%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP041^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:10:28 AM UTC 2026
% Result : Theorem 0.20s 0.31s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP041^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n015.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 19:43:49 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.31 % (4016805)Will run a generic schedule for satisfiability detection.
% 0.20/0.31 % (4016812)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2867998539:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.31 % (4016811)% WARNING: option uhcvi not known.
% 0.20/0.31 % (4016811)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1683055023:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.31 % (4016813)dis+10_1_sil=32000:sp=arity:random_seed=1881032857:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.31 % (4016810)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1980196020_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.31 % (4016814)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3795846114:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.31 % (4016815)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3258142219:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.31 % (4016816)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1291745587:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.31 % (4016811)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.31 % (4016814)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.31 % (4016812) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4016805-4016812"...
% 0.20/0.31 % (4016812)...printing done.
% 0.20/0.31 % (4016812)Refutation found. Thanks to Tanya!
% 0.20/0.31 % SZS status Theorem for theBenchmark
% 0.20/0.31 % SZS output start Proof for theBenchmark
% 0.20/0.31 thf(type_def_5, type, denota1663640101rp_ext: ($tType * $tType * $tType * $tType) > $tType).
% 0.20/0.31 thf(type_def_6, type, finite_Cartesian_vec: ($tType * $tType) > $tType).
% 0.20/0.31 thf(type_def_7, type, product_unit: $tType).
% 0.20/0.31 thf(type_def_8, type, product_prod: ($tType * $tType) > $tType).
% 0.20/0.31 thf(type_def_9, type, formula: ($tType * $tType * $tType) > $tType).
% 0.20/0.31 thf(type_def_10, type, sum_sum: ($tType * $tType) > $tType).
% 0.20/0.31 thf(type_def_11, type, filter: $tType > $tType).
% 0.20/0.31 thf(type_def_12, type, trm: ($tType * $tType) > $tType).
% 0.20/0.31 thf(type_def_13, type, ode: ($tType * $tType) > $tType).
% 0.20/0.31 thf(type_def_14, type, hp: ($tType * $tType * $tType) > $tType).
% 0.20/0.31 thf(type_def_15, type, real: $tType).
% 0.20/0.31 thf(type_def_16, type, list: $tType > $tType).
% 0.20/0.31 thf(type_def_17, type, set: $tType > $tType).
% 0.20/0.31 thf(type_def_18, type, d: $tType).
% 0.20/0.31 thf(type_def_19, type, c: $tType).
% 0.20/0.31 thf(type_def_20, type, b: $tType).
% 0.20/0.31 thf(type_def_21, type, a: $tType).
% 0.20/0.31 thf(type_def_22, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.31 thf(func_def_0, type, cARD_1: !>[X0: $tType]:($o)).
% 0.20/0.31 thf(func_def_1, type, ordere890947078_space: !>[X0: $tType]:($o)).
% 0.20/0.31 thf(func_def_2, type, type: !>[X0: $tType]:($o)).
% 0.20/0.31 thf(func_def_3, type, zero: !>[X0: $tType]:($o)).
% 0.20/0.31 thf(func_def_4, type, uminus: !>[X0: $tType]:($o)).
% 0.20/0.31 thf(func_def_5, type, ord: !>[X0: $tType]:($o)).
% 0.20/0.31 thf(func_def_6, type, order: !>[X0: $tType]:($o)).
% 0.20/0.31 thf(func_def_7, type, group_add: !>[X0: $tType]:($o)).
% 0.20/0.31 thf(func_def_8, type, no_bot: !>[X0: $tType]:($o)).
% 0.20/0.31 thf(func_def_9, type, no_top: !>[X0: $tType]:($o)).
% 0.20/0.31 thf(func_def_10, type, finite_finite: !>[X0: $tType]:($o)).
% 0.20/0.31 thf(func_def_11, type, linorder: !>[X0: $tType]:($o)).
% 0.20/0.31 thf(func_def_12, type, preorder: !>[X0: $tType]:($o)).
% 0.20/0.31 thf(func_def_13, type, boolean_algebra: !>[X0: $tType]:($o)).
% 0.20/0.31 thf(func_def_14, type, semilattice_sup: !>[X0: $tType]:($o)).
% 0.20/0.31 thf(func_def_15, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 0.20/0.31 thf(func_def_16, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 0.20/0.31 thf(func_def_17, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 0.20/0.31 thf(func_def_18, type, topolo503727757_space: !>[X0: $tType]:($o)).
% 0.20/0.31 thf(func_def_19, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 0.20/0.31 thf(func_def_20, type, lattic1601792062up_add: !>[X0: $tType]:($o)).
% 0.20/0.31 thf(func_def_21, type, real_V55928688vector: !>[X0: $tType]:($o)).
% 0.20/0.31 thf(func_def_22, type, euclid1678468529ng_gcd: !>[X0: $tType]:($o)).
% 0.20/0.31 thf(func_def_23, type, unique1598680935umeral: !>[X0: $tType]:($o)).
% 0.20/0.31 thf(func_def_24, type, euclid1155270486miring: !>[X0: $tType]:($o)).
% 0.20/0.31 thf(func_def_25, type, bNF_Ca1785829860lChain: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X0 > X1) > $o))).
% 0.20/0.31 thf(func_def_26, type, coinci1993344360de_fml: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X1 @ X2 > $o))).
% 0.20/0.31 thf(func_def_27, type, coinci32832645ide_hp: !>[X0: $tType, X1: $tType, X2: $tType]:((hp @ X0 @ X1 @ X2 > denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > $o))).
% 0.20/0.31 thf(func_def_28, type, coinci554967470ide_hp: !>[X0: $tType, X1: $tType, X2: $tType]:((hp @ X0 @ X1 @ X2 > $o))).
% 0.20/0.31 thf(func_def_29, type, coinci1495174342_equiv: !>[X0: $tType, X1: $tType, X2: $tType]:((hp @ X0 @ X1 @ X2 > denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > $o))).
% 0.20/0.31 thf(func_def_30, type, denotational_Iagree: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > set @ sum_sum @ X0 @ sum_sum @ X1 @ X2 > $o))).
% 0.20/0.31 thf(func_def_31, type, denotational_ODE_sem: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > ode @ X0 @ X2 > finite_Cartesian_vec @ real @ X2 > finite_Cartesian_vec @ real @ X2))).
% 0.20/0.31 thf(func_def_32, type, denota811733865E_vars: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > ode @ X0 @ X2 > set @ X2))).
% 0.20/0.31 thf(func_def_33, type, denotational_VSagree: !>[X0: $tType]:((finite_Cartesian_vec @ real @ X0 > finite_Cartesian_vec @ real @ X0 > set @ X0 > $o))).
% 0.20/0.31 thf(func_def_34, type, denotational_Vagree: !>[X0: $tType]:((product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0 > product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0 > set @ sum_sum @ X0 @ X0 > $o))).
% 0.20/0.31 thf(func_def_35, type, denotational_fml_sem: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > formula @ X0 @ X1 @ X2 > set @ product_prod @ finite_Cartesian_vec @ real @ X2 @ finite_Cartesian_vec @ real @ X2))).
% 0.20/0.31 thf(func_def_36, type, denotational_mk_v: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > ode @ X0 @ X2 > product_prod @ finite_Cartesian_vec @ real @ X2 @ finite_Cartesian_vec @ real @ X2 > finite_Cartesian_vec @ real @ X2 > product_prod @ finite_Cartesian_vec @ real @ X2 @ finite_Cartesian_vec @ real @ X2))).
% 0.20/0.31 thf(func_def_37, type, denotational_mk_xode: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > ode @ X0 @ X2 > finite_Cartesian_vec @ real @ X2 > product_prod @ finite_Cartesian_vec @ real @ X2 @ finite_Cartesian_vec @ real @ X2))).
% 0.20/0.31 thf(func_def_38, type, denotational_semBV: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > ode @ X0 @ X2 > set @ sum_sum @ X2 @ X2))).
% 0.20/0.31 thf(func_def_39, type, has_ve2132708402vative: !>[X0: $tType]:(((real > X0) > X0 > filter @ real > $o))).
% 0.20/0.31 thf(func_def_40, type, unique455577585es_aux: !>[X0: $tType]:((product_prod @ X0 @ X0 > $o))).
% 0.20/0.31 thf(func_def_41, type, uminus_uminus: !>[X0: $tType]:((X0 > X0))).
% 0.20/0.31 thf(func_def_42, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.20/0.31 thf(func_def_43, type, the: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_44, type, ids: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X0 > X0 > X1 > X1 > X1 > X2 > X2 > X2 > X2 > $o))).
% 0.20/0.31 thf(func_def_45, type, initia1685620758es_ode: !>[X0: $tType]:(((real > X0) > (real > X0 > X0) > set @ real > set @ X0 > $o))).
% 0.20/0.31 thf(func_def_46, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.20/0.31 thf(func_def_47, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.31 thf(func_def_48, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.20/0.31 thf(func_def_49, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.20/0.31 thf(func_def_50, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.20/0.31 thf(func_def_51, type, product_rec_set_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2 > $o))).
% 0.20/0.31 thf(func_def_52, type, product_rec_set_unit: !>[X0: $tType]:((X0 > product_unit > X0 > $o))).
% 0.20/0.31 thf(func_def_53, type, product_rec_unit: !>[X0: $tType]:((X0 > product_unit > X0))).
% 0.20/0.31 thf(func_def_54, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.20/0.31 thf(func_def_55, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 0.20/0.31 thf(func_def_56, type, set_ord_atLeast: !>[X0: $tType]:((X0 > set @ X0))).
% 0.20/0.31 thf(func_def_57, type, set_or331188842AtMost: !>[X0: $tType]:((X0 > X0 > set @ X0))).
% 0.20/0.31 thf(func_def_58, type, set_ord_atMost: !>[X0: $tType]:((X0 > set @ X0))).
% 0.20/0.31 thf(func_def_59, type, static_BVO: !>[X0: $tType, X1: $tType]:((ode @ X0 @ X1 > set @ sum_sum @ X1 @ X1))).
% 0.20/0.31 thf(func_def_60, type, static_FVF: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X1 @ X2 > set @ sum_sum @ X2 @ X2))).
% 0.20/0.31 thf(func_def_61, type, static_FVO: !>[X0: $tType, X1: $tType]:((ode @ X0 @ X1 > set @ X1))).
% 0.20/0.31 thf(func_def_62, type, static_SIGF: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X1 @ X2 > set @ sum_sum @ X0 @ sum_sum @ X1 @ X2))).
% 0.20/0.31 thf(func_def_63, type, sum_Inl: !>[X0: $tType, X1: $tType]:((X0 > sum_sum @ X0 @ X1))).
% 0.20/0.31 thf(func_def_64, type, sum_Inr: !>[X0: $tType, X1: $tType]:((X0 > sum_sum @ X1 @ X0))).
% 0.20/0.31 thf(func_def_65, type, equiv: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X1 @ X2 > formula @ X0 @ X1 @ X2 > formula @ X0 @ X1 @ X2))).
% 0.20/0.31 thf(func_def_66, type, implies: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X1 @ X2 > formula @ X0 @ X1 @ X2 > formula @ X0 @ X1 @ X2))).
% 0.20/0.31 thf(func_def_67, type, oDE_dom: !>[X0: $tType, X1: $tType]:((ode @ X0 @ X1 > set @ X1))).
% 0.20/0.31 thf(func_def_68, type, fsafe: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X1 @ X2 > $o))).
% 0.20/0.31 thf(func_def_69, type, evolveODE: !>[X0: $tType, X1: $tType, X2: $tType]:((ode @ X0 @ X1 > formula @ X0 @ X2 @ X1 > hp @ X0 @ X2 @ X1))).
% 0.20/0.31 thf(func_def_70, type, hpsafe: !>[X0: $tType, X1: $tType, X2: $tType]:((hp @ X0 @ X1 @ X2 > $o))).
% 0.20/0.31 thf(func_def_71, type, osafe: !>[X0: $tType, X1: $tType]:((ode @ X0 @ X1 > $o))).
% 0.20/0.31 thf(func_def_72, type, topolo507301023within: !>[X0: $tType]:((X0 > set @ X0 > filter @ X0))).
% 0.20/0.31 thf(func_def_73, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.20/0.31 thf(func_def_74, type, i: denota1663640101rp_ext @ a @ b @ c @ product_unit).
% 0.20/0.31 thf(func_def_75, type, j: denota1663640101rp_ext @ a @ b @ c @ product_unit).
% 0.20/0.31 thf(func_def_76, type, ode2: ode @ a @ c).
% 0.20/0.31 thf(func_def_77, type, p: formula @ a @ b @ c).
% 0.20/0.31 thf(func_def_78, type, v: set @ sum_sum @ c @ c).
% 0.20/0.31 thf(func_def_79, type, a2: finite_Cartesian_vec @ real @ c).
% 0.20/0.31 thf(func_def_80, type, aa: finite_Cartesian_vec @ real @ c).
% 0.20/0.31 thf(func_def_81, type, ab: finite_Cartesian_vec @ real @ c).
% 0.20/0.31 thf(func_def_82, type, b2: finite_Cartesian_vec @ real @ c).
% 0.20/0.31 thf(func_def_83, type, ba: finite_Cartesian_vec @ real @ c).
% 0.20/0.31 thf(func_def_84, type, bb: finite_Cartesian_vec @ real @ c).
% 0.20/0.31 thf(func_def_85, type, s: real).
% 0.20/0.31 thf(func_def_86, type, sol: (real > finite_Cartesian_vec @ real @ c)).
% 0.20/0.31 thf(func_def_87, type, t: real).
% 0.20/0.31 thf(func_def_91, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.31 thf(func_def_92, type, vAND: ($o > $o > $o)).
% 0.20/0.31 thf(func_def_93, type, vNOT: ($o > $o)).
% 0.20/0.31 thf(func_def_94, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.31 thf(func_def_95, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.31 thf(func_def_96, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.31 thf(func_def_97, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.31 thf(func_def_98, type, vIMP: ($o > $o > $o)).
% 0.20/0.31 thf(func_def_99, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.31 thf(func_def_100, type, db3: !>[X0: $tType]:(X0)).
% 0.20/0.31 thf(func_def_101, type, db4: !>[X0: $tType]:(X0)).
% 0.20/0.31 thf(func_def_102, type, vOR: ($o > $o > $o)).
% 0.20/0.31 thf(func_def_103, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.31 thf(func_def_104, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.20/0.31 thf(func_def_105, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.20/0.31 thf(func_def_106, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.20/0.31 thf(func_def_107, type, sK3: !>[X0: $tType, X1: $tType, X2: $tType]:((finite_Cartesian_vec @ real @ X1 > ode @ X2 @ X1 > denota1663640101rp_ext @ X2 @ X0 @ X1 @ product_unit > product_prod @ finite_Cartesian_vec @ real @ X1 @ finite_Cartesian_vec @ real @ X1 > product_prod @ finite_Cartesian_vec @ real @ X1 @ finite_Cartesian_vec @ real @ X1))).
% 0.20/0.31 thf(func_def_108, type, sK4: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.20/0.31 thf(func_def_109, type, sK5: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.20/0.31 thf(func_def_110, type, sK6: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 0.20/0.31 thf(func_def_111, type, sK7: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_112, type, sK8: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 0.20/0.31 thf(func_def_113, type, sK9: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_114, type, sK10: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.20/0.31 thf(func_def_115, type, sK11: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.20/0.31 thf(func_def_116, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X6))).
% 0.20/0.31 thf(func_def_117, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5))).
% 0.20/0.31 thf(func_def_118, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 0.20/0.31 thf(func_def_119, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 0.20/0.31 thf(func_def_120, type, sK16: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 0.20/0.31 thf(func_def_121, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 0.20/0.31 thf(func_def_122, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_123, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5))).
% 0.20/0.31 thf(func_def_124, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 0.20/0.31 thf(func_def_125, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 0.20/0.31 thf(func_def_126, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 0.20/0.31 thf(func_def_127, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 0.20/0.31 thf(func_def_128, type, sK24: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_129, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 0.20/0.31 thf(func_def_130, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 0.20/0.31 thf(func_def_131, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 0.20/0.31 thf(func_def_132, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 0.20/0.31 thf(func_def_133, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_134, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 0.20/0.31 thf(func_def_135, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 0.20/0.31 thf(func_def_136, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 0.20/0.31 thf(func_def_137, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_138, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 0.20/0.31 thf(func_def_139, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 0.20/0.31 thf(func_def_140, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_141, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X0))).
% 0.20/0.31 thf(func_def_142, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X1))).
% 0.20/0.31 thf(func_def_143, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X2))).
% 0.20/0.31 thf(func_def_144, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X3))).
% 0.20/0.31 thf(func_def_145, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X4))).
% 0.20/0.31 thf(func_def_146, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X5))).
% 0.20/0.31 thf(func_def_147, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X6))).
% 0.20/0.31 thf(func_def_148, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X0))).
% 0.20/0.31 thf(func_def_149, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X1))).
% 0.20/0.31 thf(func_def_150, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X2))).
% 0.20/0.31 thf(func_def_151, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X3))).
% 0.20/0.31 thf(func_def_152, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X4))).
% 0.20/0.31 thf(func_def_153, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X5))).
% 0.20/0.31 thf(func_def_154, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0))).
% 0.20/0.31 thf(func_def_155, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1))).
% 0.20/0.31 thf(func_def_156, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2))).
% 0.20/0.31 thf(func_def_157, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3))).
% 0.20/0.31 thf(func_def_158, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4))).
% 0.20/0.31 thf(func_def_159, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0))).
% 0.20/0.31 thf(func_def_160, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1))).
% 0.20/0.31 thf(func_def_161, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2))).
% 0.20/0.31 thf(func_def_162, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3))).
% 0.20/0.31 thf(func_def_163, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X0))).
% 0.20/0.31 thf(func_def_164, type, sK60: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X1))).
% 0.20/0.31 thf(func_def_165, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X2))).
% 0.20/0.31 thf(func_def_166, type, sK62: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.20/0.31 thf(func_def_167, type, sK63: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_168, type, sK64: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.20/0.31 thf(func_def_169, type, sK65: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_170, type, sK66: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 0.20/0.31 thf(func_def_171, type, sK67: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 0.20/0.31 thf(func_def_172, type, sK68: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 0.20/0.31 thf(func_def_173, type, sK69: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 0.20/0.31 thf(func_def_174, type, sK70: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 0.20/0.31 thf(func_def_175, type, sK71: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 0.20/0.31 thf(func_def_176, type, sK72: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.20/0.31 thf(func_def_177, type, sK73: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.20/0.31 thf(func_def_178, type, sK74: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.20/0.31 thf(func_def_179, type, sK75: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.20/0.31 thf(func_def_180, type, sK76: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.20/0.31 thf(func_def_181, type, sK77: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.20/0.31 thf(func_def_182, type, sK78: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.20/0.31 thf(func_def_183, type, sK79: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.20/0.31 thf(func_def_184, type, sK80: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.20/0.31 thf(func_def_185, type, sK81: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_186, type, sK82: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_187, type, sK83: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_188, type, sK84: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_189, type, sK85: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0))).
% 0.20/0.31 thf(func_def_190, type, sK86: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0))).
% 0.20/0.31 thf(func_def_191, type, sK87: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit @ product_prod @ list @ formula @ X2 @ X1 @ X0 @ list @ formula @ X2 @ X1 @ X0 > denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit))).
% 0.20/0.31 thf(func_def_192, type, sK88: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit @ product_prod @ list @ formula @ X2 @ X1 @ X0 @ list @ formula @ X2 @ X1 @ X0 > product_prod @ list @ formula @ X2 @ X1 @ X0 @ list @ formula @ X2 @ X1 @ X0))).
% 0.20/0.31 thf(func_def_193, type, sK89: !>[X0: $tType, X1: $tType, X2: $tType]:(((denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit > product_prod @ list @ formula @ X2 @ X1 @ X0 @ list @ formula @ X2 @ X1 @ X0 > $o) > denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit))).
% 0.20/0.31 thf(func_def_194, type, sK90: !>[X0: $tType, X1: $tType, X2: $tType]:(((denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit > product_prod @ list @ formula @ X2 @ X1 @ X0 @ list @ formula @ X2 @ X1 @ X0 > $o) > product_prod @ list @ formula @ X2 @ X1 @ X0 @ list @ formula @ X2 @ X1 @ X0))).
% 0.20/0.31 thf(func_def_195, type, sK91: !>[X0: $tType, X1: $tType]:(((trm @ X0 @ X1 > X1 > $o) > trm @ X0 @ X1))).
% 0.20/0.31 thf(func_def_196, type, sK92: !>[X0: $tType, X1: $tType]:(((trm @ X0 @ X1 > X1 > $o) > X1))).
% 0.20/0.31 thf(func_def_197, type, sK93: !>[X0: $tType, X1: $tType]:((product_prod @ trm @ X0 @ X1 @ X1 > trm @ X0 @ X1))).
% 0.20/0.31 thf(func_def_198, type, sK94: !>[X0: $tType, X1: $tType]:((product_prod @ trm @ X0 @ X1 @ X1 > X1))).
% 0.20/0.31 thf(func_def_199, type, sK95: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_200, type, sK96: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1))).
% 0.20/0.31 thf(func_def_201, type, sK97: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0))).
% 0.20/0.31 thf(func_def_202, type, sK98: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > X1))).
% 0.20/0.31 thf(func_def_203, type, sK99: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_204, type, sK100: !>[X0: $tType]:(((real > X0) > set @ real > (real > X0) > real))).
% 0.20/0.31 thf(func_def_205, type, sK101: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > set @ X0 > X0))).
% 0.20/0.31 thf(func_def_206, type, sK102: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_207, type, sK103: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > set @ X0 > set @ X1))).
% 0.20/0.31 thf(func_def_208, type, sK104: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > X1) > set @ X0 > X0))).
% 0.20/0.31 thf(func_def_209, type, sK105: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X1))).
% 0.20/0.31 thf(func_def_210, type, sK106: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 0.20/0.31 thf(func_def_211, type, sK107: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X0))).
% 0.20/0.31 thf(func_def_212, type, sK108: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X0 > X1))).
% 0.20/0.31 thf(func_def_213, type, sK109: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > X1) > (X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_214, type, sK110: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > (set @ X0 > $o) > set @ X0))).
% 0.20/0.31 thf(func_def_215, type, sK111: !>[X0: $tType, X1: $tType]:((set @ X1 > (set @ X0 > $o) > (X1 > X0) > set @ X1))).
% 0.20/0.31 thf(func_def_216, type, sK112: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X0 > X1))).
% 0.20/0.31 thf(func_def_217, type, sK113: !>[X0: $tType, X1: $tType]:((set @ X1 > set @ X0 > (X1 > X0) > X1))).
% 0.20/0.31 thf(func_def_218, type, sK114: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > set @ X0 > set @ X1))).
% 0.20/0.31 thf(func_def_219, type, sK115: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_220, type, sK116: !>[X0: $tType, X1: $tType, X2: $tType]:((hp @ X1 @ X0 @ X2 > denota1663640101rp_ext @ X1 @ X0 @ X2 @ product_unit))).
% 0.20/0.31 thf(func_def_221, type, sK117: !>[X0: $tType, X1: $tType, X2: $tType]:((hp @ X1 @ X0 @ X2 > denota1663640101rp_ext @ X1 @ X0 @ X2 @ product_unit))).
% 0.20/0.31 thf(func_def_222, type, sK118: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X1 @ X2 @ X0 > denota1663640101rp_ext @ X1 @ X2 @ X0 @ product_unit))).
% 0.20/0.31 thf(func_def_223, type, sK119: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X1 @ X2 @ X0 > denota1663640101rp_ext @ X1 @ X2 @ X0 @ product_unit))).
% 0.20/0.31 thf(func_def_224, type, sK120: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X2 @ X1 > product_prod @ finite_Cartesian_vec @ real @ X1 @ finite_Cartesian_vec @ real @ X1))).
% 0.20/0.31 thf(func_def_225, type, sK121: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X2 @ X1 > product_prod @ finite_Cartesian_vec @ real @ X1 @ finite_Cartesian_vec @ real @ X1))).
% 0.20/0.31 thf(func_def_226, type, sK122: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.20/0.31 thf(f2,axiom,(
% 0.20/0.31 (denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (denotational_mk_xode @ a @ b @ c @ j @ ode2 @ (sol @ s)) @ (denotational_semBV @ a @ b @ c @ j @ ode2)) & (denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (uminus_uminus @ set @ sum_sum @ c @ c @ (denotational_semBV @ a @ b @ c @ j @ ode2)))),
% 0.20/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062Vagree_A_Imk__v_AJ_AODE_A_Iaa_M_Aba_J_A_Isol_As_J_J_A_Iaa_M_Aba_J_A_I_N_AsemBV_AJ_AODE_J_A_092_060and_062_AVagree_A_Imk__v_AJ_AODE_A_Iaa_M_Aba_J_A_Isol_As_J_J_A_Imk__xode_AJ_AODE_A_Isol_As_J_J_A_IsemBV_AJ_AODE_J_092_060close_062)).
% 0.20/0.31 thf(f341,conjecture,(
% 0.20/0.31 (denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (denotational_mk_xode @ a @ b @ c @ j @ ode2 @ (sol @ s)) @ (denotational_semBV @ a @ b @ c @ j @ ode2))),
% 0.20/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.20/0.31 thf(f342,negated_conjecture,(
% 0.20/0.31 ~(denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (denotational_mk_xode @ a @ b @ c @ j @ ode2 @ (sol @ s)) @ (denotational_semBV @ a @ b @ c @ j @ ode2))),
% 0.20/0.31 inference(negated_conjecture,[status(cth)],[f341])).
% 0.20/0.31 thf(f345,plain,(
% 0.20/0.31 (denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (denotational_mk_xode @ a @ b @ c @ j @ ode2 @ (sol @ s)) @ (denotational_semBV @ a @ b @ c @ j @ ode2)) & (denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (uminus_uminus @ set @ sum_sum @ c @ c @ (denotational_semBV @ a @ b @ c @ j @ ode2)))),
% 0.20/0.31 inference(rectify,[],[f2])).
% 0.20/0.31 thf(f346,plain,(
% 0.20/0.31 (((denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (denotational_mk_xode @ a @ b @ c @ j @ ode2 @ (sol @ s)) @ (denotational_semBV @ a @ b @ c @ j @ ode2))) = $true) & (((denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (uminus_uminus @ set @ sum_sum @ c @ c @ (denotational_semBV @ a @ b @ c @ j @ ode2)))) = $true)),
% 0.20/0.31 inference(fool_elimination,[],[f345])).
% 0.20/0.31 thf(f985,plain,(
% 0.20/0.31 ~(denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (denotational_mk_xode @ a @ b @ c @ j @ ode2 @ (sol @ s)) @ (denotational_semBV @ a @ b @ c @ j @ ode2))),
% 0.20/0.31 inference(rectify,[],[f342])).
% 0.20/0.31 thf(f986,plain,(
% 0.20/0.31 ~ (((denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (denotational_mk_xode @ a @ b @ c @ j @ ode2 @ (sol @ s)) @ (denotational_semBV @ a @ b @ c @ j @ ode2))) = $true)),
% 0.20/0.31 inference(fool_elimination,[],[f985])).
% 0.20/0.31 thf(f998,plain,(
% 0.20/0.31 (((denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (denotational_mk_xode @ a @ b @ c @ j @ ode2 @ (sol @ s)) @ (denotational_semBV @ a @ b @ c @ j @ ode2))) != $true)),
% 0.20/0.31 inference(flattening,[],[f986])).
% 0.20/0.31 thf(f1388,plain,(
% 0.20/0.31 (((denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (denotational_mk_xode @ a @ b @ c @ j @ ode2 @ (sol @ s)) @ (denotational_semBV @ a @ b @ c @ j @ ode2))) = $true)),
% 0.20/0.31 inference(cnf_transformation,[],[f346])).
% 0.20/0.31 thf(f1767,plain,(
% 0.20/0.31 (((denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (denotational_mk_xode @ a @ b @ c @ j @ ode2 @ (sol @ s)) @ (denotational_semBV @ a @ b @ c @ j @ ode2))) != $true)),
% 0.20/0.31 inference(cnf_transformation,[],[f998])).
% 0.20/0.31 thf(f2202,plain,(
% 0.20/0.31 $false),
% 0.20/0.31 inference(global_subsumption,[],[f1388,f1767])).
% 0.20/0.31 % SZS output end Proof for theBenchmark
% 0.20/0.31 % (4016812)------------------------------
% 0.20/0.31 % (4016812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (4016812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (4016812)CaDiCaL version: 2.1.3
% 0.20/0.31 % (4016812)Termination reason: Refutation
% 0.20/0.31 % (4016812)Time elapsed: 0.037 s
% 0.20/0.31 % (4016812)Peak memory usage: 14 MB
% 0.20/0.31 % (4016812)Instructions burned: 146 (million)
% 0.20/0.31 % (4016805)Success in time 0.094 s
% 0.20/0.31 % Vampire exiting
%------------------------------------------------------------------------------