TSTP Solution File: DAT130^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT130^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n028.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 May 20 19:51:35 EDT 2024
% Result : Theorem 0.15s 0.49s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : DAT130^1 : TPTP v8.2.0. Released v7.0.0.
% 0.00/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.30 % Computer : n028.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Sun May 19 23:20:22 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.10/0.31 % (3064)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.33 % (3067)WARNING: value z3 for option sas not known
% 0.15/0.34 % (3067)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.34 % (3066)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.34 % (3070)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.34 % (3065)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.34 % (3069)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.34 % (3068)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.34 % (3071)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.38 % (3071)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.39 % Exception at run slice level
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39 % Exception at run slice level
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39 % Exception at run slice level
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.40 % (3072)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.15/0.40 % (3074)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.15/0.41 % (3073)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.15/0.45 % (3072)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.46 % Exception at run slice level
% 0.15/0.46 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.46 % (3073)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.47 % (3075)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.15/0.47 % (3069)First to succeed.
% 0.15/0.48 % (3069)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3064"
% 0.15/0.49 % (3069)Refutation found. Thanks to Tanya!
% 0.15/0.49 % SZS status Theorem for theBenchmark
% 0.15/0.49 % SZS output start Proof for theBenchmark
% 0.15/0.49 thf(type_def_5, type, itself: $tType > $tType).
% 0.15/0.49 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.15/0.49 thf(type_def_7, type, coindu1593790203_llist: $tType > $tType).
% 0.15/0.49 thf(type_def_8, type, set: $tType > $tType).
% 0.15/0.49 thf(type_def_9, type, a: $tType).
% 0.15/0.49 thf(func_def_0, type, coindu1593790203_llist: $tType > $tType).
% 0.15/0.49 thf(func_def_1, type, set: $tType > $tType).
% 0.15/0.49 thf(func_def_2, type, itself: $tType > $tType).
% 0.15/0.49 thf(func_def_3, type, a: $tType).
% 0.15/0.49 thf(func_def_4, type, type: !>[X0: $tType]:(itself(X0) > $o)).
% 0.15/0.49 thf(func_def_5, type, lattice: !>[X0: $tType]:(itself(X0) > $o)).
% 0.15/0.49 thf(func_def_6, type, semilattice_inf: !>[X0: $tType]:(itself(X0) > $o)).
% 0.15/0.49 thf(func_def_7, type, coindu1571841457prefix: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > $o)).
% 0.15/0.49 thf(func_def_8, type, coindu526335360e_lSup: !>[X0: $tType]:(set(coindu1593790203_llist(X0)) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_9, type, coindu268472904append: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_10, type, coindu6345450stinct: !>[X0: $tType]:(coindu1593790203_llist(X0) > $o)).
% 0.15/0.49 thf(func_def_11, type, coindu1213758845finite: !>[X0: $tType]:(coindu1593790203_llist(X0) > $o)).
% 0.15/0.49 thf(func_def_12, type, coindu2000965700_llast: !>[X0: $tType]:(coindu1593790203_llist(X0) > X0)).
% 0.15/0.49 thf(func_def_13, type, coindu300403952lexord: !>[X0: $tType]:((X0 > X0 > $o) > coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > $o)).
% 0.15/0.49 thf(func_def_14, type, coindu1121789889_LCons: !>[X0: $tType]:(X0 > coindu1593790203_llist(X0) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_15, type, coindu1598213697e_LNil: !>[X0: $tType]:(coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_16, type, coindu882539134_llist: !>[X0: $tType, X1: $tType]:(X0 > (X1 > coindu1593790203_llist(X1) > X0) > coindu1593790203_llist(X1) > X0)).
% 0.15/0.49 thf(func_def_17, type, coindu1046438764le_lhd: !>[X0: $tType]:(coindu1593790203_llist(X0) > X0)).
% 0.15/0.49 thf(func_def_18, type, coindu335574135_lnull: !>[X0: $tType]:(coindu1593790203_llist(X0) > $o)).
% 0.15/0.49 thf(func_def_19, type, coindu1112613586e_lset: !>[X0: $tType]:(coindu1593790203_llist(X0) > set(X0))).
% 0.15/0.49 thf(func_def_20, type, coindu1047225960le_ltl: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_21, type, coindu1696667936prefix: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > $o)).
% 0.15/0.49 thf(func_def_22, type, coindu574146665prefix: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > $o)).
% 0.15/0.49 thf(func_def_23, type, coindu721411036eWhile: !>[X0: $tType]:((X0 > $o) > coindu1593790203_llist(X0) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_24, type, coindu543932918sorted: !>[X0: $tType]:((X0 > X0 > $o) > coindu1593790203_llist(X0) > $o)).
% 0.15/0.49 thf(func_def_25, type, coindu1599971794_llist: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > X1) > (X0 > X0) > X0 > coindu1593790203_llist(X1))).
% 0.15/0.49 thf(func_def_26, type, comple2143767107ompact: !>[X0: $tType]:((set(X0) > X0) > (X0 > X0 > $o) > X0 > $o)).
% 0.15/0.49 thf(func_def_27, type, comple1412571634l_cont: !>[X0: $tType, X1: $tType]:((set(X0) > X0) > (X0 > X0 > $o) > (set(X1) > X1) > (X1 > X1 > $o) > (X0 > X1) > $o)).
% 0.15/0.49 thf(func_def_28, type, comple1986059218ssible: !>[X0: $tType]:((set(X0) > X0) > (X0 > X0 > $o) > (X0 > $o) > $o)).
% 0.15/0.49 thf(func_def_29, type, comple1193779247_chain: !>[X0: $tType]:((X0 > X0 > $o) > set(X0) > $o)).
% 0.15/0.49 thf(func_def_30, type, finite_finite: !>[X0: $tType]:(set(X0) > $o)).
% 0.15/0.49 thf(func_def_31, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 0.15/0.49 thf(func_def_32, type, inf_inf: !>[X0: $tType]:(X0 > X0 > X0)).
% 0.15/0.49 thf(func_def_33, type, max: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > X0)).
% 0.15/0.49 thf(func_def_34, type, min: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > X0)).
% 0.15/0.49 thf(func_def_35, type, type2: !>[X0: $tType]:(itself(X0))).
% 0.15/0.49 thf(func_def_36, type, collect: !>[X0: $tType]:((X0 > $o) > set(X0))).
% 0.15/0.49 thf(func_def_37, type, set_atLeast: !>[X0: $tType]:((X0 > X0 > $o) > X0 > set(X0))).
% 0.15/0.49 thf(func_def_38, type, set_atLeastAtMost: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > set(X0))).
% 0.15/0.49 thf(func_def_39, type, set_atMost: !>[X0: $tType]:((X0 > X0 > $o) > X0 > set(X0))).
% 0.15/0.49 thf(func_def_40, type, member: !>[X0: $tType]:(X0 > set(X0) > $o)).
% 0.15/0.49 thf(func_def_41, type, ya: set(coindu1593790203_llist(a))).
% 0.15/0.49 thf(func_def_42, type, less_eq: a > a > $o).
% 0.15/0.49 thf(func_def_43, type, xs: coindu1593790203_llist(a)).
% 0.15/0.49 thf(func_def_47, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)).
% 0.15/0.49 thf(func_def_48, type, iCOMB: !>[X0: $tType]:(X0 > X0)).
% 0.15/0.49 thf(func_def_49, type, sCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > (X0 > X1) > X0 > X2)).
% 0.15/0.49 thf(func_def_50, type, cCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > X1 > X0 > X2)).
% 0.15/0.49 thf(func_def_51, type, vAND: $o > $o > $o).
% 0.15/0.49 thf(func_def_52, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)).
% 0.15/0.49 thf(func_def_53, type, vNOT: $o > $o).
% 0.15/0.49 thf(func_def_54, type, vOR: $o > $o > $o).
% 0.15/0.49 thf(func_def_55, type, vSIGMA: !>[X0: $tType]:((X0 > $o) > $o)).
% 0.15/0.49 thf(func_def_56, type, vIMP: $o > $o > $o).
% 0.15/0.49 thf(func_def_57, type, vPI: !>[X0: $tType]:((X0 > $o) > $o)).
% 0.15/0.49 thf(func_def_58, type, sP0: coindu1593790203_llist(a) > (coindu1593790203_llist(a) > $o) > $o).
% 0.15/0.49 thf(func_def_59, type, sP1: (coindu1593790203_llist(a) > $o) > coindu1593790203_llist(a) > $o).
% 0.15/0.49 thf(func_def_60, type, sP2: !>[X0: $tType]:((coindu1593790203_llist(X0) > $o) > $o)).
% 0.15/0.49 thf(func_def_61, type, sP3: !>[X0: $tType]:((coindu1593790203_llist(X0) > $o) > $o)).
% 0.15/0.49 thf(func_def_62, type, sP4: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > $o)).
% 0.15/0.49 thf(func_def_63, type, sP5: !>[X0: $tType]:(coindu1593790203_llist(X0) > (coindu1593790203_llist(X0) > $o) > (X0 > X0 > $o) > $o)).
% 0.15/0.49 thf(func_def_64, type, sP6: !>[X0: $tType]:((coindu1593790203_llist(X0) > $o) > (X0 > X0 > $o) > coindu1593790203_llist(X0) > $o)).
% 0.15/0.49 thf(func_def_65, type, sP7: !>[X0: $tType]:((coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > $o)).
% 0.15/0.49 thf(func_def_66, type, sP8: !>[X0: $tType]:((coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > $o)).
% 0.15/0.49 thf(func_def_67, type, sP9: !>[X0: $tType]:((X0 > coindu1593790203_llist(X0) > $o) > $o)).
% 0.15/0.49 thf(func_def_68, type, sP10: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > (X0 > X0 > $o) > $o)).
% 0.15/0.49 thf(func_def_69, type, sP11: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > (X0 > X0 > $o) > $o)).
% 0.15/0.49 thf(func_def_70, type, sP12: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > (coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > $o) > (X0 > X0 > $o) > $o)).
% 0.15/0.49 thf(func_def_71, type, sK13: coindu1593790203_llist(a)).
% 0.15/0.49 thf(func_def_72, type, sK14: coindu1593790203_llist(a) > a).
% 0.15/0.49 thf(func_def_73, type, sK15: coindu1593790203_llist(a) > a).
% 0.15/0.49 thf(func_def_74, type, sK16: coindu1593790203_llist(a) > coindu1593790203_llist(a)).
% 0.15/0.49 thf(func_def_75, type, sK17: coindu1593790203_llist(a) > a).
% 0.15/0.49 thf(func_def_76, type, sK18: !>[X0: $tType]:(coindu1593790203_llist(X0) > X0)).
% 0.15/0.49 thf(func_def_77, type, sK19: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_78, type, sK20: !>[X0: $tType]:(set(coindu1593790203_llist(X0)) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_79, type, sK21: !>[X0: $tType]:(set(coindu1593790203_llist(X0)) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_80, type, sK22: (coindu1593790203_llist(a) > $o) > coindu1593790203_llist(a)).
% 0.15/0.49 thf(func_def_81, type, sK23: (coindu1593790203_llist(a) > $o) > coindu1593790203_llist(a)).
% 0.15/0.49 thf(func_def_82, type, sK24: !>[X0: $tType]:(coindu1593790203_llist(X0) > X0)).
% 0.15/0.49 thf(func_def_83, type, sK25: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_84, type, sK26: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_85, type, sK27: !>[X0: $tType]:(coindu1593790203_llist(X0) > X0)).
% 0.15/0.49 thf(func_def_86, type, sK28: !>[X0: $tType]:(set(coindu1593790203_llist(X0)) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_87, type, sK29: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 0.15/0.49 thf(func_def_88, type, sK30: !>[X0: $tType]:((coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_89, type, sK31: !>[X0: $tType]:((X0 > $o) > coindu1593790203_llist(X0) > X0)).
% 0.15/0.49 thf(func_def_90, type, sK32: !>[X0: $tType]:((coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_91, type, sK33: !>[X0: $tType]:((coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_92, type, sK34: !>[X0: $tType]:((coindu1593790203_llist(X0) > $o) > X0)).
% 0.15/0.49 thf(func_def_93, type, sK35: !>[X0: $tType]:((coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_94, type, sK36: !>[X0: $tType]:((coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_95, type, sK37: !>[X0: $tType]:((coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_96, type, sK38: !>[X0: $tType]:((coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_97, type, sK39: !>[X0: $tType]:((coindu1593790203_llist(X0) > $o) > X0)).
% 0.15/0.49 thf(func_def_98, type, sK40: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_99, type, sK41: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_100, type, sK42: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > X0)).
% 0.15/0.49 thf(func_def_101, type, sK43: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_102, type, sK44: !>[X0: $tType]:(coindu1593790203_llist(X0) > (X0 > X0 > $o) > X0)).
% 0.15/0.49 thf(func_def_103, type, sK45: !>[X0: $tType]:(coindu1593790203_llist(X0) > (X0 > X0 > $o) > X0)).
% 0.15/0.49 thf(func_def_104, type, sK46: !>[X0: $tType]:(coindu1593790203_llist(X0) > (X0 > X0 > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_105, type, sK47: !>[X0: $tType]:(coindu1593790203_llist(X0) > X0)).
% 0.15/0.49 thf(func_def_106, type, sK48: !>[X0: $tType]:(coindu1593790203_llist(X0) > X0 > X0)).
% 0.15/0.49 thf(func_def_107, type, sK49: !>[X0: $tType]:(coindu1593790203_llist(X0) > X0 > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_108, type, sK50: !>[X0: $tType]:(coindu1593790203_llist(X0) > X0 > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_109, type, sK51: !>[X0: $tType]:(coindu1593790203_llist(X0) > X0 > X0)).
% 0.15/0.49 thf(func_def_110, type, sK52: !>[X0: $tType]:(coindu1593790203_llist(X0) > X0 > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_111, type, sK53: !>[X0: $tType]:(coindu1593790203_llist(X0) > X0 > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_112, type, sK54: !>[X0: $tType]:(coindu1593790203_llist(X0) > set(coindu1593790203_llist(X0)) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_113, type, sK55: !>[X0: $tType]:(coindu1593790203_llist(X0) > set(coindu1593790203_llist(X0)) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_114, type, sK56: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > (coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_115, type, sK57: !>[X0: $tType]:((coindu1593790203_llist(X0) > $o) > X0)).
% 0.15/0.49 thf(func_def_116, type, sK58: !>[X0: $tType]:((coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_117, type, sK59: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 0.15/0.49 thf(func_def_118, type, sK60: !>[X0: $tType]:((X0 > X0 > $o) > (coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_119, type, sK61: !>[X0: $tType]:((X0 > X0 > $o) > (coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_120, type, sK62: !>[X0: $tType]:((coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_121, type, sK63: !>[X0: $tType]:((coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_122, type, sK64: !>[X0: $tType]:((coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_123, type, sK65: !>[X0: $tType]:((coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_124, type, sK66: !>[X0: $tType]:((coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_125, type, sK67: !>[X0: $tType]:((coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_126, type, sK68: !>[X0: $tType]:((coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_127, type, sK69: !>[X0: $tType]:((coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_128, type, sK70: !>[X0: $tType]:((X0 > coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_129, type, sK71: !>[X0: $tType]:((X0 > coindu1593790203_llist(X0) > $o) > X0)).
% 0.15/0.49 thf(func_def_130, type, sK72: !>[X0: $tType]:((X0 > coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_131, type, sK73: !>[X0: $tType]:((coindu1593790203_llist(X0) > $o) > X0 > X0)).
% 0.15/0.49 thf(func_def_132, type, sK74: !>[X0: $tType]:((coindu1593790203_llist(X0) > $o) > X0 > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_133, type, sK75: !>[X0: $tType]:((coindu1593790203_llist(X0) > $o) > X0 > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_134, type, sK76: !>[X0: $tType]:((coindu1593790203_llist(X0) > $o) > X0 > X0)).
% 0.15/0.49 thf(func_def_135, type, sK77: !>[X0: $tType]:((coindu1593790203_llist(X0) > $o) > X0 > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_136, type, sK78: !>[X0: $tType]:((coindu1593790203_llist(X0) > $o) > X0 > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_137, type, sK79: !>[X0: $tType]:((X0 > coindu1593790203_llist(X0) > $o) > X0)).
% 0.15/0.49 thf(func_def_138, type, sK80: !>[X0: $tType]:((X0 > coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_139, type, sK81: !>[X0: $tType]:((X0 > coindu1593790203_llist(X0) > $o) > X0)).
% 0.15/0.49 thf(func_def_140, type, sK82: !>[X0: $tType]:((X0 > coindu1593790203_llist(X0) > $o) > X0)).
% 0.15/0.49 thf(func_def_141, type, sK83: !>[X0: $tType]:((X0 > coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_142, type, sK84: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > (X0 > X0 > $o) > X0)).
% 0.15/0.49 thf(func_def_143, type, sK85: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > (X0 > X0 > $o) > X0)).
% 0.15/0.49 thf(func_def_144, type, sK86: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > (X0 > X0 > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_145, type, sK87: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > (X0 > X0 > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_146, type, sK88: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > (X0 > X0 > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_147, type, sK89: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > (X0 > X0 > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_148, type, sK90: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > (X0 > X0 > $o) > X0)).
% 0.15/0.49 thf(func_def_149, type, sK91: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_150, type, sK92: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > coindu1593790203_llist(X0) > X0)).
% 0.15/0.49 thf(func_def_151, type, sK93: !>[X0: $tType]:((X0 > X0 > $o) > (coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_152, type, sK94: !>[X0: $tType]:((X0 > X0 > $o) > (coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > $o) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_154, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)).
% 0.15/0.49 thf(func_def_155, type, sK96: !>[X0: $tType]:(coindu1593790203_llist(X0) > X0 > coindu1593790203_llist(X0) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_156, type, sK97: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > X0 > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_157, type, sK98: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0) > X0 > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_158, type, sK99: !>[X0: $tType]:((X0 > $o) > coindu1593790203_llist(X0) > X0)).
% 0.15/0.49 thf(func_def_159, type, sK100: !>[X0: $tType]:(set(coindu1593790203_llist(X0)) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_160, type, sK101: !>[X0: $tType]:(set(coindu1593790203_llist(X0)) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_161, type, sK102: !>[X0: $tType]:(set(coindu1593790203_llist(X0)) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_162, type, sK103: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_163, type, sK104: !>[X0: $tType]:(coindu1593790203_llist(X0) > coindu1593790203_llist(X0))).
% 0.15/0.49 thf(func_def_164, type, sK105: coindu1593790203_llist(a) > coindu1593790203_llist(a)).
% 0.15/0.49 thf(func_def_165, type, sK106: coindu1593790203_llist(a) > a).
% 0.15/0.49 thf(f2576,plain,(
% 0.15/0.49 $false),
% 0.15/0.49 inference(avatar_sat_refutation,[],[f2241,f2246,f2251,f2255,f2287,f2292,f2297,f2302,f2309,f2316,f2321,f2325,f2329,f2334,f2338,f2343,f2347,f2351,f2359,f2364,f2368,f2373,f2378,f2382,f2386,f2390,f2394,f2398,f2402,f2414,f2418,f2422,f2426,f2439,f2443,f2447,f2451,f2455,f2475,f2479,f2483,f2488,f2492,f2496,f2500,f2516,f2524,f2528,f2532,f2546,f2550,f2555,f2562,f2566,f2570,f2574,f2575])).
% 0.15/0.49 thf(f2575,plain,(
% 0.15/0.49 spl95_9),
% 0.15/0.49 inference(avatar_split_clause,[],[f1579,f2306])).
% 0.15/0.49 thf(f2306,plain,(
% 0.15/0.49 spl95_9 <=> (vAPP(a,$o,vAPP(a,sTfun(a,$o),less_eq,vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),xs)),vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),xs))) = $true)),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_9])])).
% 0.15/0.49 thf(f1579,plain,(
% 0.15/0.49 (vAPP(a,$o,vAPP(a,sTfun(a,$o),less_eq,vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),xs)),vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),xs))) = $true)),
% 0.15/0.49 inference(cnf_transformation,[],[f725])).
% 0.15/0.49 thf(f725,plain,(
% 0.15/0.49 (vAPP(a,$o,vAPP(a,sTfun(a,$o),less_eq,vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),xs)),vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),xs))) = $true)),
% 0.15/0.49 inference(fool_elimination,[],[f724])).
% 0.15/0.49 thf(f724,plain,(
% 0.15/0.49 vAPP(a,$o,vAPP(a,sTfun(a,$o),less_eq,vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),xs)),vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),xs)))),
% 0.15/0.49 inference(rectify,[],[f2])).
% 0.15/0.49 thf(f2,axiom,(
% 0.15/0.49 vAPP(a,$o,vAPP(a,sTfun(a,$o),less_eq,vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),xs)),vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),xs)))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062lhd_Axs_A_092_060le_062_Alhd_A_Iltl_Axs_J_092_060close_062)).
% 0.15/0.49 thf(f2574,plain,(
% 0.15/0.49 spl95_56),
% 0.15/0.49 inference(avatar_split_clause,[],[f1445,f2572])).
% 0.15/0.49 thf(f2572,plain,(
% 0.15/0.49 spl95_56 <=> ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : X0 > X0 > $o] : ($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o)),coindu300403952lexord(X0),X1),coindu1598213697e_LNil(X0)),X2))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_56])])).
% 0.15/0.49 thf(f1445,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : X0 > X0 > $o] : (($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o)),coindu300403952lexord(X0),X1),coindu1598213697e_LNil(X0)),X2))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f595])).
% 0.15/0.49 thf(f595,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : coindu1593790203_llist(X0)] : ($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o)),coindu300403952lexord(X0),X1),coindu1598213697e_LNil(X0)),X2))),
% 0.15/0.49 inference(fool_elimination,[],[f594])).
% 0.15/0.49 thf(f594,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : coindu1593790203_llist(X0)] : vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o)),coindu300403952lexord(X0),X1),coindu1598213697e_LNil(X0)),X2)),
% 0.15/0.49 inference(rectify,[],[f237])).
% 0.15/0.49 thf(f237,axiom,(
% 0.15/0.49 ! [X0 : $tType,X88 : X0 > X0 > $o,X18 : coindu1593790203_llist(X0)] : vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o)),coindu300403952lexord(X0),X88),coindu1598213697e_LNil(X0)),X18)),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_llexord__LNil)).
% 0.15/0.49 thf(f2570,plain,(
% 0.15/0.49 spl95_55),
% 0.15/0.49 inference(avatar_split_clause,[],[f2004,f2568])).
% 0.15/0.49 thf(f2568,plain,(
% 0.15/0.49 spl95_55 <=> ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : coindu1593790203_llist(X0) > $o] : ((vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X2) = $true) | (coindu1598213697e_LNil(X0) != vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK33(X0),X1)) | ($true != vAPP(coindu1593790203_llist(X0),$o,X1,X2)))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_55])])).
% 0.15/0.49 thf(f2004,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : coindu1593790203_llist(X0) > $o] : ((vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X2) = $true) | (coindu1598213697e_LNil(X0) != vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK33(X0),X1)) | ($true != vAPP(coindu1593790203_llist(X0),$o,X1,X2))) )),
% 0.15/0.49 inference(equality_proxy_clausification,[],[f1666])).
% 0.15/0.49 thf(f1666,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : coindu1593790203_llist(X0) > $o] : ((vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X2) = $true) | ($true != vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vEQ(coindu1593790203_llist(X0)),coindu1598213697e_LNil(X0)),vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK33(X0),X1))) | ($true != vAPP(coindu1593790203_llist(X0),$o,X1,X2))) )),
% 0.15/0.49 inference(definition_unfolding,[],[f1380,f1215])).
% 0.15/0.49 thf(f1215,plain,(
% 0.15/0.49 ( ! [X0 : $tType] : ((coindu335574135_lnull(X0) = vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vEQ(coindu1593790203_llist(X0)),coindu1598213697e_LNil(X0)))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f303])).
% 0.15/0.49 thf(f303,plain,(
% 0.15/0.49 ! [X0 : $tType] : (coindu335574135_lnull(X0) = vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vEQ(coindu1593790203_llist(X0)),coindu1598213697e_LNil(X0)))),
% 0.15/0.49 inference(fool_elimination,[],[f302])).
% 0.15/0.49 thf(f302,plain,(
% 0.15/0.49 ! [X0 : $tType] : (coindu335574135_lnull(X0) = (^[X1 : coindu1593790203_llist(X0)] : ((coindu1598213697e_LNil(X0) = X1))))),
% 0.15/0.49 inference(rectify,[],[f117])).
% 0.15/0.49 thf(f117,axiom,(
% 0.15/0.49 ! [X0 : $tType] : (coindu335574135_lnull(X0) = (^[X38 : coindu1593790203_llist(X0)] : ((coindu1598213697e_LNil(X0) = X38))))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_lnull__def)).
% 0.15/0.49 thf(f1380,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : coindu1593790203_llist(X0) > $o] : ((vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X2) = $true) | ($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK33(X0),X1))) | ($true != vAPP(coindu1593790203_llist(X0),$o,X1,X2))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f1090])).
% 0.15/0.49 thf(f1090,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0) > $o,X2 : coindu1593790203_llist(X0)] : ((vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X2) = $true) | (((($true != vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK33(X0),X1)))) & ($true != vAPP(coindu1593790203_llist(X0),$o,X1,vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK33(X0),X1))))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK33(X0),X1))),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK33(X0),X1)))))) & ($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK33(X0),X1))) & ($true = vAPP(coindu1593790203_llist(X0),$o,X1,vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK33(X0),X1)))) | ($true != vAPP(coindu1593790203_llist(X0),$o,X1,X2)))),
% 0.15/0.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f911,f1089])).
% 0.15/0.49 thf(f1089,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0) > $o] : (? [X3 : coindu1593790203_llist(X0)] : (((($true != vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X3))) & ($true != vAPP(coindu1593790203_llist(X0),$o,X1,vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X3)))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X3)),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X3))))) & ($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X3)) & ($true = vAPP(coindu1593790203_llist(X0),$o,X1,X3))) => (((($true != vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK33(X0),X1)))) & ($true != vAPP(coindu1593790203_llist(X0),$o,X1,vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK33(X0),X1))))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK33(X0),X1))),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK33(X0),X1)))))) & ($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK33(X0),X1))) & ($true = vAPP(coindu1593790203_llist(X0),$o,X1,vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK33(X0),X1)))))),
% 0.15/0.49 introduced(choice_axiom,[])).
% 0.15/0.49 thf(f911,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0) > $o,X2 : coindu1593790203_llist(X0)] : ((vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X2) = $true) | ? [X3 : coindu1593790203_llist(X0)] : (((($true != vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X3))) & ($true != vAPP(coindu1593790203_llist(X0),$o,X1,vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X3)))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X3)),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X3))))) & ($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X3)) & ($true = vAPP(coindu1593790203_llist(X0),$o,X1,X3))) | ($true != vAPP(coindu1593790203_llist(X0),$o,X1,X2)))),
% 0.15/0.49 inference(flattening,[],[f910])).
% 0.15/0.49 thf(f910,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0) > $o,X2 : coindu1593790203_llist(X0)] : (((vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X2) = $true) | ? [X3 : coindu1593790203_llist(X0)] : ((((($true != vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X3))) & ($true != vAPP(coindu1593790203_llist(X0),$o,X1,vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X3)))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X3)),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X3))))) & ($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X3))) & ($true = vAPP(coindu1593790203_llist(X0),$o,X1,X3)))) | ($true != vAPP(coindu1593790203_llist(X0),$o,X1,X2)))),
% 0.15/0.49 inference(ennf_transformation,[],[f780])).
% 0.15/0.49 thf(f780,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0) > $o,X2 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,X1,X2)) => (! [X3 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,X1,X3)) => (($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X3)) => ((($true = vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X3))) | ($true = vAPP(coindu1593790203_llist(X0),$o,X1,vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X3)))) & ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X3)),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X3))))))) => (vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X2) = $true)))),
% 0.15/0.49 inference(flattening,[],[f521])).
% 0.15/0.49 thf(f521,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0) > $o,X2 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,X1,X2)) => (! [X3 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,X1,X3)) => (~($true = vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X3)) => ((($true = vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X3))) | ($true = vAPP(coindu1593790203_llist(X0),$o,X1,vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X3)))) & ~($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X3)),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X3))))))) => (vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X2) = $true)))),
% 0.15/0.49 inference(fool_elimination,[],[f520])).
% 0.15/0.49 thf(f520,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0) > $o,X2 : coindu1593790203_llist(X0)] : (vAPP(coindu1593790203_llist(X0),$o,X1,X2) => (! [X3 : coindu1593790203_llist(X0)] : (vAPP(coindu1593790203_llist(X0),$o,X1,X3) => (~vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X3) => ((vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X3)) | vAPP(coindu1593790203_llist(X0),$o,X1,vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X3))) & ~vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X3)),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X3)))))) => vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X2)))),
% 0.15/0.49 inference(rectify,[],[f200])).
% 0.15/0.49 thf(f200,axiom,(
% 0.15/0.49 ! [X0 : $tType,X12 : coindu1593790203_llist(X0) > $o,X6 : coindu1593790203_llist(X0)] : (vAPP(coindu1593790203_llist(X0),$o,X12,X6) => (! [X7 : coindu1593790203_llist(X0)] : (vAPP(coindu1593790203_llist(X0),$o,X12,X7) => (~vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X7) => ((vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X7)) | vAPP(coindu1593790203_llist(X0),$o,X12,vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X7))) & ~vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X7)),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X7)))))) => vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X6)))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_ldistinct__coinduct)).
% 0.15/0.49 thf(f2566,plain,(
% 0.15/0.49 spl95_54),
% 0.15/0.49 inference(avatar_split_clause,[],[f1376,f2564])).
% 0.15/0.49 thf(f2564,plain,(
% 0.15/0.49 spl95_54 <=> ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : coindu1593790203_llist(X0) > $o] : ((vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X2) = $true) | (coindu1598213697e_LNil(X0) != vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK32(X0),X1)) | ($true != vAPP(coindu1593790203_llist(X0),$o,X1,X2)))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_54])])).
% 0.15/0.49 thf(f1376,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : coindu1593790203_llist(X0) > $o] : ((vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X2) = $true) | (coindu1598213697e_LNil(X0) != vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK32(X0),X1)) | ($true != vAPP(coindu1593790203_llist(X0),$o,X1,X2))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f1088])).
% 0.15/0.49 thf(f1088,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0) > $o,X2 : coindu1593790203_llist(X0)] : ((vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X2) = $true) | (! [X4 : X0,X5 : coindu1593790203_llist(X0)] : ((($true != vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X5)) & ($true != vAPP(coindu1593790203_llist(X0),$o,X1,X5))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),X5))) | (vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X4),X5) != vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK32(X0),X1))) & (coindu1598213697e_LNil(X0) != vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK32(X0),X1)) & ($true = vAPP(coindu1593790203_llist(X0),$o,X1,vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK32(X0),X1)))) | ($true != vAPP(coindu1593790203_llist(X0),$o,X1,X2)))),
% 0.15/0.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f909,f1087])).
% 0.15/0.49 thf(f1087,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0) > $o] : (? [X3 : coindu1593790203_llist(X0)] : (! [X4 : X0,X5 : coindu1593790203_llist(X0)] : ((($true != vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X5)) & ($true != vAPP(coindu1593790203_llist(X0),$o,X1,X5))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),X5))) | (vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X4),X5) != X3)) & (coindu1598213697e_LNil(X0) != X3) & ($true = vAPP(coindu1593790203_llist(X0),$o,X1,X3))) => (! [X5 : coindu1593790203_llist(X0),X4 : X0] : ((($true != vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X5)) & ($true != vAPP(coindu1593790203_llist(X0),$o,X1,X5))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),X5))) | (vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X4),X5) != vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK32(X0),X1))) & (coindu1598213697e_LNil(X0) != vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK32(X0),X1)) & ($true = vAPP(coindu1593790203_llist(X0),$o,X1,vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK32(X0),X1)))))),
% 0.15/0.49 introduced(choice_axiom,[])).
% 0.15/0.49 thf(f909,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0) > $o,X2 : coindu1593790203_llist(X0)] : ((vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X2) = $true) | ? [X3 : coindu1593790203_llist(X0)] : (! [X4 : X0,X5 : coindu1593790203_llist(X0)] : ((($true != vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X5)) & ($true != vAPP(coindu1593790203_llist(X0),$o,X1,X5))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),X5))) | (vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X4),X5) != X3)) & (coindu1598213697e_LNil(X0) != X3) & ($true = vAPP(coindu1593790203_llist(X0),$o,X1,X3))) | ($true != vAPP(coindu1593790203_llist(X0),$o,X1,X2)))),
% 0.15/0.49 inference(flattening,[],[f908])).
% 0.15/0.49 thf(f908,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0) > $o,X2 : coindu1593790203_llist(X0)] : (((vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X2) = $true) | ? [X3 : coindu1593790203_llist(X0)] : ((! [X4 : X0,X5 : coindu1593790203_llist(X0)] : ((($true != vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X5)) & ($true != vAPP(coindu1593790203_llist(X0),$o,X1,X5))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),X5))) | (vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X4),X5) != X3)) & (coindu1598213697e_LNil(X0) != X3)) & ($true = vAPP(coindu1593790203_llist(X0),$o,X1,X3)))) | ($true != vAPP(coindu1593790203_llist(X0),$o,X1,X2)))),
% 0.15/0.49 inference(ennf_transformation,[],[f779])).
% 0.15/0.49 thf(f779,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0) > $o,X2 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,X1,X2)) => (! [X3 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,X1,X3)) => (? [X4 : X0,X5 : coindu1593790203_llist(X0)] : ((($true = vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X5)) | ($true = vAPP(coindu1593790203_llist(X0),$o,X1,X5))) & ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),X5))) & (vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X4),X5) = X3)) | (coindu1598213697e_LNil(X0) = X3))) => (vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X2) = $true)))),
% 0.15/0.49 inference(flattening,[],[f519])).
% 0.15/0.49 thf(f519,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0) > $o,X2 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,X1,X2)) => (! [X3 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,X1,X3)) => (? [X4 : X0,X5 : coindu1593790203_llist(X0)] : ((($true = vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X5)) | ($true = vAPP(coindu1593790203_llist(X0),$o,X1,X5))) & ~($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),X5))) & (vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X4),X5) = X3)) | (coindu1598213697e_LNil(X0) = X3))) => (vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X2) = $true)))),
% 0.15/0.49 inference(fool_elimination,[],[f518])).
% 0.15/0.49 thf(f518,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0) > $o,X2 : coindu1593790203_llist(X0)] : (vAPP(coindu1593790203_llist(X0),$o,X1,X2) => (! [X3 : coindu1593790203_llist(X0)] : (vAPP(coindu1593790203_llist(X0),$o,X1,X3) => (? [X4 : X0,X5 : coindu1593790203_llist(X0)] : ((vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X5) | vAPP(coindu1593790203_llist(X0),$o,X1,X5)) & ~vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),X5)) & (vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X4),X5) = X3)) | (coindu1598213697e_LNil(X0) = X3))) => vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X2)))),
% 0.15/0.49 inference(rectify,[],[f221])).
% 0.15/0.49 thf(f221,axiom,(
% 0.15/0.49 ! [X0 : $tType,X12 : coindu1593790203_llist(X0) > $o,X15 : coindu1593790203_llist(X0)] : (vAPP(coindu1593790203_llist(X0),$o,X12,X15) => (! [X22 : coindu1593790203_llist(X0)] : (vAPP(coindu1593790203_llist(X0),$o,X12,X22) => (? [X44 : X0,X46 : coindu1593790203_llist(X0)] : ((vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X46) | vAPP(coindu1593790203_llist(X0),$o,X12,X46)) & ~vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X44),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),X46)) & (vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X44),X46) = X22)) | (coindu1598213697e_LNil(X0) = X22))) => vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X15)))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_ldistinct_Ocoinduct)).
% 0.15/0.49 thf(f2562,plain,(
% 0.15/0.49 spl95_53 | ~spl95_7 | ~spl95_40),
% 0.15/0.49 inference(avatar_split_clause,[],[f2512,f2477,f2294,f2560])).
% 0.15/0.49 thf(f2560,plain,(
% 0.15/0.49 spl95_53 <=> ! [X0 : $tType] : ($true = vAPP(itself(sTfun(X0,$o)),$o,semilattice_inf(sTfun(X0,$o)),type2(sTfun(X0,$o))))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_53])])).
% 0.15/0.49 thf(f2294,plain,(
% 0.15/0.49 spl95_7 <=> (vAPP(itself($o),$o,semilattice_inf($o),type2($o)) = $true)),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_7])])).
% 0.15/0.49 thf(f2477,plain,(
% 0.15/0.49 spl95_40 <=> ! [X1 : $tType,X0 : $tType] : (($true = vAPP(itself(sTfun(X0,X1)),$o,semilattice_inf(sTfun(X0,X1)),type2(sTfun(X0,X1)))) | (vAPP(itself(X1),$o,semilattice_inf(X1),type2(X1)) != $true))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_40])])).
% 0.15/0.49 thf(f2512,plain,(
% 0.15/0.49 ( ! [X0 : $tType] : (($true = vAPP(itself(sTfun(X0,$o)),$o,semilattice_inf(sTfun(X0,$o)),type2(sTfun(X0,$o))))) ) | (~spl95_7 | ~spl95_40)),
% 0.15/0.49 inference(trivial_inequality_removal,[],[f2507])).
% 0.15/0.49 thf(f2507,plain,(
% 0.15/0.49 ( ! [X0 : $tType] : (($true != $true) | ($true = vAPP(itself(sTfun(X0,$o)),$o,semilattice_inf(sTfun(X0,$o)),type2(sTfun(X0,$o))))) ) | (~spl95_7 | ~spl95_40)),
% 0.15/0.49 inference(superposition,[],[f2478,f2296])).
% 0.15/0.49 thf(f2296,plain,(
% 0.15/0.49 (vAPP(itself($o),$o,semilattice_inf($o),type2($o)) = $true) | ~spl95_7),
% 0.15/0.49 inference(avatar_component_clause,[],[f2294])).
% 0.15/0.49 thf(f2478,plain,(
% 0.15/0.49 ( ! [X1 : $tType,X0 : $tType] : ((vAPP(itself(X1),$o,semilattice_inf(X1),type2(X1)) != $true) | ($true = vAPP(itself(sTfun(X0,X1)),$o,semilattice_inf(sTfun(X0,X1)),type2(sTfun(X0,X1))))) ) | ~spl95_40),
% 0.15/0.49 inference(avatar_component_clause,[],[f2477])).
% 0.15/0.49 thf(f2555,plain,(
% 0.15/0.49 spl95_52),
% 0.15/0.49 inference(avatar_split_clause,[],[f1299,f2553])).
% 0.15/0.49 thf(f2553,plain,(
% 0.15/0.49 spl95_52 <=> ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),sK25(X0),X1))) | (coindu1598213697e_LNil(X0) = X1) | ($true != vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X1)))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_52])])).
% 0.15/0.49 thf(f1299,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),sK25(X0),X1))) | (coindu1598213697e_LNil(X0) = X1) | ($true != vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X1))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f1075])).
% 0.15/0.49 thf(f1075,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : ((($true = vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),sK25(X0),X1))) & ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(coindu1593790203_llist(X0),X0,sK24(X0),X1)),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),sK25(X0),X1)))) & (vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),vAPP(coindu1593790203_llist(X0),X0,sK24(X0),X1)),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),sK25(X0),X1)) = X1)) | (coindu1598213697e_LNil(X0) = X1) | ($true != vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X1)))),
% 0.15/0.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25])],[f858,f1074])).
% 0.15/0.49 thf(f1074,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : (? [X2 : X0,X3 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X3)) & ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),X3))) & (vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X2),X3) = X1)) => (($true = vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),sK25(X0),X1))) & ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(coindu1593790203_llist(X0),X0,sK24(X0),X1)),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),sK25(X0),X1)))) & (vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),vAPP(coindu1593790203_llist(X0),X0,sK24(X0),X1)),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),sK25(X0),X1)) = X1)))),
% 0.15/0.49 introduced(choice_axiom,[])).
% 0.15/0.49 thf(f858,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : (? [X2 : X0,X3 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X3)) & ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),X3))) & (vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X2),X3) = X1)) | (coindu1598213697e_LNil(X0) = X1) | ($true != vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X1)))),
% 0.15/0.49 inference(flattening,[],[f857])).
% 0.15/0.49 thf(f857,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : ((? [X2 : X0,X3 : coindu1593790203_llist(X0)] : ((($true = vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X3)) & ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),X3)))) & (vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X2),X3) = X1)) | (coindu1598213697e_LNil(X0) = X1)) | ($true != vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X1)))),
% 0.15/0.49 inference(ennf_transformation,[],[f752])).
% 0.15/0.49 thf(f752,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X1)) => ((coindu1598213697e_LNil(X0) != X1) => ~! [X2 : X0,X3 : coindu1593790203_llist(X0)] : ((vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X2),X3) = X1) => (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),X3))) => ($true != vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X3))))))),
% 0.15/0.49 inference(flattening,[],[f413])).
% 0.15/0.49 thf(f413,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X1)) => ((coindu1598213697e_LNil(X0) != X1) => ~! [X2 : X0,X3 : coindu1593790203_llist(X0)] : ((vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X2),X3) = X1) => (~($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),X3))) => ~($true = vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X3))))))),
% 0.15/0.49 inference(fool_elimination,[],[f412])).
% 0.15/0.49 thf(f412,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : (vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X1) => ((coindu1598213697e_LNil(X0) != X1) => ~! [X2 : X0,X3 : coindu1593790203_llist(X0)] : ((vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X2),X3) = X1) => (~vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),X3)) => ~vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X3)))))),
% 0.15/0.49 inference(rectify,[],[f219])).
% 0.15/0.49 thf(f219,axiom,(
% 0.15/0.49 ! [X0 : $tType,X2 : coindu1593790203_llist(X0)] : (vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X2) => ((coindu1598213697e_LNil(X0) != X2) => ~! [X22 : X0,X7 : coindu1593790203_llist(X0)] : ((vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X22),X7) = X2) => (~vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X22),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),X7)) => ~vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X7)))))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_ldistinct_Ocases)).
% 0.15/0.49 thf(f2550,plain,(
% 0.15/0.49 spl95_51),
% 0.15/0.49 inference(avatar_split_clause,[],[f2044,f2548])).
% 0.15/0.49 thf(f2548,plain,(
% 0.15/0.49 spl95_51 <=> ! [X0 : $tType,X2 : X0,X1 : coindu1593790203_llist(X0)] : ((vAPP(coindu1593790203_llist(X0),X0,coindu2000965700_llast(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X2),X1)) = X2) | (coindu1598213697e_LNil(X0) != X1))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_51])])).
% 0.15/0.49 thf(f2044,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : X0,X1 : coindu1593790203_llist(X0)] : ((vAPP(coindu1593790203_llist(X0),X0,coindu2000965700_llast(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X2),X1)) = X2) | (coindu1598213697e_LNil(X0) != X1)) )),
% 0.15/0.49 inference(equality_proxy_clausification,[],[f1646])).
% 0.15/0.49 thf(f1646,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : X0,X1 : coindu1593790203_llist(X0)] : ((vAPP(coindu1593790203_llist(X0),X0,coindu2000965700_llast(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X2),X1)) = X2) | ($true != vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vEQ(coindu1593790203_llist(X0)),coindu1598213697e_LNil(X0)),X1))) )),
% 0.15/0.49 inference(definition_unfolding,[],[f1343,f1215])).
% 0.15/0.49 thf(f1343,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : X0,X1 : coindu1593790203_llist(X0)] : ((vAPP(coindu1593790203_llist(X0),X0,coindu2000965700_llast(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X2),X1)) = X2) | ($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f878])).
% 0.15/0.49 thf(f878,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0),X2 : X0] : (((vAPP(coindu1593790203_llist(X0),X0,coindu2000965700_llast(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X2),X1)) = vAPP(coindu1593790203_llist(X0),X0,coindu2000965700_llast(X0),X1)) | ($true = vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1))) & ((vAPP(coindu1593790203_llist(X0),X0,coindu2000965700_llast(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X2),X1)) = X2) | ($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1))))),
% 0.15/0.49 inference(ennf_transformation,[],[f763])).
% 0.15/0.49 thf(f763,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0),X2 : X0] : ((($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1)) => (vAPP(coindu1593790203_llist(X0),X0,coindu2000965700_llast(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X2),X1)) = vAPP(coindu1593790203_llist(X0),X0,coindu2000965700_llast(X0),X1))) & (($true = vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1)) => (vAPP(coindu1593790203_llist(X0),X0,coindu2000965700_llast(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X2),X1)) = X2)))),
% 0.15/0.49 inference(flattening,[],[f481])).
% 0.15/0.49 thf(f481,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0),X2 : X0] : ((~($true = vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1)) => (vAPP(coindu1593790203_llist(X0),X0,coindu2000965700_llast(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X2),X1)) = vAPP(coindu1593790203_llist(X0),X0,coindu2000965700_llast(X0),X1))) & (($true = vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1)) => (vAPP(coindu1593790203_llist(X0),X0,coindu2000965700_llast(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X2),X1)) = X2)))),
% 0.15/0.49 inference(fool_elimination,[],[f480])).
% 0.15/0.49 thf(f480,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0),X2 : X0] : ((~vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1) => (vAPP(coindu1593790203_llist(X0),X0,coindu2000965700_llast(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X2),X1)) = vAPP(coindu1593790203_llist(X0),X0,coindu2000965700_llast(X0),X1))) & (vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1) => (vAPP(coindu1593790203_llist(X0),X0,coindu2000965700_llast(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X2),X1)) = X2)))),
% 0.15/0.49 inference(rectify,[],[f198])).
% 0.15/0.49 thf(f198,axiom,(
% 0.15/0.49 ! [X0 : $tType,X6 : coindu1593790203_llist(X0),X15 : X0] : ((~vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X6) => (vAPP(coindu1593790203_llist(X0),X0,coindu2000965700_llast(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X15),X6)) = vAPP(coindu1593790203_llist(X0),X0,coindu2000965700_llast(X0),X6))) & (vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X6) => (vAPP(coindu1593790203_llist(X0),X0,coindu2000965700_llast(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X15),X6)) = X15)))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_llast__LCons)).
% 0.15/0.49 thf(f2546,plain,(
% 0.15/0.49 spl95_50),
% 0.15/0.49 inference(avatar_split_clause,[],[f1887,f2544])).
% 0.15/0.49 thf(f2544,plain,(
% 0.15/0.49 spl95_50 <=> ! [X1 : $tType,X0 : X1 > coindu1593790203_llist(X1) > $o] : ((coindu1598213697e_LNil(X1) != vAPP(sTfun(X1,sTfun(coindu1593790203_llist(X1),$o)),coindu1593790203_llist(X1),sK70(X1),X0)) | ($true != vAPP(sTfun(X1,sTfun(coindu1593790203_llist(X1),$o)),$o,sP9(X1),X0)))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_50])])).
% 0.15/0.49 thf(f1887,plain,(
% 0.15/0.49 ( ! [X1 : $tType,X0 : X1 > coindu1593790203_llist(X1) > $o] : ((coindu1598213697e_LNil(X1) != vAPP(sTfun(X1,sTfun(coindu1593790203_llist(X1),$o)),coindu1593790203_llist(X1),sK70(X1),X0)) | ($true != vAPP(sTfun(X1,sTfun(coindu1593790203_llist(X1),$o)),$o,sP9(X1),X0))) )),
% 0.15/0.49 inference(equality_proxy_clausification,[],[f1744])).
% 0.15/0.49 thf(f1744,plain,(
% 0.15/0.49 ( ! [X1 : $tType,X0 : X1 > coindu1593790203_llist(X1) > $o] : (($true != vAPP(coindu1593790203_llist(X1),$o,vAPP(coindu1593790203_llist(X1),sTfun(coindu1593790203_llist(X1),$o),vEQ(coindu1593790203_llist(X1)),coindu1598213697e_LNil(X1)),vAPP(sTfun(X1,sTfun(coindu1593790203_llist(X1),$o)),coindu1593790203_llist(X1),sK70(X1),X0))) | ($true != vAPP(sTfun(X1,sTfun(coindu1593790203_llist(X1),$o)),$o,sP9(X1),X0))) )),
% 0.15/0.49 inference(definition_unfolding,[],[f1511,f1215])).
% 0.15/0.49 thf(f1511,plain,(
% 0.15/0.49 ( ! [X1 : $tType,X0 : X1 > coindu1593790203_llist(X1) > $o] : (($true != vAPP(coindu1593790203_llist(X1),$o,coindu335574135_lnull(X1),vAPP(sTfun(X1,sTfun(coindu1593790203_llist(X1),$o)),coindu1593790203_llist(X1),sK70(X1),X0))) | ($true != vAPP(sTfun(X1,sTfun(coindu1593790203_llist(X1),$o)),$o,sP9(X1),X0))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f1156])).
% 0.15/0.49 thf(f1156,plain,(
% 0.15/0.49 ! [X0 : X1 > coindu1593790203_llist(X1) > $o,X1 : $tType] : ((($true != vAPP(coindu1593790203_llist(X1),$o,vAPP(X1,sTfun(coindu1593790203_llist(X1),$o),X0,vAPP(sTfun(X1,sTfun(coindu1593790203_llist(X1),$o)),X1,sK71(X1),X0)),vAPP(sTfun(X1,sTfun(coindu1593790203_llist(X1),$o)),coindu1593790203_llist(X1),sK70(X1),X0))) & ($true = vAPP(coindu1593790203_llist(X1),$o,vAPP(X1,sTfun(coindu1593790203_llist(X1),$o),X0,vAPP(sTfun(X1,sTfun(coindu1593790203_llist(X1),$o)),X1,sK71(X1),X0)),vAPP(coindu1593790203_llist(X1),coindu1593790203_llist(X1),coindu1047225960le_ltl(X1),vAPP(sTfun(X1,sTfun(coindu1593790203_llist(X1),$o)),coindu1593790203_llist(X1),sK70(X1),X0)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(sTfun(X1,sTfun(coindu1593790203_llist(X1),$o)),X1,sK71(X1),X0)),vAPP(coindu1593790203_llist(X1),set(X1),coindu1112613586e_lset(X1),vAPP(coindu1593790203_llist(X1),coindu1593790203_llist(X1),coindu1047225960le_ltl(X1),vAPP(sTfun(X1,sTfun(coindu1593790203_llist(X1),$o)),coindu1593790203_llist(X1),sK70(X1),X0))))) & ($true != vAPP(coindu1593790203_llist(X1),$o,coindu335574135_lnull(X1),vAPP(sTfun(X1,sTfun(coindu1593790203_llist(X1),$o)),coindu1593790203_llist(X1),sK70(X1),X0)))) | ($true != vAPP(sTfun(X1,sTfun(coindu1593790203_llist(X1),$o)),$o,sP9(X1),X0)))),
% 0.15/0.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK70,sK71])],[f1154,f1155])).
% 0.15/0.49 thf(f1155,plain,(
% 0.15/0.49 ! [X1 : $tType,X0 : X1 > coindu1593790203_llist(X1) > $o] : (? [X2 : coindu1593790203_llist(X1),X3 : X1] : (($true != vAPP(coindu1593790203_llist(X1),$o,vAPP(X1,sTfun(coindu1593790203_llist(X1),$o),X0,X3),X2)) & ($true = vAPP(coindu1593790203_llist(X1),$o,vAPP(X1,sTfun(coindu1593790203_llist(X1),$o),X0,X3),vAPP(coindu1593790203_llist(X1),coindu1593790203_llist(X1),coindu1047225960le_ltl(X1),X2))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(coindu1593790203_llist(X1),set(X1),coindu1112613586e_lset(X1),vAPP(coindu1593790203_llist(X1),coindu1593790203_llist(X1),coindu1047225960le_ltl(X1),X2)))) & ($true != vAPP(coindu1593790203_llist(X1),$o,coindu335574135_lnull(X1),X2))) => (($true != vAPP(coindu1593790203_llist(X1),$o,vAPP(X1,sTfun(coindu1593790203_llist(X1),$o),X0,vAPP(sTfun(X1,sTfun(coindu1593790203_llist(X1),$o)),X1,sK71(X1),X0)),vAPP(sTfun(X1,sTfun(coindu1593790203_llist(X1),$o)),coindu1593790203_llist(X1),sK70(X1),X0))) & ($true = vAPP(coindu1593790203_llist(X1),$o,vAPP(X1,sTfun(coindu1593790203_llist(X1),$o),X0,vAPP(sTfun(X1,sTfun(coindu1593790203_llist(X1),$o)),X1,sK71(X1),X0)),vAPP(coindu1593790203_llist(X1),coindu1593790203_llist(X1),coindu1047225960le_ltl(X1),vAPP(sTfun(X1,sTfun(coindu1593790203_llist(X1),$o)),coindu1593790203_llist(X1),sK70(X1),X0)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(sTfun(X1,sTfun(coindu1593790203_llist(X1),$o)),X1,sK71(X1),X0)),vAPP(coindu1593790203_llist(X1),set(X1),coindu1112613586e_lset(X1),vAPP(coindu1593790203_llist(X1),coindu1593790203_llist(X1),coindu1047225960le_ltl(X1),vAPP(sTfun(X1,sTfun(coindu1593790203_llist(X1),$o)),coindu1593790203_llist(X1),sK70(X1),X0))))) & ($true != vAPP(coindu1593790203_llist(X1),$o,coindu335574135_lnull(X1),vAPP(sTfun(X1,sTfun(coindu1593790203_llist(X1),$o)),coindu1593790203_llist(X1),sK70(X1),X0)))))),
% 0.15/0.49 introduced(choice_axiom,[])).
% 0.15/0.49 thf(f1154,plain,(
% 0.15/0.49 ! [X0 : X1 > coindu1593790203_llist(X1) > $o,X1 : $tType] : (? [X2 : coindu1593790203_llist(X1),X3 : X1] : (($true != vAPP(coindu1593790203_llist(X1),$o,vAPP(X1,sTfun(coindu1593790203_llist(X1),$o),X0,X3),X2)) & ($true = vAPP(coindu1593790203_llist(X1),$o,vAPP(X1,sTfun(coindu1593790203_llist(X1),$o),X0,X3),vAPP(coindu1593790203_llist(X1),coindu1593790203_llist(X1),coindu1047225960le_ltl(X1),X2))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(coindu1593790203_llist(X1),set(X1),coindu1112613586e_lset(X1),vAPP(coindu1593790203_llist(X1),coindu1593790203_llist(X1),coindu1047225960le_ltl(X1),X2)))) & ($true != vAPP(coindu1593790203_llist(X1),$o,coindu335574135_lnull(X1),X2))) | ($true != vAPP(sTfun(X1,sTfun(coindu1593790203_llist(X1),$o)),$o,sP9(X1),X0)))),
% 0.15/0.49 inference(rectify,[],[f1153])).
% 0.15/0.49 thf(f1153,plain,(
% 0.15/0.49 ! [X3 : X0 > coindu1593790203_llist(X0) > $o,X0 : $tType] : (? [X5 : coindu1593790203_llist(X0),X6 : X0] : (($true != vAPP(coindu1593790203_llist(X0),$o,vAPP(X0,sTfun(coindu1593790203_llist(X0),$o),X3,X6),X5)) & ($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(X0,sTfun(coindu1593790203_llist(X0),$o),X3,X6),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X5))) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X6),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X5)))) & (vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X5) != $true)) | ($true != vAPP(sTfun(X0,sTfun(coindu1593790203_llist(X0),$o)),$o,sP9(X0),X3)))),
% 0.15/0.49 inference(nnf_transformation,[],[f1046])).
% 0.15/0.49 thf(f1046,plain,(
% 0.15/0.49 ! [X3 : X0 > coindu1593790203_llist(X0) > $o,X0 : $tType] : (? [X5 : coindu1593790203_llist(X0),X6 : X0] : (($true != vAPP(coindu1593790203_llist(X0),$o,vAPP(X0,sTfun(coindu1593790203_llist(X0),$o),X3,X6),X5)) & ($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(X0,sTfun(coindu1593790203_llist(X0),$o),X3,X6),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X5))) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X6),vAPP(coindu1593790203_llist(X0),set(X0),coindu1112613586e_lset(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X5)))) & (vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X5) != $true)) | ~($true = vAPP(sTfun(X0,sTfun(coindu1593790203_llist(X0),$o)),$o,sP9(X0),X3)))),
% 0.15/0.49 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 0.15/0.49 thf(f2532,plain,(
% 0.15/0.49 spl95_49),
% 0.15/0.49 inference(avatar_split_clause,[],[f1392,f2530])).
% 0.15/0.49 thf(f2530,plain,(
% 0.15/0.49 spl95_49 <=> ! [X1 : $tType,X0 : coindu1593790203_llist(X1) > $o] : (($true != vAPP(coindu1593790203_llist(X1),$o,X0,vAPP(sTfun(coindu1593790203_llist(X1),$o),coindu1593790203_llist(X1),sK36(X1),X0))) | ($true != vAPP(sTfun(coindu1593790203_llist(X1),$o),$o,sP3(X1),X0)))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_49])])).
% 0.15/0.49 thf(f1392,plain,(
% 0.15/0.49 ( ! [X1 : $tType,X0 : coindu1593790203_llist(X1) > $o] : (($true != vAPP(coindu1593790203_llist(X1),$o,X0,vAPP(sTfun(coindu1593790203_llist(X1),$o),coindu1593790203_llist(X1),sK36(X1),X0))) | ($true != vAPP(sTfun(coindu1593790203_llist(X1),$o),$o,sP3(X1),X0))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f1099])).
% 0.15/0.49 thf(f1099,plain,(
% 0.15/0.49 ! [X0 : coindu1593790203_llist(X1) > $o,X1 : $tType] : ((($true != vAPP(coindu1593790203_llist(X1),$o,X0,vAPP(sTfun(coindu1593790203_llist(X1),$o),coindu1593790203_llist(X1),sK36(X1),X0))) & ($true = vAPP(coindu1593790203_llist(X1),$o,X0,vAPP(coindu1593790203_llist(X1),coindu1593790203_llist(X1),coindu1047225960le_ltl(X1),vAPP(sTfun(coindu1593790203_llist(X1),$o),coindu1593790203_llist(X1),sK36(X1),X0)))) & ($true != vAPP(coindu1593790203_llist(X1),$o,coindu335574135_lnull(X1),vAPP(sTfun(coindu1593790203_llist(X1),$o),coindu1593790203_llist(X1),sK36(X1),X0))) & ($true = vAPP(coindu1593790203_llist(X1),$o,coindu1213758845finite(X1),vAPP(sTfun(coindu1593790203_llist(X1),$o),coindu1593790203_llist(X1),sK36(X1),X0)))) | ($true != vAPP(sTfun(coindu1593790203_llist(X1),$o),$o,sP3(X1),X0)))),
% 0.15/0.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK36])],[f1097,f1098])).
% 0.15/0.49 thf(f1098,plain,(
% 0.15/0.49 ! [X1 : $tType,X0 : coindu1593790203_llist(X1) > $o] : (? [X2 : coindu1593790203_llist(X1)] : (($true != vAPP(coindu1593790203_llist(X1),$o,X0,X2)) & ($true = vAPP(coindu1593790203_llist(X1),$o,X0,vAPP(coindu1593790203_llist(X1),coindu1593790203_llist(X1),coindu1047225960le_ltl(X1),X2))) & ($true != vAPP(coindu1593790203_llist(X1),$o,coindu335574135_lnull(X1),X2)) & ($true = vAPP(coindu1593790203_llist(X1),$o,coindu1213758845finite(X1),X2))) => (($true != vAPP(coindu1593790203_llist(X1),$o,X0,vAPP(sTfun(coindu1593790203_llist(X1),$o),coindu1593790203_llist(X1),sK36(X1),X0))) & ($true = vAPP(coindu1593790203_llist(X1),$o,X0,vAPP(coindu1593790203_llist(X1),coindu1593790203_llist(X1),coindu1047225960le_ltl(X1),vAPP(sTfun(coindu1593790203_llist(X1),$o),coindu1593790203_llist(X1),sK36(X1),X0)))) & ($true != vAPP(coindu1593790203_llist(X1),$o,coindu335574135_lnull(X1),vAPP(sTfun(coindu1593790203_llist(X1),$o),coindu1593790203_llist(X1),sK36(X1),X0))) & ($true = vAPP(coindu1593790203_llist(X1),$o,coindu1213758845finite(X1),vAPP(sTfun(coindu1593790203_llist(X1),$o),coindu1593790203_llist(X1),sK36(X1),X0)))))),
% 0.15/0.49 introduced(choice_axiom,[])).
% 0.15/0.49 thf(f1097,plain,(
% 0.15/0.49 ! [X0 : coindu1593790203_llist(X1) > $o,X1 : $tType] : (? [X2 : coindu1593790203_llist(X1)] : (($true != vAPP(coindu1593790203_llist(X1),$o,X0,X2)) & ($true = vAPP(coindu1593790203_llist(X1),$o,X0,vAPP(coindu1593790203_llist(X1),coindu1593790203_llist(X1),coindu1047225960le_ltl(X1),X2))) & ($true != vAPP(coindu1593790203_llist(X1),$o,coindu335574135_lnull(X1),X2)) & ($true = vAPP(coindu1593790203_llist(X1),$o,coindu1213758845finite(X1),X2))) | ($true != vAPP(sTfun(coindu1593790203_llist(X1),$o),$o,sP3(X1),X0)))),
% 0.15/0.49 inference(rectify,[],[f1096])).
% 0.15/0.49 thf(f1096,plain,(
% 0.15/0.49 ! [X2 : coindu1593790203_llist(X0) > $o,X0 : $tType] : (? [X4 : coindu1593790203_llist(X0)] : (($true != vAPP(coindu1593790203_llist(X0),$o,X2,X4)) & ($true = vAPP(coindu1593790203_llist(X0),$o,X2,vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X4))) & ($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X4)) & ($true = vAPP(coindu1593790203_llist(X0),$o,coindu1213758845finite(X0),X4))) | ($true != vAPP(sTfun(coindu1593790203_llist(X0),$o),$o,sP3(X0),X2)))),
% 0.15/0.49 inference(nnf_transformation,[],[f1034])).
% 0.15/0.49 thf(f1034,plain,(
% 0.15/0.49 ! [X2 : coindu1593790203_llist(X0) > $o,X0 : $tType] : (? [X4 : coindu1593790203_llist(X0)] : (($true != vAPP(coindu1593790203_llist(X0),$o,X2,X4)) & ($true = vAPP(coindu1593790203_llist(X0),$o,X2,vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X4))) & ($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X4)) & ($true = vAPP(coindu1593790203_llist(X0),$o,coindu1213758845finite(X0),X4))) | ~($true = vAPP(sTfun(coindu1593790203_llist(X0),$o),$o,sP3(X0),X2)))),
% 0.15/0.49 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 0.15/0.49 thf(f2528,plain,(
% 0.15/0.49 spl95_48),
% 0.15/0.49 inference(avatar_split_clause,[],[f1384,f2526])).
% 0.15/0.49 thf(f2526,plain,(
% 0.15/0.49 spl95_48 <=> ! [X0 : $tType,X1 : coindu1593790203_llist(X0) > $o] : (($true = vAPP(coindu1593790203_llist(X0),$o,X1,vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK35(X0),X1))) | ($true != vAPP(sTfun(coindu1593790203_llist(X0),$o),$o,sP2(X0),X1)))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_48])])).
% 0.15/0.49 thf(f1384,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X1 : coindu1593790203_llist(X0) > $o] : (($true = vAPP(coindu1593790203_llist(X0),$o,X1,vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK35(X0),X1))) | ($true != vAPP(sTfun(coindu1593790203_llist(X0),$o),$o,sP2(X0),X1))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f1094])).
% 0.15/0.49 thf(f1094,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0) > $o] : ((($true != vAPP(coindu1593790203_llist(X0),$o,X1,vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),vAPP(sTfun(coindu1593790203_llist(X0),$o),X0,sK34(X0),X1)),vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK35(X0),X1)))) & ($true = vAPP(coindu1593790203_llist(X0),$o,X1,vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK35(X0),X1))) & ($true = vAPP(coindu1593790203_llist(X0),$o,coindu1213758845finite(X0),vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK35(X0),X1)))) | ($true != vAPP(sTfun(coindu1593790203_llist(X0),$o),$o,sP2(X0),X1)))),
% 0.15/0.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK34,sK35])],[f1092,f1093])).
% 0.15/0.49 thf(f1093,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0) > $o] : (? [X2 : X0,X3 : coindu1593790203_llist(X0)] : (($true != vAPP(coindu1593790203_llist(X0),$o,X1,vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X2),X3))) & ($true = vAPP(coindu1593790203_llist(X0),$o,X1,X3)) & ($true = vAPP(coindu1593790203_llist(X0),$o,coindu1213758845finite(X0),X3))) => (($true != vAPP(coindu1593790203_llist(X0),$o,X1,vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),vAPP(sTfun(coindu1593790203_llist(X0),$o),X0,sK34(X0),X1)),vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK35(X0),X1)))) & ($true = vAPP(coindu1593790203_llist(X0),$o,X1,vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK35(X0),X1))) & ($true = vAPP(coindu1593790203_llist(X0),$o,coindu1213758845finite(X0),vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK35(X0),X1)))))),
% 0.15/0.49 introduced(choice_axiom,[])).
% 0.15/0.49 thf(f1092,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0) > $o] : (? [X2 : X0,X3 : coindu1593790203_llist(X0)] : (($true != vAPP(coindu1593790203_llist(X0),$o,X1,vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X2),X3))) & ($true = vAPP(coindu1593790203_llist(X0),$o,X1,X3)) & ($true = vAPP(coindu1593790203_llist(X0),$o,coindu1213758845finite(X0),X3))) | ($true != vAPP(sTfun(coindu1593790203_llist(X0),$o),$o,sP2(X0),X1)))),
% 0.15/0.49 inference(rectify,[],[f1091])).
% 0.15/0.49 thf(f1091,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0) > $o] : (? [X3 : X0,X4 : coindu1593790203_llist(X0)] : (($true != vAPP(coindu1593790203_llist(X0),$o,X1,vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X3),X4))) & ($true = vAPP(coindu1593790203_llist(X0),$o,X1,X4)) & ($true = vAPP(coindu1593790203_llist(X0),$o,coindu1213758845finite(X0),X4))) | ($true != vAPP(sTfun(coindu1593790203_llist(X0),$o),$o,sP2(X0),X1)))),
% 0.15/0.49 inference(nnf_transformation,[],[f1032])).
% 0.15/0.49 thf(f1032,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0) > $o] : (? [X3 : X0,X4 : coindu1593790203_llist(X0)] : (($true != vAPP(coindu1593790203_llist(X0),$o,X1,vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X3),X4))) & ($true = vAPP(coindu1593790203_llist(X0),$o,X1,X4)) & ($true = vAPP(coindu1593790203_llist(X0),$o,coindu1213758845finite(X0),X4))) | ~($true = vAPP(sTfun(coindu1593790203_llist(X0),$o),$o,sP2(X0),X1)))),
% 0.15/0.49 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 0.15/0.49 thf(f2524,plain,(
% 0.15/0.49 spl95_47 | ~spl95_6 | ~spl95_39),
% 0.15/0.49 inference(avatar_split_clause,[],[f2506,f2473,f2289,f2522])).
% 0.15/0.49 thf(f2522,plain,(
% 0.15/0.49 spl95_47 <=> ! [X0 : $tType] : ($true = vAPP(itself(sTfun(X0,$o)),$o,lattice(sTfun(X0,$o)),type2(sTfun(X0,$o))))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_47])])).
% 0.15/0.49 thf(f2289,plain,(
% 0.15/0.49 spl95_6 <=> (vAPP(itself($o),$o,lattice($o),type2($o)) = $true)),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_6])])).
% 0.15/0.49 thf(f2473,plain,(
% 0.15/0.49 spl95_39 <=> ! [X1 : $tType,X0 : $tType] : (($true = vAPP(itself(sTfun(X0,X1)),$o,lattice(sTfun(X0,X1)),type2(sTfun(X0,X1)))) | ($true != vAPP(itself(X1),$o,lattice(X1),type2(X1))))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_39])])).
% 0.15/0.49 thf(f2506,plain,(
% 0.15/0.49 ( ! [X0 : $tType] : (($true = vAPP(itself(sTfun(X0,$o)),$o,lattice(sTfun(X0,$o)),type2(sTfun(X0,$o))))) ) | (~spl95_6 | ~spl95_39)),
% 0.15/0.49 inference(trivial_inequality_removal,[],[f2501])).
% 0.15/0.49 thf(f2501,plain,(
% 0.15/0.49 ( ! [X0 : $tType] : (($true != $true) | ($true = vAPP(itself(sTfun(X0,$o)),$o,lattice(sTfun(X0,$o)),type2(sTfun(X0,$o))))) ) | (~spl95_6 | ~spl95_39)),
% 0.15/0.49 inference(superposition,[],[f2474,f2291])).
% 0.15/0.49 thf(f2291,plain,(
% 0.15/0.49 (vAPP(itself($o),$o,lattice($o),type2($o)) = $true) | ~spl95_6),
% 0.15/0.49 inference(avatar_component_clause,[],[f2289])).
% 0.15/0.49 thf(f2474,plain,(
% 0.15/0.49 ( ! [X1 : $tType,X0 : $tType] : (($true != vAPP(itself(X1),$o,lattice(X1),type2(X1))) | ($true = vAPP(itself(sTfun(X0,X1)),$o,lattice(sTfun(X0,X1)),type2(sTfun(X0,X1))))) ) | ~spl95_39),
% 0.15/0.49 inference(avatar_component_clause,[],[f2473])).
% 0.15/0.49 thf(f2516,plain,(
% 0.15/0.49 spl95_46),
% 0.15/0.49 inference(avatar_split_clause,[],[f1993,f2514])).
% 0.15/0.49 thf(f2514,plain,(
% 0.15/0.49 spl95_46 <=> ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : coindu1593790203_llist(X0)] : ((coindu1598213697e_LNil(X0) != X2) | (coindu1598213697e_LNil(X0) = X1) | ($true != vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1571841457prefix(X0),X1),X2)))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_46])])).
% 0.15/0.49 thf(f1993,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : coindu1593790203_llist(X0)] : ((coindu1598213697e_LNil(X0) != X2) | (coindu1598213697e_LNil(X0) = X1) | ($true != vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1571841457prefix(X0),X1),X2))) )),
% 0.15/0.49 inference(equality_proxy_clausification,[],[f1992])).
% 0.15/0.49 thf(f1992,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : coindu1593790203_llist(X0)] : ((coindu1598213697e_LNil(X0) != X2) | ($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vEQ(coindu1593790203_llist(X0)),coindu1598213697e_LNil(X0)),X1)) | ($true != vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1571841457prefix(X0),X1),X2))) )),
% 0.15/0.49 inference(equality_proxy_clausification,[],[f1685])).
% 0.15/0.49 thf(f1685,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : coindu1593790203_llist(X0)] : (($true != vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vEQ(coindu1593790203_llist(X0)),coindu1598213697e_LNil(X0)),X2)) | ($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vEQ(coindu1593790203_llist(X0)),coindu1598213697e_LNil(X0)),X1)) | ($true != vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1571841457prefix(X0),X1),X2))) )),
% 0.15/0.49 inference(definition_unfolding,[],[f1410,f1215,f1215,f1201])).
% 0.15/0.49 thf(f1201,plain,(
% 0.15/0.49 ( ! [X0 : $tType] : ((coindu1696667936prefix(X0) = coindu1571841457prefix(X0))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f181])).
% 0.15/0.49 thf(f181,axiom,(
% 0.15/0.49 ! [X0 : $tType] : (coindu1696667936prefix(X0) = coindu1571841457prefix(X0))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__def)).
% 0.15/0.49 thf(f1410,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : coindu1593790203_llist(X0)] : ((vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2) != $true) | ($true = vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1)) | ($true != vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1696667936prefix(X0),X1),X2))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f933])).
% 0.15/0.49 thf(f933,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0),X2 : coindu1593790203_llist(X0)] : ((vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2) != $true) | ($true = vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1)) | ($true != vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1696667936prefix(X0),X1),X2)))),
% 0.15/0.49 inference(flattening,[],[f932])).
% 0.15/0.49 thf(f932,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0),X2 : coindu1593790203_llist(X0)] : (((vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2) != $true) | ($true = vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1))) | ($true != vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1696667936prefix(X0),X1),X2)))),
% 0.15/0.49 inference(ennf_transformation,[],[f784])).
% 0.15/0.49 thf(f784,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0),X2 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1696667936prefix(X0),X1),X2)) => (($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1)) => (vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2) != $true)))),
% 0.15/0.49 inference(flattening,[],[f547])).
% 0.15/0.49 thf(f547,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0),X2 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1696667936prefix(X0),X1),X2)) => (~($true = vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1)) => ~(vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2) = $true)))),
% 0.15/0.49 inference(fool_elimination,[],[f546])).
% 0.15/0.49 thf(f546,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0),X2 : coindu1593790203_llist(X0)] : (vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1696667936prefix(X0),X1),X2) => (~vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1) => ~vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2)))),
% 0.15/0.49 inference(rectify,[],[f36])).
% 0.15/0.49 thf(f36,axiom,(
% 0.15/0.49 ! [X0 : $tType,X6 : coindu1593790203_llist(X0),X18 : coindu1593790203_llist(X0)] : (vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1696667936prefix(X0),X6),X18) => (~vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X6) => ~vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X18)))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_lprefix__not__lnullD)).
% 0.15/0.49 thf(f2500,plain,(
% 0.15/0.49 spl95_45),
% 0.15/0.49 inference(avatar_split_clause,[],[f2145,f2498])).
% 0.15/0.49 thf(f2498,plain,(
% 0.15/0.49 spl95_45 <=> ! [X0 : $tType,X1 : set(coindu1593790203_llist(X0))] : ((coindu1598213697e_LNil(X0) = vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),coindu526335360e_lSup(X0),X1)) | (coindu1598213697e_LNil(X0) != vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),sK20(X0),X1)))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_45])])).
% 0.15/0.49 thf(f2145,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X1 : set(coindu1593790203_llist(X0))] : ((coindu1598213697e_LNil(X0) = vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),coindu526335360e_lSup(X0),X1)) | (coindu1598213697e_LNil(X0) != vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),sK20(X0),X1))) )),
% 0.15/0.49 inference(equality_proxy_clausification,[],[f1615])).
% 0.15/0.49 thf(f1615,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X1 : set(coindu1593790203_llist(X0))] : ((coindu1598213697e_LNil(X0) = vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),coindu526335360e_lSup(X0),X1)) | ($true != vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vEQ(coindu1593790203_llist(X0)),coindu1598213697e_LNil(X0)),vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),sK20(X0),X1)))) )),
% 0.15/0.49 inference(definition_unfolding,[],[f1282,f1215])).
% 0.15/0.49 thf(f1282,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X1 : set(coindu1593790203_llist(X0))] : ((coindu1598213697e_LNil(X0) = vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),coindu526335360e_lSup(X0),X1)) | ($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),sK20(X0),X1)))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f1062])).
% 0.15/0.49 thf(f1062,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : set(coindu1593790203_llist(X0))] : ((coindu1598213697e_LNil(X0) = vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),coindu526335360e_lSup(X0),X1)) | (($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),sK20(X0),X1))) & ($true = vAPP(set(coindu1593790203_llist(X0)),$o,vAPP(coindu1593790203_llist(X0),sTfun(set(coindu1593790203_llist(X0)),$o),member(coindu1593790203_llist(X0)),vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),sK20(X0),X1)),X1))))),
% 0.15/0.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f851,f1061])).
% 0.15/0.49 thf(f1061,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : set(coindu1593790203_llist(X0))] : (? [X2 : coindu1593790203_llist(X0)] : ((vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2) != $true) & ($true = vAPP(set(coindu1593790203_llist(X0)),$o,vAPP(coindu1593790203_llist(X0),sTfun(set(coindu1593790203_llist(X0)),$o),member(coindu1593790203_llist(X0)),X2),X1))) => (($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),sK20(X0),X1))) & ($true = vAPP(set(coindu1593790203_llist(X0)),$o,vAPP(coindu1593790203_llist(X0),sTfun(set(coindu1593790203_llist(X0)),$o),member(coindu1593790203_llist(X0)),vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),sK20(X0),X1)),X1))))),
% 0.15/0.49 introduced(choice_axiom,[])).
% 0.15/0.49 thf(f851,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : set(coindu1593790203_llist(X0))] : ((coindu1598213697e_LNil(X0) = vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),coindu526335360e_lSup(X0),X1)) | ? [X2 : coindu1593790203_llist(X0)] : ((vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2) != $true) & ($true = vAPP(set(coindu1593790203_llist(X0)),$o,vAPP(coindu1593790203_llist(X0),sTfun(set(coindu1593790203_llist(X0)),$o),member(coindu1593790203_llist(X0)),X2),X1))))),
% 0.15/0.49 inference(ennf_transformation,[],[f405])).
% 0.15/0.49 thf(f405,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : set(coindu1593790203_llist(X0))] : (! [X2 : coindu1593790203_llist(X0)] : (($true = vAPP(set(coindu1593790203_llist(X0)),$o,vAPP(coindu1593790203_llist(X0),sTfun(set(coindu1593790203_llist(X0)),$o),member(coindu1593790203_llist(X0)),X2),X1)) => (vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2) = $true)) => (coindu1598213697e_LNil(X0) = vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),coindu526335360e_lSup(X0),X1)))),
% 0.15/0.49 inference(fool_elimination,[],[f404])).
% 0.15/0.49 thf(f404,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : set(coindu1593790203_llist(X0))] : (! [X2 : coindu1593790203_llist(X0)] : (vAPP(set(coindu1593790203_llist(X0)),$o,vAPP(coindu1593790203_llist(X0),sTfun(set(coindu1593790203_llist(X0)),$o),member(coindu1593790203_llist(X0)),X2),X1) => vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2)) => (coindu1598213697e_LNil(X0) = vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),coindu526335360e_lSup(X0),X1)))),
% 0.15/0.49 inference(rectify,[],[f130])).
% 0.15/0.49 thf(f130,axiom,(
% 0.15/0.49 ! [X0 : $tType,X16 : set(coindu1593790203_llist(X0))] : (! [X22 : coindu1593790203_llist(X0)] : (vAPP(set(coindu1593790203_llist(X0)),$o,vAPP(coindu1593790203_llist(X0),sTfun(set(coindu1593790203_llist(X0)),$o),member(coindu1593790203_llist(X0)),X22),X16) => vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X22)) => (vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),coindu526335360e_lSup(X0),X16) = coindu1598213697e_LNil(X0)))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_lSup_Octr_I1_J)).
% 0.15/0.49 thf(f2496,plain,(
% 0.15/0.49 spl95_44),
% 0.15/0.49 inference(avatar_split_clause,[],[f2144,f2494])).
% 0.15/0.49 thf(f2494,plain,(
% 0.15/0.49 spl95_44 <=> ! [X0 : $tType,X1 : set(coindu1593790203_llist(X0))] : ((coindu1598213697e_LNil(X0) = vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),coindu526335360e_lSup(X0),X1)) | (coindu1598213697e_LNil(X0) != vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),sK21(X0),X1)))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_44])])).
% 0.15/0.49 thf(f2144,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X1 : set(coindu1593790203_llist(X0))] : ((coindu1598213697e_LNil(X0) = vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),coindu526335360e_lSup(X0),X1)) | (coindu1598213697e_LNil(X0) != vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),sK21(X0),X1))) )),
% 0.15/0.49 inference(equality_proxy_clausification,[],[f2143])).
% 0.15/0.49 thf(f2143,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X1 : set(coindu1593790203_llist(X0))] : ((coindu1598213697e_LNil(X0) = vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),coindu526335360e_lSup(X0),X1)) | ($true != vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vEQ(coindu1593790203_llist(X0)),coindu1598213697e_LNil(X0)),vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),sK21(X0),X1)))) )),
% 0.15/0.49 inference(equality_proxy_clausification,[],[f1616])).
% 0.15/0.49 thf(f1616,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X1 : set(coindu1593790203_llist(X0))] : (($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vEQ(coindu1593790203_llist(X0)),coindu1598213697e_LNil(X0)),vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),coindu526335360e_lSup(X0),X1))) | ($true != vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vEQ(coindu1593790203_llist(X0)),coindu1598213697e_LNil(X0)),vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),sK21(X0),X1)))) )),
% 0.15/0.49 inference(definition_unfolding,[],[f1284,f1215,f1215])).
% 0.15/0.49 thf(f1284,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X1 : set(coindu1593790203_llist(X0))] : (($true = vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),coindu526335360e_lSup(X0),X1))) | ($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),sK21(X0),X1)))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f1064])).
% 0.15/0.49 thf(f1064,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : set(coindu1593790203_llist(X0))] : (($true = vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),coindu526335360e_lSup(X0),X1))) | (($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),sK21(X0),X1))) & ($true = vAPP(set(coindu1593790203_llist(X0)),$o,vAPP(coindu1593790203_llist(X0),sTfun(set(coindu1593790203_llist(X0)),$o),member(coindu1593790203_llist(X0)),vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),sK21(X0),X1)),X1))))),
% 0.15/0.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f852,f1063])).
% 0.15/0.49 thf(f1063,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : set(coindu1593790203_llist(X0))] : (? [X2 : coindu1593790203_llist(X0)] : ((vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2) != $true) & ($true = vAPP(set(coindu1593790203_llist(X0)),$o,vAPP(coindu1593790203_llist(X0),sTfun(set(coindu1593790203_llist(X0)),$o),member(coindu1593790203_llist(X0)),X2),X1))) => (($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),sK21(X0),X1))) & ($true = vAPP(set(coindu1593790203_llist(X0)),$o,vAPP(coindu1593790203_llist(X0),sTfun(set(coindu1593790203_llist(X0)),$o),member(coindu1593790203_llist(X0)),vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),sK21(X0),X1)),X1))))),
% 0.15/0.49 introduced(choice_axiom,[])).
% 0.15/0.49 thf(f852,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : set(coindu1593790203_llist(X0))] : (($true = vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),coindu526335360e_lSup(X0),X1))) | ? [X2 : coindu1593790203_llist(X0)] : ((vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2) != $true) & ($true = vAPP(set(coindu1593790203_llist(X0)),$o,vAPP(coindu1593790203_llist(X0),sTfun(set(coindu1593790203_llist(X0)),$o),member(coindu1593790203_llist(X0)),X2),X1))))),
% 0.15/0.49 inference(ennf_transformation,[],[f407])).
% 0.15/0.49 thf(f407,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : set(coindu1593790203_llist(X0))] : (! [X2 : coindu1593790203_llist(X0)] : (($true = vAPP(set(coindu1593790203_llist(X0)),$o,vAPP(coindu1593790203_llist(X0),sTfun(set(coindu1593790203_llist(X0)),$o),member(coindu1593790203_llist(X0)),X2),X1)) => (vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2) = $true)) => ($true = vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),coindu526335360e_lSup(X0),X1))))),
% 0.15/0.49 inference(fool_elimination,[],[f406])).
% 0.15/0.49 thf(f406,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : set(coindu1593790203_llist(X0))] : (! [X2 : coindu1593790203_llist(X0)] : (vAPP(set(coindu1593790203_llist(X0)),$o,vAPP(coindu1593790203_llist(X0),sTfun(set(coindu1593790203_llist(X0)),$o),member(coindu1593790203_llist(X0)),X2),X1) => vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2)) => vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),coindu526335360e_lSup(X0),X1)))),
% 0.15/0.49 inference(rectify,[],[f51])).
% 0.15/0.49 thf(f51,axiom,(
% 0.15/0.49 ! [X0 : $tType,X16 : set(coindu1593790203_llist(X0))] : (! [X22 : coindu1593790203_llist(X0)] : (vAPP(set(coindu1593790203_llist(X0)),$o,vAPP(coindu1593790203_llist(X0),sTfun(set(coindu1593790203_llist(X0)),$o),member(coindu1593790203_llist(X0)),X22),X16) => vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X22)) => vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),vAPP(set(coindu1593790203_llist(X0)),coindu1593790203_llist(X0),coindu526335360e_lSup(X0),X16)))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_lSup_Odisc_I1_J)).
% 0.15/0.49 thf(f2492,plain,(
% 0.15/0.49 spl95_43 | ~spl95_7 | ~spl95_32),
% 0.15/0.49 inference(avatar_split_clause,[],[f2434,f2420,f2294,f2490])).
% 0.15/0.49 thf(f2490,plain,(
% 0.15/0.49 spl95_43 <=> ! [X0 : $o] : (($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),inf_inf($o),X0),X0)) | ($true = X0))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_43])])).
% 0.15/0.49 thf(f2420,plain,(
% 0.15/0.49 spl95_32 <=> ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X1) = X1) | (vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0)) != $true))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_32])])).
% 0.15/0.49 thf(f2434,plain,(
% 0.15/0.49 ( ! [X0 : $o] : (($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),inf_inf($o),X0),X0)) | ($true = X0)) ) | (~spl95_7 | ~spl95_32)),
% 0.15/0.49 inference(binary_proxy_clausification,[],[f2432])).
% 0.15/0.49 thf(f2432,plain,(
% 0.15/0.49 ( ! [X0 : $o] : ((vAPP($o,$o,vAPP($o,sTfun($o,$o),inf_inf($o),X0),X0) = X0)) ) | (~spl95_7 | ~spl95_32)),
% 0.15/0.49 inference(trivial_inequality_removal,[],[f2427])).
% 0.15/0.49 thf(f2427,plain,(
% 0.15/0.49 ( ! [X0 : $o] : (($true != $true) | (vAPP($o,$o,vAPP($o,sTfun($o,$o),inf_inf($o),X0),X0) = X0)) ) | (~spl95_7 | ~spl95_32)),
% 0.15/0.49 inference(superposition,[],[f2421,f2296])).
% 0.15/0.49 thf(f2421,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X1 : X0] : ((vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0)) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X1) = X1)) ) | ~spl95_32),
% 0.15/0.49 inference(avatar_component_clause,[],[f2420])).
% 0.15/0.49 thf(f2488,plain,(
% 0.15/0.49 spl95_42),
% 0.15/0.49 inference(avatar_split_clause,[],[f1756,f2485])).
% 0.15/0.49 thf(f2485,plain,(
% 0.15/0.49 spl95_42 <=> ($true = vAPP(set(coindu1593790203_llist(a)),$o,vAPP(sTfun(coindu1593790203_llist(a),sTfun(coindu1593790203_llist(a),$o)),sTfun(set(coindu1593790203_llist(a)),$o),comple1193779247_chain(coindu1593790203_llist(a)),coindu1571841457prefix(a)),ya))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_42])])).
% 0.15/0.49 thf(f1756,plain,(
% 0.15/0.49 ($true = vAPP(set(coindu1593790203_llist(a)),$o,vAPP(sTfun(coindu1593790203_llist(a),sTfun(coindu1593790203_llist(a),$o)),sTfun(set(coindu1593790203_llist(a)),$o),comple1193779247_chain(coindu1593790203_llist(a)),coindu1571841457prefix(a)),ya))),
% 0.15/0.49 inference(definition_unfolding,[],[f1578,f1201])).
% 0.15/0.49 thf(f1578,plain,(
% 0.15/0.49 (vAPP(set(coindu1593790203_llist(a)),$o,vAPP(sTfun(coindu1593790203_llist(a),sTfun(coindu1593790203_llist(a),$o)),sTfun(set(coindu1593790203_llist(a)),$o),comple1193779247_chain(coindu1593790203_llist(a)),coindu1696667936prefix(a)),ya) = $true)),
% 0.15/0.49 inference(cnf_transformation,[],[f723])).
% 0.15/0.49 thf(f723,plain,(
% 0.15/0.49 (vAPP(set(coindu1593790203_llist(a)),$o,vAPP(sTfun(coindu1593790203_llist(a),sTfun(coindu1593790203_llist(a),$o)),sTfun(set(coindu1593790203_llist(a)),$o),comple1193779247_chain(coindu1593790203_llist(a)),coindu1696667936prefix(a)),ya) = $true)),
% 0.15/0.49 inference(fool_elimination,[],[f722])).
% 0.15/0.49 thf(f722,plain,(
% 0.15/0.49 vAPP(set(coindu1593790203_llist(a)),$o,vAPP(sTfun(coindu1593790203_llist(a),sTfun(coindu1593790203_llist(a),$o)),sTfun(set(coindu1593790203_llist(a)),$o),comple1193779247_chain(coindu1593790203_llist(a)),coindu1696667936prefix(a)),ya)),
% 0.15/0.49 inference(rectify,[],[f22])).
% 0.15/0.49 thf(f22,axiom,(
% 0.15/0.49 vAPP(set(coindu1593790203_llist(a)),$o,vAPP(sTfun(coindu1593790203_llist(a),sTfun(coindu1593790203_llist(a),$o)),sTfun(set(coindu1593790203_llist(a)),$o),comple1193779247_chain(coindu1593790203_llist(a)),coindu1696667936prefix(a)),ya)),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_chain)).
% 0.15/0.49 thf(f2483,plain,(
% 0.15/0.49 spl95_41),
% 0.15/0.49 inference(avatar_split_clause,[],[f1327,f2481])).
% 0.15/0.49 thf(f2481,plain,(
% 0.15/0.49 spl95_41 <=> ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : X0] : (vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X1),X2)) = X2)),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_41])])).
% 0.15/0.49 thf(f1327,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : X0] : ((vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X1),X2)) = X2)) )),
% 0.15/0.49 inference(cnf_transformation,[],[f757])).
% 0.15/0.49 thf(f757,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : X0,X2 : coindu1593790203_llist(X0)] : (vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X1),X2)) = X2)),
% 0.15/0.49 inference(rectify,[],[f114])).
% 0.15/0.49 thf(f114,axiom,(
% 0.15/0.49 ! [X0 : $tType,X39 : X0,X40 : coindu1593790203_llist(X0)] : (vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X39),X40)) = X40)),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_ltl__simps_I2_J)).
% 0.15/0.49 thf(f2479,plain,(
% 0.15/0.49 spl95_40),
% 0.15/0.49 inference(avatar_split_clause,[],[f1312,f2477])).
% 0.15/0.49 thf(f1312,plain,(
% 0.15/0.49 ( ! [X1 : $tType,X0 : $tType] : (($true = vAPP(itself(sTfun(X0,X1)),$o,semilattice_inf(sTfun(X0,X1)),type2(sTfun(X0,X1)))) | (vAPP(itself(X1),$o,semilattice_inf(X1),type2(X1)) != $true)) )),
% 0.15/0.49 inference(cnf_transformation,[],[f872])).
% 0.15/0.49 thf(f872,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : $tType] : (($true = vAPP(itself(sTfun(X0,X1)),$o,semilattice_inf(sTfun(X0,X1)),type2(sTfun(X0,X1)))) | (vAPP(itself(X1),$o,semilattice_inf(X1),type2(X1)) != $true))),
% 0.15/0.49 inference(ennf_transformation,[],[f437])).
% 0.15/0.49 thf(f437,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : $tType] : ((vAPP(itself(X1),$o,semilattice_inf(X1),type2(X1)) = $true) => ($true = vAPP(itself(sTfun(X0,X1)),$o,semilattice_inf(sTfun(X0,X1)),type2(sTfun(X0,X1)))))),
% 0.15/0.49 inference(fool_elimination,[],[f436])).
% 0.15/0.49 thf(f436,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : $tType] : (vAPP(itself(X1),$o,semilattice_inf(X1),type2(X1)) => vAPP(itself(sTfun(X0,X1)),$o,semilattice_inf(sTfun(X0,X1)),type2(sTfun(X0,X1))))),
% 0.15/0.49 inference(rectify,[],[f255])).
% 0.15/0.49 thf(f255,axiom,(
% 0.15/0.49 ! [X93 : $tType,X94 : $tType] : (vAPP(itself(X94),$o,semilattice_inf(X94),type2(X94)) => vAPP(itself(sTfun(X93,X94)),$o,semilattice_inf(sTfun(X93,X94)),type2(sTfun(X93,X94))))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Osemilattice__inf)).
% 0.15/0.49 thf(f2475,plain,(
% 0.15/0.49 spl95_39),
% 0.15/0.49 inference(avatar_split_clause,[],[f1309,f2473])).
% 0.15/0.49 thf(f1309,plain,(
% 0.15/0.49 ( ! [X1 : $tType,X0 : $tType] : (($true = vAPP(itself(sTfun(X0,X1)),$o,lattice(sTfun(X0,X1)),type2(sTfun(X0,X1)))) | ($true != vAPP(itself(X1),$o,lattice(X1),type2(X1)))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f869])).
% 0.15/0.49 thf(f869,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : $tType] : (($true = vAPP(itself(sTfun(X0,X1)),$o,lattice(sTfun(X0,X1)),type2(sTfun(X0,X1)))) | ($true != vAPP(itself(X1),$o,lattice(X1),type2(X1))))),
% 0.15/0.49 inference(ennf_transformation,[],[f431])).
% 0.15/0.49 thf(f431,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : $tType] : (($true = vAPP(itself(X1),$o,lattice(X1),type2(X1))) => ($true = vAPP(itself(sTfun(X0,X1)),$o,lattice(sTfun(X0,X1)),type2(sTfun(X0,X1)))))),
% 0.15/0.49 inference(fool_elimination,[],[f430])).
% 0.15/0.49 thf(f430,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : $tType] : (vAPP(itself(X1),$o,lattice(X1),type2(X1)) => vAPP(itself(sTfun(X0,X1)),$o,lattice(sTfun(X0,X1)),type2(sTfun(X0,X1))))),
% 0.15/0.49 inference(rectify,[],[f256])).
% 0.15/0.49 thf(f256,axiom,(
% 0.15/0.49 ! [X93 : $tType,X94 : $tType] : (vAPP(itself(X94),$o,lattice(X94),type2(X94)) => vAPP(itself(sTfun(X93,X94)),$o,lattice(sTfun(X93,X94)),type2(sTfun(X93,X94))))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Olattice)).
% 0.15/0.49 thf(f2455,plain,(
% 0.15/0.49 spl95_38),
% 0.15/0.49 inference(avatar_split_clause,[],[f2003,f2453])).
% 0.15/0.49 thf(f2453,plain,(
% 0.15/0.49 spl95_38 <=> ! [X1 : $tType,X0 : coindu1593790203_llist(X1) > $o] : ((coindu1598213697e_LNil(X1) != vAPP(sTfun(coindu1593790203_llist(X1),$o),coindu1593790203_llist(X1),sK36(X1),X0)) | ($true != vAPP(sTfun(coindu1593790203_llist(X1),$o),$o,sP3(X1),X0)))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_38])])).
% 0.15/0.49 thf(f2003,plain,(
% 0.15/0.49 ( ! [X1 : $tType,X0 : coindu1593790203_llist(X1) > $o] : ((coindu1598213697e_LNil(X1) != vAPP(sTfun(coindu1593790203_llist(X1),$o),coindu1593790203_llist(X1),sK36(X1),X0)) | ($true != vAPP(sTfun(coindu1593790203_llist(X1),$o),$o,sP3(X1),X0))) )),
% 0.15/0.49 inference(equality_proxy_clausification,[],[f1670])).
% 0.15/0.49 thf(f1670,plain,(
% 0.15/0.49 ( ! [X1 : $tType,X0 : coindu1593790203_llist(X1) > $o] : (($true != vAPP(coindu1593790203_llist(X1),$o,vAPP(coindu1593790203_llist(X1),sTfun(coindu1593790203_llist(X1),$o),vEQ(coindu1593790203_llist(X1)),coindu1598213697e_LNil(X1)),vAPP(sTfun(coindu1593790203_llist(X1),$o),coindu1593790203_llist(X1),sK36(X1),X0))) | ($true != vAPP(sTfun(coindu1593790203_llist(X1),$o),$o,sP3(X1),X0))) )),
% 0.15/0.49 inference(definition_unfolding,[],[f1390,f1215])).
% 0.15/0.49 thf(f1390,plain,(
% 0.15/0.49 ( ! [X1 : $tType,X0 : coindu1593790203_llist(X1) > $o] : (($true != vAPP(coindu1593790203_llist(X1),$o,coindu335574135_lnull(X1),vAPP(sTfun(coindu1593790203_llist(X1),$o),coindu1593790203_llist(X1),sK36(X1),X0))) | ($true != vAPP(sTfun(coindu1593790203_llist(X1),$o),$o,sP3(X1),X0))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f1099])).
% 0.15/0.49 thf(f2451,plain,(
% 0.15/0.49 spl95_37),
% 0.15/0.49 inference(avatar_split_clause,[],[f1372,f2449])).
% 0.15/0.49 thf(f2449,plain,(
% 0.15/0.49 spl95_37 <=> ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : coindu1593790203_llist(X0) > $o] : (($true = vAPP(coindu1593790203_llist(X0),$o,X1,X2)) | ($true != vAPP(coindu1593790203_llist(X0),$o,X1,vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK30(X0),X1))))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_37])])).
% 0.15/0.49 thf(f1372,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : coindu1593790203_llist(X0) > $o] : (($true = vAPP(coindu1593790203_llist(X0),$o,X1,X2)) | ($true != vAPP(coindu1593790203_llist(X0),$o,X1,vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK30(X0),X1)))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f1084])).
% 0.15/0.49 thf(f1084,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0) > $o,X2 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,X1,X2)) | (($true != vAPP(coindu1593790203_llist(X0),$o,X1,vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK30(X0),X1))) & ! [X4 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,X1,X4)) | ($true != vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu574146665prefix(X0),X4),vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK30(X0),X1))))))),
% 0.15/0.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f906,f1083])).
% 0.15/0.49 thf(f1083,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0) > $o] : (? [X3 : coindu1593790203_llist(X0)] : (($true != vAPP(coindu1593790203_llist(X0),$o,X1,X3)) & ! [X4 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,X1,X4)) | ($true != vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu574146665prefix(X0),X4),X3)))) => (($true != vAPP(coindu1593790203_llist(X0),$o,X1,vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK30(X0),X1))) & ! [X4 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,X1,X4)) | ($true != vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu574146665prefix(X0),X4),vAPP(sTfun(coindu1593790203_llist(X0),$o),coindu1593790203_llist(X0),sK30(X0),X1))))))),
% 0.15/0.49 introduced(choice_axiom,[])).
% 0.15/0.49 thf(f906,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0) > $o,X2 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,X1,X2)) | ? [X3 : coindu1593790203_llist(X0)] : (($true != vAPP(coindu1593790203_llist(X0),$o,X1,X3)) & ! [X4 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,X1,X4)) | ($true != vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu574146665prefix(X0),X4),X3)))))),
% 0.15/0.49 inference(ennf_transformation,[],[f515])).
% 0.15/0.49 thf(f515,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0) > $o,X2 : coindu1593790203_llist(X0)] : (! [X3 : coindu1593790203_llist(X0)] : (! [X4 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu574146665prefix(X0),X4),X3)) => ($true = vAPP(coindu1593790203_llist(X0),$o,X1,X4))) => ($true = vAPP(coindu1593790203_llist(X0),$o,X1,X3))) => ($true = vAPP(coindu1593790203_llist(X0),$o,X1,X2)))),
% 0.15/0.49 inference(fool_elimination,[],[f514])).
% 0.15/0.49 thf(f514,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0) > $o,X2 : coindu1593790203_llist(X0)] : (! [X3 : coindu1593790203_llist(X0)] : (! [X4 : coindu1593790203_llist(X0)] : (vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu574146665prefix(X0),X4),X3) => vAPP(coindu1593790203_llist(X0),$o,X1,X4)) => vAPP(coindu1593790203_llist(X0),$o,X1,X3)) => vAPP(coindu1593790203_llist(X0),$o,X1,X2))),
% 0.15/0.49 inference(rectify,[],[f175])).
% 0.15/0.49 thf(f175,axiom,(
% 0.15/0.49 ! [X0 : $tType,X24 : coindu1593790203_llist(X0) > $o,X6 : coindu1593790203_llist(X0)] : (! [X7 : coindu1593790203_llist(X0)] : (! [X62 : coindu1593790203_llist(X0)] : (vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu574146665prefix(X0),X62),X7) => vAPP(coindu1593790203_llist(X0),$o,X24,X62)) => vAPP(coindu1593790203_llist(X0),$o,X24,X7)) => vAPP(coindu1593790203_llist(X0),$o,X24,X6))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_llist__less__induct)).
% 0.15/0.49 thf(f2447,plain,(
% 0.15/0.49 spl95_36 | ~spl95_7 | ~spl95_32),
% 0.15/0.49 inference(avatar_split_clause,[],[f2433,f2420,f2294,f2445])).
% 0.15/0.49 thf(f2445,plain,(
% 0.15/0.49 spl95_36 <=> ! [X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),inf_inf($o),X0),X0)) | ($false = X0))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_36])])).
% 0.15/0.49 thf(f2433,plain,(
% 0.15/0.49 ( ! [X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),inf_inf($o),X0),X0)) | ($false = X0)) ) | (~spl95_7 | ~spl95_32)),
% 0.15/0.49 inference(binary_proxy_clausification,[],[f2432])).
% 0.15/0.49 thf(f2443,plain,(
% 0.15/0.49 spl95_35),
% 0.15/0.49 inference(avatar_split_clause,[],[f1301,f2441])).
% 0.15/0.49 thf(f2441,plain,(
% 0.15/0.49 spl95_35 <=> ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X1))) | ($true != vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X1)))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_35])])).
% 0.15/0.49 thf(f1301,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X1))) | ($true != vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X1))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f861])).
% 0.15/0.49 thf(f861,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X1))) | ($true != vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X1)))),
% 0.15/0.49 inference(ennf_transformation,[],[f417])).
% 0.15/0.49 thf(f417,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X1)) => ($true = vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X1))))),
% 0.15/0.49 inference(fool_elimination,[],[f416])).
% 0.15/0.49 thf(f416,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : (vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X1) => vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X1)))),
% 0.15/0.49 inference(rectify,[],[f195])).
% 0.15/0.49 thf(f195,axiom,(
% 0.15/0.49 ! [X0 : $tType,X6 : coindu1593790203_llist(X0)] : (vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),X6) => vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X6)))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_ldistinct__ltlI)).
% 0.15/0.49 thf(f2439,plain,(
% 0.15/0.49 spl95_34),
% 0.15/0.49 inference(avatar_split_clause,[],[f1257,f2437])).
% 0.15/0.49 thf(f2437,plain,(
% 0.15/0.49 spl95_34 <=> ! [X0 : $tType,X1 : X0] : (vAPP(coindu1593790203_llist(X0),X0,coindu2000965700_llast(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X1),coindu1598213697e_LNil(X0))) = X1)),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_34])])).
% 0.15/0.49 thf(f1257,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X1 : X0] : ((vAPP(coindu1593790203_llist(X0),X0,coindu2000965700_llast(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X1),coindu1598213697e_LNil(X0))) = X1)) )),
% 0.15/0.49 inference(cnf_transformation,[],[f739])).
% 0.15/0.49 thf(f739,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : X0] : (vAPP(coindu1593790203_llist(X0),X0,coindu2000965700_llast(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X1),coindu1598213697e_LNil(X0))) = X1)),
% 0.15/0.49 inference(rectify,[],[f191])).
% 0.15/0.49 thf(f191,axiom,(
% 0.15/0.49 ! [X0 : $tType,X15 : X0] : (vAPP(coindu1593790203_llist(X0),X0,coindu2000965700_llast(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X15),coindu1598213697e_LNil(X0))) = X15)),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_llast__singleton)).
% 0.15/0.49 thf(f2426,plain,(
% 0.15/0.49 spl95_33),
% 0.15/0.49 inference(avatar_split_clause,[],[f1326,f2424])).
% 0.15/0.49 thf(f2424,plain,(
% 0.15/0.49 spl95_33 <=> ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : X0] : (vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X1),X2)) = X1)),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_33])])).
% 0.15/0.49 thf(f1326,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : X0] : ((vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X1),X2)) = X1)) )),
% 0.15/0.49 inference(cnf_transformation,[],[f756])).
% 0.15/0.49 thf(f756,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : X0,X2 : coindu1593790203_llist(X0)] : (vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X1),X2)) = X1)),
% 0.15/0.49 inference(rectify,[],[f116])).
% 0.15/0.49 thf(f116,axiom,(
% 0.15/0.49 ! [X0 : $tType,X39 : X0,X40 : coindu1593790203_llist(X0)] : (vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X39),X40)) = X39)),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_lhd__LCons)).
% 0.15/0.49 thf(f2422,plain,(
% 0.15/0.49 spl95_32),
% 0.15/0.49 inference(avatar_split_clause,[],[f1225,f2420])).
% 0.15/0.49 thf(f1225,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X1) = X1) | (vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0)) != $true)) )),
% 0.15/0.49 inference(cnf_transformation,[],[f826])).
% 0.15/0.49 thf(f826,plain,(
% 0.15/0.49 ! [X0 : $tType] : (! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X1) = X1) | (vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0)) != $true))),
% 0.15/0.49 inference(ennf_transformation,[],[f323])).
% 0.15/0.49 thf(f323,plain,(
% 0.15/0.49 ! [X0 : $tType] : ((vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0)) = $true) => ! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X1) = X1))),
% 0.15/0.49 inference(fool_elimination,[],[f322])).
% 0.15/0.49 thf(f322,plain,(
% 0.15/0.49 ! [X0 : $tType] : (vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0)) => ! [X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X1),X1) = X1))),
% 0.15/0.49 inference(rectify,[],[f140])).
% 0.15/0.49 thf(f140,axiom,(
% 0.15/0.49 ! [X0 : $tType] : (vAPP(itself(X0),$o,semilattice_inf(X0),type2(X0)) => ! [X15 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),inf_inf(X0),X15),X15) = X15))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_inf__idem)).
% 0.15/0.49 thf(f2418,plain,(
% 0.15/0.49 spl95_31),
% 0.15/0.49 inference(avatar_split_clause,[],[f1255,f2416])).
% 0.15/0.49 thf(f2416,plain,(
% 0.15/0.49 spl95_31 <=> ! [X0 : $tType,X1 : X0 > $o] : (coindu1598213697e_LNil(X0) = vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(sTfun(X0,$o),sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu721411036eWhile(X0),X1),coindu1598213697e_LNil(X0)))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_31])])).
% 0.15/0.49 thf(f1255,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X1 : X0 > $o] : ((coindu1598213697e_LNil(X0) = vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(sTfun(X0,$o),sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu721411036eWhile(X0),X1),coindu1598213697e_LNil(X0)))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f737])).
% 0.15/0.49 thf(f737,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : X0 > $o] : (coindu1598213697e_LNil(X0) = vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(sTfun(X0,$o),sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu721411036eWhile(X0),X1),coindu1598213697e_LNil(X0)))),
% 0.15/0.49 inference(rectify,[],[f166])).
% 0.15/0.49 thf(f166,axiom,(
% 0.15/0.49 ! [X0 : $tType,X24 : X0 > $o] : (coindu1598213697e_LNil(X0) = vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(sTfun(X0,$o),sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu721411036eWhile(X0),X24),coindu1598213697e_LNil(X0)))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_ltakeWhile__LNil)).
% 0.15/0.49 thf(f2414,plain,(
% 0.15/0.49 spl95_30),
% 0.15/0.49 inference(avatar_split_clause,[],[f1192,f2411])).
% 0.15/0.49 thf(f2411,plain,(
% 0.15/0.49 spl95_30 <=> (vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),xs) = vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya)))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_30])])).
% 0.15/0.49 thf(f1192,plain,(
% 0.15/0.49 (vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),xs) = vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya)))),
% 0.15/0.49 inference(cnf_transformation,[],[f5])).
% 0.15/0.49 thf(f5,axiom,(
% 0.15/0.49 (vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),xs) = vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya)))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__092_060open_062lhd_A_IlSup_AY_J_A_061_Alhd_Axs_092_060close_062)).
% 0.15/0.49 thf(f2402,plain,(
% 0.15/0.49 spl95_29),
% 0.15/0.49 inference(avatar_split_clause,[],[f2017,f2400])).
% 0.15/0.49 thf(f2400,plain,(
% 0.15/0.49 spl95_29 <=> ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1571841457prefix(X0),X1),X2)) | (coindu1598213697e_LNil(X0) != X1))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_29])])).
% 0.15/0.49 thf(f2017,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1571841457prefix(X0),X1),X2)) | (coindu1598213697e_LNil(X0) != X1)) )),
% 0.15/0.49 inference(equality_proxy_clausification,[],[f1654])).
% 0.15/0.49 thf(f1654,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1571841457prefix(X0),X1),X2)) | ($true != vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vEQ(coindu1593790203_llist(X0)),coindu1598213697e_LNil(X0)),X1))) )),
% 0.15/0.49 inference(definition_unfolding,[],[f1357,f1201,f1215])).
% 0.15/0.49 thf(f1357,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1696667936prefix(X0),X1),X2)) | ($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f887])).
% 0.15/0.49 thf(f887,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0),X2 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1696667936prefix(X0),X1),X2)) | ((($true != vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1696667936prefix(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X1)),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X2))) | (vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X2) != vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X1)) | (vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2) = $true)) & ($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1))))),
% 0.15/0.49 inference(ennf_transformation,[],[f768])).
% 0.15/0.49 thf(f768,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0),X2 : coindu1593790203_llist(X0)] : ((($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1)) => (($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1696667936prefix(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X1)),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X2))) & (vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X2) = vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X1)) & (vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2) != $true))) => ($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1696667936prefix(X0),X1),X2)))),
% 0.15/0.49 inference(flattening,[],[f495])).
% 0.15/0.49 thf(f495,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0),X2 : coindu1593790203_llist(X0)] : ((~($true = vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1)) => (($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1696667936prefix(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X1)),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X2))) & (vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X2) = vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X1)) & ~(vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2) = $true))) => ($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1696667936prefix(X0),X1),X2)))),
% 0.15/0.49 inference(fool_elimination,[],[f494])).
% 0.15/0.49 thf(f494,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0),X2 : coindu1593790203_llist(X0)] : ((~vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1) => (vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1696667936prefix(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X1)),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X2)) & (vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X2) = vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X1)) & ~vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2))) => vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1696667936prefix(X0),X1),X2))),
% 0.15/0.49 inference(rectify,[],[f49])).
% 0.15/0.49 thf(f49,axiom,(
% 0.15/0.49 ! [X0 : $tType,X6 : coindu1593790203_llist(X0),X18 : coindu1593790203_llist(X0)] : ((~vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X6) => (vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1696667936prefix(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X6)),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X18)) & (vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X6) = vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X18)) & ~vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X18))) => vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1696667936prefix(X0),X6),X18))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_lprefix__expand)).
% 0.15/0.49 thf(f2398,plain,(
% 0.15/0.49 spl95_28),
% 0.15/0.49 inference(avatar_split_clause,[],[f1342,f2396])).
% 0.15/0.49 thf(f2396,plain,(
% 0.15/0.49 spl95_28 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$true),X1),X2) = X1)),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_28])])).
% 0.15/0.49 thf(f1342,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$true),X1),X2) = X1)) )),
% 0.15/0.49 inference(cnf_transformation,[],[f479])).
% 0.15/0.49 thf(f479,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$true),X1),X2) = X1)),
% 0.15/0.49 inference(fool_elimination,[],[f478])).
% 0.15/0.49 thf(f478,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$true),X1),X2) = X1)),
% 0.15/0.49 inference(rectify,[],[f263])).
% 0.15/0.49 thf(f263,axiom,(
% 0.15/0.49 ! [X0 : $tType,X15 : X0,X20 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$true),X15),X20) = X15)),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T)).
% 0.15/0.49 thf(f2394,plain,(
% 0.15/0.49 spl95_27),
% 0.15/0.49 inference(avatar_split_clause,[],[f1341,f2392])).
% 0.15/0.49 thf(f2392,plain,(
% 0.15/0.49 spl95_27 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$false),X1),X2) = X2)),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_27])])).
% 0.15/0.49 thf(f1341,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$false),X1),X2) = X2)) )),
% 0.15/0.49 inference(cnf_transformation,[],[f477])).
% 0.15/0.49 thf(f477,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$false),X1),X2) = X2)),
% 0.15/0.49 inference(fool_elimination,[],[f476])).
% 0.15/0.49 thf(f476,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$false),X1),X2) = X2)),
% 0.15/0.49 inference(rectify,[],[f262])).
% 0.15/0.49 thf(f262,axiom,(
% 0.15/0.49 ! [X0 : $tType,X15 : X0,X20 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),if(X0),$false),X15),X20) = X20)),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T)).
% 0.15/0.49 thf(f2390,plain,(
% 0.15/0.49 spl95_26),
% 0.15/0.49 inference(avatar_split_clause,[],[f1323,f2388])).
% 0.15/0.49 thf(f2388,plain,(
% 0.15/0.49 spl95_26 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : ($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(coindu1593790203_llist(X0),$o),coindu543932918sorted(X0),X1),coindu1598213697e_LNil(X0)))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_26])])).
% 0.15/0.49 thf(f1323,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(coindu1593790203_llist(X0),$o),coindu543932918sorted(X0),X1),coindu1598213697e_LNil(X0)))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f457])).
% 0.15/0.49 thf(f457,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : X0 > X0 > $o] : ($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(coindu1593790203_llist(X0),$o),coindu543932918sorted(X0),X1),coindu1598213697e_LNil(X0)))),
% 0.15/0.49 inference(fool_elimination,[],[f456])).
% 0.15/0.49 thf(f456,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : X0 > X0 > $o] : vAPP(coindu1593790203_llist(X0),$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(coindu1593790203_llist(X0),$o),coindu543932918sorted(X0),X1),coindu1598213697e_LNil(X0))),
% 0.15/0.49 inference(rectify,[],[f124])).
% 0.15/0.49 thf(f124,axiom,(
% 0.15/0.49 ! [X0 : $tType,X29 : X0 > X0 > $o] : vAPP(coindu1593790203_llist(X0),$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(coindu1593790203_llist(X0),$o),coindu543932918sorted(X0),X29),coindu1598213697e_LNil(X0))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_ord_OLNil)).
% 0.15/0.49 thf(f2386,plain,(
% 0.15/0.49 spl95_25),
% 0.15/0.49 inference(avatar_split_clause,[],[f1253,f2384])).
% 0.15/0.49 thf(f2384,plain,(
% 0.15/0.49 spl95_25 <=> ! [X0 : $tType,X1 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),inf_inf(set(X0)),X1),X1) = X1)),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_25])])).
% 0.15/0.49 thf(f1253,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X1 : set(X0)] : ((vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),inf_inf(set(X0)),X1),X1) = X1)) )),
% 0.15/0.49 inference(cnf_transformation,[],[f735])).
% 0.15/0.49 thf(f735,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),inf_inf(set(X0)),X1),X1) = X1)),
% 0.15/0.49 inference(rectify,[],[f158])).
% 0.15/0.49 thf(f158,axiom,(
% 0.15/0.49 ! [X0 : $tType,X16 : set(X0)] : (vAPP(set(X0),set(X0),vAPP(set(X0),sTfun(set(X0),set(X0)),inf_inf(set(X0)),X16),X16) = X16)),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_Int__absorb)).
% 0.15/0.49 thf(f2382,plain,(
% 0.15/0.49 spl95_24),
% 0.15/0.49 inference(avatar_split_clause,[],[f2036,f2380])).
% 0.15/0.49 thf(f2380,plain,(
% 0.15/0.49 spl95_24 <=> ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : coindu1593790203_llist(X0)] : ((X1 = X2) | (coindu1598213697e_LNil(X0) != X2) | (coindu1598213697e_LNil(X0) != X1))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_24])])).
% 0.15/0.49 thf(f2036,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : coindu1593790203_llist(X0)] : ((X1 = X2) | (coindu1598213697e_LNil(X0) != X2) | (coindu1598213697e_LNil(X0) != X1)) )),
% 0.15/0.49 inference(equality_proxy_clausification,[],[f2035])).
% 0.15/0.49 thf(f2035,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : coindu1593790203_llist(X0)] : ((X1 = X2) | (coindu1598213697e_LNil(X0) != X2) | ($false = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vEQ(coindu1593790203_llist(X0)),coindu1598213697e_LNil(X0)),X1))) )),
% 0.15/0.49 inference(duplicate_literal_removal,[],[f2034])).
% 0.15/0.49 thf(f2034,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : coindu1593790203_llist(X0)] : ((X1 = X2) | (coindu1598213697e_LNil(X0) != X2) | (coindu1598213697e_LNil(X0) != X2) | ($false = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vEQ(coindu1593790203_llist(X0)),coindu1598213697e_LNil(X0)),X1))) )),
% 0.15/0.49 inference(equality_proxy_clausification,[],[f2033])).
% 0.15/0.49 thf(f2033,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : coindu1593790203_llist(X0)] : ((X1 = X2) | (coindu1598213697e_LNil(X0) != X2) | ($false = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vEQ(coindu1593790203_llist(X0)),coindu1598213697e_LNil(X0)),X2)) | ($false = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vEQ(coindu1593790203_llist(X0)),coindu1598213697e_LNil(X0)),X1))) )),
% 0.15/0.49 inference(binary_proxy_clausification,[],[f2031])).
% 0.15/0.49 thf(f2031,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : coindu1593790203_llist(X0)] : ((X1 = X2) | (coindu1598213697e_LNil(X0) != X2) | (vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vEQ(coindu1593790203_llist(X0)),coindu1598213697e_LNil(X0)),X2) != vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vEQ(coindu1593790203_llist(X0)),coindu1598213697e_LNil(X0)),X1))) )),
% 0.15/0.49 inference(equality_proxy_clausification,[],[f1648])).
% 0.15/0.49 thf(f1648,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : coindu1593790203_llist(X0)] : ((X1 = X2) | ($true != vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vEQ(coindu1593790203_llist(X0)),coindu1598213697e_LNil(X0)),X2)) | (vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vEQ(coindu1593790203_llist(X0)),coindu1598213697e_LNil(X0)),X2) != vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vEQ(coindu1593790203_llist(X0)),coindu1598213697e_LNil(X0)),X1))) )),
% 0.15/0.49 inference(definition_unfolding,[],[f1349,f1215,f1215,f1215])).
% 0.15/0.49 thf(f1349,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : coindu1593790203_llist(X0)] : ((X1 = X2) | (vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2) != $true) | (vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2) != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f883])).
% 0.15/0.49 thf(f883,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0),X2 : coindu1593790203_llist(X0)] : ((X1 = X2) | (((vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X2) != vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X1)) | (vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X2) != vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X1))) & (vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2) != $true) & ($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1))) | (vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2) != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1)))),
% 0.15/0.49 inference(flattening,[],[f882])).
% 0.15/0.49 thf(f882,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0),X2 : coindu1593790203_llist(X0)] : (((X1 = X2) | ((((vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X2) != vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X1)) | (vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X2) != vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X1))) & (vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2) != $true)) & ($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1)))) | (vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2) != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1)))),
% 0.15/0.49 inference(ennf_transformation,[],[f765])).
% 0.15/0.49 thf(f765,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0),X2 : coindu1593790203_llist(X0)] : ((vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2) = vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1)) => ((($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1)) => ((vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2) != $true) => ((vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X2) = vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X1)) & (vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X2) = vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X1))))) => (X1 = X2)))),
% 0.15/0.49 inference(flattening,[],[f487])).
% 0.15/0.49 thf(f487,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0),X2 : coindu1593790203_llist(X0)] : ((vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2) = vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1)) => ((~($true = vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1)) => (~(vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2) = $true) => ((vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X2) = vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X1)) & (vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X2) = vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X1))))) => (X1 = X2)))),
% 0.15/0.49 inference(fool_elimination,[],[f486])).
% 0.15/0.49 thf(f486,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0),X2 : coindu1593790203_llist(X0)] : ((vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2) = vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1)) => ((~vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1) => (~vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X2) => ((vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X2) = vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X1)) & (vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X2) = vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X1))))) => (X1 = X2)))),
% 0.15/0.49 inference(rectify,[],[f23])).
% 0.15/0.49 thf(f23,axiom,(
% 0.15/0.49 ! [X0 : $tType,X13 : coindu1593790203_llist(X0),X14 : coindu1593790203_llist(X0)] : ((vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X13) = vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X14)) => ((~vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X13) => (~vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X14) => ((vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X13) = vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X14)) & (vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X13) = vAPP(coindu1593790203_llist(X0),X0,coindu1046438764le_lhd(X0),X14))))) => (X13 = X14)))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_llist_Oexpand)).
% 0.15/0.49 thf(f2378,plain,(
% 0.15/0.49 ~spl95_23),
% 0.15/0.49 inference(avatar_split_clause,[],[f2222,f2375])).
% 0.15/0.49 thf(f2375,plain,(
% 0.15/0.49 spl95_23 <=> (vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya)) = coindu1598213697e_LNil(a))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_23])])).
% 0.15/0.49 thf(f2222,plain,(
% 0.15/0.49 (vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya)) != coindu1598213697e_LNil(a))),
% 0.15/0.49 inference(equality_proxy_clausification,[],[f1588])).
% 0.15/0.49 thf(f1588,plain,(
% 0.15/0.49 ($true != vAPP(coindu1593790203_llist(a),$o,vAPP(coindu1593790203_llist(a),sTfun(coindu1593790203_llist(a),$o),vEQ(coindu1593790203_llist(a)),coindu1598213697e_LNil(a)),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya))))),
% 0.15/0.49 inference(definition_unfolding,[],[f1200,f1215])).
% 0.15/0.49 thf(f1200,plain,(
% 0.15/0.49 (vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya))) != $true)),
% 0.15/0.49 inference(cnf_transformation,[],[f731])).
% 0.15/0.49 thf(f731,plain,(
% 0.15/0.49 (vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya))) != $true)),
% 0.15/0.49 inference(flattening,[],[f279])).
% 0.15/0.49 thf(f279,plain,(
% 0.15/0.49 ~(vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya))) = $true)),
% 0.15/0.49 inference(fool_elimination,[],[f278])).
% 0.15/0.49 thf(f278,plain,(
% 0.15/0.49 ~vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya)))),
% 0.15/0.49 inference(rectify,[],[f11])).
% 0.15/0.49 thf(f11,axiom,(
% 0.15/0.49 ~vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya)))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_lsorted_I4_J)).
% 0.15/0.49 thf(f2373,plain,(
% 0.15/0.49 spl95_22),
% 0.15/0.49 inference(avatar_split_clause,[],[f1575,f2370])).
% 0.15/0.49 thf(f2370,plain,(
% 0.15/0.49 spl95_22 <=> (vAPP(set(coindu1593790203_llist(a)),$o,vAPP(coindu1593790203_llist(a),sTfun(set(coindu1593790203_llist(a)),$o),member(coindu1593790203_llist(a)),xs),ya) = $true)),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_22])])).
% 0.15/0.49 thf(f1575,plain,(
% 0.15/0.49 (vAPP(set(coindu1593790203_llist(a)),$o,vAPP(coindu1593790203_llist(a),sTfun(set(coindu1593790203_llist(a)),$o),member(coindu1593790203_llist(a)),xs),ya) = $true)),
% 0.15/0.49 inference(cnf_transformation,[],[f717])).
% 0.15/0.49 thf(f717,plain,(
% 0.15/0.49 (vAPP(set(coindu1593790203_llist(a)),$o,vAPP(coindu1593790203_llist(a),sTfun(set(coindu1593790203_llist(a)),$o),member(coindu1593790203_llist(a)),xs),ya) = $true)),
% 0.15/0.49 inference(fool_elimination,[],[f716])).
% 0.15/0.49 thf(f716,plain,(
% 0.15/0.49 vAPP(set(coindu1593790203_llist(a)),$o,vAPP(coindu1593790203_llist(a),sTfun(set(coindu1593790203_llist(a)),$o),member(coindu1593790203_llist(a)),xs),ya)),
% 0.15/0.49 inference(rectify,[],[f1])).
% 0.15/0.49 thf(f1,axiom,(
% 0.15/0.49 vAPP(set(coindu1593790203_llist(a)),$o,vAPP(coindu1593790203_llist(a),sTfun(set(coindu1593790203_llist(a)),$o),member(coindu1593790203_llist(a)),xs),ya)),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062xs_A_092_060in_062_AY_092_060close_062)).
% 0.15/0.49 thf(f2368,plain,(
% 0.15/0.49 spl95_21),
% 0.15/0.49 inference(avatar_split_clause,[],[f1325,f2366])).
% 0.15/0.49 thf(f2366,plain,(
% 0.15/0.49 spl95_21 <=> ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : X0] : (coindu1598213697e_LNil(X0) != vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X1),X2))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_21])])).
% 0.15/0.49 thf(f1325,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X2 : coindu1593790203_llist(X0),X1 : X0] : ((coindu1598213697e_LNil(X0) != vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X1),X2))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f755])).
% 0.15/0.49 thf(f755,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : X0,X2 : coindu1593790203_llist(X0)] : (coindu1598213697e_LNil(X0) != vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X1),X2))),
% 0.15/0.49 inference(rectify,[],[f96])).
% 0.15/0.49 thf(f96,axiom,(
% 0.15/0.49 ! [X0 : $tType,X39 : X0,X40 : coindu1593790203_llist(X0)] : (vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),vAPP(X0,sTfun(coindu1593790203_llist(X0),coindu1593790203_llist(X0)),coindu1121789889_LCons(X0),X39),X40) != coindu1598213697e_LNil(X0))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_llist_Odistinct_I1_J)).
% 0.15/0.49 thf(f2364,plain,(
% 0.15/0.49 spl95_20),
% 0.15/0.49 inference(avatar_split_clause,[],[f1194,f2361])).
% 0.15/0.49 thf(f2361,plain,(
% 0.15/0.49 spl95_20 <=> ($true = vAPP(set(coindu1593790203_llist(a)),$o,vAPP(coindu1593790203_llist(a),sTfun(set(coindu1593790203_llist(a)),$o),member(coindu1593790203_llist(a)),sK13),ya))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_20])])).
% 0.15/0.49 thf(f1194,plain,(
% 0.15/0.49 ($true = vAPP(set(coindu1593790203_llist(a)),$o,vAPP(coindu1593790203_llist(a),sTfun(set(coindu1593790203_llist(a)),$o),member(coindu1593790203_llist(a)),sK13),ya))),
% 0.15/0.49 inference(cnf_transformation,[],[f1054])).
% 0.15/0.49 thf(f1054,plain,(
% 0.15/0.49 ($true != vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),sK13))) & ($true != vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),sK13)) & ($true = vAPP(set(coindu1593790203_llist(a)),$o,vAPP(coindu1593790203_llist(a),sTfun(set(coindu1593790203_llist(a)),$o),member(coindu1593790203_llist(a)),sK13),ya))),
% 0.15/0.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f819,f1053])).
% 0.15/0.49 thf(f1053,plain,(
% 0.15/0.49 ? [X0 : coindu1593790203_llist(a)] : (($true != vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),X0))) & ($true != vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),X0)) & ($true = vAPP(set(coindu1593790203_llist(a)),$o,vAPP(coindu1593790203_llist(a),sTfun(set(coindu1593790203_llist(a)),$o),member(coindu1593790203_llist(a)),X0),ya))) => (($true != vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),sK13))) & ($true != vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),sK13)) & ($true = vAPP(set(coindu1593790203_llist(a)),$o,vAPP(coindu1593790203_llist(a),sTfun(set(coindu1593790203_llist(a)),$o),member(coindu1593790203_llist(a)),sK13),ya)))),
% 0.15/0.49 introduced(choice_axiom,[])).
% 0.15/0.49 thf(f819,plain,(
% 0.15/0.49 ? [X0 : coindu1593790203_llist(a)] : (($true != vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),X0))) & ($true != vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),X0)) & ($true = vAPP(set(coindu1593790203_llist(a)),$o,vAPP(coindu1593790203_llist(a),sTfun(set(coindu1593790203_llist(a)),$o),member(coindu1593790203_llist(a)),X0),ya)))),
% 0.15/0.49 inference(flattening,[],[f818])).
% 0.15/0.49 thf(f818,plain,(
% 0.15/0.49 ? [X0 : coindu1593790203_llist(a)] : ((($true != vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),X0))) & ($true != vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),X0))) & ($true = vAPP(set(coindu1593790203_llist(a)),$o,vAPP(coindu1593790203_llist(a),sTfun(set(coindu1593790203_llist(a)),$o),member(coindu1593790203_llist(a)),X0),ya)))),
% 0.15/0.49 inference(ennf_transformation,[],[f727])).
% 0.15/0.49 thf(f727,plain,(
% 0.15/0.49 ~! [X0 : coindu1593790203_llist(a)] : (($true = vAPP(set(coindu1593790203_llist(a)),$o,vAPP(coindu1593790203_llist(a),sTfun(set(coindu1593790203_llist(a)),$o),member(coindu1593790203_llist(a)),X0),ya)) => (($true != vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),X0)) => ($true = vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),X0)))))),
% 0.15/0.49 inference(flattening,[],[f271])).
% 0.15/0.49 thf(f271,plain,(
% 0.15/0.49 ~! [X0 : coindu1593790203_llist(a)] : (($true = vAPP(set(coindu1593790203_llist(a)),$o,vAPP(coindu1593790203_llist(a),sTfun(set(coindu1593790203_llist(a)),$o),member(coindu1593790203_llist(a)),X0),ya)) => (~($true = vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),X0)) => ($true = vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),X0)))))),
% 0.15/0.49 inference(fool_elimination,[],[f270])).
% 0.15/0.49 thf(f270,plain,(
% 0.15/0.49 ~! [X0 : coindu1593790203_llist(a)] : (vAPP(set(coindu1593790203_llist(a)),$o,vAPP(coindu1593790203_llist(a),sTfun(set(coindu1593790203_llist(a)),$o),member(coindu1593790203_llist(a)),X0),ya) => (~vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),X0) => vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),X0))))),
% 0.15/0.49 inference(rectify,[],[f15])).
% 0.15/0.49 thf(f15,axiom,(
% 0.15/0.49 ~! [X7 : coindu1593790203_llist(a)] : (vAPP(set(coindu1593790203_llist(a)),$o,vAPP(coindu1593790203_llist(a),sTfun(set(coindu1593790203_llist(a)),$o),member(coindu1593790203_llist(a)),X7),ya) => (~vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),X7) => vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),X7))))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062xs_O_A_092_060lbrakk_062xs_A_092_060in_062_AY_059_A_092_060not_062_Alnull_Axs_059_A_092_060not_062_Alnull_A_Iltl_Axs_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)).
% 0.15/0.49 thf(f2359,plain,(
% 0.15/0.49 spl95_19),
% 0.15/0.49 inference(avatar_split_clause,[],[f1320,f2357])).
% 0.15/0.49 thf(f2357,plain,(
% 0.15/0.49 spl95_19 <=> ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : ($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1571841457prefix(X0),coindu1598213697e_LNil(X0)),X1))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_19])])).
% 0.15/0.49 thf(f1320,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1571841457prefix(X0),coindu1598213697e_LNil(X0)),X1))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f451])).
% 0.15/0.49 thf(f451,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : ($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1571841457prefix(X0),coindu1598213697e_LNil(X0)),X1))),
% 0.15/0.49 inference(fool_elimination,[],[f450])).
% 0.15/0.49 thf(f450,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1571841457prefix(X0),coindu1598213697e_LNil(X0)),X1)),
% 0.15/0.49 inference(rectify,[],[f183])).
% 0.15/0.49 thf(f183,axiom,(
% 0.15/0.49 ! [X0 : $tType,X6 : coindu1593790203_llist(X0)] : vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1571841457prefix(X0),coindu1598213697e_LNil(X0)),X6)),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I2_J)).
% 0.15/0.49 thf(f2351,plain,(
% 0.15/0.49 spl95_18),
% 0.15/0.49 inference(avatar_split_clause,[],[f2136,f2349])).
% 0.15/0.49 thf(f2349,plain,(
% 0.15/0.49 spl95_18 <=> ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : ((coindu1598213697e_LNil(X0) = vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X1)) | (coindu1598213697e_LNil(X0) != X1))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_18])])).
% 0.15/0.49 thf(f2136,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : ((coindu1598213697e_LNil(X0) = vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X1)) | (coindu1598213697e_LNil(X0) != X1)) )),
% 0.15/0.49 inference(equality_proxy_clausification,[],[f2135])).
% 0.15/0.49 thf(f2135,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : ((coindu1598213697e_LNil(X0) = vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X1)) | ($true != vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vEQ(coindu1593790203_llist(X0)),coindu1598213697e_LNil(X0)),X1))) )),
% 0.15/0.49 inference(equality_proxy_clausification,[],[f1627])).
% 0.15/0.49 thf(f1627,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vEQ(coindu1593790203_llist(X0)),coindu1598213697e_LNil(X0)),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X1))) | ($true != vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),vEQ(coindu1593790203_llist(X0)),coindu1598213697e_LNil(X0)),X1))) )),
% 0.15/0.49 inference(definition_unfolding,[],[f1308,f1215,f1215])).
% 0.15/0.49 thf(f1308,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X1))) | ($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f868])).
% 0.15/0.49 thf(f868,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X1))) | ($true != vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1)))),
% 0.15/0.49 inference(ennf_transformation,[],[f429])).
% 0.15/0.49 thf(f429,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1)) => ($true = vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X1))))),
% 0.15/0.49 inference(fool_elimination,[],[f428])).
% 0.15/0.49 thf(f428,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : (vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X1) => vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X1)))),
% 0.15/0.49 inference(rectify,[],[f53])).
% 0.15/0.49 thf(f53,axiom,(
% 0.15/0.49 ! [X0 : $tType,X6 : coindu1593790203_llist(X0)] : (vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),X6) => vAPP(coindu1593790203_llist(X0),$o,coindu335574135_lnull(X0),vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),X6)))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_lnull__ltlI)).
% 0.15/0.49 thf(f2347,plain,(
% 0.15/0.49 spl95_17),
% 0.15/0.49 inference(avatar_split_clause,[],[f1633,f2345])).
% 0.15/0.49 thf(f2345,plain,(
% 0.15/0.49 spl95_17 <=> ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : ($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1571841457prefix(X0),X1),X1))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_17])])).
% 0.15/0.49 thf(f1633,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1571841457prefix(X0),X1),X1))) )),
% 0.15/0.49 inference(definition_unfolding,[],[f1318,f1201])).
% 0.15/0.49 thf(f1318,plain,(
% 0.15/0.49 ( ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : (($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1696667936prefix(X0),X1),X1))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f447])).
% 0.15/0.49 thf(f447,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : ($true = vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1696667936prefix(X0),X1),X1))),
% 0.15/0.49 inference(fool_elimination,[],[f446])).
% 0.15/0.49 thf(f446,plain,(
% 0.15/0.49 ! [X0 : $tType,X1 : coindu1593790203_llist(X0)] : vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1696667936prefix(X0),X1),X1)),
% 0.15/0.49 inference(rectify,[],[f25])).
% 0.15/0.49 thf(f25,axiom,(
% 0.15/0.49 ! [X0 : $tType,X15 : coindu1593790203_llist(X0)] : vAPP(coindu1593790203_llist(X0),$o,vAPP(coindu1593790203_llist(X0),sTfun(coindu1593790203_llist(X0),$o),coindu1696667936prefix(X0),X15),X15)),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_llist_Oleq__refl)).
% 0.15/0.49 thf(f2343,plain,(
% 0.15/0.49 ~spl95_16),
% 0.15/0.49 inference(avatar_split_clause,[],[f2223,f2340])).
% 0.15/0.49 thf(f2340,plain,(
% 0.15/0.49 spl95_16 <=> (vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya) = coindu1598213697e_LNil(a))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_16])])).
% 0.15/0.49 thf(f2223,plain,(
% 0.15/0.49 (vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya) != coindu1598213697e_LNil(a))),
% 0.15/0.49 inference(equality_proxy_clausification,[],[f1587])).
% 0.15/0.49 thf(f1587,plain,(
% 0.15/0.49 ($true != vAPP(coindu1593790203_llist(a),$o,vAPP(coindu1593790203_llist(a),sTfun(coindu1593790203_llist(a),$o),vEQ(coindu1593790203_llist(a)),coindu1598213697e_LNil(a)),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya)))),
% 0.15/0.49 inference(definition_unfolding,[],[f1199,f1215])).
% 0.15/0.49 thf(f1199,plain,(
% 0.15/0.49 (vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya)) != $true)),
% 0.15/0.49 inference(cnf_transformation,[],[f730])).
% 0.15/0.49 thf(f730,plain,(
% 0.15/0.49 (vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya)) != $true)),
% 0.15/0.49 inference(flattening,[],[f277])).
% 0.15/0.49 thf(f277,plain,(
% 0.15/0.49 ~(vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya)) = $true)),
% 0.15/0.49 inference(fool_elimination,[],[f276])).
% 0.15/0.49 thf(f276,plain,(
% 0.15/0.49 ~vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya))),
% 0.15/0.49 inference(rectify,[],[f10])).
% 0.15/0.49 thf(f10,axiom,(
% 0.15/0.49 ~vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_lsorted_I3_J)).
% 0.15/0.49 thf(f2338,plain,(
% 0.15/0.49 spl95_15),
% 0.15/0.49 inference(avatar_split_clause,[],[f1249,f2336])).
% 0.15/0.49 thf(f2336,plain,(
% 0.15/0.49 spl95_15 <=> ! [X0 : $tType] : ($true = vAPP(itself(set(X0)),$o,semilattice_inf(set(X0)),type2(set(X0))))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_15])])).
% 0.15/0.49 thf(f1249,plain,(
% 0.15/0.49 ( ! [X0 : $tType] : (($true = vAPP(itself(set(X0)),$o,semilattice_inf(set(X0)),type2(set(X0))))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f367])).
% 0.15/0.49 thf(f367,plain,(
% 0.15/0.49 ! [X0 : $tType] : ($true = vAPP(itself(set(X0)),$o,semilattice_inf(set(X0)),type2(set(X0))))),
% 0.15/0.49 inference(fool_elimination,[],[f366])).
% 0.15/0.49 thf(f366,plain,(
% 0.15/0.49 ! [X0 : $tType] : vAPP(itself(set(X0)),$o,semilattice_inf(set(X0)),type2(set(X0)))),
% 0.15/0.49 inference(rectify,[],[f257])).
% 0.15/0.49 thf(f257,axiom,(
% 0.15/0.49 ! [X93 : $tType] : vAPP(itself(set(X93)),$o,semilattice_inf(set(X93)),type2(set(X93)))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osemilattice__inf_1)).
% 0.15/0.49 thf(f2334,plain,(
% 0.15/0.49 spl95_14 | ~spl95_4 | spl95_9),
% 0.15/0.49 inference(avatar_split_clause,[],[f2311,f2306,f2253,f2331])).
% 0.15/0.49 thf(f2331,plain,(
% 0.15/0.49 spl95_14 <=> (vAPP(a,$o,vAPP(a,sTfun(a,$o),less_eq,vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),xs)),vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),xs))) = $false)),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_14])])).
% 0.15/0.49 thf(f2253,plain,(
% 0.15/0.49 spl95_4 <=> ! [X0 : $o] : (($true = X0) | ($false = X0))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_4])])).
% 0.15/0.49 thf(f2311,plain,(
% 0.15/0.49 (vAPP(a,$o,vAPP(a,sTfun(a,$o),less_eq,vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),xs)),vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),xs))) = $false) | (~spl95_4 | spl95_9)),
% 0.15/0.49 inference(trivial_inequality_removal,[],[f2310])).
% 0.15/0.49 thf(f2310,plain,(
% 0.15/0.49 ($true != $true) | (vAPP(a,$o,vAPP(a,sTfun(a,$o),less_eq,vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),xs)),vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),xs))) = $false) | (~spl95_4 | spl95_9)),
% 0.15/0.49 inference(superposition,[],[f2308,f2254])).
% 0.15/0.49 thf(f2254,plain,(
% 0.15/0.49 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) ) | ~spl95_4),
% 0.15/0.49 inference(avatar_component_clause,[],[f2253])).
% 0.15/0.49 thf(f2308,plain,(
% 0.15/0.49 (vAPP(a,$o,vAPP(a,sTfun(a,$o),less_eq,vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),xs)),vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),xs))) != $true) | spl95_9),
% 0.15/0.49 inference(avatar_component_clause,[],[f2306])).
% 0.15/0.49 thf(f2329,plain,(
% 0.15/0.49 spl95_13),
% 0.15/0.49 inference(avatar_split_clause,[],[f1248,f2327])).
% 0.15/0.49 thf(f2327,plain,(
% 0.15/0.49 spl95_13 <=> ! [X0 : $tType] : ($true = vAPP(itself(set(X0)),$o,lattice(set(X0)),type2(set(X0))))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_13])])).
% 0.15/0.49 thf(f1248,plain,(
% 0.15/0.49 ( ! [X0 : $tType] : (($true = vAPP(itself(set(X0)),$o,lattice(set(X0)),type2(set(X0))))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f365])).
% 0.15/0.49 thf(f365,plain,(
% 0.15/0.49 ! [X0 : $tType] : ($true = vAPP(itself(set(X0)),$o,lattice(set(X0)),type2(set(X0))))),
% 0.15/0.49 inference(fool_elimination,[],[f364])).
% 0.15/0.49 thf(f364,plain,(
% 0.15/0.49 ! [X0 : $tType] : vAPP(itself(set(X0)),$o,lattice(set(X0)),type2(set(X0)))),
% 0.15/0.49 inference(rectify,[],[f258])).
% 0.15/0.49 thf(f258,axiom,(
% 0.15/0.49 ! [X93 : $tType] : vAPP(itself(set(X93)),$o,lattice(set(X93)),type2(set(X93)))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Olattice_2)).
% 0.15/0.49 thf(f2325,plain,(
% 0.15/0.49 spl95_12),
% 0.15/0.49 inference(avatar_split_clause,[],[f1202,f2323])).
% 0.15/0.49 thf(f2323,plain,(
% 0.15/0.49 spl95_12 <=> ! [X0 : $tType] : (coindu1598213697e_LNil(X0) = vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),coindu1598213697e_LNil(X0)))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_12])])).
% 0.15/0.49 thf(f1202,plain,(
% 0.15/0.49 ( ! [X0 : $tType] : ((coindu1598213697e_LNil(X0) = vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),coindu1598213697e_LNil(X0)))) )),
% 0.15/0.49 inference(cnf_transformation,[],[f121])).
% 0.15/0.49 thf(f121,axiom,(
% 0.15/0.49 ! [X0 : $tType] : (coindu1598213697e_LNil(X0) = vAPP(coindu1593790203_llist(X0),coindu1593790203_llist(X0),coindu1047225960le_ltl(X0),coindu1598213697e_LNil(X0)))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_ltl__simps_I1_J)).
% 0.15/0.49 thf(f2321,plain,(
% 0.15/0.49 ~spl95_11),
% 0.15/0.49 inference(avatar_split_clause,[],[f2227,f2318])).
% 0.15/0.49 thf(f2318,plain,(
% 0.15/0.49 spl95_11 <=> (coindu1598213697e_LNil(a) = vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),sK13))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_11])])).
% 0.15/0.49 thf(f2227,plain,(
% 0.15/0.49 (coindu1598213697e_LNil(a) != vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),sK13))),
% 0.15/0.49 inference(equality_proxy_clausification,[],[f1583])).
% 0.15/0.49 thf(f1583,plain,(
% 0.15/0.49 ($true != vAPP(coindu1593790203_llist(a),$o,vAPP(coindu1593790203_llist(a),sTfun(coindu1593790203_llist(a),$o),vEQ(coindu1593790203_llist(a)),coindu1598213697e_LNil(a)),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),sK13)))),
% 0.15/0.49 inference(definition_unfolding,[],[f1196,f1215])).
% 0.15/0.49 thf(f1196,plain,(
% 0.15/0.49 ($true != vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),sK13)))),
% 0.15/0.49 inference(cnf_transformation,[],[f1054])).
% 0.15/0.49 thf(f2316,plain,(
% 0.15/0.49 ~spl95_10),
% 0.15/0.49 inference(avatar_split_clause,[],[f2224,f2313])).
% 0.15/0.49 thf(f2313,plain,(
% 0.15/0.49 spl95_10 <=> (vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),xs) = coindu1598213697e_LNil(a))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_10])])).
% 0.15/0.49 thf(f2224,plain,(
% 0.15/0.49 (vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),xs) != coindu1598213697e_LNil(a))),
% 0.15/0.49 inference(equality_proxy_clausification,[],[f1586])).
% 0.15/0.49 thf(f1586,plain,(
% 0.15/0.49 ($true != vAPP(coindu1593790203_llist(a),$o,vAPP(coindu1593790203_llist(a),sTfun(coindu1593790203_llist(a),$o),vEQ(coindu1593790203_llist(a)),coindu1598213697e_LNil(a)),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),xs)))),
% 0.15/0.49 inference(definition_unfolding,[],[f1198,f1215])).
% 0.15/0.49 thf(f1198,plain,(
% 0.15/0.49 (vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),xs)) != $true)),
% 0.15/0.49 inference(cnf_transformation,[],[f729])).
% 0.15/0.49 thf(f729,plain,(
% 0.15/0.49 (vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),xs)) != $true)),
% 0.15/0.49 inference(flattening,[],[f275])).
% 0.15/0.49 thf(f275,plain,(
% 0.15/0.49 ~(vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),xs)) = $true)),
% 0.15/0.49 inference(fool_elimination,[],[f274])).
% 0.15/0.49 thf(f274,plain,(
% 0.15/0.49 ~vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),xs))),
% 0.15/0.49 inference(rectify,[],[f12])).
% 0.15/0.49 thf(f12,axiom,(
% 0.15/0.49 ~vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),xs))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11__092_060open_062_092_060not_062_Alnull_A_Iltl_Axs_J_092_060close_062)).
% 0.15/0.49 thf(f2309,plain,(
% 0.15/0.49 ~spl95_9 | spl95_8),
% 0.15/0.49 inference(avatar_split_clause,[],[f2304,f2299,f2306])).
% 0.15/0.49 thf(f2299,plain,(
% 0.15/0.49 spl95_8 <=> (vAPP(a,$o,vAPP(a,sTfun(a,$o),less_eq,vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya))),vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya)))) = $true)),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_8])])).
% 0.15/0.49 thf(f2304,plain,(
% 0.15/0.49 (vAPP(a,$o,vAPP(a,sTfun(a,$o),less_eq,vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),xs)),vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),xs))) != $true) | spl95_8),
% 0.15/0.49 inference(forward_demodulation,[],[f2303,f1192])).
% 0.15/0.49 thf(f2303,plain,(
% 0.15/0.49 ($true != vAPP(a,$o,vAPP(a,sTfun(a,$o),less_eq,vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya))),vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),xs)))) | spl95_8),
% 0.15/0.49 inference(forward_demodulation,[],[f2301,f1193])).
% 0.15/0.49 thf(f1193,plain,(
% 0.15/0.49 (vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),xs)) = vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya))))),
% 0.15/0.49 inference(cnf_transformation,[],[f6])).
% 0.15/0.49 thf(f6,axiom,(
% 0.15/0.49 (vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),xs)) = vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya))))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__092_060open_062lhd_A_Iltl_A_IlSup_AY_J_J_A_061_Alhd_A_Iltl_Axs_J_092_060close_062)).
% 0.15/0.49 thf(f2301,plain,(
% 0.15/0.49 (vAPP(a,$o,vAPP(a,sTfun(a,$o),less_eq,vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya))),vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya)))) != $true) | spl95_8),
% 0.15/0.49 inference(avatar_component_clause,[],[f2299])).
% 0.15/0.49 thf(f2302,plain,(
% 0.15/0.49 ~spl95_8),
% 0.15/0.49 inference(avatar_split_clause,[],[f1191,f2299])).
% 0.15/0.49 thf(f1191,plain,(
% 0.15/0.49 (vAPP(a,$o,vAPP(a,sTfun(a,$o),less_eq,vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya))),vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya)))) != $true)),
% 0.15/0.49 inference(cnf_transformation,[],[f726])).
% 0.15/0.49 thf(f726,plain,(
% 0.15/0.49 (vAPP(a,$o,vAPP(a,sTfun(a,$o),less_eq,vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya))),vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya)))) != $true)),
% 0.15/0.49 inference(flattening,[],[f269])).
% 0.15/0.49 thf(f269,plain,(
% 0.15/0.49 ~(vAPP(a,$o,vAPP(a,sTfun(a,$o),less_eq,vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya))),vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya)))) = $true)),
% 0.15/0.49 inference(fool_elimination,[],[f268])).
% 0.15/0.49 thf(f268,plain,(
% 0.15/0.49 ~vAPP(a,$o,vAPP(a,sTfun(a,$o),less_eq,vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya))),vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya))))),
% 0.15/0.49 inference(rectify,[],[f265])).
% 0.15/0.49 thf(f265,negated_conjecture,(
% 0.15/0.49 ~vAPP(a,$o,vAPP(a,sTfun(a,$o),less_eq,vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya))),vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya))))),
% 0.15/0.49 inference(negated_conjecture,[],[f264])).
% 0.15/0.49 thf(f264,conjecture,(
% 0.15/0.49 vAPP(a,$o,vAPP(a,sTfun(a,$o),less_eq,vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya))),vAPP(coindu1593790203_llist(a),a,coindu1046438764le_lhd(a),vAPP(coindu1593790203_llist(a),coindu1593790203_llist(a),coindu1047225960le_ltl(a),vAPP(set(coindu1593790203_llist(a)),coindu1593790203_llist(a),coindu526335360e_lSup(a),ya))))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.15/0.49 thf(f2297,plain,(
% 0.15/0.49 spl95_7),
% 0.15/0.49 inference(avatar_split_clause,[],[f1574,f2294])).
% 0.15/0.49 thf(f1574,plain,(
% 0.15/0.49 (vAPP(itself($o),$o,semilattice_inf($o),type2($o)) = $true)),
% 0.15/0.49 inference(cnf_transformation,[],[f715])).
% 0.15/0.49 thf(f715,plain,(
% 0.15/0.49 (vAPP(itself($o),$o,semilattice_inf($o),type2($o)) = $true)),
% 0.15/0.49 inference(fool_elimination,[],[f714])).
% 0.15/0.49 thf(f714,plain,(
% 0.15/0.49 vAPP(itself($o),$o,semilattice_inf($o),type2($o))),
% 0.15/0.49 inference(rectify,[],[f259])).
% 0.15/0.49 thf(f259,axiom,(
% 0.15/0.49 vAPP(itself($o),$o,semilattice_inf($o),type2($o))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osemilattice__inf_3)).
% 0.15/0.49 thf(f2292,plain,(
% 0.15/0.49 spl95_6),
% 0.15/0.49 inference(avatar_split_clause,[],[f1573,f2289])).
% 0.15/0.49 thf(f1573,plain,(
% 0.15/0.49 (vAPP(itself($o),$o,lattice($o),type2($o)) = $true)),
% 0.15/0.49 inference(cnf_transformation,[],[f713])).
% 0.15/0.49 thf(f713,plain,(
% 0.15/0.49 (vAPP(itself($o),$o,lattice($o),type2($o)) = $true)),
% 0.15/0.49 inference(fool_elimination,[],[f712])).
% 0.15/0.49 thf(f712,plain,(
% 0.15/0.49 vAPP(itself($o),$o,lattice($o),type2($o))),
% 0.15/0.49 inference(rectify,[],[f260])).
% 0.15/0.49 thf(f260,axiom,(
% 0.15/0.49 vAPP(itself($o),$o,lattice($o),type2($o))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Olattice_4)).
% 0.15/0.49 thf(f2287,plain,(
% 0.15/0.49 spl95_5),
% 0.15/0.49 inference(avatar_split_clause,[],[f1243,f2285])).
% 0.15/0.49 thf(f2285,plain,(
% 0.15/0.49 spl95_5 <=> ! [X0 : $tType] : (vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),coindu1598213697e_LNil(X0)) = $true)),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_5])])).
% 0.15/0.49 thf(f1243,plain,(
% 0.15/0.49 ( ! [X0 : $tType] : ((vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),coindu1598213697e_LNil(X0)) = $true)) )),
% 0.15/0.49 inference(cnf_transformation,[],[f355])).
% 0.15/0.49 thf(f355,plain,(
% 0.15/0.49 ! [X0 : $tType] : (vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),coindu1598213697e_LNil(X0)) = $true)),
% 0.15/0.49 inference(fool_elimination,[],[f354])).
% 0.15/0.49 thf(f354,plain,(
% 0.15/0.49 ! [X0 : $tType] : vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),coindu1598213697e_LNil(X0))),
% 0.15/0.49 inference(rectify,[],[f193])).
% 0.15/0.49 thf(f193,axiom,(
% 0.15/0.49 ! [X0 : $tType] : vAPP(coindu1593790203_llist(X0),$o,coindu6345450stinct(X0),coindu1598213697e_LNil(X0))),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_ldistinct__LNil__code)).
% 0.15/0.49 thf(f2255,plain,(
% 0.15/0.49 spl95_4),
% 0.15/0.49 inference(avatar_split_clause,[],[f267,f2253])).
% 0.15/0.49 thf(f267,plain,(
% 0.15/0.49 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.15/0.49 introduced(fool_axiom,[])).
% 0.15/0.49 thf(f2251,plain,(
% 0.15/0.49 ~spl95_3),
% 0.15/0.49 inference(avatar_split_clause,[],[f2226,f2248])).
% 0.15/0.49 thf(f2248,plain,(
% 0.15/0.49 spl95_3 <=> (coindu1598213697e_LNil(a) = sK13)),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_3])])).
% 0.15/0.49 thf(f2226,plain,(
% 0.15/0.49 (coindu1598213697e_LNil(a) != sK13)),
% 0.15/0.49 inference(equality_proxy_clausification,[],[f1584])).
% 0.15/0.49 thf(f1584,plain,(
% 0.15/0.49 ($true != vAPP(coindu1593790203_llist(a),$o,vAPP(coindu1593790203_llist(a),sTfun(coindu1593790203_llist(a),$o),vEQ(coindu1593790203_llist(a)),coindu1598213697e_LNil(a)),sK13))),
% 0.15/0.49 inference(definition_unfolding,[],[f1195,f1215])).
% 0.15/0.49 thf(f1195,plain,(
% 0.15/0.49 ($true != vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),sK13))),
% 0.15/0.49 inference(cnf_transformation,[],[f1054])).
% 0.15/0.49 thf(f2246,plain,(
% 0.15/0.49 ~spl95_2),
% 0.15/0.49 inference(avatar_split_clause,[],[f2225,f2243])).
% 0.15/0.49 thf(f2243,plain,(
% 0.15/0.49 spl95_2 <=> (xs = coindu1598213697e_LNil(a))),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_2])])).
% 0.15/0.49 thf(f2225,plain,(
% 0.15/0.49 (xs != coindu1598213697e_LNil(a))),
% 0.15/0.49 inference(equality_proxy_clausification,[],[f1585])).
% 0.15/0.49 thf(f1585,plain,(
% 0.15/0.49 ($true != vAPP(coindu1593790203_llist(a),$o,vAPP(coindu1593790203_llist(a),sTfun(coindu1593790203_llist(a),$o),vEQ(coindu1593790203_llist(a)),coindu1598213697e_LNil(a)),xs))),
% 0.15/0.49 inference(definition_unfolding,[],[f1197,f1215])).
% 0.15/0.49 thf(f1197,plain,(
% 0.15/0.49 (vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),xs) != $true)),
% 0.15/0.49 inference(cnf_transformation,[],[f728])).
% 0.15/0.49 thf(f728,plain,(
% 0.15/0.49 (vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),xs) != $true)),
% 0.15/0.49 inference(flattening,[],[f273])).
% 0.15/0.49 thf(f273,plain,(
% 0.15/0.49 ~(vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),xs) = $true)),
% 0.15/0.49 inference(fool_elimination,[],[f272])).
% 0.15/0.49 thf(f272,plain,(
% 0.15/0.49 ~vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),xs)),
% 0.15/0.49 inference(rectify,[],[f17])).
% 0.15/0.49 thf(f17,axiom,(
% 0.15/0.49 ~vAPP(coindu1593790203_llist(a),$o,coindu335574135_lnull(a),xs)),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16__092_060open_062_092_060not_062_Alnull_Axs_092_060close_062)).
% 0.15/0.49 thf(f2241,plain,(
% 0.15/0.49 ~spl95_1),
% 0.15/0.49 inference(avatar_split_clause,[],[f266,f2238])).
% 0.15/0.49 thf(f2238,plain,(
% 0.15/0.49 spl95_1 <=> ($true = $false)),
% 0.15/0.49 introduced(avatar_definition,[new_symbols(naming,[spl95_1])])).
% 0.15/0.49 thf(f266,plain,(
% 0.15/0.49 ($true != $false)),
% 0.15/0.49 introduced(fool_axiom,[])).
% 0.15/0.49 % SZS output end Proof for theBenchmark
% 0.15/0.49 % (3069)------------------------------
% 0.15/0.49 % (3069)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.49 % (3069)Termination reason: Refutation
% 0.15/0.49
% 0.15/0.49 % (3069)Memory used [KB]: 3270
% 0.15/0.49 % (3069)Time elapsed: 0.148 s
% 0.15/0.49 % (3069)Instructions burned: 347 (million)
% 0.15/0.49 % (3064)Success in time 0.179 s
%------------------------------------------------------------------------------