TSTP Solution File: SYO174^5 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SYO174^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n003.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 : Tue May 21 09:10:29 EDT 2024
% Result : Theorem 0.21s 0.43s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYO174^5 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon May 20 10:20:52 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (27592)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (27598)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.38 % (27594)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (27597)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.38 % (27595)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.14/0.38 % (27596)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.38 % (27593)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.38 % (27599)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.38 % Exception at run slice level
% 0.14/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.38 % Exception at run slice level
% 0.14/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.38 % (27596)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.38 % Exception at run slice level
% 0.14/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.38 % (27595)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.38 % Exception at run slice level
% 0.14/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.40 WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.14/0.40 % (27600)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.40 % (27601)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_476 on theBenchmark for (476ds/0Mi)
% 0.14/0.40 % (27602)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.40 WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.14/0.40 % (27603)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.40 % (27602)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.40 % Exception at run slice level
% 0.14/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.40 % (27601)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.40 % Exception at run slice level
% 0.14/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.41 WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.21/0.41 % (27604)dis+11_4:5_nm=4:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_216 on theBenchmark for (216ds/0Mi)
% 0.21/0.42 % (27598)First to succeed.
% 0.21/0.43 % (27598)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-27592"
% 0.21/0.43 % (27598)Refutation found. Thanks to Tanya!
% 0.21/0.43 % SZS status Theorem for theBenchmark
% 0.21/0.43 % SZS output start Proof for theBenchmark
% 0.21/0.43 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.43 thf(func_def_0, type, cQ: $i > $o).
% 0.21/0.43 thf(func_def_1, type, cP: $i > $o).
% 0.21/0.43 thf(func_def_2, type, cS: $i > $o).
% 0.21/0.43 thf(func_def_3, type, cR: $i > $o).
% 0.21/0.43 thf(func_def_7, type, sP0: $o).
% 0.21/0.43 thf(func_def_8, type, sP1: $o).
% 0.21/0.43 thf(func_def_9, type, sP2: $o).
% 0.21/0.43 thf(func_def_10, type, sP3: $o).
% 0.21/0.43 thf(func_def_11, type, sP4: $o).
% 0.21/0.43 thf(func_def_14, type, sK7: $i > $i).
% 0.21/0.43 thf(func_def_23, type, sK16: $i > $i).
% 0.21/0.43 thf(func_def_26, type, sK19: $i > $i).
% 0.21/0.43 thf(func_def_35, type, sK28: $i > $i).
% 0.21/0.43 thf(func_def_38, type, sK31: $i > $i).
% 0.21/0.43 thf(func_def_47, type, sK40: $i > $i).
% 0.21/0.43 thf(func_def_50, type, sK43: $i > $i).
% 0.21/0.43 thf(func_def_59, type, sK52: $i > $i).
% 0.21/0.43 thf(func_def_61, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)).
% 0.21/0.43 thf(func_def_62, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)).
% 0.21/0.43 thf(func_def_63, type, vAND: $o > $o > $o).
% 0.21/0.43 thf(func_def_64, type, vOR: $o > $o > $o).
% 0.21/0.43 thf(func_def_65, type, vIMP: $o > $o > $o).
% 0.21/0.43 thf(func_def_66, type, vNOT: $o > $o).
% 0.21/0.43 thf(func_def_67, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)).
% 0.21/0.43 thf(f1417,plain,(
% 0.21/0.43 $false),
% 0.21/0.43 inference(avatar_sat_refutation,[],[f192,f193,f194,f195,f210,f214,f222,f223,f239,f247,f248,f249,f258,f263,f268,f269,f281,f285,f286,f287,f302,f306,f314,f315,f331,f339,f340,f341,f350,f355,f360,f361,f373,f377,f378,f379,f390,f394,f399,f400,f413,f421,f422,f423,f432,f437,f442,f443,f455,f459,f460,f461,f472,f476,f481,f482,f495,f503,f504,f505,f514,f519,f524,f525,f537,f541,f542,f543,f544,f545,f546,f547,f600,f605,f614,f616,f618,f620,f629,f632,f635,f640,f644,f651,f671,f701,f720,f753,f755,f757,f759,f766,f787,f790,f805,f809,f821,f823,f828,f838,f847,f851,f861,f875,f880,f902,f904,f907,f913,f928,f934,f957,f967,f969,f974,f1001,f1011,f1017,f1018,f1026,f1067,f1083,f1085,f1101,f1103,f1104,f1111,f1116,f1119,f1127,f1167,f1182,f1192,f1225,f1228,f1233,f1242,f1245,f1320,f1323,f1361,f1404,f1406,f1416])).
% 0.21/0.43 thf(f1416,plain,(
% 0.21/0.43 ~spl53_31 | ~spl53_67),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1415])).
% 0.21/0.43 thf(f1415,plain,(
% 0.21/0.43 $false | (~spl53_31 | ~spl53_67)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1409])).
% 0.21/0.43 thf(f1409,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_31 | ~spl53_67)),
% 0.21/0.43 inference(superposition,[],[f1408,f313])).
% 0.21/0.43 thf(f313,plain,(
% 0.21/0.43 ( ! [X2 : $i] : (($true = vAPP($i,$o,cP,X2))) ) | ~spl53_31),
% 0.21/0.43 inference(avatar_component_clause,[],[f312])).
% 0.21/0.43 thf(f312,plain,(
% 0.21/0.43 spl53_31 <=> ! [X2] : ($true = vAPP($i,$o,cP,X2))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_31])])).
% 0.21/0.43 thf(f1408,plain,(
% 0.21/0.43 ( ! [X4 : $i] : (($false = vAPP($i,$o,cP,vAPP($i,$i,sK43,X4)))) ) | (~spl53_31 | ~spl53_67)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1407])).
% 0.21/0.43 thf(f1407,plain,(
% 0.21/0.43 ( ! [X4 : $i] : (($true = $false) | ($false = vAPP($i,$o,cP,vAPP($i,$i,sK43,X4)))) ) | (~spl53_31 | ~spl53_67)),
% 0.21/0.43 inference(forward_demodulation,[],[f475,f313])).
% 0.21/0.43 thf(f475,plain,(
% 0.21/0.43 ( ! [X4 : $i] : (($false = vAPP($i,$o,cP,X4)) | ($false = vAPP($i,$o,cP,vAPP($i,$i,sK43,X4)))) ) | ~spl53_67),
% 0.21/0.43 inference(avatar_component_clause,[],[f474])).
% 0.21/0.43 thf(f474,plain,(
% 0.21/0.43 spl53_67 <=> ! [X4] : (($false = vAPP($i,$o,cP,X4)) | ($false = vAPP($i,$o,cP,vAPP($i,$i,sK43,X4))))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_67])])).
% 0.21/0.43 thf(f1406,plain,(
% 0.21/0.43 ~spl53_10 | spl53_77),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1405])).
% 0.21/0.43 thf(f1405,plain,(
% 0.21/0.43 $false | (~spl53_10 | spl53_77)),
% 0.21/0.43 inference(subsumption_resolution,[],[f522,f221])).
% 0.21/0.43 thf(f221,plain,(
% 0.21/0.43 ( ! [X2 : $i] : (($true = vAPP($i,$o,cQ,X2))) ) | ~spl53_10),
% 0.21/0.43 inference(avatar_component_clause,[],[f220])).
% 0.21/0.43 thf(f220,plain,(
% 0.21/0.43 spl53_10 <=> ! [X2] : ($true = vAPP($i,$o,cQ,X2))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_10])])).
% 0.21/0.43 thf(f522,plain,(
% 0.21/0.43 ($true != vAPP($i,$o,cQ,sK49)) | spl53_77),
% 0.21/0.43 inference(avatar_component_clause,[],[f521])).
% 0.21/0.43 thf(f521,plain,(
% 0.21/0.43 spl53_77 <=> ($true = vAPP($i,$o,cQ,sK49))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_77])])).
% 0.21/0.43 thf(f1404,plain,(
% 0.21/0.43 ~spl53_31 | spl53_76),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1403])).
% 0.21/0.43 thf(f1403,plain,(
% 0.21/0.43 $false | (~spl53_31 | spl53_76)),
% 0.21/0.43 inference(subsumption_resolution,[],[f517,f313])).
% 0.21/0.43 thf(f517,plain,(
% 0.21/0.43 ($true != vAPP($i,$o,cP,sK47)) | spl53_76),
% 0.21/0.43 inference(avatar_component_clause,[],[f516])).
% 0.21/0.43 thf(f516,plain,(
% 0.21/0.43 spl53_76 <=> ($true = vAPP($i,$o,cP,sK47))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_76])])).
% 0.21/0.43 thf(f1361,plain,(
% 0.21/0.43 spl53_20 | ~spl53_31),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1360])).
% 0.21/0.43 thf(f1360,plain,(
% 0.21/0.43 $false | (spl53_20 | ~spl53_31)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1356])).
% 0.21/0.43 thf(f1356,plain,(
% 0.21/0.43 ($true != $true) | (spl53_20 | ~spl53_31)),
% 0.21/0.43 inference(superposition,[],[f266,f313])).
% 0.21/0.43 thf(f266,plain,(
% 0.21/0.43 ($true != vAPP($i,$o,cP,sK13)) | spl53_20),
% 0.21/0.43 inference(avatar_component_clause,[],[f265])).
% 0.21/0.43 thf(f265,plain,(
% 0.21/0.43 spl53_20 <=> ($true = vAPP($i,$o,cP,sK13))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_20])])).
% 0.21/0.43 thf(f1323,plain,(
% 0.21/0.43 ~spl53_55 | ~spl53_80),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1322])).
% 0.21/0.43 thf(f1322,plain,(
% 0.21/0.43 $false | (~spl53_55 | ~spl53_80)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1321])).
% 0.21/0.43 thf(f1321,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_55 | ~spl53_80)),
% 0.21/0.43 inference(forward_demodulation,[],[f536,f420])).
% 0.21/0.43 thf(f420,plain,(
% 0.21/0.43 ( ! [X11 : $i] : (($false = vAPP($i,$o,cQ,X11))) ) | ~spl53_55),
% 0.21/0.43 inference(avatar_component_clause,[],[f419])).
% 0.21/0.43 thf(f419,plain,(
% 0.21/0.43 spl53_55 <=> ! [X11] : ($false = vAPP($i,$o,cQ,X11))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_55])])).
% 0.21/0.43 thf(f536,plain,(
% 0.21/0.43 ($true = vAPP($i,$o,cQ,sK50)) | ~spl53_80),
% 0.21/0.43 inference(avatar_component_clause,[],[f534])).
% 0.21/0.43 thf(f534,plain,(
% 0.21/0.43 spl53_80 <=> ($true = vAPP($i,$o,cQ,sK50))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_80])])).
% 0.21/0.43 thf(f1320,plain,(
% 0.21/0.43 ~spl53_55 | ~spl53_71),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1319])).
% 0.21/0.43 thf(f1319,plain,(
% 0.21/0.43 $false | (~spl53_55 | ~spl53_71)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1318])).
% 0.21/0.43 thf(f1318,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_55 | ~spl53_71)),
% 0.21/0.43 inference(forward_demodulation,[],[f494,f420])).
% 0.21/0.43 thf(f494,plain,(
% 0.21/0.43 ($true = vAPP($i,$o,cQ,sK44)) | ~spl53_71),
% 0.21/0.43 inference(avatar_component_clause,[],[f492])).
% 0.21/0.43 thf(f492,plain,(
% 0.21/0.43 spl53_71 <=> ($true = vAPP($i,$o,cQ,sK44))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_71])])).
% 0.21/0.43 thf(f1245,plain,(
% 0.21/0.43 ~spl53_14 | ~spl53_73),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1244])).
% 0.21/0.43 thf(f1244,plain,(
% 0.21/0.43 $false | (~spl53_14 | ~spl53_73)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1243])).
% 0.21/0.43 thf(f1243,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_14 | ~spl53_73)),
% 0.21/0.43 inference(forward_demodulation,[],[f238,f502])).
% 0.21/0.43 thf(f502,plain,(
% 0.21/0.43 ( ! [X11 : $i] : (($false = vAPP($i,$o,cP,X11))) ) | ~spl53_73),
% 0.21/0.43 inference(avatar_component_clause,[],[f501])).
% 0.21/0.43 thf(f501,plain,(
% 0.21/0.43 spl53_73 <=> ! [X11] : ($false = vAPP($i,$o,cP,X11))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_73])])).
% 0.21/0.43 thf(f238,plain,(
% 0.21/0.43 ($true = vAPP($i,$o,cP,sK8)) | ~spl53_14),
% 0.21/0.43 inference(avatar_component_clause,[],[f236])).
% 0.21/0.43 thf(f236,plain,(
% 0.21/0.43 spl53_14 <=> ($true = vAPP($i,$o,cP,sK8))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_14])])).
% 0.21/0.43 thf(f1242,plain,(
% 0.21/0.43 ~spl53_64 | ~spl53_73),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1241])).
% 0.21/0.43 thf(f1241,plain,(
% 0.21/0.43 $false | (~spl53_64 | ~spl53_73)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1240])).
% 0.21/0.43 thf(f1240,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_64 | ~spl53_73)),
% 0.21/0.43 inference(forward_demodulation,[],[f1239,f502])).
% 0.21/0.43 thf(f1239,plain,(
% 0.21/0.43 ( ! [X4 : $i] : (($true = vAPP($i,$o,cP,vAPP($i,$i,sK43,X4)))) ) | (~spl53_64 | ~spl53_73)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1238])).
% 0.21/0.43 thf(f1238,plain,(
% 0.21/0.43 ( ! [X4 : $i] : (($true = $false) | ($true = vAPP($i,$o,cP,vAPP($i,$i,sK43,X4)))) ) | (~spl53_64 | ~spl53_73)),
% 0.21/0.43 inference(forward_demodulation,[],[f464,f502])).
% 0.21/0.43 thf(f464,plain,(
% 0.21/0.43 ( ! [X4 : $i] : (($true = vAPP($i,$o,cP,X4)) | ($true = vAPP($i,$o,cP,vAPP($i,$i,sK43,X4)))) ) | ~spl53_64),
% 0.21/0.43 inference(avatar_component_clause,[],[f463])).
% 0.21/0.43 thf(f463,plain,(
% 0.21/0.43 spl53_64 <=> ! [X4] : (($true = vAPP($i,$o,cP,X4)) | ($true = vAPP($i,$o,cP,vAPP($i,$i,sK43,X4))))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_64])])).
% 0.21/0.43 thf(f1233,plain,(
% 0.21/0.43 ~spl53_46 | ~spl53_55),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1232])).
% 0.21/0.43 thf(f1232,plain,(
% 0.21/0.43 $false | (~spl53_46 | ~spl53_55)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1231])).
% 0.21/0.43 thf(f1231,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_46 | ~spl53_55)),
% 0.21/0.43 inference(forward_demodulation,[],[f1230,f420])).
% 0.21/0.43 thf(f1230,plain,(
% 0.21/0.43 ( ! [X4 : $i] : (($true = vAPP($i,$o,cQ,X4))) ) | (~spl53_46 | ~spl53_55)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1229])).
% 0.21/0.43 thf(f1229,plain,(
% 0.21/0.43 ( ! [X4 : $i] : (($true = $false) | ($true = vAPP($i,$o,cQ,X4))) ) | (~spl53_46 | ~spl53_55)),
% 0.21/0.43 inference(forward_demodulation,[],[f382,f420])).
% 0.21/0.43 thf(f382,plain,(
% 0.21/0.43 ( ! [X4 : $i] : (($true = vAPP($i,$o,cQ,vAPP($i,$i,sK31,X4))) | ($true = vAPP($i,$o,cQ,X4))) ) | ~spl53_46),
% 0.21/0.43 inference(avatar_component_clause,[],[f381])).
% 0.21/0.43 thf(f381,plain,(
% 0.21/0.43 spl53_46 <=> ! [X4] : (($true = vAPP($i,$o,cQ,X4)) | ($true = vAPP($i,$o,cQ,vAPP($i,$i,sK31,X4))))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_46])])).
% 0.21/0.43 thf(f1228,plain,(
% 0.21/0.43 ~spl53_55 | ~spl53_68),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1227])).
% 0.21/0.43 thf(f1227,plain,(
% 0.21/0.43 $false | (~spl53_55 | ~spl53_68)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1226])).
% 0.21/0.43 thf(f1226,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_55 | ~spl53_68)),
% 0.21/0.43 inference(forward_demodulation,[],[f480,f420])).
% 0.21/0.43 thf(f480,plain,(
% 0.21/0.43 ($true = vAPP($i,$o,cQ,sK42)) | ~spl53_68),
% 0.21/0.43 inference(avatar_component_clause,[],[f478])).
% 0.21/0.43 thf(f478,plain,(
% 0.21/0.43 spl53_68 <=> ($true = vAPP($i,$o,cQ,sK42))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_68])])).
% 0.21/0.43 thf(f1225,plain,(
% 0.21/0.43 ~spl53_9 | ~spl53_73),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1224])).
% 0.21/0.43 thf(f1224,plain,(
% 0.21/0.43 $false | (~spl53_9 | ~spl53_73)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1217])).
% 0.21/0.43 thf(f1217,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_9 | ~spl53_73)),
% 0.21/0.43 inference(backward_demodulation,[],[f218,f502])).
% 0.21/0.43 thf(f218,plain,(
% 0.21/0.43 ($true = vAPP($i,$o,cP,sK6)) | ~spl53_9),
% 0.21/0.43 inference(avatar_component_clause,[],[f216])).
% 0.21/0.43 thf(f216,plain,(
% 0.21/0.43 spl53_9 <=> ($true = vAPP($i,$o,cP,sK6))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_9])])).
% 0.21/0.43 thf(f1192,plain,(
% 0.21/0.43 ~spl53_16 | ~spl53_30),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1191])).
% 0.21/0.43 thf(f1191,plain,(
% 0.21/0.43 $false | (~spl53_16 | ~spl53_30)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1190])).
% 0.21/0.43 thf(f1190,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_16 | ~spl53_30)),
% 0.21/0.43 inference(forward_demodulation,[],[f310,f246])).
% 0.21/0.43 thf(f246,plain,(
% 0.21/0.43 ( ! [X11 : $i] : (($false = vAPP($i,$o,cS,X11))) ) | ~spl53_16),
% 0.21/0.43 inference(avatar_component_clause,[],[f245])).
% 0.21/0.43 thf(f245,plain,(
% 0.21/0.43 spl53_16 <=> ! [X11] : ($false = vAPP($i,$o,cS,X11))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_16])])).
% 0.21/0.43 thf(f310,plain,(
% 0.21/0.43 ($true = vAPP($i,$o,cS,sK18)) | ~spl53_30),
% 0.21/0.43 inference(avatar_component_clause,[],[f308])).
% 0.21/0.43 thf(f308,plain,(
% 0.21/0.43 spl53_30 <=> ($true = vAPP($i,$o,cS,sK18))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_30])])).
% 0.21/0.43 thf(f1182,plain,(
% 0.21/0.43 ~spl53_11 | ~spl53_15),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1181])).
% 0.21/0.43 thf(f1181,plain,(
% 0.21/0.43 $false | (~spl53_11 | ~spl53_15)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1180])).
% 0.21/0.43 thf(f1180,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_11 | ~spl53_15)),
% 0.21/0.43 inference(forward_demodulation,[],[f243,f227])).
% 0.21/0.43 thf(f227,plain,(
% 0.21/0.43 ($false = vAPP($i,$o,cS,sK10)) | ~spl53_11),
% 0.21/0.43 inference(avatar_component_clause,[],[f225])).
% 0.21/0.43 thf(f225,plain,(
% 0.21/0.43 spl53_11 <=> ($false = vAPP($i,$o,cS,sK10))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_11])])).
% 0.21/0.43 thf(f243,plain,(
% 0.21/0.43 ($true = vAPP($i,$o,cS,sK10)) | ~spl53_15),
% 0.21/0.43 inference(avatar_component_clause,[],[f241])).
% 0.21/0.43 thf(f241,plain,(
% 0.21/0.43 spl53_15 <=> ($true = vAPP($i,$o,cS,sK10))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_15])])).
% 0.21/0.43 thf(f1167,plain,(
% 0.21/0.43 ~spl53_55 | ~spl53_77),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1166])).
% 0.21/0.43 thf(f1166,plain,(
% 0.21/0.43 $false | (~spl53_55 | ~spl53_77)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1165])).
% 0.21/0.43 thf(f1165,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_55 | ~spl53_77)),
% 0.21/0.43 inference(forward_demodulation,[],[f523,f420])).
% 0.21/0.43 thf(f523,plain,(
% 0.21/0.43 ($true = vAPP($i,$o,cQ,sK49)) | ~spl53_77),
% 0.21/0.43 inference(avatar_component_clause,[],[f521])).
% 0.21/0.43 thf(f1127,plain,(
% 0.21/0.43 ~spl53_20 | ~spl53_73),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1126])).
% 0.21/0.43 thf(f1126,plain,(
% 0.21/0.43 $false | (~spl53_20 | ~spl53_73)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1125])).
% 0.21/0.43 thf(f1125,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_20 | ~spl53_73)),
% 0.21/0.43 inference(forward_demodulation,[],[f267,f502])).
% 0.21/0.43 thf(f267,plain,(
% 0.21/0.43 ($true = vAPP($i,$o,cP,sK13)) | ~spl53_20),
% 0.21/0.43 inference(avatar_component_clause,[],[f265])).
% 0.21/0.43 thf(f1119,plain,(
% 0.21/0.43 ~spl53_25 | ~spl53_37),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1118])).
% 0.21/0.43 thf(f1118,plain,(
% 0.21/0.43 $false | (~spl53_25 | ~spl53_37)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1117])).
% 0.21/0.43 thf(f1117,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_25 | ~spl53_37)),
% 0.21/0.43 inference(forward_demodulation,[],[f1112,f338])).
% 0.21/0.43 thf(f338,plain,(
% 0.21/0.43 ( ! [X11 : $i] : (($false = vAPP($i,$o,cR,X11))) ) | ~spl53_37),
% 0.21/0.43 inference(avatar_component_clause,[],[f337])).
% 0.21/0.43 thf(f337,plain,(
% 0.21/0.43 spl53_37 <=> ! [X11] : ($false = vAPP($i,$o,cR,X11))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_37])])).
% 0.21/0.43 thf(f1112,plain,(
% 0.21/0.43 ( ! [X4 : $i] : (($true = vAPP($i,$o,cR,vAPP($i,$i,sK19,X4)))) ) | (~spl53_25 | ~spl53_37)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1106])).
% 0.21/0.43 thf(f1106,plain,(
% 0.21/0.43 ( ! [X4 : $i] : (($true = $false) | ($true = vAPP($i,$o,cR,vAPP($i,$i,sK19,X4)))) ) | (~spl53_25 | ~spl53_37)),
% 0.21/0.43 inference(backward_demodulation,[],[f290,f338])).
% 0.21/0.43 thf(f290,plain,(
% 0.21/0.43 ( ! [X4 : $i] : (($true = vAPP($i,$o,cR,vAPP($i,$i,sK19,X4))) | ($true = vAPP($i,$o,cR,X4))) ) | ~spl53_25),
% 0.21/0.43 inference(avatar_component_clause,[],[f289])).
% 0.21/0.43 thf(f289,plain,(
% 0.21/0.43 spl53_25 <=> ! [X4] : (($true = vAPP($i,$o,cR,X4)) | ($true = vAPP($i,$o,cR,vAPP($i,$i,sK19,X4))))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_25])])).
% 0.21/0.43 thf(f1116,plain,(
% 0.21/0.43 ~spl53_37 | ~spl53_42),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1115])).
% 0.21/0.43 thf(f1115,plain,(
% 0.21/0.43 $false | (~spl53_37 | ~spl53_42)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1114])).
% 0.21/0.43 thf(f1114,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_37 | ~spl53_42)),
% 0.21/0.43 inference(forward_demodulation,[],[f1113,f338])).
% 0.21/0.43 thf(f1113,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($true = vAPP($i,$o,cR,vAPP($i,$i,sK28,X22)))) ) | (~spl53_37 | ~spl53_42)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1105])).
% 0.21/0.43 thf(f1105,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($true = $false) | ($true = vAPP($i,$o,cR,vAPP($i,$i,sK28,X22)))) ) | (~spl53_37 | ~spl53_42)),
% 0.21/0.43 inference(backward_demodulation,[],[f364,f338])).
% 0.21/0.43 thf(f364,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($true = vAPP($i,$o,cR,vAPP($i,$i,sK28,X22))) | ($true = vAPP($i,$o,cR,X22))) ) | ~spl53_42),
% 0.21/0.43 inference(avatar_component_clause,[],[f363])).
% 0.21/0.43 thf(f363,plain,(
% 0.21/0.43 spl53_42 <=> ! [X22] : (($true = vAPP($i,$o,cR,X22)) | ($true = vAPP($i,$o,cR,vAPP($i,$i,sK28,X22))))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_42])])).
% 0.21/0.43 thf(f1111,plain,(
% 0.21/0.43 ~spl53_37 | ~spl53_53),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1110])).
% 0.21/0.43 thf(f1110,plain,(
% 0.21/0.43 $false | (~spl53_37 | ~spl53_53)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1107])).
% 0.21/0.43 thf(f1107,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_37 | ~spl53_53)),
% 0.21/0.43 inference(backward_demodulation,[],[f412,f338])).
% 0.21/0.43 thf(f412,plain,(
% 0.21/0.43 ($true = vAPP($i,$o,cR,sK32)) | ~spl53_53),
% 0.21/0.43 inference(avatar_component_clause,[],[f410])).
% 0.21/0.43 thf(f410,plain,(
% 0.21/0.43 spl53_53 <=> ($true = vAPP($i,$o,cR,sK32))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_53])])).
% 0.21/0.43 thf(f1104,plain,(
% 0.21/0.43 spl53_55 | ~spl53_65),
% 0.21/0.43 inference(avatar_split_clause,[],[f1081,f466,f419])).
% 0.21/0.43 thf(f466,plain,(
% 0.21/0.43 spl53_65 <=> ! [X1] : (vAPP($i,$o,cQ,X1) != $true)),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_65])])).
% 0.21/0.43 thf(f1081,plain,(
% 0.21/0.43 ( ! [X0 : $i] : ((vAPP($i,$o,cQ,X0) = $false)) ) | ~spl53_65),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1080])).
% 0.21/0.43 thf(f1080,plain,(
% 0.21/0.43 ( ! [X0 : $i] : (($true != $true) | (vAPP($i,$o,cQ,X0) = $false)) ) | ~spl53_65),
% 0.21/0.43 inference(superposition,[],[f467,f4])).
% 0.21/0.43 thf(f4,plain,(
% 0.21/0.43 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.21/0.43 introduced(fool_axiom,[])).
% 0.21/0.43 thf(f467,plain,(
% 0.21/0.43 ( ! [X1 : $i] : ((vAPP($i,$o,cQ,X1) != $true)) ) | ~spl53_65),
% 0.21/0.43 inference(avatar_component_clause,[],[f466])).
% 0.21/0.43 thf(f1103,plain,(
% 0.21/0.43 ~spl53_60 | ~spl53_65),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1102])).
% 0.21/0.43 thf(f1102,plain,(
% 0.21/0.43 $false | (~spl53_60 | ~spl53_65)),
% 0.21/0.43 inference(subsumption_resolution,[],[f1098,f467])).
% 0.21/0.43 thf(f1098,plain,(
% 0.21/0.43 ( ! [X0 : $i] : ((vAPP($i,$o,cQ,X0) = $true)) ) | (~spl53_60 | ~spl53_65)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1070])).
% 0.21/0.43 thf(f1070,plain,(
% 0.21/0.43 ( ! [X0 : $i] : (($true != $true) | (vAPP($i,$o,cQ,X0) = $true)) ) | (~spl53_60 | ~spl53_65)),
% 0.21/0.43 inference(superposition,[],[f467,f446])).
% 0.21/0.43 thf(f446,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($true = vAPP($i,$o,cQ,vAPP($i,$i,sK40,X22))) | ($true = vAPP($i,$o,cQ,X22))) ) | ~spl53_60),
% 0.21/0.43 inference(avatar_component_clause,[],[f445])).
% 0.21/0.43 thf(f445,plain,(
% 0.21/0.43 spl53_60 <=> ! [X22] : (($true = vAPP($i,$o,cQ,X22)) | ($true = vAPP($i,$o,cQ,vAPP($i,$i,sK40,X22))))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_60])])).
% 0.21/0.43 thf(f1101,plain,(
% 0.21/0.43 ~spl53_46 | ~spl53_65),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1100])).
% 0.21/0.43 thf(f1100,plain,(
% 0.21/0.43 $false | (~spl53_46 | ~spl53_65)),
% 0.21/0.43 inference(subsumption_resolution,[],[f1099,f467])).
% 0.21/0.43 thf(f1099,plain,(
% 0.21/0.43 ( ! [X0 : $i] : ((vAPP($i,$o,cQ,X0) = $true)) ) | (~spl53_46 | ~spl53_65)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1069])).
% 0.21/0.43 thf(f1069,plain,(
% 0.21/0.43 ( ! [X0 : $i] : (($true != $true) | (vAPP($i,$o,cQ,X0) = $true)) ) | (~spl53_46 | ~spl53_65)),
% 0.21/0.43 inference(superposition,[],[f467,f382])).
% 0.21/0.43 thf(f1085,plain,(
% 0.21/0.43 ~spl53_65 | ~spl53_77),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1084])).
% 0.21/0.43 thf(f1084,plain,(
% 0.21/0.43 $false | (~spl53_65 | ~spl53_77)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1078])).
% 0.21/0.43 thf(f1078,plain,(
% 0.21/0.43 ($true != $true) | (~spl53_65 | ~spl53_77)),
% 0.21/0.43 inference(superposition,[],[f467,f523])).
% 0.21/0.43 thf(f1083,plain,(
% 0.21/0.43 ~spl53_65 | ~spl53_80),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1082])).
% 0.21/0.43 thf(f1082,plain,(
% 0.21/0.43 $false | (~spl53_65 | ~spl53_80)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1079])).
% 0.21/0.43 thf(f1079,plain,(
% 0.21/0.43 ($true != $true) | (~spl53_65 | ~spl53_80)),
% 0.21/0.43 inference(superposition,[],[f467,f536])).
% 0.21/0.43 thf(f1067,plain,(
% 0.21/0.43 ~spl53_73 | ~spl53_78),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1066])).
% 0.21/0.43 thf(f1066,plain,(
% 0.21/0.43 $false | (~spl53_73 | ~spl53_78)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1065])).
% 0.21/0.43 thf(f1065,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_73 | ~spl53_78)),
% 0.21/0.43 inference(forward_demodulation,[],[f1064,f502])).
% 0.21/0.43 thf(f1064,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($true = vAPP($i,$o,cP,vAPP($i,$i,sK52,X22)))) ) | (~spl53_73 | ~spl53_78)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1063])).
% 0.21/0.43 thf(f1063,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($true = $false) | ($true = vAPP($i,$o,cP,vAPP($i,$i,sK52,X22)))) ) | (~spl53_73 | ~spl53_78)),
% 0.21/0.43 inference(forward_demodulation,[],[f528,f502])).
% 0.21/0.43 thf(f528,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($true = vAPP($i,$o,cP,X22)) | ($true = vAPP($i,$o,cP,vAPP($i,$i,sK52,X22)))) ) | ~spl53_78),
% 0.21/0.43 inference(avatar_component_clause,[],[f527])).
% 0.21/0.43 thf(f527,plain,(
% 0.21/0.43 spl53_78 <=> ! [X22] : (($true = vAPP($i,$o,cP,X22)) | ($true = vAPP($i,$o,cP,vAPP($i,$i,sK52,X22))))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_78])])).
% 0.21/0.43 thf(f1026,plain,(
% 0.21/0.43 ~spl53_73 | spl53_74),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1025])).
% 0.21/0.43 thf(f1025,plain,(
% 0.21/0.43 $false | (~spl53_73 | spl53_74)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1024])).
% 0.21/0.43 thf(f1024,plain,(
% 0.21/0.43 ($false != $false) | (~spl53_73 | spl53_74)),
% 0.21/0.43 inference(superposition,[],[f508,f502])).
% 0.21/0.43 thf(f508,plain,(
% 0.21/0.43 ($false != vAPP($i,$o,cP,sK47)) | spl53_74),
% 0.21/0.43 inference(avatar_component_clause,[],[f507])).
% 0.21/0.43 thf(f507,plain,(
% 0.21/0.43 spl53_74 <=> ($false = vAPP($i,$o,cP,sK47))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_74])])).
% 0.21/0.43 thf(f1018,plain,(
% 0.21/0.43 spl53_73 | ~spl53_5),
% 0.21/0.43 inference(avatar_split_clause,[],[f1009,f200,f501])).
% 0.21/0.43 thf(f200,plain,(
% 0.21/0.43 spl53_5 <=> ! [X1] : (vAPP($i,$o,cP,X1) != $true)),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_5])])).
% 0.21/0.43 thf(f1009,plain,(
% 0.21/0.43 ( ! [X0 : $i] : ((vAPP($i,$o,cP,X0) = $false)) ) | ~spl53_5),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1008])).
% 0.21/0.43 thf(f1008,plain,(
% 0.21/0.43 ( ! [X0 : $i] : (($true != $true) | (vAPP($i,$o,cP,X0) = $false)) ) | ~spl53_5),
% 0.21/0.43 inference(superposition,[],[f201,f4])).
% 0.21/0.43 thf(f201,plain,(
% 0.21/0.43 ( ! [X1 : $i] : ((vAPP($i,$o,cP,X1) != $true)) ) | ~spl53_5),
% 0.21/0.43 inference(avatar_component_clause,[],[f200])).
% 0.21/0.43 thf(f1017,plain,(
% 0.21/0.43 ~spl53_5 | ~spl53_20),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1016])).
% 0.21/0.43 thf(f1016,plain,(
% 0.21/0.43 $false | (~spl53_5 | ~spl53_20)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1002])).
% 0.21/0.43 thf(f1002,plain,(
% 0.21/0.43 ($true != $true) | (~spl53_5 | ~spl53_20)),
% 0.21/0.43 inference(superposition,[],[f201,f267])).
% 0.21/0.43 thf(f1011,plain,(
% 0.21/0.43 ~spl53_5 | ~spl53_76),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1010])).
% 0.21/0.43 thf(f1010,plain,(
% 0.21/0.43 $false | (~spl53_5 | ~spl53_76)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f1007])).
% 0.21/0.43 thf(f1007,plain,(
% 0.21/0.43 ($true != $true) | (~spl53_5 | ~spl53_76)),
% 0.21/0.43 inference(superposition,[],[f201,f518])).
% 0.21/0.43 thf(f518,plain,(
% 0.21/0.43 ($true = vAPP($i,$o,cP,sK47)) | ~spl53_76),
% 0.21/0.43 inference(avatar_component_clause,[],[f516])).
% 0.21/0.43 thf(f1001,plain,(
% 0.21/0.43 ~spl53_12 | ~spl53_24),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f1000])).
% 0.21/0.43 thf(f1000,plain,(
% 0.21/0.43 $false | (~spl53_12 | ~spl53_24)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f994])).
% 0.21/0.43 thf(f994,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_12 | ~spl53_24)),
% 0.21/0.43 inference(superposition,[],[f990,f230])).
% 0.21/0.43 thf(f230,plain,(
% 0.21/0.43 ( ! [X11 : $i] : (($true = vAPP($i,$o,cS,X11))) ) | ~spl53_12),
% 0.21/0.43 inference(avatar_component_clause,[],[f229])).
% 0.21/0.43 thf(f229,plain,(
% 0.21/0.43 spl53_12 <=> ! [X11] : ($true = vAPP($i,$o,cS,X11))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_12])])).
% 0.21/0.43 thf(f990,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($false = vAPP($i,$o,cS,vAPP($i,$i,sK16,X22)))) ) | (~spl53_12 | ~spl53_24)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f989])).
% 0.21/0.43 thf(f989,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($true = $false) | ($false = vAPP($i,$o,cS,vAPP($i,$i,sK16,X22)))) ) | (~spl53_12 | ~spl53_24)),
% 0.21/0.43 inference(forward_demodulation,[],[f284,f230])).
% 0.21/0.43 thf(f284,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($false = vAPP($i,$o,cS,X22)) | ($false = vAPP($i,$o,cS,vAPP($i,$i,sK16,X22)))) ) | ~spl53_24),
% 0.21/0.43 inference(avatar_component_clause,[],[f283])).
% 0.21/0.43 thf(f283,plain,(
% 0.21/0.43 spl53_24 <=> ! [X22] : (($false = vAPP($i,$o,cS,X22)) | ($false = vAPP($i,$o,cS,vAPP($i,$i,sK16,X22))))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_24])])).
% 0.21/0.43 thf(f974,plain,(
% 0.21/0.43 ~spl53_51 | ~spl53_54),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f973])).
% 0.21/0.43 thf(f973,plain,(
% 0.21/0.43 $false | (~spl53_51 | ~spl53_54)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f972])).
% 0.21/0.43 thf(f972,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_51 | ~spl53_54)),
% 0.21/0.43 inference(forward_demodulation,[],[f417,f404])).
% 0.21/0.43 thf(f404,plain,(
% 0.21/0.43 ($false = vAPP($i,$o,cQ,sK34)) | ~spl53_51),
% 0.21/0.43 inference(avatar_component_clause,[],[f402])).
% 0.21/0.43 thf(f402,plain,(
% 0.21/0.43 spl53_51 <=> ($false = vAPP($i,$o,cQ,sK34))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_51])])).
% 0.21/0.43 thf(f417,plain,(
% 0.21/0.43 ($true = vAPP($i,$o,cQ,sK34)) | ~spl53_54),
% 0.21/0.43 inference(avatar_component_clause,[],[f415])).
% 0.21/0.43 thf(f415,plain,(
% 0.21/0.43 spl53_54 <=> ($true = vAPP($i,$o,cQ,sK34))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_54])])).
% 0.21/0.43 thf(f969,plain,(
% 0.21/0.43 ~spl53_12 | spl53_52),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f968])).
% 0.21/0.43 thf(f968,plain,(
% 0.21/0.43 $false | (~spl53_12 | spl53_52)),
% 0.21/0.43 inference(subsumption_resolution,[],[f408,f230])).
% 0.21/0.43 thf(f408,plain,(
% 0.21/0.43 ($true != vAPP($i,$o,cS,sK33)) | spl53_52),
% 0.21/0.43 inference(avatar_component_clause,[],[f406])).
% 0.21/0.43 thf(f406,plain,(
% 0.21/0.43 spl53_52 <=> ($true = vAPP($i,$o,cS,sK33))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_52])])).
% 0.21/0.43 thf(f967,plain,(
% 0.21/0.43 ~spl53_12 | spl53_48),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f966])).
% 0.21/0.43 thf(f966,plain,(
% 0.21/0.43 $false | (~spl53_12 | spl53_48)),
% 0.21/0.43 inference(subsumption_resolution,[],[f389,f230])).
% 0.21/0.43 thf(f389,plain,(
% 0.21/0.43 ($true != vAPP($i,$o,cS,sK29)) | spl53_48),
% 0.21/0.43 inference(avatar_component_clause,[],[f387])).
% 0.21/0.43 thf(f387,plain,(
% 0.21/0.43 spl53_48 <=> ($true = vAPP($i,$o,cS,sK29))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_48])])).
% 0.21/0.43 thf(f957,plain,(
% 0.21/0.43 ~spl53_10 | ~spl53_49),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f956])).
% 0.21/0.43 thf(f956,plain,(
% 0.21/0.43 $false | (~spl53_10 | ~spl53_49)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f950])).
% 0.21/0.43 thf(f950,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_10 | ~spl53_49)),
% 0.21/0.43 inference(superposition,[],[f931,f221])).
% 0.21/0.43 thf(f931,plain,(
% 0.21/0.43 ( ! [X4 : $i] : (($false = vAPP($i,$o,cQ,vAPP($i,$i,sK31,X4)))) ) | (~spl53_10 | ~spl53_49)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f930])).
% 0.21/0.43 thf(f930,plain,(
% 0.21/0.43 ( ! [X4 : $i] : (($true = $false) | ($false = vAPP($i,$o,cQ,vAPP($i,$i,sK31,X4)))) ) | (~spl53_10 | ~spl53_49)),
% 0.21/0.43 inference(forward_demodulation,[],[f393,f221])).
% 0.21/0.43 thf(f393,plain,(
% 0.21/0.43 ( ! [X4 : $i] : (($false = vAPP($i,$o,cQ,vAPP($i,$i,sK31,X4))) | ($false = vAPP($i,$o,cQ,X4))) ) | ~spl53_49),
% 0.21/0.43 inference(avatar_component_clause,[],[f392])).
% 0.21/0.43 thf(f392,plain,(
% 0.21/0.43 spl53_49 <=> ! [X4] : (($false = vAPP($i,$o,cQ,X4)) | ($false = vAPP($i,$o,cQ,vAPP($i,$i,sK31,X4))))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_49])])).
% 0.21/0.43 thf(f934,plain,(
% 0.21/0.43 ~spl53_37 | ~spl53_59),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f933])).
% 0.21/0.43 thf(f933,plain,(
% 0.21/0.43 $false | (~spl53_37 | ~spl53_59)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f932])).
% 0.21/0.43 thf(f932,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_37 | ~spl53_59)),
% 0.21/0.43 inference(forward_demodulation,[],[f441,f338])).
% 0.21/0.43 thf(f441,plain,(
% 0.21/0.43 ($true = vAPP($i,$o,cR,sK37)) | ~spl53_59),
% 0.21/0.43 inference(avatar_component_clause,[],[f439])).
% 0.21/0.43 thf(f439,plain,(
% 0.21/0.43 spl53_59 <=> ($true = vAPP($i,$o,cR,sK37))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_59])])).
% 0.21/0.43 thf(f928,plain,(
% 0.21/0.43 ~spl53_37 | ~spl53_50),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f927])).
% 0.21/0.43 thf(f927,plain,(
% 0.21/0.43 $false | (~spl53_37 | ~spl53_50)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f926])).
% 0.21/0.43 thf(f926,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_37 | ~spl53_50)),
% 0.21/0.43 inference(forward_demodulation,[],[f398,f338])).
% 0.21/0.43 thf(f398,plain,(
% 0.21/0.43 ($true = vAPP($i,$o,cR,sK30)) | ~spl53_50),
% 0.21/0.43 inference(avatar_component_clause,[],[f396])).
% 0.21/0.43 thf(f396,plain,(
% 0.21/0.43 spl53_50 <=> ($true = vAPP($i,$o,cR,sK30))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_50])])).
% 0.21/0.43 thf(f913,plain,(
% 0.21/0.43 ~spl53_38 | ~spl53_40),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f912])).
% 0.21/0.43 thf(f912,plain,(
% 0.21/0.43 $false | (~spl53_38 | ~spl53_40)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f911])).
% 0.21/0.43 thf(f911,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_38 | ~spl53_40)),
% 0.21/0.43 inference(forward_demodulation,[],[f354,f345])).
% 0.21/0.43 thf(f345,plain,(
% 0.21/0.43 ($false = vAPP($i,$o,cR,sK23)) | ~spl53_38),
% 0.21/0.43 inference(avatar_component_clause,[],[f343])).
% 0.21/0.43 thf(f343,plain,(
% 0.21/0.43 spl53_38 <=> ($false = vAPP($i,$o,cR,sK23))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_38])])).
% 0.21/0.43 thf(f354,plain,(
% 0.21/0.43 ($true = vAPP($i,$o,cR,sK23)) | ~spl53_40),
% 0.21/0.43 inference(avatar_component_clause,[],[f352])).
% 0.21/0.43 thf(f352,plain,(
% 0.21/0.43 spl53_40 <=> ($true = vAPP($i,$o,cR,sK23))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_40])])).
% 0.21/0.43 thf(f907,plain,(
% 0.21/0.43 ~spl53_16 | ~spl53_44),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f906])).
% 0.21/0.43 thf(f906,plain,(
% 0.21/0.43 $false | (~spl53_16 | ~spl53_44)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f905])).
% 0.21/0.43 thf(f905,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_16 | ~spl53_44)),
% 0.21/0.43 inference(forward_demodulation,[],[f372,f246])).
% 0.21/0.43 thf(f372,plain,(
% 0.21/0.43 ($true = vAPP($i,$o,cS,sK26)) | ~spl53_44),
% 0.21/0.43 inference(avatar_component_clause,[],[f370])).
% 0.21/0.43 thf(f370,plain,(
% 0.21/0.43 spl53_44 <=> ($true = vAPP($i,$o,cS,sK26))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_44])])).
% 0.21/0.43 thf(f904,plain,(
% 0.21/0.43 ~spl53_31 | spl53_43),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f903])).
% 0.21/0.43 thf(f903,plain,(
% 0.21/0.43 $false | (~spl53_31 | spl53_43)),
% 0.21/0.43 inference(subsumption_resolution,[],[f368,f313])).
% 0.21/0.43 thf(f368,plain,(
% 0.21/0.43 ($true != vAPP($i,$o,cP,sK27)) | spl53_43),
% 0.21/0.43 inference(avatar_component_clause,[],[f366])).
% 0.21/0.43 thf(f366,plain,(
% 0.21/0.43 spl53_43 <=> ($true = vAPP($i,$o,cP,sK27))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_43])])).
% 0.21/0.43 thf(f902,plain,(
% 0.21/0.43 ~spl53_33 | ~spl53_45),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f901])).
% 0.21/0.43 thf(f901,plain,(
% 0.21/0.43 $false | (~spl53_33 | ~spl53_45)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f895])).
% 0.21/0.43 thf(f895,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_33 | ~spl53_45)),
% 0.21/0.43 inference(superposition,[],[f894,f322])).
% 0.21/0.43 thf(f322,plain,(
% 0.21/0.43 ( ! [X11 : $i] : (($true = vAPP($i,$o,cR,X11))) ) | ~spl53_33),
% 0.21/0.43 inference(avatar_component_clause,[],[f321])).
% 0.21/0.43 thf(f321,plain,(
% 0.21/0.43 spl53_33 <=> ! [X11] : ($true = vAPP($i,$o,cR,X11))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_33])])).
% 0.21/0.43 thf(f894,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($false = vAPP($i,$o,cR,vAPP($i,$i,sK28,X22)))) ) | (~spl53_33 | ~spl53_45)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f893])).
% 0.21/0.43 thf(f893,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($true = $false) | ($false = vAPP($i,$o,cR,vAPP($i,$i,sK28,X22)))) ) | (~spl53_33 | ~spl53_45)),
% 0.21/0.43 inference(forward_demodulation,[],[f376,f322])).
% 0.21/0.43 thf(f376,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($false = vAPP($i,$o,cR,vAPP($i,$i,sK28,X22))) | ($false = vAPP($i,$o,cR,X22))) ) | ~spl53_45),
% 0.21/0.43 inference(avatar_component_clause,[],[f375])).
% 0.21/0.43 thf(f375,plain,(
% 0.21/0.43 spl53_45 <=> ! [X22] : (($false = vAPP($i,$o,cR,X22)) | ($false = vAPP($i,$o,cR,vAPP($i,$i,sK28,X22))))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_45])])).
% 0.21/0.43 thf(f880,plain,(
% 0.21/0.43 ~spl53_16 | ~spl53_21),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f879])).
% 0.21/0.43 thf(f879,plain,(
% 0.21/0.43 $false | (~spl53_16 | ~spl53_21)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f878])).
% 0.21/0.43 thf(f878,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_16 | ~spl53_21)),
% 0.21/0.43 inference(forward_demodulation,[],[f877,f246])).
% 0.21/0.43 thf(f877,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($true = vAPP($i,$o,cS,vAPP($i,$i,sK16,X22)))) ) | (~spl53_16 | ~spl53_21)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f876])).
% 0.21/0.43 thf(f876,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($true = $false) | ($true = vAPP($i,$o,cS,vAPP($i,$i,sK16,X22)))) ) | (~spl53_16 | ~spl53_21)),
% 0.21/0.43 inference(forward_demodulation,[],[f272,f246])).
% 0.21/0.43 thf(f272,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($true = vAPP($i,$o,cS,X22)) | ($true = vAPP($i,$o,cS,vAPP($i,$i,sK16,X22)))) ) | ~spl53_21),
% 0.21/0.43 inference(avatar_component_clause,[],[f271])).
% 0.21/0.43 thf(f271,plain,(
% 0.21/0.43 spl53_21 <=> ! [X22] : (($true = vAPP($i,$o,cS,X22)) | ($true = vAPP($i,$o,cS,vAPP($i,$i,sK16,X22))))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_21])])).
% 0.21/0.43 thf(f875,plain,(
% 0.21/0.43 ~spl53_4 | ~spl53_16),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f874])).
% 0.21/0.43 thf(f874,plain,(
% 0.21/0.43 $false | (~spl53_4 | ~spl53_16)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f873])).
% 0.21/0.43 thf(f873,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_4 | ~spl53_16)),
% 0.21/0.43 inference(forward_demodulation,[],[f872,f246])).
% 0.21/0.43 thf(f872,plain,(
% 0.21/0.43 ( ! [X4 : $i] : (($true = vAPP($i,$o,cS,vAPP($i,$i,sK7,X4)))) ) | (~spl53_4 | ~spl53_16)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f871])).
% 0.21/0.43 thf(f871,plain,(
% 0.21/0.43 ( ! [X4 : $i] : (($true = $false) | ($true = vAPP($i,$o,cS,vAPP($i,$i,sK7,X4)))) ) | (~spl53_4 | ~spl53_16)),
% 0.21/0.43 inference(forward_demodulation,[],[f198,f246])).
% 0.21/0.43 thf(f198,plain,(
% 0.21/0.43 ( ! [X4 : $i] : (($true = vAPP($i,$o,cS,X4)) | ($true = vAPP($i,$o,cS,vAPP($i,$i,sK7,X4)))) ) | ~spl53_4),
% 0.21/0.43 inference(avatar_component_clause,[],[f197])).
% 0.21/0.43 thf(f197,plain,(
% 0.21/0.43 spl53_4 <=> ! [X4] : (($true = vAPP($i,$o,cS,X4)) | ($true = vAPP($i,$o,cS,vAPP($i,$i,sK7,X4))))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_4])])).
% 0.21/0.43 thf(f861,plain,(
% 0.21/0.43 ~spl53_56 | ~spl53_58),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f860])).
% 0.21/0.43 thf(f860,plain,(
% 0.21/0.43 $false | (~spl53_56 | ~spl53_58)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f859])).
% 0.21/0.43 thf(f859,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_56 | ~spl53_58)),
% 0.21/0.43 inference(forward_demodulation,[],[f436,f427])).
% 0.21/0.43 thf(f427,plain,(
% 0.21/0.43 ($false = vAPP($i,$o,cQ,sK35)) | ~spl53_56),
% 0.21/0.43 inference(avatar_component_clause,[],[f425])).
% 0.21/0.43 thf(f425,plain,(
% 0.21/0.43 spl53_56 <=> ($false = vAPP($i,$o,cQ,sK35))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_56])])).
% 0.21/0.43 thf(f436,plain,(
% 0.21/0.43 ($true = vAPP($i,$o,cQ,sK35)) | ~spl53_58),
% 0.21/0.43 inference(avatar_component_clause,[],[f434])).
% 0.21/0.43 thf(f434,plain,(
% 0.21/0.43 spl53_58 <=> ($true = vAPP($i,$o,cQ,sK35))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_58])])).
% 0.21/0.43 thf(f851,plain,(
% 0.21/0.43 ~spl53_16 | ~spl53_41),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f850])).
% 0.21/0.43 thf(f850,plain,(
% 0.21/0.43 $false | (~spl53_16 | ~spl53_41)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f849])).
% 0.21/0.43 thf(f849,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_16 | ~spl53_41)),
% 0.21/0.43 inference(forward_demodulation,[],[f359,f246])).
% 0.21/0.43 thf(f359,plain,(
% 0.21/0.43 ($true = vAPP($i,$o,cS,sK25)) | ~spl53_41),
% 0.21/0.43 inference(avatar_component_clause,[],[f357])).
% 0.21/0.43 thf(f357,plain,(
% 0.21/0.43 spl53_41 <=> ($true = vAPP($i,$o,cS,sK25))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_41])])).
% 0.21/0.43 thf(f847,plain,(
% 0.21/0.43 ~spl53_16 | ~spl53_35),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f846])).
% 0.21/0.43 thf(f846,plain,(
% 0.21/0.43 $false | (~spl53_16 | ~spl53_35)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f845])).
% 0.21/0.43 thf(f845,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_16 | ~spl53_35)),
% 0.21/0.43 inference(forward_demodulation,[],[f330,f246])).
% 0.21/0.43 thf(f330,plain,(
% 0.21/0.43 ($true = vAPP($i,$o,cS,sK20)) | ~spl53_35),
% 0.21/0.43 inference(avatar_component_clause,[],[f328])).
% 0.21/0.43 thf(f328,plain,(
% 0.21/0.43 spl53_35 <=> ($true = vAPP($i,$o,cS,sK20))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_35])])).
% 0.21/0.43 thf(f838,plain,(
% 0.21/0.43 spl53_16 | ~spl53_26),
% 0.21/0.43 inference(avatar_split_clause,[],[f835,f292,f245])).
% 0.21/0.43 thf(f292,plain,(
% 0.21/0.43 spl53_26 <=> ! [X1] : (vAPP($i,$o,cS,X1) != $true)),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_26])])).
% 0.21/0.43 thf(f835,plain,(
% 0.21/0.43 ( ! [X0 : $i] : ((vAPP($i,$o,cS,X0) = $false)) ) | ~spl53_26),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f834])).
% 0.21/0.43 thf(f834,plain,(
% 0.21/0.43 ( ! [X0 : $i] : (($true != $true) | (vAPP($i,$o,cS,X0) = $false)) ) | ~spl53_26),
% 0.21/0.43 inference(superposition,[],[f293,f4])).
% 0.21/0.43 thf(f293,plain,(
% 0.21/0.43 ( ! [X1 : $i] : ((vAPP($i,$o,cS,X1) != $true)) ) | ~spl53_26),
% 0.21/0.43 inference(avatar_component_clause,[],[f292])).
% 0.21/0.43 thf(f828,plain,(
% 0.21/0.43 ~spl53_17 | ~spl53_19),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f827])).
% 0.21/0.43 thf(f827,plain,(
% 0.21/0.43 $false | (~spl53_17 | ~spl53_19)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f826])).
% 0.21/0.43 thf(f826,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_17 | ~spl53_19)),
% 0.21/0.43 inference(forward_demodulation,[],[f262,f253])).
% 0.21/0.43 thf(f253,plain,(
% 0.21/0.43 ($false = vAPP($i,$o,cS,sK11)) | ~spl53_17),
% 0.21/0.43 inference(avatar_component_clause,[],[f251])).
% 0.21/0.43 thf(f251,plain,(
% 0.21/0.43 spl53_17 <=> ($false = vAPP($i,$o,cS,sK11))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_17])])).
% 0.21/0.43 thf(f262,plain,(
% 0.21/0.43 ($true = vAPP($i,$o,cS,sK11)) | ~spl53_19),
% 0.21/0.43 inference(avatar_component_clause,[],[f260])).
% 0.21/0.43 thf(f260,plain,(
% 0.21/0.43 spl53_19 <=> ($true = vAPP($i,$o,cS,sK11))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_19])])).
% 0.21/0.43 thf(f823,plain,(
% 0.21/0.43 spl53_27 | ~spl53_31),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f822])).
% 0.21/0.43 thf(f822,plain,(
% 0.21/0.43 $false | (spl53_27 | ~spl53_31)),
% 0.21/0.43 inference(subsumption_resolution,[],[f297,f313])).
% 0.21/0.43 thf(f297,plain,(
% 0.21/0.43 ($true != vAPP($i,$o,cP,sK17)) | spl53_27),
% 0.21/0.43 inference(avatar_component_clause,[],[f295])).
% 0.21/0.43 thf(f295,plain,(
% 0.21/0.43 spl53_27 <=> ($true = vAPP($i,$o,cP,sK17))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_27])])).
% 0.21/0.43 thf(f821,plain,(
% 0.21/0.43 ~spl53_29 | ~spl53_33),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f820])).
% 0.21/0.43 thf(f820,plain,(
% 0.21/0.43 $false | (~spl53_29 | ~spl53_33)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f814])).
% 0.21/0.43 thf(f814,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_29 | ~spl53_33)),
% 0.21/0.43 inference(superposition,[],[f813,f322])).
% 0.21/0.43 thf(f813,plain,(
% 0.21/0.43 ( ! [X4 : $i] : (($false = vAPP($i,$o,cR,vAPP($i,$i,sK19,X4)))) ) | (~spl53_29 | ~spl53_33)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f812])).
% 0.21/0.43 thf(f812,plain,(
% 0.21/0.43 ( ! [X4 : $i] : (($true = $false) | ($false = vAPP($i,$o,cR,vAPP($i,$i,sK19,X4)))) ) | (~spl53_29 | ~spl53_33)),
% 0.21/0.43 inference(forward_demodulation,[],[f305,f322])).
% 0.21/0.43 thf(f305,plain,(
% 0.21/0.43 ( ! [X4 : $i] : (($false = vAPP($i,$o,cR,vAPP($i,$i,sK19,X4))) | ($false = vAPP($i,$o,cR,X4))) ) | ~spl53_29),
% 0.21/0.43 inference(avatar_component_clause,[],[f304])).
% 0.21/0.43 thf(f304,plain,(
% 0.21/0.43 spl53_29 <=> ! [X4] : (($false = vAPP($i,$o,cR,X4)) | ($false = vAPP($i,$o,cR,vAPP($i,$i,sK19,X4))))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_29])])).
% 0.21/0.43 thf(f809,plain,(
% 0.21/0.43 ~spl53_31 | spl53_39),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f808])).
% 0.21/0.43 thf(f808,plain,(
% 0.21/0.43 $false | (~spl53_31 | spl53_39)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f806])).
% 0.21/0.43 thf(f806,plain,(
% 0.21/0.43 ($true != $true) | (~spl53_31 | spl53_39)),
% 0.21/0.43 inference(superposition,[],[f349,f313])).
% 0.21/0.43 thf(f349,plain,(
% 0.21/0.43 ($true != vAPP($i,$o,cP,sK24)) | spl53_39),
% 0.21/0.43 inference(avatar_component_clause,[],[f347])).
% 0.21/0.43 thf(f347,plain,(
% 0.21/0.43 spl53_39 <=> ($true = vAPP($i,$o,cP,sK24))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_39])])).
% 0.21/0.43 thf(f805,plain,(
% 0.21/0.43 ~spl53_74 | ~spl53_76),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f804])).
% 0.21/0.43 thf(f804,plain,(
% 0.21/0.43 $false | (~spl53_74 | ~spl53_76)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f803])).
% 0.21/0.43 thf(f803,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_74 | ~spl53_76)),
% 0.21/0.43 inference(forward_demodulation,[],[f518,f509])).
% 0.21/0.43 thf(f509,plain,(
% 0.21/0.43 ($false = vAPP($i,$o,cP,sK47)) | ~spl53_74),
% 0.21/0.43 inference(avatar_component_clause,[],[f507])).
% 0.21/0.43 thf(f790,plain,(
% 0.21/0.43 ~spl53_69 | ~spl53_72),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f789])).
% 0.21/0.43 thf(f789,plain,(
% 0.21/0.43 $false | (~spl53_69 | ~spl53_72)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f788])).
% 0.21/0.43 thf(f788,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_69 | ~spl53_72)),
% 0.21/0.43 inference(forward_demodulation,[],[f499,f486])).
% 0.21/0.43 thf(f486,plain,(
% 0.21/0.43 ($false = vAPP($i,$o,cP,sK46)) | ~spl53_69),
% 0.21/0.43 inference(avatar_component_clause,[],[f484])).
% 0.21/0.43 thf(f484,plain,(
% 0.21/0.43 spl53_69 <=> ($false = vAPP($i,$o,cP,sK46))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_69])])).
% 0.21/0.43 thf(f499,plain,(
% 0.21/0.43 ($true = vAPP($i,$o,cP,sK46)) | ~spl53_72),
% 0.21/0.43 inference(avatar_component_clause,[],[f497])).
% 0.21/0.43 thf(f497,plain,(
% 0.21/0.43 spl53_72 <=> ($true = vAPP($i,$o,cP,sK46))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_72])])).
% 0.21/0.43 thf(f787,plain,(
% 0.21/0.43 ~spl53_23 | ~spl53_73),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f786])).
% 0.21/0.43 thf(f786,plain,(
% 0.21/0.43 $false | (~spl53_23 | ~spl53_73)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f779])).
% 0.21/0.43 thf(f779,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_23 | ~spl53_73)),
% 0.21/0.43 inference(backward_demodulation,[],[f280,f502])).
% 0.21/0.43 thf(f280,plain,(
% 0.21/0.43 ($true = vAPP($i,$o,cP,sK14)) | ~spl53_23),
% 0.21/0.43 inference(avatar_component_clause,[],[f278])).
% 0.21/0.43 thf(f278,plain,(
% 0.21/0.43 spl53_23 <=> ($true = vAPP($i,$o,cP,sK14))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_23])])).
% 0.21/0.43 thf(f766,plain,(
% 0.21/0.43 ~spl53_10 | ~spl53_65),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f765])).
% 0.21/0.43 thf(f765,plain,(
% 0.21/0.43 $false | (~spl53_10 | ~spl53_65)),
% 0.21/0.43 inference(subsumption_resolution,[],[f467,f221])).
% 0.21/0.43 thf(f759,plain,(
% 0.21/0.43 ~spl53_33 | spl53_66),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f758])).
% 0.21/0.43 thf(f758,plain,(
% 0.21/0.43 $false | (~spl53_33 | spl53_66)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f733])).
% 0.21/0.43 thf(f733,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_33 | spl53_66)),
% 0.21/0.43 inference(superposition,[],[f322,f676])).
% 0.21/0.43 thf(f676,plain,(
% 0.21/0.43 ($false = vAPP($i,$o,cR,sK41)) | spl53_66),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f675])).
% 0.21/0.43 thf(f675,plain,(
% 0.21/0.43 ($true != $true) | ($false = vAPP($i,$o,cR,sK41)) | spl53_66),
% 0.21/0.43 inference(superposition,[],[f471,f4])).
% 0.21/0.43 thf(f471,plain,(
% 0.21/0.43 ($true != vAPP($i,$o,cR,sK41)) | spl53_66),
% 0.21/0.43 inference(avatar_component_clause,[],[f469])).
% 0.21/0.43 thf(f469,plain,(
% 0.21/0.43 spl53_66 <=> ($true = vAPP($i,$o,cR,sK41))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_66])])).
% 0.21/0.43 thf(f757,plain,(
% 0.21/0.43 ~spl53_33 | spl53_70),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f756])).
% 0.21/0.43 thf(f756,plain,(
% 0.21/0.43 $false | (~spl53_33 | spl53_70)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f734])).
% 0.21/0.43 thf(f734,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_33 | spl53_70)),
% 0.21/0.43 inference(superposition,[],[f322,f678])).
% 0.21/0.43 thf(f678,plain,(
% 0.21/0.43 ($false = vAPP($i,$o,cR,sK45)) | spl53_70),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f677])).
% 0.21/0.43 thf(f677,plain,(
% 0.21/0.43 ($true != $true) | ($false = vAPP($i,$o,cR,sK45)) | spl53_70),
% 0.21/0.43 inference(superposition,[],[f490,f4])).
% 0.21/0.43 thf(f490,plain,(
% 0.21/0.43 ($true != vAPP($i,$o,cR,sK45)) | spl53_70),
% 0.21/0.43 inference(avatar_component_clause,[],[f488])).
% 0.21/0.43 thf(f488,plain,(
% 0.21/0.43 spl53_70 <=> ($true = vAPP($i,$o,cR,sK45))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_70])])).
% 0.21/0.43 thf(f755,plain,(
% 0.21/0.43 ~spl53_33 | spl53_75),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f754])).
% 0.21/0.43 thf(f754,plain,(
% 0.21/0.43 $false | (~spl53_33 | spl53_75)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f735])).
% 0.21/0.43 thf(f735,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_33 | spl53_75)),
% 0.21/0.43 inference(superposition,[],[f322,f680])).
% 0.21/0.43 thf(f680,plain,(
% 0.21/0.43 ($false = vAPP($i,$o,cR,sK48)) | spl53_75),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f679])).
% 0.21/0.43 thf(f679,plain,(
% 0.21/0.43 ($true != $true) | ($false = vAPP($i,$o,cR,sK48)) | spl53_75),
% 0.21/0.43 inference(superposition,[],[f513,f4])).
% 0.21/0.43 thf(f513,plain,(
% 0.21/0.43 ($true != vAPP($i,$o,cR,sK48)) | spl53_75),
% 0.21/0.43 inference(avatar_component_clause,[],[f511])).
% 0.21/0.43 thf(f511,plain,(
% 0.21/0.43 spl53_75 <=> ($true = vAPP($i,$o,cR,sK48))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_75])])).
% 0.21/0.43 thf(f753,plain,(
% 0.21/0.43 ~spl53_33 | spl53_79),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f752])).
% 0.21/0.43 thf(f752,plain,(
% 0.21/0.43 $false | (~spl53_33 | spl53_79)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f736])).
% 0.21/0.43 thf(f736,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_33 | spl53_79)),
% 0.21/0.43 inference(superposition,[],[f322,f682])).
% 0.21/0.43 thf(f682,plain,(
% 0.21/0.43 ($false = vAPP($i,$o,cR,sK51)) | spl53_79),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f681])).
% 0.21/0.43 thf(f681,plain,(
% 0.21/0.43 ($true != $true) | ($false = vAPP($i,$o,cR,sK51)) | spl53_79),
% 0.21/0.43 inference(superposition,[],[f532,f4])).
% 0.21/0.43 thf(f532,plain,(
% 0.21/0.43 ($true != vAPP($i,$o,cR,sK51)) | spl53_79),
% 0.21/0.43 inference(avatar_component_clause,[],[f530])).
% 0.21/0.43 thf(f530,plain,(
% 0.21/0.43 spl53_79 <=> ($true = vAPP($i,$o,cR,sK51))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_79])])).
% 0.21/0.43 thf(f720,plain,(
% 0.21/0.43 ~spl53_31 | ~spl53_81),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f719])).
% 0.21/0.43 thf(f719,plain,(
% 0.21/0.43 $false | (~spl53_31 | ~spl53_81)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f713])).
% 0.21/0.43 thf(f713,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_31 | ~spl53_81)),
% 0.21/0.43 inference(superposition,[],[f712,f313])).
% 0.21/0.43 thf(f712,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($false = vAPP($i,$o,cP,vAPP($i,$i,sK52,X22)))) ) | (~spl53_31 | ~spl53_81)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f711])).
% 0.21/0.43 thf(f711,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($true = $false) | ($false = vAPP($i,$o,cP,vAPP($i,$i,sK52,X22)))) ) | (~spl53_31 | ~spl53_81)),
% 0.21/0.43 inference(forward_demodulation,[],[f540,f313])).
% 0.21/0.43 thf(f540,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($false = vAPP($i,$o,cP,X22)) | ($false = vAPP($i,$o,cP,vAPP($i,$i,sK52,X22)))) ) | ~spl53_81),
% 0.21/0.43 inference(avatar_component_clause,[],[f539])).
% 0.21/0.43 thf(f539,plain,(
% 0.21/0.43 spl53_81 <=> ! [X22] : (($false = vAPP($i,$o,cP,X22)) | ($false = vAPP($i,$o,cP,vAPP($i,$i,sK52,X22))))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_81])])).
% 0.21/0.43 thf(f701,plain,(
% 0.21/0.43 ~spl53_8 | ~spl53_12),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f700])).
% 0.21/0.43 thf(f700,plain,(
% 0.21/0.43 $false | (~spl53_8 | ~spl53_12)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f694])).
% 0.21/0.43 thf(f694,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_8 | ~spl53_12)),
% 0.21/0.43 inference(superposition,[],[f687,f230])).
% 0.21/0.43 thf(f687,plain,(
% 0.21/0.43 ( ! [X4 : $i] : (($false = vAPP($i,$o,cS,vAPP($i,$i,sK7,X4)))) ) | (~spl53_8 | ~spl53_12)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f686])).
% 0.21/0.43 thf(f686,plain,(
% 0.21/0.43 ( ! [X4 : $i] : (($true = $false) | ($false = vAPP($i,$o,cS,vAPP($i,$i,sK7,X4)))) ) | (~spl53_8 | ~spl53_12)),
% 0.21/0.43 inference(forward_demodulation,[],[f213,f230])).
% 0.21/0.43 thf(f213,plain,(
% 0.21/0.43 ( ! [X4 : $i] : (($false = vAPP($i,$o,cS,X4)) | ($false = vAPP($i,$o,cS,vAPP($i,$i,sK7,X4)))) ) | ~spl53_8),
% 0.21/0.43 inference(avatar_component_clause,[],[f212])).
% 0.21/0.43 thf(f212,plain,(
% 0.21/0.43 spl53_8 <=> ! [X4] : (($false = vAPP($i,$o,cS,X4)) | ($false = vAPP($i,$o,cS,vAPP($i,$i,sK7,X4))))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_8])])).
% 0.21/0.43 thf(f671,plain,(
% 0.21/0.43 ~spl53_10 | ~spl53_63),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f670])).
% 0.21/0.43 thf(f670,plain,(
% 0.21/0.43 $false | (~spl53_10 | ~spl53_63)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f664])).
% 0.21/0.43 thf(f664,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_10 | ~spl53_63)),
% 0.21/0.43 inference(superposition,[],[f653,f221])).
% 0.21/0.43 thf(f653,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($false = vAPP($i,$o,cQ,vAPP($i,$i,sK40,X22)))) ) | (~spl53_10 | ~spl53_63)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f652])).
% 0.21/0.43 thf(f652,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($true = $false) | ($false = vAPP($i,$o,cQ,vAPP($i,$i,sK40,X22)))) ) | (~spl53_10 | ~spl53_63)),
% 0.21/0.43 inference(forward_demodulation,[],[f458,f221])).
% 0.21/0.43 thf(f458,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($false = vAPP($i,$o,cQ,X22)) | ($false = vAPP($i,$o,cQ,vAPP($i,$i,sK40,X22)))) ) | ~spl53_63),
% 0.21/0.43 inference(avatar_component_clause,[],[f457])).
% 0.21/0.43 thf(f457,plain,(
% 0.21/0.43 spl53_63 <=> ! [X22] : (($false = vAPP($i,$o,cQ,X22)) | ($false = vAPP($i,$o,cQ,vAPP($i,$i,sK40,X22))))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_63])])).
% 0.21/0.43 thf(f651,plain,(
% 0.21/0.43 spl53_37 | ~spl53_47),
% 0.21/0.43 inference(avatar_split_clause,[],[f648,f384,f337])).
% 0.21/0.43 thf(f384,plain,(
% 0.21/0.43 spl53_47 <=> ! [X1] : (vAPP($i,$o,cR,X1) != $true)),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_47])])).
% 0.21/0.43 thf(f648,plain,(
% 0.21/0.43 ( ! [X0 : $i] : ((vAPP($i,$o,cR,X0) = $false)) ) | ~spl53_47),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f647])).
% 0.21/0.43 thf(f647,plain,(
% 0.21/0.43 ( ! [X0 : $i] : (($true != $true) | (vAPP($i,$o,cR,X0) = $false)) ) | ~spl53_47),
% 0.21/0.43 inference(superposition,[],[f385,f4])).
% 0.21/0.43 thf(f385,plain,(
% 0.21/0.43 ( ! [X1 : $i] : ((vAPP($i,$o,cR,X1) != $true)) ) | ~spl53_47),
% 0.21/0.43 inference(avatar_component_clause,[],[f384])).
% 0.21/0.43 thf(f644,plain,(
% 0.21/0.43 ~spl53_33 | ~spl53_47),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f643])).
% 0.21/0.43 thf(f643,plain,(
% 0.21/0.43 $false | (~spl53_33 | ~spl53_47)),
% 0.21/0.43 inference(subsumption_resolution,[],[f385,f322])).
% 0.21/0.43 thf(f640,plain,(
% 0.21/0.43 ~spl53_32 | ~spl53_36),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f639])).
% 0.21/0.43 thf(f639,plain,(
% 0.21/0.43 $false | (~spl53_32 | ~spl53_36)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f638])).
% 0.21/0.43 thf(f638,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_32 | ~spl53_36)),
% 0.21/0.43 inference(forward_demodulation,[],[f335,f319])).
% 0.21/0.43 thf(f319,plain,(
% 0.21/0.43 ($false = vAPP($i,$o,cR,sK22)) | ~spl53_32),
% 0.21/0.43 inference(avatar_component_clause,[],[f317])).
% 0.21/0.43 thf(f317,plain,(
% 0.21/0.43 spl53_32 <=> ($false = vAPP($i,$o,cR,sK22))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_32])])).
% 0.21/0.43 thf(f335,plain,(
% 0.21/0.43 ($true = vAPP($i,$o,cR,sK22)) | ~spl53_36),
% 0.21/0.43 inference(avatar_component_clause,[],[f333])).
% 0.21/0.43 thf(f333,plain,(
% 0.21/0.43 spl53_36 <=> ($true = vAPP($i,$o,cR,sK22))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_36])])).
% 0.21/0.43 thf(f635,plain,(
% 0.21/0.43 ~spl53_37 | ~spl53_62),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f634])).
% 0.21/0.43 thf(f634,plain,(
% 0.21/0.43 $false | (~spl53_37 | ~spl53_62)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f633])).
% 0.21/0.43 thf(f633,plain,(
% 0.21/0.43 ($true = $false) | (~spl53_37 | ~spl53_62)),
% 0.21/0.43 inference(forward_demodulation,[],[f454,f338])).
% 0.21/0.43 thf(f454,plain,(
% 0.21/0.43 ($true = vAPP($i,$o,cR,sK38)) | ~spl53_62),
% 0.21/0.43 inference(avatar_component_clause,[],[f452])).
% 0.21/0.43 thf(f452,plain,(
% 0.21/0.43 spl53_62 <=> ($true = vAPP($i,$o,cR,sK38))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_62])])).
% 0.21/0.43 thf(f632,plain,(
% 0.21/0.43 ~spl53_12 | spl53_61),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f631])).
% 0.21/0.43 thf(f631,plain,(
% 0.21/0.43 $false | (~spl53_12 | spl53_61)),
% 0.21/0.43 inference(subsumption_resolution,[],[f450,f230])).
% 0.21/0.43 thf(f450,plain,(
% 0.21/0.43 ($true != vAPP($i,$o,cS,sK39)) | spl53_61),
% 0.21/0.43 inference(avatar_component_clause,[],[f448])).
% 0.21/0.43 thf(f448,plain,(
% 0.21/0.43 spl53_61 <=> ($true = vAPP($i,$o,cS,sK39))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_61])])).
% 0.21/0.43 thf(f629,plain,(
% 0.21/0.43 ~spl53_12 | spl53_57),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f628])).
% 0.21/0.43 thf(f628,plain,(
% 0.21/0.43 $false | (~spl53_12 | spl53_57)),
% 0.21/0.43 inference(subsumption_resolution,[],[f431,f230])).
% 0.21/0.43 thf(f431,plain,(
% 0.21/0.43 ($true != vAPP($i,$o,cS,sK36)) | spl53_57),
% 0.21/0.43 inference(avatar_component_clause,[],[f429])).
% 0.21/0.43 thf(f429,plain,(
% 0.21/0.43 spl53_57 <=> ($true = vAPP($i,$o,cS,sK36))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_57])])).
% 0.21/0.43 thf(f620,plain,(
% 0.21/0.43 ~spl53_31 | spl53_34),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f619])).
% 0.21/0.43 thf(f619,plain,(
% 0.21/0.43 $false | (~spl53_31 | spl53_34)),
% 0.21/0.43 inference(subsumption_resolution,[],[f326,f313])).
% 0.21/0.43 thf(f326,plain,(
% 0.21/0.43 ($true != vAPP($i,$o,cP,sK21)) | spl53_34),
% 0.21/0.43 inference(avatar_component_clause,[],[f324])).
% 0.21/0.43 thf(f324,plain,(
% 0.21/0.43 spl53_34 <=> ($true = vAPP($i,$o,cP,sK21))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_34])])).
% 0.21/0.43 thf(f618,plain,(
% 0.21/0.43 ~spl53_12 | ~spl53_26),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f617])).
% 0.21/0.43 thf(f617,plain,(
% 0.21/0.43 $false | (~spl53_12 | ~spl53_26)),
% 0.21/0.43 inference(subsumption_resolution,[],[f293,f230])).
% 0.21/0.43 thf(f616,plain,(
% 0.21/0.43 ~spl53_10 | spl53_22),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f615])).
% 0.21/0.43 thf(f615,plain,(
% 0.21/0.43 $false | (~spl53_10 | spl53_22)),
% 0.21/0.43 inference(subsumption_resolution,[],[f276,f221])).
% 0.21/0.43 thf(f276,plain,(
% 0.21/0.43 ($true != vAPP($i,$o,cQ,sK15)) | spl53_22),
% 0.21/0.43 inference(avatar_component_clause,[],[f274])).
% 0.21/0.43 thf(f274,plain,(
% 0.21/0.43 spl53_22 <=> ($true = vAPP($i,$o,cQ,sK15))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_22])])).
% 0.21/0.43 thf(f614,plain,(
% 0.21/0.43 ~spl53_10 | spl53_18),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f613])).
% 0.21/0.43 thf(f613,plain,(
% 0.21/0.43 $false | (~spl53_10 | spl53_18)),
% 0.21/0.43 inference(subsumption_resolution,[],[f257,f221])).
% 0.21/0.43 thf(f257,plain,(
% 0.21/0.43 ($true != vAPP($i,$o,cQ,sK12)) | spl53_18),
% 0.21/0.43 inference(avatar_component_clause,[],[f255])).
% 0.21/0.43 thf(f255,plain,(
% 0.21/0.43 spl53_18 <=> ($true = vAPP($i,$o,cQ,sK12))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_18])])).
% 0.21/0.43 thf(f605,plain,(
% 0.21/0.43 ~spl53_10 | spl53_13),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f604])).
% 0.21/0.43 thf(f604,plain,(
% 0.21/0.43 $false | (~spl53_10 | spl53_13)),
% 0.21/0.43 inference(subsumption_resolution,[],[f234,f221])).
% 0.21/0.43 thf(f234,plain,(
% 0.21/0.43 ($true != vAPP($i,$o,cQ,sK9)) | spl53_13),
% 0.21/0.43 inference(avatar_component_clause,[],[f232])).
% 0.21/0.43 thf(f232,plain,(
% 0.21/0.43 spl53_13 <=> ($true = vAPP($i,$o,cQ,sK9))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_13])])).
% 0.21/0.43 thf(f600,plain,(
% 0.21/0.43 spl53_6 | ~spl53_10),
% 0.21/0.43 inference(avatar_contradiction_clause,[],[f599])).
% 0.21/0.43 thf(f599,plain,(
% 0.21/0.43 $false | (spl53_6 | ~spl53_10)),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f598])).
% 0.21/0.43 thf(f598,plain,(
% 0.21/0.43 ($true != $true) | (spl53_6 | ~spl53_10)),
% 0.21/0.43 inference(superposition,[],[f205,f221])).
% 0.21/0.43 thf(f205,plain,(
% 0.21/0.43 ($true != vAPP($i,$o,cQ,sK5)) | spl53_6),
% 0.21/0.43 inference(avatar_component_clause,[],[f203])).
% 0.21/0.43 thf(f203,plain,(
% 0.21/0.43 spl53_6 <=> ($true = vAPP($i,$o,cQ,sK5))),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_6])])).
% 0.21/0.43 thf(f547,plain,(
% 0.21/0.43 spl53_3 | ~spl53_28 | spl53_7),
% 0.21/0.43 inference(avatar_split_clause,[],[f112,f207,f299,f189])).
% 0.21/0.43 thf(f189,plain,(
% 0.21/0.43 spl53_3 <=> ($true = sP4)),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_3])])).
% 0.21/0.43 thf(f299,plain,(
% 0.21/0.43 spl53_28 <=> ($true = sP2)),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_28])])).
% 0.21/0.43 thf(f207,plain,(
% 0.21/0.43 spl53_7 <=> ($true = sP3)),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_7])])).
% 0.21/0.43 thf(f112,plain,(
% 0.21/0.43 ($true = sP3) | ($true != sP2) | ($true = sP4)),
% 0.21/0.43 inference(cnf_transformation,[],[f75])).
% 0.21/0.43 thf(f75,plain,(
% 0.21/0.43 (((($true != sP3) | ($true != sP2)) & (($true = sP3) | ($true = sP2))) | ($true != sP4)) & (((($true = sP2) | ($true != sP3)) & (($true = sP3) | ($true != sP2))) | ($true = sP4))),
% 0.21/0.43 inference(nnf_transformation,[],[f13])).
% 0.21/0.43 thf(f13,plain,(
% 0.21/0.43 ($true = sP4) <~> (($true = sP2) <=> ($true = sP3))),
% 0.21/0.43 inference(definition_folding,[],[f7,f12,f11,f10,f9,f8])).
% 0.21/0.43 thf(f8,plain,(
% 0.21/0.43 ($true = sP0) <=> (? [X0] : ! [X1] : (vAPP($i,$o,cP,X0) = vAPP($i,$o,cP,X1)) <=> (? [X2] : ($true = vAPP($i,$o,cQ,X2)) <=> ! [X3] : ($true = vAPP($i,$o,cR,X3))))),
% 0.21/0.43 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 0.21/0.43 thf(f9,plain,(
% 0.21/0.43 ($true = sP1) <=> (? [X4] : ! [X5] : (vAPP($i,$o,cQ,X4) = vAPP($i,$o,cQ,X5)) <=> (? [X6] : ($true = vAPP($i,$o,cR,X6)) <=> ! [X7] : ($true = vAPP($i,$o,cS,X7))))),
% 0.21/0.43 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 0.21/0.43 thf(f10,plain,(
% 0.21/0.43 ($true = sP2) <=> (? [X8] : ! [X9] : (vAPP($i,$o,cR,X8) = vAPP($i,$o,cR,X9)) <=> (? [X10] : ($true = vAPP($i,$o,cS,X10)) <=> ! [X11] : ($true = vAPP($i,$o,cP,X11))))),
% 0.21/0.43 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 0.21/0.43 thf(f11,plain,(
% 0.21/0.43 ($true = sP3) <=> (? [X12] : ! [X13] : (vAPP($i,$o,cS,X12) = vAPP($i,$o,cS,X13)) <=> (? [X14] : ($true = vAPP($i,$o,cP,X14)) <=> ! [X15] : ($true = vAPP($i,$o,cQ,X15))))),
% 0.21/0.43 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 0.21/0.43 thf(f12,plain,(
% 0.21/0.43 ($true = sP4) <=> (($true = sP0) <=> ($true = sP1))),
% 0.21/0.43 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 0.21/0.43 thf(f7,plain,(
% 0.21/0.43 ((? [X0] : ! [X1] : (vAPP($i,$o,cP,X0) = vAPP($i,$o,cP,X1)) <=> (? [X2] : ($true = vAPP($i,$o,cQ,X2)) <=> ! [X3] : ($true = vAPP($i,$o,cR,X3)))) <=> (? [X4] : ! [X5] : (vAPP($i,$o,cQ,X4) = vAPP($i,$o,cQ,X5)) <=> (? [X6] : ($true = vAPP($i,$o,cR,X6)) <=> ! [X7] : ($true = vAPP($i,$o,cS,X7))))) <~> ((? [X8] : ! [X9] : (vAPP($i,$o,cR,X8) = vAPP($i,$o,cR,X9)) <=> (? [X10] : ($true = vAPP($i,$o,cS,X10)) <=> ! [X11] : ($true = vAPP($i,$o,cP,X11)))) <=> (? [X12] : ! [X13] : (vAPP($i,$o,cS,X12) = vAPP($i,$o,cS,X13)) <=> (? [X14] : ($true = vAPP($i,$o,cP,X14)) <=> ! [X15] : ($true = vAPP($i,$o,cQ,X15)))))),
% 0.21/0.43 inference(ennf_transformation,[],[f6])).
% 0.21/0.43 thf(f6,plain,(
% 0.21/0.43 ~(((? [X0] : ! [X1] : (vAPP($i,$o,cP,X0) = vAPP($i,$o,cP,X1)) <=> (? [X2] : ($true = vAPP($i,$o,cQ,X2)) <=> ! [X3] : ($true = vAPP($i,$o,cR,X3)))) <=> (? [X4] : ! [X5] : (vAPP($i,$o,cQ,X4) = vAPP($i,$o,cQ,X5)) <=> (? [X6] : ($true = vAPP($i,$o,cR,X6)) <=> ! [X7] : ($true = vAPP($i,$o,cS,X7))))) <=> ((? [X8] : ! [X9] : (vAPP($i,$o,cR,X8) = vAPP($i,$o,cR,X9)) <=> (? [X10] : ($true = vAPP($i,$o,cS,X10)) <=> ! [X11] : ($true = vAPP($i,$o,cP,X11)))) <=> (? [X12] : ! [X13] : (vAPP($i,$o,cS,X12) = vAPP($i,$o,cS,X13)) <=> (? [X14] : ($true = vAPP($i,$o,cP,X14)) <=> ! [X15] : ($true = vAPP($i,$o,cQ,X15))))))),
% 0.21/0.43 inference(fool_elimination,[],[f5])).
% 0.21/0.43 thf(f5,plain,(
% 0.21/0.43 ~(((? [X0] : ! [X1] : (vAPP($i,$o,cP,X0) <=> vAPP($i,$o,cP,X1)) <=> (? [X2] : vAPP($i,$o,cQ,X2) <=> ! [X3] : vAPP($i,$o,cR,X3))) <=> (? [X4] : ! [X5] : (vAPP($i,$o,cQ,X4) <=> vAPP($i,$o,cQ,X5)) <=> (? [X6] : vAPP($i,$o,cR,X6) <=> ! [X7] : vAPP($i,$o,cS,X7)))) <=> ((? [X8] : ! [X9] : (vAPP($i,$o,cR,X8) <=> vAPP($i,$o,cR,X9)) <=> (? [X10] : vAPP($i,$o,cS,X10) <=> ! [X11] : vAPP($i,$o,cP,X11))) <=> (? [X12] : ! [X13] : (vAPP($i,$o,cS,X12) <=> vAPP($i,$o,cS,X13)) <=> (? [X14] : vAPP($i,$o,cP,X14) <=> ! [X15] : vAPP($i,$o,cQ,X15)))))),
% 0.21/0.43 inference(rectify,[],[f2])).
% 0.21/0.43 thf(f2,negated_conjecture,(
% 0.21/0.43 ~(((? [X0] : ! [X1] : (vAPP($i,$o,cP,X0) <=> vAPP($i,$o,cP,X1)) <=> (? [X0] : vAPP($i,$o,cQ,X0) <=> ! [X1] : vAPP($i,$o,cR,X1))) <=> (? [X0] : ! [X1] : (vAPP($i,$o,cQ,X0) <=> vAPP($i,$o,cQ,X1)) <=> (? [X0] : vAPP($i,$o,cR,X0) <=> ! [X1] : vAPP($i,$o,cS,X1)))) <=> ((? [X0] : ! [X1] : (vAPP($i,$o,cR,X0) <=> vAPP($i,$o,cR,X1)) <=> (? [X0] : vAPP($i,$o,cS,X0) <=> ! [X1] : vAPP($i,$o,cP,X1))) <=> (? [X0] : ! [X1] : (vAPP($i,$o,cS,X0) <=> vAPP($i,$o,cS,X1)) <=> (? [X0] : vAPP($i,$o,cP,X0) <=> ! [X1] : vAPP($i,$o,cQ,X1)))))),
% 0.21/0.43 inference(negated_conjecture,[],[f1])).
% 0.21/0.43 thf(f1,conjecture,(
% 0.21/0.43 ((? [X0] : ! [X1] : (vAPP($i,$o,cP,X0) <=> vAPP($i,$o,cP,X1)) <=> (? [X0] : vAPP($i,$o,cQ,X0) <=> ! [X1] : vAPP($i,$o,cR,X1))) <=> (? [X0] : ! [X1] : (vAPP($i,$o,cQ,X0) <=> vAPP($i,$o,cQ,X1)) <=> (? [X0] : vAPP($i,$o,cR,X0) <=> ! [X1] : vAPP($i,$o,cS,X1)))) <=> ((? [X0] : ! [X1] : (vAPP($i,$o,cR,X0) <=> vAPP($i,$o,cR,X1)) <=> (? [X0] : vAPP($i,$o,cS,X0) <=> ! [X1] : vAPP($i,$o,cP,X1))) <=> (? [X0] : ! [X1] : (vAPP($i,$o,cS,X0) <=> vAPP($i,$o,cS,X1)) <=> (? [X0] : vAPP($i,$o,cP,X0) <=> ! [X1] : vAPP($i,$o,cQ,X1))))),
% 0.21/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM138)).
% 0.21/0.43 thf(f546,plain,(
% 0.21/0.43 spl53_3 | ~spl53_7 | spl53_28),
% 0.21/0.43 inference(avatar_split_clause,[],[f113,f299,f207,f189])).
% 0.21/0.43 thf(f113,plain,(
% 0.21/0.43 ($true = sP2) | ($true != sP3) | ($true = sP4)),
% 0.21/0.43 inference(cnf_transformation,[],[f75])).
% 0.21/0.43 thf(f545,plain,(
% 0.21/0.43 ~spl53_3 | spl53_28 | spl53_7),
% 0.21/0.43 inference(avatar_split_clause,[],[f114,f207,f299,f189])).
% 0.21/0.43 thf(f114,plain,(
% 0.21/0.43 ($true = sP3) | ($true = sP2) | ($true != sP4)),
% 0.21/0.43 inference(cnf_transformation,[],[f75])).
% 0.21/0.43 thf(f544,plain,(
% 0.21/0.43 ~spl53_3 | ~spl53_28 | ~spl53_7),
% 0.21/0.43 inference(avatar_split_clause,[],[f115,f207,f299,f189])).
% 0.21/0.43 thf(f115,plain,(
% 0.21/0.43 ($true != sP3) | ($true != sP2) | ($true != sP4)),
% 0.21/0.43 inference(cnf_transformation,[],[f75])).
% 0.21/0.43 thf(f543,plain,(
% 0.21/0.43 ~spl53_1 | spl53_81 | spl53_65 | spl53_33),
% 0.21/0.43 inference(avatar_split_clause,[],[f117,f321,f466,f539,f181])).
% 0.21/0.43 thf(f181,plain,(
% 0.21/0.43 spl53_1 <=> ($true = sP0)),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_1])])).
% 0.21/0.43 thf(f117,plain,(
% 0.21/0.43 ( ! [X21 : $i,X22 : $i,X20 : $i] : (($true = vAPP($i,$o,cR,X20)) | ($true != vAPP($i,$o,cQ,X21)) | ($false = vAPP($i,$o,cP,X22)) | ($true != sP0) | ($false = vAPP($i,$o,cP,vAPP($i,$i,sK52,X22)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f104])).
% 0.21/0.43 thf(f104,plain,(
% 0.21/0.43 ( ! [X21 : $i,X22 : $i,X20 : $i] : (($true = vAPP($i,$o,cR,X20)) | ($true != vAPP($i,$o,cQ,X21)) | (vAPP($i,$o,cP,X22) != vAPP($i,$o,cP,vAPP($i,$i,sK52,X22))) | ($true != sP0)) )),
% 0.21/0.43 inference(cnf_transformation,[],[f74])).
% 0.21/0.43 thf(f74,plain,(
% 0.21/0.43 (($true = sP0) | ((((($true != vAPP($i,$o,cR,sK41)) | ! [X1] : (vAPP($i,$o,cQ,X1) != $true)) & (! [X2] : ($true = vAPP($i,$o,cR,X2)) | ($true = vAPP($i,$o,cQ,sK42)))) | ! [X4] : (vAPP($i,$o,cP,X4) != vAPP($i,$o,cP,vAPP($i,$i,sK43,X4)))) & (((($true = vAPP($i,$o,cQ,sK44)) | ($true != vAPP($i,$o,cR,sK45))) & (! [X8] : ($true = vAPP($i,$o,cR,X8)) | ! [X9] : ($true != vAPP($i,$o,cQ,X9)))) | ! [X11] : (vAPP($i,$o,cP,X11) = vAPP($i,$o,cP,sK46))))) & (((! [X13] : (vAPP($i,$o,cP,X13) = vAPP($i,$o,cP,sK47)) | ((($true != vAPP($i,$o,cR,sK48)) | ! [X15] : ($true != vAPP($i,$o,cQ,X15))) & (! [X16] : ($true = vAPP($i,$o,cR,X16)) | ($true = vAPP($i,$o,cQ,sK49))))) & (((($true = vAPP($i,$o,cQ,sK50)) | ($true != vAPP($i,$o,cR,sK51))) & (! [X20] : ($true = vAPP($i,$o,cR,X20)) | ! [X21] : ($true != vAPP($i,$o,cQ,X21)))) | ! [X22] : (vAPP($i,$o,cP,X22) != vAPP($i,$o,cP,vAPP($i,$i,sK52,X22))))) | ($true != sP0))),
% 0.21/0.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK41,sK42,sK43,sK44,sK45,sK46,sK47,sK48,sK49,sK50,sK51,sK52])],[f61,f73,f72,f71,f70,f69,f68,f67,f66,f65,f64,f63,f62])).
% 0.21/0.43 thf(f62,plain,(
% 0.21/0.43 ? [X0] : (vAPP($i,$o,cR,X0) != $true) => ($true != vAPP($i,$o,cR,sK41))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f63,plain,(
% 0.21/0.43 ? [X3] : ($true = vAPP($i,$o,cQ,X3)) => ($true = vAPP($i,$o,cQ,sK42))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f64,plain,(
% 0.21/0.43 ! [X4] : (? [X5] : (vAPP($i,$o,cP,X4) != vAPP($i,$o,cP,X5)) => (vAPP($i,$o,cP,X4) != vAPP($i,$o,cP,vAPP($i,$i,sK43,X4))))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f65,plain,(
% 0.21/0.43 ? [X6] : ($true = vAPP($i,$o,cQ,X6)) => ($true = vAPP($i,$o,cQ,sK44))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f66,plain,(
% 0.21/0.43 ? [X7] : ($true != vAPP($i,$o,cR,X7)) => ($true != vAPP($i,$o,cR,sK45))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f67,plain,(
% 0.21/0.43 ? [X10] : ! [X11] : (vAPP($i,$o,cP,X11) = vAPP($i,$o,cP,X10)) => ! [X11] : (vAPP($i,$o,cP,X11) = vAPP($i,$o,cP,sK46))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f68,plain,(
% 0.21/0.43 ? [X12] : ! [X13] : (vAPP($i,$o,cP,X12) = vAPP($i,$o,cP,X13)) => ! [X13] : (vAPP($i,$o,cP,X13) = vAPP($i,$o,cP,sK47))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f69,plain,(
% 0.21/0.43 ? [X14] : ($true != vAPP($i,$o,cR,X14)) => ($true != vAPP($i,$o,cR,sK48))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f70,plain,(
% 0.21/0.43 ? [X17] : ($true = vAPP($i,$o,cQ,X17)) => ($true = vAPP($i,$o,cQ,sK49))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f71,plain,(
% 0.21/0.43 ? [X18] : ($true = vAPP($i,$o,cQ,X18)) => ($true = vAPP($i,$o,cQ,sK50))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f72,plain,(
% 0.21/0.43 ? [X19] : ($true != vAPP($i,$o,cR,X19)) => ($true != vAPP($i,$o,cR,sK51))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f73,plain,(
% 0.21/0.43 ! [X22] : (? [X23] : (vAPP($i,$o,cP,X22) != vAPP($i,$o,cP,X23)) => (vAPP($i,$o,cP,X22) != vAPP($i,$o,cP,vAPP($i,$i,sK52,X22))))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f61,plain,(
% 0.21/0.43 (($true = sP0) | ((((? [X0] : (vAPP($i,$o,cR,X0) != $true) | ! [X1] : (vAPP($i,$o,cQ,X1) != $true)) & (! [X2] : ($true = vAPP($i,$o,cR,X2)) | ? [X3] : ($true = vAPP($i,$o,cQ,X3)))) | ! [X4] : ? [X5] : (vAPP($i,$o,cP,X4) != vAPP($i,$o,cP,X5))) & (((? [X6] : ($true = vAPP($i,$o,cQ,X6)) | ? [X7] : ($true != vAPP($i,$o,cR,X7))) & (! [X8] : ($true = vAPP($i,$o,cR,X8)) | ! [X9] : ($true != vAPP($i,$o,cQ,X9)))) | ? [X10] : ! [X11] : (vAPP($i,$o,cP,X11) = vAPP($i,$o,cP,X10))))) & (((? [X12] : ! [X13] : (vAPP($i,$o,cP,X12) = vAPP($i,$o,cP,X13)) | ((? [X14] : ($true != vAPP($i,$o,cR,X14)) | ! [X15] : ($true != vAPP($i,$o,cQ,X15))) & (! [X16] : ($true = vAPP($i,$o,cR,X16)) | ? [X17] : ($true = vAPP($i,$o,cQ,X17))))) & (((? [X18] : ($true = vAPP($i,$o,cQ,X18)) | ? [X19] : ($true != vAPP($i,$o,cR,X19))) & (! [X20] : ($true = vAPP($i,$o,cR,X20)) | ! [X21] : ($true != vAPP($i,$o,cQ,X21)))) | ! [X22] : ? [X23] : (vAPP($i,$o,cP,X22) != vAPP($i,$o,cP,X23)))) | ($true != sP0))),
% 0.21/0.43 inference(rectify,[],[f60])).
% 0.21/0.43 thf(f60,plain,(
% 0.21/0.43 (($true = sP0) | ((((? [X3] : ($true != vAPP($i,$o,cR,X3)) | ! [X2] : ($true != vAPP($i,$o,cQ,X2))) & (! [X3] : ($true = vAPP($i,$o,cR,X3)) | ? [X2] : ($true = vAPP($i,$o,cQ,X2)))) | ! [X0] : ? [X1] : (vAPP($i,$o,cP,X0) != vAPP($i,$o,cP,X1))) & (((? [X2] : ($true = vAPP($i,$o,cQ,X2)) | ? [X3] : ($true != vAPP($i,$o,cR,X3))) & (! [X3] : ($true = vAPP($i,$o,cR,X3)) | ! [X2] : ($true != vAPP($i,$o,cQ,X2)))) | ? [X0] : ! [X1] : (vAPP($i,$o,cP,X0) = vAPP($i,$o,cP,X1))))) & (((? [X0] : ! [X1] : (vAPP($i,$o,cP,X0) = vAPP($i,$o,cP,X1)) | ((? [X3] : ($true != vAPP($i,$o,cR,X3)) | ! [X2] : ($true != vAPP($i,$o,cQ,X2))) & (! [X3] : ($true = vAPP($i,$o,cR,X3)) | ? [X2] : ($true = vAPP($i,$o,cQ,X2))))) & (((? [X2] : ($true = vAPP($i,$o,cQ,X2)) | ? [X3] : ($true != vAPP($i,$o,cR,X3))) & (! [X3] : ($true = vAPP($i,$o,cR,X3)) | ! [X2] : ($true != vAPP($i,$o,cQ,X2)))) | ! [X0] : ? [X1] : (vAPP($i,$o,cP,X0) != vAPP($i,$o,cP,X1)))) | ($true != sP0))),
% 0.21/0.43 inference(nnf_transformation,[],[f8])).
% 0.21/0.43 thf(f542,plain,(
% 0.21/0.43 ~spl53_1 | spl53_78 | spl53_65 | spl53_33),
% 0.21/0.43 inference(avatar_split_clause,[],[f116,f321,f466,f527,f181])).
% 0.21/0.43 thf(f116,plain,(
% 0.21/0.43 ( ! [X21 : $i,X22 : $i,X20 : $i] : (($true = vAPP($i,$o,cR,X20)) | ($true != vAPP($i,$o,cQ,X21)) | ($true = vAPP($i,$o,cP,X22)) | ($true != sP0) | ($true = vAPP($i,$o,cP,vAPP($i,$i,sK52,X22)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f104])).
% 0.21/0.43 thf(f541,plain,(
% 0.21/0.43 ~spl53_1 | spl53_81 | ~spl53_79 | spl53_80),
% 0.21/0.43 inference(avatar_split_clause,[],[f119,f534,f530,f539,f181])).
% 0.21/0.43 thf(f119,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($true = vAPP($i,$o,cQ,sK50)) | ($true != vAPP($i,$o,cR,sK51)) | ($false = vAPP($i,$o,cP,X22)) | ($true != sP0) | ($false = vAPP($i,$o,cP,vAPP($i,$i,sK52,X22)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f105])).
% 0.21/0.43 thf(f105,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($true = vAPP($i,$o,cQ,sK50)) | ($true != vAPP($i,$o,cR,sK51)) | (vAPP($i,$o,cP,X22) != vAPP($i,$o,cP,vAPP($i,$i,sK52,X22))) | ($true != sP0)) )),
% 0.21/0.43 inference(cnf_transformation,[],[f74])).
% 0.21/0.43 thf(f537,plain,(
% 0.21/0.43 ~spl53_1 | spl53_78 | ~spl53_79 | spl53_80),
% 0.21/0.43 inference(avatar_split_clause,[],[f118,f534,f530,f527,f181])).
% 0.21/0.43 thf(f118,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($true = vAPP($i,$o,cQ,sK50)) | ($true != vAPP($i,$o,cR,sK51)) | ($true = vAPP($i,$o,cP,X22)) | ($true != sP0) | ($true = vAPP($i,$o,cP,vAPP($i,$i,sK52,X22)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f105])).
% 0.21/0.43 thf(f525,plain,(
% 0.21/0.43 spl53_76 | ~spl53_1 | spl53_77 | spl53_33 | spl53_73),
% 0.21/0.43 inference(avatar_split_clause,[],[f121,f501,f321,f521,f181,f516])).
% 0.21/0.43 thf(f121,plain,(
% 0.21/0.43 ( ! [X16 : $i,X13 : $i] : (($false = vAPP($i,$o,cP,X13)) | ($true = vAPP($i,$o,cR,X16)) | ($true = vAPP($i,$o,cQ,sK49)) | ($true != sP0) | ($true = vAPP($i,$o,cP,sK47))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f106])).
% 0.21/0.43 thf(f106,plain,(
% 0.21/0.43 ( ! [X16 : $i,X13 : $i] : ((vAPP($i,$o,cP,X13) = vAPP($i,$o,cP,sK47)) | ($true = vAPP($i,$o,cR,X16)) | ($true = vAPP($i,$o,cQ,sK49)) | ($true != sP0)) )),
% 0.21/0.43 inference(cnf_transformation,[],[f74])).
% 0.21/0.43 thf(f524,plain,(
% 0.21/0.43 spl53_74 | ~spl53_1 | spl53_77 | spl53_33 | spl53_31),
% 0.21/0.43 inference(avatar_split_clause,[],[f120,f312,f321,f521,f181,f507])).
% 0.21/0.43 thf(f120,plain,(
% 0.21/0.43 ( ! [X16 : $i,X13 : $i] : (($true = vAPP($i,$o,cP,X13)) | ($true = vAPP($i,$o,cR,X16)) | ($true = vAPP($i,$o,cQ,sK49)) | ($true != sP0) | ($false = vAPP($i,$o,cP,sK47))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f106])).
% 0.21/0.43 thf(f519,plain,(
% 0.21/0.43 spl53_76 | ~spl53_1 | spl53_65 | ~spl53_75 | spl53_73),
% 0.21/0.43 inference(avatar_split_clause,[],[f123,f501,f511,f466,f181,f516])).
% 0.21/0.43 thf(f123,plain,(
% 0.21/0.43 ( ! [X15 : $i,X13 : $i] : (($false = vAPP($i,$o,cP,X13)) | ($true != vAPP($i,$o,cR,sK48)) | ($true != vAPP($i,$o,cQ,X15)) | ($true != sP0) | ($true = vAPP($i,$o,cP,sK47))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f107])).
% 0.21/0.43 thf(f107,plain,(
% 0.21/0.43 ( ! [X15 : $i,X13 : $i] : ((vAPP($i,$o,cP,X13) = vAPP($i,$o,cP,sK47)) | ($true != vAPP($i,$o,cR,sK48)) | ($true != vAPP($i,$o,cQ,X15)) | ($true != sP0)) )),
% 0.21/0.43 inference(cnf_transformation,[],[f74])).
% 0.21/0.43 thf(f514,plain,(
% 0.21/0.43 spl53_74 | ~spl53_1 | spl53_65 | ~spl53_75 | spl53_31),
% 0.21/0.43 inference(avatar_split_clause,[],[f122,f312,f511,f466,f181,f507])).
% 0.21/0.43 thf(f122,plain,(
% 0.21/0.43 ( ! [X15 : $i,X13 : $i] : (($true = vAPP($i,$o,cP,X13)) | ($true != vAPP($i,$o,cR,sK48)) | ($true != vAPP($i,$o,cQ,X15)) | ($true != sP0) | ($false = vAPP($i,$o,cP,sK47))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f107])).
% 0.21/0.43 thf(f505,plain,(
% 0.21/0.43 spl53_72 | spl53_73 | spl53_65 | spl53_33 | spl53_1),
% 0.21/0.43 inference(avatar_split_clause,[],[f125,f181,f321,f466,f501,f497])).
% 0.21/0.43 thf(f125,plain,(
% 0.21/0.43 ( ! [X11 : $i,X8 : $i,X9 : $i] : (($true = sP0) | ($true = vAPP($i,$o,cR,X8)) | ($true != vAPP($i,$o,cQ,X9)) | ($false = vAPP($i,$o,cP,X11)) | ($true = vAPP($i,$o,cP,sK46))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f108])).
% 0.21/0.43 thf(f108,plain,(
% 0.21/0.43 ( ! [X11 : $i,X8 : $i,X9 : $i] : (($true = sP0) | ($true = vAPP($i,$o,cR,X8)) | ($true != vAPP($i,$o,cQ,X9)) | (vAPP($i,$o,cP,X11) = vAPP($i,$o,cP,sK46))) )),
% 0.21/0.43 inference(cnf_transformation,[],[f74])).
% 0.21/0.43 thf(f504,plain,(
% 0.21/0.43 spl53_69 | spl53_31 | spl53_65 | spl53_33 | spl53_1),
% 0.21/0.43 inference(avatar_split_clause,[],[f124,f181,f321,f466,f312,f484])).
% 0.21/0.43 thf(f124,plain,(
% 0.21/0.43 ( ! [X11 : $i,X8 : $i,X9 : $i] : (($true = sP0) | ($true = vAPP($i,$o,cR,X8)) | ($true != vAPP($i,$o,cQ,X9)) | ($true = vAPP($i,$o,cP,X11)) | ($false = vAPP($i,$o,cP,sK46))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f108])).
% 0.21/0.43 thf(f503,plain,(
% 0.21/0.43 spl53_72 | spl53_73 | ~spl53_70 | spl53_71 | spl53_1),
% 0.21/0.43 inference(avatar_split_clause,[],[f127,f181,f492,f488,f501,f497])).
% 0.21/0.43 thf(f127,plain,(
% 0.21/0.43 ( ! [X11 : $i] : (($true = sP0) | ($true = vAPP($i,$o,cQ,sK44)) | ($true != vAPP($i,$o,cR,sK45)) | ($false = vAPP($i,$o,cP,X11)) | ($true = vAPP($i,$o,cP,sK46))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f109])).
% 0.21/0.43 thf(f109,plain,(
% 0.21/0.43 ( ! [X11 : $i] : (($true = sP0) | ($true = vAPP($i,$o,cQ,sK44)) | ($true != vAPP($i,$o,cR,sK45)) | (vAPP($i,$o,cP,X11) = vAPP($i,$o,cP,sK46))) )),
% 0.21/0.43 inference(cnf_transformation,[],[f74])).
% 0.21/0.43 thf(f495,plain,(
% 0.21/0.43 spl53_69 | spl53_31 | ~spl53_70 | spl53_71 | spl53_1),
% 0.21/0.43 inference(avatar_split_clause,[],[f126,f181,f492,f488,f312,f484])).
% 0.21/0.43 thf(f126,plain,(
% 0.21/0.43 ( ! [X11 : $i] : (($true = sP0) | ($true = vAPP($i,$o,cQ,sK44)) | ($true != vAPP($i,$o,cR,sK45)) | ($true = vAPP($i,$o,cP,X11)) | ($false = vAPP($i,$o,cP,sK46))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f109])).
% 0.21/0.43 thf(f482,plain,(
% 0.21/0.43 spl53_67 | spl53_68 | spl53_33 | spl53_1),
% 0.21/0.43 inference(avatar_split_clause,[],[f129,f181,f321,f478,f474])).
% 0.21/0.43 thf(f129,plain,(
% 0.21/0.43 ( ! [X2 : $i,X4 : $i] : (($true = sP0) | ($true = vAPP($i,$o,cR,X2)) | ($true = vAPP($i,$o,cQ,sK42)) | ($false = vAPP($i,$o,cP,X4)) | ($false = vAPP($i,$o,cP,vAPP($i,$i,sK43,X4)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f110])).
% 0.21/0.43 thf(f110,plain,(
% 0.21/0.43 ( ! [X2 : $i,X4 : $i] : (($true = sP0) | ($true = vAPP($i,$o,cR,X2)) | ($true = vAPP($i,$o,cQ,sK42)) | (vAPP($i,$o,cP,X4) != vAPP($i,$o,cP,vAPP($i,$i,sK43,X4)))) )),
% 0.21/0.43 inference(cnf_transformation,[],[f74])).
% 0.21/0.43 thf(f481,plain,(
% 0.21/0.43 spl53_64 | spl53_68 | spl53_33 | spl53_1),
% 0.21/0.43 inference(avatar_split_clause,[],[f128,f181,f321,f478,f463])).
% 0.21/0.43 thf(f128,plain,(
% 0.21/0.43 ( ! [X2 : $i,X4 : $i] : (($true = sP0) | ($true = vAPP($i,$o,cR,X2)) | ($true = vAPP($i,$o,cQ,sK42)) | ($true = vAPP($i,$o,cP,X4)) | ($true = vAPP($i,$o,cP,vAPP($i,$i,sK43,X4)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f110])).
% 0.21/0.43 thf(f476,plain,(
% 0.21/0.43 spl53_67 | spl53_65 | ~spl53_66 | spl53_1),
% 0.21/0.43 inference(avatar_split_clause,[],[f131,f181,f469,f466,f474])).
% 0.21/0.43 thf(f131,plain,(
% 0.21/0.43 ( ! [X1 : $i,X4 : $i] : (($true = sP0) | ($true != vAPP($i,$o,cR,sK41)) | (vAPP($i,$o,cQ,X1) != $true) | ($false = vAPP($i,$o,cP,X4)) | ($false = vAPP($i,$o,cP,vAPP($i,$i,sK43,X4)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f111])).
% 0.21/0.43 thf(f111,plain,(
% 0.21/0.43 ( ! [X1 : $i,X4 : $i] : (($true = sP0) | ($true != vAPP($i,$o,cR,sK41)) | (vAPP($i,$o,cQ,X1) != $true) | (vAPP($i,$o,cP,X4) != vAPP($i,$o,cP,vAPP($i,$i,sK43,X4)))) )),
% 0.21/0.43 inference(cnf_transformation,[],[f74])).
% 0.21/0.43 thf(f472,plain,(
% 0.21/0.43 spl53_64 | spl53_65 | ~spl53_66 | spl53_1),
% 0.21/0.43 inference(avatar_split_clause,[],[f130,f181,f469,f466,f463])).
% 0.21/0.43 thf(f130,plain,(
% 0.21/0.43 ( ! [X1 : $i,X4 : $i] : (($true = sP0) | ($true != vAPP($i,$o,cR,sK41)) | (vAPP($i,$o,cQ,X1) != $true) | ($true = vAPP($i,$o,cP,X4)) | ($true = vAPP($i,$o,cP,vAPP($i,$i,sK43,X4)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f111])).
% 0.21/0.43 thf(f461,plain,(
% 0.21/0.43 ~spl53_2 | spl53_63 | spl53_47 | spl53_12),
% 0.21/0.43 inference(avatar_split_clause,[],[f133,f229,f384,f457,f185])).
% 0.21/0.43 thf(f185,plain,(
% 0.21/0.43 spl53_2 <=> ($true = sP1)),
% 0.21/0.43 introduced(avatar_definition,[new_symbols(naming,[spl53_2])])).
% 0.21/0.43 thf(f133,plain,(
% 0.21/0.43 ( ! [X21 : $i,X22 : $i,X20 : $i] : (($true = vAPP($i,$o,cS,X20)) | ($true != vAPP($i,$o,cR,X21)) | ($false = vAPP($i,$o,cQ,X22)) | ($true != sP1) | ($false = vAPP($i,$o,cQ,vAPP($i,$i,sK40,X22)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f96])).
% 0.21/0.43 thf(f96,plain,(
% 0.21/0.43 ( ! [X21 : $i,X22 : $i,X20 : $i] : (($true = vAPP($i,$o,cS,X20)) | ($true != vAPP($i,$o,cR,X21)) | (vAPP($i,$o,cQ,X22) != vAPP($i,$o,cQ,vAPP($i,$i,sK40,X22))) | ($true != sP1)) )),
% 0.21/0.43 inference(cnf_transformation,[],[f59])).
% 0.21/0.43 thf(f59,plain,(
% 0.21/0.43 (($true = sP1) | ((((($true != vAPP($i,$o,cS,sK29)) | ! [X1] : (vAPP($i,$o,cR,X1) != $true)) & (! [X2] : ($true = vAPP($i,$o,cS,X2)) | ($true = vAPP($i,$o,cR,sK30)))) | ! [X4] : (vAPP($i,$o,cQ,X4) != vAPP($i,$o,cQ,vAPP($i,$i,sK31,X4)))) & (((($true = vAPP($i,$o,cR,sK32)) | ($true != vAPP($i,$o,cS,sK33))) & (! [X8] : ($true = vAPP($i,$o,cS,X8)) | ! [X9] : ($true != vAPP($i,$o,cR,X9)))) | ! [X11] : (vAPP($i,$o,cQ,X11) = vAPP($i,$o,cQ,sK34))))) & (((! [X13] : (vAPP($i,$o,cQ,X13) = vAPP($i,$o,cQ,sK35)) | ((($true != vAPP($i,$o,cS,sK36)) | ! [X15] : ($true != vAPP($i,$o,cR,X15))) & (! [X16] : ($true = vAPP($i,$o,cS,X16)) | ($true = vAPP($i,$o,cR,sK37))))) & (((($true = vAPP($i,$o,cR,sK38)) | ($true != vAPP($i,$o,cS,sK39))) & (! [X20] : ($true = vAPP($i,$o,cS,X20)) | ! [X21] : ($true != vAPP($i,$o,cR,X21)))) | ! [X22] : (vAPP($i,$o,cQ,X22) != vAPP($i,$o,cQ,vAPP($i,$i,sK40,X22))))) | ($true != sP1))),
% 0.21/0.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30,sK31,sK32,sK33,sK34,sK35,sK36,sK37,sK38,sK39,sK40])],[f46,f58,f57,f56,f55,f54,f53,f52,f51,f50,f49,f48,f47])).
% 0.21/0.43 thf(f47,plain,(
% 0.21/0.43 ? [X0] : (vAPP($i,$o,cS,X0) != $true) => ($true != vAPP($i,$o,cS,sK29))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f48,plain,(
% 0.21/0.43 ? [X3] : ($true = vAPP($i,$o,cR,X3)) => ($true = vAPP($i,$o,cR,sK30))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f49,plain,(
% 0.21/0.43 ! [X4] : (? [X5] : (vAPP($i,$o,cQ,X4) != vAPP($i,$o,cQ,X5)) => (vAPP($i,$o,cQ,X4) != vAPP($i,$o,cQ,vAPP($i,$i,sK31,X4))))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f50,plain,(
% 0.21/0.43 ? [X6] : ($true = vAPP($i,$o,cR,X6)) => ($true = vAPP($i,$o,cR,sK32))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f51,plain,(
% 0.21/0.43 ? [X7] : ($true != vAPP($i,$o,cS,X7)) => ($true != vAPP($i,$o,cS,sK33))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f52,plain,(
% 0.21/0.43 ? [X10] : ! [X11] : (vAPP($i,$o,cQ,X10) = vAPP($i,$o,cQ,X11)) => ! [X11] : (vAPP($i,$o,cQ,X11) = vAPP($i,$o,cQ,sK34))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f53,plain,(
% 0.21/0.43 ? [X12] : ! [X13] : (vAPP($i,$o,cQ,X12) = vAPP($i,$o,cQ,X13)) => ! [X13] : (vAPP($i,$o,cQ,X13) = vAPP($i,$o,cQ,sK35))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f54,plain,(
% 0.21/0.43 ? [X14] : ($true != vAPP($i,$o,cS,X14)) => ($true != vAPP($i,$o,cS,sK36))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f55,plain,(
% 0.21/0.43 ? [X17] : ($true = vAPP($i,$o,cR,X17)) => ($true = vAPP($i,$o,cR,sK37))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f56,plain,(
% 0.21/0.43 ? [X18] : ($true = vAPP($i,$o,cR,X18)) => ($true = vAPP($i,$o,cR,sK38))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f57,plain,(
% 0.21/0.43 ? [X19] : ($true != vAPP($i,$o,cS,X19)) => ($true != vAPP($i,$o,cS,sK39))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f58,plain,(
% 0.21/0.43 ! [X22] : (? [X23] : (vAPP($i,$o,cQ,X22) != vAPP($i,$o,cQ,X23)) => (vAPP($i,$o,cQ,X22) != vAPP($i,$o,cQ,vAPP($i,$i,sK40,X22))))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f46,plain,(
% 0.21/0.43 (($true = sP1) | ((((? [X0] : (vAPP($i,$o,cS,X0) != $true) | ! [X1] : (vAPP($i,$o,cR,X1) != $true)) & (! [X2] : ($true = vAPP($i,$o,cS,X2)) | ? [X3] : ($true = vAPP($i,$o,cR,X3)))) | ! [X4] : ? [X5] : (vAPP($i,$o,cQ,X4) != vAPP($i,$o,cQ,X5))) & (((? [X6] : ($true = vAPP($i,$o,cR,X6)) | ? [X7] : ($true != vAPP($i,$o,cS,X7))) & (! [X8] : ($true = vAPP($i,$o,cS,X8)) | ! [X9] : ($true != vAPP($i,$o,cR,X9)))) | ? [X10] : ! [X11] : (vAPP($i,$o,cQ,X10) = vAPP($i,$o,cQ,X11))))) & (((? [X12] : ! [X13] : (vAPP($i,$o,cQ,X12) = vAPP($i,$o,cQ,X13)) | ((? [X14] : ($true != vAPP($i,$o,cS,X14)) | ! [X15] : ($true != vAPP($i,$o,cR,X15))) & (! [X16] : ($true = vAPP($i,$o,cS,X16)) | ? [X17] : ($true = vAPP($i,$o,cR,X17))))) & (((? [X18] : ($true = vAPP($i,$o,cR,X18)) | ? [X19] : ($true != vAPP($i,$o,cS,X19))) & (! [X20] : ($true = vAPP($i,$o,cS,X20)) | ! [X21] : ($true != vAPP($i,$o,cR,X21)))) | ! [X22] : ? [X23] : (vAPP($i,$o,cQ,X22) != vAPP($i,$o,cQ,X23)))) | ($true != sP1))),
% 0.21/0.43 inference(rectify,[],[f45])).
% 0.21/0.43 thf(f45,plain,(
% 0.21/0.43 (($true = sP1) | ((((? [X7] : ($true != vAPP($i,$o,cS,X7)) | ! [X6] : ($true != vAPP($i,$o,cR,X6))) & (! [X7] : ($true = vAPP($i,$o,cS,X7)) | ? [X6] : ($true = vAPP($i,$o,cR,X6)))) | ! [X4] : ? [X5] : (vAPP($i,$o,cQ,X4) != vAPP($i,$o,cQ,X5))) & (((? [X6] : ($true = vAPP($i,$o,cR,X6)) | ? [X7] : ($true != vAPP($i,$o,cS,X7))) & (! [X7] : ($true = vAPP($i,$o,cS,X7)) | ! [X6] : ($true != vAPP($i,$o,cR,X6)))) | ? [X4] : ! [X5] : (vAPP($i,$o,cQ,X4) = vAPP($i,$o,cQ,X5))))) & (((? [X4] : ! [X5] : (vAPP($i,$o,cQ,X4) = vAPP($i,$o,cQ,X5)) | ((? [X7] : ($true != vAPP($i,$o,cS,X7)) | ! [X6] : ($true != vAPP($i,$o,cR,X6))) & (! [X7] : ($true = vAPP($i,$o,cS,X7)) | ? [X6] : ($true = vAPP($i,$o,cR,X6))))) & (((? [X6] : ($true = vAPP($i,$o,cR,X6)) | ? [X7] : ($true != vAPP($i,$o,cS,X7))) & (! [X7] : ($true = vAPP($i,$o,cS,X7)) | ! [X6] : ($true != vAPP($i,$o,cR,X6)))) | ! [X4] : ? [X5] : (vAPP($i,$o,cQ,X4) != vAPP($i,$o,cQ,X5)))) | ($true != sP1))),
% 0.21/0.43 inference(nnf_transformation,[],[f9])).
% 0.21/0.43 thf(f460,plain,(
% 0.21/0.43 ~spl53_2 | spl53_60 | spl53_47 | spl53_12),
% 0.21/0.43 inference(avatar_split_clause,[],[f132,f229,f384,f445,f185])).
% 0.21/0.43 thf(f132,plain,(
% 0.21/0.43 ( ! [X21 : $i,X22 : $i,X20 : $i] : (($true = vAPP($i,$o,cS,X20)) | ($true != vAPP($i,$o,cR,X21)) | ($true = vAPP($i,$o,cQ,X22)) | ($true != sP1) | ($true = vAPP($i,$o,cQ,vAPP($i,$i,sK40,X22)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f96])).
% 0.21/0.43 thf(f459,plain,(
% 0.21/0.43 ~spl53_2 | spl53_63 | ~spl53_61 | spl53_62),
% 0.21/0.43 inference(avatar_split_clause,[],[f135,f452,f448,f457,f185])).
% 0.21/0.43 thf(f135,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($true = vAPP($i,$o,cR,sK38)) | ($true != vAPP($i,$o,cS,sK39)) | ($false = vAPP($i,$o,cQ,X22)) | ($true != sP1) | ($false = vAPP($i,$o,cQ,vAPP($i,$i,sK40,X22)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f97])).
% 0.21/0.43 thf(f97,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($true = vAPP($i,$o,cR,sK38)) | ($true != vAPP($i,$o,cS,sK39)) | (vAPP($i,$o,cQ,X22) != vAPP($i,$o,cQ,vAPP($i,$i,sK40,X22))) | ($true != sP1)) )),
% 0.21/0.43 inference(cnf_transformation,[],[f59])).
% 0.21/0.43 thf(f455,plain,(
% 0.21/0.43 ~spl53_2 | spl53_60 | ~spl53_61 | spl53_62),
% 0.21/0.43 inference(avatar_split_clause,[],[f134,f452,f448,f445,f185])).
% 0.21/0.43 thf(f134,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($true = vAPP($i,$o,cR,sK38)) | ($true != vAPP($i,$o,cS,sK39)) | ($true = vAPP($i,$o,cQ,X22)) | ($true != sP1) | ($true = vAPP($i,$o,cQ,vAPP($i,$i,sK40,X22)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f97])).
% 0.21/0.43 thf(f443,plain,(
% 0.21/0.43 spl53_58 | ~spl53_2 | spl53_59 | spl53_12 | spl53_55),
% 0.21/0.43 inference(avatar_split_clause,[],[f137,f419,f229,f439,f185,f434])).
% 0.21/0.43 thf(f137,plain,(
% 0.21/0.43 ( ! [X16 : $i,X13 : $i] : (($false = vAPP($i,$o,cQ,X13)) | ($true = vAPP($i,$o,cS,X16)) | ($true = vAPP($i,$o,cR,sK37)) | ($true != sP1) | ($true = vAPP($i,$o,cQ,sK35))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f98])).
% 0.21/0.43 thf(f98,plain,(
% 0.21/0.43 ( ! [X16 : $i,X13 : $i] : ((vAPP($i,$o,cQ,X13) = vAPP($i,$o,cQ,sK35)) | ($true = vAPP($i,$o,cS,X16)) | ($true = vAPP($i,$o,cR,sK37)) | ($true != sP1)) )),
% 0.21/0.43 inference(cnf_transformation,[],[f59])).
% 0.21/0.43 thf(f442,plain,(
% 0.21/0.43 spl53_56 | ~spl53_2 | spl53_59 | spl53_12 | spl53_10),
% 0.21/0.43 inference(avatar_split_clause,[],[f136,f220,f229,f439,f185,f425])).
% 0.21/0.43 thf(f136,plain,(
% 0.21/0.43 ( ! [X16 : $i,X13 : $i] : (($true = vAPP($i,$o,cQ,X13)) | ($true = vAPP($i,$o,cS,X16)) | ($true = vAPP($i,$o,cR,sK37)) | ($true != sP1) | ($false = vAPP($i,$o,cQ,sK35))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f98])).
% 0.21/0.43 thf(f437,plain,(
% 0.21/0.43 spl53_58 | ~spl53_2 | spl53_47 | ~spl53_57 | spl53_55),
% 0.21/0.43 inference(avatar_split_clause,[],[f139,f419,f429,f384,f185,f434])).
% 0.21/0.43 thf(f139,plain,(
% 0.21/0.43 ( ! [X15 : $i,X13 : $i] : (($false = vAPP($i,$o,cQ,X13)) | ($true != vAPP($i,$o,cS,sK36)) | ($true != vAPP($i,$o,cR,X15)) | ($true != sP1) | ($true = vAPP($i,$o,cQ,sK35))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f99])).
% 0.21/0.43 thf(f99,plain,(
% 0.21/0.43 ( ! [X15 : $i,X13 : $i] : ((vAPP($i,$o,cQ,X13) = vAPP($i,$o,cQ,sK35)) | ($true != vAPP($i,$o,cS,sK36)) | ($true != vAPP($i,$o,cR,X15)) | ($true != sP1)) )),
% 0.21/0.43 inference(cnf_transformation,[],[f59])).
% 0.21/0.43 thf(f432,plain,(
% 0.21/0.43 spl53_56 | ~spl53_2 | spl53_47 | ~spl53_57 | spl53_10),
% 0.21/0.43 inference(avatar_split_clause,[],[f138,f220,f429,f384,f185,f425])).
% 0.21/0.43 thf(f138,plain,(
% 0.21/0.43 ( ! [X15 : $i,X13 : $i] : (($true = vAPP($i,$o,cQ,X13)) | ($true != vAPP($i,$o,cS,sK36)) | ($true != vAPP($i,$o,cR,X15)) | ($true != sP1) | ($false = vAPP($i,$o,cQ,sK35))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f99])).
% 0.21/0.43 thf(f423,plain,(
% 0.21/0.43 spl53_54 | spl53_55 | spl53_47 | spl53_12 | spl53_2),
% 0.21/0.43 inference(avatar_split_clause,[],[f141,f185,f229,f384,f419,f415])).
% 0.21/0.43 thf(f141,plain,(
% 0.21/0.43 ( ! [X11 : $i,X8 : $i,X9 : $i] : (($true = sP1) | ($true = vAPP($i,$o,cS,X8)) | ($true != vAPP($i,$o,cR,X9)) | ($false = vAPP($i,$o,cQ,X11)) | ($true = vAPP($i,$o,cQ,sK34))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f100])).
% 0.21/0.43 thf(f100,plain,(
% 0.21/0.43 ( ! [X11 : $i,X8 : $i,X9 : $i] : (($true = sP1) | ($true = vAPP($i,$o,cS,X8)) | ($true != vAPP($i,$o,cR,X9)) | (vAPP($i,$o,cQ,X11) = vAPP($i,$o,cQ,sK34))) )),
% 0.21/0.43 inference(cnf_transformation,[],[f59])).
% 0.21/0.43 thf(f422,plain,(
% 0.21/0.43 spl53_51 | spl53_10 | spl53_47 | spl53_12 | spl53_2),
% 0.21/0.43 inference(avatar_split_clause,[],[f140,f185,f229,f384,f220,f402])).
% 0.21/0.43 thf(f140,plain,(
% 0.21/0.43 ( ! [X11 : $i,X8 : $i,X9 : $i] : (($true = sP1) | ($true = vAPP($i,$o,cS,X8)) | ($true != vAPP($i,$o,cR,X9)) | ($true = vAPP($i,$o,cQ,X11)) | ($false = vAPP($i,$o,cQ,sK34))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f100])).
% 0.21/0.43 thf(f421,plain,(
% 0.21/0.43 spl53_54 | spl53_55 | ~spl53_52 | spl53_53 | spl53_2),
% 0.21/0.43 inference(avatar_split_clause,[],[f143,f185,f410,f406,f419,f415])).
% 0.21/0.43 thf(f143,plain,(
% 0.21/0.43 ( ! [X11 : $i] : (($true = sP1) | ($true = vAPP($i,$o,cR,sK32)) | ($true != vAPP($i,$o,cS,sK33)) | ($false = vAPP($i,$o,cQ,X11)) | ($true = vAPP($i,$o,cQ,sK34))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f101])).
% 0.21/0.43 thf(f101,plain,(
% 0.21/0.43 ( ! [X11 : $i] : (($true = sP1) | ($true = vAPP($i,$o,cR,sK32)) | ($true != vAPP($i,$o,cS,sK33)) | (vAPP($i,$o,cQ,X11) = vAPP($i,$o,cQ,sK34))) )),
% 0.21/0.43 inference(cnf_transformation,[],[f59])).
% 0.21/0.43 thf(f413,plain,(
% 0.21/0.43 spl53_51 | spl53_10 | ~spl53_52 | spl53_53 | spl53_2),
% 0.21/0.43 inference(avatar_split_clause,[],[f142,f185,f410,f406,f220,f402])).
% 0.21/0.43 thf(f142,plain,(
% 0.21/0.43 ( ! [X11 : $i] : (($true = sP1) | ($true = vAPP($i,$o,cR,sK32)) | ($true != vAPP($i,$o,cS,sK33)) | ($true = vAPP($i,$o,cQ,X11)) | ($false = vAPP($i,$o,cQ,sK34))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f101])).
% 0.21/0.43 thf(f400,plain,(
% 0.21/0.43 spl53_49 | spl53_50 | spl53_12 | spl53_2),
% 0.21/0.43 inference(avatar_split_clause,[],[f145,f185,f229,f396,f392])).
% 0.21/0.43 thf(f145,plain,(
% 0.21/0.43 ( ! [X2 : $i,X4 : $i] : (($true = sP1) | ($true = vAPP($i,$o,cS,X2)) | ($true = vAPP($i,$o,cR,sK30)) | ($false = vAPP($i,$o,cQ,X4)) | ($false = vAPP($i,$o,cQ,vAPP($i,$i,sK31,X4)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f102])).
% 0.21/0.43 thf(f102,plain,(
% 0.21/0.43 ( ! [X2 : $i,X4 : $i] : (($true = sP1) | ($true = vAPP($i,$o,cS,X2)) | ($true = vAPP($i,$o,cR,sK30)) | (vAPP($i,$o,cQ,X4) != vAPP($i,$o,cQ,vAPP($i,$i,sK31,X4)))) )),
% 0.21/0.43 inference(cnf_transformation,[],[f59])).
% 0.21/0.43 thf(f399,plain,(
% 0.21/0.43 spl53_46 | spl53_50 | spl53_12 | spl53_2),
% 0.21/0.43 inference(avatar_split_clause,[],[f144,f185,f229,f396,f381])).
% 0.21/0.43 thf(f144,plain,(
% 0.21/0.43 ( ! [X2 : $i,X4 : $i] : (($true = sP1) | ($true = vAPP($i,$o,cS,X2)) | ($true = vAPP($i,$o,cR,sK30)) | ($true = vAPP($i,$o,cQ,X4)) | ($true = vAPP($i,$o,cQ,vAPP($i,$i,sK31,X4)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f102])).
% 0.21/0.43 thf(f394,plain,(
% 0.21/0.43 spl53_49 | spl53_47 | ~spl53_48 | spl53_2),
% 0.21/0.43 inference(avatar_split_clause,[],[f147,f185,f387,f384,f392])).
% 0.21/0.43 thf(f147,plain,(
% 0.21/0.43 ( ! [X1 : $i,X4 : $i] : (($true = sP1) | ($true != vAPP($i,$o,cS,sK29)) | (vAPP($i,$o,cR,X1) != $true) | ($false = vAPP($i,$o,cQ,X4)) | ($false = vAPP($i,$o,cQ,vAPP($i,$i,sK31,X4)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f103])).
% 0.21/0.43 thf(f103,plain,(
% 0.21/0.43 ( ! [X1 : $i,X4 : $i] : (($true = sP1) | ($true != vAPP($i,$o,cS,sK29)) | (vAPP($i,$o,cR,X1) != $true) | (vAPP($i,$o,cQ,X4) != vAPP($i,$o,cQ,vAPP($i,$i,sK31,X4)))) )),
% 0.21/0.43 inference(cnf_transformation,[],[f59])).
% 0.21/0.43 thf(f390,plain,(
% 0.21/0.43 spl53_46 | spl53_47 | ~spl53_48 | spl53_2),
% 0.21/0.43 inference(avatar_split_clause,[],[f146,f185,f387,f384,f381])).
% 0.21/0.43 thf(f146,plain,(
% 0.21/0.43 ( ! [X1 : $i,X4 : $i] : (($true = sP1) | ($true != vAPP($i,$o,cS,sK29)) | (vAPP($i,$o,cR,X1) != $true) | ($true = vAPP($i,$o,cQ,X4)) | ($true = vAPP($i,$o,cQ,vAPP($i,$i,sK31,X4)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f103])).
% 0.21/0.43 thf(f379,plain,(
% 0.21/0.43 ~spl53_28 | spl53_45 | spl53_26 | spl53_31),
% 0.21/0.43 inference(avatar_split_clause,[],[f149,f312,f292,f375,f299])).
% 0.21/0.43 thf(f149,plain,(
% 0.21/0.43 ( ! [X21 : $i,X22 : $i,X20 : $i] : (($true = vAPP($i,$o,cP,X20)) | ($true != vAPP($i,$o,cS,X21)) | ($false = vAPP($i,$o,cR,X22)) | ($true != sP2) | ($false = vAPP($i,$o,cR,vAPP($i,$i,sK28,X22)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f88])).
% 0.21/0.43 thf(f88,plain,(
% 0.21/0.43 ( ! [X21 : $i,X22 : $i,X20 : $i] : (($true = vAPP($i,$o,cP,X20)) | ($true != vAPP($i,$o,cS,X21)) | (vAPP($i,$o,cR,X22) != vAPP($i,$o,cR,vAPP($i,$i,sK28,X22))) | ($true != sP2)) )),
% 0.21/0.43 inference(cnf_transformation,[],[f44])).
% 0.21/0.43 thf(f44,plain,(
% 0.21/0.43 (($true = sP2) | ((((($true != vAPP($i,$o,cP,sK17)) | ! [X1] : (vAPP($i,$o,cS,X1) != $true)) & (! [X2] : ($true = vAPP($i,$o,cP,X2)) | ($true = vAPP($i,$o,cS,sK18)))) | ! [X4] : (vAPP($i,$o,cR,X4) != vAPP($i,$o,cR,vAPP($i,$i,sK19,X4)))) & (((($true = vAPP($i,$o,cS,sK20)) | ($true != vAPP($i,$o,cP,sK21))) & (! [X8] : ($true = vAPP($i,$o,cP,X8)) | ! [X9] : ($true != vAPP($i,$o,cS,X9)))) | ! [X11] : (vAPP($i,$o,cR,X11) = vAPP($i,$o,cR,sK22))))) & (((! [X13] : (vAPP($i,$o,cR,X13) = vAPP($i,$o,cR,sK23)) | ((($true != vAPP($i,$o,cP,sK24)) | ! [X15] : ($true != vAPP($i,$o,cS,X15))) & (! [X16] : ($true = vAPP($i,$o,cP,X16)) | ($true = vAPP($i,$o,cS,sK25))))) & (((($true = vAPP($i,$o,cS,sK26)) | ($true != vAPP($i,$o,cP,sK27))) & (! [X20] : ($true = vAPP($i,$o,cP,X20)) | ! [X21] : ($true != vAPP($i,$o,cS,X21)))) | ! [X22] : (vAPP($i,$o,cR,X22) != vAPP($i,$o,cR,vAPP($i,$i,sK28,X22))))) | ($true != sP2))),
% 0.21/0.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18,sK19,sK20,sK21,sK22,sK23,sK24,sK25,sK26,sK27,sK28])],[f31,f43,f42,f41,f40,f39,f38,f37,f36,f35,f34,f33,f32])).
% 0.21/0.43 thf(f32,plain,(
% 0.21/0.43 ? [X0] : (vAPP($i,$o,cP,X0) != $true) => ($true != vAPP($i,$o,cP,sK17))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f33,plain,(
% 0.21/0.43 ? [X3] : ($true = vAPP($i,$o,cS,X3)) => ($true = vAPP($i,$o,cS,sK18))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f34,plain,(
% 0.21/0.43 ! [X4] : (? [X5] : (vAPP($i,$o,cR,X4) != vAPP($i,$o,cR,X5)) => (vAPP($i,$o,cR,X4) != vAPP($i,$o,cR,vAPP($i,$i,sK19,X4))))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f35,plain,(
% 0.21/0.43 ? [X6] : ($true = vAPP($i,$o,cS,X6)) => ($true = vAPP($i,$o,cS,sK20))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f36,plain,(
% 0.21/0.43 ? [X7] : ($true != vAPP($i,$o,cP,X7)) => ($true != vAPP($i,$o,cP,sK21))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f37,plain,(
% 0.21/0.43 ? [X10] : ! [X11] : (vAPP($i,$o,cR,X10) = vAPP($i,$o,cR,X11)) => ! [X11] : (vAPP($i,$o,cR,X11) = vAPP($i,$o,cR,sK22))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f38,plain,(
% 0.21/0.43 ? [X12] : ! [X13] : (vAPP($i,$o,cR,X12) = vAPP($i,$o,cR,X13)) => ! [X13] : (vAPP($i,$o,cR,X13) = vAPP($i,$o,cR,sK23))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f39,plain,(
% 0.21/0.43 ? [X14] : ($true != vAPP($i,$o,cP,X14)) => ($true != vAPP($i,$o,cP,sK24))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f40,plain,(
% 0.21/0.43 ? [X17] : ($true = vAPP($i,$o,cS,X17)) => ($true = vAPP($i,$o,cS,sK25))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f41,plain,(
% 0.21/0.43 ? [X18] : ($true = vAPP($i,$o,cS,X18)) => ($true = vAPP($i,$o,cS,sK26))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f42,plain,(
% 0.21/0.43 ? [X19] : ($true != vAPP($i,$o,cP,X19)) => ($true != vAPP($i,$o,cP,sK27))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f43,plain,(
% 0.21/0.43 ! [X22] : (? [X23] : (vAPP($i,$o,cR,X22) != vAPP($i,$o,cR,X23)) => (vAPP($i,$o,cR,X22) != vAPP($i,$o,cR,vAPP($i,$i,sK28,X22))))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f31,plain,(
% 0.21/0.43 (($true = sP2) | ((((? [X0] : (vAPP($i,$o,cP,X0) != $true) | ! [X1] : (vAPP($i,$o,cS,X1) != $true)) & (! [X2] : ($true = vAPP($i,$o,cP,X2)) | ? [X3] : ($true = vAPP($i,$o,cS,X3)))) | ! [X4] : ? [X5] : (vAPP($i,$o,cR,X4) != vAPP($i,$o,cR,X5))) & (((? [X6] : ($true = vAPP($i,$o,cS,X6)) | ? [X7] : ($true != vAPP($i,$o,cP,X7))) & (! [X8] : ($true = vAPP($i,$o,cP,X8)) | ! [X9] : ($true != vAPP($i,$o,cS,X9)))) | ? [X10] : ! [X11] : (vAPP($i,$o,cR,X10) = vAPP($i,$o,cR,X11))))) & (((? [X12] : ! [X13] : (vAPP($i,$o,cR,X12) = vAPP($i,$o,cR,X13)) | ((? [X14] : ($true != vAPP($i,$o,cP,X14)) | ! [X15] : ($true != vAPP($i,$o,cS,X15))) & (! [X16] : ($true = vAPP($i,$o,cP,X16)) | ? [X17] : ($true = vAPP($i,$o,cS,X17))))) & (((? [X18] : ($true = vAPP($i,$o,cS,X18)) | ? [X19] : ($true != vAPP($i,$o,cP,X19))) & (! [X20] : ($true = vAPP($i,$o,cP,X20)) | ! [X21] : ($true != vAPP($i,$o,cS,X21)))) | ! [X22] : ? [X23] : (vAPP($i,$o,cR,X22) != vAPP($i,$o,cR,X23)))) | ($true != sP2))),
% 0.21/0.43 inference(rectify,[],[f30])).
% 0.21/0.43 thf(f30,plain,(
% 0.21/0.43 (($true = sP2) | ((((? [X11] : ($true != vAPP($i,$o,cP,X11)) | ! [X10] : ($true != vAPP($i,$o,cS,X10))) & (! [X11] : ($true = vAPP($i,$o,cP,X11)) | ? [X10] : ($true = vAPP($i,$o,cS,X10)))) | ! [X8] : ? [X9] : (vAPP($i,$o,cR,X8) != vAPP($i,$o,cR,X9))) & (((? [X10] : ($true = vAPP($i,$o,cS,X10)) | ? [X11] : ($true != vAPP($i,$o,cP,X11))) & (! [X11] : ($true = vAPP($i,$o,cP,X11)) | ! [X10] : ($true != vAPP($i,$o,cS,X10)))) | ? [X8] : ! [X9] : (vAPP($i,$o,cR,X8) = vAPP($i,$o,cR,X9))))) & (((? [X8] : ! [X9] : (vAPP($i,$o,cR,X8) = vAPP($i,$o,cR,X9)) | ((? [X11] : ($true != vAPP($i,$o,cP,X11)) | ! [X10] : ($true != vAPP($i,$o,cS,X10))) & (! [X11] : ($true = vAPP($i,$o,cP,X11)) | ? [X10] : ($true = vAPP($i,$o,cS,X10))))) & (((? [X10] : ($true = vAPP($i,$o,cS,X10)) | ? [X11] : ($true != vAPP($i,$o,cP,X11))) & (! [X11] : ($true = vAPP($i,$o,cP,X11)) | ! [X10] : ($true != vAPP($i,$o,cS,X10)))) | ! [X8] : ? [X9] : (vAPP($i,$o,cR,X8) != vAPP($i,$o,cR,X9)))) | ($true != sP2))),
% 0.21/0.43 inference(nnf_transformation,[],[f10])).
% 0.21/0.43 thf(f378,plain,(
% 0.21/0.43 ~spl53_28 | spl53_42 | spl53_26 | spl53_31),
% 0.21/0.43 inference(avatar_split_clause,[],[f148,f312,f292,f363,f299])).
% 0.21/0.43 thf(f148,plain,(
% 0.21/0.43 ( ! [X21 : $i,X22 : $i,X20 : $i] : (($true = vAPP($i,$o,cP,X20)) | ($true != vAPP($i,$o,cS,X21)) | ($true = vAPP($i,$o,cR,X22)) | ($true != sP2) | ($true = vAPP($i,$o,cR,vAPP($i,$i,sK28,X22)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f88])).
% 0.21/0.43 thf(f377,plain,(
% 0.21/0.43 ~spl53_28 | spl53_45 | ~spl53_43 | spl53_44),
% 0.21/0.43 inference(avatar_split_clause,[],[f151,f370,f366,f375,f299])).
% 0.21/0.43 thf(f151,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($true = vAPP($i,$o,cS,sK26)) | ($true != vAPP($i,$o,cP,sK27)) | ($false = vAPP($i,$o,cR,X22)) | ($true != sP2) | ($false = vAPP($i,$o,cR,vAPP($i,$i,sK28,X22)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f89])).
% 0.21/0.43 thf(f89,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($true = vAPP($i,$o,cS,sK26)) | ($true != vAPP($i,$o,cP,sK27)) | (vAPP($i,$o,cR,X22) != vAPP($i,$o,cR,vAPP($i,$i,sK28,X22))) | ($true != sP2)) )),
% 0.21/0.43 inference(cnf_transformation,[],[f44])).
% 0.21/0.43 thf(f373,plain,(
% 0.21/0.43 ~spl53_28 | spl53_42 | ~spl53_43 | spl53_44),
% 0.21/0.43 inference(avatar_split_clause,[],[f150,f370,f366,f363,f299])).
% 0.21/0.43 thf(f150,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($true = vAPP($i,$o,cS,sK26)) | ($true != vAPP($i,$o,cP,sK27)) | ($true = vAPP($i,$o,cR,X22)) | ($true != sP2) | ($true = vAPP($i,$o,cR,vAPP($i,$i,sK28,X22)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f89])).
% 0.21/0.43 thf(f361,plain,(
% 0.21/0.43 spl53_40 | ~spl53_28 | spl53_41 | spl53_31 | spl53_37),
% 0.21/0.43 inference(avatar_split_clause,[],[f153,f337,f312,f357,f299,f352])).
% 0.21/0.43 thf(f153,plain,(
% 0.21/0.43 ( ! [X16 : $i,X13 : $i] : (($false = vAPP($i,$o,cR,X13)) | ($true = vAPP($i,$o,cP,X16)) | ($true = vAPP($i,$o,cS,sK25)) | ($true != sP2) | ($true = vAPP($i,$o,cR,sK23))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f90])).
% 0.21/0.43 thf(f90,plain,(
% 0.21/0.43 ( ! [X16 : $i,X13 : $i] : ((vAPP($i,$o,cR,X13) = vAPP($i,$o,cR,sK23)) | ($true = vAPP($i,$o,cP,X16)) | ($true = vAPP($i,$o,cS,sK25)) | ($true != sP2)) )),
% 0.21/0.43 inference(cnf_transformation,[],[f44])).
% 0.21/0.43 thf(f360,plain,(
% 0.21/0.43 spl53_38 | ~spl53_28 | spl53_41 | spl53_31 | spl53_33),
% 0.21/0.43 inference(avatar_split_clause,[],[f152,f321,f312,f357,f299,f343])).
% 0.21/0.43 thf(f152,plain,(
% 0.21/0.43 ( ! [X16 : $i,X13 : $i] : (($true = vAPP($i,$o,cR,X13)) | ($true = vAPP($i,$o,cP,X16)) | ($true = vAPP($i,$o,cS,sK25)) | ($true != sP2) | ($false = vAPP($i,$o,cR,sK23))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f90])).
% 0.21/0.43 thf(f355,plain,(
% 0.21/0.43 spl53_40 | ~spl53_28 | spl53_26 | ~spl53_39 | spl53_37),
% 0.21/0.43 inference(avatar_split_clause,[],[f155,f337,f347,f292,f299,f352])).
% 0.21/0.43 thf(f155,plain,(
% 0.21/0.43 ( ! [X15 : $i,X13 : $i] : (($false = vAPP($i,$o,cR,X13)) | ($true != vAPP($i,$o,cP,sK24)) | ($true != vAPP($i,$o,cS,X15)) | ($true != sP2) | ($true = vAPP($i,$o,cR,sK23))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f91])).
% 0.21/0.43 thf(f91,plain,(
% 0.21/0.43 ( ! [X15 : $i,X13 : $i] : ((vAPP($i,$o,cR,X13) = vAPP($i,$o,cR,sK23)) | ($true != vAPP($i,$o,cP,sK24)) | ($true != vAPP($i,$o,cS,X15)) | ($true != sP2)) )),
% 0.21/0.43 inference(cnf_transformation,[],[f44])).
% 0.21/0.43 thf(f350,plain,(
% 0.21/0.43 spl53_38 | ~spl53_28 | spl53_26 | ~spl53_39 | spl53_33),
% 0.21/0.43 inference(avatar_split_clause,[],[f154,f321,f347,f292,f299,f343])).
% 0.21/0.43 thf(f154,plain,(
% 0.21/0.43 ( ! [X15 : $i,X13 : $i] : (($true = vAPP($i,$o,cR,X13)) | ($true != vAPP($i,$o,cP,sK24)) | ($true != vAPP($i,$o,cS,X15)) | ($true != sP2) | ($false = vAPP($i,$o,cR,sK23))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f91])).
% 0.21/0.43 thf(f341,plain,(
% 0.21/0.43 spl53_36 | spl53_37 | spl53_26 | spl53_31 | spl53_28),
% 0.21/0.43 inference(avatar_split_clause,[],[f157,f299,f312,f292,f337,f333])).
% 0.21/0.43 thf(f157,plain,(
% 0.21/0.43 ( ! [X11 : $i,X8 : $i,X9 : $i] : (($true = sP2) | ($true = vAPP($i,$o,cP,X8)) | ($true != vAPP($i,$o,cS,X9)) | ($false = vAPP($i,$o,cR,X11)) | ($true = vAPP($i,$o,cR,sK22))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f92])).
% 0.21/0.43 thf(f92,plain,(
% 0.21/0.43 ( ! [X11 : $i,X8 : $i,X9 : $i] : (($true = sP2) | ($true = vAPP($i,$o,cP,X8)) | ($true != vAPP($i,$o,cS,X9)) | (vAPP($i,$o,cR,X11) = vAPP($i,$o,cR,sK22))) )),
% 0.21/0.43 inference(cnf_transformation,[],[f44])).
% 0.21/0.43 thf(f340,plain,(
% 0.21/0.43 spl53_32 | spl53_33 | spl53_26 | spl53_31 | spl53_28),
% 0.21/0.43 inference(avatar_split_clause,[],[f156,f299,f312,f292,f321,f317])).
% 0.21/0.43 thf(f156,plain,(
% 0.21/0.43 ( ! [X11 : $i,X8 : $i,X9 : $i] : (($true = sP2) | ($true = vAPP($i,$o,cP,X8)) | ($true != vAPP($i,$o,cS,X9)) | ($true = vAPP($i,$o,cR,X11)) | ($false = vAPP($i,$o,cR,sK22))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f92])).
% 0.21/0.43 thf(f339,plain,(
% 0.21/0.43 spl53_36 | spl53_37 | ~spl53_34 | spl53_35 | spl53_28),
% 0.21/0.43 inference(avatar_split_clause,[],[f159,f299,f328,f324,f337,f333])).
% 0.21/0.43 thf(f159,plain,(
% 0.21/0.43 ( ! [X11 : $i] : (($true = sP2) | ($true = vAPP($i,$o,cS,sK20)) | ($true != vAPP($i,$o,cP,sK21)) | ($false = vAPP($i,$o,cR,X11)) | ($true = vAPP($i,$o,cR,sK22))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f93])).
% 0.21/0.43 thf(f93,plain,(
% 0.21/0.43 ( ! [X11 : $i] : (($true = sP2) | ($true = vAPP($i,$o,cS,sK20)) | ($true != vAPP($i,$o,cP,sK21)) | (vAPP($i,$o,cR,X11) = vAPP($i,$o,cR,sK22))) )),
% 0.21/0.43 inference(cnf_transformation,[],[f44])).
% 0.21/0.43 thf(f331,plain,(
% 0.21/0.43 spl53_32 | spl53_33 | ~spl53_34 | spl53_35 | spl53_28),
% 0.21/0.43 inference(avatar_split_clause,[],[f158,f299,f328,f324,f321,f317])).
% 0.21/0.43 thf(f158,plain,(
% 0.21/0.43 ( ! [X11 : $i] : (($true = sP2) | ($true = vAPP($i,$o,cS,sK20)) | ($true != vAPP($i,$o,cP,sK21)) | ($true = vAPP($i,$o,cR,X11)) | ($false = vAPP($i,$o,cR,sK22))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f93])).
% 0.21/0.43 thf(f315,plain,(
% 0.21/0.43 spl53_29 | spl53_30 | spl53_31 | spl53_28),
% 0.21/0.43 inference(avatar_split_clause,[],[f161,f299,f312,f308,f304])).
% 0.21/0.43 thf(f161,plain,(
% 0.21/0.43 ( ! [X2 : $i,X4 : $i] : (($true = sP2) | ($true = vAPP($i,$o,cP,X2)) | ($true = vAPP($i,$o,cS,sK18)) | ($false = vAPP($i,$o,cR,X4)) | ($false = vAPP($i,$o,cR,vAPP($i,$i,sK19,X4)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f94])).
% 0.21/0.43 thf(f94,plain,(
% 0.21/0.43 ( ! [X2 : $i,X4 : $i] : (($true = sP2) | ($true = vAPP($i,$o,cP,X2)) | ($true = vAPP($i,$o,cS,sK18)) | (vAPP($i,$o,cR,X4) != vAPP($i,$o,cR,vAPP($i,$i,sK19,X4)))) )),
% 0.21/0.43 inference(cnf_transformation,[],[f44])).
% 0.21/0.43 thf(f314,plain,(
% 0.21/0.43 spl53_25 | spl53_30 | spl53_31 | spl53_28),
% 0.21/0.43 inference(avatar_split_clause,[],[f160,f299,f312,f308,f289])).
% 0.21/0.43 thf(f160,plain,(
% 0.21/0.43 ( ! [X2 : $i,X4 : $i] : (($true = sP2) | ($true = vAPP($i,$o,cP,X2)) | ($true = vAPP($i,$o,cS,sK18)) | ($true = vAPP($i,$o,cR,X4)) | ($true = vAPP($i,$o,cR,vAPP($i,$i,sK19,X4)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f94])).
% 0.21/0.43 thf(f306,plain,(
% 0.21/0.43 spl53_29 | spl53_26 | ~spl53_27 | spl53_28),
% 0.21/0.43 inference(avatar_split_clause,[],[f163,f299,f295,f292,f304])).
% 0.21/0.43 thf(f163,plain,(
% 0.21/0.43 ( ! [X1 : $i,X4 : $i] : (($true = sP2) | ($true != vAPP($i,$o,cP,sK17)) | (vAPP($i,$o,cS,X1) != $true) | ($false = vAPP($i,$o,cR,X4)) | ($false = vAPP($i,$o,cR,vAPP($i,$i,sK19,X4)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f95])).
% 0.21/0.43 thf(f95,plain,(
% 0.21/0.43 ( ! [X1 : $i,X4 : $i] : (($true = sP2) | ($true != vAPP($i,$o,cP,sK17)) | (vAPP($i,$o,cS,X1) != $true) | (vAPP($i,$o,cR,X4) != vAPP($i,$o,cR,vAPP($i,$i,sK19,X4)))) )),
% 0.21/0.43 inference(cnf_transformation,[],[f44])).
% 0.21/0.43 thf(f302,plain,(
% 0.21/0.43 spl53_25 | spl53_26 | ~spl53_27 | spl53_28),
% 0.21/0.43 inference(avatar_split_clause,[],[f162,f299,f295,f292,f289])).
% 0.21/0.43 thf(f162,plain,(
% 0.21/0.43 ( ! [X1 : $i,X4 : $i] : (($true = sP2) | ($true != vAPP($i,$o,cP,sK17)) | (vAPP($i,$o,cS,X1) != $true) | ($true = vAPP($i,$o,cR,X4)) | ($true = vAPP($i,$o,cR,vAPP($i,$i,sK19,X4)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f95])).
% 0.21/0.43 thf(f287,plain,(
% 0.21/0.43 ~spl53_7 | spl53_24 | spl53_5 | spl53_10),
% 0.21/0.43 inference(avatar_split_clause,[],[f165,f220,f200,f283,f207])).
% 0.21/0.43 thf(f165,plain,(
% 0.21/0.43 ( ! [X21 : $i,X22 : $i,X20 : $i] : (($true = vAPP($i,$o,cQ,X20)) | ($true != vAPP($i,$o,cP,X21)) | ($false = vAPP($i,$o,cS,X22)) | ($true != sP3) | ($false = vAPP($i,$o,cS,vAPP($i,$i,sK16,X22)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f80])).
% 0.21/0.43 thf(f80,plain,(
% 0.21/0.43 ( ! [X21 : $i,X22 : $i,X20 : $i] : (($true = vAPP($i,$o,cQ,X20)) | ($true != vAPP($i,$o,cP,X21)) | (vAPP($i,$o,cS,X22) != vAPP($i,$o,cS,vAPP($i,$i,sK16,X22))) | ($true != sP3)) )),
% 0.21/0.43 inference(cnf_transformation,[],[f29])).
% 0.21/0.43 thf(f29,plain,(
% 0.21/0.43 (($true = sP3) | ((((($true != vAPP($i,$o,cQ,sK5)) | ! [X1] : (vAPP($i,$o,cP,X1) != $true)) & (! [X2] : ($true = vAPP($i,$o,cQ,X2)) | ($true = vAPP($i,$o,cP,sK6)))) | ! [X4] : (vAPP($i,$o,cS,X4) != vAPP($i,$o,cS,vAPP($i,$i,sK7,X4)))) & (((($true = vAPP($i,$o,cP,sK8)) | ($true != vAPP($i,$o,cQ,sK9))) & (! [X8] : ($true = vAPP($i,$o,cQ,X8)) | ! [X9] : ($true != vAPP($i,$o,cP,X9)))) | ! [X11] : (vAPP($i,$o,cS,X11) = vAPP($i,$o,cS,sK10))))) & (((! [X13] : (vAPP($i,$o,cS,X13) = vAPP($i,$o,cS,sK11)) | ((($true != vAPP($i,$o,cQ,sK12)) | ! [X15] : ($true != vAPP($i,$o,cP,X15))) & (! [X16] : ($true = vAPP($i,$o,cQ,X16)) | ($true = vAPP($i,$o,cP,sK13))))) & (((($true = vAPP($i,$o,cP,sK14)) | ($true != vAPP($i,$o,cQ,sK15))) & (! [X20] : ($true = vAPP($i,$o,cQ,X20)) | ! [X21] : ($true != vAPP($i,$o,cP,X21)))) | ! [X22] : (vAPP($i,$o,cS,X22) != vAPP($i,$o,cS,vAPP($i,$i,sK16,X22))))) | ($true != sP3))),
% 0.21/0.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14,sK15,sK16])],[f16,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17])).
% 0.21/0.43 thf(f17,plain,(
% 0.21/0.43 ? [X0] : (vAPP($i,$o,cQ,X0) != $true) => ($true != vAPP($i,$o,cQ,sK5))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f18,plain,(
% 0.21/0.43 ? [X3] : ($true = vAPP($i,$o,cP,X3)) => ($true = vAPP($i,$o,cP,sK6))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f19,plain,(
% 0.21/0.43 ! [X4] : (? [X5] : (vAPP($i,$o,cS,X4) != vAPP($i,$o,cS,X5)) => (vAPP($i,$o,cS,X4) != vAPP($i,$o,cS,vAPP($i,$i,sK7,X4))))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f20,plain,(
% 0.21/0.43 ? [X6] : ($true = vAPP($i,$o,cP,X6)) => ($true = vAPP($i,$o,cP,sK8))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f21,plain,(
% 0.21/0.43 ? [X7] : ($true != vAPP($i,$o,cQ,X7)) => ($true != vAPP($i,$o,cQ,sK9))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f22,plain,(
% 0.21/0.43 ? [X10] : ! [X11] : (vAPP($i,$o,cS,X10) = vAPP($i,$o,cS,X11)) => ! [X11] : (vAPP($i,$o,cS,X11) = vAPP($i,$o,cS,sK10))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f23,plain,(
% 0.21/0.43 ? [X12] : ! [X13] : (vAPP($i,$o,cS,X12) = vAPP($i,$o,cS,X13)) => ! [X13] : (vAPP($i,$o,cS,X13) = vAPP($i,$o,cS,sK11))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f24,plain,(
% 0.21/0.43 ? [X14] : ($true != vAPP($i,$o,cQ,X14)) => ($true != vAPP($i,$o,cQ,sK12))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f25,plain,(
% 0.21/0.43 ? [X17] : ($true = vAPP($i,$o,cP,X17)) => ($true = vAPP($i,$o,cP,sK13))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f26,plain,(
% 0.21/0.43 ? [X18] : ($true = vAPP($i,$o,cP,X18)) => ($true = vAPP($i,$o,cP,sK14))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f27,plain,(
% 0.21/0.43 ? [X19] : ($true != vAPP($i,$o,cQ,X19)) => ($true != vAPP($i,$o,cQ,sK15))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f28,plain,(
% 0.21/0.43 ! [X22] : (? [X23] : (vAPP($i,$o,cS,X22) != vAPP($i,$o,cS,X23)) => (vAPP($i,$o,cS,X22) != vAPP($i,$o,cS,vAPP($i,$i,sK16,X22))))),
% 0.21/0.43 introduced(choice_axiom,[])).
% 0.21/0.43 thf(f16,plain,(
% 0.21/0.43 (($true = sP3) | ((((? [X0] : (vAPP($i,$o,cQ,X0) != $true) | ! [X1] : (vAPP($i,$o,cP,X1) != $true)) & (! [X2] : ($true = vAPP($i,$o,cQ,X2)) | ? [X3] : ($true = vAPP($i,$o,cP,X3)))) | ! [X4] : ? [X5] : (vAPP($i,$o,cS,X4) != vAPP($i,$o,cS,X5))) & (((? [X6] : ($true = vAPP($i,$o,cP,X6)) | ? [X7] : ($true != vAPP($i,$o,cQ,X7))) & (! [X8] : ($true = vAPP($i,$o,cQ,X8)) | ! [X9] : ($true != vAPP($i,$o,cP,X9)))) | ? [X10] : ! [X11] : (vAPP($i,$o,cS,X10) = vAPP($i,$o,cS,X11))))) & (((? [X12] : ! [X13] : (vAPP($i,$o,cS,X12) = vAPP($i,$o,cS,X13)) | ((? [X14] : ($true != vAPP($i,$o,cQ,X14)) | ! [X15] : ($true != vAPP($i,$o,cP,X15))) & (! [X16] : ($true = vAPP($i,$o,cQ,X16)) | ? [X17] : ($true = vAPP($i,$o,cP,X17))))) & (((? [X18] : ($true = vAPP($i,$o,cP,X18)) | ? [X19] : ($true != vAPP($i,$o,cQ,X19))) & (! [X20] : ($true = vAPP($i,$o,cQ,X20)) | ! [X21] : ($true != vAPP($i,$o,cP,X21)))) | ! [X22] : ? [X23] : (vAPP($i,$o,cS,X22) != vAPP($i,$o,cS,X23)))) | ($true != sP3))),
% 0.21/0.43 inference(rectify,[],[f15])).
% 0.21/0.43 thf(f15,plain,(
% 0.21/0.43 (($true = sP3) | ((((? [X15] : ($true != vAPP($i,$o,cQ,X15)) | ! [X14] : ($true != vAPP($i,$o,cP,X14))) & (! [X15] : ($true = vAPP($i,$o,cQ,X15)) | ? [X14] : ($true = vAPP($i,$o,cP,X14)))) | ! [X12] : ? [X13] : (vAPP($i,$o,cS,X12) != vAPP($i,$o,cS,X13))) & (((? [X14] : ($true = vAPP($i,$o,cP,X14)) | ? [X15] : ($true != vAPP($i,$o,cQ,X15))) & (! [X15] : ($true = vAPP($i,$o,cQ,X15)) | ! [X14] : ($true != vAPP($i,$o,cP,X14)))) | ? [X12] : ! [X13] : (vAPP($i,$o,cS,X12) = vAPP($i,$o,cS,X13))))) & (((? [X12] : ! [X13] : (vAPP($i,$o,cS,X12) = vAPP($i,$o,cS,X13)) | ((? [X15] : ($true != vAPP($i,$o,cQ,X15)) | ! [X14] : ($true != vAPP($i,$o,cP,X14))) & (! [X15] : ($true = vAPP($i,$o,cQ,X15)) | ? [X14] : ($true = vAPP($i,$o,cP,X14))))) & (((? [X14] : ($true = vAPP($i,$o,cP,X14)) | ? [X15] : ($true != vAPP($i,$o,cQ,X15))) & (! [X15] : ($true = vAPP($i,$o,cQ,X15)) | ! [X14] : ($true != vAPP($i,$o,cP,X14)))) | ! [X12] : ? [X13] : (vAPP($i,$o,cS,X12) != vAPP($i,$o,cS,X13)))) | ($true != sP3))),
% 0.21/0.43 inference(nnf_transformation,[],[f11])).
% 0.21/0.43 thf(f286,plain,(
% 0.21/0.43 ~spl53_7 | spl53_21 | spl53_5 | spl53_10),
% 0.21/0.43 inference(avatar_split_clause,[],[f164,f220,f200,f271,f207])).
% 0.21/0.43 thf(f164,plain,(
% 0.21/0.43 ( ! [X21 : $i,X22 : $i,X20 : $i] : (($true = vAPP($i,$o,cQ,X20)) | ($true != vAPP($i,$o,cP,X21)) | ($true = vAPP($i,$o,cS,X22)) | ($true != sP3) | ($true = vAPP($i,$o,cS,vAPP($i,$i,sK16,X22)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f80])).
% 0.21/0.43 thf(f285,plain,(
% 0.21/0.43 ~spl53_7 | spl53_24 | ~spl53_22 | spl53_23),
% 0.21/0.43 inference(avatar_split_clause,[],[f167,f278,f274,f283,f207])).
% 0.21/0.43 thf(f167,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($true = vAPP($i,$o,cP,sK14)) | ($true != vAPP($i,$o,cQ,sK15)) | ($false = vAPP($i,$o,cS,X22)) | ($true != sP3) | ($false = vAPP($i,$o,cS,vAPP($i,$i,sK16,X22)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f81])).
% 0.21/0.43 thf(f81,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($true = vAPP($i,$o,cP,sK14)) | ($true != vAPP($i,$o,cQ,sK15)) | (vAPP($i,$o,cS,X22) != vAPP($i,$o,cS,vAPP($i,$i,sK16,X22))) | ($true != sP3)) )),
% 0.21/0.43 inference(cnf_transformation,[],[f29])).
% 0.21/0.43 thf(f281,plain,(
% 0.21/0.43 ~spl53_7 | spl53_21 | ~spl53_22 | spl53_23),
% 0.21/0.43 inference(avatar_split_clause,[],[f166,f278,f274,f271,f207])).
% 0.21/0.43 thf(f166,plain,(
% 0.21/0.43 ( ! [X22 : $i] : (($true = vAPP($i,$o,cP,sK14)) | ($true != vAPP($i,$o,cQ,sK15)) | ($true = vAPP($i,$o,cS,X22)) | ($true != sP3) | ($true = vAPP($i,$o,cS,vAPP($i,$i,sK16,X22)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f81])).
% 0.21/0.43 thf(f269,plain,(
% 0.21/0.43 spl53_19 | ~spl53_7 | spl53_20 | spl53_10 | spl53_16),
% 0.21/0.43 inference(avatar_split_clause,[],[f169,f245,f220,f265,f207,f260])).
% 0.21/0.43 thf(f169,plain,(
% 0.21/0.43 ( ! [X16 : $i,X13 : $i] : (($false = vAPP($i,$o,cS,X13)) | ($true = vAPP($i,$o,cQ,X16)) | ($true = vAPP($i,$o,cP,sK13)) | ($true != sP3) | ($true = vAPP($i,$o,cS,sK11))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f82])).
% 0.21/0.43 thf(f82,plain,(
% 0.21/0.43 ( ! [X16 : $i,X13 : $i] : ((vAPP($i,$o,cS,X13) = vAPP($i,$o,cS,sK11)) | ($true = vAPP($i,$o,cQ,X16)) | ($true = vAPP($i,$o,cP,sK13)) | ($true != sP3)) )),
% 0.21/0.43 inference(cnf_transformation,[],[f29])).
% 0.21/0.43 thf(f268,plain,(
% 0.21/0.43 spl53_17 | ~spl53_7 | spl53_20 | spl53_10 | spl53_12),
% 0.21/0.43 inference(avatar_split_clause,[],[f168,f229,f220,f265,f207,f251])).
% 0.21/0.43 thf(f168,plain,(
% 0.21/0.43 ( ! [X16 : $i,X13 : $i] : (($true = vAPP($i,$o,cS,X13)) | ($true = vAPP($i,$o,cQ,X16)) | ($true = vAPP($i,$o,cP,sK13)) | ($true != sP3) | ($false = vAPP($i,$o,cS,sK11))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f82])).
% 0.21/0.43 thf(f263,plain,(
% 0.21/0.43 spl53_19 | ~spl53_7 | spl53_5 | ~spl53_18 | spl53_16),
% 0.21/0.43 inference(avatar_split_clause,[],[f171,f245,f255,f200,f207,f260])).
% 0.21/0.43 thf(f171,plain,(
% 0.21/0.43 ( ! [X15 : $i,X13 : $i] : (($false = vAPP($i,$o,cS,X13)) | ($true != vAPP($i,$o,cQ,sK12)) | ($true != vAPP($i,$o,cP,X15)) | ($true != sP3) | ($true = vAPP($i,$o,cS,sK11))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f83])).
% 0.21/0.43 thf(f83,plain,(
% 0.21/0.43 ( ! [X15 : $i,X13 : $i] : ((vAPP($i,$o,cS,X13) = vAPP($i,$o,cS,sK11)) | ($true != vAPP($i,$o,cQ,sK12)) | ($true != vAPP($i,$o,cP,X15)) | ($true != sP3)) )),
% 0.21/0.43 inference(cnf_transformation,[],[f29])).
% 0.21/0.43 thf(f258,plain,(
% 0.21/0.43 spl53_17 | ~spl53_7 | spl53_5 | ~spl53_18 | spl53_12),
% 0.21/0.43 inference(avatar_split_clause,[],[f170,f229,f255,f200,f207,f251])).
% 0.21/0.43 thf(f170,plain,(
% 0.21/0.43 ( ! [X15 : $i,X13 : $i] : (($true = vAPP($i,$o,cS,X13)) | ($true != vAPP($i,$o,cQ,sK12)) | ($true != vAPP($i,$o,cP,X15)) | ($true != sP3) | ($false = vAPP($i,$o,cS,sK11))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f83])).
% 0.21/0.43 thf(f249,plain,(
% 0.21/0.43 spl53_15 | spl53_16 | spl53_5 | spl53_10 | spl53_7),
% 0.21/0.43 inference(avatar_split_clause,[],[f173,f207,f220,f200,f245,f241])).
% 0.21/0.43 thf(f173,plain,(
% 0.21/0.43 ( ! [X11 : $i,X8 : $i,X9 : $i] : (($true = sP3) | ($true = vAPP($i,$o,cQ,X8)) | ($true != vAPP($i,$o,cP,X9)) | ($false = vAPP($i,$o,cS,X11)) | ($true = vAPP($i,$o,cS,sK10))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f84])).
% 0.21/0.43 thf(f84,plain,(
% 0.21/0.43 ( ! [X11 : $i,X8 : $i,X9 : $i] : (($true = sP3) | ($true = vAPP($i,$o,cQ,X8)) | ($true != vAPP($i,$o,cP,X9)) | (vAPP($i,$o,cS,X11) = vAPP($i,$o,cS,sK10))) )),
% 0.21/0.43 inference(cnf_transformation,[],[f29])).
% 0.21/0.43 thf(f248,plain,(
% 0.21/0.43 spl53_11 | spl53_12 | spl53_5 | spl53_10 | spl53_7),
% 0.21/0.43 inference(avatar_split_clause,[],[f172,f207,f220,f200,f229,f225])).
% 0.21/0.43 thf(f172,plain,(
% 0.21/0.43 ( ! [X11 : $i,X8 : $i,X9 : $i] : (($true = sP3) | ($true = vAPP($i,$o,cQ,X8)) | ($true != vAPP($i,$o,cP,X9)) | ($true = vAPP($i,$o,cS,X11)) | ($false = vAPP($i,$o,cS,sK10))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f84])).
% 0.21/0.43 thf(f247,plain,(
% 0.21/0.43 spl53_15 | spl53_16 | ~spl53_13 | spl53_14 | spl53_7),
% 0.21/0.43 inference(avatar_split_clause,[],[f175,f207,f236,f232,f245,f241])).
% 0.21/0.43 thf(f175,plain,(
% 0.21/0.43 ( ! [X11 : $i] : (($true = sP3) | ($true = vAPP($i,$o,cP,sK8)) | ($true != vAPP($i,$o,cQ,sK9)) | ($false = vAPP($i,$o,cS,X11)) | ($true = vAPP($i,$o,cS,sK10))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f85])).
% 0.21/0.43 thf(f85,plain,(
% 0.21/0.43 ( ! [X11 : $i] : (($true = sP3) | ($true = vAPP($i,$o,cP,sK8)) | ($true != vAPP($i,$o,cQ,sK9)) | (vAPP($i,$o,cS,X11) = vAPP($i,$o,cS,sK10))) )),
% 0.21/0.43 inference(cnf_transformation,[],[f29])).
% 0.21/0.43 thf(f239,plain,(
% 0.21/0.43 spl53_11 | spl53_12 | ~spl53_13 | spl53_14 | spl53_7),
% 0.21/0.43 inference(avatar_split_clause,[],[f174,f207,f236,f232,f229,f225])).
% 0.21/0.43 thf(f174,plain,(
% 0.21/0.43 ( ! [X11 : $i] : (($true = sP3) | ($true = vAPP($i,$o,cP,sK8)) | ($true != vAPP($i,$o,cQ,sK9)) | ($true = vAPP($i,$o,cS,X11)) | ($false = vAPP($i,$o,cS,sK10))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f85])).
% 0.21/0.43 thf(f223,plain,(
% 0.21/0.43 spl53_8 | spl53_9 | spl53_10 | spl53_7),
% 0.21/0.43 inference(avatar_split_clause,[],[f177,f207,f220,f216,f212])).
% 0.21/0.43 thf(f177,plain,(
% 0.21/0.43 ( ! [X2 : $i,X4 : $i] : (($true = sP3) | ($true = vAPP($i,$o,cQ,X2)) | ($true = vAPP($i,$o,cP,sK6)) | ($false = vAPP($i,$o,cS,X4)) | ($false = vAPP($i,$o,cS,vAPP($i,$i,sK7,X4)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f86])).
% 0.21/0.43 thf(f86,plain,(
% 0.21/0.43 ( ! [X2 : $i,X4 : $i] : (($true = sP3) | ($true = vAPP($i,$o,cQ,X2)) | ($true = vAPP($i,$o,cP,sK6)) | (vAPP($i,$o,cS,X4) != vAPP($i,$o,cS,vAPP($i,$i,sK7,X4)))) )),
% 0.21/0.43 inference(cnf_transformation,[],[f29])).
% 0.21/0.43 thf(f222,plain,(
% 0.21/0.43 spl53_4 | spl53_9 | spl53_10 | spl53_7),
% 0.21/0.43 inference(avatar_split_clause,[],[f176,f207,f220,f216,f197])).
% 0.21/0.43 thf(f176,plain,(
% 0.21/0.43 ( ! [X2 : $i,X4 : $i] : (($true = sP3) | ($true = vAPP($i,$o,cQ,X2)) | ($true = vAPP($i,$o,cP,sK6)) | ($true = vAPP($i,$o,cS,X4)) | ($true = vAPP($i,$o,cS,vAPP($i,$i,sK7,X4)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f86])).
% 0.21/0.43 thf(f214,plain,(
% 0.21/0.43 spl53_8 | spl53_5 | ~spl53_6 | spl53_7),
% 0.21/0.43 inference(avatar_split_clause,[],[f179,f207,f203,f200,f212])).
% 0.21/0.43 thf(f179,plain,(
% 0.21/0.43 ( ! [X1 : $i,X4 : $i] : (($true = sP3) | ($true != vAPP($i,$o,cQ,sK5)) | (vAPP($i,$o,cP,X1) != $true) | ($false = vAPP($i,$o,cS,X4)) | ($false = vAPP($i,$o,cS,vAPP($i,$i,sK7,X4)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f87])).
% 0.21/0.43 thf(f87,plain,(
% 0.21/0.43 ( ! [X1 : $i,X4 : $i] : (($true = sP3) | ($true != vAPP($i,$o,cQ,sK5)) | (vAPP($i,$o,cP,X1) != $true) | (vAPP($i,$o,cS,X4) != vAPP($i,$o,cS,vAPP($i,$i,sK7,X4)))) )),
% 0.21/0.43 inference(cnf_transformation,[],[f29])).
% 0.21/0.43 thf(f210,plain,(
% 0.21/0.43 spl53_4 | spl53_5 | ~spl53_6 | spl53_7),
% 0.21/0.43 inference(avatar_split_clause,[],[f178,f207,f203,f200,f197])).
% 0.21/0.43 thf(f178,plain,(
% 0.21/0.43 ( ! [X1 : $i,X4 : $i] : (($true = sP3) | ($true != vAPP($i,$o,cQ,sK5)) | (vAPP($i,$o,cP,X1) != $true) | ($true = vAPP($i,$o,cS,X4)) | ($true = vAPP($i,$o,cS,vAPP($i,$i,sK7,X4)))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f87])).
% 0.21/0.43 thf(f195,plain,(
% 0.21/0.43 ~spl53_3 | ~spl53_1 | spl53_2),
% 0.21/0.43 inference(avatar_split_clause,[],[f76,f185,f181,f189])).
% 0.21/0.43 thf(f76,plain,(
% 0.21/0.43 ($true = sP1) | ($true != sP0) | ($true != sP4)),
% 0.21/0.43 inference(cnf_transformation,[],[f14])).
% 0.21/0.43 thf(f14,plain,(
% 0.21/0.43 (($true = sP4) | ((($true != sP1) | ($true != sP0)) & (($true = sP1) | ($true = sP0)))) & (((($true = sP0) | ($true != sP1)) & (($true = sP1) | ($true != sP0))) | ($true != sP4))),
% 0.21/0.43 inference(nnf_transformation,[],[f12])).
% 0.21/0.43 thf(f194,plain,(
% 0.21/0.43 ~spl53_3 | ~spl53_2 | spl53_1),
% 0.21/0.43 inference(avatar_split_clause,[],[f77,f181,f185,f189])).
% 0.21/0.43 thf(f77,plain,(
% 0.21/0.43 ($true = sP0) | ($true != sP1) | ($true != sP4)),
% 0.21/0.43 inference(cnf_transformation,[],[f14])).
% 0.21/0.43 thf(f193,plain,(
% 0.21/0.43 spl53_1 | spl53_2 | spl53_3),
% 0.21/0.43 inference(avatar_split_clause,[],[f78,f189,f185,f181])).
% 0.21/0.43 thf(f78,plain,(
% 0.21/0.43 ($true = sP4) | ($true = sP1) | ($true = sP0)),
% 0.21/0.43 inference(cnf_transformation,[],[f14])).
% 0.21/0.43 thf(f192,plain,(
% 0.21/0.43 ~spl53_1 | ~spl53_2 | spl53_3),
% 0.21/0.43 inference(avatar_split_clause,[],[f79,f189,f185,f181])).
% 0.21/0.43 thf(f79,plain,(
% 0.21/0.43 ($true = sP4) | ($true != sP1) | ($true != sP0)),
% 0.21/0.43 inference(cnf_transformation,[],[f14])).
% 0.21/0.43 % SZS output end Proof for theBenchmark
% 0.21/0.43 % (27598)------------------------------
% 0.21/0.43 % (27598)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.43 % (27598)Termination reason: Refutation
% 0.21/0.43
% 0.21/0.43 % (27598)Memory used [KB]: 1189
% 0.21/0.43 % (27598)Time elapsed: 0.052 s
% 0.21/0.43 % (27598)Instructions burned: 91 (million)
% 0.21/0.43 % (27592)Success in time 0.069 s
%------------------------------------------------------------------------------