_1 A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'A_ell2$'|) (A__questionmark_v1 |tptp.'A_ell2$'|)) (=> (and (not (= A__questionmark_v0 |tptp.'zero$'|)) (not (= A__questionmark_v1 |tptp.'zero$'|))) (not (= (|tptp.'tensor_ell2$c'| A__questionmark_v0 A__questionmark_v1) |tptp.'zero$c'|)))) (forall ((A__questionmark_v0 |tptp.'A_ell2$'|) (A__questionmark_v1 |tptp.'B_ell2$'|)) (=> (and (not (= A__questionmark_v0 |tptp.'zero$'|)) (not (= A__questionmark_v1 |tptp.'zero$a'|))) (not (= (|tptp.'fun_app$e'| (|tptp.'tensor_ell2$'| A__questionmark_v0) A__questionmark_v1) |tptp.'zero$b'|)))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat_set$'|)) (=> (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) |tptp.'top$'|) (= (|tptp.'fun_app$a'| (|tptp.'member$'| (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v1) A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2$'|) (A__questionmark_v2 |tptp.'B_ell2_set$'|)) (=> (|tptp.'inj_on$a'| A__questionmark_v0 |tptp.'top$a'|) (= (|tptp.'fun_app$m'| (|tptp.'member$a'| (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'member$b'| A__questionmark_v1 A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_nat_fun$'|) (A__questionmark_v1 |tptp.'B_ell2$'|) (A__questionmark_v2 |tptp.'B_ell2_set$'|)) (=> (|tptp.'inj_on$c'| A__questionmark_v0 |tptp.'top$a'|) (= (|tptp.'fun_app$a'| (|tptp.'member$'| (|tptp.'fun_app$q'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'image$b'| A__questionmark_v0 A__questionmark_v2)) (|tptp.'member$b'| A__questionmark_v1 A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_nat_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2$'|) (A__questionmark_v2 |tptp.'A_b_prod_ell2_set$'|)) (=> (|tptp.'fun_app$m'| (|tptp.'inj_on$d'| A__questionmark_v0) |tptp.'top$b'|) (= (|tptp.'fun_app$a'| (|tptp.'member$'| (|tptp.'fun_app$r'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'image$c'| A__questionmark_v0 A__questionmark_v2)) (|tptp.'fun_app$m'| (|tptp.'member$a'| A__questionmark_v1) A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_set$'|)) (let ((_let_1 (|tptp.'image$a'| A__questionmark_v0))) (=> (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) |tptp.'top$'|) (= (= (|tptp.'fun_app$o'| _let_1 A__questionmark_v1) (|tptp.'fun_app$o'| _let_1 A__questionmark_v2)) (= A__questionmark_v1 A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'B_ell2_set$'|)) (let ((_let_1 (|tptp.'image$'| A__questionmark_v0))) (=> (|tptp.'inj_on$a'| A__questionmark_v0 |tptp.'top$a'|) (= (= (|tptp.'fun_app$n'| _let_1 A__questionmark_v1) (|tptp.'fun_app$n'| _let_1 A__questionmark_v2)) (= A__questionmark_v1 A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) |tptp.'top$'|) (= (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v1) (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v0) |tptp.'top$'|)) (exists ((A__questionmark_v2 |tptp.'Nat$'|)) (and (= A__questionmark_v1 (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v2)) (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (=> (= A__questionmark_v1 (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v3)) (= A__questionmark_v3 A__questionmark_v2)))))))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2$'|)) (=> (|tptp.'inj_on$a'| A__questionmark_v0 |tptp.'top$a'|) (= (|tptp.'fun_app$m'| (|tptp.'member$a'| A__questionmark_v1) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) |tptp.'top$a'|)) (exists ((A__questionmark_v2 |tptp.'B_ell2$'|)) (and (= A__questionmark_v1 (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v2)) (forall ((A__questionmark_v3 |tptp.'B_ell2$'|)) (=> (= A__questionmark_v1 (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v3)) (= A__questionmark_v3 A__questionmark_v2)))))))) (forall ((A__questionmark_v0 |tptp.'B_ell2_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (|tptp.'inj_on$c'| A__questionmark_v0 |tptp.'top$a'|) (= (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v1) (|tptp.'image$b'| A__questionmark_v0 |tptp.'top$a'|)) (exists ((A__questionmark_v2 |tptp.'B_ell2$'|)) (and (= A__questionmark_v1 (|tptp.'fun_app$q'| A__questionmark_v0 A__questionmark_v2)) (forall ((A__questionmark_v3 |tptp.'B_ell2$'|)) (=> (= A__questionmark_v1 (|tptp.'fun_app$q'| A__questionmark_v0 A__questionmark_v3)) (= A__questionmark_v3 A__questionmark_v2)))))))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$m'| (|tptp.'inj_on$d'| A__questionmark_v0) |tptp.'top$b'|) (= (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v1) (|tptp.'image$c'| A__questionmark_v0 |tptp.'top$b'|)) (exists ((A__questionmark_v2 |tptp.'A_b_prod_ell2$'|)) (and (= A__questionmark_v1 (|tptp.'fun_app$r'| A__questionmark_v0 A__questionmark_v2)) (forall ((A__questionmark_v3 |tptp.'A_b_prod_ell2$'|)) (=> (= A__questionmark_v1 (|tptp.'fun_app$r'| A__questionmark_v0 A__questionmark_v3)) (= A__questionmark_v3 A__questionmark_v2)))))))) (forall ((A__questionmark_v0 |tptp.'A_ell2$'|)) (=> (not (= A__questionmark_v0 |tptp.'zero$'|)) (|tptp.'fun_app$m'| (|tptp.'inj_on$e'| (|tptp.'tensor_ell2$d'| A__questionmark_v0)) |tptp.'top$b'|))) (forall ((A__questionmark_v0 |tptp.'A_ell2$'|)) (=> (not (= A__questionmark_v0 |tptp.'zero$'|)) (|tptp.'inj_on$a'| (|tptp.'tensor_ell2$'| A__questionmark_v0) |tptp.'top$a'|))) (forall ((A__questionmark_v0 |tptp.'A_ell2$'|)) (=> (not (= A__questionmark_v0 |tptp.'zero$'|)) (|tptp.'inj_on$f'| (|tptp.'uud$'| A__questionmark_v0) |tptp.'top$a'|))) (forall ((A__questionmark_v0 |tptp.'A_ell2$'|)) (=> (not (= A__questionmark_v0 |tptp.'zero$'|)) (|tptp.'fun_app$m'| (|tptp.'inj_on$g'| (|tptp.'uue$'| A__questionmark_v0)) |tptp.'top$b'|))) (forall ((A__questionmark_v0 |tptp.'B_ell2$'|)) (=> (not (= A__questionmark_v0 |tptp.'zero$a'|)) (|tptp.'inj_on$h'| (|tptp.'uuf$'| A__questionmark_v0) |tptp.'top$e'|))) (exists ((A__questionmark_v0 |tptp.'Nat$'|)) (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v0) |tptp.'top$'|)) (exists ((A__questionmark_v0 |tptp.'B_ell2$'|)) (|tptp.'member$b'| A__questionmark_v0 |tptp.'top$a'|)) (exists ((A__questionmark_v0 |tptp.'A_b_prod_ell2$'|)) (|tptp.'fun_app$m'| (|tptp.'member$a'| A__questionmark_v0) |tptp.'top$b'|)) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|)) (=> (forall ((A__questionmark_v1 |tptp.'Nat$'|)) (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v1) A__questionmark_v0)) (= |tptp.'top$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'B_ell2_set$'|)) (=> (forall ((A__questionmark_v1 |tptp.'B_ell2$'|)) (|tptp.'member$b'| A__questionmark_v1 A__questionmark_v0)) (= |tptp.'top$a'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_set$'|)) (=> (forall ((A__questionmark_v1 |tptp.'A_b_prod_ell2$'|)) (|tptp.'fun_app$m'| (|tptp.'member$a'| A__questionmark_v1) A__questionmark_v0)) (= |tptp.'top$b'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'B_ell2$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'A_b_prod_ell2$'|) (A__questionmark_v3 |tptp.'B_ell2_a_b_prod_ell2_fun$'|)) (=> (and (|tptp.'member$b'| A__questionmark_v0 A__questionmark_v1) (= A__questionmark_v2 (|tptp.'fun_app$e'| A__questionmark_v3 A__questionmark_v0))) (|tptp.'fun_app$m'| (|tptp.'member$a'| A__questionmark_v2) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v3) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat_nat_fun$'|)) (=> (and (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v0) A__questionmark_v1) (= A__questionmark_v2 (|tptp.'fun_app$c'| A__questionmark_v3 A__questionmark_v0))) (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v2) (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v3) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'A_b_prod_ell2_bool_fun$'|)) (=> (forall ((A__questionmark_v3 |tptp.'A_b_prod_ell2$'|)) (=> (|tptp.'fun_app$m'| (|tptp.'member$a'| A__questionmark_v3) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$l'| A__questionmark_v2 A__questionmark_v3))) (forall ((A__questionmark_v3 |tptp.'B_ell2$'|)) (=> (|tptp.'member$b'| A__questionmark_v3 A__questionmark_v1) (|tptp.'fun_app$l'| A__questionmark_v2 (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v3)))))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_bool_fun$'|)) (=> (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v3) (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$b'| A__questionmark_v2 A__questionmark_v3))) (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v3) A__questionmark_v1) (|tptp.'fun_app$b'| A__questionmark_v2 (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v3)))))) (forall ((A__questionmark_v0 |tptp.'B_ell2_set$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v3 |tptp.'B_ell2_a_b_prod_ell2_fun$'|)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (forall ((A__questionmark_v4 |tptp.'B_ell2$'|)) (=> (|tptp.'member$b'| A__questionmark_v4 A__questionmark_v1) (= (|tptp.'fun_app$e'| A__questionmark_v2 A__questionmark_v4) (|tptp.'fun_app$e'| A__questionmark_v3 A__questionmark_v4))))) (= (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v2) A__questionmark_v0) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v3) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'A_b_prod_ell2_bool_fun$'|)) (=> (exists ((A__questionmark_v3 |tptp.'A_b_prod_ell2$'|)) (and (|tptp.'fun_app$m'| (|tptp.'member$a'| A__questionmark_v3) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$l'| A__questionmark_v2 A__questionmark_v3))) (exists ((A__questionmark_v3 |tptp.'B_ell2$'|)) (and (|tptp.'member$b'| A__questionmark_v3 A__questionmark_v1) (|tptp.'fun_app$l'| A__questionmark_v2 (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v3)))))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_bool_fun$'|)) (=> (exists ((A__questionmark_v3 |tptp.'Nat$'|)) (and (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v3) (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$b'| A__questionmark_v2 A__questionmark_v3))) (exists ((A__questionmark_v3 |tptp.'Nat$'|)) (and (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v3) A__questionmark_v1) (|tptp.'fun_app$b'| A__questionmark_v2 (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v3)))))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v2 |tptp.'B_ell2_set$'|)) (= (|tptp.'fun_app$m'| (|tptp.'member$a'| A__questionmark_v0) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v1) A__questionmark_v2)) (exists ((A__questionmark_v3 |tptp.'B_ell2$'|)) (and (|tptp.'member$b'| A__questionmark_v3 A__questionmark_v2) (= A__questionmark_v0 (|tptp.'fun_app$e'| A__questionmark_v1 A__questionmark_v3)))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat_nat_fun$'|) (A__questionmark_v2 |tptp.'Nat_set$'|)) (= (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v0) (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v1) A__questionmark_v2)) (exists ((A__questionmark_v3 |tptp.'Nat$'|)) (and (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v3) A__questionmark_v2) (= A__questionmark_v0 (|tptp.'fun_app$c'| A__questionmark_v1 A__questionmark_v3)))))) (forall ((A__questionmark_v0 |tptp.'B_ell2$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'B_ell2_a_b_prod_ell2_fun$'|)) (=> (|tptp.'member$b'| A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$m'| (|tptp.'member$a'| (|tptp.'fun_app$e'| A__questionmark_v2 A__questionmark_v0)) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v2) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_nat_fun$'|)) (=> (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'member$'| (|tptp.'fun_app$c'| A__questionmark_v2 A__questionmark_v0)) (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v2) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat_bool_fun$'|)) (= (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v0) (|tptp.'collect$b'| A__questionmark_v1)) (|tptp.'fun_app$b'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|)) (= (|tptp.'collect$b'| (|tptp.'uug$'| A__questionmark_v0)) A__questionmark_v0)) (= |tptp.'top$a'| (|tptp.'collect$'| |tptp.'uuh$'|)) (= |tptp.'top$b'| (|tptp.'collect$a'| |tptp.'uui$'|)) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'A_b_prod_ell2_bool_fun$'|)) (= (|tptp.'collect$a'| (|tptp.'uuj$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) (|tptp.'collect$'| (|tptp.'uuk$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_bool_fun$'|)) (= (|tptp.'collect$b'| (|tptp.'uul$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v0) (|tptp.'collect$b'| (|tptp.'uum$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v2 |tptp.'B_ell2_set$'|)) (= (|tptp.'image$d'| A__questionmark_v0 (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$n'| (|tptp.'image$'| (|tptp.'uu$'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_b_ell2_fun$'|) (A__questionmark_v2 |tptp.'B_ell2_set$'|)) (= (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) (|tptp.'image$e'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$n'| (|tptp.'image$'| (|tptp.'uua$'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v2 |tptp.'B_ell2_set$'|)) (=> (and (|tptp.'fun_app$m'| (|tptp.'member$a'| A__questionmark_v0) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v1) A__questionmark_v2)) (forall ((A__questionmark_v3 |tptp.'B_ell2$'|)) (=> (and (= A__questionmark_v0 (|tptp.'fun_app$e'| A__questionmark_v1 A__questionmark_v3)) (|tptp.'member$b'| A__questionmark_v3 A__questionmark_v2)) false))) false)) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat_nat_fun$'|) (A__questionmark_v2 |tptp.'Nat_set$'|)) (=> (and (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v0) (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v1) A__questionmark_v2)) (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (= A__questionmark_v0 (|tptp.'fun_app$c'| A__questionmark_v1 A__questionmark_v3)) (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v3) A__questionmark_v2)) false))) false)) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v2 |tptp.'B_ell2$'|)) (=> (= A__questionmark_v0 (|tptp.'fun_app$e'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$m'| (|tptp.'member$a'| A__questionmark_v0) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v1) |tptp.'top$a'|)))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'B_ell2_nat_fun$'|) (A__questionmark_v2 |tptp.'B_ell2$'|)) (=> (= A__questionmark_v0 (|tptp.'fun_app$q'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v0) (|tptp.'image$b'| A__questionmark_v1 |tptp.'top$a'|)))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2_nat_fun$'|) (A__questionmark_v2 |tptp.'A_b_prod_ell2$'|)) (=> (= A__questionmark_v0 (|tptp.'fun_app$r'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v0) (|tptp.'image$c'| A__questionmark_v1 |tptp.'top$b'|)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_b_ell2_fun$'|)) (= (= (|tptp.'image$e'| A__questionmark_v0 |tptp.'top$a'|) |tptp.'top$a'|) (forall ((A__questionmark_v1 |tptp.'B_ell2$'|)) (exists ((A__questionmark_v2 |tptp.'B_ell2$'|)) (= A__questionmark_v1 (|tptp.'fun_app$j'| A__questionmark_v0 A__questionmark_v2)))))) _let_13 (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_b_ell2_fun$'|)) (= (= (|tptp.'image$f'| A__questionmark_v0 |tptp.'top$b'|) |tptp.'top$a'|) (forall ((A__questionmark_v1 |tptp.'B_ell2$'|)) (exists ((A__questionmark_v2 |tptp.'A_b_prod_ell2$'|)) (= A__questionmark_v1 (|tptp.'fun_app$k'| A__questionmark_v0 A__questionmark_v2)))))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|)) (= (= (|tptp.'image$d'| A__questionmark_v0 |tptp.'top$b'|) |tptp.'top$b'|) (forall ((A__questionmark_v1 |tptp.'A_b_prod_ell2$'|)) (exists ((A__questionmark_v2 |tptp.'A_b_prod_ell2$'|)) (= A__questionmark_v1 (|tptp.'fun_app$i'| A__questionmark_v0 A__questionmark_v2)))))) (|tptp.'fun_app$a'| (|tptp.'member$'| |tptp.'zero$d'|) |tptp.'top$'|) _let_12 (|tptp.'member$d'| |tptp.'zero$e'| |tptp.'top$f'|) _let_11 (|tptp.'fun_app$a'| (|tptp.'inj_on$'| |tptp.'uuc$'|) |tptp.'top$'|) _let_12 _let_11 _let_12 _let_11 (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|)) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) (|tptp.'collect$b'| (|tptp.'uun$'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_b_ell2_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2_set$'|)) (=> (|tptp.'fun_app$m'| (|tptp.'inj_on$i'| A__questionmark_v0) A__questionmark_v1) (= (|tptp.'fun_app$n'| (|tptp.'image$'| (|tptp.'the_inv_into$'| A__questionmark_v1 A__questionmark_v0)) (|tptp.'image$f'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|)) (=> (|tptp.'inj_on$a'| A__questionmark_v0 A__questionmark_v1) (= (|tptp.'image$f'| (|tptp.'the_inv_into$a'| A__questionmark_v1 A__questionmark_v0) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|)) (=> (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) A__questionmark_v1) (= (|tptp.'fun_app$o'| (|tptp.'image$a'| (|tptp.'the_inv_into$b'| A__questionmark_v1 A__questionmark_v0)) (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'B_ell2_set$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v3 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v4 |tptp.'A_b_prod_ell2_set_a_b_prod_ell2_fun$'|)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (forall ((A__questionmark_v5 |tptp.'B_ell2$'|)) (=> (|tptp.'member$b'| A__questionmark_v5 A__questionmark_v1) (= (|tptp.'fun_app$e'| A__questionmark_v2 A__questionmark_v5) (|tptp.'fun_app$e'| A__questionmark_v3 A__questionmark_v5))))) (= (|tptp.'fun_app$s'| A__questionmark_v4 (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v2) A__questionmark_v0)) (|tptp.'fun_app$s'| A__questionmark_v4 (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v3) A__questionmark_v1))))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'B_ell2$'|) (A__questionmark_v3 |tptp.'A_b_prod_ell2$'|)) (=> (and (|tptp.'inj_on$a'| A__questionmark_v0 A__questionmark_v1) (= (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v2) A__questionmark_v3) (|tptp.'member$b'| A__questionmark_v2 A__questionmark_v1)) (= (|tptp.'fun_app$k'| (|tptp.'the_inv_into$a'| A__questionmark_v1 A__questionmark_v0) A__questionmark_v3) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) A__questionmark_v1) (= (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v2) A__questionmark_v1)) (= (|tptp.'fun_app$c'| (|tptp.'the_inv_into$b'| A__questionmark_v1 A__questionmark_v0) A__questionmark_v3) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'B_ell2$'|)) (=> (and (|tptp.'inj_on$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'member$b'| A__questionmark_v2 A__questionmark_v1)) (= (|tptp.'fun_app$k'| (|tptp.'the_inv_into$a'| A__questionmark_v1 A__questionmark_v0) (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v2)) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v2) A__questionmark_v1)) (= (|tptp.'fun_app$c'| (|tptp.'the_inv_into$b'| A__questionmark_v1 A__questionmark_v0) (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v2)) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) |tptp.'top$'|) (= (|tptp.'fun_app$c'| (|tptp.'the_inv_into$b'| |tptp.'top$'| A__questionmark_v0) (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2$'|)) (=> (|tptp.'inj_on$a'| A__questionmark_v0 |tptp.'top$a'|) (= (|tptp.'fun_app$k'| (|tptp.'the_inv_into$a'| |tptp.'top$a'| A__questionmark_v0) (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_b_ell2_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2_set$'|)) (=> (|tptp.'fun_app$m'| (|tptp.'inj_on$i'| A__questionmark_v0) A__questionmark_v1) (|tptp.'inj_on$a'| (|tptp.'the_inv_into$'| A__questionmark_v1 A__questionmark_v0) (|tptp.'image$f'| A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|)) (=> (|tptp.'inj_on$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$m'| (|tptp.'inj_on$i'| (|tptp.'the_inv_into$a'| A__questionmark_v1 A__questionmark_v0)) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|)) (=> (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| (|tptp.'the_inv_into$b'| A__questionmark_v1 A__questionmark_v0)) (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'A_b_prod_ell2$'|)) (=> (and (|tptp.'inj_on$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$m'| (|tptp.'member$a'| A__questionmark_v2) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) A__questionmark_v1))) (= (|tptp.'fun_app$e'| A__questionmark_v0 (|tptp.'fun_app$k'| (|tptp.'the_inv_into$a'| A__questionmark_v1 A__questionmark_v0) A__questionmark_v2)) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v2) (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v0) A__questionmark_v1))) (= (|tptp.'fun_app$c'| A__questionmark_v0 (|tptp.'fun_app$c'| (|tptp.'the_inv_into$b'| A__questionmark_v1 A__questionmark_v0) A__questionmark_v2)) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'A_ell2$'|)) (= (= |tptp.'zero$'| A__questionmark_v0) (= A__questionmark_v0 |tptp.'zero$'|))) (forall ((A__questionmark_v0 |tptp.'Enat$'|)) (= (= |tptp.'zero$e'| A__questionmark_v0) (= A__questionmark_v0 |tptp.'zero$e'|))) (forall ((A__questionmark_v0 Int)) (= (= 0 A__questionmark_v0) (= A__questionmark_v0 0))) (forall ((A__questionmark_v0 |tptp.'B_ell2_set$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v3 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v4 |tptp.'A_b_prod_ell2_set_a_b_prod_ell2_fun$'|)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (forall ((A__questionmark_v5 |tptp.'B_ell2$'|)) (=> (|tptp.'member$b'| A__questionmark_v5 A__questionmark_v1) (= (|tptp.'fun_app$e'| A__questionmark_v2 A__questionmark_v5) (|tptp.'fun_app$e'| A__questionmark_v3 A__questionmark_v5))))) (= (|tptp.'fun_app$s'| A__questionmark_v4 (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v2) A__questionmark_v0)) (|tptp.'fun_app$s'| A__questionmark_v4 (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v3) A__questionmark_v1))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (|tptp.'fun_app$b'| |tptp.'top$h'| A__questionmark_v0) (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v0) |tptp.'top$'|))) (forall ((A__questionmark_v0 |tptp.'B_ell2$'|)) (= (|tptp.'fun_app$p'| |tptp.'top$c'| A__questionmark_v0) (|tptp.'member$b'| A__questionmark_v0 |tptp.'top$a'|))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2$'|)) (= (|tptp.'fun_app$l'| |tptp.'top$d'| A__questionmark_v0) (|tptp.'fun_app$m'| (|tptp.'member$a'| A__questionmark_v0) |tptp.'top$b'|))) (forall ((A__questionmark_v0 |tptp.'B_ell2_set$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|)) (= (|tptp.'folding_insort_key_axioms$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'inj_on$a'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|) (A__questionmark_v1 |tptp.'Nat_nat_fun$'|)) (= (|tptp.'folding_insort_key_axioms$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v1) A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|)) (=> (|tptp.'inj_on$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'folding_insort_key_axioms$'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|)) (=> (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'folding_insort_key_axioms$a'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'A_b_prod_ell2$'|) (A__questionmark_v3 |tptp.'B_ell2_set$'|)) (=> (and (|tptp.'inj_on$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$m'| (|tptp.'member$a'| A__questionmark_v2) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'less_eq$'| A__questionmark_v1 A__questionmark_v3)) (|tptp.'member$b'| (|tptp.'fun_app$k'| (|tptp.'the_inv_into$a'| A__questionmark_v1 A__questionmark_v0) A__questionmark_v2) A__questionmark_v3))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat_set$'|)) (=> (and (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v2) (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| A__questionmark_v1) A__questionmark_v3)) (|tptp.'fun_app$a'| (|tptp.'member$'| (|tptp.'fun_app$c'| (|tptp.'the_inv_into$b'| A__questionmark_v1 A__questionmark_v0) A__questionmark_v2)) A__questionmark_v3))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_set$'|)) (let ((_let_1 (|tptp.'image$a'| A__questionmark_v0))) (=> (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) |tptp.'top$'|) (= (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| (|tptp.'fun_app$o'| _let_1 A__questionmark_v1)) (|tptp.'fun_app$o'| _let_1 A__questionmark_v2)) (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| A__questionmark_v1) A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'B_ell2_set$'|)) (let ((_let_1 (|tptp.'image$'| A__questionmark_v0))) (=> (|tptp.'inj_on$a'| A__questionmark_v0 |tptp.'top$a'|) (= (|tptp.'fun_app$m'| (|tptp.'less_eq$b'| (|tptp.'fun_app$n'| _let_1 A__questionmark_v1)) (|tptp.'fun_app$n'| _let_1 A__questionmark_v2)) (|tptp.'less_eq$'| A__questionmark_v1 A__questionmark_v2))))) (exists ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|)) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) |tptp.'top$'|)) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_nat_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v2 |tptp.'B_ell2_set$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v1) A__questionmark_v2))) (=> (and (|tptp.'fun_app$m'| (|tptp.'inj_on$d'| A__questionmark_v0) _let_1) (|tptp.'inj_on$a'| A__questionmark_v1 A__questionmark_v2) (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v3) (|tptp.'image$c'| A__questionmark_v0 _let_1))) (= (|tptp.'fun_app$t'| (|tptp.'the_inv_into$c'| A__questionmark_v2 (|tptp.'comp$'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v3) (|tptp.'fun_app$t'| (|tptp.'comp$a'| (|tptp.'the_inv_into$a'| A__questionmark_v2 A__questionmark_v1) (|tptp.'the_inv_into$d'| _let_1 A__questionmark_v0)) A__questionmark_v3))))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_nat_fun$'|) (A__questionmark_v2 |tptp.'Nat_set$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v1) A__questionmark_v2))) (=> (and (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) _let_1) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v3) (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v0) _let_1))) (= (|tptp.'fun_app$c'| (|tptp.'the_inv_into$b'| A__questionmark_v2 (|tptp.'comp$b'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v3) (|tptp.'fun_app$c'| (|tptp.'comp$b'| (|tptp.'the_inv_into$b'| A__questionmark_v2 A__questionmark_v1) (|tptp.'the_inv_into$b'| _let_1 A__questionmark_v0)) A__questionmark_v3))))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_set$'|)) (let ((_let_1 (|tptp.'image$a'| A__questionmark_v0))) (=> (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) |tptp.'top$'|) (= (|tptp.'fun_app$o'| _let_1 (|tptp.'minus$b'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'minus$b'| (|tptp.'fun_app$o'| _let_1 A__questionmark_v1) (|tptp.'fun_app$o'| _let_1 A__questionmark_v2)))))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'B_ell2_set$'|)) (let ((_let_1 (|tptp.'image$'| A__questionmark_v0))) (=> (|tptp.'inj_on$a'| A__questionmark_v0 |tptp.'top$a'|) (= (|tptp.'fun_app$n'| _let_1 (|tptp.'minus$c'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'minus$d'| (|tptp.'fun_app$n'| _let_1 A__questionmark_v1) (|tptp.'fun_app$n'| _let_1 A__questionmark_v2)))))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'Enat$'|)) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) A__questionmark_v0)) (forall ((A__questionmark_v0 Int)) (<= A__questionmark_v0 A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'Enat$'|)) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) A__questionmark_v0)) (forall ((A__questionmark_v0 Int)) (<= A__questionmark_v0 A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|) (A__questionmark_v1 |tptp.'Nat_set$'|)) (=> (forall ((A__questionmark_v2 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'member$'| A__questionmark_v2))) (=> (|tptp.'fun_app$a'| _let_1 A__questionmark_v0) (|tptp.'fun_app$a'| _let_1 A__questionmark_v1)))) (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| A__questionmark_v0) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_set$'|)) (let ((_let_1 (|tptp.'member$'| A__questionmark_v0))) (= (|tptp.'fun_app$a'| _let_1 (|tptp.'minus$b'| A__questionmark_v1 A__questionmark_v2)) (and (|tptp.'fun_app$a'| _let_1 A__questionmark_v1) (not (|tptp.'fun_app$a'| _let_1 A__questionmark_v2)))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_set$'|)) (let ((_let_1 (|tptp.'member$'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$a'| _let_1 A__questionmark_v1) (not (|tptp.'fun_app$a'| _let_1 A__questionmark_v2))) (|tptp.'fun_app$a'| _let_1 (|tptp.'minus$b'| A__questionmark_v1 A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'Enat$'|)) (= (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) |tptp.'zero$e'|) (= A__questionmark_v0 |tptp.'zero$e'|))) (forall ((A__questionmark_v0 |tptp.'A_ell2$'|)) (= (|tptp.'fun_app$y'| (|tptp.'minus$e'| A__questionmark_v0) A__questionmark_v0) |tptp.'zero$'|)) (forall ((A__questionmark_v0 Int)) (= (- A__questionmark_v0 A__questionmark_v0) 0)) (forall ((A__questionmark_v0 |tptp.'A_ell2$'|)) (= (|tptp.'fun_app$y'| (|tptp.'minus$e'| A__questionmark_v0) |tptp.'zero$'|) A__questionmark_v0)) (forall ((A__questionmark_v0 Int)) (= (- A__questionmark_v0 0) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'A_ell2$'|)) (= (|tptp.'fun_app$y'| (|tptp.'minus$e'| A__questionmark_v0) |tptp.'zero$'|) A__questionmark_v0)) (forall ((A__questionmark_v0 Int)) (= (- A__questionmark_v0 0) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'A_ell2$'|)) (= (|tptp.'fun_app$y'| (|tptp.'minus$e'| A__questionmark_v0) A__questionmark_v0) |tptp.'zero$'|)) (forall ((A__questionmark_v0 Int)) (= (- A__questionmark_v0 A__questionmark_v0) 0)) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (|tptp.'member$e'| A__questionmark_v0 |tptp.'top$g'|) (|tptp.'member$e'| A__questionmark_v1 |tptp.'top$g'|)) (|tptp.'member$e'| (- A__questionmark_v0 A__questionmark_v1) |tptp.'top$g'|))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (<= 0 (- A__questionmark_v0 A__questionmark_v1)) (<= A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_ell2$'|) (A__questionmark_v1 |tptp.'A_ell2$'|)) (=> (and (|tptp.'member$c'| A__questionmark_v0 |tptp.'top$e'|) (|tptp.'member$c'| A__questionmark_v1 |tptp.'top$e'|)) (= (= (|tptp.'fun_app$y'| (|tptp.'minus$e'| A__questionmark_v0) A__questionmark_v1) |tptp.'zero$'|) (= A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (|tptp.'member$e'| A__questionmark_v0 |tptp.'top$g'|) (|tptp.'member$e'| A__questionmark_v1 |tptp.'top$g'|)) (= (= (- A__questionmark_v0 A__questionmark_v1) 0) (= A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'B_ell2$'|)) (= (|tptp.'image$e'| (|tptp.'uup$'| A__questionmark_v0) |tptp.'top$a'|) |tptp.'top$a'|)) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2$'|)) (= (|tptp.'image$d'| (|tptp.'uuq$'| A__questionmark_v0) |tptp.'top$b'|) |tptp.'top$b'|)) (forall ((A__questionmark_v0 Int)) (= (|tptp.'image$g'| (|tptp.'uur$'| A__questionmark_v0) |tptp.'top$g'|) |tptp.'top$g'|)) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (<= A__questionmark_v0 A__questionmark_v1) (<= (- A__questionmark_v0 A__questionmark_v1) 0))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (- (- A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (- (- A__questionmark_v0 A__questionmark_v2) A__questionmark_v1))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (= (- A__questionmark_v0 A__questionmark_v1) (- A__questionmark_v2 A__questionmark_v3)) (= (<= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v2 A__questionmark_v3)))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (<= A__questionmark_v0 A__questionmark_v1) (<= (- A__questionmark_v0 A__questionmark_v2) (- A__questionmark_v1 A__questionmark_v2)))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (<= A__questionmark_v0 A__questionmark_v1) (<= (- A__questionmark_v2 A__questionmark_v1) (- A__questionmark_v2 A__questionmark_v0)))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v2 A__questionmark_v3)) (<= (- A__questionmark_v0 A__questionmark_v3) (- A__questionmark_v1 A__questionmark_v2)))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (= (- A__questionmark_v0 A__questionmark_v1) (- A__questionmark_v2 A__questionmark_v3)) (= (= A__questionmark_v0 A__questionmark_v1) (= A__questionmark_v2 A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'B_ell2_set$'|)) (let ((_let_1 (|tptp.'image$'| A__questionmark_v0))) (|tptp.'fun_app$m'| (|tptp.'less_eq$b'| (|tptp.'minus$d'| (|tptp.'fun_app$n'| _let_1 A__questionmark_v1) (|tptp.'fun_app$n'| _let_1 A__questionmark_v2))) (|tptp.'fun_app$n'| _let_1 (|tptp.'minus$c'| A__questionmark_v1 A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (=> (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v1) (= (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v1) A__questionmark_v0) (= A__questionmark_v1 A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat$'|)) (=> (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) A__questionmark_v1) (= (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v1) A__questionmark_v0) (= A__questionmark_v1 A__questionmark_v0)))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (<= A__questionmark_v0 A__questionmark_v1) (= (<= A__questionmark_v1 A__questionmark_v0) (= A__questionmark_v1 A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (=> (and (=> (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v1) false) (=> (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v1) A__questionmark_v0) false)) false)) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat$'|)) (=> (and (=> (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) A__questionmark_v1) false) (=> (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v1) A__questionmark_v0) false)) false)) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (=> (<= A__questionmark_v0 A__questionmark_v1) false) (=> (<= A__questionmark_v1 A__questionmark_v0) false)) false)) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|) (A__questionmark_v2 |tptp.'Num_num_fun$'|) (A__questionmark_v3 |tptp.'Num$'|)) (=> (and (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v1) (= (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v1) A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Num$'|) (A__questionmark_v5 |tptp.'Num$'|)) (=> (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v4) A__questionmark_v5) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v4)) (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v5))))) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v0)) A__questionmark_v3))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|) (A__questionmark_v2 |tptp.'Num_enat_fun$'|) (A__questionmark_v3 |tptp.'Enat$'|)) (=> (and (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v1) (= (|tptp.'fun_app$aa'| A__questionmark_v2 A__questionmark_v1) A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Num$'|) (A__questionmark_v5 |tptp.'Num$'|)) (=> (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v4) A__questionmark_v5) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| (|tptp.'fun_app$aa'| A__questionmark_v2 A__questionmark_v4)) (|tptp.'fun_app$aa'| A__questionmark_v2 A__questionmark_v5))))) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| (|tptp.'fun_app$aa'| A__questionmark_v2 A__questionmark_v0)) A__questionmark_v3))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|) (A__questionmark_v2 |tptp.'Num_int_fun$'|) (A__questionmark_v3 Int)) (=> (and (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v1) (= (|tptp.'fun_app$ab'| A__questionmark_v2 A__questionmark_v1) A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Num$'|) (A__questionmark_v5 |tptp.'Num$'|)) (=> (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v4) A__questionmark_v5) (<= (|tptp.'fun_app$ab'| A__questionmark_v2 A__questionmark_v4) (|tptp.'fun_app$ab'| A__questionmark_v2 A__questionmark_v5))))) (<= (|tptp.'fun_app$ab'| A__questionmark_v2 A__questionmark_v0) A__questionmark_v3))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat$'|) (A__questionmark_v2 |tptp.'Enat_num_fun$'|) (A__questionmark_v3 |tptp.'Num$'|)) (=> (and (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) A__questionmark_v1) (= (|tptp.'fun_app$ac'| A__questionmark_v2 A__questionmark_v1) A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Enat$'|) (A__questionmark_v5 |tptp.'Enat$'|)) (=> (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v4) A__questionmark_v5) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| (|tptp.'fun_app$ac'| A__questionmark_v2 A__questionmark_v4)) (|tptp.'fun_app$ac'| A__questionmark_v2 A__questionmark_v5))))) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| (|tptp.'fun_app$ac'| A__questionmark_v2 A__questionmark_v0)) A__questionmark_v3))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat$'|) (A__questionmark_v2 |tptp.'Enat_enat_fun$'|) (A__questionmark_v3 |tptp.'Enat$'|)) (=> (and (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) A__questionmark_v1) (= (|tptp.'fun_app$ad'| A__questionmark_v2 A__questionmark_v1) A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Enat$'|) (A__questionmark_v5 |tptp.'Enat$'|)) (=> (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v4) A__questionmark_v5) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| (|tptp.'fun_app$ad'| A__questionmark_v2 A__questionmark_v4)) (|tptp.'fun_app$ad'| A__questionmark_v2 A__questionmark_v5))))) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| (|tptp.'fun_app$ad'| A__questionmark_v2 A__questionmark_v0)) A__questionmark_v3))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat$'|) (A__questionmark_v2 |tptp.'Enat_int_fun$'|) (A__questionmark_v3 Int)) (=> (and (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) A__questionmark_v1) (= (|tptp.'fun_app$ae'| A__questionmark_v2 A__questionmark_v1) A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Enat$'|) (A__questionmark_v5 |tptp.'Enat$'|)) (=> (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v4) A__questionmark_v5) (<= (|tptp.'fun_app$ae'| A__questionmark_v2 A__questionmark_v4) (|tptp.'fun_app$ae'| A__questionmark_v2 A__questionmark_v5))))) (<= (|tptp.'fun_app$ae'| A__questionmark_v2 A__questionmark_v0) A__questionmark_v3))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 |tptp.'Int_num_fun$'|) (A__questionmark_v3 |tptp.'Num$'|)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (= (|tptp.'fun_app$af'| A__questionmark_v2 A__questionmark_v1) A__questionmark_v3) (forall ((A__questionmark_v4 Int) (A__questionmark_v5 Int)) (=> (<= A__questionmark_v4 A__questionmark_v5) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| (|tptp.'fun_app$af'| A__questionmark_v2 A__questionmark_v4)) (|tptp.'fun_app$af'| A__questionmark_v2 A__questionmark_v5))))) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| (|tptp.'fun_app$af'| A__questionmark_v2 A__questionmark_v0)) A__questionmark_v3))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 |tptp.'Int_enat_fun$'|) (A__questionmark_v3 |tptp.'Enat$'|)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (= (|tptp.'fun_app$ag'| A__questionmark_v2 A__questionmark_v1) A__questionmark_v3) (forall ((A__questionmark_v4 Int) (A__questionmark_v5 Int)) (=> (<= A__questionmark_v4 A__questionmark_v5) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| (|tptp.'fun_app$ag'| A__questionmark_v2 A__questionmark_v4)) (|tptp.'fun_app$ag'| A__questionmark_v2 A__questionmark_v5))))) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| (|tptp.'fun_app$ag'| A__questionmark_v2 A__questionmark_v0)) A__questionmark_v3))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 |tptp.'Int_int_fun$'|) (A__questionmark_v3 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (= (|tptp.'fun_app$h'| A__questionmark_v2 A__questionmark_v1) A__questionmark_v3) (forall ((A__questionmark_v4 Int) (A__questionmark_v5 Int)) (=> (<= A__questionmark_v4 A__questionmark_v5) (<= (|tptp.'fun_app$h'| A__questionmark_v2 A__questionmark_v4) (|tptp.'fun_app$h'| A__questionmark_v2 A__questionmark_v5))))) (<= (|tptp.'fun_app$h'| A__questionmark_v2 A__questionmark_v0) A__questionmark_v3))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num_num_fun$'|) (A__questionmark_v2 |tptp.'Num$'|) (A__questionmark_v3 |tptp.'Num$'|)) (=> (and (= A__questionmark_v0 (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v2) A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Num$'|) (A__questionmark_v5 |tptp.'Num$'|)) (=> (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v4) A__questionmark_v5) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v4)) (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v5))))) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Num_enat_fun$'|) (A__questionmark_v2 |tptp.'Num$'|) (A__questionmark_v3 |tptp.'Num$'|)) (=> (and (= A__questionmark_v0 (|tptp.'fun_app$aa'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v2) A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Num$'|) (A__questionmark_v5 |tptp.'Num$'|)) (=> (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v4) A__questionmark_v5) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| (|tptp.'fun_app$aa'| A__questionmark_v1 A__questionmark_v4)) (|tptp.'fun_app$aa'| A__questionmark_v1 A__questionmark_v5))))) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) (|tptp.'fun_app$aa'| A__questionmark_v1 A__questionmark_v3)))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 |tptp.'Num_int_fun$'|) (A__questionmark_v2 |tptp.'Num$'|) (A__questionmark_v3 |tptp.'Num$'|)) (=> (and (= A__questionmark_v0 (|tptp.'fun_app$ab'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v2) A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Num$'|) (A__questionmark_v5 |tptp.'Num$'|)) (=> (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v4) A__questionmark_v5) (<= (|tptp.'fun_app$ab'| A__questionmark_v1 A__questionmark_v4) (|tptp.'fun_app$ab'| A__questionmark_v1 A__questionmark_v5))))) (<= A__questionmark_v0 (|tptp.'fun_app$ab'| A__questionmark_v1 A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Enat_num_fun$'|) (A__questionmark_v2 |tptp.'Enat$'|) (A__questionmark_v3 |tptp.'Enat$'|)) (=> (and (= A__questionmark_v0 (|tptp.'fun_app$ac'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v2) A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Enat$'|) (A__questionmark_v5 |tptp.'Enat$'|)) (=> (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v4) A__questionmark_v5) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| (|tptp.'fun_app$ac'| A__questionmark_v1 A__questionmark_v4)) (|tptp.'fun_app$ac'| A__questionmark_v1 A__questionmark_v5))))) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) (|tptp.'fun_app$ac'| A__questionmark_v1 A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat_enat_fun$'|) (A__questionmark_v2 |tptp.'Enat$'|) (A__questionmark_v3 |tptp.'Enat$'|)) (=> (and (= A__questionmark_v0 (|tptp.'fun_app$ad'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v2) A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Enat$'|) (A__questionmark_v5 |tptp.'Enat$'|)) (=> (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v4) A__questionmark_v5) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| (|tptp.'fun_app$ad'| A__questionmark_v1 A__questionmark_v4)) (|tptp.'fun_app$ad'| A__questionmark_v1 A__questionmark_v5))))) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) (|tptp.'fun_app$ad'| A__questionmark_v1 A__questionmark_v3)))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 |tptp.'Enat_int_fun$'|) (A__questionmark_v2 |tptp.'Enat$'|) (A__questionmark_v3 |tptp.'Enat$'|)) (=> (and (= A__questionmark_v0 (|tptp.'fun_app$ae'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v2) A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Enat$'|) (A__questionmark_v5 |tptp.'Enat$'|)) (=> (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v4) A__questionmark_v5) (<= (|tptp.'fun_app$ae'| A__questionmark_v1 A__questionmark_v4) (|tptp.'fun_app$ae'| A__questionmark_v1 A__questionmark_v5))))) (<= A__questionmark_v0 (|tptp.'fun_app$ae'| A__questionmark_v1 A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Int_num_fun$'|) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (and (= A__questionmark_v0 (|tptp.'fun_app$af'| A__questionmark_v1 A__questionmark_v2)) (<= A__questionmark_v2 A__questionmark_v3) (forall ((A__questionmark_v4 Int) (A__questionmark_v5 Int)) (=> (<= A__questionmark_v4 A__questionmark_v5) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| (|tptp.'fun_app$af'| A__questionmark_v1 A__questionmark_v4)) (|tptp.'fun_app$af'| A__questionmark_v1 A__questionmark_v5))))) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) (|tptp.'fun_app$af'| A__questionmark_v1 A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Int_enat_fun$'|) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (and (= A__questionmark_v0 (|tptp.'fun_app$ag'| A__questionmark_v1 A__questionmark_v2)) (<= A__questionmark_v2 A__questionmark_v3) (forall ((A__questionmark_v4 Int) (A__questionmark_v5 Int)) (=> (<= A__questionmark_v4 A__questionmark_v5) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| (|tptp.'fun_app$ag'| A__questionmark_v1 A__questionmark_v4)) (|tptp.'fun_app$ag'| A__questionmark_v1 A__questionmark_v5))))) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) (|tptp.'fun_app$ag'| A__questionmark_v1 A__questionmark_v3)))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 |tptp.'Int_int_fun$'|) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (and (= A__questionmark_v0 (|tptp.'fun_app$h'| A__questionmark_v1 A__questionmark_v2)) (<= A__questionmark_v2 A__questionmark_v3) (forall ((A__questionmark_v4 Int) (A__questionmark_v5 Int)) (=> (<= A__questionmark_v4 A__questionmark_v5) (<= (|tptp.'fun_app$h'| A__questionmark_v1 A__questionmark_v4) (|tptp.'fun_app$h'| A__questionmark_v1 A__questionmark_v5))))) (<= A__questionmark_v0 (|tptp.'fun_app$h'| A__questionmark_v1 A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (or (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v1) A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat$'|)) (or (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v1) A__questionmark_v0))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (or (<= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (=> (= A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat$'|)) (=> (= A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) A__questionmark_v1))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v0 A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|) (A__questionmark_v2 |tptp.'Num_num_fun$'|) (A__questionmark_v3 |tptp.'Num$'|)) (=> (and (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v1)) A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Num$'|) (A__questionmark_v5 |tptp.'Num$'|)) (=> (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v4) A__questionmark_v5) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v4)) (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v5))))) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v0)) A__questionmark_v3))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|) (A__questionmark_v2 |tptp.'Num_enat_fun$'|) (A__questionmark_v3 |tptp.'Enat$'|)) (=> (and (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| (|tptp.'fun_app$aa'| A__questionmark_v2 A__questionmark_v1)) A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Num$'|) (A__questionmark_v5 |tptp.'Num$'|)) (=> (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v4) A__questionmark_v5) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| (|tptp.'fun_app$aa'| A__questionmark_v2 A__questionmark_v4)) (|tptp.'fun_app$aa'| A__questionmark_v2 A__questionmark_v5))))) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| (|tptp.'fun_app$aa'| A__questionmark_v2 A__questionmark_v0)) A__questionmark_v3))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|) (A__questionmark_v2 |tptp.'Num_int_fun$'|) (A__questionmark_v3 Int)) (=> (and (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v1) (<= (|tptp.'fun_app$ab'| A__questionmark_v2 A__questionmark_v1) A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Num$'|) (A__questionmark_v5 |tptp.'Num$'|)) (=> (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v4) A__questionmark_v5) (<= (|tptp.'fun_app$ab'| A__questionmark_v2 A__questionmark_v4) (|tptp.'fun_app$ab'| A__questionmark_v2 A__questionmark_v5))))) (<= (|tptp.'fun_app$ab'| A__questionmark_v2 A__questionmark_v0) A__questionmark_v3))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat$'|) (A__questionmark_v2 |tptp.'Enat_num_fun$'|) (A__questionmark_v3 |tptp.'Num$'|)) (=> (and (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| (|tptp.'fun_app$ac'| A__questionmark_v2 A__questionmark_v1)) A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Enat$'|) (A__questionmark_v5 |tptp.'Enat$'|)) (=> (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v4) A__questionmark_v5) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| (|tptp.'fun_app$ac'| A__questionmark_v2 A__questionmark_v4)) (|tptp.'fun_app$ac'| A__questionmark_v2 A__questionmark_v5))))) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| (|tptp.'fun_app$ac'| A__questionmark_v2 A__questionmark_v0)) A__questionmark_v3))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat$'|) (A__questionmark_v2 |tptp.'Enat_enat_fun$'|) (A__questionmark_v3 |tptp.'Enat$'|)) (=> (and (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| (|tptp.'fun_app$ad'| A__questionmark_v2 A__questionmark_v1)) A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Enat$'|) (A__questionmark_v5 |tptp.'Enat$'|)) (=> (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v4) A__questionmark_v5) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| (|tptp.'fun_app$ad'| A__questionmark_v2 A__questionmark_v4)) (|tptp.'fun_app$ad'| A__questionmark_v2 A__questionmark_v5))))) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| (|tptp.'fun_app$ad'| A__questionmark_v2 A__questionmark_v0)) A__questionmark_v3))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat$'|) (A__questionmark_v2 |tptp.'Enat_int_fun$'|) (A__questionmark_v3 Int)) (=> (and (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) A__questionmark_v1) (<= (|tptp.'fun_app$ae'| A__questionmark_v2 A__questionmark_v1) A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Enat$'|) (A__questionmark_v5 |tptp.'Enat$'|)) (=> (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v4) A__questionmark_v5) (<= (|tptp.'fun_app$ae'| A__questionmark_v2 A__questionmark_v4) (|tptp.'fun_app$ae'| A__questionmark_v2 A__questionmark_v5))))) (<= (|tptp.'fun_app$ae'| A__questionmark_v2 A__questionmark_v0) A__questionmark_v3))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 |tptp.'Int_num_fun$'|) (A__questionmark_v3 |tptp.'Num$'|)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| (|tptp.'fun_app$af'| A__questionmark_v2 A__questionmark_v1)) A__questionmark_v3) (forall ((A__questionmark_v4 Int) (A__questionmark_v5 Int)) (=> (<= A__questionmark_v4 A__questionmark_v5) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| (|tptp.'fun_app$af'| A__questionmark_v2 A__questionmark_v4)) (|tptp.'fun_app$af'| A__questionmark_v2 A__questionmark_v5))))) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| (|tptp.'fun_app$af'| A__questionmark_v2 A__questionmark_v0)) A__questionmark_v3))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 |tptp.'Int_enat_fun$'|) (A__questionmark_v3 |tptp.'Enat$'|)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| (|tptp.'fun_app$ag'| A__questionmark_v2 A__questionmark_v1)) A__questionmark_v3) (forall ((A__questionmark_v4 Int) (A__questionmark_v5 Int)) (=> (<= A__questionmark_v4 A__questionmark_v5) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| (|tptp.'fun_app$ag'| A__questionmark_v2 A__questionmark_v4)) (|tptp.'fun_app$ag'| A__questionmark_v2 A__questionmark_v5))))) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| (|tptp.'fun_app$ag'| A__questionmark_v2 A__questionmark_v0)) A__questionmark_v3))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 |tptp.'Int_int_fun$'|) (A__questionmark_v3 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (<= (|tptp.'fun_app$h'| A__questionmark_v2 A__questionmark_v1) A__questionmark_v3) (forall ((A__questionmark_v4 Int) (A__questionmark_v5 Int)) (=> (<= A__questionmark_v4 A__questionmark_v5) (<= (|tptp.'fun_app$h'| A__questionmark_v2 A__questionmark_v4) (|tptp.'fun_app$h'| A__questionmark_v2 A__questionmark_v5))))) (<= (|tptp.'fun_app$h'| A__questionmark_v2 A__questionmark_v0) A__questionmark_v3))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num_num_fun$'|) (A__questionmark_v2 |tptp.'Num$'|) (A__questionmark_v3 |tptp.'Num$'|)) (let ((_let_1 (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$u'| _let_1 (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v2) A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Num$'|) (A__questionmark_v5 |tptp.'Num$'|)) (=> (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v4) A__questionmark_v5) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v4)) (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v5))))) (|tptp.'fun_app$u'| _let_1 (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v3))))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Enat_num_fun$'|) (A__questionmark_v2 |tptp.'Enat$'|) (A__questionmark_v3 |tptp.'Enat$'|)) (let ((_let_1 (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$u'| _let_1 (|tptp.'fun_app$ac'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v2) A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Enat$'|) (A__questionmark_v5 |tptp.'Enat$'|)) (=> (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v4) A__questionmark_v5) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| (|tptp.'fun_app$ac'| A__questionmark_v1 A__questionmark_v4)) (|tptp.'fun_app$ac'| A__questionmark_v1 A__questionmark_v5))))) (|tptp.'fun_app$u'| _let_1 (|tptp.'fun_app$ac'| A__questionmark_v1 A__questionmark_v3))))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Int_num_fun$'|) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (let ((_let_1 (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$u'| _let_1 (|tptp.'fun_app$af'| A__questionmark_v1 A__questionmark_v2)) (<= A__questionmark_v2 A__questionmark_v3) (forall ((A__questionmark_v4 Int) (A__questionmark_v5 Int)) (=> (<= A__questionmark_v4 A__questionmark_v5) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| (|tptp.'fun_app$af'| A__questionmark_v1 A__questionmark_v4)) (|tptp.'fun_app$af'| A__questionmark_v1 A__questionmark_v5))))) (|tptp.'fun_app$u'| _let_1 (|tptp.'fun_app$af'| A__questionmark_v1 A__questionmark_v3))))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Num_enat_fun$'|) (A__questionmark_v2 |tptp.'Num$'|) (A__questionmark_v3 |tptp.'Num$'|)) (let ((_let_1 (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$w'| _let_1 (|tptp.'fun_app$aa'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v2) A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Num$'|) (A__questionmark_v5 |tptp.'Num$'|)) (=> (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v4) A__questionmark_v5) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| (|tptp.'fun_app$aa'| A__questionmark_v1 A__questionmark_v4)) (|tptp.'fun_app$aa'| A__questionmark_v1 A__questionmark_v5))))) (|tptp.'fun_app$w'| _let_1 (|tptp.'fun_app$aa'| A__questionmark_v1 A__questionmark_v3))))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat_enat_fun$'|) (A__questionmark_v2 |tptp.'Enat$'|) (A__questionmark_v3 |tptp.'Enat$'|)) (let ((_let_1 (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$w'| _let_1 (|tptp.'fun_app$ad'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v2) A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Enat$'|) (A__questionmark_v5 |tptp.'Enat$'|)) (=> (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v4) A__questionmark_v5) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| (|tptp.'fun_app$ad'| A__questionmark_v1 A__questionmark_v4)) (|tptp.'fun_app$ad'| A__questionmark_v1 A__questionmark_v5))))) (|tptp.'fun_app$w'| _let_1 (|tptp.'fun_app$ad'| A__questionmark_v1 A__questionmark_v3))))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Int_enat_fun$'|) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (let ((_let_1 (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$w'| _let_1 (|tptp.'fun_app$ag'| A__questionmark_v1 A__questionmark_v2)) (<= A__questionmark_v2 A__questionmark_v3) (forall ((A__questionmark_v4 Int) (A__questionmark_v5 Int)) (=> (<= A__questionmark_v4 A__questionmark_v5) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| (|tptp.'fun_app$ag'| A__questionmark_v1 A__questionmark_v4)) (|tptp.'fun_app$ag'| A__questionmark_v1 A__questionmark_v5))))) (|tptp.'fun_app$w'| _let_1 (|tptp.'fun_app$ag'| A__questionmark_v1 A__questionmark_v3))))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 |tptp.'Num_int_fun$'|) (A__questionmark_v2 |tptp.'Num$'|) (A__questionmark_v3 |tptp.'Num$'|)) (=> (and (<= A__questionmark_v0 (|tptp.'fun_app$ab'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v2) A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Num$'|) (A__questionmark_v5 |tptp.'Num$'|)) (=> (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v4) A__questionmark_v5) (<= (|tptp.'fun_app$ab'| A__questionmark_v1 A__questionmark_v4) (|tptp.'fun_app$ab'| A__questionmark_v1 A__questionmark_v5))))) (<= A__questionmark_v0 (|tptp.'fun_app$ab'| A__questionmark_v1 A__questionmark_v3)))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 |tptp.'Enat_int_fun$'|) (A__questionmark_v2 |tptp.'Enat$'|) (A__questionmark_v3 |tptp.'Enat$'|)) (=> (and (<= A__questionmark_v0 (|tptp.'fun_app$ae'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v2) A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Enat$'|) (A__questionmark_v5 |tptp.'Enat$'|)) (=> (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v4) A__questionmark_v5) (<= (|tptp.'fun_app$ae'| A__questionmark_v1 A__questionmark_v4) (|tptp.'fun_app$ae'| A__questionmark_v1 A__questionmark_v5))))) (<= A__questionmark_v0 (|tptp.'fun_app$ae'| A__questionmark_v1 A__questionmark_v3)))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 |tptp.'Int_int_fun$'|) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (and (<= A__questionmark_v0 (|tptp.'fun_app$h'| A__questionmark_v1 A__questionmark_v2)) (<= A__questionmark_v2 A__questionmark_v3) (forall ((A__questionmark_v4 Int) (A__questionmark_v5 Int)) (=> (<= A__questionmark_v4 A__questionmark_v5) (<= (|tptp.'fun_app$h'| A__questionmark_v1 A__questionmark_v4) (|tptp.'fun_app$h'| A__questionmark_v1 A__questionmark_v5))))) (<= A__questionmark_v0 (|tptp.'fun_app$h'| A__questionmark_v1 A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (= (= A__questionmark_v0 A__questionmark_v1) (and (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v1) A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat$'|)) (= (= A__questionmark_v0 A__questionmark_v1) (and (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v1) A__questionmark_v0)))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (= A__questionmark_v0 A__questionmark_v1) (and (<= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v1 A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (=> (and (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v1) A__questionmark_v0)) (= A__questionmark_v0 A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat$'|)) (=> (and (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v1) A__questionmark_v0)) (= A__questionmark_v0 A__questionmark_v1))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v1 A__questionmark_v0)) (= A__questionmark_v0 A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|) (A__questionmark_v1 |tptp.'Nat_set$'|)) (= (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| A__questionmark_v0) A__questionmark_v1) (forall ((A__questionmark_v2 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'member$'| A__questionmark_v2))) (=> (|tptp.'fun_app$a'| _let_1 A__questionmark_v0) (|tptp.'fun_app$a'| _let_1 A__questionmark_v1)))))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|) (A__questionmark_v1 |tptp.'Nat_set$'|)) (= (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| A__questionmark_v0) A__questionmark_v1) (forall ((A__questionmark_v2 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'member$'| A__questionmark_v2))) (=> (|tptp.'fun_app$a'| _let_1 A__questionmark_v0) (|tptp.'fun_app$a'| _let_1 A__questionmark_v1)))))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'member$'| A__questionmark_v2))) (=> (and (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$a'| _let_1 A__questionmark_v0)) (|tptp.'fun_app$a'| _let_1 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'member$'| A__questionmark_v2))) (=> (and (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$a'| _let_1 A__questionmark_v0)) (|tptp.'fun_app$a'| _let_1 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_set$'|)) (let ((_let_1 (|tptp.'member$'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$a'| _let_1 (|tptp.'minus$b'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$a'| _let_1 A__questionmark_v2)) false))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_set$'|)) (let ((_let_1 (|tptp.'member$'| A__questionmark_v0))) (=> (|tptp.'fun_app$a'| _let_1 (|tptp.'minus$b'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$a'| _let_1 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_set$'|)) (let ((_let_1 (|tptp.'member$'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$a'| _let_1 (|tptp.'minus$b'| A__questionmark_v1 A__questionmark_v2)) (=> (and (|tptp.'fun_app$a'| _let_1 A__questionmark_v1) (not (|tptp.'fun_app$a'| _let_1 A__questionmark_v2))) false)) false))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|) (A__questionmark_v2 |tptp.'Num$'|)) (let ((_let_1 (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v2))) (=> (and (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$u'| _let_1 A__questionmark_v0)) (|tptp.'fun_app$u'| _let_1 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat$'|) (A__questionmark_v2 |tptp.'Enat$'|)) (let ((_let_1 (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v2))) (=> (and (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$w'| _let_1 A__questionmark_v0)) (|tptp.'fun_app$w'| _let_1 A__questionmark_v1)))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v2 A__questionmark_v0)) (<= A__questionmark_v2 A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (=> (and (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v1) A__questionmark_v0)) (= A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat$'|)) (=> (and (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v1) A__questionmark_v0)) (= A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v1 A__questionmark_v0)) (= A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (= (= A__questionmark_v0 A__questionmark_v1) (and (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v1) A__questionmark_v0) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat$'|)) (= (= A__questionmark_v0 A__questionmark_v1) (and (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v1) A__questionmark_v0) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (= A__questionmark_v0 A__questionmark_v1) (and (<= A__questionmark_v1 A__questionmark_v0) (<= A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'Num_num_bool_fun_fun$'|) (A__questionmark_v1 |tptp.'Num$'|) (A__questionmark_v2 |tptp.'Num$'|)) (=> (and (forall ((A__questionmark_v3 |tptp.'Num$'|) (A__questionmark_v4 |tptp.'Num$'|)) (=> (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v3) A__questionmark_v4) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| A__questionmark_v0 A__questionmark_v3) A__questionmark_v4))) (forall ((A__questionmark_v3 |tptp.'Num$'|) (A__questionmark_v4 |tptp.'Num$'|)) (=> (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| A__questionmark_v0 A__questionmark_v4) A__questionmark_v3) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| A__questionmark_v0 A__questionmark_v3) A__questionmark_v4)))) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'Enat_enat_bool_fun_fun$'|) (A__questionmark_v1 |tptp.'Enat$'|) (A__questionmark_v2 |tptp.'Enat$'|)) (=> (and (forall ((A__questionmark_v3 |tptp.'Enat$'|) (A__questionmark_v4 |tptp.'Enat$'|)) (=> (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v3) A__questionmark_v4) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| A__questionmark_v0 A__questionmark_v3) A__questionmark_v4))) (forall ((A__questionmark_v3 |tptp.'Enat$'|) (A__questionmark_v4 |tptp.'Enat$'|)) (=> (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| A__questionmark_v0 A__questionmark_v4) A__questionmark_v3) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| A__questionmark_v0 A__questionmark_v3) A__questionmark_v4)))) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'Int_int_bool_fun_fun$'|) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (forall ((A__questionmark_v3 Int) (A__questionmark_v4 Int)) (=> (<= A__questionmark_v3 A__questionmark_v4) (|tptp.'fun_app$ah'| (|tptp.'fun_app$ai'| A__questionmark_v0 A__questionmark_v3) A__questionmark_v4))) (forall ((A__questionmark_v3 Int) (A__questionmark_v4 Int)) (=> (|tptp.'fun_app$ah'| (|tptp.'fun_app$ai'| A__questionmark_v0 A__questionmark_v4) A__questionmark_v3) (|tptp.'fun_app$ah'| (|tptp.'fun_app$ai'| A__questionmark_v0 A__questionmark_v3) A__questionmark_v4)))) (|tptp.'fun_app$ah'| (|tptp.'fun_app$ai'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|) (A__questionmark_v2 |tptp.'Num$'|)) (let ((_let_1 (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$u'| _let_1 A__questionmark_v1) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$u'| _let_1 A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat$'|) (A__questionmark_v2 |tptp.'Enat$'|)) (let ((_let_1 (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$w'| _let_1 A__questionmark_v1) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$w'| _let_1 A__questionmark_v2)))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v1 A__questionmark_v2)) (<= A__questionmark_v0 A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|) (A__questionmark_v2 |tptp.'Num$'|)) (let ((_let_1 (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$u'| _let_1 A__questionmark_v1) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$u'| _let_1 A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat$'|) (A__questionmark_v2 |tptp.'Enat$'|)) (let ((_let_1 (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$w'| _let_1 A__questionmark_v1) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$w'| _let_1 A__questionmark_v2)))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v1 A__questionmark_v2)) (<= A__questionmark_v0 A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (=> (and (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v1) A__questionmark_v0)) (= A__questionmark_v0 A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat$'|)) (=> (and (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v1) A__questionmark_v0)) (= A__questionmark_v0 A__questionmark_v1))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v1 A__questionmark_v0)) (= A__questionmark_v0 A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|) (A__questionmark_v2 |tptp.'Num$'|)) (let ((_let_1 (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$u'| _let_1 A__questionmark_v1) (= A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$u'| _let_1 A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat$'|) (A__questionmark_v2 |tptp.'Enat$'|)) (let ((_let_1 (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$w'| _let_1 A__questionmark_v1) (= A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$w'| _let_1 A__questionmark_v2)))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (= A__questionmark_v1 A__questionmark_v2)) (<= A__questionmark_v0 A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|) (A__questionmark_v2 |tptp.'Num$'|)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat$'|) (A__questionmark_v2 |tptp.'Enat$'|)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) A__questionmark_v2))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v1 A__questionmark_v2)) (<= A__questionmark_v0 A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (= (= A__questionmark_v0 A__questionmark_v1) (and (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v1) A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat$'|)) (= (= A__questionmark_v0 A__questionmark_v1) (and (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v1) A__questionmark_v0)))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (= A__questionmark_v0 A__questionmark_v1) (and (<= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v1 A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|) (A__questionmark_v2 |tptp.'Num$'|)) (let ((_let_1 (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0))) (let ((_let_2 (|tptp.'fun_app$u'| _let_1 A__questionmark_v1))) (let ((_let_3 (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v2))) (let ((_let_4 (|tptp.'fun_app$u'| _let_3 A__questionmark_v0))) (let ((_let_5 (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v1))) (let ((_let_6 (|tptp.'fun_app$u'| _let_5 A__questionmark_v2))) (let ((_let_7 (|tptp.'fun_app$u'| _let_5 A__questionmark_v0))) (let ((_let_8 (|tptp.'fun_app$u'| _let_3 A__questionmark_v1))) (let ((_let_9 (|tptp.'fun_app$u'| _let_1 A__questionmark_v2))) (=> (and (=> (and _let_2 _let_6) false) (=> (and _let_7 _let_9) false) (=> (and _let_9 _let_8) false) (=> (and _let_8 _let_7) false) (=> (and _let_6 _let_4) false) (=> (and _let_4 _let_2) false)) false))))))))))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat$'|) (A__questionmark_v2 |tptp.'Enat$'|)) (let ((_let_1 (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0))) (let ((_let_2 (|tptp.'fun_app$w'| _let_1 A__questionmark_v1))) (let ((_let_3 (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v2))) (let ((_let_4 (|tptp.'fun_app$w'| _let_3 A__questionmark_v0))) (let ((_let_5 (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v1))) (let ((_let_6 (|tptp.'fun_app$w'| _let_5 A__questionmark_v2))) (let ((_let_7 (|tptp.'fun_app$w'| _let_5 A__questionmark_v0))) (let ((_let_8 (|tptp.'fun_app$w'| _let_3 A__questionmark_v1))) (let ((_let_9 (|tptp.'fun_app$w'| _let_1 A__questionmark_v2))) (=> (and (=> (and _let_2 _let_6) false) (=> (and _let_7 _let_9) false) (=> (and _let_9 _let_8) false) (=> (and _let_8 _let_7) false) (=> (and _let_6 _let_4) false) (=> (and _let_4 _let_2) false)) false))))))))))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (let ((_let_1 (<= A__questionmark_v0 A__questionmark_v1))) (let ((_let_2 (<= A__questionmark_v2 A__questionmark_v0))) (let ((_let_3 (<= A__questionmark_v1 A__questionmark_v2))) (let ((_let_4 (<= A__questionmark_v1 A__questionmark_v0))) (let ((_let_5 (<= A__questionmark_v2 A__questionmark_v1))) (let ((_let_6 (<= A__questionmark_v0 A__questionmark_v2))) (=> (and (=> (and _let_1 _let_3) false) (=> (and _let_4 _let_6) false) (=> (and _let_6 _let_5) false) (=> (and _let_5 _let_4) false) (=> (and _let_3 _let_2) false) (=> (and _let_2 _let_1) false)) false)))))))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (= (not (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v1)) (and (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v1) A__questionmark_v0) (not (= A__questionmark_v1 A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat$'|)) (= (not (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) A__questionmark_v1)) (and (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v1) A__questionmark_v0) (not (= A__questionmark_v1 A__questionmark_v0))))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (not (<= A__questionmark_v0 A__questionmark_v1)) (and (<= A__questionmark_v1 A__questionmark_v0) (not (= A__questionmark_v1 A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|) (A__questionmark_v1 |tptp.'Nat_set$'|)) (= (|tptp.'minus$b'| A__questionmark_v0 A__questionmark_v1) (|tptp.'collect$b'| (|tptp.'uus$'| A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|) (A__questionmark_v1 |tptp.'Nat_bool_fun$'|)) (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| (|tptp.'collect$b'| (|tptp.'uut$'| A__questionmark_v0 A__questionmark_v1))) A__questionmark_v0)) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 |tptp.'Int_set$'|) (A__questionmark_v2 |tptp.'Int_set$'|)) (let ((_let_1 (|tptp.'uur$'| A__questionmark_v0))) (= (|tptp.'image$g'| _let_1 (|tptp.'minus$f'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'minus$f'| (|tptp.'image$g'| _let_1 A__questionmark_v1) (|tptp.'image$g'| _let_1 A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'B_ell2_set$'|) (A__questionmark_v3 |tptp.'B_ell2_set$'|)) (let ((_let_1 (|tptp.'image$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'minus$c'| A__questionmark_v2 A__questionmark_v3))) (=> (and (|tptp.'inj_on$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'less_eq$'| _let_2 A__questionmark_v1) (|tptp.'less_eq$'| A__questionmark_v3 A__questionmark_v1)) (= (|tptp.'fun_app$n'| _let_1 _let_2) (|tptp.'minus$d'| (|tptp.'fun_app$n'| _let_1 A__questionmark_v2) (|tptp.'fun_app$n'| _let_1 A__questionmark_v3))))))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_set$'|) (A__questionmark_v3 |tptp.'Nat_set$'|)) (let ((_let_1 (|tptp.'image$a'| A__questionmark_v0))) (let ((_let_2 (|tptp.'minus$b'| A__questionmark_v2 A__questionmark_v3))) (=> (and (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| _let_2) A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| A__questionmark_v3) A__questionmark_v1)) (= (|tptp.'fun_app$o'| _let_1 _let_2) (|tptp.'minus$b'| (|tptp.'fun_app$o'| _let_1 A__questionmark_v2) (|tptp.'fun_app$o'| _let_1 A__questionmark_v3))))))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v3 |tptp.'B_ell2_set$'|) (A__questionmark_v4 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|)) (=> (= (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v2) A__questionmark_v3)) (= (|tptp.'fun_app$n'| (|tptp.'image$'| (|tptp.'comp$c'| A__questionmark_v4 A__questionmark_v0)) A__questionmark_v1) (|tptp.'fun_app$n'| (|tptp.'image$'| (|tptp.'comp$c'| A__questionmark_v4 A__questionmark_v2)) A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v2 |tptp.'B_ell2_set$'|)) (= (|tptp.'image$d'| A__questionmark_v0 (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$n'| (|tptp.'image$'| (|tptp.'comp$c'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_b_ell2_fun$'|) (A__questionmark_v2 |tptp.'B_ell2_set$'|)) (= (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) (|tptp.'image$e'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$n'| (|tptp.'image$'| (|tptp.'comp$d'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_set_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v2 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v3 |tptp.'B_ell2_set$'|)) (= (|tptp.'fun_app$s'| A__questionmark_v0 (|tptp.'image$d'| A__questionmark_v1 (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v2) A__questionmark_v3))) (|tptp.'fun_app$s'| A__questionmark_v0 (|tptp.'fun_app$n'| (|tptp.'image$'| (|tptp.'comp$c'| A__questionmark_v1 A__questionmark_v2)) A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_set_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v2 |tptp.'B_ell2_b_ell2_fun$'|) (A__questionmark_v3 |tptp.'B_ell2_set$'|)) (= (|tptp.'fun_app$s'| A__questionmark_v0 (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v1) (|tptp.'image$e'| A__questionmark_v2 A__questionmark_v3))) (|tptp.'fun_app$s'| A__questionmark_v0 (|tptp.'fun_app$n'| (|tptp.'image$'| (|tptp.'comp$d'| A__questionmark_v1 A__questionmark_v2)) A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_set_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v2 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v3 |tptp.'B_ell2_set$'|)) (= (|tptp.'fun_app$s'| A__questionmark_v0 (|tptp.'image$d'| A__questionmark_v1 (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v2) A__questionmark_v3))) (|tptp.'fun_app$s'| A__questionmark_v0 (|tptp.'fun_app$n'| (|tptp.'image$'| (|tptp.'comp$c'| A__questionmark_v1 A__questionmark_v2)) A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_set_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v2 |tptp.'B_ell2_b_ell2_fun$'|) (A__questionmark_v3 |tptp.'B_ell2_set$'|)) (= (|tptp.'fun_app$s'| A__questionmark_v0 (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v1) (|tptp.'image$e'| A__questionmark_v2 A__questionmark_v3))) (|tptp.'fun_app$s'| A__questionmark_v0 (|tptp.'fun_app$n'| (|tptp.'image$'| (|tptp.'comp$d'| A__questionmark_v1 A__questionmark_v2)) A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v2 |tptp.'B_ell2_set$'|)) (=> (|tptp.'inj_on$a'| (|tptp.'comp$c'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'inj_on$a'| A__questionmark_v1 A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_nat_fun$'|) (A__questionmark_v2 |tptp.'Nat_set$'|)) (=> (|tptp.'fun_app$a'| (|tptp.'inj_on$'| (|tptp.'comp$b'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v1) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'A_ell2$'|) (A__questionmark_v1 |tptp.'A_ell2$'|)) (= (= A__questionmark_v0 A__questionmark_v1) (= (|tptp.'fun_app$y'| (|tptp.'minus$e'| A__questionmark_v0) A__questionmark_v1) |tptp.'zero$'|))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (= A__questionmark_v0 A__questionmark_v1) (= (- A__questionmark_v0 A__questionmark_v1) 0))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (|tptp.'member$e'| A__questionmark_v0 |tptp.'top$g'|) (|tptp.'member$e'| A__questionmark_v1 |tptp.'top$g'|)) (|tptp.'member$e'| (- A__questionmark_v0 A__questionmark_v1) |tptp.'top$g'|))) (forall ((A__questionmark_v0 |tptp.'Enat$'|)) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| |tptp.'zero$e'|) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'B_ell2_set$'|)) (=> (|tptp.'less_eq$'| |tptp.'top$a'| A__questionmark_v0) (= A__questionmark_v0 |tptp.'top$a'|))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_set$'|)) (=> (|tptp.'fun_app$m'| (|tptp.'less_eq$b'| |tptp.'top$b'|) A__questionmark_v0) (= A__questionmark_v0 |tptp.'top$b'|))) (forall ((A__questionmark_v0 |tptp.'Enat$'|)) (=> (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| |tptp.'top$i'|) A__questionmark_v0) (= A__questionmark_v0 |tptp.'top$i'|))) (forall ((A__questionmark_v0 |tptp.'B_ell2_set$'|)) (= (|tptp.'less_eq$'| |tptp.'top$a'| A__questionmark_v0) (= A__questionmark_v0 |tptp.'top$a'|))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_set$'|)) (= (|tptp.'fun_app$m'| (|tptp.'less_eq$b'| |tptp.'top$b'|) A__questionmark_v0) (= A__questionmark_v0 |tptp.'top$b'|))) (forall ((A__questionmark_v0 |tptp.'Enat$'|)) (= (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| |tptp.'top$i'|) A__questionmark_v0) (= A__questionmark_v0 |tptp.'top$i'|))) (forall ((A__questionmark_v0 |tptp.'B_ell2_set$'|)) (|tptp.'less_eq$'| A__questionmark_v0 |tptp.'top$a'|)) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_set$'|)) (|tptp.'fun_app$m'| (|tptp.'less_eq$b'| A__questionmark_v0) |tptp.'top$b'|)) (forall ((A__questionmark_v0 |tptp.'Enat$'|)) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) |tptp.'top$i'|)) (forall ((A__questionmark_v0 |tptp.'B_ell2_set$'|)) (|tptp.'less_eq$'| A__questionmark_v0 |tptp.'top$a'|)) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_set$'|)) (|tptp.'fun_app$m'| (|tptp.'less_eq$b'| A__questionmark_v0) |tptp.'top$b'|)) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_set$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v2 |tptp.'B_ell2_set$'|)) (= (|tptp.'fun_app$m'| (|tptp.'less_eq$b'| A__questionmark_v0) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v1) A__questionmark_v2)) (exists ((A__questionmark_v3 |tptp.'B_ell2_set$'|)) (and (|tptp.'less_eq$'| A__questionmark_v3 A__questionmark_v2) (= A__questionmark_v0 (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v1) A__questionmark_v3)))))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'A_b_prod_ell2_set$'|)) (= (|tptp.'fun_app$m'| (|tptp.'less_eq$b'| (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v2) (forall ((A__questionmark_v3 |tptp.'B_ell2$'|)) (=> (|tptp.'member$b'| A__questionmark_v3 A__questionmark_v1) (|tptp.'fun_app$m'| (|tptp.'member$a'| (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v3)) A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_set$'|)) (= (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v2) (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v3) A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'member$'| (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v3)) A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_set$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v2 |tptp.'B_ell2_set$'|)) (=> (and (|tptp.'fun_app$m'| (|tptp.'less_eq$b'| A__questionmark_v0) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v1) A__questionmark_v2)) (forall ((A__questionmark_v3 |tptp.'B_ell2_set$'|)) (=> (and (|tptp.'less_eq$'| A__questionmark_v3 A__questionmark_v2) (= A__questionmark_v0 (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v1) A__questionmark_v3))) false))) false)) (forall ((A__questionmark_v0 |tptp.'B_ell2_set$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v2 |tptp.'A_b_prod_ell2_set$'|)) (=> (forall ((A__questionmark_v3 |tptp.'B_ell2$'|)) (=> (|tptp.'member$b'| A__questionmark_v3 A__questionmark_v0) (|tptp.'fun_app$m'| (|tptp.'member$a'| (|tptp.'fun_app$e'| A__questionmark_v1 A__questionmark_v3)) A__questionmark_v2))) (|tptp.'fun_app$m'| (|tptp.'less_eq$b'| (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v1) A__questionmark_v0)) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|) (A__questionmark_v1 |tptp.'Nat_nat_fun$'|) (A__questionmark_v2 |tptp.'Nat_set$'|)) (=> (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v3) A__questionmark_v0) (|tptp.'fun_app$a'| (|tptp.'member$'| (|tptp.'fun_app$c'| A__questionmark_v1 A__questionmark_v3)) A__questionmark_v2))) (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v1) A__questionmark_v0)) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'B_ell2_set$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'B_ell2_a_b_prod_ell2_fun$'|)) (let ((_let_1 (|tptp.'image$'| A__questionmark_v2))) (=> (|tptp.'less_eq$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$m'| (|tptp.'less_eq$b'| (|tptp.'fun_app$n'| _let_1 A__questionmark_v0)) (|tptp.'fun_app$n'| _let_1 A__questionmark_v1))))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'B_ell2_set$'|)) (=> (|tptp.'inj_on$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'inj_on$a'| A__questionmark_v0 (|tptp.'minus$c'| A__questionmark_v1 A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_set$'|)) (let ((_let_1 (|tptp.'inj_on$'| A__questionmark_v0))) (=> (|tptp.'fun_app$a'| _let_1 A__questionmark_v1) (|tptp.'fun_app$a'| _let_1 (|tptp.'minus$b'| A__questionmark_v1 A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'B_ell2_set$'|)) (=> (and (|tptp.'inj_on$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'less_eq$'| A__questionmark_v2 A__questionmark_v1)) (|tptp.'inj_on$a'| A__questionmark_v0 A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_set$'|)) (let ((_let_1 (|tptp.'inj_on$'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$a'| _let_1 A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| A__questionmark_v2) A__questionmark_v1)) (|tptp.'fun_app$a'| _let_1 A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'B_ell2_set$'|)) (=> (and (|tptp.'inj_on$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'less_eq$'| A__questionmark_v2 A__questionmark_v1)) (|tptp.'inj_on$a'| A__questionmark_v0 A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_set$'|)) (let ((_let_1 (|tptp.'inj_on$'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$a'| _let_1 A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| A__questionmark_v2) A__questionmark_v1)) (|tptp.'fun_app$a'| _let_1 A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_b_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_b_ell2_fun$'|)) (=> (and (= (|tptp.'image$e'| A__questionmark_v0 |tptp.'top$a'|) |tptp.'top$a'|) (= (|tptp.'image$e'| A__questionmark_v1 |tptp.'top$a'|) |tptp.'top$a'|)) (= (|tptp.'image$e'| (|tptp.'comp$e'| A__questionmark_v1 A__questionmark_v0) |tptp.'top$a'|) |tptp.'top$a'|))) (forall ((A__questionmark_v0 |tptp.'B_ell2_b_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|)) (=> (and (= (|tptp.'image$e'| A__questionmark_v0 |tptp.'top$a'|) |tptp.'top$a'|) (= (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v1) |tptp.'top$a'|) |tptp.'top$b'|)) (= (|tptp.'fun_app$n'| (|tptp.'image$'| (|tptp.'comp$d'| A__questionmark_v1 A__questionmark_v0)) |tptp.'top$a'|) |tptp.'top$b'|))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2_b_ell2_fun$'|)) (=> (and (= (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) |tptp.'top$a'|) |tptp.'top$b'|) (= (|tptp.'image$f'| A__questionmark_v1 |tptp.'top$b'|) |tptp.'top$a'|)) (= (|tptp.'image$e'| (|tptp.'comp$f'| A__questionmark_v1 A__questionmark_v0) |tptp.'top$a'|) |tptp.'top$a'|))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|)) (=> (and (= (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) |tptp.'top$a'|) |tptp.'top$b'|) (= (|tptp.'image$d'| A__questionmark_v1 |tptp.'top$b'|) |tptp.'top$b'|)) (= (|tptp.'fun_app$n'| (|tptp.'image$'| (|tptp.'comp$c'| A__questionmark_v1 A__questionmark_v0)) |tptp.'top$a'|) |tptp.'top$b'|))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_b_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_b_ell2_fun$'|)) (=> (and (= (|tptp.'image$f'| A__questionmark_v0 |tptp.'top$b'|) |tptp.'top$a'|) (= (|tptp.'image$e'| A__questionmark_v1 |tptp.'top$a'|) |tptp.'top$a'|)) (= (|tptp.'image$f'| (|tptp.'comp$g'| A__questionmark_v1 A__questionmark_v0) |tptp.'top$b'|) |tptp.'top$a'|))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_b_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|)) (=> (and (= (|tptp.'image$f'| A__questionmark_v0 |tptp.'top$b'|) |tptp.'top$a'|) (= (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v1) |tptp.'top$a'|) |tptp.'top$b'|)) (= (|tptp.'image$d'| (|tptp.'comp$h'| A__questionmark_v1 A__questionmark_v0) |tptp.'top$b'|) |tptp.'top$b'|))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2_b_ell2_fun$'|)) (=> (and (= (|tptp.'image$d'| A__questionmark_v0 |tptp.'top$b'|) |tptp.'top$b'|) (= (|tptp.'image$f'| A__questionmark_v1 |tptp.'top$b'|) |tptp.'top$a'|)) (= (|tptp.'image$f'| (|tptp.'comp$i'| A__questionmark_v1 A__questionmark_v0) |tptp.'top$b'|) |tptp.'top$a'|))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|)) (=> (and (= (|tptp.'image$d'| A__questionmark_v0 |tptp.'top$b'|) |tptp.'top$b'|) (= (|tptp.'image$d'| A__questionmark_v1 |tptp.'top$b'|) |tptp.'top$b'|)) (= (|tptp.'image$d'| (|tptp.'comp$j'| A__questionmark_v1 A__questionmark_v0) |tptp.'top$b'|) |tptp.'top$b'|))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_nat_fun$'|)) (=> (and (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) |tptp.'top$'|) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v1) |tptp.'top$'|)) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| (|tptp.'comp$b'| A__questionmark_v0 A__questionmark_v1)) |tptp.'top$'|))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_nat_fun$'|)) (=> (and (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) |tptp.'top$'|) (|tptp.'inj_on$c'| A__questionmark_v1 |tptp.'top$a'|)) (|tptp.'inj_on$c'| (|tptp.'comp$k'| A__questionmark_v0 A__questionmark_v1) |tptp.'top$a'|))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2_nat_fun$'|)) (=> (and (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) |tptp.'top$'|) (|tptp.'fun_app$m'| (|tptp.'inj_on$d'| A__questionmark_v1) |tptp.'top$b'|)) (|tptp.'fun_app$m'| (|tptp.'inj_on$d'| (|tptp.'comp$l'| A__questionmark_v0 A__questionmark_v1)) |tptp.'top$b'|))) (forall ((A__questionmark_v0 |tptp.'B_ell2_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_b_ell2_fun$'|)) (=> (and (|tptp.'inj_on$c'| A__questionmark_v0 |tptp.'top$a'|) (|tptp.'fun_app$a'| (|tptp.'inj_on$j'| A__questionmark_v1) |tptp.'top$'|)) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| (|tptp.'comp$m'| A__questionmark_v0 A__questionmark_v1)) |tptp.'top$'|))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_b_ell2_fun$'|)) (=> (and (|tptp.'inj_on$a'| A__questionmark_v0 |tptp.'top$a'|) (|tptp.'inj_on$b'| A__questionmark_v1 |tptp.'top$a'|)) (|tptp.'inj_on$a'| (|tptp.'comp$d'| A__questionmark_v0 A__questionmark_v1) |tptp.'top$a'|))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2_b_ell2_fun$'|)) (=> (and (|tptp.'inj_on$a'| A__questionmark_v0 |tptp.'top$a'|) (|tptp.'fun_app$m'| (|tptp.'inj_on$i'| A__questionmark_v1) |tptp.'top$b'|)) (|tptp.'fun_app$m'| (|tptp.'inj_on$k'| (|tptp.'comp$h'| A__questionmark_v0 A__questionmark_v1)) |tptp.'top$b'|))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_a_b_prod_ell2_fun$'|)) (=> (and (|tptp.'fun_app$m'| (|tptp.'inj_on$d'| A__questionmark_v0) |tptp.'top$b'|) (|tptp.'fun_app$a'| (|tptp.'inj_on$l'| A__questionmark_v1) |tptp.'top$'|)) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| (|tptp.'comp$n'| A__questionmark_v0 A__questionmark_v1)) |tptp.'top$'|))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|)) (=> (and (|tptp.'fun_app$m'| (|tptp.'inj_on$k'| A__questionmark_v0) |tptp.'top$b'|) (|tptp.'inj_on$a'| A__questionmark_v1 |tptp.'top$a'|)) (|tptp.'inj_on$a'| (|tptp.'comp$c'| A__questionmark_v0 A__questionmark_v1) |tptp.'top$a'|))) (forall ((A__questionmark_v0 |tptp.'B_ell2_b_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'B_ell2_a_b_prod_ell2_fun$'|)) (=> (and (|tptp.'inj_on$b'| A__questionmark_v0 A__questionmark_v1) (|tptp.'inj_on$a'| A__questionmark_v2 (|tptp.'image$e'| A__questionmark_v0 A__questionmark_v1))) (|tptp.'inj_on$a'| (|tptp.'comp$d'| A__questionmark_v2 A__questionmark_v0) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|)) (=> (and (|tptp.'inj_on$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$m'| (|tptp.'inj_on$k'| A__questionmark_v2) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) A__questionmark_v1))) (|tptp.'inj_on$a'| (|tptp.'comp$c'| A__questionmark_v2 A__questionmark_v0) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_nat_fun$'|)) (=> (and (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v2) (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v0) A__questionmark_v1))) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| (|tptp.'comp$b'| A__questionmark_v2 A__questionmark_v0)) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v2 |tptp.'B_ell2_set$'|)) (=> (|tptp.'inj_on$a'| (|tptp.'comp$c'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$m'| (|tptp.'inj_on$k'| A__questionmark_v0) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v1) A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_b_ell2_fun$'|) (A__questionmark_v2 |tptp.'B_ell2_set$'|)) (=> (|tptp.'inj_on$a'| (|tptp.'comp$d'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'inj_on$a'| A__questionmark_v0 (|tptp.'image$e'| A__questionmark_v1 A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_nat_fun$'|) (A__questionmark_v2 |tptp.'Nat_set$'|)) (=> (|tptp.'fun_app$a'| (|tptp.'inj_on$'| (|tptp.'comp$b'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v1) A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_b_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'B_ell2_a_b_prod_ell2_fun$'|)) (=> (|tptp.'inj_on$b'| A__questionmark_v0 A__questionmark_v1) (= (|tptp.'inj_on$a'| A__questionmark_v2 (|tptp.'image$e'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'inj_on$a'| (|tptp.'comp$d'| A__questionmark_v2 A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|)) (=> (|tptp.'inj_on$a'| A__questionmark_v0 A__questionmark_v1) (= (|tptp.'fun_app$m'| (|tptp.'inj_on$k'| A__questionmark_v2) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'inj_on$a'| (|tptp.'comp$c'| A__questionmark_v2 A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_nat_fun$'|)) (=> (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) A__questionmark_v1) (= (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v2) (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| (|tptp.'comp$b'| A__questionmark_v2 A__questionmark_v0)) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2_set$'|) (A__questionmark_v2 |tptp.'B_ell2$'|)) (=> (|tptp.'fun_app$m'| (|tptp.'less_eq$b'| (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) |tptp.'top$a'|)) A__questionmark_v1) (|tptp.'fun_app$m'| (|tptp.'member$a'| (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v2)) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'B_ell2_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'B_ell2$'|)) (=> (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| (|tptp.'image$b'| A__questionmark_v0 |tptp.'top$a'|)) A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'member$'| (|tptp.'fun_app$q'| A__questionmark_v0 A__questionmark_v2)) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'A_b_prod_ell2$'|)) (=> (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| (|tptp.'image$c'| A__questionmark_v0 |tptp.'top$b'|)) A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'member$'| (|tptp.'fun_app$r'| A__questionmark_v0 A__questionmark_v2)) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'B_ell2_set$'|) (A__questionmark_v3 |tptp.'B_ell2_set$'|)) (let ((_let_1 (|tptp.'image$'| A__questionmark_v0))) (=> (and (|tptp.'inj_on$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'less_eq$'| A__questionmark_v2 A__questionmark_v1) (|tptp.'less_eq$'| A__questionmark_v3 A__questionmark_v1)) (= (= (|tptp.'fun_app$n'| _let_1 A__questionmark_v2) (|tptp.'fun_app$n'| _let_1 A__questionmark_v3)) (= A__questionmark_v2 A__questionmark_v3))))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_set$'|) (A__questionmark_v3 |tptp.'Nat_set$'|)) (let ((_let_1 (|tptp.'image$a'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| A__questionmark_v2) A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| A__questionmark_v3) A__questionmark_v1)) (= (= (|tptp.'fun_app$o'| _let_1 A__questionmark_v2) (|tptp.'fun_app$o'| _let_1 A__questionmark_v3)) (= A__questionmark_v2 A__questionmark_v3))))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'B_ell2$'|) (A__questionmark_v3 |tptp.'B_ell2_set$'|)) (=> (and (|tptp.'inj_on$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'member$b'| A__questionmark_v2 A__questionmark_v1) (|tptp.'less_eq$'| A__questionmark_v3 A__questionmark_v1)) (= (|tptp.'fun_app$m'| (|tptp.'member$a'| (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v2)) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) A__questionmark_v3)) (|tptp.'member$b'| A__questionmark_v2 A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat_set$'|)) (let ((_let_1 (|tptp.'member$'| A__questionmark_v2))) (=> (and (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$a'| _let_1 A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| A__questionmark_v3) A__questionmark_v1)) (= (|tptp.'fun_app$a'| (|tptp.'member$'| (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v2)) (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v0) A__questionmark_v3)) (|tptp.'fun_app$a'| _let_1 A__questionmark_v3))))) (forall ((A__questionmark_v0 |tptp.'B_ell2$'|)) (|tptp.'inj_on$b'| (|tptp.'uup$'| A__questionmark_v0) |tptp.'top$a'|)) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2$'|)) (|tptp.'fun_app$m'| (|tptp.'inj_on$k'| (|tptp.'uuq$'| A__questionmark_v0)) |tptp.'top$b'|)) (forall ((A__questionmark_v0 Int)) (|tptp.'inj_on$m'| (|tptp.'uur$'| A__questionmark_v0) |tptp.'top$g'|)) (= |tptp.'zero$'| |tptp.'zero$'|) (forall ((A__questionmark_v0 |tptp.'B_ell2$'|)) (= (|tptp.'image$e'| (|tptp.'minus$a'| A__questionmark_v0) |tptp.'top$a'|) |tptp.'top$a'|)) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2$'|)) (= (|tptp.'image$d'| (|tptp.'minus$'| A__questionmark_v0) |tptp.'top$b'|) |tptp.'top$b'|)) (forall ((A__questionmark_v0 Int)) (= (|tptp.'image$g'| (|tptp.'uuo$'| A__questionmark_v0) |tptp.'top$g'|) |tptp.'top$g'|)) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_nat_fun$'|)) (=> (and (= (|tptp.'image$b'| (|tptp.'comp$k'| A__questionmark_v0 A__questionmark_v1) |tptp.'top$a'|) |tptp.'top$'|) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) |tptp.'top$'|)) (= (|tptp.'image$b'| A__questionmark_v1 |tptp.'top$a'|) |tptp.'top$'|))) (forall ((A__questionmark_v0 |tptp.'B_ell2_b_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_b_ell2_fun$'|)) (=> (and (= (|tptp.'image$e'| (|tptp.'comp$e'| A__questionmark_v0 A__questionmark_v1) |tptp.'top$a'|) |tptp.'top$a'|) (|tptp.'inj_on$b'| A__questionmark_v0 |tptp.'top$a'|)) (= (|tptp.'image$e'| A__questionmark_v1 |tptp.'top$a'|) |tptp.'top$a'|))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_b_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|)) (=> (and (= (|tptp.'image$e'| (|tptp.'comp$f'| A__questionmark_v0 A__questionmark_v1) |tptp.'top$a'|) |tptp.'top$a'|) (|tptp.'fun_app$m'| (|tptp.'inj_on$i'| A__questionmark_v0) |tptp.'top$b'|)) (= (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v1) |tptp.'top$a'|) |tptp.'top$b'|))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_b_ell2_fun$'|)) (=> (and (= (|tptp.'fun_app$n'| (|tptp.'image$'| (|tptp.'comp$d'| A__questionmark_v0 A__questionmark_v1)) |tptp.'top$a'|) |tptp.'top$b'|) (|tptp.'inj_on$a'| A__questionmark_v0 |tptp.'top$a'|)) (= (|tptp.'image$e'| A__questionmark_v1 |tptp.'top$a'|) |tptp.'top$a'|))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|)) (=> (and (= (|tptp.'fun_app$n'| (|tptp.'image$'| (|tptp.'comp$c'| A__questionmark_v0 A__questionmark_v1)) |tptp.'top$a'|) |tptp.'top$b'|) (|tptp.'fun_app$m'| (|tptp.'inj_on$k'| A__questionmark_v0) |tptp.'top$b'|)) (= (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v1) |tptp.'top$a'|) |tptp.'top$b'|))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2_nat_fun$'|)) (=> (and (= (|tptp.'image$c'| (|tptp.'comp$l'| A__questionmark_v0 A__questionmark_v1) |tptp.'top$b'|) |tptp.'top$'|) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) |tptp.'top$'|)) (= (|tptp.'image$c'| A__questionmark_v1 |tptp.'top$b'|) |tptp.'top$'|))) (forall ((A__questionmark_v0 |tptp.'B_ell2_b_ell2_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2_b_ell2_fun$'|)) (=> (and (= (|tptp.'image$f'| (|tptp.'comp$g'| A__questionmark_v0 A__questionmark_v1) |tptp.'top$b'|) |tptp.'top$a'|) (|tptp.'inj_on$b'| A__questionmark_v0 |tptp.'top$a'|)) (= (|tptp.'image$f'| A__questionmark_v1 |tptp.'top$b'|) |tptp.'top$a'|))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_b_ell2_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|)) (=> (and (= (|tptp.'image$f'| (|tptp.'comp$i'| A__questionmark_v0 A__questionmark_v1) |tptp.'top$b'|) |tptp.'top$a'|) (|tptp.'fun_app$m'| (|tptp.'inj_on$i'| A__questionmark_v0) |tptp.'top$b'|)) (= (|tptp.'image$d'| A__questionmark_v1 |tptp.'top$b'|) |tptp.'top$b'|))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2_b_ell2_fun$'|)) (=> (and (= (|tptp.'image$d'| (|tptp.'comp$h'| A__questionmark_v0 A__questionmark_v1) |tptp.'top$b'|) |tptp.'top$b'|) (|tptp.'inj_on$a'| A__questionmark_v0 |tptp.'top$a'|)) (= (|tptp.'image$f'| A__questionmark_v1 |tptp.'top$b'|) |tptp.'top$a'|))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|)) (=> (and (= (|tptp.'image$d'| (|tptp.'comp$j'| A__questionmark_v0 A__questionmark_v1) |tptp.'top$b'|) |tptp.'top$b'|) (|tptp.'fun_app$m'| (|tptp.'inj_on$k'| A__questionmark_v0) |tptp.'top$b'|)) (= (|tptp.'image$d'| A__questionmark_v1 |tptp.'top$b'|) |tptp.'top$b'|))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_set$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v2 |tptp.'B_ell2_set$'|)) (= (|tptp.'fun_app$m'| (|tptp.'less_eq$b'| A__questionmark_v0) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v1) A__questionmark_v2)) (exists ((A__questionmark_v3 |tptp.'B_ell2_set$'|)) (and (|tptp.'less_eq$'| A__questionmark_v3 A__questionmark_v2) (|tptp.'inj_on$a'| A__questionmark_v1 A__questionmark_v3) (= A__questionmark_v0 (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v1) A__questionmark_v3)))))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|) (A__questionmark_v1 |tptp.'Nat_nat_fun$'|) (A__questionmark_v2 |tptp.'Nat_set$'|)) (= (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| A__questionmark_v0) (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v1) A__questionmark_v2)) (exists ((A__questionmark_v3 |tptp.'Nat_set$'|)) (and (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| A__questionmark_v3) A__questionmark_v2) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v1) A__questionmark_v3) (= A__questionmark_v0 (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v1) A__questionmark_v3)))))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'A_b_prod_ell2_set_bool_fun$'|)) (= (exists ((A__questionmark_v3 |tptp.'A_b_prod_ell2_set$'|)) (and (|tptp.'fun_app$m'| (|tptp.'less_eq$b'| A__questionmark_v3) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$m'| A__questionmark_v2 A__questionmark_v3))) (exists ((A__questionmark_v3 |tptp.'B_ell2_set$'|)) (and (|tptp.'less_eq$'| A__questionmark_v3 A__questionmark_v1) (|tptp.'inj_on$a'| A__questionmark_v0 A__questionmark_v3) (|tptp.'fun_app$m'| A__questionmark_v2 (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) A__questionmark_v3)))))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_set_bool_fun$'|)) (= (exists ((A__questionmark_v3 |tptp.'Nat_set$'|)) (and (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| A__questionmark_v3) (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$a'| A__questionmark_v2 A__questionmark_v3))) (exists ((A__questionmark_v3 |tptp.'Nat_set$'|)) (and (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| A__questionmark_v3) A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) A__questionmark_v3) (|tptp.'fun_app$a'| A__questionmark_v2 (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v0) A__questionmark_v3)))))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'A_b_prod_ell2_set_bool_fun$'|)) (= (forall ((A__questionmark_v3 |tptp.'A_b_prod_ell2_set$'|)) (=> (|tptp.'fun_app$m'| (|tptp.'less_eq$b'| A__questionmark_v3) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$m'| A__questionmark_v2 A__questionmark_v3))) (forall ((A__questionmark_v3 |tptp.'B_ell2_set$'|)) (=> (and (|tptp.'less_eq$'| A__questionmark_v3 A__questionmark_v1) (|tptp.'inj_on$a'| A__questionmark_v0 A__questionmark_v3)) (|tptp.'fun_app$m'| A__questionmark_v2 (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) A__questionmark_v3)))))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_set_bool_fun$'|)) (= (forall ((A__questionmark_v3 |tptp.'Nat_set$'|)) (=> (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| A__questionmark_v3) (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$a'| A__questionmark_v2 A__questionmark_v3))) (forall ((A__questionmark_v3 |tptp.'Nat_set$'|)) (=> (and (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| A__questionmark_v3) A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) A__questionmark_v3)) (|tptp.'fun_app$a'| A__questionmark_v2 (|tptp.'fun_app$o'| (|tptp.'image$a'| A__questionmark_v0) A__questionmark_v3)))))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|) (A__questionmark_v1 |tptp.'Nat_set$'|)) (= (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'less_eq$e'| (|tptp.'uug$'| A__questionmark_v0) (|tptp.'uug$'| A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|) (A__questionmark_v1 |tptp.'Nat_set$'|)) (= (|tptp.'less_eq$e'| (|tptp.'uug$'| A__questionmark_v0) (|tptp.'uug$'| A__questionmark_v1)) (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| A__questionmark_v0) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|) (A__questionmark_v1 |tptp.'Nat_set$'|)) (= (|tptp.'minus$b'| A__questionmark_v0 A__questionmark_v1) (|tptp.'collect$b'| (|tptp.'minus$g'| (|tptp.'uug$'| A__questionmark_v0) (|tptp.'uug$'| A__questionmark_v1))))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|) (A__questionmark_v1 |tptp.'Nat_bool_fun$'|)) (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| (|tptp.'collect$b'| (|tptp.'uut$'| A__questionmark_v0 A__questionmark_v1))) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_set$'|) (A__questionmark_v3 |tptp.'Nat_bool_fun$'|)) (=> (and (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| A__questionmark_v1) (|tptp.'collect$b'| (|tptp.'uut$'| A__questionmark_v2 A__questionmark_v3)))) (|tptp.'fun_app$b'| A__questionmark_v3 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'B_ell2_bool_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v2 |tptp.'A_b_prod_ell2_set$'|)) (=> (forall ((A__questionmark_v3 |tptp.'B_ell2$'|)) (=> (|tptp.'fun_app$p'| A__questionmark_v0 A__questionmark_v3) (|tptp.'fun_app$m'| (|tptp.'member$a'| (|tptp.'fun_app$e'| A__questionmark_v1 A__questionmark_v3)) A__questionmark_v2))) (|tptp.'fun_app$m'| (|tptp.'less_eq$b'| (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v1) (|tptp.'collect$'| A__questionmark_v0))) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_a_b_prod_ell2_fun$'|)) (= (|tptp.'fun_app$n'| (|tptp.'image$'| (|tptp.'comp$c'| A__questionmark_v0 A__questionmark_v1)) |tptp.'top$a'|) (|tptp.'image$d'| A__questionmark_v0 (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v1) |tptp.'top$a'|)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_b_ell2_fun$'|)) (= (|tptp.'fun_app$n'| (|tptp.'image$'| (|tptp.'comp$d'| A__questionmark_v0 A__questionmark_v1)) |tptp.'top$a'|) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) (|tptp.'image$e'| A__questionmark_v1 |tptp.'top$a'|)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2_b_ell2_fun$'|)) (= (|tptp.'image$d'| (|tptp.'comp$h'| A__questionmark_v0 A__questionmark_v1) |tptp.'top$b'|) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) (|tptp.'image$f'| A__questionmark_v1 |tptp.'top$b'|)))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (<= A__questionmark_v0 A__questionmark_v1) (<= 0 (- A__questionmark_v1 A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'A_b_prod_ell2_set_bool_fun$'|)) (= (forall ((A__questionmark_v3 |tptp.'A_b_prod_ell2_set$'|)) (=> (|tptp.'fun_app$m'| (|tptp.'less_eq$b'| A__questionmark_v3) (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$m'| A__questionmark_v2 A__questionmark_v3))) (forall ((A__questionmark_v3 |tptp.'B_ell2_set$'|)) (=> (|tptp.'less_eq$'| A__questionmark_v3 A__questionmark_v1) (|tptp.'fun_app$m'| A__questionmark_v2 (|tptp.'fun_app$n'| (|tptp.'image$'| A__questionmark_v0) A__questionmark_v3)))))) (|tptp.'fun_app$w'| _let_5 |tptp.'zero$e'|) (<= 0 0) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| |tptp.'to_nat$'|) |tptp.'top$'|) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_bool_fun$'|) (A__questionmark_v3 |tptp.'Nat_bool_fun$'|)) (=> (and (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| A__questionmark_v0) A__questionmark_v1) (forall ((A__questionmark_v4 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v4) A__questionmark_v0) (|tptp.'fun_app$b'| A__questionmark_v2 A__questionmark_v4)) (|tptp.'fun_app$b'| A__questionmark_v3 A__questionmark_v4)))) (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| (|tptp.'collect$b'| (|tptp.'uut$'| A__questionmark_v0 A__questionmark_v2))) (|tptp.'collect$b'| (|tptp.'uut$'| A__questionmark_v1 A__questionmark_v3))))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_bool_fun$'|)) (let ((_let_1 (|tptp.'less_eq$a'| A__questionmark_v0))) (=> (|tptp.'fun_app$a'| _let_1 A__questionmark_v1) (= (|tptp.'fun_app$a'| _let_1 (|tptp.'collect$b'| (|tptp.'uut$'| A__questionmark_v1 A__questionmark_v2))) (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v3) A__questionmark_v0) (|tptp.'fun_app$b'| A__questionmark_v2 A__questionmark_v3))))))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|)) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| |tptp.'to_nat$'|) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|)) (let ((_let_1 (|tptp.'image$a'| A__questionmark_v0))) (=> (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) |tptp.'top$'|) (|tptp.'fun_app$a'| (|tptp.'less_eq$a'| (|tptp.'fun_app$o'| _let_1 (|tptp.'uminus$'| A__questionmark_v1))) (|tptp.'uminus$'| (|tptp.'fun_app$o'| _let_1 A__questionmark_v1)))))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|)) (let ((_let_1 (|tptp.'image$'| A__questionmark_v0))) (=> (|tptp.'inj_on$a'| A__questionmark_v0 |tptp.'top$a'|) (|tptp.'fun_app$m'| (|tptp.'less_eq$b'| (|tptp.'fun_app$n'| _let_1 (|tptp.'uminus$a'| A__questionmark_v1))) (|tptp.'uminus$b'| (|tptp.'fun_app$n'| _let_1 A__questionmark_v1)))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat_set$'|)) (let ((_let_1 (|tptp.'member$'| A__questionmark_v0))) (= (|tptp.'fun_app$a'| _let_1 (|tptp.'uminus$'| A__questionmark_v1)) (not (|tptp.'fun_app$a'| _let_1 A__questionmark_v1))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat_set$'|)) (let ((_let_1 (|tptp.'member$'| A__questionmark_v0))) (=> (=> (|tptp.'fun_app$a'| _let_1 A__questionmark_v1) false) (|tptp.'fun_app$a'| _let_1 (|tptp.'uminus$'| A__questionmark_v1))))) _let_10 _let_9 _let_10 _let_9 (forall ((A__questionmark_v0 |tptp.'A_ell2$'|)) (= (= |tptp.'zero$'| (|tptp.'uminus$c'| A__questionmark_v0)) (= |tptp.'zero$'| A__questionmark_v0))) (forall ((A__questionmark_v0 Int)) (= (= 0 (- A__questionmark_v0)) (= 0 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_ell2$'|)) (= (= (|tptp.'uminus$c'| A__questionmark_v0) |tptp.'zero$'|) (= A__questionmark_v0 |tptp.'zero$'|))) (forall ((A__questionmark_v0 Int)) (= (= (- A__questionmark_v0) 0) (= A__questionmark_v0 0))) (forall ((A__questionmark_v0 Int)) (= (= A__questionmark_v0 (- A__questionmark_v0)) (= A__questionmark_v0 0))) (forall ((A__questionmark_v0 Int)) (= (= (- A__questionmark_v0) A__questionmark_v0) (= A__questionmark_v0 0))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (<= (- A__questionmark_v0) (- A__questionmark_v1)) (<= A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (- (- A__questionmark_v0 A__questionmark_v1)) (- A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 Int)) (= (<= 0 (- A__questionmark_v0)) (<= A__questionmark_v0 0))) (forall ((A__questionmark_v0 Int)) (= (<= (- A__questionmark_v0) 0) (<= 0 A__questionmark_v0))) (forall ((A__questionmark_v0 Int)) (= (<= A__questionmark_v0 (- A__questionmark_v0)) (<= A__questionmark_v0 0))) (forall ((A__questionmark_v0 Int)) (= (<= (- A__questionmark_v0) A__questionmark_v0) (<= 0 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_ell2$'|)) (=> (|tptp.'member$c'| A__questionmark_v0 |tptp.'top$e'|) (= (= (|tptp.'uminus$c'| A__questionmark_v0) |tptp.'zero$'|) (= A__questionmark_v0 |tptp.'zero$'|)))) (forall ((A__questionmark_v0 Int)) (=> (|tptp.'member$e'| A__questionmark_v0 |tptp.'top$g'|) (= (= (- A__questionmark_v0) 0) (= A__questionmark_v0 0)))) (forall ((A__questionmark_v0 |tptp.'A_ell2$'|)) (= (|tptp.'fun_app$y'| (|tptp.'minus$e'| |tptp.'zero$'|) A__questionmark_v0) (|tptp.'uminus$c'| A__questionmark_v0))) (forall ((A__questionmark_v0 Int)) (= (- 0 A__questionmark_v0) (- A__questionmark_v0))) _let_10 _let_9 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat_set$'|)) (let ((_let_1 (|tptp.'member$'| A__questionmark_v0))) (=> (|tptp.'fun_app$a'| _let_1 (|tptp.'uminus$'| A__questionmark_v1)) (not (|tptp.'fun_app$a'| _let_1 A__questionmark_v1))))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|)) (= (|tptp.'uminus$'| A__questionmark_v0) (|tptp.'collect$b'| (|tptp.'uuu$'| A__questionmark_v0)))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (- (- A__questionmark_v0) A__questionmark_v1) (- (- A__questionmark_v1) A__questionmark_v0))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (<= A__questionmark_v0 A__questionmark_v1) (<= (- A__questionmark_v1) (- A__questionmark_v0)))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (<= (- A__questionmark_v0) A__questionmark_v1) (<= (- A__questionmark_v1) A__questionmark_v0))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (<= A__questionmark_v0 (- A__questionmark_v1)) (<= A__questionmark_v1 (- A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_ell2$'|)) (=> (and (|tptp.'member$c'| A__questionmark_v0 |tptp.'top$e'|) (not (= A__questionmark_v0 |tptp.'zero$'|))) (not (= (|tptp.'uminus$c'| A__questionmark_v0) |tptp.'zero$'|)))) (forall ((A__questionmark_v0 Int)) (=> (and (|tptp.'member$e'| A__questionmark_v0 |tptp.'top$g'|) (not (= A__questionmark_v0 0))) (not (= (- A__questionmark_v0) 0)))) (forall ((A__questionmark_v0 |tptp.'B_ell2_set$'|)) (= (|tptp.'uminus$a'| A__questionmark_v0) (|tptp.'minus$c'| |tptp.'top$a'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_set$'|)) (= (|tptp.'uminus$b'| A__questionmark_v0) (|tptp.'minus$d'| |tptp.'top$b'| A__questionmark_v0))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 |tptp.'Int_set$'|)) (let ((_let_1 (|tptp.'uur$'| A__questionmark_v0))) (= (|tptp.'image$g'| _let_1 (|tptp.'uminus$d'| A__questionmark_v1)) (|tptp.'uminus$d'| (|tptp.'image$g'| _let_1 A__questionmark_v1))))) (forall ((A__questionmark_v0 |tptp.'B_ell2_b_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|)) (=> (= (|tptp.'image$e'| A__questionmark_v0 |tptp.'top$a'|) |tptp.'top$a'|) (|tptp.'less_eq$'| (|tptp.'uminus$a'| (|tptp.'image$e'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'image$e'| A__questionmark_v0 (|tptp.'uminus$a'| A__questionmark_v1))))) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|)) (let ((_let_1 (|tptp.'image$'| A__questionmark_v0))) (=> (= (|tptp.'fun_app$n'| _let_1 |tptp.'top$a'|) |tptp.'top$b'|) (|tptp.'fun_app$m'| (|tptp.'less_eq$b'| (|tptp.'uminus$b'| (|tptp.'fun_app$n'| _let_1 A__questionmark_v1))) (|tptp.'fun_app$n'| _let_1 (|tptp.'uminus$a'| A__questionmark_v1)))))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_b_ell2_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2_set$'|)) (=> (= (|tptp.'image$f'| A__questionmark_v0 |tptp.'top$b'|) |tptp.'top$a'|) (|tptp.'less_eq$'| (|tptp.'uminus$a'| (|tptp.'image$f'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'image$f'| A__questionmark_v0 (|tptp.'uminus$b'| A__questionmark_v1))))) (forall ((A__questionmark_v0 |tptp.'A_b_prod_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'A_b_prod_ell2_set$'|)) (=> (= (|tptp.'image$d'| A__questionmark_v0 |tptp.'top$b'|) |tptp.'top$b'|) (|tptp.'fun_app$m'| (|tptp.'less_eq$b'| (|tptp.'uminus$b'| (|tptp.'image$d'| A__questionmark_v0 A__questionmark_v1))) (|tptp.'image$d'| A__questionmark_v0 (|tptp.'uminus$b'| A__questionmark_v1))))) (forall ((A__questionmark_v0 |tptp.'A_ell2$'|)) (= (|tptp.'fun_app$y'| (|tptp.'minus$e'| |tptp.'zero$'|) A__questionmark_v0) (|tptp.'uminus$c'| A__questionmark_v0))) (forall ((A__questionmark_v0 Int)) (= (- 0 A__questionmark_v0) (- A__questionmark_v0))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (- (- A__questionmark_v0) (- A__questionmark_v1)) (- (- A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|)) (= (|tptp.'uminus$'| A__questionmark_v0) (|tptp.'collect$b'| (|tptp.'uminus$e'| (|tptp.'uug$'| A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (or (= A__questionmark_v0 A__questionmark_v1) (not (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v1)) (not (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v1) A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat$'|)) (or (= A__questionmark_v0 A__questionmark_v1) (not (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) A__questionmark_v1)) (not (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v1) A__questionmark_v0)))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (or (= A__questionmark_v0 A__questionmark_v1) (not (<= A__questionmark_v0 A__questionmark_v1)) (not (<= A__questionmark_v1 A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'Enat$'|)) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) A__questionmark_v0)) (forall ((A__questionmark_v0 Int)) (<= A__questionmark_v0 A__questionmark_v0)) (= (|tptp.'fun_app$y'| (|tptp.'minus$e'| _let_2) _let_2) |tptp.'zero$'|) (= (- (- 1) (- 1)) 0) (= |tptp.'to_nat$'| (|tptp.'eps$'| |tptp.'uuv$'|)) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|)) (=> (|tptp.'inj_on$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'inj_on$n'| (|tptp.'image$'| A__questionmark_v0) (|tptp.'fpow$'| A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat_set$'|)) (=> (|tptp.'fun_app$a'| (|tptp.'inj_on$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'inj_on$o'| (|tptp.'image$a'| A__questionmark_v0) (|tptp.'fpow$a'| A__questionmark_v1)))) (|tptp.'fun_app$a'| (|tptp.'member$'| |tptp.'one$a'|) |tptp.'top$'|) _let_8 (= (|tptp.'fun_app$y'| (|tptp.'minus$e'| |tptp.'one$'|) |tptp.'one$'|) |tptp.'zero$'|) (= (- 1 1) 0) (not (= 1 (- 1))) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|) (A__questionmark_v1 |tptp.'Nat_bool_fun$'|) (A__questionmark_v2 |tptp.'Nat_bool_fun$'|)) (=> (and (exists ((A__questionmark_v3 |tptp.'Nat$'|)) (and (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v3) A__questionmark_v0) (|tptp.'fun_app$b'| A__questionmark_v1 A__questionmark_v3))) (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v3) A__questionmark_v0) (|tptp.'fun_app$b'| A__questionmark_v1 A__questionmark_v3)) (|tptp.'fun_app$b'| A__questionmark_v2 A__questionmark_v3)))) (|tptp.'fun_app$b'| A__questionmark_v2 (|tptp.'eps$a'| (|tptp.'uut$'| A__questionmark_v0 A__questionmark_v1))))) (forall ((A__questionmark_v0 Int)) (= (= 1 A__questionmark_v0) (= A__questionmark_v0 1))) _let_3 (|tptp.'fun_app$w'| _let_7 |tptp.'one$b'|) (<= 1 1) _let_8 _let_8 (not (= _let_2 |tptp.'zero$'|)) (not (= |tptp.'zero$'| _let_2)) (not (= 0 (- 1))) (<= (- 1) 1) (not (<= 1 (- 1))) (not (<= 0 (- 1))) (<= (- 1) 0) (forall ((A__questionmark_v0 |tptp.'B_ell2_a_b_prod_ell2_fun$'|) (A__questionmark_v1 |tptp.'B_ell2_set$'|) (A__questionmark_v2 |tptp.'A_b_prod_ell2_set$'|)) (let ((_let_1 (|tptp.'image$'| A__questionmark_v0))) (=> (|tptp.'fun_app$m'| (|tptp.'less_eq$b'| (|tptp.'fun_app$n'| _let_1 A__questionmark_v1)) A__questionmark_v2) (|tptp.'less_eq$f'| (|tptp.'image$h'| _let_1 (|tptp.'fpow$'| A__questionmark_v1)) (|tptp.'fpow$b'| A__questionmark_v2))))) (not (|tptp.'fun_app$w'| _let_7 |tptp.'zero$e'|)) (not (<= 1 0)) _let_6 _let_4 _let_6 _let_4 _let_3 (not (= |tptp.'zero$e'| |tptp.'one$b'|)) (not (= 0 1)) (= (|tptp.'dbl_dec$'| |tptp.'zero$'|) _let_2) (= (|tptp.'fun_app$h'| |tptp.'dbl_dec$a'| 0) (- 1)) (= (|tptp.'fun_app$h'| |tptp.'dbl_dec$a'| 1) 1) (= (|tptp.'fun_app$h'| |tptp.'dbl_inc$'| (- 1)) (- 1)) (= (|tptp.'dbl_inc$a'| |tptp.'zero$'|) |tptp.'one$'|) (= (|tptp.'fun_app$h'| |tptp.'dbl_inc$'| 0) 1) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (let ((_let_1 (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0))) (= (|tptp.'fun_app$h'| |tptp.'dbl_dec$a'| (- _let_1)) (- (|tptp.'fun_app$h'| |tptp.'dbl_inc$'| _let_1))))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (let ((_let_1 (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0))) (= (|tptp.'fun_app$h'| |tptp.'dbl_inc$'| (- _let_1)) (- (|tptp.'fun_app$h'| |tptp.'dbl_dec$a'| _let_1))))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (= (= (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0) (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v1)) (= A__questionmark_v0 A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (= (= (|tptp.'fun_app$aa'| |tptp.'numeral$a'| A__questionmark_v0) (|tptp.'fun_app$aa'| |tptp.'numeral$a'| A__questionmark_v1)) (= A__questionmark_v0 A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (= (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| (|tptp.'fun_app$aa'| |tptp.'numeral$a'| A__questionmark_v0)) (|tptp.'fun_app$aa'| |tptp.'numeral$a'| A__questionmark_v1)) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (= (<= (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0) (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v1)) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (= (= (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0)) (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v1))) (= A__questionmark_v0 A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (= (<= (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0)) (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v1))) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v1) A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (not (= (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0) (- 1)))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (not (= 1 (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (not (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| (|tptp.'fun_app$aa'| |tptp.'numeral$a'| A__questionmark_v0)) |tptp.'zero$e'|))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (not (<= (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0) 0))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| |tptp.'zero$e'|) (|tptp.'fun_app$aa'| |tptp.'numeral$a'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (<= 0 (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (not (= |tptp.'zero$'| (|tptp.'numeral$b'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (not (= 0 (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (not (= |tptp.'zero$e'| (|tptp.'fun_app$aa'| |tptp.'numeral$a'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (not (= (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0)) (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (not (= (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0) (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v1))))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (<= (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0)) (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (not (<= (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0) (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v1))))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (not (= |tptp.'zero$'| (|tptp.'uminus$c'| (|tptp.'numeral$b'| A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (not (= 0 (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| |tptp.'one$b'|) (|tptp.'fun_app$aa'| |tptp.'numeral$a'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (<= 1 (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (not (<= 0 (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (<= (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0)) 0)) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (not (<= 1 (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (not (<= (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0) (- 1)))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (<= (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0)) (- 1))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (<= (- 1) (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (<= (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0)) 1)) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (- (- 1) (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0)) (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| (|tptp.'fun_app$z'| |tptp.'inc$'| A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0) (- 1)) (|tptp.'fun_app$ab'| |tptp.'numeral$'| (|tptp.'fun_app$z'| |tptp.'inc$'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (let ((_let_1 (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0))) (= (|tptp.'fun_app$h'| |tptp.'dbl$'| (- _let_1)) (- (|tptp.'fun_app$h'| |tptp.'dbl$'| _let_1))))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| (|tptp.'fun_app$aa'| |tptp.'numeral$a'| A__questionmark_v0)) |tptp.'one$b'|) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) |tptp.'one$c'|))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (<= (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0) 1) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) |tptp.'one$c'|))) (= (|tptp.'dbl$a'| |tptp.'zero$'|) |tptp.'zero$'|) (= (|tptp.'fun_app$h'| |tptp.'dbl$'| 0) 0) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (= 1 (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0)) (= |tptp.'one$c'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (= |tptp.'one$b'| (|tptp.'fun_app$aa'| |tptp.'numeral$a'| A__questionmark_v0)) (= |tptp.'one$c'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (= (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0) 1) (= A__questionmark_v0 |tptp.'one$c'|))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (= (|tptp.'fun_app$aa'| |tptp.'numeral$a'| A__questionmark_v0) |tptp.'one$b'|) (= A__questionmark_v0 |tptp.'one$c'|))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (= (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0)) (- 1)) (= A__questionmark_v0 |tptp.'one$c'|))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (= (- 1) (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0))) (= A__questionmark_v0 |tptp.'one$c'|))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (not (<= (- 1) (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0)))) (not (= A__questionmark_v0 |tptp.'one$c'|)))) (forall ((A__questionmark_v0 |tptp.'Num_bool_fun$'|) (A__questionmark_v1 |tptp.'Num$'|)) (=> (and (|tptp.'fun_app$u'| A__questionmark_v0 |tptp.'one$c'|) (forall ((A__questionmark_v2 |tptp.'Num$'|)) (=> (|tptp.'fun_app$u'| A__questionmark_v0 A__questionmark_v2) (|tptp.'fun_app$u'| A__questionmark_v0 (|tptp.'fun_app$z'| |tptp.'inc$'| A__questionmark_v2))))) (|tptp.'fun_app$u'| A__questionmark_v0 A__questionmark_v1))) _let_1 _let_1 (= (|tptp.'fun_app$aa'| |tptp.'numeral$a'| |tptp.'one$c'|) |tptp.'one$b'|) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) |tptp.'one$c'|) (= A__questionmark_v0 |tptp.'one$c'|))) (= (- 1) (- 1)) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| |tptp.'one$c'|) A__questionmark_v0) true)) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (- (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0)) (- 1)) (|tptp.'fun_app$ab'| (|tptp.'sub$'| |tptp.'one$c'|) A__questionmark_v0))) (= (|tptp.'sub$a'| |tptp.'one$c'| |tptp.'one$c'|) |tptp.'zero$'|) (= (|tptp.'fun_app$ab'| (|tptp.'sub$'| |tptp.'one$c'|) |tptp.'one$c'|) 0) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (= (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0) (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v1)) (|tptp.'fun_app$ab'| (|tptp.'sub$'| A__questionmark_v0) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (= (- (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0)) (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v1))) (|tptp.'fun_app$ab'| (|tptp.'sub$'| A__questionmark_v1) A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (- 1 (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0)) (|tptp.'fun_app$ab'| (|tptp.'sub$'| |tptp.'one$c'|) A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0) 1) (|tptp.'fun_app$ab'| (|tptp.'sub$'| A__questionmark_v0) |tptp.'one$c'|))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (- (- (|tptp.'fun_app$ab'| (|tptp.'sub$'| A__questionmark_v0) |tptp.'one$c'|)) 1) (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (- (- 1) (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0))) (|tptp.'fun_app$ab'| (|tptp.'sub$'| A__questionmark_v0) |tptp.'one$c'|))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (= (|tptp.'fun_app$ab'| (|tptp.'sub$'| A__questionmark_v0) A__questionmark_v1) (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0) (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (= (<= 0 (|tptp.'fun_app$ab'| (|tptp.'sub$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v1) A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (= (<= (|tptp.'fun_app$ab'| (|tptp.'sub$'| A__questionmark_v0) A__questionmark_v1) 0) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (|tptp.'fun_app$ab'| (|tptp.'sub$'| (|tptp.'fun_app$z'| |tptp.'inc$'| A__questionmark_v0)) |tptp.'one$c'|) (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (= (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| (|tptp.'fun_app$aa'| |tptp.'numeral$a'| A__questionmark_v0)) (|tptp.'fun_app$aa'| |tptp.'numeral$a'| A__questionmark_v1)) (<= (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0) (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v1)))) (= (|tptp.'fun_app$h'| |tptp.'dbl$'| (- 1)) (- 2)) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (= (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| (|tptp.'fun_app$z'| |tptp.'bit0$'| A__questionmark_v0)) (|tptp.'fun_app$z'| |tptp.'bit0$'| A__questionmark_v1)) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| (|tptp.'fun_app$z'| |tptp.'bit0$'| A__questionmark_v0)) |tptp.'one$c'|) false)) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (|tptp.'fun_app$h'| |tptp.'dbl$'| (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0)) (|tptp.'fun_app$ab'| |tptp.'numeral$'| (|tptp.'fun_app$z'| |tptp.'bit0$'| A__questionmark_v0)))) (= (|tptp.'fun_app$h'| |tptp.'dbl$'| 1) 2) (= (- 1 (- 1)) 2) (= (- (- 1) 1) (- 2)) (= (|tptp.'fun_app$z'| |tptp.'inc$'| |tptp.'one$c'|) (|tptp.'fun_app$z'| |tptp.'bit0$'| |tptp.'one$c'|)) (forall ((A__questionmark_v0 |tptp.'Enat$'|)) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| |tptp.'zero$e'|) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'Enat$'|)) (= (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| A__questionmark_v0) |tptp.'zero$e'|) (= A__questionmark_v0 |tptp.'zero$e'|))) (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (<= 0 (|tptp.'of_nat$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (<= 0 (|tptp.'of_nat$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v0))) (let ((_let_2 (< _let_1 _let_1))) (and (=> _let_2 (= 0 0)) (=> (not _let_2) (= (- _let_1 _let_1) 0)))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v0))) (let ((_let_2 (< 0 _let_1))) (and (=> _let_2 (= 0 0)) (=> (not _let_2) (= (- 0 _let_1) 0)))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'of_nat$'| A__questionmark_v1))) (let ((_let_3 (- _let_2 _let_1))) (let ((_let_4 (< _let_2 _let_1))) (let ((_let_5 (not _let_4))) (let ((_let_6 (and (=> _let_4 (< _let_2 0)) (=> _let_5 (< _let_2 _let_3))))) (=> (<= _let_1 _let_2) (and (=> _let_6 (= 0 _let_1)) (=> (not _let_6) (and (=> _let_4 (= (- _let_2 0) _let_1)) (=> _let_5 (= (- _let_2 _let_3) _let_1))))))))))))) (forall ((A__questionmark_v0 |tptp.'Enat$'|)) (= (|tptp.'fun_app$ad'| (|tptp.'minus$h'| |tptp.'zero$e'|) A__questionmark_v0) |tptp.'zero$e'|)) (forall ((A__questionmark_v0 |tptp.'Enat$'|)) (= (|tptp.'fun_app$ad'| (|tptp.'minus$h'| A__questionmark_v0) |tptp.'zero$e'|) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v1))) (let ((_let_2 (|tptp.'of_nat$'| A__questionmark_v0))) (let ((_let_3 (< _let_2 _let_1))) (=> (<= _let_2 _let_1) (and (=> _let_3 (= 0 0)) (=> (not _let_3) (= (- _let_2 _let_1) 0)))))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v1))) (let ((_let_2 (|tptp.'of_nat$'| A__questionmark_v0))) (let ((_let_3 (< _let_2 _let_1))) (= (and (=> _let_3 (= 0 0)) (=> (not _let_3) (= (- _let_2 _let_1) 0))) (<= _let_2 _let_1)))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v1))) (let ((_let_2 (|tptp.'of_nat$'| A__questionmark_v0))) (let ((_let_3 (< _let_1 _let_2))) (let ((_let_4 (= 0 0))) (let ((_let_5 (< _let_2 _let_1))) (=> (and (=> _let_5 _let_4) (=> (not _let_5) (= (- _let_2 _let_1) 0)) (=> _let_3 _let_4) (=> (not _let_3) (= (- _let_1 _let_2) 0))) (= _let_2 _let_1)))))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v0))) (let ((_let_2 (< _let_1 0))) (and (=> _let_2 (= 0 _let_1)) (=> (not _let_2) (= (- _let_1 0) _let_1)))))) (forall ((A__questionmark_v0 |tptp.'Nat_bool_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$b'| A__questionmark_v0 A__questionmark_v1) (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$b'| A__questionmark_v0 A__questionmark_v3) (<= (|tptp.'of_nat$'| A__questionmark_v3) (|tptp.'of_nat$'| A__questionmark_v2))))) (exists ((A__questionmark_v3 |tptp.'Nat$'|)) (and (|tptp.'fun_app$b'| A__questionmark_v0 A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$b'| A__questionmark_v0 A__questionmark_v4) (<= (|tptp.'of_nat$'| A__questionmark_v4) (|tptp.'of_nat$'| A__questionmark_v3)))))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'of_nat$'| A__questionmark_v1))) (or (<= _let_1 _let_2) (<= _let_2 _let_1))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'of_nat$'| A__questionmark_v2))) (let ((_let_3 (- _let_2 _let_1))) (let ((_let_4 (|tptp.'of_nat$'| A__questionmark_v1))) (let ((_let_5 (- _let_2 _let_4))) (let ((_let_6 (< _let_2 _let_1))) (let ((_let_7 (not _let_6))) (let ((_let_8 (< _let_2 _let_4))) (=> (<= _let_1 _let_4) (and (=> _let_8 (and (=> _let_6 (<= 0 0)) (=> _let_7 (<= 0 _let_3)))) (=> (not _let_8) (and (=> _let_6 (<= _let_5 0)) (=> _let_7 (<= _let_5 _let_3))))))))))))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'of_nat$'| A__questionmark_v2))) (let ((_let_3 (|tptp.'of_nat$'| A__questionmark_v1))) (let ((_let_4 (- _let_3 _let_2))) (let ((_let_5 (- _let_3 _let_1))) (let ((_let_6 (< _let_3 _let_2))) (let ((_let_7 (not _let_6))) (let ((_let_8 (< _let_3 _let_1))) (=> (and (<= _let_1 _let_3) (<= _let_2 _let_3)) (= (and (=> _let_8 (and (=> _let_6 (<= 0 0)) (=> _let_7 (<= 0 _let_4)))) (=> (not _let_8) (and (=> _let_6 (<= _let_5 0)) (=> _let_7 (<= _let_5 _let_4))))) (<= _let_2 _let_1)))))))))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'of_nat$'| A__questionmark_v1))) (let ((_let_3 (< _let_1 _let_2))) (and (=> _let_3 (<= 0 _let_1)) (=> (not _let_3) (<= (- _let_1 _let_2) _let_1))))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v2))) (let ((_let_2 (|tptp.'of_nat$'| A__questionmark_v1))) (let ((_let_3 (- _let_2 _let_1))) (let ((_let_4 (|tptp.'of_nat$'| A__questionmark_v0))) (let ((_let_5 (- _let_4 _let_1))) (let ((_let_6 (< _let_2 _let_1))) (let ((_let_7 (not _let_6))) (let ((_let_8 (< _let_4 _let_1))) (=> (<= _let_4 _let_2) (and (=> _let_8 (and (=> _let_6 (<= 0 0)) (=> _let_7 (<= 0 _let_3)))) (=> (not _let_8) (and (=> _let_6 (<= _let_5 0)) (=> _let_7 (<= _let_5 _let_3))))))))))))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v2))) (let ((_let_2 (|tptp.'of_nat$'| A__questionmark_v1))) (let ((_let_3 (- _let_2 _let_1))) (let ((_let_4 (|tptp.'of_nat$'| A__questionmark_v0))) (let ((_let_5 (- _let_1 _let_4))) (let ((_let_6 (- _let_2 _let_4))) (let ((_let_7 (- _let_6 _let_5))) (let ((_let_8 (< _let_2 _let_1))) (let ((_let_9 (not _let_8))) (let ((_let_10 (< _let_1 _let_4))) (let ((_let_11 (not _let_10))) (let ((_let_12 (- _let_6 0))) (let ((_let_13 (< _let_2 _let_4))) (let ((_let_14 (not _let_13))) (let ((_let_15 (- 0 _let_5))) (let ((_let_16 (- 0 0))) (let ((_let_17 (and (=> _let_13 (and (=> _let_10 (< 0 0)) (=> _let_11 (< 0 _let_5)))) (=> _let_14 (and (=> _let_10 (< _let_6 0)) (=> _let_11 (< _let_6 _let_5))))))) (=> (and (<= _let_4 _let_2) (<= _let_4 _let_1)) (and (=> _let_17 (and (=> _let_8 (= 0 0)) (=> _let_9 (= 0 _let_3)))) (=> (not _let_17) (and (=> _let_13 (and (=> _let_10 (and (=> _let_8 (= _let_16 0)) (=> _let_9 (= _let_16 _let_3)))) (=> _let_11 (and (=> _let_8 (= _let_15 0)) (=> _let_9 (= _let_15 _let_3)))))) (=> _let_14 (and (=> _let_10 (and (=> _let_8 (= _let_12 0)) (=> _let_9 (= _let_12 _let_3)))) (=> _let_11 (and (=> _let_8 (= _let_7 0)) (=> _let_9 (= _let_7 _let_3)))))))))))))))))))))))))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v2))) (let ((_let_2 (|tptp.'of_nat$'| A__questionmark_v1))) (let ((_let_3 (|tptp.'of_nat$'| A__questionmark_v0))) (let ((_let_4 (- _let_1 _let_3))) (let ((_let_5 (- _let_2 _let_3))) (let ((_let_6 (< _let_1 _let_3))) (let ((_let_7 (not _let_6))) (let ((_let_8 (< _let_2 _let_3))) (=> (and (<= _let_3 _let_2) (<= _let_3 _let_1)) (= (and (=> _let_8 (and (=> _let_6 (<= 0 0)) (=> _let_7 (<= 0 _let_4)))) (=> (not _let_8) (and (=> _let_6 (<= _let_5 0)) (=> _let_7 (<= _let_5 _let_4))))) (<= _let_2 _let_1)))))))))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v2))) (let ((_let_2 (|tptp.'of_nat$'| A__questionmark_v1))) (let ((_let_3 (|tptp.'of_nat$'| A__questionmark_v0))) (let ((_let_4 (- _let_1 _let_3))) (let ((_let_5 (- _let_2 _let_3))) (let ((_let_6 (< _let_1 _let_3))) (let ((_let_7 (not _let_6))) (let ((_let_8 (< _let_2 _let_3))) (=> (and (<= _let_3 _let_2) (<= _let_3 _let_1)) (= (and (=> _let_8 (and (=> _let_6 (= 0 0)) (=> _let_7 (= 0 _let_4)))) (=> (not _let_8) (and (=> _let_6 (= _let_5 0)) (=> _let_7 (= _let_5 _let_4))))) (= _let_2 _let_1)))))))))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v1))) (let ((_let_2 (|tptp.'of_nat$'| A__questionmark_v0))) (=> (and (<= _let_2 _let_1) (<= _let_1 _let_2)) (= _let_2 _let_1))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v1))) (let ((_let_2 (|tptp.'of_nat$'| A__questionmark_v0))) (=> (= _let_2 _let_1) (<= _let_2 _let_1))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v2))) (let ((_let_2 (|tptp.'of_nat$'| A__questionmark_v0))) (let ((_let_3 (|tptp.'of_nat$'| A__questionmark_v1))) (=> (and (<= _let_2 _let_3) (<= _let_3 _let_1)) (<= _let_2 _let_1)))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v0))) (<= _let_1 _let_1))) (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v0))) (= (<= _let_1 0) (= _let_1 0)))) (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v0))) (=> (<= _let_1 0) (= _let_1 0)))) (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v0))) (= (<= _let_1 0) (= _let_1 0)))) (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (<= 0 (|tptp.'of_nat$'| A__questionmark_v0)) true)) (forall ((A__questionmark_v0 |tptp.'Nat_set$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (forall ((A__questionmark_v2 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$a'| (|tptp.'member$'| A__questionmark_v2) A__questionmark_v0) (<= (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v2)))) (|tptp.'fun_app$a'| (|tptp.'inj_on$'| (|tptp.'uuw$'| A__questionmark_v1)) A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (|tptp.'fun_app$ab'| (|tptp.'sub$'| |tptp.'one$c'|) (|tptp.'fun_app$z'| |tptp.'bit0$'| A__questionmark_v0)) (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| (|tptp.'fun_app$z'| |tptp.'bitM$'| A__questionmark_v0))))) (= (|tptp.'fun_app$h'| |tptp.'dbl_dec$a'| (- 1)) (- 3)) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (= (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| (|tptp.'fun_app$z'| |tptp.'bit1$'| A__questionmark_v0)) (|tptp.'fun_app$z'| |tptp.'bit1$'| A__questionmark_v1)) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'Num$'|) (A__questionmark_v1 |tptp.'Num$'|)) (= (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| (|tptp.'fun_app$z'| |tptp.'bit0$'| A__questionmark_v0)) (|tptp.'fun_app$z'| |tptp.'bit1$'| A__questionmark_v1)) (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| A__questionmark_v0) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (|tptp.'fun_app$u'| (|tptp.'fun_app$v'| |tptp.'less_eq$c'| (|tptp.'fun_app$z'| |tptp.'bit1$'| A__questionmark_v0)) |tptp.'one$c'|) false)) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (|tptp.'fun_app$h'| |tptp.'dbl_inc$'| (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0)) (|tptp.'fun_app$ab'| |tptp.'numeral$'| (|tptp.'fun_app$z'| |tptp.'bit1$'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (|tptp.'fun_app$h'| |tptp.'dbl_dec$a'| (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0)) (|tptp.'fun_app$ab'| |tptp.'numeral$'| (|tptp.'fun_app$z'| |tptp.'bitM$'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (|tptp.'fun_app$ab'| (|tptp.'sub$'| (|tptp.'fun_app$z'| |tptp.'bit1$'| A__questionmark_v0)) |tptp.'one$c'|) (|tptp.'fun_app$ab'| |tptp.'numeral$'| (|tptp.'fun_app$z'| |tptp.'bit0$'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (|tptp.'fun_app$ab'| (|tptp.'sub$'| (|tptp.'fun_app$z'| |tptp.'bit0$'| A__questionmark_v0)) |tptp.'one$c'|) (|tptp.'fun_app$ab'| |tptp.'numeral$'| (|tptp.'fun_app$z'| |tptp.'bitM$'| A__questionmark_v0)))) (= (|tptp.'fun_app$h'| |tptp.'dbl_inc$'| 1) 3) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (|tptp.'fun_app$ab'| (|tptp.'sub$'| |tptp.'one$c'|) (|tptp.'fun_app$z'| |tptp.'bit1$'| A__questionmark_v0)) (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| (|tptp.'fun_app$z'| |tptp.'bit0$'| A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v1))) (let ((_let_2 (|tptp.'of_nat$'| A__questionmark_v2))) (let ((_let_3 (|tptp.'of_nat$'| A__questionmark_v0))) (let ((_let_4 (- _let_3 _let_2))) (let ((_let_5 (- _let_4 _let_1))) (let ((_let_6 (- _let_3 _let_1))) (let ((_let_7 (- _let_6 _let_2))) (let ((_let_8 (< _let_3 _let_2))) (let ((_let_9 (not _let_8))) (let ((_let_10 (- 0 _let_1))) (let ((_let_11 (and (=> _let_8 (< 0 _let_1)) (=> _let_9 (< _let_4 _let_1))))) (let ((_let_12 (not _let_11))) (let ((_let_13 (< _let_3 _let_1))) (let ((_let_14 (not _let_13))) (let ((_let_15 (- 0 _let_2))) (let ((_let_16 (and (=> _let_13 (< 0 _let_2)) (=> _let_14 (< _let_6 _let_2))))) (and (=> _let_16 (and (=> _let_11 (= 0 0)) (=> _let_12 (and (=> _let_8 (= 0 _let_10)) (=> _let_9 (= 0 _let_5)))))) (=> (not _let_16) (and (=> _let_13 (and (=> _let_11 (= _let_15 0)) (=> _let_12 (and (=> _let_8 (= _let_15 _let_10)) (=> _let_9 (= _let_15 _let_5)))))) (=> _let_14 (and (=> _let_11 (= _let_7 0)) (=> _let_12 (and (=> _let_8 (= _let_7 _let_10)) (=> _let_9 (= _let_7 _let_5)))))))))))))))))))))))))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (|tptp.'fun_app$z'| |tptp.'inc$'| (|tptp.'fun_app$z'| |tptp.'bitM$'| A__questionmark_v0)) (|tptp.'fun_app$z'| |tptp.'bit0$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (|tptp.'fun_app$z'| |tptp.'bitM$'| (|tptp.'fun_app$z'| |tptp.'inc$'| A__questionmark_v0)) (|tptp.'fun_app$z'| |tptp.'bit1$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (=> (and (=> (= A__questionmark_v0 |tptp.'one$c'|) false) (forall ((A__questionmark_v1 |tptp.'Num$'|)) (=> (= A__questionmark_v0 (|tptp.'fun_app$z'| |tptp.'bit0$'| A__questionmark_v1)) false)) (forall ((A__questionmark_v1 |tptp.'Num$'|)) (=> (= A__questionmark_v0 (|tptp.'fun_app$z'| |tptp.'bit1$'| A__questionmark_v1)) false))) false)) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (|tptp.'fun_app$z'| |tptp.'inc$'| (|tptp.'fun_app$z'| |tptp.'bit1$'| A__questionmark_v0)) (|tptp.'fun_app$z'| |tptp.'bit0$'| (|tptp.'fun_app$z'| |tptp.'inc$'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (|tptp.'fun_app$z'| |tptp.'inc$'| (|tptp.'fun_app$z'| |tptp.'bit0$'| A__questionmark_v0)) (|tptp.'fun_app$z'| |tptp.'bit1$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (|tptp.'fun_app$ab'| |tptp.'numeral$'| (|tptp.'fun_app$z'| |tptp.'bitM$'| A__questionmark_v0)) (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| (|tptp.'fun_app$z'| |tptp.'bit0$'| A__questionmark_v0)) 1))) (forall ((A__questionmark_v0 |tptp.'Enat$'|) (A__questionmark_v1 |tptp.'Enat$'|)) (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'less_eq$d'| (|tptp.'fun_app$ad'| (|tptp.'minus$h'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'Num$'|)) (= (+ 1 (- (|tptp.'fun_app$ab'| |tptp.'numeral$'| A__questionmark_v0))) (|tptp.'fun_app$ab'| (|tptp.'sub$'| |tptp.'one$c'|) A__questionmark_v0))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (= (+ A__questionmark_v0 A__questionmark_v1) (+ A__questionmark_v2 A__questionmark_v1)) (= A__questionmark_v0 A__questionmark_v2))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (= (+ A__questionmark_v0 A__questionmark_v1) (+ A__questionmark_v0 A__questionmark_v2)) (= A__questionmark_v1 A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v2))) (let ((_let_2 (|tptp.'of_nat$'| A__questionmark_v1))) (let ((_let_3 (|tptp.'of_nat$'| A__questionmark_v0))) (= (<= (+ _let_3 _let_2) (+ _let_3 _let_1)) (<= _let_2 _let_1)))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v2))) (let ((_let_2 (|tptp.'of_nat$'| A__questionmark_v1))) (let ((_let_3 (+ _let_2 _let_1))) (let ((_let_4 (|tptp.'of_nat$'| A__questionmark_v0))) (let ((_let_5 (- _let_4 _let_3))) (let ((_let_6 (- _let_4 _let_2))) (let ((_let_7 (- _let_6 _let_1))) (let ((_let_8 (< _let_4 _let_3))) (let ((_let_9 (not _let_8))) (let ((_let_10 (< _let_4 _let_2))) (let ((_let_11 (not _let_10))) (let ((_let_12 (- 0 _let_1))) (let ((_let_13 (and (=> _let_10 (< 0 _let_1)) (=> _let_11 (< _let_6 _let_1))))) (and (=> _let_13 (and (=> _let_8 (= 0 0)) (=> _let_9 (= 0 _let_5)))) (=> (not _let_13) (and (=> _let_10 (and (=> _let_8 (= _let_12 0)) (=> _let_9 (= _let_12 _let_5)))) (=> _let_11 (and (=> _let_8 (= _let_7 0)) (=> _let_9 (= _let_7 _let_5))))))))))))))))))))) (forall ((A__questionmark_v0 |tptp.'A_ell2$'|)) (= (|tptp.'plus$'| A__questionmark_v0 |tptp.'zero$'|) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'Enat$'|)) (= (|tptp.'fun_app$ad'| (|tptp.'plus$a'| A__questionmark_v0) |tptp.'zero$e'|) A__questionmark_v0)) (forall ((A__questionmark_v0 Int)) (= (+ A__questionmark_v0 0) A__questionmark_v0)) (forall ((A__questionmark_v0 Int)) (= (= 0 (+ A__questionmark_v0 A__questionmark_v0)) (= A__questionmark_v0 0))) (forall ((A__questionmark_v0 |tptp.'A_ell2$'|) (A__questionmark_v1 |tptp.'A_ell2$'|)) (= (= (|tptp.'plus$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v1) (= A__questionmark_v0 |tptp.'zero$'|))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (= (+ A__questionmark_v0 A__questionmark_v1) A__questionmark_v1) (= A__questionmark_v0 0))) (forall ((A__questionmark_v0 |tptp.'A_ell2$'|) (A__questionmark_v1 |tptp.'A_ell2$'|)) (= (= (|tptp.'plus$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v0) (= A__questionmark_v1 |tptp.'zero$'|))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (= (+ A__questionmark_v0 A__questionmark_v1) A__questionmark_v0) (= A__questionmark_v1 0))) (forall ((A__questionmark_v0 |tptp.'A_ell2$'|) (A__questionmark_v1 |tptp.'A_ell2$'|)) (= (= A__questionmark_v0 (|tptp.'plus$'| A__questionmark_v1 A__questionmark_v0)) (= A__questionmark_v1 |tptp.'zero$'|))) (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (= A__questionmark_v0 (+ A__questionmark_v1 A__questionmark_v0)) (= A__questionmark_v1 0))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'of_nat$'| A__questionmark_v1))) (let ((_let_3 (|tptp.'of_nat$'| A__questionmark_v2))) (let ((_let_4 (+ _let_3 _let_2))) (let ((_let_5 (- _let_4 _let_1))) (let ((_let_6 (+ _let_3 (- _let_2 _let_1)))) (let ((_let_7 (< _let_4 _let_1))) (let ((_let_8 (not _let_7))) (let ((_let_9 (< _let_2 _let_1))) (let ((_let_10 (+ _let_3 0))) (=> (<= _let_1 _let_2) (and (=> _let_9 (and (=> _let_7 (= _let_10 0)) (=> _let_8 (= _let_10 _let_5)))) (=> (not _let_9) (and (=> _let_7 (= _let_6 0)) (=> _let_8 (= _let_6 _let_5))))))))))))))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (let ((_let_1 (|tptp.'of_nat$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'of_nat$'| A__questionmark_v2))) (let ((_let_3 (|tptp.'of_nat$'| A__questionmark_v1))) (let ((_let_4 (+ _let_3 _let_2))) (let ((_let_5 (- _let_4 _let_1))) (let ((_let_6 (+ (- _let_3 _let_1) _let_2))) (let ((_let_7 (< _let_4 _let_1))) (let ((_let_8 (not _let_7))) (let ((_let_9 (< _let_3 _let_1))) (let ((_let_10 (+ 0 _let_2))) (=> (<= _let_1 _let_3) (and (=> _let_9 (and (=> _let_7 (= _let_10 0)) (=> _let_8 (= _let_10 _let_5)))) (=> (not _let_9) (and (=> _let_7 (= _let_6 0)) (=> _let_8 (= _let_6 _let_5))))))))))))))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (<= 0 (|tptp.'of_nat$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (|tptp.'nat$'| (|tptp.'of_nat$'| A__questionmark_v0)) A__questionmark_v0)) (forall ((A__questionmark_v0 Int)) (let ((_let_1 (|tptp.'of_nat$'| (|tptp.'nat$'| A__questionmark_v0)))) (let ((_let_2 (<= 0 A__questionmark_v0))) (and (=> _let_2 (= _let_1 A__questionmark_v0)) (=> (not _let_2) (= _let_1 0)))))) true))))))))))))))))))))))))))
% 15.85/16.45 )
% 15.85/16.45 % SZS output end Proof for ITP001_1
% 15.85/16.45 % cvc5---1.0.5 exiting
% 15.85/16.45 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------