%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : ITP011+1 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n005.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 03:14:39 EDT 2023

% Result   : Theorem 31.46s 31.65s
% Output   : Proof 31.46s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem    : ITP011+1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.13/0.15  % Command    : do_cvc5 %s %d
% 0.16/0.37  % Computer : n005.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Sun Aug 27 10:41:38 EDT 2023
% 0.16/0.37  % CPUTime    : 
% 0.23/0.52  %----Proving TF0_NAR, FOF, or CNF
% 31.46/31.65  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.xOzosC5Ani/cvc5---1.0.5_19637.p...
% 31.46/31.65  ------- get file name : TPTP file name is ITP011+1
% 31.46/31.65  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_19637.smt2...
% 31.46/31.65  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 31.46/31.65  --- Run --no-e-matching --full-saturate-quant at 5...
% 31.46/31.65  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 31.46/31.65  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 31.46/31.65  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 31.46/31.65  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 31.46/31.65  % SZS status Theorem for ITP011+1
% 31.46/31.65  % SZS output start Proof for ITP011+1
% 31.46/31.65  (
% 31.46/31.65  (let ((_let_1 (not (forall ((A_27a $$unsorted) (V0y_2E0 $$unsorted) (V1x_2E0 $$unsorted) (V2R_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27a V0y_2E0))) (let ((_let_2 (tptp.s A_27a V1x_2E0))) (let ((_let_3 (tptp.tyop_2Emin_2Efun A_27a tptp.tyop_2Emin_2Ebool))) (let ((_let_4 (tptp.s (tptp.tyop_2Emin_2Efun A_27a _let_3) V2R_2E0))) (let ((_let_5 (tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_6 (tptp.s _let_5 (tptp.c_2Eoption_2ESOME_2E1 _let_1)))) (let ((_let_7 (tptp.s _let_5 (tptp.c_2Eoption_2ESOME_2E1 _let_2)))) (let ((_let_8 (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2EF_2E0))) (let ((_let_9 (tptp.s _let_5 tptp.c_2Eoption_2ENONE_2E0))) (and (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eoption_2EOPTREL_2E3 _let_4 _let_9 _let_9)) (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2ET_2E0)) (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eoption_2EOPTREL_2E3 _let_4 _let_7 _let_9)) _let_8) (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eoption_2EOPTREL_2E3 _let_4 _let_9 _let_6)) _let_8) (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eoption_2EOPTREL_2E3 _let_4 _let_7 _let_6)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s _let_3 (tptp.app_2E2 _let_4 _let_2)) _let_1))))))))))))))))) (let ((_let_2 (forall ((A_27a $$unsorted) (A_27b $$unsorted) (V0R_2E0 $$unsorted) (V1x_2E0 $$unsorted) (V2y_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Eoption_2Eoption A_27b))) (let ((_let_2 (tptp.s _let_1 V2y_2E0))) (let ((_let_3 (tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_4 (tptp.s _let_3 V1x_2E0))) (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eoption_2EOPTREL_2E3 (tptp.s (tptp.tyop_2Emin_2Efun A_27a (tptp.tyop_2Emin_2Efun A_27b tptp.tyop_2Emin_2Ebool)) V0R_2E0) _let_4 _let_2))) (or (and (= _let_4 (tptp.s _let_3 tptp.c_2Eoption_2ENONE_2E0)) (= _let_2 (tptp.s _let_1 tptp.c_2Eoption_2ENONE_2E0))) (exists ((V3x0_2E0 $$unsorted) (V4y0_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27b V4y0_2E0))) (let ((_let_2 (tptp.s A_27a V3x0_2E0))) (let ((_let_3 (tptp.tyop_2Emin_2Efun A_27b tptp.tyop_2Emin_2Ebool))) (let ((_let_4 (tptp.tyop_2Eoption_2Eoption A_27b))) (let ((_let_5 (tptp.tyop_2Eoption_2Eoption A_27a))) (and (= (tptp.s _let_5 V1x_2E0) (tptp.s _let_5 (tptp.c_2Eoption_2ESOME_2E1 _let_2))) (= (tptp.s _let_4 V2y_2E0) (tptp.s _let_4 (tptp.c_2Eoption_2ESOME_2E1 _let_1))) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s _let_3 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun A_27a _let_3) V0R_2E0) _let_2)) _let_1))))))))))))))))))) (let ((_let_3 (forall ((A_27a $$unsorted) (A_27b $$unsorted) (V0f_2E0 $$unsorted) (V1e_2E0 $$unsorted) (V2e_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (tptp.s _let_1 tptp.c_2Eoption_2ENONE_2E0))) (and (forall ((V3x_2E0 $$unsorted) (V4y_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27a V4y_2E0))) (let ((_let_2 (tptp.s A_27a V3x_2E0))) (let ((_let_3 (tptp.tyop_2Eoption_2Eoption A_27a))) (= (= (tptp.s _let_3 (tptp.c_2Eoption_2ESOME_2E1 _let_2)) (tptp.s _let_3 (tptp.c_2Eoption_2ESOME_2E1 _let_1))) (= _let_2 _let_1)))))) (forall ((V5x_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27a V5x_2E0))) (= (tptp.s A_27a (tptp.c_2Eoption_2ETHE_2E1 (tptp.s (tptp.tyop_2Eoption_2Eoption A_27a) (tptp.c_2Eoption_2ESOME_2E1 _let_1)))) _let_1))) (forall ((V6x_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Eoption_2Eoption A_27a))) (not (= (tptp.s _let_1 tptp.c_2Eoption_2ENONE_2E0) (tptp.s _let_1 (tptp.c_2Eoption_2ESOME_2E1 (tptp.s A_27a V6x_2E0))))))) (forall ((V7x_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Eoption_2Eoption A_27a))) (not (= (tptp.s _let_1 (tptp.c_2Eoption_2ESOME_2E1 (tptp.s A_27a V7x_2E0))) (tptp.s _let_1 tptp.c_2Eoption_2ENONE_2E0))))) (forall ((V8x_2E0 $$unsorted)) (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eoption_2EIS__SOME_2E1 (tptp.s (tptp.tyop_2Eoption_2Eoption A_27a) (tptp.c_2Eoption_2ESOME_2E1 (tptp.s A_27a V8x_2E0))))) (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2ET_2E0))) (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eoption_2EIS__SOME_2E1 _let_2)) (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2EF_2E0)) (forall ((V9x_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (tptp.s _let_1 V9x_2E0))) (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eoption_2EIS__NONE_2E1 _let_2))) (= _let_2 (tptp.s _let_1 tptp.c_2Eoption_2ENONE_2E0)))))) (forall ((V10x_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (tptp.s _let_1 V10x_2E0))) (= (not (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eoption_2EIS__SOME_2E1 _let_2)))) (= _let_2 (tptp.s _let_1 tptp.c_2Eoption_2ENONE_2E0)))))) (forall ((V11x_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (tptp.s _let_1 V11x_2E0))) (=> (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eoption_2EIS__SOME_2E1 _let_2))) (= (tptp.s _let_1 (tptp.c_2Eoption_2ESOME_2E1 (tptp.s A_27a (tptp.c_2Eoption_2ETHE_2E1 _let_2)))) _let_2))))) (forall ((V12x_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (tptp.s _let_1 V12x_2E0))) (= (tptp.s _let_1 (tptp.c_2Eoption_2Eoption__CASE_2E3 _let_2 (tptp.s _let_1 tptp.c_2Eoption_2ENONE_2E0) (tptp.s (tptp.tyop_2Emin_2Efun A_27a _let_1) tptp.c_2Eoption_2ESOME_2E0))) _let_2)))) (forall ((V13x_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (tptp.s _let_1 V13x_2E0))) (= (tptp.s _let_1 (tptp.c_2Eoption_2Eoption__CASE_2E3 _let_2 _let_2 (tptp.s (tptp.tyop_2Emin_2Efun A_27a _let_1) tptp.c_2Eoption_2ESOME_2E0))) _let_2)))) (forall ((V14x_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27b V2e_2E0))) (let ((_let_2 (tptp.s (tptp.tyop_2Eoption_2Eoption A_27a) V14x_2E0))) (=> (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eoption_2EIS__NONE_2E1 _let_2))) (= (tptp.s A_27b (tptp.c_2Eoption_2Eoption__CASE_2E3 _let_2 _let_1 (tptp.s (tptp.tyop_2Emin_2Efun A_27a A_27b) V0f_2E0))) _let_1))))) (forall ((V15x_2E0 $$unsorted)) (let ((_let_1 (tptp.s (tptp.tyop_2Eoption_2Eoption A_27a) V15x_2E0))) (let ((_let_2 (tptp.s (tptp.tyop_2Emin_2Efun A_27a A_27b) V0f_2E0))) (=> (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eoption_2EIS__SOME_2E1 _let_1))) (= (tptp.s A_27b (tptp.c_2Eoption_2Eoption__CASE_2E3 _let_1 (tptp.s A_27b V2e_2E0) _let_2)) (tptp.s A_27b (tptp.app_2E2 _let_2 (tptp.s A_27a (tptp.c_2Eoption_2ETHE_2E1 _let_1))))))))) (forall ((V16x_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (tptp.s _let_1 V16x_2E0))) (=> (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eoption_2EIS__SOME_2E1 _let_2))) (= (tptp.s _let_1 (tptp.c_2Eoption_2Eoption__CASE_2E3 _let_2 (tptp.s _let_1 V1e_2E0) (tptp.s (tptp.tyop_2Emin_2Efun A_27a _let_1) tptp.c_2Eoption_2ESOME_2E0))) _let_2))))) (forall ((V17v_2E0 $$unsorted) (V18f_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27b V17v_2E0))) (= (tptp.s A_27b (tptp.c_2Eoption_2Eoption__CASE_2E3 (tptp.s (tptp.tyop_2Eoption_2Eoption A_27a) tptp.c_2Eoption_2ENONE_2E0) _let_1 (tptp.s (tptp.tyop_2Emin_2Efun A_27a A_27b) V18f_2E0))) _let_1))) (forall ((V19x_2E0 $$unsorted) (V20v_2E0 $$unsorted) (V21f_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27a V19x_2E0))) (let ((_let_2 (tptp.s (tptp.tyop_2Emin_2Efun A_27a A_27b) V21f_2E0))) (= (tptp.s A_27b (tptp.c_2Eoption_2Eoption__CASE_2E3 (tptp.s (tptp.tyop_2Eoption_2Eoption A_27a) (tptp.c_2Eoption_2ESOME_2E1 _let_1)) (tptp.s A_27b V20v_2E0) _let_2)) (tptp.s A_27b (tptp.app_2E2 _let_2 _let_1)))))) (forall ((V22f_2E0 $$unsorted) (V23x_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27a V23x_2E0))) (let ((_let_2 (tptp.s (tptp.tyop_2Emin_2Efun A_27a A_27b) V22f_2E0))) (let ((_let_3 (tptp.tyop_2Eoption_2Eoption A_27b))) (= (tptp.s _let_3 (tptp.c_2Eoption_2EOPTION__MAP_2E2 _let_2 (tptp.s (tptp.tyop_2Eoption_2Eoption A_27a) (tptp.c_2Eoption_2ESOME_2E1 _let_1)))) (tptp.s _let_3 (tptp.c_2Eoption_2ESOME_2E1 (tptp.s A_27b (tptp.app_2E2 _let_2 _let_1))))))))) (forall ((V24f_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Eoption_2Eoption A_27b))) (= (tptp.s _let_1 (tptp.c_2Eoption_2EOPTION__MAP_2E2 (tptp.s (tptp.tyop_2Emin_2Efun A_27a A_27b) V24f_2E0) (tptp.s (tptp.tyop_2Eoption_2Eoption A_27a) tptp.c_2Eoption_2ENONE_2E0))) (tptp.s _let_1 tptp.c_2Eoption_2ENONE_2E0)))) (= (tptp.s _let_1 (tptp.c_2Eoption_2EOPTION__JOIN_2E1 (tptp.s (tptp.tyop_2Eoption_2Eoption _let_1) tptp.c_2Eoption_2ENONE_2E0))) _let_2) (forall ((V25x_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (tptp.s _let_1 V25x_2E0))) (= (tptp.s _let_1 (tptp.c_2Eoption_2EOPTION__JOIN_2E1 (tptp.s (tptp.tyop_2Eoption_2Eoption _let_1) (tptp.c_2Eoption_2ESOME_2E1 _let_2)))) _let_2)))))))))) (let ((_let_4 (forall ((V0t_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Emin_2Ebool V0t_2E0))) (let ((_let_2 (tptp.p _let_1))) (let ((_let_3 (not _let_2))) (let ((_let_4 (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2EF_2E0))) (let ((_let_5 (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2ET_2E0))) (and (= (= _let_5 _let_1) _let_2) (= (= _let_1 _let_5) _let_2) (= (= _let_4 _let_1) _let_3) (= (= _let_1 _let_4) _let_3)))))))))) (let ((_let_5 (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2ET_2E0))) (let ((_let_6 (tptp.p _let_5))) (let ((_let_7 (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2EF_2E0))) (let ((_let_8 (tptp.p _let_7))) (let ((_let_9 (not _let_8))) (let ((_let_10 (not _let_6))) (let ((_let_11 (forall ((V0t_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Emin_2Ebool V0t_2E0))) (or (= _let_1 (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2ET_2E0)) (= _let_1 (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2EF_2E0))))))) (let ((_let_12 (tptp.s SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_13 (tptp.s SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_14 (tptp.tyop_2Emin_2Efun SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 tptp.tyop_2Emin_2Ebool))) (let ((_let_15 (tptp.s (tptp.tyop_2Emin_2Efun SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 _let_14) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))) (let ((_let_16 (tptp.app_2E2 (tptp.s _let_14 (tptp.app_2E2 _let_15 _let_13)) _let_12))) (let ((_let_17 (tptp.s tptp.tyop_2Emin_2Ebool _let_16))) (let ((_let_18 (= _let_5 _let_17))) (let ((_let_19 (tptp.p _let_17))) (let ((_let_20 (ASSUME :args (_let_6)))) (let ((_let_21 (= _let_7 _let_17))) (let ((_let_22 (or _let_18 _let_21))) (let ((_let_23 (forall ((V0t_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Emin_2Ebool V0t_2E0))) (or (= (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2ET_2E0) _let_1) (= (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2EF_2E0) _let_1)))))) (let ((_let_24 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_25 (_let_23))) (let ((_let_26 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (_let_16 QUANTIFIERS_INST_CBQI_PROP)) :args _let_25)) _let_24 :args (_let_22 false _let_23)))) (let ((_let_27 (tptp.c_2Eoption_2ESOME_2E1 _let_12))) (let ((_let_28 (tptp.tyop_2Eoption_2Eoption SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_29 (tptp.s _let_28 _let_27))) (let ((_let_30 (tptp.c_2Eoption_2ESOME_2E1 _let_13))) (let ((_let_31 (tptp.s _let_28 _let_30))) (let ((_let_32 (tptp.c_2Eoption_2EOPTREL_2E3 _let_15 _let_31 _let_29))) (let ((_let_33 (tptp.s tptp.tyop_2Emin_2Ebool _let_32))) (let ((_let_34 (= _let_7 _let_33))) (let ((_let_35 (= _let_33 _let_17))) (let ((_let_36 (not _let_21))) (let ((_let_37 (= _let_5 _let_33))) (let ((_let_38 (or _let_37 _let_34))) (let ((_let_39 (tptp.p _let_33))) (let ((_let_40 (forall ((V3x0_2E0 $$unsorted) (V4y0_2E0 $$unsorted)) (let ((_let_1 (tptp.s SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 V4y0_2E0))) (let ((_let_2 (tptp.s SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 V3x0_2E0))) (let ((_let_3 (tptp.tyop_2Emin_2Efun SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 tptp.tyop_2Emin_2Ebool))) (let ((_let_4 (tptp.tyop_2Eoption_2Eoption SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (or (not (= (tptp.s _let_4 (tptp.c_2Eoption_2ESOME_2E1 (tptp.s SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (tptp.s _let_4 (tptp.c_2Eoption_2ESOME_2E1 _let_2)))) (not (= (tptp.s _let_4 (tptp.c_2Eoption_2ESOME_2E1 (tptp.s SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (tptp.s _let_4 (tptp.c_2Eoption_2ESOME_2E1 _let_1)))) (not (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s _let_3 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 _let_3) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25) _let_2)) _let_1)))))))))))) (let ((_let_41 (not _let_40))) (let ((_let_42 (tptp.s _let_28 tptp.c_2Eoption_2ENONE_2E0))) (let ((_let_43 (= _let_31 _let_42))) (let ((_let_44 (and _let_43 (= _let_29 _let_42)))) (let ((_let_45 (or _let_44 _let_41))) (let ((_let_46 (= _let_39 _let_45))) (let ((_let_47 (tptp.s SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31))) (let ((_let_48 (tptp.s SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30))) (let ((_let_49 (tptp.app_2E2 (tptp.s _let_14 (tptp.app_2E2 _let_15 _let_48)) _let_47))) (let ((_let_50 (tptp.s tptp.tyop_2Emin_2Ebool _let_49))) (let ((_let_51 (tptp.p _let_50))) (let ((_let_52 (not _let_51))) (let ((_let_53 (= _let_29 (tptp.s _let_28 (tptp.c_2Eoption_2ESOME_2E1 _let_47))))) (let ((_let_54 (not _let_53))) (let ((_let_55 (= _let_31 (tptp.s _let_28 (tptp.c_2Eoption_2ESOME_2E1 _let_48))))) (let ((_let_56 (not _let_55))) (let ((_let_57 (or _let_56 _let_54 _let_52))) (let ((_let_58 (= _let_13 _let_48))) (let ((_let_59 (= _let_55 _let_58))) (let ((_let_60 (= _let_12 _let_47))) (let ((_let_61 (= _let_53 _let_60))) (let ((_let_62 (= _let_7 _let_50))) (let ((_let_63 (= _let_52 _let_62))) (let ((_let_64 (not _let_37))) (let ((_let_65 (forall ((BOUND_VARIABLE_2403 $$unsorted) (BOUND_VARIABLE_2405 $$unsorted) (BOUND_VARIABLE_2407 $$unsorted) (BOUND_VARIABLE_2409 $$unsorted)) (let ((_let_1 (tptp.s BOUND_VARIABLE_2403 BOUND_VARIABLE_2405))) (let ((_let_2 (tptp.s BOUND_VARIABLE_2403 BOUND_VARIABLE_2407))) (let ((_let_3 (tptp.tyop_2Emin_2Efun BOUND_VARIABLE_2403 tptp.tyop_2Emin_2Ebool))) (let ((_let_4 (tptp.s (tptp.tyop_2Emin_2Efun BOUND_VARIABLE_2403 _let_3) BOUND_VARIABLE_2409))) (let ((_let_5 (tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2403))) (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eoption_2EOPTREL_2E3 _let_4 (tptp.s _let_5 (tptp.c_2Eoption_2ESOME_2E1 _let_2)) (tptp.s _let_5 (tptp.c_2Eoption_2ESOME_2E1 _let_1)))) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s _let_3 (tptp.app_2E2 _let_4 _let_2)) _let_1))))))))))) (let ((_let_66 (not _let_35))) (let ((_let_67 (forall ((BOUND_VARIABLE_2382 $$unsorted) (BOUND_VARIABLE_2384 $$unsorted) (BOUND_VARIABLE_2388 $$unsorted)) (let ((_let_1 (tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2382))) (= (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2EF_2E0) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eoption_2EOPTREL_2E3 (tptp.s (tptp.tyop_2Emin_2Efun BOUND_VARIABLE_2382 (tptp.tyop_2Emin_2Efun BOUND_VARIABLE_2382 tptp.tyop_2Emin_2Ebool)) BOUND_VARIABLE_2388) (tptp.s _let_1 tptp.c_2Eoption_2ENONE_2E0) (tptp.s _let_1 (tptp.c_2Eoption_2ESOME_2E1 (tptp.s BOUND_VARIABLE_2382 BOUND_VARIABLE_2384)))))))))) (let ((_let_68 (forall ((BOUND_VARIABLE_2361 $$unsorted) (BOUND_VARIABLE_2365 $$unsorted) (BOUND_VARIABLE_2367 $$unsorted)) (let ((_let_1 (tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2361))) (= (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2EF_2E0) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eoption_2EOPTREL_2E3 (tptp.s (tptp.tyop_2Emin_2Efun BOUND_VARIABLE_2361 (tptp.tyop_2Emin_2Efun BOUND_VARIABLE_2361 tptp.tyop_2Emin_2Ebool)) BOUND_VARIABLE_2367) (tptp.s _let_1 (tptp.c_2Eoption_2ESOME_2E1 (tptp.s BOUND_VARIABLE_2361 BOUND_VARIABLE_2365))) (tptp.s _let_1 tptp.c_2Eoption_2ENONE_2E0)))))))) (let ((_let_69 (forall ((BOUND_VARIABLE_2343 $$unsorted) (BOUND_VARIABLE_2349 $$unsorted)) (let ((_let_1 (tptp.s (tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2343) tptp.c_2Eoption_2ENONE_2E0))) (= (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2ET_2E0) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eoption_2EOPTREL_2E3 (tptp.s (tptp.tyop_2Emin_2Efun BOUND_VARIABLE_2343 (tptp.tyop_2Emin_2Efun BOUND_VARIABLE_2343 tptp.tyop_2Emin_2Ebool)) BOUND_VARIABLE_2349) _let_1 _let_1))))))) (let ((_let_70 (not _let_65))) (let ((_let_71 (tptp.c_2Eoption_2ESOME_2E1 (tptp.s SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17)))) (let ((_let_72 (tptp.tyop_2Eoption_2Eoption SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_73 (tptp.s _let_72 _let_71))) (let ((_let_74 (tptp.s _let_72 tptp.c_2Eoption_2ENONE_2E0))) (let ((_let_75 (tptp.tyop_2Emin_2Efun SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 tptp.tyop_2Emin_2Ebool))) (let ((_let_76 (tptp.s (tptp.tyop_2Emin_2Efun SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 _let_75) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_77 (tptp.c_2Eoption_2EOPTREL_2E3 _let_76 _let_74 _let_73))) (let ((_let_78 (tptp.s tptp.tyop_2Emin_2Ebool _let_77))) (let ((_let_79 (= _let_7 _let_78))) (let ((_let_80 (= _let_5 _let_78))) (let ((_let_81 (or _let_80 _let_79))) (let ((_let_82 (tptp.p _let_78))) (let ((_let_83 (not _let_80))) (let ((_let_84 (forall ((V3x0_2E0 $$unsorted) (V4y0_2E0 $$unsorted)) (let ((_let_1 (tptp.s SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 V4y0_2E0))) (let ((_let_2 (tptp.s SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 V3x0_2E0))) (let ((_let_3 (tptp.tyop_2Emin_2Efun SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 tptp.tyop_2Emin_2Ebool))) (let ((_let_4 (tptp.tyop_2Eoption_2Eoption SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (or (not (= (tptp.s _let_4 tptp.c_2Eoption_2ENONE_2E0) (tptp.s _let_4 (tptp.c_2Eoption_2ESOME_2E1 _let_2)))) (not (= (tptp.s _let_4 (tptp.c_2Eoption_2ESOME_2E1 (tptp.s SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (tptp.s _let_4 (tptp.c_2Eoption_2ESOME_2E1 _let_1)))) (not (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s _let_3 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 _let_3) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18) _let_2)) _let_1)))))))))))) (let ((_let_85 (not _let_84))) (let ((_let_86 (= _let_74 _let_73))) (let ((_let_87 (or _let_86 _let_85))) (let ((_let_88 (= _let_82 _let_87))) (let ((_let_89 (not _let_82))) (let ((_let_90 (forall ((A_27a $$unsorted) (A_27b $$unsorted) (V0R_2E0 $$unsorted) (V1x_2E0 $$unsorted) (V2y_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Eoption_2Eoption A_27b))) (let ((_let_2 (tptp.s _let_1 V2y_2E0))) (let ((_let_3 (tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_4 (tptp.s _let_3 V1x_2E0))) (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eoption_2EOPTREL_2E3 (tptp.s (tptp.tyop_2Emin_2Efun A_27a (tptp.tyop_2Emin_2Efun A_27b tptp.tyop_2Emin_2Ebool)) V0R_2E0) _let_4 _let_2))) (or (and (= _let_4 (tptp.s _let_3 tptp.c_2Eoption_2ENONE_2E0)) (= _let_2 (tptp.s _let_1 tptp.c_2Eoption_2ENONE_2E0))) (not (forall ((V3x0_2E0 $$unsorted) (V4y0_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27b V4y0_2E0))) (let ((_let_2 (tptp.s A_27a V3x0_2E0))) (let ((_let_3 (tptp.tyop_2Emin_2Efun A_27b tptp.tyop_2Emin_2Ebool))) (let ((_let_4 (tptp.tyop_2Eoption_2Eoption A_27b))) (let ((_let_5 (tptp.tyop_2Eoption_2Eoption A_27a))) (or (not (= (tptp.s _let_5 V1x_2E0) (tptp.s _let_5 (tptp.c_2Eoption_2ESOME_2E1 _let_2)))) (not (= (tptp.s _let_4 V2y_2E0) (tptp.s _let_4 (tptp.c_2Eoption_2ESOME_2E1 _let_1)))) (not (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s _let_3 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun A_27a _let_3) V0R_2E0) _let_2)) _let_1))))))))))))))))))))) (let ((_let_91 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_92 (_let_90))) (let ((_let_93 ((tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eoption_2EOPTREL_2E3 (tptp.s (tptp.tyop_2Emin_2Efun A_27a (tptp.tyop_2Emin_2Efun A_27b tptp.tyop_2Emin_2Ebool)) V0R_2E0) (tptp.s (tptp.tyop_2Eoption_2Eoption A_27a) V1x_2E0) (tptp.s (tptp.tyop_2Eoption_2Eoption A_27b) V2y_2E0))))))) (let ((_let_94 (not _let_87))) (let ((_let_95 (tptp.s SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_96 (tptp.s SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_97 (= _let_74 (tptp.s _let_72 (tptp.c_2Eoption_2ESOME_2E1 _let_96))))) (let ((_let_98 (not _let_97))) (let ((_let_99 (or _let_98 (not (= _let_73 (tptp.s _let_72 (tptp.c_2Eoption_2ESOME_2E1 _let_95)))) (not (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s _let_75 (tptp.app_2E2 _let_76 _let_96)) _let_95))))))) (let ((_let_100 (forall ((BOUND_VARIABLE_1815 $$unsorted) (V6x_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_1815))) (not (= (tptp.s _let_1 tptp.c_2Eoption_2ENONE_2E0) (tptp.s _let_1 (tptp.c_2Eoption_2ESOME_2E1 (tptp.s BOUND_VARIABLE_1815 V6x_2E0))))))))) (let ((_let_101 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_102 (AND_ELIM _let_101 :args (2)))) (let ((_let_103 (_let_100))) (let ((_let_104 (ASSUME :args _let_103))) (let ((_let_105 (or))) (let ((_let_106 (_let_85))) (let ((_let_107 ((tptp.s (tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_1815) (tptp.c_2Eoption_2ESOME_2E1 (tptp.s BOUND_VARIABLE_1815 V6x_2E0)))))) (let ((_let_108 (REFL :args (_let_10)))) (let ((_let_109 (TRUE_INTRO _let_20))) (let ((_let_110 (APPLY_UF tptp.p))) (let ((_let_111 (not _let_67))) (let ((_let_112 (_let_111))) (let ((_let_113 (tptp.tyop_2Eoption_2Eoption SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_114 (tptp.s _let_113 tptp.c_2Eoption_2ENONE_2E0))) (let ((_let_115 (tptp.c_2Eoption_2ESOME_2E1 (tptp.s SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))) (let ((_let_116 (tptp.s _let_113 _let_115))) (let ((_let_117 (tptp.tyop_2Emin_2Efun SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.tyop_2Emin_2Ebool))) (let ((_let_118 (tptp.s (tptp.tyop_2Emin_2Efun SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_117) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_119 (tptp.c_2Eoption_2EOPTREL_2E3 _let_118 _let_116 _let_114))) (let ((_let_120 (tptp.s tptp.tyop_2Emin_2Ebool _let_119))) (let ((_let_121 (= _let_7 _let_120))) (let ((_let_122 (= _let_5 _let_120))) (let ((_let_123 (or _let_122 _let_121))) (let ((_let_124 (tptp.p _let_120))) (let ((_let_125 (not _let_122))) (let ((_let_126 (forall ((V3x0_2E0 $$unsorted) (V4y0_2E0 $$unsorted)) (let ((_let_1 (tptp.s SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 V4y0_2E0))) (let ((_let_2 (tptp.s SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 V3x0_2E0))) (let ((_let_3 (tptp.tyop_2Emin_2Efun SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.tyop_2Emin_2Ebool))) (let ((_let_4 (tptp.tyop_2Eoption_2Eoption SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (or (not (= (tptp.s _let_4 (tptp.c_2Eoption_2ESOME_2E1 (tptp.s SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (tptp.s _let_4 (tptp.c_2Eoption_2ESOME_2E1 _let_2)))) (not (= (tptp.s _let_4 tptp.c_2Eoption_2ENONE_2E0) (tptp.s _let_4 (tptp.c_2Eoption_2ESOME_2E1 _let_1)))) (not (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s _let_3 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun 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(V1g_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Emin_2Efun A_27a A_27b))) (=> (forall ((V2x_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27a V2x_2E0))) (let ((_let_2 (tptp.tyop_2Emin_2Efun A_27a A_27b))) (= (tptp.s A_27b (tptp.app_2E2 (tptp.s _let_2 V0f_2E0) _let_1)) (tptp.s A_27b (tptp.app_2E2 (tptp.s _let_2 V1g_2E0) _let_1)))))) (= (tptp.s _let_1 V0f_2E0) (tptp.s _let_1 V1g_2E0))))) (forall ((V0_2E0 $$unsorted) (V1_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Emin_2Ebool V1_2E0))) (let ((_let_2 (tptp.s tptp.tyop_2Emin_2Ebool V0_2E0))) (=> (= (tptp.p _let_2) (tptp.p _let_1)) (= _let_2 _let_1))))) _let_6 _let_9 _let_11 (forall ((A_27a $$unsorted) (V0x_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27a V0x_2E0))) (= (tptp.s A_27a (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun A_27a A_27a) tptp.combin_i_2E0) _let_1)) _let_1))) (forall ((A_27a $$unsorted) (A_27b $$unsorted) (V0x_2E0 $$unsorted) (V1y_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27a V0x_2E0))) (let ((_let_2 (tptp.tyop_2Emin_2Efun A_27b A_27a))) (= (tptp.s A_27a (tptp.app_2E2 (tptp.s _let_2 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun A_27a _let_2) tptp.combin_k_2E0) _let_1)) (tptp.s A_27b V1y_2E0))) _let_1)))) (forall ((A_27a $$unsorted) (A_27b $$unsorted) (A_27c $$unsorted) (V0f_2E0 $$unsorted) (V1g_2E0 $$unsorted) (V2x_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27a V2x_2E0))) (let ((_let_2 (tptp.tyop_2Emin_2Efun A_27a A_27b))) (let ((_let_3 (tptp.s _let_2 V1g_2E0))) (let ((_let_4 (tptp.tyop_2Emin_2Efun A_27b A_27c))) (let ((_let_5 (tptp.tyop_2Emin_2Efun A_27a _let_4))) (let ((_let_6 (tptp.s _let_5 V0f_2E0))) (let ((_let_7 (tptp.tyop_2Emin_2Efun A_27a A_27c))) (let ((_let_8 (tptp.tyop_2Emin_2Efun _let_2 _let_7))) (= (tptp.s A_27c (tptp.app_2E2 (tptp.s _let_7 (tptp.app_2E2 (tptp.s _let_8 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun _let_5 _let_8) tptp.combin_s_2E0) _let_6)) _let_3)) _let_1)) (tptp.s A_27c (tptp.app_2E2 (tptp.s _let_4 (tptp.app_2E2 _let_6 _let_1)) (tptp.s A_27b (tptp.app_2E2 _let_3 _let_1)))))))))))))) (forall ((V0_2E0 $$unsorted) (V1_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Emin_2Ebool V1_2E0))) (let ((_let_2 (tptp.s tptp.tyop_2Emin_2Ebool V0_2E0))) (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_2F_5C_2E2 _let_2 _let_1))) (and (tptp.p _let_2) (tptp.p _let_1)))))) (forall ((V0_2E0 $$unsorted) (V1_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Emin_2Ebool V1_2E0))) (let ((_let_2 (tptp.s tptp.tyop_2Emin_2Ebool V0_2E0))) (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_5C_2F_2E2 _let_2 _let_1))) (or (tptp.p _let_2) (tptp.p _let_1)))))) (forall ((V0_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Emin_2Ebool V0_2E0))) (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_7E_2E1 _let_1))) (not (tptp.p _let_1))))) (forall ((V0_2E0 $$unsorted) (V1_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Emin_2Ebool V1_2E0))) (let ((_let_2 (tptp.s tptp.tyop_2Emin_2Ebool V0_2E0))) (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Emin_2E_3D_3D_3E_2E2 _let_2 _let_1))) (=> (tptp.p _let_2) (tptp.p _let_1)))))) (forall ((A_27a $$unsorted) (V0_2E0 $$unsorted) (V1_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27a V1_2E0))) (let ((_let_2 (tptp.s A_27a V0_2E0))) (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Emin_2E_3D_2E2 _let_2 _let_1))) (= _let_2 _let_1))))) (forall ((A_27a $$unsorted) (V0f_2E0 $$unsorted)) (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_21_2E1 (tptp.s (tptp.tyop_2Emin_2Efun A_27a tptp.tyop_2Emin_2Ebool) V0f_2E0)))) (forall ((V1x_2E0 $$unsorted)) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun A_27a tptp.tyop_2Emin_2Ebool) V0f_2E0) (tptp.s A_27a V1x_2E0))))))) (forall ((A_27a $$unsorted) (V0f_2E0 $$unsorted)) (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_3F_2E1 (tptp.s (tptp.tyop_2Emin_2Efun A_27a tptp.tyop_2Emin_2Ebool) V0f_2E0)))) (exists ((V1x_2E0 $$unsorted)) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun A_27a tptp.tyop_2Emin_2Ebool) V0f_2E0) (tptp.s A_27a V1x_2E0))))))) (forall ((X0_2E0 $$unsorted) (X1_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Emin_2Ebool X1_2E0))) (let ((_let_2 (tptp.s tptp.tyop_2Emin_2Ebool X0_2E0))) (let ((_let_3 (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool tptp.tyop_2Emin_2Ebool))) (= (and (tptp.p _let_2) (tptp.p _let_1)) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s _let_3 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool _let_3) tptp.c_2Ebool_2E_2F_5C_2E0) _let_2)) _let_1)))))))) (forall ((X0_2E0 $$unsorted) (X1_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Emin_2Ebool X1_2E0))) (let ((_let_2 (tptp.s tptp.tyop_2Emin_2Ebool X0_2E0))) (let ((_let_3 (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool tptp.tyop_2Emin_2Ebool))) (= (or (tptp.p _let_2) (tptp.p _let_1)) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s _let_3 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool _let_3) tptp.c_2Ebool_2E_5C_2F_2E0) _let_2)) _let_1)))))))) (forall ((X0_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Emin_2Ebool X0_2E0))) (= (not (tptp.p _let_1)) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool tptp.tyop_2Emin_2Ebool) tptp.c_2Ebool_2E_7E_2E0) _let_1)))))) (forall ((X0_2E0 $$unsorted) (X1_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Emin_2Ebool X1_2E0))) (let ((_let_2 (tptp.s tptp.tyop_2Emin_2Ebool X0_2E0))) (let ((_let_3 (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool tptp.tyop_2Emin_2Ebool))) (= (=> (tptp.p _let_2) (tptp.p _let_1)) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s _let_3 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool _let_3) tptp.c_2Emin_2E_3D_3D_3E_2E0) _let_2)) _let_1)))))))) (forall ((A_27a $$unsorted) (X0_2E0 $$unsorted) (X1_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27a X1_2E0))) (let ((_let_2 (tptp.s A_27a X0_2E0))) (let ((_let_3 (tptp.tyop_2Emin_2Efun A_27a tptp.tyop_2Emin_2Ebool))) (= (= _let_2 _let_1) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s _let_3 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun A_27a _let_3) tptp.c_2Emin_2E_3D_2E0) _let_2)) _let_1)))))))) (forall ((A_27a $$unsorted) (X0_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Emin_2Efun A_27a tptp.tyop_2Emin_2Ebool))) (let ((_let_2 (tptp.s _let_1 X0_2E0))) (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_21_2E1 _let_2)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun _let_1 tptp.tyop_2Emin_2Ebool) tptp.c_2Ebool_2E_21_2E0) _let_2)))))) (forall ((A_27a $$unsorted) (X0_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Emin_2Efun A_27a tptp.tyop_2Emin_2Ebool))) (let ((_let_2 (tptp.s _let_1 X0_2E0))) (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_3F_2E1 _let_2)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun _let_1 tptp.tyop_2Emin_2Ebool) tptp.c_2Ebool_2E_3F_2E0) _let_2)))))) (forall ((A_27a $$unsorted) (X0_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (tptp.s _let_1 X0_2E0))) (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eoption_2EIS__NONE_2E1 _let_2)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun _let_1 tptp.tyop_2Emin_2Ebool) tptp.c_2Eoption_2EIS__NONE_2E0) _let_2)))))) (forall ((A_27a $$unsorted) (X0_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (tptp.s _let_1 X0_2E0))) (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eoption_2EIS__SOME_2E1 _let_2)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun _let_1 tptp.tyop_2Emin_2Ebool) tptp.c_2Eoption_2EIS__SOME_2E0) _let_2)))))) (forall ((A_27a $$unsorted) (X0_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27a X0_2E0))) (let ((_let_2 (tptp.tyop_2Eoption_2Eoption A_27a))) (= (tptp.s _let_2 (tptp.c_2Eoption_2ESOME_2E1 _let_1)) (tptp.s _let_2 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun A_27a _let_2) tptp.c_2Eoption_2ESOME_2E0) _let_1)))))) (forall ((A_27a $$unsorted) (X0_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (tptp.tyop_2Eoption_2Eoption _let_1))) (let ((_let_3 (tptp.s _let_2 X0_2E0))) (= (tptp.s _let_1 (tptp.c_2Eoption_2EOPTION__JOIN_2E1 _let_3)) (tptp.s _let_1 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun _let_2 _let_1) tptp.c_2Eoption_2EOPTION__JOIN_2E0) _let_3))))))) (forall ((A_27a $$unsorted) (X0_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (tptp.s _let_1 X0_2E0))) (let ((_let_3 (tptp.tyop_2Eoption_2Eoption _let_1))) (= (tptp.s _let_3 (tptp.c_2Eoption_2ESOME_2E1 _let_2)) (tptp.s _let_3 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun _let_1 _let_3) tptp.c_2Eoption_2ESOME_2E0) _let_2))))))) (forall ((A_27a $$unsorted) (X0_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (tptp.s _let_1 X0_2E0))) (= (tptp.s A_27a (tptp.c_2Eoption_2ETHE_2E1 _let_2)) (tptp.s A_27a (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun _let_1 A_27a) tptp.c_2Eoption_2ETHE_2E0) _let_2)))))) (forall ((A_27b $$unsorted) (X0_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27b X0_2E0))) (let ((_let_2 (tptp.tyop_2Eoption_2Eoption A_27b))) (= (tptp.s _let_2 (tptp.c_2Eoption_2ESOME_2E1 _let_1)) (tptp.s _let_2 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun A_27b _let_2) tptp.c_2Eoption_2ESOME_2E0) _let_1)))))) (forall ((A_27a $$unsorted) (A_27b $$unsorted) (X0_2E0 $$unsorted) (X1_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (tptp.s _let_1 X1_2E0))) (let ((_let_3 (tptp.tyop_2Emin_2Efun A_27a A_27b))) (let ((_let_4 (tptp.s _let_3 X0_2E0))) (let ((_let_5 (tptp.tyop_2Eoption_2Eoption A_27b))) (let ((_let_6 (tptp.tyop_2Emin_2Efun _let_1 _let_5))) (= (tptp.s _let_5 (tptp.c_2Eoption_2EOPTION__MAP_2E2 _let_4 _let_2)) (tptp.s _let_5 (tptp.app_2E2 (tptp.s _let_6 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun _let_3 _let_6) tptp.c_2Eoption_2EOPTION__MAP_2E0) _let_4)) _let_2)))))))))) (forall ((A_27a $$unsorted) (X0_2E0 $$unsorted) (X1_2E0 $$unsorted) (X2_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (tptp.s _let_1 X2_2E0))) (let ((_let_3 (tptp.s _let_1 X1_2E0))) (let ((_let_4 (tptp.tyop_2Emin_2Efun A_27a (tptp.tyop_2Emin_2Efun A_27a tptp.tyop_2Emin_2Ebool)))) (let ((_let_5 (tptp.s _let_4 X0_2E0))) (let ((_let_6 (tptp.tyop_2Emin_2Efun _let_1 tptp.tyop_2Emin_2Ebool))) (let ((_let_7 (tptp.tyop_2Emin_2Efun _let_1 _let_6))) (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eoption_2EOPTREL_2E3 _let_5 _let_3 _let_2)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s _let_6 (tptp.app_2E2 (tptp.s _let_7 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun _let_4 _let_7) tptp.c_2Eoption_2EOPTREL_2E0) _let_5)) _let_3)) _let_2))))))))))) (forall ((A_27a $$unsorted) (A_27b $$unsorted) (X0_2E0 $$unsorted) (X1_2E0 $$unsorted) (X2_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Eoption_2Eoption A_27b))) (let ((_let_2 (tptp.s _let_1 X2_2E0))) (let ((_let_3 (tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_4 (tptp.s _let_3 X1_2E0))) (let ((_let_5 (tptp.tyop_2Emin_2Efun A_27a (tptp.tyop_2Emin_2Efun A_27b tptp.tyop_2Emin_2Ebool)))) (let ((_let_6 (tptp.s _let_5 X0_2E0))) (let ((_let_7 (tptp.tyop_2Emin_2Efun _let_1 tptp.tyop_2Emin_2Ebool))) (let ((_let_8 (tptp.tyop_2Emin_2Efun _let_3 _let_7))) (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Eoption_2EOPTREL_2E3 _let_6 _let_4 _let_2)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s _let_7 (tptp.app_2E2 (tptp.s _let_8 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun _let_5 _let_8) tptp.c_2Eoption_2EOPTREL_2E0) _let_6)) _let_4)) _let_2)))))))))))) (forall ((A_27a $$unsorted) (A_27b $$unsorted) (X0_2E0 $$unsorted) (X1_2E0 $$unsorted) (X2_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Emin_2Efun A_27a A_27b))) (let ((_let_2 (tptp.s _let_1 X2_2E0))) (let ((_let_3 (tptp.s A_27b X1_2E0))) (let ((_let_4 (tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_5 (tptp.s _let_4 X0_2E0))) (let ((_let_6 (tptp.tyop_2Emin_2Efun _let_1 A_27b))) (let ((_let_7 (tptp.tyop_2Emin_2Efun A_27b _let_6))) (= (tptp.s A_27b (tptp.c_2Eoption_2Eoption__CASE_2E3 _let_5 _let_3 _let_2)) (tptp.s A_27b (tptp.app_2E2 (tptp.s _let_6 (tptp.app_2E2 (tptp.s _let_7 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun _let_4 _let_7) tptp.c_2Eoption_2Eoption__CASE_2E0) _let_5)) _let_3)) _let_2))))))))))) (forall ((A_27a $$unsorted) (X0_2E0 $$unsorted) (X1_2E0 $$unsorted) (X2_2E0 $$unsorted)) (let ((_let_1 (tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (tptp.tyop_2Emin_2Efun A_27a _let_1))) (let ((_let_3 (tptp.s _let_2 X2_2E0))) (let ((_let_4 (tptp.s _let_1 X1_2E0))) (let ((_let_5 (tptp.s _let_1 X0_2E0))) (let ((_let_6 (tptp.tyop_2Emin_2Efun _let_2 _let_1))) (let ((_let_7 (tptp.tyop_2Emin_2Efun _let_1 _let_6))) (= (tptp.s _let_1 (tptp.c_2Eoption_2Eoption__CASE_2E3 _let_5 _let_4 _let_3)) (tptp.s _let_1 (tptp.app_2E2 (tptp.s _let_6 (tptp.app_2E2 (tptp.s _let_7 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun _let_1 _let_7) tptp.c_2Eoption_2Eoption__CASE_2E0) _let_5)) _let_4)) _let_3))))))))))) _let_6 (forall ((V0t1_2E0 $$unsorted) (V1t2_2E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.tyop_2Emin_2Ebool V1t2_2E0))) (let ((_let_2 (tptp.s tptp.tyop_2Emin_2Ebool V0t1_2E0))) (let ((_let_3 (tptp.p _let_2))) (let ((_let_4 (tptp.p _let_1))) (=> (=> _let_3 _let_4) (=> (=> _let_4 _let_3) (= _let_2 _let_1)))))))) (forall ((V0t_2E0 $$unsorted)) (=> (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2EF_2E0)) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool V0t_2E0)))) (forall ((A_27a $$unsorted) (V0t_2E0 $$unsorted)) (= (exists ((V1x_2E0 $$unsorted)) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool V0t_2E0))) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool V0t_2E0)))) (forall ((V0t_2E0 $$unsorted)) (let ((_let_1 (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool V0t_2E0)))) (let ((_let_2 (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2EF_2E0)))) (let ((_let_3 (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2ET_2E0)))) (and (= (and _let_3 _let_1) _let_1) (= (and _let_1 _let_3) _let_1) (= (and _let_2 _let_1) _let_2) (= (and _let_1 _let_2) _let_2) (= (and _let_1 _let_1) _let_1)))))) (forall ((V0t_2E0 $$unsorted)) (let ((_let_1 (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool V0t_2E0)))) (let ((_let_2 (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2EF_2E0)))) (let ((_let_3 (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2ET_2E0)))) (and (= (or _let_3 _let_1) _let_3) (= (or _let_1 _let_3) _let_3) (= (or _let_2 _let_1) _let_1) (= (or _let_1 _let_2) _let_1) (= (or _let_1 _let_1) _let_1)))))) (and (forall ((V0t_2E0 $$unsorted)) (let ((_let_1 (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool V0t_2E0)))) (= (not (not _let_1)) _let_1))) (= _let_10 _let_8) (= _let_9 _let_6)) (forall ((A_27a $$unsorted) (V0x_2E0 $$unsorted)) (let ((_let_1 (tptp.s A_27a V0x_2E0))) (= (= _let_1 _let_1) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2ET_2E0))))) _let_4 _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 31.46/31.66  )
% 31.46/31.66  % SZS output end Proof for ITP011+1
% 31.46/31.66  % cvc5---1.0.5 exiting
% 31.46/31.66  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------