TSTP Solution File: SYN036^5 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SYN036^5 : 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 : n021.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 08:33:47 EDT 2024
% Result : Theorem 0.21s 0.39s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN036^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n021.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 20 15:21:08 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % (4015)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.36 % (4019)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.36 % Exception at run slice level
% 0.15/0.36 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.37 % (4018)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.37 % (4020)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)
% 0.15/0.37 % (4021)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.15/0.37 % (4023)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.15/0.37 % (4024)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)
% 0.15/0.37 % (4022)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.15/0.37 % Exception at run slice level
% 0.15/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.37 % (4020)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.37 % (4021)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.37 % Exception at run slice level
% 0.15/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.37 % Exception at run slice level
% 0.15/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.37 % (4026)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)
% 0.15/0.37 % Exception at run slice level
% 0.15/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.38 WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.21/0.38 % (4035)dis+11_4:5_nm=4:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_216 on theBenchmark for (216ds/0Mi)
% 0.21/0.38 % (4023)First to succeed.
% 0.21/0.39 WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.21/0.39 WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.21/0.39 % (4031)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)
% 0.21/0.39 % (4032)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)
% 0.21/0.39 % (4033)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)
% 0.21/0.39 % (4023)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4015"
% 0.21/0.39 % (4031)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.39 % (4032)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.39 % (4020)Also succeeded, but the first one will report.
% 0.21/0.39 % Exception at run slice level
% 0.21/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.39 % (4035)Also succeeded, but the first one will report.
% 0.21/0.39 % (4023)Refutation found. Thanks to Tanya!
% 0.21/0.39 % SZS status Theorem for theBenchmark
% 0.21/0.39 % SZS output start Proof for theBenchmark
% 0.21/0.39 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.39 thf(func_def_0, type, cQ: $i > $o).
% 0.21/0.39 thf(func_def_1, type, cP: $i > $o).
% 0.21/0.39 thf(func_def_5, type, sP0: $o).
% 0.21/0.39 thf(func_def_6, type, sP1: $o).
% 0.21/0.39 thf(func_def_9, type, sK4: $i > $i).
% 0.21/0.39 thf(func_def_18, type, sK13: $i > $i).
% 0.21/0.39 thf(func_def_21, type, sK16: $i > $i).
% 0.21/0.39 thf(func_def_30, type, sK25: $i > $i).
% 0.21/0.39 thf(func_def_32, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)).
% 0.21/0.39 thf(func_def_33, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)).
% 0.21/0.39 thf(func_def_34, type, vAND: $o > $o > $o).
% 0.21/0.39 thf(func_def_35, type, vOR: $o > $o > $o).
% 0.21/0.39 thf(func_def_36, type, vIMP: $o > $o > $o).
% 0.21/0.39 thf(func_def_37, type, vNOT: $o > $o).
% 0.21/0.39 thf(func_def_38, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)).
% 0.21/0.39 thf(f617,plain,(
% 0.21/0.39 $false),
% 0.21/0.39 inference(avatar_sat_refutation,[],[f110,f118,f141,f142,f161,f162,f178,f179,f199,f207,f230,f231,f250,f251,f267,f268,f269,f270,f271,f313,f315,f320,f335,f344,f352,f354,f375,f377,f379,f395,f407,f416,f419,f421,f430,f485,f490,f500,f503,f526,f542,f552,f562,f602,f605,f616])).
% 0.21/0.39 thf(f616,plain,(
% 0.21/0.39 ~spl26_6 | ~spl26_32),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f615])).
% 0.21/0.39 thf(f615,plain,(
% 0.21/0.39 $false | (~spl26_6 | ~spl26_32)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f608])).
% 0.21/0.39 thf(f608,plain,(
% 0.21/0.39 ($true = $false) | (~spl26_6 | ~spl26_32)),
% 0.21/0.39 inference(backward_demodulation,[],[f114,f228])).
% 0.21/0.39 thf(f228,plain,(
% 0.21/0.39 ( ! [X11 : $i] : (($false = vAPP($i,$o,cP,X11))) ) | ~spl26_32),
% 0.21/0.39 inference(avatar_component_clause,[],[f227])).
% 0.21/0.39 thf(f227,plain,(
% 0.21/0.39 spl26_32 <=> ! [X11] : ($false = vAPP($i,$o,cP,X11))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_32])])).
% 0.21/0.39 thf(f114,plain,(
% 0.21/0.39 ($true = vAPP($i,$o,cP,sK3)) | ~spl26_6),
% 0.21/0.39 inference(avatar_component_clause,[],[f112])).
% 0.21/0.39 thf(f112,plain,(
% 0.21/0.39 spl26_6 <=> ($true = vAPP($i,$o,cP,sK3))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_6])])).
% 0.21/0.39 thf(f605,plain,(
% 0.21/0.39 ~spl26_12 | ~spl26_36),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f604])).
% 0.21/0.39 thf(f604,plain,(
% 0.21/0.39 $false | (~spl26_12 | ~spl26_36)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f603])).
% 0.21/0.39 thf(f603,plain,(
% 0.21/0.39 ($true = $false) | (~spl26_12 | ~spl26_36)),
% 0.21/0.39 inference(forward_demodulation,[],[f249,f139])).
% 0.21/0.39 thf(f139,plain,(
% 0.21/0.39 ( ! [X11 : $i] : (($false = vAPP($i,$o,cQ,X11))) ) | ~spl26_12),
% 0.21/0.39 inference(avatar_component_clause,[],[f138])).
% 0.21/0.39 thf(f138,plain,(
% 0.21/0.39 spl26_12 <=> ! [X11] : ($false = vAPP($i,$o,cQ,X11))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_12])])).
% 0.21/0.39 thf(f249,plain,(
% 0.21/0.39 ($true = vAPP($i,$o,cQ,sK22)) | ~spl26_36),
% 0.21/0.39 inference(avatar_component_clause,[],[f247])).
% 0.21/0.39 thf(f247,plain,(
% 0.21/0.39 spl26_36 <=> ($true = vAPP($i,$o,cQ,sK22))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_36])])).
% 0.21/0.39 thf(f602,plain,(
% 0.21/0.39 ~spl26_33 | ~spl26_35),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f601])).
% 0.21/0.39 thf(f601,plain,(
% 0.21/0.39 $false | (~spl26_33 | ~spl26_35)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f600])).
% 0.21/0.39 thf(f600,plain,(
% 0.21/0.39 ($true = $false) | (~spl26_33 | ~spl26_35)),
% 0.21/0.39 inference(forward_demodulation,[],[f244,f235])).
% 0.21/0.39 thf(f235,plain,(
% 0.21/0.39 ($false = vAPP($i,$o,cP,sK20)) | ~spl26_33),
% 0.21/0.39 inference(avatar_component_clause,[],[f233])).
% 0.21/0.39 thf(f233,plain,(
% 0.21/0.39 spl26_33 <=> ($false = vAPP($i,$o,cP,sK20))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_33])])).
% 0.21/0.39 thf(f244,plain,(
% 0.21/0.39 ($true = vAPP($i,$o,cP,sK20)) | ~spl26_35),
% 0.21/0.39 inference(avatar_component_clause,[],[f242])).
% 0.21/0.39 thf(f242,plain,(
% 0.21/0.39 spl26_35 <=> ($true = vAPP($i,$o,cP,sK20))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_35])])).
% 0.21/0.39 thf(f562,plain,(
% 0.21/0.39 ~spl26_7 | ~spl26_20),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f561])).
% 0.21/0.39 thf(f561,plain,(
% 0.21/0.39 $false | (~spl26_7 | ~spl26_20)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f555])).
% 0.21/0.39 thf(f555,plain,(
% 0.21/0.39 ($true = $false) | (~spl26_7 | ~spl26_20)),
% 0.21/0.39 inference(superposition,[],[f554,f117])).
% 0.21/0.39 thf(f117,plain,(
% 0.21/0.39 ( ! [X2 : $i] : (($true = vAPP($i,$o,cQ,X2))) ) | ~spl26_7),
% 0.21/0.39 inference(avatar_component_clause,[],[f116])).
% 0.21/0.39 thf(f116,plain,(
% 0.21/0.39 spl26_7 <=> ! [X2] : ($true = vAPP($i,$o,cQ,X2))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_7])])).
% 0.21/0.39 thf(f554,plain,(
% 0.21/0.39 ( ! [X22 : $i] : (($false = vAPP($i,$o,cQ,vAPP($i,$i,sK13,X22)))) ) | (~spl26_7 | ~spl26_20)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f553])).
% 0.21/0.39 thf(f553,plain,(
% 0.21/0.39 ( ! [X22 : $i] : (($true = $false) | ($false = vAPP($i,$o,cQ,vAPP($i,$i,sK13,X22)))) ) | (~spl26_7 | ~spl26_20)),
% 0.21/0.39 inference(forward_demodulation,[],[f177,f117])).
% 0.21/0.39 thf(f177,plain,(
% 0.21/0.39 ( ! [X22 : $i] : (($false = vAPP($i,$o,cQ,vAPP($i,$i,sK13,X22))) | ($false = vAPP($i,$o,cQ,X22))) ) | ~spl26_20),
% 0.21/0.39 inference(avatar_component_clause,[],[f176])).
% 0.21/0.39 thf(f176,plain,(
% 0.21/0.39 spl26_20 <=> ! [X22] : (($false = vAPP($i,$o,cQ,X22)) | ($false = vAPP($i,$o,cQ,vAPP($i,$i,sK13,X22))))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_20])])).
% 0.21/0.39 thf(f552,plain,(
% 0.21/0.39 ~spl26_5 | ~spl26_7),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f551])).
% 0.21/0.39 thf(f551,plain,(
% 0.21/0.39 $false | (~spl26_5 | ~spl26_7)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f545])).
% 0.21/0.39 thf(f545,plain,(
% 0.21/0.39 ($true = $false) | (~spl26_5 | ~spl26_7)),
% 0.21/0.39 inference(superposition,[],[f544,f117])).
% 0.21/0.39 thf(f544,plain,(
% 0.21/0.39 ( ! [X4 : $i] : (($false = vAPP($i,$o,cQ,vAPP($i,$i,sK4,X4)))) ) | (~spl26_5 | ~spl26_7)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f543])).
% 0.21/0.39 thf(f543,plain,(
% 0.21/0.39 ( ! [X4 : $i] : (($true = $false) | ($false = vAPP($i,$o,cQ,vAPP($i,$i,sK4,X4)))) ) | (~spl26_5 | ~spl26_7)),
% 0.21/0.39 inference(forward_demodulation,[],[f109,f117])).
% 0.21/0.39 thf(f109,plain,(
% 0.21/0.39 ( ! [X4 : $i] : (($false = vAPP($i,$o,cQ,vAPP($i,$i,sK4,X4))) | ($false = vAPP($i,$o,cQ,X4))) ) | ~spl26_5),
% 0.21/0.39 inference(avatar_component_clause,[],[f108])).
% 0.21/0.39 thf(f108,plain,(
% 0.21/0.39 spl26_5 <=> ! [X4] : (($false = vAPP($i,$o,cQ,X4)) | ($false = vAPP($i,$o,cQ,vAPP($i,$i,sK4,X4))))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_5])])).
% 0.21/0.39 thf(f542,plain,(
% 0.21/0.39 ~spl26_7 | spl26_39),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f541])).
% 0.21/0.39 thf(f541,plain,(
% 0.21/0.39 $false | (~spl26_7 | spl26_39)),
% 0.21/0.39 inference(subsumption_resolution,[],[f261,f117])).
% 0.21/0.39 thf(f261,plain,(
% 0.21/0.39 ($true != vAPP($i,$o,cQ,sK23)) | spl26_39),
% 0.21/0.39 inference(avatar_component_clause,[],[f260])).
% 0.21/0.39 thf(f260,plain,(
% 0.21/0.39 spl26_39 <=> ($true = vAPP($i,$o,cQ,sK23))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_39])])).
% 0.21/0.39 thf(f526,plain,(
% 0.21/0.39 spl26_3 | ~spl26_7),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f525])).
% 0.21/0.39 thf(f525,plain,(
% 0.21/0.39 $false | (spl26_3 | ~spl26_7)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f515])).
% 0.21/0.39 thf(f515,plain,(
% 0.21/0.39 ($true = $false) | (spl26_3 | ~spl26_7)),
% 0.21/0.39 inference(superposition,[],[f117,f387])).
% 0.21/0.39 thf(f387,plain,(
% 0.21/0.39 ($false = vAPP($i,$o,cQ,sK2)) | spl26_3),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f386])).
% 0.21/0.39 thf(f386,plain,(
% 0.21/0.39 ($true != $true) | ($false = vAPP($i,$o,cQ,sK2)) | spl26_3),
% 0.21/0.39 inference(superposition,[],[f101,f4])).
% 0.21/0.39 thf(f4,plain,(
% 0.21/0.39 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.21/0.39 introduced(fool_axiom,[])).
% 0.21/0.39 thf(f101,plain,(
% 0.21/0.39 ($true != vAPP($i,$o,cQ,sK2)) | spl26_3),
% 0.21/0.39 inference(avatar_component_clause,[],[f99])).
% 0.21/0.39 thf(f99,plain,(
% 0.21/0.39 spl26_3 <=> ($true = vAPP($i,$o,cQ,sK2))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_3])])).
% 0.21/0.39 thf(f503,plain,(
% 0.21/0.39 ~spl26_12 | ~spl26_26),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f502])).
% 0.21/0.39 thf(f502,plain,(
% 0.21/0.39 $false | (~spl26_12 | ~spl26_26)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f501])).
% 0.21/0.39 thf(f501,plain,(
% 0.21/0.39 ($true = $false) | (~spl26_12 | ~spl26_26)),
% 0.21/0.39 inference(forward_demodulation,[],[f203,f139])).
% 0.21/0.39 thf(f203,plain,(
% 0.21/0.39 ($true = vAPP($i,$o,cQ,sK15)) | ~spl26_26),
% 0.21/0.39 inference(avatar_component_clause,[],[f201])).
% 0.21/0.39 thf(f201,plain,(
% 0.21/0.39 spl26_26 <=> ($true = vAPP($i,$o,cQ,sK15))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_26])])).
% 0.21/0.39 thf(f500,plain,(
% 0.21/0.39 ~spl26_1 | ~spl26_12),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f499])).
% 0.21/0.39 thf(f499,plain,(
% 0.21/0.39 $false | (~spl26_1 | ~spl26_12)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f498])).
% 0.21/0.39 thf(f498,plain,(
% 0.21/0.39 ($true = $false) | (~spl26_1 | ~spl26_12)),
% 0.21/0.39 inference(forward_demodulation,[],[f497,f139])).
% 0.21/0.39 thf(f497,plain,(
% 0.21/0.39 ( ! [X4 : $i] : (($true = vAPP($i,$o,cQ,vAPP($i,$i,sK4,X4)))) ) | (~spl26_1 | ~spl26_12)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f491])).
% 0.21/0.39 thf(f491,plain,(
% 0.21/0.39 ( ! [X4 : $i] : (($true = $false) | ($true = vAPP($i,$o,cQ,vAPP($i,$i,sK4,X4)))) ) | (~spl26_1 | ~spl26_12)),
% 0.21/0.39 inference(backward_demodulation,[],[f94,f139])).
% 0.21/0.39 thf(f94,plain,(
% 0.21/0.39 ( ! [X4 : $i] : (($true = vAPP($i,$o,cQ,vAPP($i,$i,sK4,X4))) | ($true = vAPP($i,$o,cQ,X4))) ) | ~spl26_1),
% 0.21/0.39 inference(avatar_component_clause,[],[f93])).
% 0.21/0.39 thf(f93,plain,(
% 0.21/0.39 spl26_1 <=> ! [X4] : (($true = vAPP($i,$o,cQ,X4)) | ($true = vAPP($i,$o,cQ,vAPP($i,$i,sK4,X4))))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_1])])).
% 0.21/0.39 thf(f490,plain,(
% 0.21/0.39 ~spl26_32 | ~spl26_37),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f489])).
% 0.21/0.39 thf(f489,plain,(
% 0.21/0.39 $false | (~spl26_32 | ~spl26_37)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f488])).
% 0.21/0.39 thf(f488,plain,(
% 0.21/0.39 ($true = $false) | (~spl26_32 | ~spl26_37)),
% 0.21/0.39 inference(forward_demodulation,[],[f487,f228])).
% 0.21/0.39 thf(f487,plain,(
% 0.21/0.39 ( ! [X22 : $i] : (($true = vAPP($i,$o,cP,vAPP($i,$i,sK25,X22)))) ) | (~spl26_32 | ~spl26_37)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f486])).
% 0.21/0.39 thf(f486,plain,(
% 0.21/0.39 ( ! [X22 : $i] : (($true = $false) | ($true = vAPP($i,$o,cP,vAPP($i,$i,sK25,X22)))) ) | (~spl26_32 | ~spl26_37)),
% 0.21/0.39 inference(forward_demodulation,[],[f254,f228])).
% 0.21/0.39 thf(f254,plain,(
% 0.21/0.39 ( ! [X22 : $i] : (($true = vAPP($i,$o,cP,X22)) | ($true = vAPP($i,$o,cP,vAPP($i,$i,sK25,X22)))) ) | ~spl26_37),
% 0.21/0.39 inference(avatar_component_clause,[],[f253])).
% 0.21/0.39 thf(f253,plain,(
% 0.21/0.39 spl26_37 <=> ! [X22] : (($true = vAPP($i,$o,cP,X22)) | ($true = vAPP($i,$o,cP,vAPP($i,$i,sK25,X22))))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_37])])).
% 0.21/0.39 thf(f485,plain,(
% 0.21/0.39 ~spl26_21 | ~spl26_32),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f484])).
% 0.21/0.39 thf(f484,plain,(
% 0.21/0.39 $false | (~spl26_21 | ~spl26_32)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f483])).
% 0.21/0.39 thf(f483,plain,(
% 0.21/0.39 ($true = $false) | (~spl26_21 | ~spl26_32)),
% 0.21/0.39 inference(forward_demodulation,[],[f482,f228])).
% 0.21/0.39 thf(f482,plain,(
% 0.21/0.39 ( ! [X4 : $i] : (($true = vAPP($i,$o,cP,vAPP($i,$i,sK16,X4)))) ) | (~spl26_21 | ~spl26_32)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f481])).
% 0.21/0.39 thf(f481,plain,(
% 0.21/0.39 ( ! [X4 : $i] : (($true = $false) | ($true = vAPP($i,$o,cP,vAPP($i,$i,sK16,X4)))) ) | (~spl26_21 | ~spl26_32)),
% 0.21/0.39 inference(forward_demodulation,[],[f183,f228])).
% 0.21/0.39 thf(f183,plain,(
% 0.21/0.39 ( ! [X4 : $i] : (($true = vAPP($i,$o,cP,X4)) | ($true = vAPP($i,$o,cP,vAPP($i,$i,sK16,X4)))) ) | ~spl26_21),
% 0.21/0.39 inference(avatar_component_clause,[],[f182])).
% 0.21/0.39 thf(f182,plain,(
% 0.21/0.39 spl26_21 <=> ! [X4] : (($true = vAPP($i,$o,cP,X4)) | ($true = vAPP($i,$o,cP,vAPP($i,$i,sK16,X4))))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_21])])).
% 0.21/0.39 thf(f430,plain,(
% 0.21/0.39 spl26_32 | ~spl26_2),
% 0.21/0.39 inference(avatar_split_clause,[],[f425,f96,f227])).
% 0.21/0.39 thf(f96,plain,(
% 0.21/0.39 spl26_2 <=> ! [X1] : (vAPP($i,$o,cP,X1) != $true)),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_2])])).
% 0.21/0.39 thf(f425,plain,(
% 0.21/0.39 ( ! [X0 : $i] : ((vAPP($i,$o,cP,X0) = $false)) ) | ~spl26_2),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f424])).
% 0.21/0.39 thf(f424,plain,(
% 0.21/0.39 ( ! [X0 : $i] : (($true != $true) | (vAPP($i,$o,cP,X0) = $false)) ) | ~spl26_2),
% 0.21/0.39 inference(superposition,[],[f97,f4])).
% 0.21/0.39 thf(f97,plain,(
% 0.21/0.39 ( ! [X1 : $i] : ((vAPP($i,$o,cP,X1) != $true)) ) | ~spl26_2),
% 0.21/0.39 inference(avatar_component_clause,[],[f96])).
% 0.21/0.39 thf(f421,plain,(
% 0.21/0.39 ~spl26_2 | ~spl26_27),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f420])).
% 0.21/0.39 thf(f420,plain,(
% 0.21/0.39 $false | (~spl26_2 | ~spl26_27)),
% 0.21/0.39 inference(subsumption_resolution,[],[f97,f206])).
% 0.21/0.39 thf(f206,plain,(
% 0.21/0.39 ( ! [X2 : $i] : (($true = vAPP($i,$o,cP,X2))) ) | ~spl26_27),
% 0.21/0.39 inference(avatar_component_clause,[],[f205])).
% 0.21/0.39 thf(f205,plain,(
% 0.21/0.39 spl26_27 <=> ! [X2] : ($true = vAPP($i,$o,cP,X2))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_27])])).
% 0.21/0.39 thf(f419,plain,(
% 0.21/0.39 ~spl26_12 | ~spl26_39),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f418])).
% 0.21/0.39 thf(f418,plain,(
% 0.21/0.39 $false | (~spl26_12 | ~spl26_39)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f417])).
% 0.21/0.39 thf(f417,plain,(
% 0.21/0.39 ($true = $false) | (~spl26_12 | ~spl26_39)),
% 0.21/0.39 inference(forward_demodulation,[],[f262,f139])).
% 0.21/0.39 thf(f262,plain,(
% 0.21/0.39 ($true = vAPP($i,$o,cQ,sK23)) | ~spl26_39),
% 0.21/0.39 inference(avatar_component_clause,[],[f260])).
% 0.21/0.39 thf(f416,plain,(
% 0.21/0.39 ~spl26_27 | ~spl26_40),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f415])).
% 0.21/0.39 thf(f415,plain,(
% 0.21/0.39 $false | (~spl26_27 | ~spl26_40)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f409])).
% 0.21/0.39 thf(f409,plain,(
% 0.21/0.39 ($true = $false) | (~spl26_27 | ~spl26_40)),
% 0.21/0.39 inference(superposition,[],[f383,f206])).
% 0.21/0.39 thf(f383,plain,(
% 0.21/0.39 ( ! [X22 : $i] : (($false = vAPP($i,$o,cP,vAPP($i,$i,sK25,X22)))) ) | (~spl26_27 | ~spl26_40)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f382])).
% 0.21/0.39 thf(f382,plain,(
% 0.21/0.39 ( ! [X22 : $i] : (($true = $false) | ($false = vAPP($i,$o,cP,vAPP($i,$i,sK25,X22)))) ) | (~spl26_27 | ~spl26_40)),
% 0.21/0.39 inference(forward_demodulation,[],[f266,f206])).
% 0.21/0.39 thf(f266,plain,(
% 0.21/0.39 ( ! [X22 : $i] : (($false = vAPP($i,$o,cP,X22)) | ($false = vAPP($i,$o,cP,vAPP($i,$i,sK25,X22)))) ) | ~spl26_40),
% 0.21/0.39 inference(avatar_component_clause,[],[f265])).
% 0.21/0.39 thf(f265,plain,(
% 0.21/0.39 spl26_40 <=> ! [X22] : (($false = vAPP($i,$o,cP,X22)) | ($false = vAPP($i,$o,cP,vAPP($i,$i,sK25,X22))))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_40])])).
% 0.21/0.39 thf(f407,plain,(
% 0.21/0.39 ~spl26_12 | ~spl26_17),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f406])).
% 0.21/0.39 thf(f406,plain,(
% 0.21/0.39 $false | (~spl26_12 | ~spl26_17)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f405])).
% 0.21/0.39 thf(f405,plain,(
% 0.21/0.39 ($true = $false) | (~spl26_12 | ~spl26_17)),
% 0.21/0.39 inference(forward_demodulation,[],[f404,f139])).
% 0.21/0.39 thf(f404,plain,(
% 0.21/0.39 ( ! [X22 : $i] : (($true = vAPP($i,$o,cQ,vAPP($i,$i,sK13,X22)))) ) | (~spl26_12 | ~spl26_17)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f397])).
% 0.21/0.39 thf(f397,plain,(
% 0.21/0.39 ( ! [X22 : $i] : (($true = $false) | ($true = vAPP($i,$o,cQ,vAPP($i,$i,sK13,X22)))) ) | (~spl26_12 | ~spl26_17)),
% 0.21/0.39 inference(backward_demodulation,[],[f165,f139])).
% 0.21/0.39 thf(f165,plain,(
% 0.21/0.39 ( ! [X22 : $i] : (($true = vAPP($i,$o,cQ,vAPP($i,$i,sK13,X22))) | ($true = vAPP($i,$o,cQ,X22))) ) | ~spl26_17),
% 0.21/0.39 inference(avatar_component_clause,[],[f164])).
% 0.21/0.39 thf(f164,plain,(
% 0.21/0.39 spl26_17 <=> ! [X22] : (($true = vAPP($i,$o,cQ,X22)) | ($true = vAPP($i,$o,cQ,vAPP($i,$i,sK13,X22))))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_17])])).
% 0.21/0.39 thf(f395,plain,(
% 0.21/0.39 ~spl26_8 | ~spl26_11),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f394])).
% 0.21/0.39 thf(f394,plain,(
% 0.21/0.39 $false | (~spl26_8 | ~spl26_11)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f393])).
% 0.21/0.39 thf(f393,plain,(
% 0.21/0.39 ($true = $false) | (~spl26_8 | ~spl26_11)),
% 0.21/0.39 inference(forward_demodulation,[],[f136,f123])).
% 0.21/0.39 thf(f123,plain,(
% 0.21/0.39 ($false = vAPP($i,$o,cQ,sK7)) | ~spl26_8),
% 0.21/0.39 inference(avatar_component_clause,[],[f121])).
% 0.21/0.39 thf(f121,plain,(
% 0.21/0.39 spl26_8 <=> ($false = vAPP($i,$o,cQ,sK7))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_8])])).
% 0.21/0.39 thf(f136,plain,(
% 0.21/0.39 ($true = vAPP($i,$o,cQ,sK7)) | ~spl26_11),
% 0.21/0.39 inference(avatar_component_clause,[],[f134])).
% 0.21/0.39 thf(f134,plain,(
% 0.21/0.39 spl26_11 <=> ($true = vAPP($i,$o,cQ,sK7))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_11])])).
% 0.21/0.39 thf(f379,plain,(
% 0.21/0.39 ~spl26_27 | spl26_38),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f378])).
% 0.21/0.39 thf(f378,plain,(
% 0.21/0.39 $false | (~spl26_27 | spl26_38)),
% 0.21/0.39 inference(subsumption_resolution,[],[f258,f206])).
% 0.21/0.39 thf(f258,plain,(
% 0.21/0.39 ($true != vAPP($i,$o,cP,sK24)) | spl26_38),
% 0.21/0.39 inference(avatar_component_clause,[],[f256])).
% 0.21/0.39 thf(f256,plain,(
% 0.21/0.39 spl26_38 <=> ($true = vAPP($i,$o,cP,sK24))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_38])])).
% 0.21/0.39 thf(f377,plain,(
% 0.21/0.39 spl26_23 | ~spl26_27),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f376])).
% 0.21/0.39 thf(f376,plain,(
% 0.21/0.39 $false | (spl26_23 | ~spl26_27)),
% 0.21/0.39 inference(subsumption_resolution,[],[f190,f206])).
% 0.21/0.39 thf(f190,plain,(
% 0.21/0.39 ($true != vAPP($i,$o,cP,sK14)) | spl26_23),
% 0.21/0.39 inference(avatar_component_clause,[],[f188])).
% 0.21/0.39 thf(f188,plain,(
% 0.21/0.39 spl26_23 <=> ($true = vAPP($i,$o,cP,sK14))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_23])])).
% 0.21/0.39 thf(f375,plain,(
% 0.21/0.39 ~spl26_25 | ~spl26_27),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f374])).
% 0.21/0.39 thf(f374,plain,(
% 0.21/0.39 $false | (~spl26_25 | ~spl26_27)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f368])).
% 0.21/0.39 thf(f368,plain,(
% 0.21/0.39 ($true = $false) | (~spl26_25 | ~spl26_27)),
% 0.21/0.39 inference(superposition,[],[f367,f206])).
% 0.21/0.39 thf(f367,plain,(
% 0.21/0.39 ( ! [X4 : $i] : (($false = vAPP($i,$o,cP,vAPP($i,$i,sK16,X4)))) ) | (~spl26_25 | ~spl26_27)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f366])).
% 0.21/0.39 thf(f366,plain,(
% 0.21/0.39 ( ! [X4 : $i] : (($true = $false) | ($false = vAPP($i,$o,cP,vAPP($i,$i,sK16,X4)))) ) | (~spl26_25 | ~spl26_27)),
% 0.21/0.39 inference(forward_demodulation,[],[f198,f206])).
% 0.21/0.39 thf(f198,plain,(
% 0.21/0.39 ( ! [X4 : $i] : (($false = vAPP($i,$o,cP,X4)) | ($false = vAPP($i,$o,cP,vAPP($i,$i,sK16,X4)))) ) | ~spl26_25),
% 0.21/0.39 inference(avatar_component_clause,[],[f197])).
% 0.21/0.39 thf(f197,plain,(
% 0.21/0.39 spl26_25 <=> ! [X4] : (($false = vAPP($i,$o,cP,X4)) | ($false = vAPP($i,$o,cP,vAPP($i,$i,sK16,X4))))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_25])])).
% 0.21/0.39 thf(f354,plain,(
% 0.21/0.39 ~spl26_16 | ~spl26_32),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f353])).
% 0.21/0.39 thf(f353,plain,(
% 0.21/0.39 $false | (~spl26_16 | ~spl26_32)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f346])).
% 0.21/0.39 thf(f346,plain,(
% 0.21/0.39 ($true = $false) | (~spl26_16 | ~spl26_32)),
% 0.21/0.39 inference(backward_demodulation,[],[f160,f228])).
% 0.21/0.39 thf(f160,plain,(
% 0.21/0.39 ($true = vAPP($i,$o,cP,sK10)) | ~spl26_16),
% 0.21/0.39 inference(avatar_component_clause,[],[f158])).
% 0.21/0.39 thf(f158,plain,(
% 0.21/0.39 spl26_16 <=> ($true = vAPP($i,$o,cP,sK10))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_16])])).
% 0.21/0.39 thf(f352,plain,(
% 0.21/0.39 ~spl26_19 | ~spl26_32),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f351])).
% 0.21/0.39 thf(f351,plain,(
% 0.21/0.39 $false | (~spl26_19 | ~spl26_32)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f347])).
% 0.21/0.39 thf(f347,plain,(
% 0.21/0.39 ($true = $false) | (~spl26_19 | ~spl26_32)),
% 0.21/0.39 inference(backward_demodulation,[],[f173,f228])).
% 0.21/0.39 thf(f173,plain,(
% 0.21/0.39 ($true = vAPP($i,$o,cP,sK11)) | ~spl26_19),
% 0.21/0.39 inference(avatar_component_clause,[],[f171])).
% 0.21/0.39 thf(f171,plain,(
% 0.21/0.39 spl26_19 <=> ($true = vAPP($i,$o,cP,sK11))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_19])])).
% 0.21/0.39 thf(f344,plain,(
% 0.21/0.39 ~spl26_28 | ~spl26_31),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f343])).
% 0.21/0.39 thf(f343,plain,(
% 0.21/0.39 $false | (~spl26_28 | ~spl26_31)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f342])).
% 0.21/0.39 thf(f342,plain,(
% 0.21/0.39 ($true = $false) | (~spl26_28 | ~spl26_31)),
% 0.21/0.39 inference(forward_demodulation,[],[f225,f212])).
% 0.21/0.39 thf(f212,plain,(
% 0.21/0.39 ($false = vAPP($i,$o,cP,sK19)) | ~spl26_28),
% 0.21/0.39 inference(avatar_component_clause,[],[f210])).
% 0.21/0.39 thf(f210,plain,(
% 0.21/0.39 spl26_28 <=> ($false = vAPP($i,$o,cP,sK19))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_28])])).
% 0.21/0.39 thf(f225,plain,(
% 0.21/0.39 ($true = vAPP($i,$o,cP,sK19)) | ~spl26_31),
% 0.21/0.39 inference(avatar_component_clause,[],[f223])).
% 0.21/0.39 thf(f223,plain,(
% 0.21/0.39 spl26_31 <=> ($true = vAPP($i,$o,cP,sK19))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_31])])).
% 0.21/0.39 thf(f335,plain,(
% 0.21/0.39 spl26_12 | ~spl26_22),
% 0.21/0.39 inference(avatar_split_clause,[],[f332,f185,f138])).
% 0.21/0.39 thf(f185,plain,(
% 0.21/0.39 spl26_22 <=> ! [X1] : (vAPP($i,$o,cQ,X1) != $true)),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_22])])).
% 0.21/0.39 thf(f332,plain,(
% 0.21/0.39 ( ! [X0 : $i] : ((vAPP($i,$o,cQ,X0) = $false)) ) | ~spl26_22),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f331])).
% 0.21/0.39 thf(f331,plain,(
% 0.21/0.39 ( ! [X0 : $i] : (($true != $true) | (vAPP($i,$o,cQ,X0) = $false)) ) | ~spl26_22),
% 0.21/0.39 inference(superposition,[],[f186,f4])).
% 0.21/0.39 thf(f186,plain,(
% 0.21/0.39 ( ! [X1 : $i] : ((vAPP($i,$o,cQ,X1) != $true)) ) | ~spl26_22),
% 0.21/0.39 inference(avatar_component_clause,[],[f185])).
% 0.21/0.39 thf(f320,plain,(
% 0.21/0.39 ~spl26_13 | ~spl26_15),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f319])).
% 0.21/0.39 thf(f319,plain,(
% 0.21/0.39 $false | (~spl26_13 | ~spl26_15)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f318])).
% 0.21/0.39 thf(f318,plain,(
% 0.21/0.39 ($true = $false) | (~spl26_13 | ~spl26_15)),
% 0.21/0.39 inference(forward_demodulation,[],[f155,f146])).
% 0.21/0.39 thf(f146,plain,(
% 0.21/0.39 ($false = vAPP($i,$o,cQ,sK8)) | ~spl26_13),
% 0.21/0.39 inference(avatar_component_clause,[],[f144])).
% 0.21/0.39 thf(f144,plain,(
% 0.21/0.39 spl26_13 <=> ($false = vAPP($i,$o,cQ,sK8))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_13])])).
% 0.21/0.39 thf(f155,plain,(
% 0.21/0.39 ($true = vAPP($i,$o,cQ,sK8)) | ~spl26_15),
% 0.21/0.39 inference(avatar_component_clause,[],[f153])).
% 0.21/0.39 thf(f153,plain,(
% 0.21/0.39 spl26_15 <=> ($true = vAPP($i,$o,cQ,sK8))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_15])])).
% 0.21/0.39 thf(f315,plain,(
% 0.21/0.39 ~spl26_7 | ~spl26_22),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f314])).
% 0.21/0.39 thf(f314,plain,(
% 0.21/0.39 $false | (~spl26_7 | ~spl26_22)),
% 0.21/0.39 inference(subsumption_resolution,[],[f186,f117])).
% 0.21/0.39 thf(f313,plain,(
% 0.21/0.39 ~spl26_7 | spl26_18),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f312])).
% 0.21/0.39 thf(f312,plain,(
% 0.21/0.39 $false | (~spl26_7 | spl26_18)),
% 0.21/0.39 inference(subsumption_resolution,[],[f169,f117])).
% 0.21/0.39 thf(f169,plain,(
% 0.21/0.39 ($true != vAPP($i,$o,cQ,sK12)) | spl26_18),
% 0.21/0.39 inference(avatar_component_clause,[],[f167])).
% 0.21/0.39 thf(f167,plain,(
% 0.21/0.39 spl26_18 <=> ($true = vAPP($i,$o,cQ,sK12))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_18])])).
% 0.21/0.39 thf(f271,plain,(
% 0.21/0.39 spl26_24 | spl26_4),
% 0.21/0.39 inference(avatar_split_clause,[],[f58,f103,f192])).
% 0.21/0.39 thf(f192,plain,(
% 0.21/0.39 spl26_24 <=> ($true = sP0)),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_24])])).
% 0.21/0.39 thf(f103,plain,(
% 0.21/0.39 spl26_4 <=> ($true = sP1)),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl26_4])])).
% 0.21/0.39 thf(f58,plain,(
% 0.21/0.39 ($true = sP1) | ($true = sP0)),
% 0.21/0.39 inference(cnf_transformation,[],[f41])).
% 0.21/0.39 thf(f41,plain,(
% 0.21/0.39 (($true != sP1) | ($true != sP0)) & (($true = sP1) | ($true = sP0))),
% 0.21/0.39 inference(nnf_transformation,[],[f10])).
% 0.21/0.39 thf(f10,plain,(
% 0.21/0.39 ($true = sP0) <~> ($true = sP1)),
% 0.21/0.39 inference(definition_folding,[],[f7,f9,f8])).
% 0.21/0.39 thf(f8,plain,(
% 0.21/0.39 ($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,cP,X3))))),
% 0.21/0.39 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 0.21/0.39 thf(f9,plain,(
% 0.21/0.39 ($true = sP1) <=> (? [X4] : ! [X5] : (vAPP($i,$o,cQ,X4) = vAPP($i,$o,cQ,X5)) <=> (? [X6] : ($true = vAPP($i,$o,cP,X6)) <=> ! [X7] : ($true = vAPP($i,$o,cQ,X7))))),
% 0.21/0.39 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 0.21/0.39 thf(f7,plain,(
% 0.21/0.39 (? [X0] : ! [X1] : (vAPP($i,$o,cP,X0) = vAPP($i,$o,cP,X1)) <=> (? [X2] : ($true = vAPP($i,$o,cQ,X2)) <=> ! [X3] : ($true = vAPP($i,$o,cP,X3)))) <~> (? [X4] : ! [X5] : (vAPP($i,$o,cQ,X4) = vAPP($i,$o,cQ,X5)) <=> (? [X6] : ($true = vAPP($i,$o,cP,X6)) <=> ! [X7] : ($true = vAPP($i,$o,cQ,X7))))),
% 0.21/0.39 inference(ennf_transformation,[],[f6])).
% 0.21/0.39 thf(f6,plain,(
% 0.21/0.39 ~((? [X0] : ! [X1] : (vAPP($i,$o,cP,X0) = vAPP($i,$o,cP,X1)) <=> (? [X2] : ($true = vAPP($i,$o,cQ,X2)) <=> ! [X3] : ($true = vAPP($i,$o,cP,X3)))) <=> (? [X4] : ! [X5] : (vAPP($i,$o,cQ,X4) = vAPP($i,$o,cQ,X5)) <=> (? [X6] : ($true = vAPP($i,$o,cP,X6)) <=> ! [X7] : ($true = vAPP($i,$o,cQ,X7)))))),
% 0.21/0.39 inference(fool_elimination,[],[f5])).
% 0.21/0.39 thf(f5,plain,(
% 0.21/0.39 ~((? [X0] : ! [X1] : (vAPP($i,$o,cP,X0) <=> vAPP($i,$o,cP,X1)) <=> (? [X2] : vAPP($i,$o,cQ,X2) <=> ! [X3] : vAPP($i,$o,cP,X3))) <=> (? [X4] : ! [X5] : (vAPP($i,$o,cQ,X4) <=> vAPP($i,$o,cQ,X5)) <=> (? [X6] : vAPP($i,$o,cP,X6) <=> ! [X7] : vAPP($i,$o,cQ,X7))))),
% 0.21/0.39 inference(rectify,[],[f2])).
% 0.21/0.39 thf(f2,negated_conjecture,(
% 0.21/0.39 ~((? [X0] : ! [X1] : (vAPP($i,$o,cP,X0) <=> vAPP($i,$o,cP,X1)) <=> (? [X0] : vAPP($i,$o,cQ,X0) <=> ! [X1] : vAPP($i,$o,cP,X1))) <=> (? [X0] : ! [X1] : (vAPP($i,$o,cQ,X0) <=> vAPP($i,$o,cQ,X1)) <=> (? [X0] : vAPP($i,$o,cP,X0) <=> ! [X1] : vAPP($i,$o,cQ,X1))))),
% 0.21/0.39 inference(negated_conjecture,[],[f1])).
% 0.21/0.39 thf(f1,conjecture,(
% 0.21/0.39 (? [X0] : ! [X1] : (vAPP($i,$o,cP,X0) <=> vAPP($i,$o,cP,X1)) <=> (? [X0] : vAPP($i,$o,cQ,X0) <=> ! [X1] : vAPP($i,$o,cP,X1))) <=> (? [X0] : ! [X1] : (vAPP($i,$o,cQ,X0) <=> vAPP($i,$o,cQ,X1)) <=> (? [X0] : vAPP($i,$o,cP,X0) <=> ! [X1] : vAPP($i,$o,cQ,X1)))),
% 0.21/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX2129)).
% 0.21/0.39 thf(f270,plain,(
% 0.21/0.39 ~spl26_24 | ~spl26_4),
% 0.21/0.39 inference(avatar_split_clause,[],[f59,f103,f192])).
% 0.21/0.39 thf(f59,plain,(
% 0.21/0.39 ($true != sP1) | ($true != sP0)),
% 0.21/0.39 inference(cnf_transformation,[],[f41])).
% 0.21/0.39 thf(f269,plain,(
% 0.21/0.39 ~spl26_24 | spl26_40 | spl26_22 | spl26_27),
% 0.21/0.39 inference(avatar_split_clause,[],[f61,f205,f185,f265,f192])).
% 0.21/0.39 thf(f61,plain,(
% 0.21/0.39 ( ! [X21 : $i,X22 : $i,X20 : $i] : (($true = vAPP($i,$o,cP,X20)) | ($true != vAPP($i,$o,cQ,X21)) | ($false = vAPP($i,$o,cP,X22)) | ($true != sP0) | ($false = vAPP($i,$o,cP,vAPP($i,$i,sK25,X22)))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f50])).
% 0.21/0.39 thf(f50,plain,(
% 0.21/0.39 ( ! [X21 : $i,X22 : $i,X20 : $i] : (($true = vAPP($i,$o,cP,X20)) | ($true != vAPP($i,$o,cQ,X21)) | (vAPP($i,$o,cP,X22) != vAPP($i,$o,cP,vAPP($i,$i,sK25,X22))) | ($true != sP0)) )),
% 0.21/0.39 inference(cnf_transformation,[],[f40])).
% 0.21/0.39 thf(f40,plain,(
% 0.21/0.39 (($true = sP0) | ((((($true != vAPP($i,$o,cP,sK14)) | ! [X1] : (vAPP($i,$o,cQ,X1) != $true)) & (! [X2] : ($true = vAPP($i,$o,cP,X2)) | ($true = vAPP($i,$o,cQ,sK15)))) | ! [X4] : (vAPP($i,$o,cP,X4) != vAPP($i,$o,cP,vAPP($i,$i,sK16,X4)))) & (((($true = vAPP($i,$o,cQ,sK17)) | ($true != vAPP($i,$o,cP,sK18))) & (! [X8] : ($true = vAPP($i,$o,cP,X8)) | ! [X9] : ($true != vAPP($i,$o,cQ,X9)))) | ! [X11] : (vAPP($i,$o,cP,X11) = vAPP($i,$o,cP,sK19))))) & (((! [X13] : (vAPP($i,$o,cP,X13) = vAPP($i,$o,cP,sK20)) | ((($true != vAPP($i,$o,cP,sK21)) | ! [X15] : ($true != vAPP($i,$o,cQ,X15))) & (! [X16] : ($true = vAPP($i,$o,cP,X16)) | ($true = vAPP($i,$o,cQ,sK22))))) & (((($true = vAPP($i,$o,cQ,sK23)) | ($true != vAPP($i,$o,cP,sK24))) & (! [X20] : ($true = vAPP($i,$o,cP,X20)) | ! [X21] : ($true != vAPP($i,$o,cQ,X21)))) | ! [X22] : (vAPP($i,$o,cP,X22) != vAPP($i,$o,cP,vAPP($i,$i,sK25,X22))))) | ($true != sP0))),
% 0.21/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17,sK18,sK19,sK20,sK21,sK22,sK23,sK24,sK25])],[f27,f39,f38,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28])).
% 0.21/0.39 thf(f28,plain,(
% 0.21/0.39 ? [X0] : (vAPP($i,$o,cP,X0) != $true) => ($true != vAPP($i,$o,cP,sK14))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f29,plain,(
% 0.21/0.39 ? [X3] : ($true = vAPP($i,$o,cQ,X3)) => ($true = vAPP($i,$o,cQ,sK15))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f30,plain,(
% 0.21/0.39 ! [X4] : (? [X5] : (vAPP($i,$o,cP,X4) != vAPP($i,$o,cP,X5)) => (vAPP($i,$o,cP,X4) != vAPP($i,$o,cP,vAPP($i,$i,sK16,X4))))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f31,plain,(
% 0.21/0.39 ? [X6] : ($true = vAPP($i,$o,cQ,X6)) => ($true = vAPP($i,$o,cQ,sK17))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f32,plain,(
% 0.21/0.39 ? [X7] : ($true != vAPP($i,$o,cP,X7)) => ($true != vAPP($i,$o,cP,sK18))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f33,plain,(
% 0.21/0.39 ? [X10] : ! [X11] : (vAPP($i,$o,cP,X10) = vAPP($i,$o,cP,X11)) => ! [X11] : (vAPP($i,$o,cP,X11) = vAPP($i,$o,cP,sK19))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f34,plain,(
% 0.21/0.39 ? [X12] : ! [X13] : (vAPP($i,$o,cP,X12) = vAPP($i,$o,cP,X13)) => ! [X13] : (vAPP($i,$o,cP,X13) = vAPP($i,$o,cP,sK20))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f35,plain,(
% 0.21/0.39 ? [X14] : ($true != vAPP($i,$o,cP,X14)) => ($true != vAPP($i,$o,cP,sK21))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f36,plain,(
% 0.21/0.39 ? [X17] : ($true = vAPP($i,$o,cQ,X17)) => ($true = vAPP($i,$o,cQ,sK22))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f37,plain,(
% 0.21/0.39 ? [X18] : ($true = vAPP($i,$o,cQ,X18)) => ($true = vAPP($i,$o,cQ,sK23))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f38,plain,(
% 0.21/0.39 ? [X19] : ($true != vAPP($i,$o,cP,X19)) => ($true != vAPP($i,$o,cP,sK24))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f39,plain,(
% 0.21/0.39 ! [X22] : (? [X23] : (vAPP($i,$o,cP,X22) != vAPP($i,$o,cP,X23)) => (vAPP($i,$o,cP,X22) != vAPP($i,$o,cP,vAPP($i,$i,sK25,X22))))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f27,plain,(
% 0.21/0.39 (($true = sP0) | ((((? [X0] : (vAPP($i,$o,cP,X0) != $true) | ! [X1] : (vAPP($i,$o,cQ,X1) != $true)) & (! [X2] : ($true = vAPP($i,$o,cP,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,$o,cP,X7))) & (! [X8] : ($true = vAPP($i,$o,cP,X8)) | ! [X9] : ($true != vAPP($i,$o,cQ,X9)))) | ? [X10] : ! [X11] : (vAPP($i,$o,cP,X10) = vAPP($i,$o,cP,X11))))) & (((? [X12] : ! [X13] : (vAPP($i,$o,cP,X12) = vAPP($i,$o,cP,X13)) | ((? [X14] : ($true != vAPP($i,$o,cP,X14)) | ! [X15] : ($true != vAPP($i,$o,cQ,X15))) & (! [X16] : ($true = vAPP($i,$o,cP,X16)) | ? [X17] : ($true = vAPP($i,$o,cQ,X17))))) & (((? [X18] : ($true = vAPP($i,$o,cQ,X18)) | ? [X19] : ($true != vAPP($i,$o,cP,X19))) & (! [X20] : ($true = vAPP($i,$o,cP,X20)) | ! [X21] : ($true != vAPP($i,$o,cQ,X21)))) | ! [X22] : ? [X23] : (vAPP($i,$o,cP,X22) != vAPP($i,$o,cP,X23)))) | ($true != sP0))),
% 0.21/0.39 inference(rectify,[],[f26])).
% 0.21/0.39 thf(f26,plain,(
% 0.21/0.39 (($true = sP0) | ((((? [X3] : ($true != vAPP($i,$o,cP,X3)) | ! [X2] : ($true != vAPP($i,$o,cQ,X2))) & (! [X3] : ($true = vAPP($i,$o,cP,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,$o,cP,X3))) & (! [X3] : ($true = vAPP($i,$o,cP,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,cP,X3)) | ! [X2] : ($true != vAPP($i,$o,cQ,X2))) & (! [X3] : ($true = vAPP($i,$o,cP,X3)) | ? [X2] : ($true = vAPP($i,$o,cQ,X2))))) & (((? [X2] : ($true = vAPP($i,$o,cQ,X2)) | ? [X3] : ($true != vAPP($i,$o,cP,X3))) & (! [X3] : ($true = vAPP($i,$o,cP,X3)) | ! [X2] : ($true != vAPP($i,$o,cQ,X2)))) | ! [X0] : ? [X1] : (vAPP($i,$o,cP,X0) != vAPP($i,$o,cP,X1)))) | ($true != sP0))),
% 0.21/0.39 inference(nnf_transformation,[],[f8])).
% 0.21/0.39 thf(f268,plain,(
% 0.21/0.39 ~spl26_24 | spl26_37 | spl26_22 | spl26_27),
% 0.21/0.39 inference(avatar_split_clause,[],[f60,f205,f185,f253,f192])).
% 0.21/0.39 thf(f60,plain,(
% 0.21/0.39 ( ! [X21 : $i,X22 : $i,X20 : $i] : (($true = vAPP($i,$o,cP,X20)) | ($true != vAPP($i,$o,cQ,X21)) | ($true = vAPP($i,$o,cP,X22)) | ($true != sP0) | ($true = vAPP($i,$o,cP,vAPP($i,$i,sK25,X22)))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f50])).
% 0.21/0.39 thf(f267,plain,(
% 0.21/0.39 ~spl26_24 | spl26_40 | ~spl26_38 | spl26_39),
% 0.21/0.39 inference(avatar_split_clause,[],[f63,f260,f256,f265,f192])).
% 0.21/0.39 thf(f63,plain,(
% 0.21/0.39 ( ! [X22 : $i] : (($true = vAPP($i,$o,cQ,sK23)) | ($true != vAPP($i,$o,cP,sK24)) | ($false = vAPP($i,$o,cP,X22)) | ($true != sP0) | ($false = vAPP($i,$o,cP,vAPP($i,$i,sK25,X22)))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f51])).
% 0.21/0.39 thf(f51,plain,(
% 0.21/0.39 ( ! [X22 : $i] : (($true = vAPP($i,$o,cQ,sK23)) | ($true != vAPP($i,$o,cP,sK24)) | (vAPP($i,$o,cP,X22) != vAPP($i,$o,cP,vAPP($i,$i,sK25,X22))) | ($true != sP0)) )),
% 0.21/0.39 inference(cnf_transformation,[],[f40])).
% 0.21/0.39 thf(f251,plain,(
% 0.21/0.39 spl26_35 | ~spl26_24 | spl26_36 | spl26_27 | spl26_32),
% 0.21/0.39 inference(avatar_split_clause,[],[f65,f227,f205,f247,f192,f242])).
% 0.21/0.39 thf(f65,plain,(
% 0.21/0.39 ( ! [X16 : $i,X13 : $i] : (($false = vAPP($i,$o,cP,X13)) | ($true = vAPP($i,$o,cP,X16)) | ($true = vAPP($i,$o,cQ,sK22)) | ($true != sP0) | ($true = vAPP($i,$o,cP,sK20))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f52])).
% 0.21/0.39 thf(f52,plain,(
% 0.21/0.39 ( ! [X16 : $i,X13 : $i] : ((vAPP($i,$o,cP,X13) = vAPP($i,$o,cP,sK20)) | ($true = vAPP($i,$o,cP,X16)) | ($true = vAPP($i,$o,cQ,sK22)) | ($true != sP0)) )),
% 0.21/0.39 inference(cnf_transformation,[],[f40])).
% 0.21/0.39 thf(f250,plain,(
% 0.21/0.39 spl26_33 | ~spl26_24 | spl26_36 | spl26_27 | spl26_27),
% 0.21/0.39 inference(avatar_split_clause,[],[f64,f205,f205,f247,f192,f233])).
% 0.21/0.39 thf(f64,plain,(
% 0.21/0.39 ( ! [X16 : $i,X13 : $i] : (($true = vAPP($i,$o,cP,X13)) | ($true = vAPP($i,$o,cP,X16)) | ($true = vAPP($i,$o,cQ,sK22)) | ($true != sP0) | ($false = vAPP($i,$o,cP,sK20))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f52])).
% 0.21/0.39 thf(f231,plain,(
% 0.21/0.39 spl26_31 | spl26_32 | spl26_22 | spl26_27 | spl26_24),
% 0.21/0.39 inference(avatar_split_clause,[],[f69,f192,f205,f185,f227,f223])).
% 0.21/0.39 thf(f69,plain,(
% 0.21/0.39 ( ! [X11 : $i,X8 : $i,X9 : $i] : (($true = sP0) | ($true = vAPP($i,$o,cP,X8)) | ($true != vAPP($i,$o,cQ,X9)) | ($false = vAPP($i,$o,cP,X11)) | ($true = vAPP($i,$o,cP,sK19))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f54])).
% 0.21/0.39 thf(f54,plain,(
% 0.21/0.39 ( ! [X11 : $i,X8 : $i,X9 : $i] : (($true = sP0) | ($true = vAPP($i,$o,cP,X8)) | ($true != vAPP($i,$o,cQ,X9)) | (vAPP($i,$o,cP,X11) = vAPP($i,$o,cP,sK19))) )),
% 0.21/0.39 inference(cnf_transformation,[],[f40])).
% 0.21/0.39 thf(f230,plain,(
% 0.21/0.39 spl26_28 | spl26_27 | spl26_22 | spl26_27 | spl26_24),
% 0.21/0.39 inference(avatar_split_clause,[],[f68,f192,f205,f185,f205,f210])).
% 0.21/0.39 thf(f68,plain,(
% 0.21/0.39 ( ! [X11 : $i,X8 : $i,X9 : $i] : (($true = sP0) | ($true = vAPP($i,$o,cP,X8)) | ($true != vAPP($i,$o,cQ,X9)) | ($true = vAPP($i,$o,cP,X11)) | ($false = vAPP($i,$o,cP,sK19))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f54])).
% 0.21/0.39 thf(f207,plain,(
% 0.21/0.39 spl26_21 | spl26_26 | spl26_27 | spl26_24),
% 0.21/0.39 inference(avatar_split_clause,[],[f72,f192,f205,f201,f182])).
% 0.21/0.39 thf(f72,plain,(
% 0.21/0.39 ( ! [X2 : $i,X4 : $i] : (($true = sP0) | ($true = vAPP($i,$o,cP,X2)) | ($true = vAPP($i,$o,cQ,sK15)) | ($true = vAPP($i,$o,cP,X4)) | ($true = vAPP($i,$o,cP,vAPP($i,$i,sK16,X4)))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f56])).
% 0.21/0.39 thf(f56,plain,(
% 0.21/0.39 ( ! [X2 : $i,X4 : $i] : (($true = sP0) | ($true = vAPP($i,$o,cP,X2)) | ($true = vAPP($i,$o,cQ,sK15)) | (vAPP($i,$o,cP,X4) != vAPP($i,$o,cP,vAPP($i,$i,sK16,X4)))) )),
% 0.21/0.39 inference(cnf_transformation,[],[f40])).
% 0.21/0.39 thf(f199,plain,(
% 0.21/0.39 spl26_25 | spl26_22 | ~spl26_23 | spl26_24),
% 0.21/0.39 inference(avatar_split_clause,[],[f75,f192,f188,f185,f197])).
% 0.21/0.39 thf(f75,plain,(
% 0.21/0.39 ( ! [X1 : $i,X4 : $i] : (($true = sP0) | ($true != vAPP($i,$o,cP,sK14)) | (vAPP($i,$o,cQ,X1) != $true) | ($false = vAPP($i,$o,cP,X4)) | ($false = vAPP($i,$o,cP,vAPP($i,$i,sK16,X4)))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f57])).
% 0.21/0.39 thf(f57,plain,(
% 0.21/0.39 ( ! [X1 : $i,X4 : $i] : (($true = sP0) | ($true != vAPP($i,$o,cP,sK14)) | (vAPP($i,$o,cQ,X1) != $true) | (vAPP($i,$o,cP,X4) != vAPP($i,$o,cP,vAPP($i,$i,sK16,X4)))) )),
% 0.21/0.39 inference(cnf_transformation,[],[f40])).
% 0.21/0.39 thf(f179,plain,(
% 0.21/0.39 ~spl26_4 | spl26_17 | spl26_2 | spl26_7),
% 0.21/0.39 inference(avatar_split_clause,[],[f76,f116,f96,f164,f103])).
% 0.21/0.39 thf(f76,plain,(
% 0.21/0.39 ( ! [X21 : $i,X22 : $i,X20 : $i] : (($true = vAPP($i,$o,cQ,X20)) | ($true != vAPP($i,$o,cP,X21)) | ($true = vAPP($i,$o,cQ,X22)) | ($true != sP1) | ($true = vAPP($i,$o,cQ,vAPP($i,$i,sK13,X22)))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f42])).
% 0.21/0.39 thf(f42,plain,(
% 0.21/0.39 ( ! [X21 : $i,X22 : $i,X20 : $i] : (($true = vAPP($i,$o,cQ,X20)) | ($true != vAPP($i,$o,cP,X21)) | (vAPP($i,$o,cQ,X22) != vAPP($i,$o,cQ,vAPP($i,$i,sK13,X22))) | ($true != sP1)) )),
% 0.21/0.39 inference(cnf_transformation,[],[f25])).
% 0.21/0.39 thf(f25,plain,(
% 0.21/0.39 (($true = sP1) | ((((($true != vAPP($i,$o,cQ,sK2)) | ! [X1] : (vAPP($i,$o,cP,X1) != $true)) & (! [X2] : ($true = vAPP($i,$o,cQ,X2)) | ($true = vAPP($i,$o,cP,sK3)))) | ! [X4] : (vAPP($i,$o,cQ,X4) != vAPP($i,$o,cQ,vAPP($i,$i,sK4,X4)))) & (((($true = vAPP($i,$o,cP,sK5)) | ($true != vAPP($i,$o,cQ,sK6))) & (! [X8] : ($true = vAPP($i,$o,cQ,X8)) | ! [X9] : ($true != vAPP($i,$o,cP,X9)))) | ! [X11] : (vAPP($i,$o,cQ,X11) = vAPP($i,$o,cQ,sK7))))) & (((! [X13] : (vAPP($i,$o,cQ,X13) = vAPP($i,$o,cQ,sK8)) | ((($true != vAPP($i,$o,cQ,sK9)) | ! [X15] : ($true != vAPP($i,$o,cP,X15))) & (! [X16] : ($true = vAPP($i,$o,cQ,X16)) | ($true = vAPP($i,$o,cP,sK10))))) & (((($true = vAPP($i,$o,cP,sK11)) | ($true != vAPP($i,$o,cQ,sK12))) & (! [X20] : ($true = vAPP($i,$o,cQ,X20)) | ! [X21] : ($true != vAPP($i,$o,cP,X21)))) | ! [X22] : (vAPP($i,$o,cQ,X22) != vAPP($i,$o,cQ,vAPP($i,$i,sK13,X22))))) | ($true != sP1))),
% 0.21/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13])],[f12,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14,f13])).
% 0.21/0.39 thf(f13,plain,(
% 0.21/0.39 ? [X0] : (vAPP($i,$o,cQ,X0) != $true) => ($true != vAPP($i,$o,cQ,sK2))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f14,plain,(
% 0.21/0.39 ? [X3] : ($true = vAPP($i,$o,cP,X3)) => ($true = vAPP($i,$o,cP,sK3))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f15,plain,(
% 0.21/0.39 ! [X4] : (? [X5] : (vAPP($i,$o,cQ,X4) != vAPP($i,$o,cQ,X5)) => (vAPP($i,$o,cQ,X4) != vAPP($i,$o,cQ,vAPP($i,$i,sK4,X4))))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f16,plain,(
% 0.21/0.39 ? [X6] : ($true = vAPP($i,$o,cP,X6)) => ($true = vAPP($i,$o,cP,sK5))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f17,plain,(
% 0.21/0.39 ? [X7] : ($true != vAPP($i,$o,cQ,X7)) => ($true != vAPP($i,$o,cQ,sK6))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f18,plain,(
% 0.21/0.39 ? [X10] : ! [X11] : (vAPP($i,$o,cQ,X10) = vAPP($i,$o,cQ,X11)) => ! [X11] : (vAPP($i,$o,cQ,X11) = vAPP($i,$o,cQ,sK7))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f19,plain,(
% 0.21/0.39 ? [X12] : ! [X13] : (vAPP($i,$o,cQ,X12) = vAPP($i,$o,cQ,X13)) => ! [X13] : (vAPP($i,$o,cQ,X13) = vAPP($i,$o,cQ,sK8))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f20,plain,(
% 0.21/0.39 ? [X14] : ($true != vAPP($i,$o,cQ,X14)) => ($true != vAPP($i,$o,cQ,sK9))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f21,plain,(
% 0.21/0.39 ? [X17] : ($true = vAPP($i,$o,cP,X17)) => ($true = vAPP($i,$o,cP,sK10))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f22,plain,(
% 0.21/0.39 ? [X18] : ($true = vAPP($i,$o,cP,X18)) => ($true = vAPP($i,$o,cP,sK11))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f23,plain,(
% 0.21/0.39 ? [X19] : ($true != vAPP($i,$o,cQ,X19)) => ($true != vAPP($i,$o,cQ,sK12))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f24,plain,(
% 0.21/0.39 ! [X22] : (? [X23] : (vAPP($i,$o,cQ,X22) != vAPP($i,$o,cQ,X23)) => (vAPP($i,$o,cQ,X22) != vAPP($i,$o,cQ,vAPP($i,$i,sK13,X22))))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f12,plain,(
% 0.21/0.39 (($true = sP1) | ((((? [X0] : (vAPP($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,$o,cQ,X4) != vAPP($i,$o,cQ,X5))) & (((? [X6] : ($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,$o,cQ,X10) = vAPP($i,$o,cQ,X11))))) & (((? [X12] : ! [X13] : (vAPP($i,$o,cQ,X12) = vAPP($i,$o,cQ,X13)) | ((? [X14] : ($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,$o,cQ,X22) != vAPP($i,$o,cQ,X23)))) | ($true != sP1))),
% 0.21/0.39 inference(rectify,[],[f11])).
% 0.21/0.39 thf(f11,plain,(
% 0.21/0.39 (($true = sP1) | ((((? [X7] : ($true != vAPP($i,$o,cQ,X7)) | ! [X6] : ($true != vAPP($i,$o,cP,X6))) & (! [X7] : ($true = vAPP($i,$o,cQ,X7)) | ? [X6] : ($true = vAPP($i,$o,cP,X6)))) | ! [X4] : ? [X5] : (vAPP($i,$o,cQ,X4) != vAPP($i,$o,cQ,X5))) & (((? [X6] : ($true = vAPP($i,$o,cP,X6)) | ? [X7] : ($true != vAPP($i,$o,cQ,X7))) & (! [X7] : ($true = vAPP($i,$o,cQ,X7)) | ! [X6] : ($true != vAPP($i,$o,cP,X6)))) | ? [X4] : ! [X5] : (vAPP($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,cQ,X7)) | ! [X6] : ($true != vAPP($i,$o,cP,X6))) & (! [X7] : ($true = vAPP($i,$o,cQ,X7)) | ? [X6] : ($true = vAPP($i,$o,cP,X6))))) & (((? [X6] : ($true = vAPP($i,$o,cP,X6)) | ? [X7] : ($true != vAPP($i,$o,cQ,X7))) & (! [X7] : ($true = vAPP($i,$o,cQ,X7)) | ! [X6] : ($true != vAPP($i,$o,cP,X6)))) | ! [X4] : ? [X5] : (vAPP($i,$o,cQ,X4) != vAPP($i,$o,cQ,X5)))) | ($true != sP1))),
% 0.21/0.39 inference(nnf_transformation,[],[f9])).
% 0.21/0.39 thf(f178,plain,(
% 0.21/0.39 ~spl26_4 | spl26_20 | ~spl26_18 | spl26_19),
% 0.21/0.39 inference(avatar_split_clause,[],[f79,f171,f167,f176,f103])).
% 0.21/0.39 thf(f79,plain,(
% 0.21/0.39 ( ! [X22 : $i] : (($true = vAPP($i,$o,cP,sK11)) | ($true != vAPP($i,$o,cQ,sK12)) | ($false = vAPP($i,$o,cQ,X22)) | ($true != sP1) | ($false = vAPP($i,$o,cQ,vAPP($i,$i,sK13,X22)))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f43])).
% 0.21/0.39 thf(f43,plain,(
% 0.21/0.39 ( ! [X22 : $i] : (($true = vAPP($i,$o,cP,sK11)) | ($true != vAPP($i,$o,cQ,sK12)) | (vAPP($i,$o,cQ,X22) != vAPP($i,$o,cQ,vAPP($i,$i,sK13,X22))) | ($true != sP1)) )),
% 0.21/0.39 inference(cnf_transformation,[],[f25])).
% 0.21/0.39 thf(f162,plain,(
% 0.21/0.39 spl26_15 | ~spl26_4 | spl26_16 | spl26_7 | spl26_12),
% 0.21/0.39 inference(avatar_split_clause,[],[f81,f138,f116,f158,f103,f153])).
% 0.21/0.39 thf(f81,plain,(
% 0.21/0.39 ( ! [X16 : $i,X13 : $i] : (($false = vAPP($i,$o,cQ,X13)) | ($true = vAPP($i,$o,cQ,X16)) | ($true = vAPP($i,$o,cP,sK10)) | ($true != sP1) | ($true = vAPP($i,$o,cQ,sK8))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f44])).
% 0.21/0.39 thf(f44,plain,(
% 0.21/0.39 ( ! [X16 : $i,X13 : $i] : ((vAPP($i,$o,cQ,X13) = vAPP($i,$o,cQ,sK8)) | ($true = vAPP($i,$o,cQ,X16)) | ($true = vAPP($i,$o,cP,sK10)) | ($true != sP1)) )),
% 0.21/0.39 inference(cnf_transformation,[],[f25])).
% 0.21/0.39 thf(f161,plain,(
% 0.21/0.39 spl26_13 | ~spl26_4 | spl26_16 | spl26_7 | spl26_7),
% 0.21/0.39 inference(avatar_split_clause,[],[f80,f116,f116,f158,f103,f144])).
% 0.21/0.39 thf(f80,plain,(
% 0.21/0.39 ( ! [X16 : $i,X13 : $i] : (($true = vAPP($i,$o,cQ,X13)) | ($true = vAPP($i,$o,cQ,X16)) | ($true = vAPP($i,$o,cP,sK10)) | ($true != sP1) | ($false = vAPP($i,$o,cQ,sK8))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f44])).
% 0.21/0.39 thf(f142,plain,(
% 0.21/0.39 spl26_11 | spl26_12 | spl26_2 | spl26_7 | spl26_4),
% 0.21/0.39 inference(avatar_split_clause,[],[f85,f103,f116,f96,f138,f134])).
% 0.21/0.39 thf(f85,plain,(
% 0.21/0.39 ( ! [X11 : $i,X8 : $i,X9 : $i] : (($true = sP1) | ($true = vAPP($i,$o,cQ,X8)) | ($true != vAPP($i,$o,cP,X9)) | ($false = vAPP($i,$o,cQ,X11)) | ($true = vAPP($i,$o,cQ,sK7))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f46])).
% 0.21/0.39 thf(f46,plain,(
% 0.21/0.39 ( ! [X11 : $i,X8 : $i,X9 : $i] : (($true = sP1) | ($true = vAPP($i,$o,cQ,X8)) | ($true != vAPP($i,$o,cP,X9)) | (vAPP($i,$o,cQ,X11) = vAPP($i,$o,cQ,sK7))) )),
% 0.21/0.39 inference(cnf_transformation,[],[f25])).
% 0.21/0.39 thf(f141,plain,(
% 0.21/0.39 spl26_8 | spl26_7 | spl26_2 | spl26_7 | spl26_4),
% 0.21/0.39 inference(avatar_split_clause,[],[f84,f103,f116,f96,f116,f121])).
% 0.21/0.39 thf(f84,plain,(
% 0.21/0.39 ( ! [X11 : $i,X8 : $i,X9 : $i] : (($true = sP1) | ($true = vAPP($i,$o,cQ,X8)) | ($true != vAPP($i,$o,cP,X9)) | ($true = vAPP($i,$o,cQ,X11)) | ($false = vAPP($i,$o,cQ,sK7))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f46])).
% 0.21/0.39 thf(f118,plain,(
% 0.21/0.39 spl26_1 | spl26_6 | spl26_7 | spl26_4),
% 0.21/0.39 inference(avatar_split_clause,[],[f88,f103,f116,f112,f93])).
% 0.21/0.39 thf(f88,plain,(
% 0.21/0.39 ( ! [X2 : $i,X4 : $i] : (($true = sP1) | ($true = vAPP($i,$o,cQ,X2)) | ($true = vAPP($i,$o,cP,sK3)) | ($true = vAPP($i,$o,cQ,X4)) | ($true = vAPP($i,$o,cQ,vAPP($i,$i,sK4,X4)))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f48])).
% 0.21/0.39 thf(f48,plain,(
% 0.21/0.39 ( ! [X2 : $i,X4 : $i] : (($true = sP1) | ($true = vAPP($i,$o,cQ,X2)) | ($true = vAPP($i,$o,cP,sK3)) | (vAPP($i,$o,cQ,X4) != vAPP($i,$o,cQ,vAPP($i,$i,sK4,X4)))) )),
% 0.21/0.39 inference(cnf_transformation,[],[f25])).
% 0.21/0.39 thf(f110,plain,(
% 0.21/0.39 spl26_5 | spl26_2 | ~spl26_3 | spl26_4),
% 0.21/0.39 inference(avatar_split_clause,[],[f91,f103,f99,f96,f108])).
% 0.21/0.39 thf(f91,plain,(
% 0.21/0.39 ( ! [X1 : $i,X4 : $i] : (($true = sP1) | ($true != vAPP($i,$o,cQ,sK2)) | (vAPP($i,$o,cP,X1) != $true) | ($false = vAPP($i,$o,cQ,X4)) | ($false = vAPP($i,$o,cQ,vAPP($i,$i,sK4,X4)))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f49])).
% 0.21/0.39 thf(f49,plain,(
% 0.21/0.39 ( ! [X1 : $i,X4 : $i] : (($true = sP1) | ($true != vAPP($i,$o,cQ,sK2)) | (vAPP($i,$o,cP,X1) != $true) | (vAPP($i,$o,cQ,X4) != vAPP($i,$o,cQ,vAPP($i,$i,sK4,X4)))) )),
% 0.21/0.39 inference(cnf_transformation,[],[f25])).
% 0.21/0.39 % SZS output end Proof for theBenchmark
% 0.21/0.39 % (4023)------------------------------
% 0.21/0.39 % (4023)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.39 % (4023)Termination reason: Refutation
% 0.21/0.39
% 0.21/0.39 % (4023)Memory used [KB]: 968
% 0.21/0.39 % (4023)Time elapsed: 0.021 s
% 0.21/0.39 % (4023)Instructions burned: 34 (million)
% 0.21/0.39 % (4015)Success in time 0.033 s
%------------------------------------------------------------------------------