TSTP Solution File: SWW469+5 by ConnectPP---0.3.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SWW469+5 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% Computer : n024.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 : Mon Mar 25 14:40:37 EDT 2024
% Result : Theorem 0.47s 0.63s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW469+5 : TPTP v8.1.2. Released v5.3.0.
% 0.03/0.12 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Mar 21 01:32:46 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.47/0.63 % SZS status Theorem for theBenchmark
% 0.47/0.63 % SZS output start Proof for theBenchmark
% 0.47/0.63
% 0.47/0.63 % Formula: tsy_c_HOL_Oequal__class_Oequal_res ( axiom ) converted to clauses:
% 0.47/0.63 cnf(tsy_c_HOL_Oequal__class_Oequal_res-1, axiom, ( ~cl_HOL_Oequal(_u0) | ( ti(fun(_u0, fun(_u0, bool)), equal_equal(_u0)) = equal_equal(_u0)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: tsy_c_HOL_Oinduct__equal_res ( axiom ) converted to clauses:
% 0.47/0.63 cnf(tsy_c_HOL_Oinduct__equal_res-1, axiom, ( ( ti(fun(_u1, fun(_u1, bool)), induct_equal(_u1)) = induct_equal(_u1)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: tsy_c_HOL_Oinduct__false_res ( axiom ) converted to clauses:
% 0.47/0.63 cnf(tsy_c_HOL_Oinduct__false_res-1, axiom, ( ( ti(bool, induct_false) = induct_false) )).
% 0.47/0.63
% 0.47/0.63 % Formula: tsy_c_HOL_Oinduct__true_res ( axiom ) converted to clauses:
% 0.47/0.63 cnf(tsy_c_HOL_Oinduct__true_res-1, axiom, ( ( ti(bool, induct_true) = induct_true) )).
% 0.47/0.63
% 0.47/0.63 % Formula: tsy_c_HOL_Oundefined_res ( axiom ) converted to clauses:
% 0.47/0.63 cnf(tsy_c_HOL_Oundefined_res-1, axiom, ( ( ti(_u2, undefined(_u2)) = undefined(_u2)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: tsy_c_Hoare__Mirabelle__pjuwniqynr_OAbs__triple_res ( axiom ) converted to clauses:
% 0.47/0.63 cnf(tsy_c_Hoare__Mirabelle__pjuwniqynr_OAbs__triple_res-1, axiom, ( ( ti(fun(fun(node(sum_sum(com, fun(_u3, fun(state, bool))), sum_sum(state, _u3)), bool), hoare_509422987triple(_u3)), hoare_244953527triple(_u3)) = hoare_244953527triple(_u3)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: tsy_c_Hoare__Mirabelle__pjuwniqynr_ORep__triple_res ( axiom ) converted to clauses:
% 0.47/0.63 cnf(tsy_c_Hoare__Mirabelle__pjuwniqynr_ORep__triple_res-1, axiom, ( ( ti(fun(hoare_509422987triple(_u4), fun(node(sum_sum(com, fun(_u4, fun(state, bool))), sum_sum(state, _u4)), bool)), hoare_2037801986triple(_u4)) = hoare_2037801986triple(_u4)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: tsy_c_Hoare__Mirabelle__pjuwniqynr_Ostate__not__singleton_res ( hypothesis ) converted to clauses:
% 0.47/0.63 cnf(tsy_c_Hoare__Mirabelle__pjuwniqynr_Ostate__not__singleton_res-1, hypothesis, ( ( ti(bool, hoare_1883395792gleton) = hoare_1883395792gleton) )).
% 0.47/0.63
% 0.47/0.63 % Formula: tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple__rep__set_res ( axiom ) converted to clauses:
% 0.47/0.63 cnf(tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple__rep__set_res-1, axiom, ( ( ti(fun(fun(node(sum_sum(com, fun(_u5, fun(state, bool))), sum_sum(state, _u5)), bool), bool), hoare_1580379338ep_set(_u5)) = hoare_1580379338ep_set(_u5)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: tsy_c_Set_OCollect_res ( axiom ) converted to clauses:
% 0.47/0.63 cnf(tsy_c_Set_OCollect_res-1, axiom, ( ( ti(fun(fun(_u6, bool), fun(_u6, bool)), collect(_u6)) = collect(_u6)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: tsy_c_Typedef_Otype__definition_res ( axiom ) converted to clauses:
% 0.47/0.63 cnf(tsy_c_Typedef_Otype__definition_res-1, axiom, ( ( ti(fun(fun(_u8, _u7), fun(fun(_u7, _u8), fun(fun(_u7, bool), bool))), type_definition(_u8, _u7)) = type_definition(_u8, _u7)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: tsy_c_fequal_res ( axiom ) converted to clauses:
% 0.47/0.63 cnf(tsy_c_fequal_res-1, axiom, ( ( ti(fun(_u9, fun(_u9, bool)), fequal(_u9)) = fequal(_u9)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: tsy_c_hAPP_arg1 ( axiom ) converted to clauses:
% 0.47/0.63 cnf(tsy_c_hAPP_arg1-1, axiom, ( ( hAPP(_u13, _u12, ti(fun(_u13, _u12), _u11), _u10) = hAPP(_u13, _u12, _u11, _u10)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: tsy_c_hAPP_arg2 ( axiom ) converted to clauses:
% 0.47/0.63 cnf(tsy_c_hAPP_arg2-1, axiom, ( ( hAPP(_u17, _u16, _u15, ti(_u17, _u14)) = hAPP(_u17, _u16, _u15, _u14)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: tsy_c_hAPP_res ( axiom ) converted to clauses:
% 0.47/0.63 cnf(tsy_c_hAPP_res-1, axiom, ( ( ti(_u21, hAPP(_u20, _u21, _u19, _u18)) = hAPP(_u20, _u21, _u19, _u18)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: tsy_c_hBOOL_arg1 ( hypothesis ) converted to clauses:
% 0.47/0.63 cnf(tsy_c_hBOOL_arg1-1, hypothesis, ( ~hBOOL(ti(bool, _u23)) | hBOOL(_u23) )).
% 0.47/0.63 cnf(tsy_c_hBOOL_arg1-2, hypothesis, ( ~hBOOL(_u24) | hBOOL(ti(bool, _u24)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: tsy_c_member_res ( axiom ) converted to clauses:
% 0.47/0.63 cnf(tsy_c_member_res-1, axiom, ( ( ti(fun(_u25, fun(fun(_u25, bool), bool)), member(_u25)) = member(_u25)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_0_state__not__singleton__def ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_0_state__not__singleton__def-1, axiom, ( ~hBOOL(hoare_1883395792gleton) | ( ti(state, skolem1) != ti(state, skolem2)) )).
% 0.47/0.63 cnf(fact_0_state__not__singleton__def-2, axiom, ( ( ti(state, _u29) = ti(state, _u28)) | hBOOL(hoare_1883395792gleton) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_1_equal__triple__def ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_1_equal__triple__def-1, axiom, ( ~hBOOL(hAPP(hoare_509422987triple(_u37), bool, hAPP(hoare_509422987triple(_u37), fun(hoare_509422987triple(_u37), bool), equal_equal(hoare_509422987triple(_u37)), _u35), _u33)) | ( _u35 = _u33) )).
% 0.47/0.63 cnf(fact_1_equal__triple__def-2, axiom, ( ( _u36 != _u34) | hBOOL(hAPP(hoare_509422987triple(_u38), bool, hAPP(hoare_509422987triple(_u38), fun(hoare_509422987triple(_u38), bool), equal_equal(hoare_509422987triple(_u38)), _u36), _u34)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_2_Rep__triple__inject ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_2_Rep__triple__inject-1, axiom, ( ( hAPP(hoare_509422987triple(_u46), fun(node(sum_sum(com, fun(_u46, fun(state, bool))), sum_sum(state, _u46)), bool), hoare_2037801986triple(_u46), _u44) != hAPP(hoare_509422987triple(_u46), fun(node(sum_sum(com, fun(_u46, fun(state, bool))), sum_sum(state, _u46)), bool), hoare_2037801986triple(_u46), _u42)) | ( _u44 = _u42) )).
% 0.47/0.63 cnf(fact_2_Rep__triple__inject-2, axiom, ( ( _u45 != _u43) | ( hAPP(hoare_509422987triple(_u47), fun(node(sum_sum(com, fun(_u47, fun(state, bool))), sum_sum(state, _u47)), bool), hoare_2037801986triple(_u47), _u45) = hAPP(hoare_509422987triple(_u47), fun(node(sum_sum(com, fun(_u47, fun(state, bool))), sum_sum(state, _u47)), bool), hoare_2037801986triple(_u47), _u43)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_3_equal ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_3_equal-1, axiom, ( ~cl_HOL_Oequal(_u48) | ( equal_equal(_u48) = fequal(_u48)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_4_equal__refl ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_4_equal__refl-1, axiom, ( ~cl_HOL_Oequal(_u50) | hBOOL(hAPP(_u50, bool, hAPP(_u50, fun(_u50, bool), equal_equal(_u50), _u49), _u49)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_5_equal__eq ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_5_equal__eq-1, axiom, ( ~cl_HOL_Oequal(_u53) | ~hBOOL(hAPP(_u53, bool, hAPP(_u53, fun(_u53, bool), equal_equal(_u53), _u56), _u54)) | ( ti(_u53, _u56) = ti(_u53, _u54)) )).
% 0.47/0.63 cnf(fact_5_equal__eq-2, axiom, ( ~cl_HOL_Oequal(_u53) | ( ti(_u53, _u57) != ti(_u53, _u55)) | hBOOL(hAPP(_u53, bool, hAPP(_u53, fun(_u53, bool), equal_equal(_u53), _u57), _u55)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_6_eq__equal ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_6_eq__equal-1, axiom, ( ~cl_HOL_Oequal(_u58) | ( fequal(_u58) = equal_equal(_u58)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_7_Rep__triple__inverse ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_7_Rep__triple__inverse-1, axiom, ( ( hAPP(fun(node(sum_sum(com, fun(_u60, fun(state, bool))), sum_sum(state, _u60)), bool), hoare_509422987triple(_u60), hoare_244953527triple(_u60), hAPP(hoare_509422987triple(_u60), fun(node(sum_sum(com, fun(_u60, fun(state, bool))), sum_sum(state, _u60)), bool), hoare_2037801986triple(_u60), _u59)) = _u59) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_8_Rep__triple ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_8_Rep__triple-1, axiom, ( hBOOL(hAPP(fun(fun(node(sum_sum(com, fun(_u62, fun(state, bool))), sum_sum(state, _u62)), bool), bool), bool, hAPP(fun(node(sum_sum(com, fun(_u62, fun(state, bool))), sum_sum(state, _u62)), bool), fun(fun(fun(node(sum_sum(com, fun(_u62, fun(state, bool))), sum_sum(state, _u62)), bool), bool), bool), member(fun(node(sum_sum(com, fun(_u62, fun(state, bool))), sum_sum(state, _u62)), bool)), hAPP(hoare_509422987triple(_u62), fun(node(sum_sum(com, fun(_u62, fun(state, bool))), sum_sum(state, _u62)), bool), hoare_2037801986triple(_u62), _u61)), hAPP(fun(fun(node(sum_sum(com, fun(_u62, fun(state, bool))), sum_sum(state, _u62)), bool), bool), fun(fun(node(sum_sum(com, fun(_u62, fun(state, bool))), sum_sum(state, _u62)), bool), bool), collect(fun(node(sum_sum(com, fun(_u62, fun(state, bool))), sum_sum(state, _u62)), bool)), hoare_1580379338ep_set(_u62)))) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_9_Rep__triple__induct ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_9_Rep__triple__induct-1, axiom, ( ~hBOOL(hAPP(fun(fun(node(sum_sum(com, fun(_u66, fun(state, bool))), sum_sum(state, _u66)), bool), bool), bool, hAPP(fun(node(sum_sum(com, fun(_u66, fun(state, bool))), sum_sum(state, _u66)), bool), fun(fun(fun(node(sum_sum(com, fun(_u66, fun(state, bool))), sum_sum(state, _u66)), bool), bool), bool), member(fun(node(sum_sum(com, fun(_u66, fun(state, bool))), sum_sum(state, _u66)), bool)), _u64), hAPP(fun(fun(node(sum_sum(com, fun(_u66, fun(state, bool))), sum_sum(state, _u66)), bool), bool), fun(fun(node(sum_sum(com, fun(_u66, fun(state, bool))), sum_sum(state, _u66)), bool), bool), collect(fun(node(sum_sum(com, fun(_u66, fun(state, bool))), sum_sum(state, _u66)), bool)), hoare_1580379338ep_set(_u66)))) | ~hBOOL(hAPP(fun(node(sum_sum(com, fun(_u66, fun(state, bool))), sum_sum(state, _u66)), bool), bool, _u65, hAPP(hoare_509422987triple(_u66), fun(node(sum_sum(com, fun(_u66, fun(state, bool))), sum_sum(state, _u66)), bool), hoare_2037801986triple(_u66), skolem3(_u66, _u65, _u64)))) | hBOOL(hAPP(fun(node(sum_sum(com, fun(_u66, fun(state, bool))), sum_sum(state, _u66)), bool), bool, _u65, _u64)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_10_Rep__triple__cases ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_10_Rep__triple__cases-1, axiom, ( ~hBOOL(hAPP(fun(fun(node(sum_sum(com, fun(_u69, fun(state, bool))), sum_sum(state, _u69)), bool), bool), bool, hAPP(fun(node(sum_sum(com, fun(_u69, fun(state, bool))), sum_sum(state, _u69)), bool), fun(fun(fun(node(sum_sum(com, fun(_u69, fun(state, bool))), sum_sum(state, _u69)), bool), bool), bool), member(fun(node(sum_sum(com, fun(_u69, fun(state, bool))), sum_sum(state, _u69)), bool)), _u68), hAPP(fun(fun(node(sum_sum(com, fun(_u69, fun(state, bool))), sum_sum(state, _u69)), bool), bool), fun(fun(node(sum_sum(com, fun(_u69, fun(state, bool))), sum_sum(state, _u69)), bool), bool), collect(fun(node(sum_sum(com, fun(_u69, fun(state, bool))), sum_sum(state, _u69)), bool)), hoare_1580379338ep_set(_u69)))) | ( _u68 = hAPP(hoare_509422987triple(_u69), fun(node(sum_sum(com, fun(_u69, fun(state, bool))), sum_sum(state, _u69)), bool), hoare_2037801986triple(_u69), skolem4(_u69, _u68))) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_11_Abs__triple__inverse ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_11_Abs__triple__inverse-1, axiom, ( ~hBOOL(hAPP(fun(fun(node(sum_sum(com, fun(_u71, fun(state, bool))), sum_sum(state, _u71)), bool), bool), bool, hAPP(fun(node(sum_sum(com, fun(_u71, fun(state, bool))), sum_sum(state, _u71)), bool), fun(fun(fun(node(sum_sum(com, fun(_u71, fun(state, bool))), sum_sum(state, _u71)), bool), bool), bool), member(fun(node(sum_sum(com, fun(_u71, fun(state, bool))), sum_sum(state, _u71)), bool)), _u70), hAPP(fun(fun(node(sum_sum(com, fun(_u71, fun(state, bool))), sum_sum(state, _u71)), bool), bool), fun(fun(node(sum_sum(com, fun(_u71, fun(state, bool))), sum_sum(state, _u71)), bool), bool), collect(fun(node(sum_sum(com, fun(_u71, fun(state, bool))), sum_sum(state, _u71)), bool)), hoare_1580379338ep_set(_u71)))) | ( hAPP(hoare_509422987triple(_u71), fun(node(sum_sum(com, fun(_u71, fun(state, bool))), sum_sum(state, _u71)), bool), hoare_2037801986triple(_u71), hAPP(fun(node(sum_sum(com, fun(_u71, fun(state, bool))), sum_sum(state, _u71)), bool), hoare_509422987triple(_u71), hoare_244953527triple(_u71), _u70)) = _u70) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_12_type__definition__triple ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_12_type__definition__triple-1, axiom, ( hBOOL(hAPP(fun(fun(node(sum_sum(com, fun(_u72, fun(state, bool))), sum_sum(state, _u72)), bool), bool), bool, hAPP(fun(fun(node(sum_sum(com, fun(_u72, fun(state, bool))), sum_sum(state, _u72)), bool), hoare_509422987triple(_u72)), fun(fun(fun(node(sum_sum(com, fun(_u72, fun(state, bool))), sum_sum(state, _u72)), bool), bool), bool), hAPP(fun(hoare_509422987triple(_u72), fun(node(sum_sum(com, fun(_u72, fun(state, bool))), sum_sum(state, _u72)), bool)), fun(fun(fun(node(sum_sum(com, fun(_u72, fun(state, bool))), sum_sum(state, _u72)), bool), hoare_509422987triple(_u72)), fun(fun(fun(node(sum_sum(com, fun(_u72, fun(state, bool))), sum_sum(state, _u72)), bool), bool), bool)), type_definition(hoare_509422987triple(_u72), fun(node(sum_sum(com, fun(_u72, fun(state, bool))), sum_sum(state, _u72)), bool)), hoare_2037801986triple(_u72)), hoare_244953527triple(_u72)), hAPP(fun(fun(node(sum_sum(com, fun(_u72, fun(state, bool))), sum_sum(state, _u72)), bool), bool), fun(fun(node(sum_sum(com, fun(_u72, fun(state, bool))), sum_sum(state, _u72)), bool), bool), collect(fun(node(sum_sum(com, fun(_u72, fun(state, bool))), sum_sum(state, _u72)), bool)), hoare_1580379338ep_set(_u72)))) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_13_Abs__triple__inject ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_13_Abs__triple__inject-1, axiom, ( ~hBOOL(hAPP(fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), bool, hAPP(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), fun(fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), bool), member(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool)), _u73), hAPP(fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), collect(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool)), hoare_1580379338ep_set(_u75)))) | ~hBOOL(hAPP(fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), bool, hAPP(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), fun(fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), bool), member(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool)), _u74), hAPP(fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), collect(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool)), hoare_1580379338ep_set(_u75)))) | ( hAPP(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), hoare_509422987triple(_u75), hoare_244953527triple(_u75), _u73) != hAPP(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), hoare_509422987triple(_u75), hoare_244953527triple(_u75), _u74)) | ( _u73 = _u74) )).
% 0.47/0.63 cnf(fact_13_Abs__triple__inject-2, axiom, ( ~hBOOL(hAPP(fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), bool, hAPP(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), fun(fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), bool), member(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool)), _u73), hAPP(fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), collect(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool)), hoare_1580379338ep_set(_u75)))) | ~hBOOL(hAPP(fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), bool, hAPP(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), fun(fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), bool), member(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool)), _u74), hAPP(fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), collect(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool)), hoare_1580379338ep_set(_u75)))) | ( _u73 != _u74) | ( hAPP(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), hoare_509422987triple(_u75), hoare_244953527triple(_u75), _u73) = hAPP(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), hoare_509422987triple(_u75), hoare_244953527triple(_u75), _u74)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_14_Abs__triple__induct ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_14_Abs__triple__induct-1, axiom, ( hBOOL(hAPP(hoare_509422987triple(_u79), bool, _u77, _u78)) | hBOOL(hAPP(fun(fun(node(sum_sum(com, fun(_u79, fun(state, bool))), sum_sum(state, _u79)), bool), bool), bool, hAPP(fun(node(sum_sum(com, fun(_u79, fun(state, bool))), sum_sum(state, _u79)), bool), fun(fun(fun(node(sum_sum(com, fun(_u79, fun(state, bool))), sum_sum(state, _u79)), bool), bool), bool), member(fun(node(sum_sum(com, fun(_u79, fun(state, bool))), sum_sum(state, _u79)), bool)), skolem5(_u79, _u78, _u77)), hAPP(fun(fun(node(sum_sum(com, fun(_u79, fun(state, bool))), sum_sum(state, _u79)), bool), bool), fun(fun(node(sum_sum(com, fun(_u79, fun(state, bool))), sum_sum(state, _u79)), bool), bool), collect(fun(node(sum_sum(com, fun(_u79, fun(state, bool))), sum_sum(state, _u79)), bool)), hoare_1580379338ep_set(_u79)))) )).
% 0.47/0.63 cnf(fact_14_Abs__triple__induct-2, axiom, ( hBOOL(hAPP(hoare_509422987triple(_u79), bool, _u77, _u78)) | ~hBOOL(hAPP(hoare_509422987triple(_u79), bool, _u77, hAPP(fun(node(sum_sum(com, fun(_u79, fun(state, bool))), sum_sum(state, _u79)), bool), hoare_509422987triple(_u79), hoare_244953527triple(_u79), skolem5(_u79, _u78, _u77)))) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_15_Abs__triple__cases ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_15_Abs__triple__cases-1, axiom, ( ( _u81 = hAPP(fun(node(sum_sum(com, fun(_u82, fun(state, bool))), sum_sum(state, _u82)), bool), hoare_509422987triple(_u82), hoare_244953527triple(_u82), skolem6(_u82, _u81))) )).
% 0.47/0.63 cnf(fact_15_Abs__triple__cases-2, axiom, ( hBOOL(hAPP(fun(fun(node(sum_sum(com, fun(_u82, fun(state, bool))), sum_sum(state, _u82)), bool), bool), bool, hAPP(fun(node(sum_sum(com, fun(_u82, fun(state, bool))), sum_sum(state, _u82)), bool), fun(fun(fun(node(sum_sum(com, fun(_u82, fun(state, bool))), sum_sum(state, _u82)), bool), bool), bool), member(fun(node(sum_sum(com, fun(_u82, fun(state, bool))), sum_sum(state, _u82)), bool)), skolem6(_u82, _u81)), hAPP(fun(fun(node(sum_sum(com, fun(_u82, fun(state, bool))), sum_sum(state, _u82)), bool), bool), fun(fun(node(sum_sum(com, fun(_u82, fun(state, bool))), sum_sum(state, _u82)), bool), bool), collect(fun(node(sum_sum(com, fun(_u82, fun(state, bool))), sum_sum(state, _u82)), bool)), hoare_1580379338ep_set(_u82)))) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_16_type__definition_OAbs__inject ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_16_type__definition_OAbs__inject-1, axiom, ( ~hBOOL(hAPP(fun(_u89, bool), bool, hAPP(fun(_u89, _u88), fun(fun(_u89, bool), bool), hAPP(fun(_u88, _u89), fun(fun(_u89, _u88), fun(fun(_u89, bool), bool)), type_definition(_u88, _u89), _u85), _u84), _u83)) | ~hBOOL(hAPP(fun(_u89, bool), bool, hAPP(_u89, fun(fun(_u89, bool), bool), member(_u89), _u86), _u83)) | ~hBOOL(hAPP(fun(_u89, bool), bool, hAPP(_u89, fun(fun(_u89, bool), bool), member(_u89), _u87), _u83)) | ( hAPP(_u89, _u88, _u84, _u86) != hAPP(_u89, _u88, _u84, _u87)) | ( ti(_u89, _u86) = ti(_u89, _u87)) )).
% 0.47/0.63 cnf(fact_16_type__definition_OAbs__inject-2, axiom, ( ~hBOOL(hAPP(fun(_u89, bool), bool, hAPP(fun(_u89, _u88), fun(fun(_u89, bool), bool), hAPP(fun(_u88, _u89), fun(fun(_u89, _u88), fun(fun(_u89, bool), bool)), type_definition(_u88, _u89), _u85), _u84), _u83)) | ~hBOOL(hAPP(fun(_u89, bool), bool, hAPP(_u89, fun(fun(_u89, bool), bool), member(_u89), _u86), _u83)) | ~hBOOL(hAPP(fun(_u89, bool), bool, hAPP(_u89, fun(fun(_u89, bool), bool), member(_u89), _u87), _u83)) | ( ti(_u89, _u86) != ti(_u89, _u87)) | ( hAPP(_u89, _u88, _u84, _u86) = hAPP(_u89, _u88, _u84, _u87)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_17_type__definition_OAbs__inverse ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_17_type__definition_OAbs__inverse-1, axiom, ( ~hBOOL(hAPP(fun(_u95, bool), bool, hAPP(fun(_u95, _u94), fun(fun(_u95, bool), bool), hAPP(fun(_u94, _u95), fun(fun(_u95, _u94), fun(fun(_u95, bool), bool)), type_definition(_u94, _u95), _u92), _u91), _u90)) | ~hBOOL(hAPP(fun(_u95, bool), bool, hAPP(_u95, fun(fun(_u95, bool), bool), member(_u95), _u93), _u90)) | ( hAPP(_u94, _u95, _u92, hAPP(_u95, _u94, _u91, _u93)) = ti(_u95, _u93)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_18_type__definition_ORep__inject ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_18_type__definition_ORep__inject-1, axiom, ( ~hBOOL(hAPP(fun(_u102, bool), bool, hAPP(fun(_u102, _u101), fun(fun(_u102, bool), bool), hAPP(fun(_u101, _u102), fun(fun(_u102, _u101), fun(fun(_u102, bool), bool)), type_definition(_u101, _u102), _u98), _u97), _u96)) | ( hAPP(_u101, _u102, _u98, _u100) != hAPP(_u101, _u102, _u98, _u99)) | ( ti(_u101, _u100) = ti(_u101, _u99)) )).
% 0.47/0.63 cnf(fact_18_type__definition_ORep__inject-2, axiom, ( ~hBOOL(hAPP(fun(_u102, bool), bool, hAPP(fun(_u102, _u101), fun(fun(_u102, bool), bool), hAPP(fun(_u101, _u102), fun(fun(_u102, _u101), fun(fun(_u102, bool), bool)), type_definition(_u101, _u102), _u98), _u97), _u96)) | ( ti(_u101, _u100) != ti(_u101, _u99)) | ( hAPP(_u101, _u102, _u98, _u100) = hAPP(_u101, _u102, _u98, _u99)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_19_type__definition_ORep__inverse ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_19_type__definition_ORep__inverse-1, axiom, ( ( hAPP(_u108, _u107, _u104, hAPP(_u107, _u108, _u105, _u106)) = ti(_u107, _u106)) | ~hBOOL(hAPP(fun(_u108, bool), bool, hAPP(fun(_u108, _u107), fun(fun(_u108, bool), bool), hAPP(fun(_u107, _u108), fun(fun(_u108, _u107), fun(fun(_u108, bool), bool)), type_definition(_u107, _u108), _u105), _u104), _u103)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_20_type__definition_ORep ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_20_type__definition_ORep-1, axiom, ( ~hBOOL(hAPP(fun(_u114, bool), bool, hAPP(fun(_u114, _u113), fun(fun(_u114, bool), bool), hAPP(fun(_u113, _u114), fun(fun(_u114, _u113), fun(fun(_u114, bool), bool)), type_definition(_u113, _u114), _u111), _u110), _u109)) | hBOOL(hAPP(fun(_u114, bool), bool, hAPP(_u114, fun(fun(_u114, bool), bool), member(_u114), hAPP(_u113, _u114, _u111, _u112)), _u109)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_21_induct__false__def ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_21_induct__false__def-1, axiom, ( ~hBOOL(induct_false) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_22_type__definition_ORep__cases ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_22_type__definition_ORep__cases-1, axiom, ( ~hBOOL(hAPP(fun(_u121, bool), bool, hAPP(fun(_u121, _u120), fun(fun(_u121, bool), bool), hAPP(fun(_u120, _u121), fun(fun(_u121, _u120), fun(fun(_u121, bool), bool)), type_definition(_u120, _u121), _u118), _u117), _u116)) | ~hBOOL(hAPP(fun(_u121, bool), bool, hAPP(_u121, fun(fun(_u121, bool), bool), member(_u121), _u119), _u116)) | ( ti(_u121, _u119) = hAPP(_u120, _u121, _u118, skolem7(_u121, _u120, _u119, _u118, _u117, _u116))) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_23_type__definition_OAbs__cases ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_23_type__definition_OAbs__cases-1, axiom, ( ~hBOOL(hAPP(fun(_u128, bool), bool, hAPP(fun(_u128, _u127), fun(fun(_u128, bool), bool), hAPP(fun(_u127, _u128), fun(fun(_u128, _u127), fun(fun(_u128, bool), bool)), type_definition(_u127, _u128), _u125), _u124), _u123)) | ( ti(_u127, _u126) = hAPP(_u128, _u127, _u124, skolem8(_u128, _u127, _u126, _u125, _u124, _u123))) )).
% 0.47/0.63 cnf(fact_23_type__definition_OAbs__cases-2, axiom, ( ~hBOOL(hAPP(fun(_u128, bool), bool, hAPP(fun(_u128, _u127), fun(fun(_u128, bool), bool), hAPP(fun(_u127, _u128), fun(fun(_u128, _u127), fun(fun(_u128, bool), bool)), type_definition(_u127, _u128), _u125), _u124), _u123)) | hBOOL(hAPP(fun(_u128, bool), bool, hAPP(_u128, fun(fun(_u128, bool), bool), member(_u128), skolem8(_u128, _u127, _u126, _u125, _u124, _u123)), _u123)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_24_type__definition_OAbs__induct ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_24_type__definition_OAbs__induct-1, axiom, ( ~hBOOL(hAPP(fun(_u136, bool), bool, hAPP(fun(_u136, _u135), fun(fun(_u136, bool), bool), hAPP(fun(_u135, _u136), fun(fun(_u136, _u135), fun(fun(_u136, bool), bool)), type_definition(_u135, _u136), _u132), _u131), _u130)) | hBOOL(hAPP(_u135, bool, _u133, _u134)) | hBOOL(hAPP(fun(_u136, bool), bool, hAPP(_u136, fun(fun(_u136, bool), bool), member(_u136), skolem9(_u136, _u135, _u134, _u133, _u132, _u131, _u130)), _u130)) )).
% 0.47/0.63 cnf(fact_24_type__definition_OAbs__induct-2, axiom, ( ~hBOOL(hAPP(fun(_u136, bool), bool, hAPP(fun(_u136, _u135), fun(fun(_u136, bool), bool), hAPP(fun(_u135, _u136), fun(fun(_u136, _u135), fun(fun(_u136, bool), bool)), type_definition(_u135, _u136), _u132), _u131), _u130)) | hBOOL(hAPP(_u135, bool, _u133, _u134)) | ~hBOOL(hAPP(_u135, bool, _u133, hAPP(_u136, _u135, _u131, skolem9(_u136, _u135, _u134, _u133, _u132, _u131, _u130)))) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_25_type__definition_ORep__induct ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_25_type__definition_ORep__induct-1, axiom, ( ~hBOOL(hAPP(fun(_u144, bool), bool, hAPP(fun(_u144, _u143), fun(fun(_u144, bool), bool), hAPP(fun(_u143, _u144), fun(fun(_u144, _u143), fun(fun(_u144, bool), bool)), type_definition(_u143, _u144), _u140), _u139), _u138)) | ~hBOOL(hAPP(fun(_u144, bool), bool, hAPP(_u144, fun(fun(_u144, bool), bool), member(_u144), _u141), _u138)) | ~hBOOL(hAPP(_u144, bool, _u142, hAPP(_u143, _u144, _u140, skolem10(_u144, _u143, _u142, _u141, _u140, _u139, _u138)))) | hBOOL(hAPP(_u144, bool, _u142, _u141)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_26_induct__trueI ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_26_induct__trueI-1, axiom, ( hBOOL(induct_true) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_27_induct__true__def ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_27_induct__true__def-1, axiom, ( hBOOL(induct_true) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_28_induct__equal__def ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_28_induct__equal__def-1, axiom, ( ~hBOOL(hAPP(_u152, bool, hAPP(_u152, fun(_u152, bool), induct_equal(_u152), _u150), _u148)) | ( ti(_u152, _u150) = ti(_u152, _u148)) )).
% 0.47/0.63 cnf(fact_28_induct__equal__def-2, axiom, ( ( ti(_u153, _u151) != ti(_u153, _u149)) | hBOOL(hAPP(_u153, bool, hAPP(_u153, fun(_u153, bool), induct_equal(_u153), _u151), _u149)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_29_ext ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_29_ext-1, axiom, ( ( hAPP(_u158, _u157, _u156, skolem11(_u158, _u157, _u156, _u155)) != hAPP(_u158, _u157, _u155, skolem11(_u158, _u157, _u156, _u155))) | ( ti(fun(_u158, _u157), _u156) = ti(fun(_u158, _u157), _u155)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_30_mem__def ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_30_mem__def-1, axiom, ( ~hBOOL(hAPP(fun(_u166, bool), bool, hAPP(_u166, fun(fun(_u166, bool), bool), member(_u166), _u164), _u162)) | hBOOL(hAPP(_u166, bool, _u162, _u164)) )).
% 0.47/0.63 cnf(fact_30_mem__def-2, axiom, ( ~hBOOL(hAPP(_u167, bool, _u163, _u165)) | hBOOL(hAPP(fun(_u167, bool), bool, hAPP(_u167, fun(fun(_u167, bool), bool), member(_u167), _u165), _u163)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: fact_31_Collect__def ( axiom ) converted to clauses:
% 0.47/0.63 cnf(fact_31_Collect__def-1, axiom, ( ( hAPP(fun(_u169, bool), fun(_u169, bool), collect(_u169), _u168) = ti(fun(_u169, bool), _u168)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: arity_sum___Enum_Oenum ( axiom ) converted to clauses:
% 0.47/0.63 cnf(arity_sum___Enum_Oenum-1, axiom, ( ~enum(_u170) | ~enum(_u171) | enum(sum_sum(_u171, _u170)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: arity_HOL_Obool___Enum_Oenum ( axiom ) converted to clauses:
% 0.47/0.63 cnf(arity_HOL_Obool___Enum_Oenum-1, axiom, ( enum(bool) )).
% 0.47/0.63
% 0.47/0.63 % Formula: arity_fun___Enum_Oenum ( axiom ) converted to clauses:
% 0.47/0.63 cnf(arity_fun___Enum_Oenum-1, axiom, ( ~enum(_u172) | ~enum(_u173) | enum(fun(_u173, _u172)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: arity_fun___HOL_Oequal ( axiom ) converted to clauses:
% 0.47/0.63 cnf(arity_fun___HOL_Oequal-1, axiom, ( ~cl_HOL_Oequal(_u174) | ~enum(_u175) | cl_HOL_Oequal(fun(_u175, _u174)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: arity_Com_Ocom___HOL_Oequal ( axiom ) converted to clauses:
% 0.47/0.63 cnf(arity_Com_Ocom___HOL_Oequal-1, axiom, ( cl_HOL_Oequal(com) )).
% 0.47/0.63
% 0.47/0.63 % Formula: arity_HOL_Obool___HOL_Oequal ( axiom ) converted to clauses:
% 0.47/0.63 cnf(arity_HOL_Obool___HOL_Oequal-1, axiom, ( cl_HOL_Oequal(bool) )).
% 0.47/0.63
% 0.47/0.63 % Formula: arity_Com_Ostate___HOL_Oequal ( axiom ) converted to clauses:
% 0.47/0.63 cnf(arity_Com_Ostate___HOL_Oequal-1, axiom, ( cl_HOL_Oequal(state) )).
% 0.47/0.63
% 0.47/0.63 % Formula: arity_sum___HOL_Oequal ( axiom ) converted to clauses:
% 0.47/0.63 cnf(arity_sum___HOL_Oequal-1, axiom, ( cl_HOL_Oequal(sum_sum(_u177, _u176)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: arity_Hoare__Mirabelle__pjuwniqynr_Otriple___HOL_Oequal ( axiom ) converted to clauses:
% 0.47/0.63 cnf(arity_Hoare__Mirabelle__pjuwniqynr_Otriple___HOL_Oequal-1, axiom, ( cl_HOL_Oequal(hoare_509422987triple(_u178)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: help_ti_idem ( axiom ) converted to clauses:
% 0.47/0.63 cnf(help_ti_idem-1, axiom, ( ( ti(_u180, ti(_u180, _u179)) = ti(_u180, _u179)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: help_fequal_1_1_T ( axiom ) converted to clauses:
% 0.47/0.63 cnf(help_fequal_1_1_T-1, axiom, ( ~hBOOL(hAPP(_u183, bool, hAPP(_u183, fun(_u183, bool), fequal(_u183), _u182), _u181)) | ( ti(_u183, _u182) = ti(_u183, _u181)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: help_fequal_2_1_T ( axiom ) converted to clauses:
% 0.47/0.63 cnf(help_fequal_2_1_T-1, axiom, ( ( ti(_u186, _u185) != ti(_u186, _u184)) | hBOOL(hAPP(_u186, bool, hAPP(_u186, fun(_u186, bool), fequal(_u186), _u185), _u184)) )).
% 0.47/0.63
% 0.47/0.63 % Formula: conj_0 ( hypothesis ) converted to clauses:
% 0.47/0.63 cnf(conj_0-1, hypothesis, ( hBOOL(hoare_1883395792gleton) )).
% 0.47/0.63
% 0.47/0.63 % Formula: conj_1 ( conjecture ) (definitionally) converted to clauses:
% 0.47/0.63 cnf(conj_1-1, negated_conjecture, ( ( ti(state, _u187) = ti(state, skolem12)) )).
% 0.47/0.63
% 0.47/0.63 % Problem matrix:
% 0.47/0.63 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 0.47/0.63 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 0.47/0.63 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 0.47/0.63 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( fun(__eqx_0, __eqx_1) = fun(__eqy_0, __eqy_1)) )).
% 0.47/0.63 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( equal_equal(__eqx_0) = equal_equal(__eqy_0)) )).
% 0.47/0.63 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( ti(__eqx_0, __eqx_1) = ti(__eqy_0, __eqy_1)) )).
% 0.47/0.63 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( induct_equal(__eqx_0) = induct_equal(__eqy_0)) )).
% 0.47/0.63 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( undefined(__eqx_0) = undefined(__eqy_0)) )).
% 0.47/0.63 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( sum_sum(__eqx_0, __eqx_1) = sum_sum(__eqy_0, __eqy_1)) )).
% 0.47/0.63 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( node(__eqx_0, __eqx_1) = node(__eqy_0, __eqy_1)) )).
% 0.47/0.63 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( hoare_509422987triple(__eqx_0) = hoare_509422987triple(__eqy_0)) )).
% 0.47/0.63 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( hoare_244953527triple(__eqx_0) = hoare_244953527triple(__eqy_0)) )).
% 0.47/0.63 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( hoare_2037801986triple(__eqx_0) = hoare_2037801986triple(__eqy_0)) )).
% 0.47/0.63 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( hoare_1580379338ep_set(__eqx_0) = hoare_1580379338ep_set(__eqy_0)) )).
% 0.47/0.63 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( collect(__eqx_0) = collect(__eqy_0)) )).
% 0.47/0.63 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( type_definition(__eqx_0, __eqx_1) = type_definition(__eqy_0, __eqy_1)) )).
% 0.47/0.63 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( fequal(__eqx_0) = fequal(__eqy_0)) )).
% 0.47/0.63 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( hAPP(__eqx_0, __eqx_1, __eqx_2, __eqx_3) = hAPP(__eqy_0, __eqy_1, __eqy_2, __eqy_3)) )).
% 0.47/0.63 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( member(__eqx_0) = member(__eqy_0)) )).
% 0.47/0.63 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem3(__eqx_0, __eqx_1, __eqx_2) = skolem3(__eqy_0, __eqy_1, __eqy_2)) )).
% 0.47/0.63 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem4(__eqx_0, __eqx_1) = skolem4(__eqy_0, __eqy_1)) )).
% 0.47/0.63 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem5(__eqx_0, __eqx_1, __eqx_2) = skolem5(__eqy_0, __eqy_1, __eqy_2)) )).
% 0.47/0.63 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem6(__eqx_0, __eqx_1) = skolem6(__eqy_0, __eqy_1)) )).
% 0.47/0.63 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( __eqx_4 != __eqy_4) | ( __eqx_5 != __eqy_5) | ( skolem7(__eqx_0, __eqx_1, __eqx_2, __eqx_3, __eqx_4, __eqx_5) = skolem7(__eqy_0, __eqy_1, __eqy_2, __eqy_3, __eqy_4, __eqy_5)) )).
% 0.47/0.63 cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( __eqx_4 != __eqy_4) | ( __eqx_5 != __eqy_5) | ( skolem8(__eqx_0, __eqx_1, __eqx_2, __eqx_3, __eqx_4, __eqx_5) = skolem8(__eqy_0, __eqy_1, __eqy_2, __eqy_3, __eqy_4, __eqy_5)) )).
% 0.47/0.63 cnf(matrix-25, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( __eqx_4 != __eqy_4) | ( __eqx_5 != __eqy_5) | ( __eqx_6 != __eqy_6) | ( skolem9(__eqx_0, __eqx_1, __eqx_2, __eqx_3, __eqx_4, __eqx_5, __eqx_6) = skolem9(__eqy_0, __eqy_1, __eqy_2, __eqy_3, __eqy_4, __eqy_5, __eqy_6)) )).
% 0.47/0.63 cnf(matrix-26, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( __eqx_4 != __eqy_4) | ( __eqx_5 != __eqy_5) | ( __eqx_6 != __eqy_6) | ( skolem10(__eqx_0, __eqx_1, __eqx_2, __eqx_3, __eqx_4, __eqx_5, __eqx_6) = skolem10(__eqy_0, __eqy_1, __eqy_2, __eqy_3, __eqy_4, __eqy_5, __eqy_6)) )).
% 0.47/0.63 cnf(matrix-27, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( skolem11(__eqx_0, __eqx_1, __eqx_2, __eqx_3) = skolem11(__eqy_0, __eqy_1, __eqy_2, __eqy_3)) )).
% 0.47/0.63 cnf(matrix-28, plain, ( ( __eqx_0 != __eqy_0) | ~cl_HOL_Oequal(__eqx_0) | cl_HOL_Oequal(__eqy_0) )).
% 0.47/0.63 cnf(matrix-29, plain, ( ( __eqx_0 != __eqy_0) | ~hBOOL(__eqx_0) | hBOOL(__eqy_0) )).
% 0.47/0.63 cnf(matrix-30, plain, ( ( __eqx_0 != __eqy_0) | ~enum(__eqx_0) | enum(__eqy_0) )).
% 0.47/0.63 cnf(matrix-31, plain, ( ~cl_HOL_Oequal(_u0) | ( ti(fun(_u0, fun(_u0, bool)), equal_equal(_u0)) = equal_equal(_u0)) )).
% 0.47/0.63 cnf(matrix-32, plain, ( ( ti(fun(_u1, fun(_u1, bool)), induct_equal(_u1)) = induct_equal(_u1)) )).
% 0.47/0.63 cnf(matrix-33, plain, ( ( ti(bool, induct_false) = induct_false) )).
% 0.47/0.63 cnf(matrix-34, plain, ( ( ti(bool, induct_true) = induct_true) )).
% 0.47/0.63 cnf(matrix-35, plain, ( ( ti(_u2, undefined(_u2)) = undefined(_u2)) )).
% 0.47/0.63 cnf(matrix-36, plain, ( ( ti(fun(fun(node(sum_sum(com, fun(_u3, fun(state, bool))), sum_sum(state, _u3)), bool), hoare_509422987triple(_u3)), hoare_244953527triple(_u3)) = hoare_244953527triple(_u3)) )).
% 0.47/0.63 cnf(matrix-37, plain, ( ( ti(fun(hoare_509422987triple(_u4), fun(node(sum_sum(com, fun(_u4, fun(state, bool))), sum_sum(state, _u4)), bool)), hoare_2037801986triple(_u4)) = hoare_2037801986triple(_u4)) )).
% 0.47/0.63 cnf(matrix-38, plain, ( ( ti(bool, hoare_1883395792gleton) = hoare_1883395792gleton) )).
% 0.47/0.63 cnf(matrix-39, plain, ( ( ti(fun(fun(node(sum_sum(com, fun(_u5, fun(state, bool))), sum_sum(state, _u5)), bool), bool), hoare_1580379338ep_set(_u5)) = hoare_1580379338ep_set(_u5)) )).
% 0.47/0.63 cnf(matrix-40, plain, ( ( ti(fun(fun(_u6, bool), fun(_u6, bool)), collect(_u6)) = collect(_u6)) )).
% 0.47/0.63 cnf(matrix-41, plain, ( ( ti(fun(fun(_u8, _u7), fun(fun(_u7, _u8), fun(fun(_u7, bool), bool))), type_definition(_u8, _u7)) = type_definition(_u8, _u7)) )).
% 0.47/0.63 cnf(matrix-42, plain, ( ( ti(fun(_u9, fun(_u9, bool)), fequal(_u9)) = fequal(_u9)) )).
% 0.47/0.63 cnf(matrix-43, plain, ( ( hAPP(_u13, _u12, ti(fun(_u13, _u12), _u11), _u10) = hAPP(_u13, _u12, _u11, _u10)) )).
% 0.47/0.63 cnf(matrix-44, plain, ( ( hAPP(_u17, _u16, _u15, ti(_u17, _u14)) = hAPP(_u17, _u16, _u15, _u14)) )).
% 0.47/0.63 cnf(matrix-45, plain, ( ( ti(_u21, hAPP(_u20, _u21, _u19, _u18)) = hAPP(_u20, _u21, _u19, _u18)) )).
% 0.47/0.63 cnf(matrix-46, plain, ( ~hBOOL(ti(bool, _u23)) | hBOOL(_u23) )).
% 0.47/0.63 cnf(matrix-47, plain, ( ~hBOOL(_u24) | hBOOL(ti(bool, _u24)) )).
% 0.47/0.63 cnf(matrix-48, plain, ( ( ti(fun(_u25, fun(fun(_u25, bool), bool)), member(_u25)) = member(_u25)) )).
% 0.47/0.63 cnf(matrix-49, plain, ( ~hBOOL(hoare_1883395792gleton) | ( ti(state, skolem1) != ti(state, skolem2)) )).
% 0.47/0.63 cnf(matrix-50, plain, ( ( ti(state, _u29) = ti(state, _u28)) | hBOOL(hoare_1883395792gleton) )).
% 0.47/0.63 cnf(matrix-51, plain, ( ~hBOOL(hAPP(hoare_509422987triple(_u37), bool, hAPP(hoare_509422987triple(_u37), fun(hoare_509422987triple(_u37), bool), equal_equal(hoare_509422987triple(_u37)), _u35), _u33)) | ( _u35 = _u33) )).
% 0.47/0.63 cnf(matrix-52, plain, ( ( _u36 != _u34) | hBOOL(hAPP(hoare_509422987triple(_u38), bool, hAPP(hoare_509422987triple(_u38), fun(hoare_509422987triple(_u38), bool), equal_equal(hoare_509422987triple(_u38)), _u36), _u34)) )).
% 0.47/0.63 cnf(matrix-53, plain, ( ( hAPP(hoare_509422987triple(_u46), fun(node(sum_sum(com, fun(_u46, fun(state, bool))), sum_sum(state, _u46)), bool), hoare_2037801986triple(_u46), _u44) != hAPP(hoare_509422987triple(_u46), fun(node(sum_sum(com, fun(_u46, fun(state, bool))), sum_sum(state, _u46)), bool), hoare_2037801986triple(_u46), _u42)) | ( _u44 = _u42) )).
% 0.47/0.63 cnf(matrix-54, plain, ( ( _u45 != _u43) | ( hAPP(hoare_509422987triple(_u47), fun(node(sum_sum(com, fun(_u47, fun(state, bool))), sum_sum(state, _u47)), bool), hoare_2037801986triple(_u47), _u45) = hAPP(hoare_509422987triple(_u47), fun(node(sum_sum(com, fun(_u47, fun(state, bool))), sum_sum(state, _u47)), bool), hoare_2037801986triple(_u47), _u43)) )).
% 0.47/0.63 cnf(matrix-55, plain, ( ~cl_HOL_Oequal(_u48) | ( equal_equal(_u48) = fequal(_u48)) )).
% 0.47/0.63 cnf(matrix-56, plain, ( ~cl_HOL_Oequal(_u50) | hBOOL(hAPP(_u50, bool, hAPP(_u50, fun(_u50, bool), equal_equal(_u50), _u49), _u49)) )).
% 0.47/0.63 cnf(matrix-57, plain, ( ~cl_HOL_Oequal(_u53) | ~hBOOL(hAPP(_u53, bool, hAPP(_u53, fun(_u53, bool), equal_equal(_u53), _u56), _u54)) | ( ti(_u53, _u56) = ti(_u53, _u54)) )).
% 0.47/0.63 cnf(matrix-58, plain, ( ~cl_HOL_Oequal(_u53) | ( ti(_u53, _u57) != ti(_u53, _u55)) | hBOOL(hAPP(_u53, bool, hAPP(_u53, fun(_u53, bool), equal_equal(_u53), _u57), _u55)) )).
% 0.47/0.63 cnf(matrix-59, plain, ( ~cl_HOL_Oequal(_u58) | ( fequal(_u58) = equal_equal(_u58)) )).
% 0.47/0.63 cnf(matrix-60, plain, ( ( hAPP(fun(node(sum_sum(com, fun(_u60, fun(state, bool))), sum_sum(state, _u60)), bool), hoare_509422987triple(_u60), hoare_244953527triple(_u60), hAPP(hoare_509422987triple(_u60), fun(node(sum_sum(com, fun(_u60, fun(state, bool))), sum_sum(state, _u60)), bool), hoare_2037801986triple(_u60), _u59)) = _u59) )).
% 0.47/0.63 cnf(matrix-61, plain, ( hBOOL(hAPP(fun(fun(node(sum_sum(com, fun(_u62, fun(state, bool))), sum_sum(state, _u62)), bool), bool), bool, hAPP(fun(node(sum_sum(com, fun(_u62, fun(state, bool))), sum_sum(state, _u62)), bool), fun(fun(fun(node(sum_sum(com, fun(_u62, fun(state, bool))), sum_sum(state, _u62)), bool), bool), bool), member(fun(node(sum_sum(com, fun(_u62, fun(state, bool))), sum_sum(state, _u62)), bool)), hAPP(hoare_509422987triple(_u62), fun(node(sum_sum(com, fun(_u62, fun(state, bool))), sum_sum(state, _u62)), bool), hoare_2037801986triple(_u62), _u61)), hAPP(fun(fun(node(sum_sum(com, fun(_u62, fun(state, bool))), sum_sum(state, _u62)), bool), bool), fun(fun(node(sum_sum(com, fun(_u62, fun(state, bool))), sum_sum(state, _u62)), bool), bool), collect(fun(node(sum_sum(com, fun(_u62, fun(state, bool))), sum_sum(state, _u62)), bool)), hoare_1580379338ep_set(_u62)))) )).
% 0.47/0.63 cnf(matrix-62, plain, ( ~hBOOL(hAPP(fun(fun(node(sum_sum(com, fun(_u66, fun(state, bool))), sum_sum(state, _u66)), bool), bool), bool, hAPP(fun(node(sum_sum(com, fun(_u66, fun(state, bool))), sum_sum(state, _u66)), bool), fun(fun(fun(node(sum_sum(com, fun(_u66, fun(state, bool))), sum_sum(state, _u66)), bool), bool), bool), member(fun(node(sum_sum(com, fun(_u66, fun(state, bool))), sum_sum(state, _u66)), bool)), _u64), hAPP(fun(fun(node(sum_sum(com, fun(_u66, fun(state, bool))), sum_sum(state, _u66)), bool), bool), fun(fun(node(sum_sum(com, fun(_u66, fun(state, bool))), sum_sum(state, _u66)), bool), bool), collect(fun(node(sum_sum(com, fun(_u66, fun(state, bool))), sum_sum(state, _u66)), bool)), hoare_1580379338ep_set(_u66)))) | ~hBOOL(hAPP(fun(node(sum_sum(com, fun(_u66, fun(state, bool))), sum_sum(state, _u66)), bool), bool, _u65, hAPP(hoare_509422987triple(_u66), fun(node(sum_sum(com, fun(_u66, fun(state, bool))), sum_sum(state, _u66)), bool), hoare_2037801986triple(_u66), skolem3(_u66, _u65, _u64)))) | hBOOL(hAPP(fun(node(sum_sum(com, fun(_u66, fun(state, bool))), sum_sum(state, _u66)), bool), bool, _u65, _u64)) )).
% 0.47/0.63 cnf(matrix-63, plain, ( ~hBOOL(hAPP(fun(fun(node(sum_sum(com, fun(_u69, fun(state, bool))), sum_sum(state, _u69)), bool), bool), bool, hAPP(fun(node(sum_sum(com, fun(_u69, fun(state, bool))), sum_sum(state, _u69)), bool), fun(fun(fun(node(sum_sum(com, fun(_u69, fun(state, bool))), sum_sum(state, _u69)), bool), bool), bool), member(fun(node(sum_sum(com, fun(_u69, fun(state, bool))), sum_sum(state, _u69)), bool)), _u68), hAPP(fun(fun(node(sum_sum(com, fun(_u69, fun(state, bool))), sum_sum(state, _u69)), bool), bool), fun(fun(node(sum_sum(com, fun(_u69, fun(state, bool))), sum_sum(state, _u69)), bool), bool), collect(fun(node(sum_sum(com, fun(_u69, fun(state, bool))), sum_sum(state, _u69)), bool)), hoare_1580379338ep_set(_u69)))) | ( _u68 = hAPP(hoare_509422987triple(_u69), fun(node(sum_sum(com, fun(_u69, fun(state, bool))), sum_sum(state, _u69)), bool), hoare_2037801986triple(_u69), skolem4(_u69, _u68))) )).
% 0.47/0.63 cnf(matrix-64, plain, ( ~hBOOL(hAPP(fun(fun(node(sum_sum(com, fun(_u71, fun(state, bool))), sum_sum(state, _u71)), bool), bool), bool, hAPP(fun(node(sum_sum(com, fun(_u71, fun(state, bool))), sum_sum(state, _u71)), bool), fun(fun(fun(node(sum_sum(com, fun(_u71, fun(state, bool))), sum_sum(state, _u71)), bool), bool), bool), member(fun(node(sum_sum(com, fun(_u71, fun(state, bool))), sum_sum(state, _u71)), bool)), _u70), hAPP(fun(fun(node(sum_sum(com, fun(_u71, fun(state, bool))), sum_sum(state, _u71)), bool), bool), fun(fun(node(sum_sum(com, fun(_u71, fun(state, bool))), sum_sum(state, _u71)), bool), bool), collect(fun(node(sum_sum(com, fun(_u71, fun(state, bool))), sum_sum(state, _u71)), bool)), hoare_1580379338ep_set(_u71)))) | ( hAPP(hoare_509422987triple(_u71), fun(node(sum_sum(com, fun(_u71, fun(state, bool))), sum_sum(state, _u71)), bool), hoare_2037801986triple(_u71), hAPP(fun(node(sum_sum(com, fun(_u71, fun(state, bool))), sum_sum(state, _u71)), bool), hoare_509422987triple(_u71), hoare_244953527triple(_u71), _u70)) = _u70) )).
% 0.47/0.63 cnf(matrix-65, plain, ( hBOOL(hAPP(fun(fun(node(sum_sum(com, fun(_u72, fun(state, bool))), sum_sum(state, _u72)), bool), bool), bool, hAPP(fun(fun(node(sum_sum(com, fun(_u72, fun(state, bool))), sum_sum(state, _u72)), bool), hoare_509422987triple(_u72)), fun(fun(fun(node(sum_sum(com, fun(_u72, fun(state, bool))), sum_sum(state, _u72)), bool), bool), bool), hAPP(fun(hoare_509422987triple(_u72), fun(node(sum_sum(com, fun(_u72, fun(state, bool))), sum_sum(state, _u72)), bool)), fun(fun(fun(node(sum_sum(com, fun(_u72, fun(state, bool))), sum_sum(state, _u72)), bool), hoare_509422987triple(_u72)), fun(fun(fun(node(sum_sum(com, fun(_u72, fun(state, bool))), sum_sum(state, _u72)), bool), bool), bool)), type_definition(hoare_509422987triple(_u72), fun(node(sum_sum(com, fun(_u72, fun(state, bool))), sum_sum(state, _u72)), bool)), hoare_2037801986triple(_u72)), hoare_244953527triple(_u72)), hAPP(fun(fun(node(sum_sum(com, fun(_u72, fun(state, bool))), sum_sum(state, _u72)), bool), bool), fun(fun(node(sum_sum(com, fun(_u72, fun(state, bool))), sum_sum(state, _u72)), bool), bool), collect(fun(node(sum_sum(com, fun(_u72, fun(state, bool))), sum_sum(state, _u72)), bool)), hoare_1580379338ep_set(_u72)))) )).
% 0.47/0.63 cnf(matrix-66, plain, ( ~hBOOL(hAPP(fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), bool, hAPP(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), fun(fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), bool), member(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool)), _u73), hAPP(fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), collect(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool)), hoare_1580379338ep_set(_u75)))) | ~hBOOL(hAPP(fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), bool, hAPP(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), fun(fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), bool), member(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool)), _u74), hAPP(fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), collect(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool)), hoare_1580379338ep_set(_u75)))) | ( hAPP(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), hoare_509422987triple(_u75), hoare_244953527triple(_u75), _u73) != hAPP(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), hoare_509422987triple(_u75), hoare_244953527triple(_u75), _u74)) | ( _u73 = _u74) )).
% 0.47/0.63 cnf(matrix-67, plain, ( ~hBOOL(hAPP(fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), bool, hAPP(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), fun(fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), bool), member(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool)), _u73), hAPP(fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), collect(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool)), hoare_1580379338ep_set(_u75)))) | ~hBOOL(hAPP(fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), bool, hAPP(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), fun(fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), bool), member(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool)), _u74), hAPP(fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), fun(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), bool), collect(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool)), hoare_1580379338ep_set(_u75)))) | ( _u73 != _u74) | ( hAPP(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), hoare_509422987triple(_u75), hoare_244953527triple(_u75), _u73) = hAPP(fun(node(sum_sum(com, fun(_u75, fun(state, bool))), sum_sum(state, _u75)), bool), hoare_509422987triple(_u75), hoare_244953527triple(_u75), _u74)) )).
% 0.47/0.63 cnf(matrix-68, plain, ( hBOOL(hAPP(hoare_509422987triple(_u79), bool, _u77, _u78)) | hBOOL(hAPP(fun(fun(node(sum_sum(com, fun(_u79, fun(state, bool))), sum_sum(state, _u79)), bool), bool), bool, hAPP(fun(node(sum_sum(com, fun(_u79, fun(state, bool))), sum_sum(state, _u79)), bool), fun(fun(fun(node(sum_sum(com, fun(_u79, fun(state, bool))), sum_sum(state, _u79)), bool), bool), bool), member(fun(node(sum_sum(com, fun(_u79, fun(state, bool))), sum_sum(state, _u79)), bool)), skolem5(_u79, _u78, _u77)), hAPP(fun(fun(node(sum_sum(com, fun(_u79, fun(state, bool))), sum_sum(state, _u79)), bool), bool), fun(fun(node(sum_sum(com, fun(_u79, fun(state, bool))), sum_sum(state, _u79)), bool), bool), collect(fun(node(sum_sum(com, fun(_u79, fun(state, bool))), sum_sum(state, _u79)), bool)), hoare_1580379338ep_set(_u79)))) )).
% 0.47/0.63 cnf(matrix-69, plain, ( hBOOL(hAPP(hoare_509422987triple(_u79), bool, _u77, _u78)) | ~hBOOL(hAPP(hoare_509422987triple(_u79), bool, _u77, hAPP(fun(node(sum_sum(com, fun(_u79, fun(state, bool))), sum_sum(state, _u79)), bool), hoare_509422987triple(_u79), hoare_244953527triple(_u79), skolem5(_u79, _u78, _u77)))) )).
% 0.47/0.63 cnf(matrix-70, plain, ( ( _u81 = hAPP(fun(node(sum_sum(com, fun(_u82, fun(state, bool))), sum_sum(state, _u82)), bool), hoare_509422987triple(_u82), hoare_244953527triple(_u82), skolem6(_u82, _u81))) )).
% 0.47/0.63 cnf(matrix-71, plain, ( hBOOL(hAPP(fun(fun(node(sum_sum(com, fun(_u82, fun(state, bool))), sum_sum(state, _u82)), bool), bool), bool, hAPP(fun(node(sum_sum(com, fun(_u82, fun(state, bool))), sum_sum(state, _u82)), bool), fun(fun(fun(node(sum_sum(com, fun(_u82, fun(state, bool))), sum_sum(state, _u82)), bool), bool), bool), member(fun(node(sum_sum(com, fun(_u82, fun(state, bool))), sum_sum(state, _u82)), bool)), skolem6(_u82, _u81)), hAPP(fun(fun(node(sum_sum(com, fun(_u82, fun(state, bool))), sum_sum(state, _u82)), bool), bool), fun(fun(node(sum_sum(com, fun(_u82, fun(state, bool))), sum_sum(state, _u82)), bool), bool), collect(fun(node(sum_sum(com, fun(_u82, fun(state, bool))), sum_sum(state, _u82)), bool)), hoare_1580379338ep_set(_u82)))) )).
% 0.47/0.63 cnf(matrix-72, plain, ( ~hBOOL(hAPP(fun(_u89, bool), bool, hAPP(fun(_u89, _u88), fun(fun(_u89, bool), bool), hAPP(fun(_u88, _u89), fun(fun(_u89, _u88), fun(fun(_u89, bool), bool)), type_definition(_u88, _u89), _u85), _u84), _u83)) | ~hBOOL(hAPP(fun(_u89, bool), bool, hAPP(_u89, fun(fun(_u89, bool), bool), member(_u89), _u86), _u83)) | ~hBOOL(hAPP(fun(_u89, bool), bool, hAPP(_u89, fun(fun(_u89, bool), bool), member(_u89), _u87), _u83)) | ( hAPP(_u89, _u88, _u84, _u86) != hAPP(_u89, _u88, _u84, _u87)) | ( ti(_u89, _u86) = ti(_u89, _u87)) )).
% 0.47/0.63 cnf(matrix-73, plain, ( ~hBOOL(hAPP(fun(_u89, bool), bool, hAPP(fun(_u89, _u88), fun(fun(_u89, bool), bool), hAPP(fun(_u88, _u89), fun(fun(_u89, _u88), fun(fun(_u89, bool), bool)), type_definition(_u88, _u89), _u85), _u84), _u83)) | ~hBOOL(hAPP(fun(_u89, bool), bool, hAPP(_u89, fun(fun(_u89, bool), bool), member(_u89), _u86), _u83)) | ~hBOOL(hAPP(fun(_u89, bool), bool, hAPP(_u89, fun(fun(_u89, bool), bool), member(_u89), _u87), _u83)) | ( ti(_u89, _u86) != ti(_u89, _u87)) | ( hAPP(_u89, _u88, _u84, _u86) = hAPP(_u89, _u88, _u84, _u87)) )).
% 0.47/0.63 cnf(matrix-74, plain, ( ~hBOOL(hAPP(fun(_u95, bool), bool, hAPP(fun(_u95, _u94), fun(fun(_u95, bool), bool), hAPP(fun(_u94, _u95), fun(fun(_u95, _u94), fun(fun(_u95, bool), bool)), type_definition(_u94, _u95), _u92), _u91), _u90)) | ~hBOOL(hAPP(fun(_u95, bool), bool, hAPP(_u95, fun(fun(_u95, bool), bool), member(_u95), _u93), _u90)) | ( hAPP(_u94, _u95, _u92, hAPP(_u95, _u94, _u91, _u93)) = ti(_u95, _u93)) )).
% 0.47/0.63 cnf(matrix-75, plain, ( ~hBOOL(hAPP(fun(_u102, bool), bool, hAPP(fun(_u102, _u101), fun(fun(_u102, bool), bool), hAPP(fun(_u101, _u102), fun(fun(_u102, _u101), fun(fun(_u102, bool), bool)), type_definition(_u101, _u102), _u98), _u97), _u96)) | ( hAPP(_u101, _u102, _u98, _u100) != hAPP(_u101, _u102, _u98, _u99)) | ( ti(_u101, _u100) = ti(_u101, _u99)) )).
% 0.47/0.63 cnf(matrix-76, plain, ( ~hBOOL(hAPP(fun(_u102, bool), bool, hAPP(fun(_u102, _u101), fun(fun(_u102, bool), bool), hAPP(fun(_u101, _u102), fun(fun(_u102, _u101), fun(fun(_u102, bool), bool)), type_definition(_u101, _u102), _u98), _u97), _u96)) | ( ti(_u101, _u100) != ti(_u101, _u99)) | ( hAPP(_u101, _u102, _u98, _u100) = hAPP(_u101, _u102, _u98, _u99)) )).
% 0.47/0.63 cnf(matrix-77, plain, ( ( hAPP(_u108, _u107, _u104, hAPP(_u107, _u108, _u105, _u106)) = ti(_u107, _u106)) | ~hBOOL(hAPP(fun(_u108, bool), bool, hAPP(fun(_u108, _u107), fun(fun(_u108, bool), bool), hAPP(fun(_u107, _u108), fun(fun(_u108, _u107), fun(fun(_u108, bool), bool)), type_definition(_u107, _u108), _u105), _u104), _u103)) )).
% 0.47/0.63 cnf(matrix-78, plain, ( ~hBOOL(hAPP(fun(_u114, bool), bool, hAPP(fun(_u114, _u113), fun(fun(_u114, bool), bool), hAPP(fun(_u113, _u114), fun(fun(_u114, _u113), fun(fun(_u114, bool), bool)), type_definition(_u113, _u114), _u111), _u110), _u109)) | hBOOL(hAPP(fun(_u114, bool), bool, hAPP(_u114, fun(fun(_u114, bool), bool), member(_u114), hAPP(_u113, _u114, _u111, _u112)), _u109)) )).
% 0.47/0.63 cnf(matrix-79, plain, ( ~hBOOL(induct_false) )).
% 0.47/0.63 cnf(matrix-80, plain, ( ~hBOOL(hAPP(fun(_u121, bool), bool, hAPP(fun(_u121, _u120), fun(fun(_u121, bool), bool), hAPP(fun(_u120, _u121), fun(fun(_u121, _u120), fun(fun(_u121, bool), bool)), type_definition(_u120, _u121), _u118), _u117), _u116)) | ~hBOOL(hAPP(fun(_u121, bool), bool, hAPP(_u121, fun(fun(_u121, bool), bool), member(_u121), _u119), _u116)) | ( ti(_u121, _u119) = hAPP(_u120, _u121, _u118, skolem7(_u121, _u120, _u119, _u118, _u117, _u116))) )).
% 0.47/0.63 cnf(matrix-81, plain, ( ~hBOOL(hAPP(fun(_u128, bool), bool, hAPP(fun(_u128, _u127), fun(fun(_u128, bool), bool), hAPP(fun(_u127, _u128), fun(fun(_u128, _u127), fun(fun(_u128, bool), bool)), type_definition(_u127, _u128), _u125), _u124), _u123)) | ( ti(_u127, _u126) = hAPP(_u128, _u127, _u124, skolem8(_u128, _u127, _u126, _u125, _u124, _u123))) )).
% 0.47/0.63 cnf(matrix-82, plain, ( ~hBOOL(hAPP(fun(_u128, bool), bool, hAPP(fun(_u128, _u127), fun(fun(_u128, bool), bool), hAPP(fun(_u127, _u128), fun(fun(_u128, _u127), fun(fun(_u128, bool), bool)), type_definition(_u127, _u128), _u125), _u124), _u123)) | hBOOL(hAPP(fun(_u128, bool), bool, hAPP(_u128, fun(fun(_u128, bool), bool), member(_u128), skolem8(_u128, _u127, _u126, _u125, _u124, _u123)), _u123)) )).
% 0.47/0.63 cnf(matrix-83, plain, ( ~hBOOL(hAPP(fun(_u136, bool), bool, hAPP(fun(_u136, _u135), fun(fun(_u136, bool), bool), hAPP(fun(_u135, _u136), fun(fun(_u136, _u135), fun(fun(_u136, bool), bool)), type_definition(_u135, _u136), _u132), _u131), _u130)) | hBOOL(hAPP(_u135, bool, _u133, _u134)) | hBOOL(hAPP(fun(_u136, bool), bool, hAPP(_u136, fun(fun(_u136, bool), bool), member(_u136), skolem9(_u136, _u135, _u134, _u133, _u132, _u131, _u130)), _u130)) )).
% 0.47/0.63 cnf(matrix-84, plain, ( ~hBOOL(hAPP(fun(_u136, bool), bool, hAPP(fun(_u136, _u135), fun(fun(_u136, bool), bool), hAPP(fun(_u135, _u136), fun(fun(_u136, _u135), fun(fun(_u136, bool), bool)), type_definition(_u135, _u136), _u132), _u131), _u130)) | hBOOL(hAPP(_u135, bool, _u133, _u134)) | ~hBOOL(hAPP(_u135, bool, _u133, hAPP(_u136, _u135, _u131, skolem9(_u136, _u135, _u134, _u133, _u132, _u131, _u130)))) )).
% 0.47/0.63 cnf(matrix-85, plain, ( ~hBOOL(hAPP(fun(_u144, bool), bool, hAPP(fun(_u144, _u143), fun(fun(_u144, bool), bool), hAPP(fun(_u143, _u144), fun(fun(_u144, _u143), fun(fun(_u144, bool), bool)), type_definition(_u143, _u144), _u140), _u139), _u138)) | ~hBOOL(hAPP(fun(_u144, bool), bool, hAPP(_u144, fun(fun(_u144, bool), bool), member(_u144), _u141), _u138)) | ~hBOOL(hAPP(_u144, bool, _u142, hAPP(_u143, _u144, _u140, skolem10(_u144, _u143, _u142, _u141, _u140, _u139, _u138)))) | hBOOL(hAPP(_u144, bool, _u142, _u141)) )).
% 0.47/0.63 cnf(matrix-86, plain, ( hBOOL(induct_true) )).
% 0.47/0.63 cnf(matrix-87, plain, ( hBOOL(induct_true) )).
% 0.47/0.63 cnf(matrix-88, plain, ( ~hBOOL(hAPP(_u152, bool, hAPP(_u152, fun(_u152, bool), induct_equal(_u152), _u150), _u148)) | ( ti(_u152, _u150) = ti(_u152, _u148)) )).
% 0.47/0.63 cnf(matrix-89, plain, ( ( ti(_u153, _u151) != ti(_u153, _u149)) | hBOOL(hAPP(_u153, bool, hAPP(_u153, fun(_u153, bool), induct_equal(_u153), _u151), _u149)) )).
% 0.47/0.63 cnf(matrix-90, plain, ( ( hAPP(_u158, _u157, _u156, skolem11(_u158, _u157, _u156, _u155)) != hAPP(_u158, _u157, _u155, skolem11(_u158, _u157, _u156, _u155))) | ( ti(fun(_u158, _u157), _u156) = ti(fun(_u158, _u157), _u155)) )).
% 0.47/0.63 cnf(matrix-91, plain, ( ~hBOOL(hAPP(fun(_u166, bool), bool, hAPP(_u166, fun(fun(_u166, bool), bool), member(_u166), _u164), _u162)) | hBOOL(hAPP(_u166, bool, _u162, _u164)) )).
% 0.47/0.63 cnf(matrix-92, plain, ( ~hBOOL(hAPP(_u167, bool, _u163, _u165)) | hBOOL(hAPP(fun(_u167, bool), bool, hAPP(_u167, fun(fun(_u167, bool), bool), member(_u167), _u165), _u163)) )).
% 0.47/0.63 cnf(matrix-93, plain, ( ( hAPP(fun(_u169, bool), fun(_u169, bool), collect(_u169), _u168) = ti(fun(_u169, bool), _u168)) )).
% 0.47/0.63 cnf(matrix-94, plain, ( ~enum(_u170) | ~enum(_u171) | enum(sum_sum(_u171, _u170)) )).
% 0.47/0.63 cnf(matrix-95, plain, ( enum(bool) )).
% 0.47/0.63 cnf(matrix-96, plain, ( ~enum(_u172) | ~enum(_u173) | enum(fun(_u173, _u172)) )).
% 0.47/0.63 cnf(matrix-97, plain, ( ~cl_HOL_Oequal(_u174) | ~enum(_u175) | cl_HOL_Oequal(fun(_u175, _u174)) )).
% 0.47/0.63 cnf(matrix-98, plain, ( cl_HOL_Oequal(com) )).
% 0.47/0.63 cnf(matrix-99, plain, ( cl_HOL_Oequal(bool) )).
% 0.47/0.63 cnf(matrix-100, plain, ( cl_HOL_Oequal(state) )).
% 0.47/0.63 cnf(matrix-101, plain, ( cl_HOL_Oequal(sum_sum(_u177, _u176)) )).
% 0.47/0.63 cnf(matrix-102, plain, ( cl_HOL_Oequal(hoare_509422987triple(_u178)) )).
% 0.47/0.63 cnf(matrix-103, plain, ( ( ti(_u180, ti(_u180, _u179)) = ti(_u180, _u179)) )).
% 0.47/0.63 cnf(matrix-104, plain, ( ~hBOOL(hAPP(_u183, bool, hAPP(_u183, fun(_u183, bool), fequal(_u183), _u182), _u181)) | ( ti(_u183, _u182) = ti(_u183, _u181)) )).
% 0.47/0.63 cnf(matrix-105, plain, ( ( ti(_u186, _u185) != ti(_u186, _u184)) | hBOOL(hAPP(_u186, bool, hAPP(_u186, fun(_u186, bool), fequal(_u186), _u185), _u184)) )).
% 0.47/0.63 cnf(matrix-106, plain, ( hBOOL(hoare_1883395792gleton) )).
% 0.47/0.63 cnf(matrix-107, plain, ( ( ti(state, _u187) = ti(state, skolem12)) )).
% 0.47/0.63
% 0.47/0.63 % Proof stack:
% 0.47/0.63 cnf(proof-stack, plain,
% 0.47/0.63 proof_stack(
% 0.47/0.63 start(49),
% 0.47/0.63 left_branch(0, 106, 0, 2),
% 0.47/0.63 right_branch(2),
% 0.47/0.63 left_branch(0, 2, 2, 3),
% 0.47/0.63 left_branch(0, 107, 0, 4),
% 0.47/0.63 right_branch(4),
% 0.47/0.63 left_branch(0, 1, 1, 5),
% 0.47/0.63 left_branch(0, 107, 0, 6),
% 0.47/0.63 right_branch(6),
% 0.47/0.63 right_branch(5),
% 0.47/0.63 right_branch(3)
% 0.47/0.63 )).
% 0.47/0.63 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------