TSTP Solution File: SWW470+5 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW470+5 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n015.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 : Fri Sep 1 00:20:57 EDT 2023
% Result : Theorem 26.35s 26.54s
% Output : Proof 26.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.17 % Problem : SWW470+5 : TPTP v8.1.2. Released v5.3.0.
% 0.12/0.18 % Command : do_cvc5 %s %d
% 0.17/0.39 % Computer : n015.cluster.edu
% 0.17/0.39 % Model : x86_64 x86_64
% 0.17/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39 % Memory : 8042.1875MB
% 0.17/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39 % CPULimit : 300
% 0.17/0.39 % WCLimit : 300
% 0.17/0.39 % DateTime : Sun Aug 27 18:36:24 EDT 2023
% 0.17/0.39 % CPUTime :
% 0.24/0.56 %----Proving TF0_NAR, FOF, or CNF
% 26.35/26.54 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.25k4nqPzI3/cvc5---1.0.5_9989.p...
% 26.35/26.54 ------- get file name : TPTP file name is SWW470+5
% 26.35/26.54 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_9989.smt2...
% 26.35/26.54 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 26.35/26.54 --- Run --no-e-matching --full-saturate-quant at 5...
% 26.35/26.54 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 26.35/26.54 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 26.35/26.54 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 26.35/26.54 % SZS status Theorem for SWW470+5
% 26.35/26.54 % SZS output start Proof for SWW470+5
% 26.35/26.54 (
% 26.35/26.54 (let ((_let_1 (tptp.hoare_509422987triple tptp.x_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.fun tptp.state tptp.bool))) (let ((_let_5 (tptp.fun _let_4 _let_4))) (let ((_let_6 (tptp.fun tptp.bool tptp.bool))) (let ((_let_7 (tptp.fun tptp.state _let_6))) (let ((_let_8 (tptp.fun _let_4 _let_7))) (let ((_let_9 (tptp.fun tptp.bool _let_6))) (let ((_let_10 (tptp.fun tptp.x_a _let_7))) (let ((_let_11 (tptp.fun tptp.x_a _let_4))) (let ((_let_12 (tptp.fun tptp.x_a _let_5))) (let ((_let_13 (tptp.hAPP _let_4 _let_11 (tptp.hAPP _let_12 (tptp.fun _let_4 _let_11) (tptp.combc tptp.x_a _let_4 _let_4) (tptp.hAPP _let_10 _let_12 (tptp.hAPP (tptp.fun _let_7 _let_5) (tptp.fun _let_10 _let_12) (tptp.combb _let_7 _let_5 tptp.x_a) (tptp.combs tptp.state tptp.bool tptp.bool)) (tptp.hAPP _let_11 _let_10 (tptp.hAPP _let_8 (tptp.fun _let_11 _let_10) (tptp.combb _let_4 _let_7 tptp.x_a) (tptp.hAPP _let_9 _let_8 (tptp.combb tptp.bool _let_6 tptp.state) tptp.fconj)) tptp.p))) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_6 _let_5 (tptp.combb tptp.bool tptp.bool tptp.state) tptp.fNot) tptp.b)))) (let ((_let_14 (tptp.combk tptp.bool tptp.state))) (let ((_let_15 (tptp.hAPP tptp.bool _let_4 _let_14 tptp.fFalse))) (let ((_let_16 (tptp.combk _let_4 tptp.x_a))) (let ((_let_17 (tptp.hAPP _let_4 _let_11 _let_16 _let_15))) (let ((_let_18 (tptp.hoare_1008221573triple tptp.x_a))) (let ((_let_19 (tptp.fun _let_11 _let_1))) (let ((_let_20 (tptp.fun tptp.com _let_19))) (let ((_let_21 (tptp.insert _let_1))) (let ((_let_22 (tptp.fun _let_2 _let_2))) (let ((_let_23 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_122391849derivs tptp.x_a) tptp.g))) (let ((_let_24 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_23 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_22 _let_21 (tptp.hAPP _let_11 _let_1 (tptp.hAPP tptp.com _let_19 (tptp.hAPP _let_11 _let_20 _let_18 _let_17) tptp.c) _let_13)) _let_3))))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.hBOOL tptp.fFalse))) (let ((_let_27 (not _let_26))) (let ((_let_28 (forall ((X_b $$unsorted) (X_a $$unsorted) (P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP X_b X_a (tptp.hAPP X_a (tptp.fun X_b X_a) (tptp.combk X_a X_b) P) Q) (tptp.ti X_a P))))) (let ((_let_29 (forall ((X_b $$unsorted) (Ga $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.hoare_509422987triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_4 (tptp.fun _let_3 _let_1))) (=> (forall ((Z_1 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.hoare_509422987triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun tptp.state tptp.bool))) (let ((_let_4 (tptp.combk _let_3 X_b))) (let ((_let_5 (tptp.fun X_b _let_3))) (let ((_let_6 (tptp.fun tptp.state _let_3))) (let ((_let_7 (tptp.fun _let_5 _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_3 Pa Z_1) S)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_122391849derivs X_b) Ga) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_7 (tptp.hAPP _let_5 (tptp.fun tptp.com _let_7) (tptp.hoare_1008221573triple X_b) (tptp.hAPP _let_3 _let_5 _let_4 (tptp.hAPP tptp.state _let_3 (tptp.hAPP _let_6 _let_6 (tptp.combc tptp.state tptp.state tptp.bool) (tptp.fequal tptp.state)) S))) Ca) (tptp.hAPP _let_3 _let_5 _let_4 (tptp.hAPP X_b _let_3 Q_1 Z_1)))) (tptp.bot_bot _let_2))))))))))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_122391849derivs X_b) Ga) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) (tptp.hAPP _let_3 _let_1 (tptp.hAPP tptp.com _let_4 (tptp.hAPP _let_3 (tptp.fun tptp.com _let_4) (tptp.hoare_1008221573triple X_b) Pa) Ca) Q_1)) (tptp.bot_bot _let_2)))))))))))) (let ((_let_30 (forall ((X_c $$unsorted) (X_a $$unsorted) (B_1_1 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_c B_1_1 B_2))) (= (tptp.ti X_c _let_1) _let_1))))) (let ((_let_31 (tptp.ti tptp.bool tptp.fFalse))) (let ((_let_32 (= _let_31 tptp.fFalse))) (let ((_let_33 (= tptp.fFalse _let_31))) (let ((_let_34 (tptp.ti _let_4 _let_15))) (let ((_let_35 (= _let_15 _let_34))) (let ((_let_36 (tptp.hAPP tptp.x_a _let_4 _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_37 (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool _let_36 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)))) (let ((_let_38 (= _let_34 _let_36))) (let ((_let_39 (= _let_31 (tptp.hAPP tptp.state tptp.bool _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)))) (let ((_let_40 (SYMM (ASSUME :args (_let_32))))) (let ((_let_41 (ASSUME :args (_let_27)))) (let ((_let_42 (forall ((X_c $$unsorted) (X_a $$unsorted) (B_1_1 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_c B_1_1 B_2))) (= _let_1 (tptp.ti X_c _let_1)))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (tptp.fun tptp.state _let_4))) (let ((_let_45 (not _let_37))) (let ((_let_46 (or _let_45 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_23 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_22 _let_21 (tptp.hAPP _let_11 _let_1 (tptp.hAPP tptp.com _let_19 (tptp.hAPP _let_11 _let_20 _let_18 (tptp.hAPP _let_4 _let_11 _let_16 (tptp.hAPP tptp.state _let_4 (tptp.hAPP _let_44 _let_44 (tptp.combc tptp.state tptp.state tptp.bool) (tptp.fequal tptp.state)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) tptp.c) (tptp.hAPP _let_4 _let_11 _let_16 (tptp.hAPP tptp.x_a _let_4 _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))) _let_3)))))) (let ((_let_47 (forall ((Z_1 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.hoare_509422987triple tptp.x_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun tptp.state tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (let ((_let_5 (tptp.fun tptp.bool tptp.bool))) (let ((_let_6 (tptp.fun tptp.state _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.fun tptp.x_a _let_6))) (let ((_let_9 (tptp.fun tptp.x_a _let_3))) (let ((_let_10 (tptp.fun tptp.x_a _let_4))) (let ((_let_11 (tptp.combk _let_3 tptp.x_a))) (let ((_let_12 (tptp.fun tptp.state _let_3))) (let ((_let_13 (tptp.fun _let_9 _let_1))) (or (not (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP tptp.x_a _let_3 (tptp.hAPP _let_3 _let_9 _let_11 (tptp.hAPP tptp.bool _let_3 (tptp.combk tptp.bool tptp.state) tptp.fFalse)) Z_1) S))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_122391849derivs tptp.x_a) tptp.g) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) (tptp.hAPP _let_9 _let_1 (tptp.hAPP tptp.com _let_13 (tptp.hAPP _let_9 (tptp.fun tptp.com _let_13) (tptp.hoare_1008221573triple tptp.x_a) (tptp.hAPP _let_3 _let_9 _let_11 (tptp.hAPP tptp.state _let_3 (tptp.hAPP _let_12 _let_12 (tptp.combc tptp.state tptp.state tptp.bool) (tptp.fequal tptp.state)) S))) tptp.c) (tptp.hAPP _let_3 _let_9 _let_11 (tptp.hAPP tptp.x_a _let_3 (tptp.hAPP _let_3 _let_9 (tptp.hAPP _let_10 (tptp.fun _let_3 _let_9) (tptp.combc tptp.x_a _let_3 _let_3) (tptp.hAPP _let_8 _let_10 (tptp.hAPP (tptp.fun _let_6 _let_4) (tptp.fun _let_8 _let_10) (tptp.combb _let_6 _let_4 tptp.x_a) (tptp.combs tptp.state tptp.bool tptp.bool)) (tptp.hAPP _let_9 _let_8 (tptp.hAPP _let_7 (tptp.fun _let_9 _let_8) (tptp.combb _let_3 _let_6 tptp.x_a) (tptp.hAPP (tptp.fun tptp.bool _let_5) _let_7 (tptp.combb tptp.bool _let_5 tptp.state) tptp.fconj)) tptp.p))) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_5 _let_4 (tptp.combb tptp.bool tptp.bool tptp.state) tptp.fNot) tptp.b)) Z_1)))) (tptp.bot_bot _let_2))))))))))))))))))))) (let ((_let_48 (not _let_46))) (let ((_let_49 (not _let_47))) (let ((_let_50 (or _let_49 _let_24))) (let ((_let_51 (forall ((X_b $$unsorted) (Ga $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.hoare_509422987triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_4 (tptp.fun _let_3 _let_1))) (or (not (forall ((Z_1 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.hoare_509422987triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun tptp.state tptp.bool))) (let ((_let_4 (tptp.combk _let_3 X_b))) (let ((_let_5 (tptp.fun X_b _let_3))) (let ((_let_6 (tptp.fun tptp.state _let_3))) (let ((_let_7 (tptp.fun _let_5 _let_1))) (or (not (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_3 Pa Z_1) S))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_122391849derivs X_b) Ga) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_7 (tptp.hAPP _let_5 (tptp.fun tptp.com _let_7) (tptp.hoare_1008221573triple X_b) (tptp.hAPP _let_3 _let_5 _let_4 (tptp.hAPP tptp.state _let_3 (tptp.hAPP _let_6 _let_6 (tptp.combc tptp.state tptp.state tptp.bool) (tptp.fequal tptp.state)) S))) Ca) (tptp.hAPP _let_3 _let_5 _let_4 (tptp.hAPP X_b _let_3 Q_1 Z_1)))) (tptp.bot_bot _let_2)))))))))))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_122391849derivs X_b) Ga) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) (tptp.hAPP _let_3 _let_1 (tptp.hAPP tptp.com _let_4 (tptp.hAPP _let_3 (tptp.fun tptp.com _let_4) (tptp.hoare_1008221573triple X_b) Pa) Ca) Q_1)) (tptp.bot_bot _let_2)))))))))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (tptp.hoare_509422987triple X_b))) (let ((_let_54 (tptp.fun _let_53 tptp.bool))) (let ((_let_55 (tptp.fun X_b _let_4))) (let ((_let_56 (tptp.fun _let_55 _let_53))) (let ((_let_57 (or))) (let ((_let_58 (_let_49))) (let ((_let_59 (_let_28))) (let ((_let_60 (ASSUME :args _let_59))) (let ((_let_61 (ASSUME :args (_let_39)))) (let ((_let_62 (ASSUME :args (_let_35)))) (let ((_let_63 (ASSUME :args (_let_38)))) (let ((_let_64 (ASSUME :args (_let_37)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_41 _let_40 _let_61 _let_62 _let_63 _let_64) :args (_let_27 _let_33 _let_35 _let_37 _let_38 _let_39)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_64)) (CONG (TRANS (CONG (REFL :args (tptp.state)) (REFL :args (tptp.bool)) (TRANS (SYMM _let_63) (SYMM _let_62)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) :args (APPLY_UF tptp.hAPP)) (SYMM _let_61) (SYMM _let_40)) :args (APPLY_UF tptp.hBOOL)) (FALSE_INTRO _let_41))) :args (_let_27 _let_33 _let_39 _let_35 _let_38 _let_37)) :args ((not (and _let_27 _let_33 _let_35 _let_37 _let_38 _let_39)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) (REFL :args ((not _let_33))) (REFL :args ((not _let_35))) (REFL :args (_let_45)) (REFL :args ((not _let_38))) (REFL :args ((not _let_39))) :args _let_57)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_60 :args (tptp.state tptp.bool tptp.fFalse SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_CBQI_PROP)) :args _let_59))) _let_60 :args (_let_39 false _let_28)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_60 :args (tptp.x_a _let_4 _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_CBQI_PROP)) :args _let_59))) _let_60 :args (_let_38 false _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 0)) (CONG (REFL :args (_let_46)) (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_37))) :args _let_57)) :args ((or _let_37 _let_46))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_58)) :args _let_58)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_47))) (REFL :args (_let_48)) :args _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_24 _let_49 (not _let_50)))) (ASSUME :args (_let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (tptp.x_a tptp.g tptp.c _let_13 _let_17 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP _let_54 tptp.bool (tptp.hAPP _let_54 (tptp.fun _let_54 tptp.bool) (tptp.hoare_122391849derivs X_b) Ga) (tptp.hAPP _let_54 _let_54 (tptp.hAPP _let_53 (tptp.fun _let_54 _let_54) (tptp.insert _let_53) (tptp.hAPP _let_55 _let_53 (tptp.hAPP tptp.com _let_56 (tptp.hAPP _let_55 (tptp.fun tptp.com _let_56) (tptp.hoare_1008221573triple X_b) Pa) Ca) Q_1)) (tptp.bot_bot _let_54)))))) :args (_let_51))) _let_52 :args (_let_50 false _let_51)) :args (_let_49 true _let_24 false _let_50)) :args (_let_48 true _let_47)) :args (_let_37 true _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (_let_4 tptp.bool _let_14 tptp.fFalse QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP X_a X_c B_1_1 B_2)))) :args (_let_42))) _let_43 :args (_let_35 false _let_42)) _let_41 _let_40 :args (false false _let_39 false _let_38 false _let_37 false _let_35 true _let_26 false _let_33)) :args ((forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.combb X_b X_c X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_a X_b) (tptp.fun X_a X_c))) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.combc X_a X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_b X_c)) (tptp.fun X_b (tptp.fun X_a X_c))) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.combk X_a X_b))) (= (tptp.ti (tptp.fun X_a (tptp.fun X_b X_a)) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.combs X_a X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_b X_c)) (tptp.fun (tptp.fun X_a X_b) (tptp.fun X_a X_c))) _let_1) _let_1))) (= (tptp.ti tptp.com tptp.skip) tptp.skip) (= (tptp.ti (tptp.fun tptp.com (tptp.fun tptp.com tptp.com)) tptp.semi) tptp.semi) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.finite_finite_1 X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) _let_1) _let_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.finite_fold1 X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun (tptp.fun X_b tptp.bool) X_b)) _let_1) _let_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.finite_fold1Set X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_2 _let_2)) _let_1) _let_1)))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.finite_fold_graph X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_c X_c)) (tptp.fun X_c (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)))) _let_1) _let_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.finite_folding_one X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool)) _let_1) _let_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.finite2073411215e_idem X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool)) _let_1) _let_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.the X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_b tptp.bool) X_b) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.undefined X_a))) (= (tptp.ti X_a _let_1) _let_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.hoare_122391849derivs X_b))) (let ((_let_2 (tptp.fun (tptp.hoare_509422987triple X_b) tptp.bool))) (= (tptp.ti (tptp.fun _let_2 (tptp.fun _let_2 tptp.bool)) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.hoare_1008221573triple X_b))) (let ((_let_2 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (= (tptp.ti (tptp.fun _let_2 (tptp.fun tptp.com (tptp.fun _let_2 (tptp.hoare_509422987triple X_b)))) _let_1) _let_1)))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.hoare_885240885e_case X_c X_b))) (let ((_let_2 (tptp.fun X_c (tptp.fun tptp.state tptp.bool)))) (= (tptp.ti (tptp.fun (tptp.fun _let_2 (tptp.fun tptp.com (tptp.fun _let_2 X_b))) (tptp.fun (tptp.hoare_509422987triple X_c) X_b)) _let_1) _let_1)))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.hoare_728318379le_rec X_c X_b))) (let ((_let_2 (tptp.fun X_c (tptp.fun tptp.state tptp.bool)))) (= (tptp.ti (tptp.fun (tptp.fun _let_2 (tptp.fun tptp.com (tptp.fun _let_2 X_b))) (tptp.fun (tptp.hoare_509422987triple X_c) X_b)) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.bot_bot X_b))) (=> (tptp.bot X_b) (= (tptp.ti X_b _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.collect X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.ti (tptp.fun _let_2 _let_2) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.insert X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.ti (tptp.fun X_b (tptp.fun _let_2 _let_2)) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.the_elem X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_b tptp.bool) X_b) _let_1) _let_1))) _let_32 (= (tptp.ti _let_6 tptp.fNot) tptp.fNot) (= (tptp.ti tptp.bool tptp.fTrue) tptp.fTrue) (= (tptp.ti _let_9 tptp.fconj) tptp.fconj) (= (tptp.ti _let_9 tptp.fdisj) tptp.fdisj) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fequal X_a))) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.bool)) _let_1) _let_1))) (= (tptp.ti _let_9 tptp.fimplies) tptp.fimplies) (forall ((X_a $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2 $$unsorted)) (= (tptp.hAPP X_a X_c (tptp.ti (tptp.fun X_a X_c) B_1_1) B_2) (tptp.hAPP X_a X_c B_1_1 B_2))) (forall ((X_a $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2 $$unsorted)) (= (tptp.hAPP X_a X_c B_1_1 (tptp.ti X_a B_2)) (tptp.hAPP X_a X_c B_1_1 B_2))) _let_30 (forall ((B_1_1 $$unsorted)) (= (tptp.hBOOL (tptp.ti tptp.bool B_1_1)) (tptp.hBOOL B_1_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.member X_b))) (= (tptp.ti (tptp.fun X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool)) _let_1) _let_1))) (= (tptp.ti _let_2 tptp.g) tptp.g) (= (tptp.ti _let_11 tptp.p) tptp.p) (= (tptp.ti _let_4 tptp.b) tptp.b) (= (tptp.ti tptp.com tptp.c) tptp.c) (forall ((X_b $$unsorted) (Ga $$unsorted)) (let ((_let_1 (tptp.fun (tptp.hoare_509422987triple X_b) tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.hoare_122391849derivs X_b) Ga) (tptp.bot_bot _let_1))))) (forall ((X_b $$unsorted) (Fun1_1 $$unsorted) (Com_1 $$unsorted) (Fun2_1 $$unsorted) (Fun1_2 $$unsorted) (Com_2 $$unsorted) (Fun2_2 $$unsorted)) (let ((_let_1 (tptp.hoare_1008221573triple X_b))) (let ((_let_2 (tptp.hoare_509422987triple X_b))) (let ((_let_3 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_4 (tptp.fun _let_3 _let_2))) (let ((_let_5 (tptp.fun tptp.com _let_4))) (= (= (tptp.hAPP _let_3 _let_2 (tptp.hAPP tptp.com _let_4 (tptp.hAPP _let_3 _let_5 _let_1 Fun1_1) Com_1) Fun2_1) (tptp.hAPP _let_3 _let_2 (tptp.hAPP tptp.com _let_4 (tptp.hAPP _let_3 _let_5 _let_1 Fun1_2) Com_2) Fun2_2)) (and (= Fun1_1 Fun1_2) (= Com_1 Com_2) (= Fun2_1 Fun2_2))))))))) (forall ((X_b $$unsorted) (Ga $$unsorted) (G_1 $$unsorted) (Ts $$unsorted)) (let ((_let_1 (tptp.hoare_122391849derivs X_b))) (let ((_let_2 (tptp.fun (tptp.hoare_509422987triple X_b) tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.hAPP _let_2 _let_3 _let_1 Ga))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_3 _let_1 G_1) Ts)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 G_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 Ts))))))))) (forall ((X_b $$unsorted) (Ts $$unsorted) (Ga $$unsorted) (T_3 $$unsorted)) (let ((_let_1 (tptp.hoare_509422987triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) T_3))) (let ((_let_4 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_122391849derivs X_b) Ga))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_2 _let_2 _let_3 (tptp.bot_bot _let_2)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 Ts)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_2 _let_2 _let_3 Ts)))))))))) (forall ((X_b $$unsorted) (Ga $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hoare_509422987triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun tptp.state _let_4))) (let ((_let_6 (tptp.fun tptp.state tptp.bool))) (let ((_let_7 (tptp.fun _let_6 _let_5))) (let ((_let_8 (tptp.fun X_b _let_5))) (let ((_let_9 (tptp.fun X_b _let_6))) (let ((_let_10 (tptp.fun tptp.bool _let_6))) (let ((_let_11 (tptp.fun X_b _let_10))) (let ((_let_12 (tptp.hoare_1008221573triple X_b))) (let ((_let_13 (tptp.fun _let_9 _let_1))) (let ((_let_14 (tptp.fun tptp.com _let_13))) (let ((_let_15 (tptp.insert _let_1))) (let ((_let_16 (tptp.fun _let_2 _let_2))) (let ((_let_17 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_122391849derivs X_b) Ga))) (=> (=> (tptp.hBOOL C) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_17 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_16 _let_15 (tptp.hAPP _let_9 _let_1 (tptp.hAPP tptp.com _let_13 (tptp.hAPP _let_9 _let_14 _let_12 Pa) Ca) Q_1)) _let_3)))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_17 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_16 _let_15 (tptp.hAPP _let_9 _let_1 (tptp.hAPP tptp.com _let_13 (tptp.hAPP _let_9 _let_14 _let_12 (tptp.hAPP tptp.bool _let_9 (tptp.hAPP _let_11 (tptp.fun tptp.bool _let_9) (tptp.combc X_b tptp.bool _let_6) (tptp.hAPP _let_8 _let_11 (tptp.hAPP (tptp.fun _let_5 _let_10) (tptp.fun _let_8 _let_11) (tptp.combb _let_5 _let_10 X_b) (tptp.combc tptp.state tptp.bool tptp.bool)) (tptp.hAPP _let_9 _let_8 (tptp.hAPP _let_7 (tptp.fun _let_9 _let_8) (tptp.combb _let_6 _let_5 X_b) (tptp.hAPP (tptp.fun tptp.bool _let_4) _let_7 (tptp.combb tptp.bool _let_4 tptp.state) tptp.fconj)) Pa))) C)) Ca) Q_1)) _let_3)))))))))))))))))))))) _let_29 (forall ((X_b $$unsorted) (Q_1 $$unsorted) (Ga $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.hoare_509422987triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_5 (tptp.fun _let_4 _let_1))) (let ((_let_6 (tptp.hAPP tptp.com _let_5 (tptp.hAPP _let_4 (tptp.fun tptp.com _let_5) (tptp.hoare_1008221573triple X_b) Pa) Ca))) (let ((_let_7 (tptp.insert _let_1))) (let ((_let_8 (tptp.fun _let_2 _let_2))) (let ((_let_9 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_122391849derivs X_b) Ga))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_9 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP _let_4 _let_1 _let_6 Q_3)) _let_3))) (=> (forall ((Z_1 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_1 Q_3 Z_1) S)) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_1 Q_1 Z_1) S))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_9 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_8 _let_7 (tptp.hAPP _let_4 _let_1 _let_6 Q_1)) _let_3))))))))))))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (Ga $$unsorted) (P_2 $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.hoare_509422987triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.hoare_1008221573triple X_b))) (let ((_let_5 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_6 (tptp.fun _let_5 _let_1))) (let ((_let_7 (tptp.fun tptp.com _let_6))) (let ((_let_8 (tptp.insert _let_1))) (let ((_let_9 (tptp.fun _let_2 _let_2))) (let ((_let_10 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_122391849derivs X_b) Ga))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_10 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_9 _let_8 (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_6 (tptp.hAPP _let_5 _let_7 _let_4 P_2) Ca) Q_1)) _let_3))) (=> (forall ((Z_1 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_1 Pa Z_1) S)) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_1 P_2 Z_1) S))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_10 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_9 _let_8 (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_6 (tptp.hAPP _let_5 _let_7 _let_4 Pa) Ca) Q_1)) _let_3)))))))))))))))) (forall ((X_b $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted) (Ga $$unsorted) (P_2 $$unsorted) (Ca $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.hoare_509422987triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.hoare_1008221573triple X_b))) (let ((_let_5 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_6 (tptp.fun _let_5 _let_1))) (let ((_let_7 (tptp.fun tptp.com _let_6))) (let ((_let_8 (tptp.insert _let_1))) (let ((_let_9 (tptp.fun _let_2 _let_2))) (let ((_let_10 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_122391849derivs X_b) Ga))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_10 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_9 _let_8 (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_6 (tptp.hAPP _let_5 _let_7 _let_4 P_2) Ca) Q_3)) _let_3))) (=> (forall ((Z_1 $$unsorted) (S $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b (tptp.fun tptp.state tptp.bool) Pa Z_1) S)) (forall ((S_1 $$unsorted)) (=> (forall ((Z_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_1 P_2 Z_2) S)) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_1 Q_3 Z_2) S_1))))) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b (tptp.fun tptp.state tptp.bool) Q_1 Z_1) S_1)))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_10 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_9 _let_8 (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_6 (tptp.hAPP _let_5 _let_7 _let_4 Pa) Ca) Q_1)) _let_3)))))))))))))))) (forall ((X_b $$unsorted) (A_4 $$unsorted) (Ba $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_4))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) Ba) A_1))) (=> (not (= (tptp.ti X_b A_4) (tptp.ti X_b Ba))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1))))))) (forall ((X_b $$unsorted) (Ba $$unsorted) (A_4 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_4))) (=> (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_1))) (= (tptp.ti X_b A_4) (tptp.ti X_b Ba))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) Ba) B_1))))))) (forall ((X_b $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_4) (tptp.bot_bot _let_1)))))) (forall ((X_b $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP X_b _let_1 (tptp.fequal X_b) A_4)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_4) (tptp.bot_bot _let_1))))) (forall ((X_b $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP X_b _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_4)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_4) (tptp.bot_bot _let_1)))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun tptp.bool tptp.bool))) (let ((_let_4 (tptp.fun X_b _let_3))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_5 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_4 (tptp.hAPP (tptp.fun tptp.bool _let_3) (tptp.fun _let_1 _let_4) (tptp.combb tptp.bool _let_3 X_b) tptp.fconj) (tptp.hAPP X_b _let_1 (tptp.fequal X_b) A_4))) Pa)))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_4)))) (and (=> _let_7 (= _let_6 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_5 (tptp.insert X_b) A_4) _let_2))) (=> (not _let_7) (= _let_6 _let_2))))))))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun X_b _let_1))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_6 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fconj) (tptp.hAPP X_b _let_1 (tptp.hAPP _let_3 _let_3 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_4))) Pa)))) (let ((_let_8 (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_4)))) (and (=> _let_8 (= _let_7 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_6 (tptp.insert X_b) A_4) _let_2))) (=> (not _let_8) (= _let_7 _let_2)))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F1 $$unsorted) (Fun1_1 $$unsorted) (Com_1 $$unsorted) (Fun2_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c (tptp.fun tptp.state tptp.bool)))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun tptp.com _let_2))) (let ((_let_4 (tptp.hoare_509422987triple X_c))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (= (tptp.hAPP _let_4 X_b (tptp.hAPP (tptp.fun _let_1 _let_3) (tptp.fun _let_4 X_b) (tptp.hoare_728318379le_rec X_c X_b) F1) (tptp.hAPP _let_1 _let_4 (tptp.hAPP tptp.com _let_5 (tptp.hAPP _let_1 (tptp.fun tptp.com _let_5) (tptp.hoare_1008221573triple X_c) Fun1_1) Com_1) Fun2_1)) (tptp.hAPP _let_1 X_b (tptp.hAPP tptp.com _let_2 (tptp.hAPP _let_1 _let_3 F1 Fun1_1) Com_1) Fun2_1)))))))) (forall ((X_b $$unsorted) (A_4 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_4) A_1)))))) (forall ((X_b $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (= (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) Pa) (tptp.bot_bot _let_1)) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2))))))) (forall ((X_b $$unsorted) (Ca $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ca) (tptp.bot_bot _let_1)))))) (forall ((X_b $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (= (tptp.bot_bot _let_1) (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) Pa)) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) A_1)))) (not (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1)))))) (forall ((X_b $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) A_1))))) (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1))))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.bot_bot _let_1) (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP tptp.bool _let_1 (tptp.combk tptp.bool X_b) tptp.fFalse))))) (forall ((X_b $$unsorted) (A_4 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_4) A_1)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_4) A_1) (tptp.ti _let_1 A_1))))) (forall ((X_b $$unsorted) (Ba $$unsorted) (A_4 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_4))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) Ba) B_1))))))) (forall ((X_b $$unsorted) (B_1 $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1))) (let ((_let_3 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_1))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_1))) (= (= (tptp.hAPP _let_1 _let_1 _let_2 A_1) (tptp.hAPP _let_1 _let_1 _let_2 B_1)) (= (tptp.ti _let_1 A_1) (tptp.ti _let_1 B_1))))))))) (forall ((X_b $$unsorted) (Y_2 $$unsorted) (A_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) Y_2) A_1) X_1)) (or (= (tptp.ti X_b Y_2) (tptp.ti X_b X_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool A_1 X_1)))))) (forall ((X_b $$unsorted) (A_4 $$unsorted) (Ba $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_4))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) Ba) A_1))) (or (= (tptp.ti X_b A_4) (tptp.ti X_b Ba)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.insert X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.hAPP X_b _let_3 _let_1 X_1))) (let ((_let_5 (tptp.hAPP X_b _let_3 _let_1 Y_2))) (= (tptp.hAPP _let_2 _let_2 _let_4 (tptp.hAPP _let_2 _let_2 _let_5 A_1)) (tptp.hAPP _let_2 _let_2 _let_5 (tptp.hAPP _let_2 _let_2 _let_4 A_1))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_1 _let_2 A_1))) (= (tptp.hAPP _let_1 _let_1 _let_2 _let_3) _let_3))))) (forall ((X_b $$unsorted) (A_4 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (let ((_let_6 (tptp.collect X_b))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 (tptp.insert X_b) A_4) (tptp.hAPP _let_1 _let_1 _let_6 Pa)) (tptp.hAPP _let_1 _let_1 _let_6 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_3 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fimplies) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_3 (tptp.combb tptp.bool tptp.bool X_b) tptp.fNot) (tptp.hAPP X_b _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_4)))) Pa)))))))))) (forall ((X_b $$unsorted) (A_4 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_b _let_1))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_4) B_1) (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_2 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fdisj) (tptp.hAPP X_b _let_1 (tptp.hAPP _let_3 _let_3 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_4))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun _let_1 tptp.bool)) _let_2 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)) B_1)))))))))) (forall ((X_b $$unsorted) (A_4 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_4) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_4) B_1))))) (forall ((X_b $$unsorted) (X_2 $$unsorted) (Xa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_b _let_1))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) X_2) Xa) (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_2 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fdisj) (tptp.hAPP X_b _let_1 (tptp.hAPP _let_3 _let_3 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) X_2))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun _let_1 tptp.bool)) _let_2 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)) Xa)))))))))) (forall ((X_b $$unsorted) (A_4 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.insert X_b))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (=> (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_4 _let_3 A_4) _let_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_4 _let_3 Ba) _let_2)) (= (tptp.ti X_b A_4) (tptp.ti X_b Ba)))))))) (forall ((X_b $$unsorted) (Ba $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ba) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_4) (tptp.bot_bot _let_1)))) (= (tptp.ti X_b Ba) (tptp.ti X_b A_4))))) (forall ((X_b $$unsorted) (A_4 $$unsorted) (Ba $$unsorted) (Ca $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.ti X_b Ca))) (let ((_let_2 (tptp.ti X_b Ba))) (let ((_let_3 (tptp.ti X_b D))) (let ((_let_4 (tptp.ti X_b A_4))) (let ((_let_5 (tptp.fun X_b tptp.bool))) (let ((_let_6 (tptp.bot_bot _let_5))) (let ((_let_7 (tptp.insert X_b))) (let ((_let_8 (tptp.fun _let_5 _let_5))) (= (= (tptp.hAPP _let_5 _let_5 (tptp.hAPP X_b _let_8 _let_7 A_4) (tptp.hAPP _let_5 _let_5 (tptp.hAPP X_b _let_8 _let_7 Ba) _let_6)) (tptp.hAPP _let_5 _let_5 (tptp.hAPP X_b _let_8 _let_7 Ca) (tptp.hAPP _let_5 _let_5 (tptp.hAPP X_b _let_8 _let_7 D) _let_6))) (or (and (= _let_4 _let_1) (= _let_2 _let_3)) (and (= _let_4 _let_3) (= _let_2 _let_1))))))))))))) (forall ((X_b $$unsorted) (Ba $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Ba) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_4) (tptp.bot_bot _let_1)))) (= (tptp.ti X_b Ba) (tptp.ti X_b A_4))))) (forall ((X_b $$unsorted) (A_4 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (not (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_4) A_1) (tptp.bot_bot _let_1))))) (forall ((X_b $$unsorted) (A_4 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (not (= (tptp.bot_bot _let_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_4) A_1))))) (forall ((X_b $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 X_b (tptp.the_elem X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) (tptp.bot_bot _let_1))) (tptp.ti X_b X_1)))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F1 $$unsorted) (Fun1_1 $$unsorted) (Com_1 $$unsorted) (Fun2_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c (tptp.fun tptp.state tptp.bool)))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun tptp.com _let_2))) (let ((_let_4 (tptp.hoare_509422987triple X_c))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (= (tptp.hAPP _let_4 X_b (tptp.hAPP (tptp.fun _let_1 _let_3) (tptp.fun _let_4 X_b) (tptp.hoare_885240885e_case X_c X_b) F1) (tptp.hAPP _let_1 _let_4 (tptp.hAPP tptp.com _let_5 (tptp.hAPP _let_1 (tptp.fun tptp.com _let_5) (tptp.hoare_1008221573triple X_c) Fun1_1) Com_1) Fun2_1)) (tptp.hAPP _let_1 X_b (tptp.hAPP tptp.com _let_2 (tptp.hAPP _let_1 _let_3 F1 Fun1_1) Com_1) Fun2_1)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (tptp.bot X_b) (forall ((X_1 $$unsorted)) (= (tptp.hAPP X_c X_b (tptp.bot_bot (tptp.fun X_c X_b)) X_1) (tptp.bot_bot X_b))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.bot X_c) (forall ((X_2 $$unsorted)) (= (tptp.hAPP X_b X_c (tptp.bot_bot (tptp.fun X_b X_c)) X_2) (tptp.bot_bot X_c))))) (forall ((X_b $$unsorted) (Ga $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.hoare_509422987triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_4 (tptp.fun _let_3 _let_1))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_122391849derivs X_b) Ga) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) (tptp.hAPP _let_3 _let_1 (tptp.hAPP tptp.com _let_4 (tptp.hAPP _let_3 (tptp.fun tptp.com _let_4) (tptp.hoare_1008221573triple X_b) Pa) tptp.skip) Pa)) (tptp.bot_bot _let_2))))))))) (forall ((X_b $$unsorted) (D $$unsorted) (R_1 $$unsorted) (Ga $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.hoare_509422987triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.hoare_1008221573triple X_b))) (let ((_let_5 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_6 (tptp.fun _let_5 _let_1))) (let ((_let_7 (tptp.fun tptp.com _let_6))) (let ((_let_8 (tptp.hAPP _let_5 _let_7 _let_4 Pa))) (let ((_let_9 (tptp.insert _let_1))) (let ((_let_10 (tptp.fun _let_2 _let_2))) (let ((_let_11 (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_122391849derivs X_b) Ga))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_11 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_10 _let_9 (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_6 _let_8 Ca) Q_1)) _let_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_11 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_10 _let_9 (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_6 (tptp.hAPP _let_5 _let_7 _let_4 Q_1) D) R_1)) _let_3))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_11 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 _let_10 _let_9 (tptp.hAPP _let_5 _let_1 (tptp.hAPP tptp.com _let_6 _let_8 (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com (tptp.fun tptp.com tptp.com) tptp.semi Ca) D)) R_1)) _let_3))))))))))))))))) (forall ((X_b $$unsorted) (Y_2 $$unsorted)) (not (forall ((Fun1 $$unsorted) (Com $$unsorted) (Fun2 $$unsorted)) (let ((_let_1 (tptp.hoare_509422987triple X_b))) (let ((_let_2 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (not (= Y_2 (tptp.hAPP _let_2 _let_1 (tptp.hAPP tptp.com _let_3 (tptp.hAPP _let_2 (tptp.fun tptp.com _let_3) (tptp.hoare_1008221573triple X_b) Fun1) Com) Fun2))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_1)) (not (forall ((B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (= (tptp.ti _let_1 A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) B))))))))) (forall ((Com1_2 $$unsorted) (Com2_2 $$unsorted)) (not (= (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com (tptp.fun tptp.com tptp.com) tptp.semi Com1_2) Com2_2) tptp.skip))) (forall ((Com1_2 $$unsorted) (Com2_2 $$unsorted)) (not (= tptp.skip (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com (tptp.fun tptp.com tptp.com) tptp.semi Com1_2) Com2_2)))) (forall ((X_b $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.hAPP _let_1 X_b (tptp.the_elem X_b) X_3) (tptp.hAPP _let_1 X_b (tptp.the X_b) (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.combb _let_1 tptp.bool X_b) (tptp.hAPP _let_1 _let_3 (tptp.fequal _let_1) X_3)) (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_b (tptp.fun _let_1 _let_1)) (tptp.fun _let_1 _let_2) (tptp.combc X_b _let_1 _let_1) (tptp.insert X_b)) (tptp.bot_bot _let_1))))))))) (forall ((X_b $$unsorted) (A_4 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_4) A_1)) (exists ((B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (and (= (tptp.ti _let_1 A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_4) B)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_4) B))))))))) (forall ((Com1_1 $$unsorted) (Com2_1 $$unsorted) (Com1 $$unsorted) (Com2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.com tptp.com))) (= (= (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com _let_1 tptp.semi Com1_1) Com2_1) (tptp.hAPP tptp.com tptp.com (tptp.hAPP tptp.com _let_1 tptp.semi Com1) Com2)) (and (= Com1_1 Com1) (= Com2_1 Com2))))) (forall ((X_b $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 X_b (tptp.the X_b) (tptp.hAPP X_b _let_1 (tptp.fequal X_b) X_1)) (tptp.ti X_b X_1)))) (forall ((X_b $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (= (tptp.hAPP _let_1 X_b (tptp.the X_b) (tptp.hAPP X_b _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_4)) (tptp.ti X_b A_4))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.hAPP _let_2 _let_2 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.combb tptp.bool tptp.bool X_b))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun X_b _let_4))) (let ((_let_8 (tptp.hAPP _let_1 X_b (tptp.the X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_7 _let_6 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_7 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_7) (tptp.combb tptp.bool _let_4 X_b) tptp.fconj) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_6 _let_5 (tptp.hAPP tptp.bool _let_4 tptp.fimplies Pa)) (tptp.hAPP X_b _let_1 _let_3 X_1)))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_6 _let_5 (tptp.hAPP tptp.bool _let_4 tptp.fimplies (tptp.hAPP tptp.bool tptp.bool tptp.fNot Pa))) (tptp.hAPP X_b _let_1 _let_3 Y_2)))))) (let ((_let_9 (tptp.hBOOL Pa))) (and (=> _let_9 (= (tptp.ti X_b X_1) _let_8)) (=> (not _let_9) (= (tptp.ti X_b Y_2) _let_8))))))))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (forall ((Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Y_1) A_1))))) (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (A_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_4)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)) (= (tptp.ti X_b X_2) (tptp.ti X_b A_4)))) (= (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the X_b) Pa) (tptp.ti X_b A_4))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (A_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_4)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)) (= (tptp.ti X_b X_2) (tptp.ti X_b A_4)))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the X_b) Pa)))))) (forall ((X_b $$unsorted) (A_4 $$unsorted) (Pa $$unsorted)) (=> (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)) (forall ((Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa Y_1)) (= (tptp.ti X_b Y_1) (tptp.ti X_b X_2)))))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_4)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the X_b) Pa) (tptp.ti X_b A_4))))) (forall ((X_b $$unsorted) (Pa $$unsorted)) (=> (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)) (forall ((Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa Y_1)) (= (tptp.ti X_b Y_1) (tptp.ti X_b X_2)))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the X_b) Pa))))) (forall ((X_b $$unsorted) (Q_1 $$unsorted) (Ga $$unsorted) (Ca $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.hoare_509422987triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_4 (tptp.fun _let_3 _let_1))) (=> (forall ((Z_1 $$unsorted) (S $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b (tptp.fun tptp.state tptp.bool) Pa Z_1) S)) (exists ((P_1 $$unsorted) (Q_2 $$unsorted)) (let ((_let_1 (tptp.hoare_509422987triple X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_b (tptp.fun tptp.state tptp.bool)))) (let ((_let_4 (tptp.fun _let_3 _let_1))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_122391849derivs X_b) Ga) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) (tptp.hAPP _let_3 _let_1 (tptp.hAPP tptp.com _let_4 (tptp.hAPP _let_3 (tptp.fun tptp.com _let_4) (tptp.hoare_1008221573triple X_b) P_1) Ca) Q_2)) (tptp.bot_bot _let_2)))) (forall ((S_1 $$unsorted)) (=> (forall ((Z_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.state tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_1 P_1 Z_2) S)) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b _let_1 Q_2 Z_2) S_1))))) (tptp.hBOOL (tptp.hAPP tptp.state tptp.bool (tptp.hAPP X_b (tptp.fun tptp.state tptp.bool) Q_1 Z_1) S_1)))))))))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.hoare_122391849derivs X_b) Ga) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.insert _let_1) (tptp.hAPP _let_3 _let_1 (tptp.hAPP tptp.com _let_4 (tptp.hAPP _let_3 (tptp.fun tptp.com _let_4) (tptp.hoare_1008221573triple X_b) Pa) Ca) Q_1)) (tptp.bot_bot _let_2)))))))))) (forall ((X_b $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (not (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1))) (exists ((X_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (and (= (tptp.ti _let_1 A_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_2) B)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) B))))))))) (forall ((X_b $$unsorted) (F_1 $$unsorted) (A_4 $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) _let_2 (tptp.finite_fold1Set X_b) F_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_4) (tptp.bot_bot _let_1))) Ba)) (= (tptp.ti X_b A_4) (tptp.ti X_b Ba)))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_2 tptp.bool) (tptp.finite_folding_one X_b) F_1) F)) (= (tptp.hAPP _let_1 X_b F (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) (tptp.bot_bot _let_1))) (tptp.ti X_b X_1)))))) (forall ((X_b $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_2 X_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) _let_2)))))) (forall ((X_b $$unsorted) (F_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 _let_1) (tptp.finite_fold1Set X_b) F_1) (tptp.bot_bot _let_1)) X_1))))) (forall ((X_b $$unsorted) (F_1 $$unsorted) (A_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 _let_1) (tptp.finite_fold1Set X_b) F_1) A_1) X_1)) (not (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1)))))) (forall ((X_b $$unsorted) (F_1 $$unsorted) (A_4 $$unsorted) (A_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_b (tptp.fun X_b X_b)))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.hAPP _let_3 (tptp.fun X_b _let_2) (tptp.finite_fold_graph X_b X_b) F_1) A_4) A_1) X_1)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_4) A_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 _let_2 (tptp.finite_fold1Set X_b) F_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_4) A_1)) X_1)))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_3 tptp.bool) (tptp.finite_folding_one X_b) F_1) F)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_1))) (=> (not (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1))) (= (tptp.hAPP _let_1 X_b F (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) A_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 F_1 X_1) (tptp.hAPP _let_1 X_b F A_1))))))))))) (forall ((X_b $$unsorted) (F_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b (tptp.fun X_b X_b)))) (= (tptp.hAPP _let_1 X_b (tptp.hAPP _let_2 (tptp.fun _let_1 X_b) (tptp.finite_fold1 X_b) F_1) A_1) (tptp.hAPP _let_1 X_b (tptp.the X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_1) (tptp.finite_fold1Set X_b) F_1) A_1)))))) (forall ((X_b $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun tptp.bool tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.collect X_b))) (let ((_let_5 (tptp.finite_finite_1 X_b))) (=> (or (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 (tptp.hAPP _let_3 _let_3 _let_4 Pa))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 (tptp.hAPP _let_3 _let_3 _let_4 Q_1)))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 (tptp.hAPP _let_3 _let_3 _let_4 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_3) (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.bool _let_1) (tptp.fun _let_3 _let_2) (tptp.combb tptp.bool _let_1 X_b) tptp.fconj) Pa)) Q_1))))))))))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) (tptp.bot_bot _let_1))))) (forall ((X_b $$unsorted) (A_4 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.finite_finite_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_4) A_1))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (F_1 $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (=> (forall ((X_2 $$unsorted)) (= (tptp.hAPP X_b X_c F_1 X_2) (tptp.hAPP X_b X_c G X_2))) (= (tptp.ti _let_1 F_1) (tptp.ti _let_1 G))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool A_1 X_1))))) (forall ((X_b $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) Pa) (tptp.ti _let_1 Pa)))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun X_b (tptp.fun X_b X_b)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_2 tptp.bool) (tptp.finite_folding_one X_b) F_1) F)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (= (tptp.hAPP _let_1 X_b F A_1) (tptp.hAPP _let_1 X_b (tptp.hAPP _let_3 _let_2 (tptp.finite_fold1 X_b) F_1) A_1)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_c _let_3 (tptp.hAPP (tptp.fun X_b (tptp.fun X_c X_c)) (tptp.fun X_c _let_3) (tptp.finite_fold_graph X_b X_c) F_1) Z) (tptp.bot_bot _let_1)) Z)))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F_1 $$unsorted) (Z $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_c _let_3 (tptp.hAPP (tptp.fun X_b (tptp.fun X_c X_c)) (tptp.fun X_c _let_3) (tptp.finite_fold_graph X_b X_c) F_1) Z) (tptp.bot_bot _let_1)) X_1)) (= (tptp.ti X_c X_1) (tptp.ti X_c Z))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F_1 $$unsorted) (Z $$unsorted) (Y_2 $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c X_c))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_c tptp.bool))) (let ((_let_4 (tptp.fun _let_2 _let_3))) (let ((_let_5 (tptp.hAPP X_c _let_4 (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun X_c _let_4) (tptp.finite_fold_graph X_b X_c) F_1) Z))) (=> (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_1))) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_2 _let_3 _let_5 A_1) Y_2)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_2 _let_3 _let_5 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) X_1) A_1)) (tptp.hAPP X_c X_c (tptp.hAPP X_b _let_1 F_1 X_1) Y_2))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.finite_finite X_b) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite_1 X_b) A_1))))) (forall ((X_b $$unsorted)) (=> (tptp.finite_finite X_b) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite_1 X_b) A_1))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.collect X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.finite_finite_1 X_b))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_5 (tptp.fun _let_2 _let_2) (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_2 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fdisj) Pa)) Q_1)))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 _let_1 Pa))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 _let_1 Q_1))))))))))) (forall ((X_b $$unsorted) (A_4 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.finite_finite_1 X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) A_4) A_1))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_1)))))) (forall ((X_b $$unsorted) (A_4 $$unsorted) (G $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (= G (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 X_b) (tptp.finite_fold1 X_b) F_1)) (= (tptp.hAPP _let_1 X_b G (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_4) (tptp.bot_bot _let_1))) (tptp.ti X_b A_4))))) (forall ((X_b $$unsorted) (F_1 $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 X_b) (tptp.finite_fold1 X_b) F_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_4) (tptp.bot_bot _let_1))) (tptp.ti X_b A_4)))) (forall ((X_b $$unsorted) (A_1 $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_2 tptp.bool) (tptp.finite_folding_one X_b) F_1) F)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (not (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1))) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.insert X_b))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) F_1 X_2) Y_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 _let_2 X_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 _let_2 Y_1) (tptp.bot_bot _let_1))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP _let_1 X_b F A_1)) A_1))))))))) (forall ((X_b $$unsorted) (F_1 $$unsorted) (A_4 $$unsorted) (X_3 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) _let_2 (tptp.finite_fold1Set X_b) F_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_4) X_3)) X_1)) (not (forall ((A_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.insert X_b))) (=> (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 _let_3 A_4) X_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 _let_3 A_3) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b _let_2) (tptp.finite_fold_graph X_b X_b) F_1) A_3) A_2) X_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_3) A_2))))))))))))) (forall ((X_b $$unsorted) (F_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (not (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1))) (exists ((X1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 _let_1) (tptp.finite_fold1Set X_b) F_1) A_1) X1)))))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) F)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.bot_bot _let_1))) (=> (forall ((X_2 $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) F_2)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa F_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_2) F_2)))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa F))))))) (forall ((X_b $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_4)) (or (= (tptp.ti _let_1 A_4) (tptp.bot_bot _let_1)) (exists ((A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (and (= (tptp.ti _let_1 A_4) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_3) A_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_2))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F_1 $$unsorted) (Z $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite_1 X_b) A_1)) (exists ((X1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_2 _let_1 (tptp.hAPP X_c _let_3 (tptp.hAPP (tptp.fun X_b (tptp.fun X_c X_c)) (tptp.fun X_c _let_3) (tptp.finite_fold_graph X_b X_c) F_1) Z) A_1) X1)))))))) (forall ((X_b $$unsorted) (F_1 $$unsorted) (A1 $$unsorted) (A2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_1 _let_1) (tptp.finite_fold1Set X_b) F_1) A1) A2)) (exists ((A_3 $$unsorted) (A_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (and (= (tptp.ti _let_1 A1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_3) A_2)) (= (tptp.ti X_b A2) (tptp.ti X_b X_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b _let_2) (tptp.finite_fold_graph X_b X_b) F_1) A_3) A_2) X_2)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_3) A_2)))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F_1 $$unsorted) (Z $$unsorted) (A1 $$unsorted) (A2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (= (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_c _let_3 (tptp.hAPP (tptp.fun X_b (tptp.fun X_c X_c)) (tptp.fun X_c _let_3) (tptp.finite_fold_graph X_b X_c) F_1) Z) A1) A2)) (or (and (= (tptp.ti _let_1 A1) (tptp.bot_bot _let_1)) (= (tptp.ti X_c A2) (tptp.ti X_c Z))) (exists ((X_2 $$unsorted) (A_2 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.fun X_c X_c))) (and (= (tptp.ti _let_2 A1) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) X_2) A_2)) (= (tptp.ti X_c A2) (tptp.hAPP X_c X_c (tptp.hAPP X_b _let_4 F_1 X_2) Y_1)) (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_2) A_2))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_2 _let_1 (tptp.hAPP X_c _let_3 (tptp.hAPP (tptp.fun X_b _let_4) (tptp.fun X_c _let_3) (tptp.finite_fold_graph X_b X_c) F_1) Z) A_2) Y_1)))))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_3 tptp.bool) (tptp.finite2073411215e_idem X_b) F_1) F)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (not (= (tptp.ti _let_1 A_1) (tptp.bot_bot _let_1))) (= (tptp.hAPP _let_1 X_b F (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) A_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 F_1 X_1) (tptp.hAPP _let_1 X_b F A_1)))))))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) F)) (=> (not (= (tptp.ti _let_1 F) (tptp.bot_bot _let_1))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_2) (tptp.bot_bot _let_1)))))) (=> (forall ((X_2 $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) F_2)) (=> (not (= (tptp.ti _let_1 F_2) (tptp.bot_bot _let_1))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa F_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_2) F_2))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa F)))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.fun (tptp.fun X_b tptp.bool) X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun _let_2 tptp.bool) (tptp.finite2073411215e_idem X_b) F_1) F)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 F_1 X_1) X_1) (tptp.ti X_b X_1)))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_1 $$unsorted) (F_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 X_b F A_1))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun _let_4 tptp.bool) (tptp.finite2073411215e_idem X_b) F_1) F)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) A_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_1)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 F_1 X_1) _let_2) _let_2))))))))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (and (tptp.finite_finite T_1) (tptp.finite_finite T_2)) (tptp.finite_finite (tptp.fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.bot T_1) (tptp.bot (tptp.fun T_2 T_1)))) (tptp.finite_finite tptp.bool) (tptp.bot tptp.bool) (forall ((T $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.ti T A))) (= (tptp.ti T _let_1) _let_1))) (forall ((P $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool tptp.fNot P))) (not (tptp.hBOOL P)))) (forall ((P $$unsorted)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool tptp.fNot P)))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_1 (tptp.fun X_a X_c))) (let ((_let_2 (tptp.fun X_a X_b))) (= (tptp.hAPP X_a X_c (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.combb X_b X_c X_a) P) Q) R) (tptp.hAPP X_b X_c P (tptp.hAPP X_a X_b Q R)))))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (let ((_let_2 (tptp.fun X_a X_c))) (= (tptp.hAPP X_a X_c (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun X_b _let_2) (tptp.combc X_a X_b X_c) P) Q) R) (tptp.hAPP X_b X_c (tptp.hAPP X_a _let_1 P R) Q))))) _let_28 (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (let ((_let_2 (tptp.fun X_a X_c))) (let ((_let_3 (tptp.fun X_a X_b))) (= (tptp.hAPP X_a X_c (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun _let_3 _let_2) (tptp.combs X_a X_b X_c) P) Q) R) (tptp.hAPP X_b X_c (tptp.hAPP X_a _let_1 P R) (tptp.hAPP X_a X_b Q R))))))) (forall ((Q $$unsorted) (P $$unsorted)) (or (not (tptp.hBOOL P)) (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fconj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fconj P) Q))) (tptp.hBOOL P))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fconj P) Q))) (tptp.hBOOL Q))) (forall ((Q $$unsorted) (P $$unsorted)) (or (not (tptp.hBOOL P)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fdisj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fdisj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fdisj P) Q))) (tptp.hBOOL P) (tptp.hBOOL Q))) _let_27 (forall ((P $$unsorted)) (let ((_let_1 (tptp.ti tptp.bool P))) (or (= _let_1 tptp.fTrue) (= _let_1 tptp.fFalse)))) (forall ((X_a $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.fequal X_a) X) Y))) (= (tptp.ti X_a X) (tptp.ti X_a Y)))) (forall ((X_a $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.fequal X_a) X) Y)))) (forall ((Q $$unsorted) (P $$unsorted)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fimplies P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fimplies P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fimplies P) Q))) (not (tptp.hBOOL P)) (tptp.hBOOL Q))) _let_25 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 26.35/26.54 )
% 26.35/26.54 % SZS output end Proof for SWW470+5
% 26.35/26.54 % cvc5---1.0.5 exiting
% 26.35/26.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------