TSTP Solution File: PUZ081^1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : PUZ081^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n015.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 02:29:55 EDT 2024
% Result : Theorem 0.11s 0.35s
% Output : Refutation 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : PUZ081^1 : TPTP v8.2.0. Released v3.6.0.
% 0.06/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n015.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat May 18 11:15:38 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % (15555)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.34 % (15558)WARNING: value z3 for option sas not known
% 0.11/0.34 % (15558)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.34 % (15557)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.34 % (15559)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.34 % (15560)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.11/0.34 % (15561)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.11/0.34 % (15562)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.11/0.34 % (15556)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.34 % (15562)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.11/0.34 % Exception at run slice level% Exception at run slice level% Exception at run slice level
% 0.11/0.34
% 0.11/0.34 User error: User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructsFinite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.34
% 0.11/0.34
% 0.11/0.34 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.35 % (15560)First to succeed.
% 0.11/0.35 % (15558)Also succeeded, but the first one will report.
% 0.11/0.35 % (15560)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-15555"
% 0.11/0.35 % (15561)Also succeeded, but the first one will report.
% 0.11/0.35 % (15560)Refutation found. Thanks to Tanya!
% 0.11/0.35 % SZS status Theorem for theBenchmark
% 0.11/0.35 % SZS output start Proof for theBenchmark
% 0.11/0.35 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.11/0.35 thf(func_def_3, type, says: $i > $o > $o).
% 0.11/0.35 thf(func_def_6, type, is_a: $i > $i > $o).
% 0.11/0.35 thf(func_def_10, type, vNOT: $o > $o).
% 0.11/0.35 thf(func_def_11, type, vOR: $o > $o > $o).
% 0.11/0.35 thf(func_def_13, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)).
% 0.11/0.35 thf(func_def_14, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)).
% 0.11/0.35 thf(func_def_15, type, vAND: $o > $o > $o).
% 0.11/0.35 thf(func_def_16, type, vIMP: $o > $o > $o).
% 0.11/0.35 thf(func_def_17, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)).
% 0.11/0.35 thf(f339,plain,(
% 0.11/0.35 $false),
% 0.11/0.35 inference(avatar_sat_refutation,[],[f60,f64,f105,f118,f127,f132,f137,f142,f148,f158,f178,f179,f187,f199,f210,f220,f228,f237,f243,f245,f247,f254,f261,f276,f279,f284,f292,f295,f303,f323,f338])).
% 0.11/0.35 thf(f338,plain,(
% 0.11/0.35 spl0_4 | ~spl0_3 | ~spl0_6),
% 0.11/0.35 inference(avatar_split_clause,[],[f296,f111,f94,f98])).
% 0.11/0.35 thf(f98,plain,(
% 0.11/0.35 spl0_4 <=> ($true = vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knight))),
% 0.11/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.11/0.35 thf(f94,plain,(
% 0.11/0.35 spl0_3 <=> (knight = knave)),
% 0.11/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.11/0.35 thf(f111,plain,(
% 0.11/0.35 spl0_6 <=> (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave) = $true)),
% 0.11/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])).
% 0.11/0.35 thf(f296,plain,(
% 0.11/0.35 ($true = vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knight)) | (~spl0_3 | ~spl0_6)),
% 0.11/0.35 inference(forward_demodulation,[],[f112,f96])).
% 0.11/0.35 thf(f96,plain,(
% 0.11/0.35 (knight = knave) | ~spl0_3),
% 0.11/0.35 inference(avatar_component_clause,[],[f94])).
% 0.11/0.35 thf(f112,plain,(
% 0.11/0.35 (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave) = $true) | ~spl0_6),
% 0.11/0.35 inference(avatar_component_clause,[],[f111])).
% 0.11/0.35 thf(f323,plain,(
% 0.11/0.35 ~spl0_3 | ~spl0_7 | ~spl0_14),
% 0.11/0.35 inference(avatar_contradiction_clause,[],[f322])).
% 0.11/0.35 thf(f322,plain,(
% 0.11/0.35 $false | (~spl0_3 | ~spl0_7 | ~spl0_14)),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f321])).
% 0.11/0.35 thf(f321,plain,(
% 0.11/0.35 ($true = $false) | (~spl0_3 | ~spl0_7 | ~spl0_14)),
% 0.11/0.35 inference(forward_demodulation,[],[f319,f177])).
% 0.11/0.35 thf(f177,plain,(
% 0.11/0.35 ($false = vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knight)) | ~spl0_14),
% 0.11/0.35 inference(avatar_component_clause,[],[f175])).
% 0.11/0.35 thf(f175,plain,(
% 0.11/0.35 spl0_14 <=> ($false = vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knight))),
% 0.11/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_14])])).
% 0.11/0.35 thf(f319,plain,(
% 0.11/0.35 ($true = vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knight)) | (~spl0_3 | ~spl0_7)),
% 0.11/0.35 inference(superposition,[],[f116,f96])).
% 0.11/0.35 thf(f116,plain,(
% 0.11/0.35 (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knave) = $true) | ~spl0_7),
% 0.11/0.35 inference(avatar_component_clause,[],[f115])).
% 0.11/0.35 thf(f115,plain,(
% 0.11/0.35 spl0_7 <=> (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knave) = $true)),
% 0.11/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_7])])).
% 0.11/0.35 thf(f303,plain,(
% 0.11/0.35 ~spl0_2 | ~spl0_3 | ~spl0_4 | ~spl0_17 | spl0_18),
% 0.11/0.35 inference(avatar_contradiction_clause,[],[f302])).
% 0.11/0.35 thf(f302,plain,(
% 0.11/0.35 $false | (~spl0_2 | ~spl0_3 | ~spl0_4 | ~spl0_17 | spl0_18)),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f301])).
% 0.11/0.35 thf(f301,plain,(
% 0.11/0.35 ($true = $false) | (~spl0_2 | ~spl0_3 | ~spl0_4 | ~spl0_17 | spl0_18)),
% 0.11/0.35 inference(forward_demodulation,[],[f300,f283])).
% 0.11/0.35 thf(f283,plain,(
% 0.11/0.35 ($false = vAPP($o,$o,vAPP($i,sTfun($o,$o),says,mel),$false)) | (~spl0_2 | spl0_18)),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f282])).
% 0.11/0.35 thf(f282,plain,(
% 0.11/0.35 ($true != $true) | ($false = vAPP($o,$o,vAPP($i,sTfun($o,$o),says,mel),$false)) | (~spl0_2 | spl0_18)),
% 0.11/0.35 inference(superposition,[],[f226,f63])).
% 0.11/0.35 thf(f63,plain,(
% 0.11/0.35 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) ) | ~spl0_2),
% 0.11/0.35 inference(avatar_component_clause,[],[f62])).
% 0.11/0.35 thf(f62,plain,(
% 0.11/0.35 spl0_2 <=> ! [X0 : $o] : (($true = X0) | ($false = X0))),
% 0.11/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.11/0.35 thf(f226,plain,(
% 0.11/0.35 ($true != vAPP($o,$o,vAPP($i,sTfun($o,$o),says,mel),$false)) | spl0_18),
% 0.11/0.35 inference(avatar_component_clause,[],[f225])).
% 0.11/0.35 thf(f225,plain,(
% 0.11/0.35 spl0_18 <=> ($true = vAPP($o,$o,vAPP($i,sTfun($o,$o),says,mel),$false))),
% 0.11/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_18])])).
% 0.11/0.35 thf(f300,plain,(
% 0.11/0.35 ($true = vAPP($o,$o,vAPP($i,sTfun($o,$o),says,mel),$false)) | (~spl0_3 | ~spl0_4 | ~spl0_17)),
% 0.11/0.35 inference(boolean_simplification,[],[f299])).
% 0.11/0.35 thf(f299,plain,(
% 0.11/0.35 ($true = vAPP($o,$o,vAPP($i,sTfun($o,$o),says,mel),vAPP($o,$o,vNOT,$true))) | (~spl0_3 | ~spl0_4 | ~spl0_17)),
% 0.11/0.35 inference(boolean_simplification,[],[f298])).
% 0.11/0.35 thf(f298,plain,(
% 0.11/0.35 ($true = vAPP($o,$o,vAPP($i,sTfun($o,$o),says,mel),vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knight)),$true)))) | (~spl0_3 | ~spl0_4 | ~spl0_17)),
% 0.11/0.35 inference(forward_demodulation,[],[f297,f99])).
% 0.11/0.35 thf(f99,plain,(
% 0.11/0.35 ($true = vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knight)) | ~spl0_4),
% 0.11/0.35 inference(avatar_component_clause,[],[f98])).
% 0.11/0.35 thf(f297,plain,(
% 0.11/0.35 ($true = vAPP($o,$o,vAPP($i,sTfun($o,$o),says,mel),vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knight)),vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knight))))) | (~spl0_3 | ~spl0_17)),
% 0.11/0.35 inference(forward_demodulation,[],[f219,f96])).
% 0.11/0.35 thf(f219,plain,(
% 0.11/0.35 ($true = vAPP($o,$o,vAPP($i,sTfun($o,$o),says,mel),vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knave)),vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave))))) | ~spl0_17),
% 0.11/0.35 inference(avatar_component_clause,[],[f217])).
% 0.11/0.35 thf(f217,plain,(
% 0.11/0.35 spl0_17 <=> ($true = vAPP($o,$o,vAPP($i,sTfun($o,$o),says,mel),vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knave)),vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave)))))),
% 0.11/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_17])])).
% 0.11/0.35 thf(f295,plain,(
% 0.11/0.35 ~spl0_6 | ~spl0_20),
% 0.11/0.35 inference(avatar_contradiction_clause,[],[f294])).
% 0.11/0.35 thf(f294,plain,(
% 0.11/0.35 $false | (~spl0_6 | ~spl0_20)),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f293])).
% 0.11/0.35 thf(f293,plain,(
% 0.11/0.35 ($true = $false) | (~spl0_6 | ~spl0_20)),
% 0.11/0.35 inference(forward_demodulation,[],[f112,f275])).
% 0.11/0.35 thf(f275,plain,(
% 0.11/0.35 (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave) = $false) | ~spl0_20),
% 0.11/0.35 inference(avatar_component_clause,[],[f273])).
% 0.11/0.35 thf(f273,plain,(
% 0.11/0.35 spl0_20 <=> (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave) = $false)),
% 0.11/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_20])])).
% 0.11/0.35 thf(f292,plain,(
% 0.11/0.35 ~spl0_2 | ~spl0_7 | ~spl0_17 | spl0_18 | ~spl0_20),
% 0.11/0.35 inference(avatar_contradiction_clause,[],[f291])).
% 0.11/0.35 thf(f291,plain,(
% 0.11/0.35 $false | (~spl0_2 | ~spl0_7 | ~spl0_17 | spl0_18 | ~spl0_20)),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f290])).
% 0.11/0.35 thf(f290,plain,(
% 0.11/0.35 ($true = $false) | (~spl0_2 | ~spl0_7 | ~spl0_17 | spl0_18 | ~spl0_20)),
% 0.11/0.35 inference(forward_demodulation,[],[f289,f283])).
% 0.11/0.35 thf(f289,plain,(
% 0.11/0.35 ($true = vAPP($o,$o,vAPP($i,sTfun($o,$o),says,mel),$false)) | (~spl0_7 | ~spl0_17 | ~spl0_20)),
% 0.11/0.35 inference(boolean_simplification,[],[f288])).
% 0.11/0.35 thf(f288,plain,(
% 0.11/0.35 ($true = vAPP($o,$o,vAPP($i,sTfun($o,$o),says,mel),vAPP($o,$o,vNOT,$true))) | (~spl0_7 | ~spl0_17 | ~spl0_20)),
% 0.11/0.35 inference(forward_demodulation,[],[f287,f116])).
% 0.11/0.35 thf(f287,plain,(
% 0.11/0.35 ($true = vAPP($o,$o,vAPP($i,sTfun($o,$o),says,mel),vAPP($o,$o,vNOT,vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knave)))) | (~spl0_17 | ~spl0_20)),
% 0.11/0.35 inference(boolean_simplification,[],[f286])).
% 0.11/0.35 thf(f286,plain,(
% 0.11/0.35 ($true = vAPP($o,$o,vAPP($i,sTfun($o,$o),says,mel),vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knave)),$false)))) | (~spl0_17 | ~spl0_20)),
% 0.11/0.35 inference(forward_demodulation,[],[f219,f275])).
% 0.11/0.35 thf(f284,plain,(
% 0.11/0.35 spl0_18 | ~spl0_2 | spl0_6 | ~spl0_7 | ~spl0_17),
% 0.11/0.35 inference(avatar_split_clause,[],[f268,f217,f115,f111,f62,f225])).
% 0.11/0.35 thf(f268,plain,(
% 0.11/0.35 ($true = vAPP($o,$o,vAPP($i,sTfun($o,$o),says,mel),$false)) | (~spl0_2 | spl0_6 | ~spl0_7 | ~spl0_17)),
% 0.11/0.35 inference(boolean_simplification,[],[f267])).
% 0.11/0.35 thf(f267,plain,(
% 0.11/0.35 ($true = vAPP($o,$o,vAPP($i,sTfun($o,$o),says,mel),vAPP($o,$o,vNOT,$true))) | (~spl0_2 | spl0_6 | ~spl0_7 | ~spl0_17)),
% 0.11/0.35 inference(forward_demodulation,[],[f266,f116])).
% 0.11/0.35 thf(f266,plain,(
% 0.11/0.35 ($true = vAPP($o,$o,vAPP($i,sTfun($o,$o),says,mel),vAPP($o,$o,vNOT,vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knave)))) | (~spl0_2 | spl0_6 | ~spl0_17)),
% 0.11/0.35 inference(boolean_simplification,[],[f265])).
% 0.11/0.35 thf(f265,plain,(
% 0.11/0.35 ($true = vAPP($o,$o,vAPP($i,sTfun($o,$o),says,mel),vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knave)),$false)))) | (~spl0_2 | spl0_6 | ~spl0_17)),
% 0.11/0.35 inference(forward_demodulation,[],[f219,f120])).
% 0.11/0.35 thf(f120,plain,(
% 0.11/0.35 (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave) = $false) | (~spl0_2 | spl0_6)),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f119])).
% 0.11/0.35 thf(f119,plain,(
% 0.11/0.35 ($true != $true) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave) = $false) | (~spl0_2 | spl0_6)),
% 0.11/0.35 inference(superposition,[],[f113,f63])).
% 0.11/0.35 thf(f113,plain,(
% 0.11/0.35 (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave) != $true) | spl0_6),
% 0.11/0.35 inference(avatar_component_clause,[],[f111])).
% 0.11/0.35 thf(f279,plain,(
% 0.11/0.35 ~spl0_4 | ~spl0_15 | ~spl0_18),
% 0.11/0.35 inference(avatar_split_clause,[],[f231,f225,f185,f98])).
% 0.11/0.35 thf(f185,plain,(
% 0.11/0.35 spl0_15 <=> ! [X0,X1 : $o] : (($true = X1) | (vAPP($o,$o,vAPP($i,sTfun($o,$o),says,X0),X1) != $true) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knight) != $true))),
% 0.11/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_15])])).
% 0.11/0.35 thf(f231,plain,(
% 0.11/0.35 ($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knight)) | (~spl0_15 | ~spl0_18)),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f230])).
% 0.11/0.35 thf(f230,plain,(
% 0.11/0.35 ($true != $true) | ($true = $false) | ($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knight)) | (~spl0_15 | ~spl0_18)),
% 0.11/0.35 inference(superposition,[],[f186,f227])).
% 0.11/0.35 thf(f227,plain,(
% 0.11/0.35 ($true = vAPP($o,$o,vAPP($i,sTfun($o,$o),says,mel),$false)) | ~spl0_18),
% 0.11/0.35 inference(avatar_component_clause,[],[f225])).
% 0.11/0.35 thf(f186,plain,(
% 0.11/0.35 ( ! [X0 : $i,X1 : $o] : ((vAPP($o,$o,vAPP($i,sTfun($o,$o),says,X0),X1) != $true) | ($true = X1) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knight) != $true)) ) | ~spl0_15),
% 0.11/0.35 inference(avatar_component_clause,[],[f185])).
% 0.11/0.35 thf(f276,plain,(
% 0.11/0.35 spl0_20 | ~spl0_2 | spl0_6),
% 0.11/0.35 inference(avatar_split_clause,[],[f120,f111,f62,f273])).
% 0.11/0.35 thf(f261,plain,(
% 0.11/0.35 ~spl0_7 | ~spl0_19),
% 0.11/0.35 inference(avatar_contradiction_clause,[],[f260])).
% 0.11/0.35 thf(f260,plain,(
% 0.11/0.35 $false | (~spl0_7 | ~spl0_19)),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f259])).
% 0.11/0.35 thf(f259,plain,(
% 0.11/0.35 ($true = $false) | (~spl0_7 | ~spl0_19)),
% 0.11/0.35 inference(forward_demodulation,[],[f116,f236])).
% 0.11/0.35 thf(f236,plain,(
% 0.11/0.35 (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knave) = $false) | ~spl0_19),
% 0.11/0.35 inference(avatar_component_clause,[],[f234])).
% 0.11/0.35 thf(f234,plain,(
% 0.11/0.35 spl0_19 <=> (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knave) = $false)),
% 0.11/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_19])])).
% 0.11/0.35 thf(f254,plain,(
% 0.11/0.35 ~spl0_8 | ~spl0_14 | ~spl0_16 | ~spl0_19),
% 0.11/0.35 inference(avatar_contradiction_clause,[],[f253])).
% 0.11/0.35 thf(f253,plain,(
% 0.11/0.35 $false | (~spl0_8 | ~spl0_14 | ~spl0_16 | ~spl0_19)),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f252])).
% 0.11/0.35 thf(f252,plain,(
% 0.11/0.35 ($true = $false) | (~spl0_8 | ~spl0_14 | ~spl0_16 | ~spl0_19)),
% 0.11/0.35 inference(forward_demodulation,[],[f251,f236])).
% 0.11/0.35 thf(f251,plain,(
% 0.11/0.35 (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knave) = $true) | (~spl0_8 | ~spl0_14 | ~spl0_16)),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f250])).
% 0.11/0.35 thf(f250,plain,(
% 0.11/0.35 ($true = $false) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knave) = $true) | (~spl0_8 | ~spl0_14 | ~spl0_16)),
% 0.11/0.35 inference(forward_demodulation,[],[f205,f177])).
% 0.11/0.35 thf(f205,plain,(
% 0.11/0.35 ($true = vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knight)) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knave) = $true) | (~spl0_8 | ~spl0_16)),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f200])).
% 0.11/0.35 thf(f200,plain,(
% 0.11/0.35 ($true != $true) | ($true = vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knight)) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knave) = $true) | (~spl0_8 | ~spl0_16)),
% 0.11/0.35 inference(superposition,[],[f198,f126])).
% 0.11/0.35 thf(f126,plain,(
% 0.11/0.35 (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),islander) = $true) | ~spl0_8),
% 0.11/0.35 inference(avatar_component_clause,[],[f124])).
% 0.11/0.35 thf(f124,plain,(
% 0.11/0.35 spl0_8 <=> (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),islander) = $true)),
% 0.11/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_8])])).
% 0.11/0.35 thf(f198,plain,(
% 0.11/0.35 ( ! [X0 : $i] : ((vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),islander) != $true) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knight) = $true) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knave) = $true)) ) | ~spl0_16),
% 0.11/0.35 inference(avatar_component_clause,[],[f197])).
% 0.11/0.35 thf(f197,plain,(
% 0.11/0.35 spl0_16 <=> ! [X0] : ((vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knave) = $true) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knight) = $true) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),islander) != $true))),
% 0.11/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_16])])).
% 0.11/0.35 thf(f247,plain,(
% 0.11/0.35 spl0_5 | ~spl0_2 | spl0_7 | ~spl0_8 | ~spl0_16),
% 0.11/0.35 inference(avatar_split_clause,[],[f213,f197,f124,f115,f62,f102])).
% 0.11/0.35 thf(f102,plain,(
% 0.11/0.35 spl0_5 <=> ($true = vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knight))),
% 0.11/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])).
% 0.11/0.35 thf(f213,plain,(
% 0.11/0.35 ($true = vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knight)) | (~spl0_2 | spl0_7 | ~spl0_8 | ~spl0_16)),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f212])).
% 0.11/0.35 thf(f212,plain,(
% 0.11/0.35 ($true = $false) | ($true = vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knight)) | (~spl0_2 | spl0_7 | ~spl0_8 | ~spl0_16)),
% 0.11/0.35 inference(forward_demodulation,[],[f205,f122])).
% 0.11/0.35 thf(f122,plain,(
% 0.11/0.35 (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knave) = $false) | (~spl0_2 | spl0_7)),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f121])).
% 0.11/0.35 thf(f121,plain,(
% 0.11/0.35 ($true != $true) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knave) = $false) | (~spl0_2 | spl0_7)),
% 0.11/0.35 inference(superposition,[],[f117,f63])).
% 0.11/0.35 thf(f117,plain,(
% 0.11/0.35 (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knave) != $true) | spl0_7),
% 0.11/0.35 inference(avatar_component_clause,[],[f115])).
% 0.11/0.35 thf(f245,plain,(
% 0.11/0.35 spl0_6 | ~spl0_9 | ~spl0_10 | ~spl0_16),
% 0.11/0.35 inference(avatar_split_clause,[],[f207,f197,f134,f129,f111])).
% 0.11/0.35 thf(f129,plain,(
% 0.11/0.35 spl0_9 <=> ($false = vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knight))),
% 0.11/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_9])])).
% 0.11/0.35 thf(f134,plain,(
% 0.11/0.35 spl0_10 <=> (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),islander) = $true)),
% 0.11/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_10])])).
% 0.11/0.35 thf(f207,plain,(
% 0.11/0.35 (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave) = $true) | (~spl0_9 | ~spl0_10 | ~spl0_16)),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f206])).
% 0.11/0.35 thf(f206,plain,(
% 0.11/0.35 ($true = $false) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave) = $true) | (~spl0_9 | ~spl0_10 | ~spl0_16)),
% 0.11/0.35 inference(forward_demodulation,[],[f204,f131])).
% 0.11/0.35 thf(f131,plain,(
% 0.11/0.35 ($false = vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knight)) | ~spl0_9),
% 0.11/0.35 inference(avatar_component_clause,[],[f129])).
% 0.11/0.35 thf(f204,plain,(
% 0.11/0.35 ($true = vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knight)) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave) = $true) | (~spl0_10 | ~spl0_16)),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f201])).
% 0.11/0.35 thf(f201,plain,(
% 0.11/0.35 ($true != $true) | ($true = vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knight)) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave) = $true) | (~spl0_10 | ~spl0_16)),
% 0.11/0.35 inference(superposition,[],[f198,f136])).
% 0.11/0.35 thf(f136,plain,(
% 0.11/0.35 (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),islander) = $true) | ~spl0_10),
% 0.11/0.35 inference(avatar_component_clause,[],[f134])).
% 0.11/0.35 thf(f243,plain,(
% 0.11/0.35 ~spl0_5 | ~spl0_12 | ~spl0_15),
% 0.11/0.35 inference(avatar_split_clause,[],[f192,f185,f145,f102])).
% 0.11/0.35 thf(f145,plain,(
% 0.11/0.35 spl0_12 <=> ($true = vAPP($o,$o,vAPP($i,sTfun($o,$o),says,zoey),$false))),
% 0.11/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_12])])).
% 0.11/0.35 thf(f192,plain,(
% 0.11/0.35 ($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knight)) | (~spl0_12 | ~spl0_15)),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f189])).
% 0.11/0.35 thf(f189,plain,(
% 0.11/0.35 ($true != $true) | ($true = $false) | ($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knight)) | (~spl0_12 | ~spl0_15)),
% 0.11/0.35 inference(superposition,[],[f186,f147])).
% 0.11/0.35 thf(f147,plain,(
% 0.11/0.35 ($true = vAPP($o,$o,vAPP($i,sTfun($o,$o),says,zoey),$false)) | ~spl0_12),
% 0.11/0.35 inference(avatar_component_clause,[],[f145])).
% 0.11/0.35 thf(f237,plain,(
% 0.11/0.35 spl0_19 | ~spl0_2 | spl0_7),
% 0.11/0.35 inference(avatar_split_clause,[],[f122,f115,f62,f234])).
% 0.11/0.35 thf(f228,plain,(
% 0.11/0.35 spl0_18 | ~spl0_9 | ~spl0_10 | ~spl0_16 | ~spl0_17),
% 0.11/0.35 inference(avatar_split_clause,[],[f223,f217,f197,f134,f129,f225])).
% 0.11/0.35 thf(f223,plain,(
% 0.11/0.35 ($true = vAPP($o,$o,vAPP($i,sTfun($o,$o),says,mel),$false)) | (~spl0_9 | ~spl0_10 | ~spl0_16 | ~spl0_17)),
% 0.11/0.35 inference(boolean_simplification,[],[f222])).
% 0.11/0.35 thf(f222,plain,(
% 0.11/0.35 ($true = vAPP($o,$o,vAPP($i,sTfun($o,$o),says,mel),vAPP($o,$o,vNOT,$true))) | (~spl0_9 | ~spl0_10 | ~spl0_16 | ~spl0_17)),
% 0.11/0.35 inference(boolean_simplification,[],[f221])).
% 0.11/0.35 thf(f221,plain,(
% 0.11/0.35 ($true = vAPP($o,$o,vAPP($i,sTfun($o,$o),says,mel),vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knave)),$true)))) | (~spl0_9 | ~spl0_10 | ~spl0_16 | ~spl0_17)),
% 0.11/0.35 inference(forward_demodulation,[],[f219,f207])).
% 0.11/0.35 thf(f220,plain,(
% 0.11/0.35 spl0_17),
% 0.11/0.35 inference(avatar_split_clause,[],[f42,f217])).
% 0.11/0.35 thf(f42,plain,(
% 0.11/0.35 ($true = vAPP($o,$o,vAPP($i,sTfun($o,$o),says,mel),vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knave)),vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave)))))),
% 0.11/0.35 inference(cnf_transformation,[],[f24])).
% 0.11/0.35 thf(f24,plain,(
% 0.11/0.35 ($true = vAPP($o,$o,vAPP($i,sTfun($o,$o),says,mel),vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knave)),vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave)))))),
% 0.11/0.35 inference(fool_elimination,[],[f23])).
% 0.11/0.35 thf(f23,plain,(
% 0.11/0.35 vAPP($o,$o,vAPP($i,sTfun($o,$o),says,mel),~(vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave) | vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knave)))),
% 0.11/0.35 inference(rectify,[],[f6])).
% 0.11/0.35 thf(f6,axiom,(
% 0.11/0.35 vAPP($o,$o,vAPP($i,sTfun($o,$o),says,mel),~(vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave) | vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knave)))),
% 0.11/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kk_6_6)).
% 0.11/0.35 thf(f210,plain,(
% 0.11/0.35 ~spl0_2 | spl0_6 | ~spl0_9 | ~spl0_10 | ~spl0_16),
% 0.11/0.35 inference(avatar_contradiction_clause,[],[f209])).
% 0.11/0.35 thf(f209,plain,(
% 0.11/0.35 $false | (~spl0_2 | spl0_6 | ~spl0_9 | ~spl0_10 | ~spl0_16)),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f208])).
% 0.11/0.35 thf(f208,plain,(
% 0.11/0.35 ($true = $false) | (~spl0_2 | spl0_6 | ~spl0_9 | ~spl0_10 | ~spl0_16)),
% 0.11/0.35 inference(forward_demodulation,[],[f207,f120])).
% 0.11/0.35 thf(f199,plain,(
% 0.11/0.35 spl0_16),
% 0.11/0.35 inference(avatar_split_clause,[],[f38,f197])).
% 0.11/0.35 thf(f38,plain,(
% 0.11/0.35 ( ! [X0 : $i] : ((vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knave) = $true) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knight) = $true) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),islander) != $true)) )),
% 0.11/0.35 inference(cnf_transformation,[],[f28])).
% 0.11/0.35 thf(f28,plain,(
% 0.11/0.35 ! [X0] : ((vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knave) = $true) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knight) = $true) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),islander) != $true))),
% 0.11/0.35 inference(flattening,[],[f27])).
% 0.11/0.35 thf(f27,plain,(
% 0.11/0.35 ! [X0] : (((vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knave) = $true) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knight) = $true)) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),islander) != $true))),
% 0.11/0.35 inference(ennf_transformation,[],[f16])).
% 0.11/0.35 thf(f16,plain,(
% 0.11/0.35 ! [X0] : ((vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),islander) = $true) => ((vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knave) = $true) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knight) = $true)))),
% 0.11/0.35 inference(fool_elimination,[],[f15])).
% 0.11/0.35 thf(f15,plain,(
% 0.11/0.35 ! [X0] : (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),islander) => (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knave) | vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knight)))),
% 0.11/0.35 inference(rectify,[],[f1])).
% 0.11/0.35 thf(f1,axiom,(
% 0.11/0.35 ! [X0] : (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),islander) => (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knave) | vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knight)))),
% 0.11/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kk_6_1)).
% 0.11/0.35 thf(f187,plain,(
% 0.11/0.35 spl0_15),
% 0.11/0.35 inference(avatar_split_clause,[],[f39,f185])).
% 0.11/0.35 thf(f39,plain,(
% 0.11/0.35 ( ! [X0 : $i,X1 : $o] : (($true = X1) | (vAPP($o,$o,vAPP($i,sTfun($o,$o),says,X0),X1) != $true) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knight) != $true)) )),
% 0.11/0.35 inference(cnf_transformation,[],[f29])).
% 0.11/0.35 thf(f29,plain,(
% 0.11/0.35 ! [X0] : (! [X1 : $o] : (($true = X1) | (vAPP($o,$o,vAPP($i,sTfun($o,$o),says,X0),X1) != $true)) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knight) != $true))),
% 0.11/0.35 inference(ennf_transformation,[],[f18])).
% 0.11/0.35 thf(f18,plain,(
% 0.11/0.35 ! [X0] : ((vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knight) = $true) => ! [X1 : $o] : ((vAPP($o,$o,vAPP($i,sTfun($o,$o),says,X0),X1) = $true) => ($true = X1)))),
% 0.11/0.35 inference(fool_elimination,[],[f17])).
% 0.11/0.35 thf(f17,plain,(
% 0.11/0.35 ! [X0] : (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knight) => ! [X1 : $o] : (vAPP($o,$o,vAPP($i,sTfun($o,$o),says,X0),X1) => X1))),
% 0.11/0.35 inference(rectify,[],[f2])).
% 0.11/0.35 thf(f2,axiom,(
% 0.11/0.35 ! [X0] : (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knight) => ! [X1 : $o] : (vAPP($o,$o,vAPP($i,sTfun($o,$o),says,X0),X1) => X1))),
% 0.11/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kk_6_2)).
% 0.11/0.35 thf(f179,plain,(
% 0.11/0.35 spl0_3 | ~spl0_6 | ~spl0_5),
% 0.11/0.35 inference(avatar_split_clause,[],[f53,f102,f111,f94])).
% 0.11/0.35 thf(f53,plain,(
% 0.11/0.35 ($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knight)) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave) != $true) | (knight = knave)),
% 0.11/0.35 inference(duplicate_literal_removal,[],[f48])).
% 0.11/0.35 thf(f48,plain,(
% 0.11/0.35 ($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knight)) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave) != $true) | (knight = knave) | (knight = knave)),
% 0.11/0.35 inference(equality_resolution,[],[f47])).
% 0.11/0.35 thf(f47,plain,(
% 0.11/0.35 ( ! [X0 : $i] : (($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knight)) | ($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),X0)) | (knight = knave) | (knight = X0) | (knave != X0)) )),
% 0.11/0.35 inference(equality_resolution,[],[f33])).
% 0.11/0.35 thf(f33,plain,(
% 0.11/0.35 ( ! [X0 : $i,X1 : $i] : (($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),X1)) | ($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),X0)) | (knave = X1) | (knight != X1) | (knight = X0) | (knave != X0)) )),
% 0.11/0.35 inference(cnf_transformation,[],[f31])).
% 0.11/0.35 thf(f31,plain,(
% 0.11/0.35 ! [X0,X1] : (($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),X1)) | ($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),X0)) | (((knight = X1) | (knave != X1)) & ((knave = X1) | (knight != X1))) | (((knight = X0) | (knave != X0)) & ((knave = X0) | (knight != X0))))),
% 0.11/0.35 inference(nnf_transformation,[],[f26])).
% 0.11/0.35 thf(f26,plain,(
% 0.11/0.35 ! [X0,X1] : (($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),X1)) | ($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),X0)) | ((knight = X1) <=> (knave = X1)) | ((knight = X0) <=> (knave = X0)))),
% 0.11/0.35 inference(ennf_transformation,[],[f12])).
% 0.11/0.35 thf(f12,plain,(
% 0.11/0.35 ~? [X0,X1] : (($true = vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),X1)) & ($true = vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),X0)) & ((knight = X1) <~> (knave = X1)) & ((knight = X0) <~> (knave = X0)))),
% 0.11/0.35 inference(fool_elimination,[],[f11])).
% 0.11/0.35 thf(f11,plain,(
% 0.11/0.35 ~? [X0,X1] : (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),X1) & vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),X0) & ((knight = X1) <~> (knave = X1)) & ((knight = X0) <~> (knave = X0)))),
% 0.11/0.35 inference(rectify,[],[f8])).
% 0.11/0.35 thf(f8,negated_conjecture,(
% 0.11/0.35 ~? [X2,X3] : (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),X3) & vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),X2) & ((knight = X3) <~> (knave = X3)) & ((knight = X2) <~> (knave = X2)))),
% 0.11/0.35 inference(negated_conjecture,[],[f7])).
% 0.11/0.35 thf(f7,conjecture,(
% 0.11/0.35 ? [X2,X3] : (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),X3) & vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),X2) & ((knight = X3) <~> (knave = X3)) & ((knight = X2) <~> (knave = X2)))),
% 0.11/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',query)).
% 0.11/0.35 thf(f178,plain,(
% 0.11/0.35 spl0_14 | ~spl0_2 | spl0_5),
% 0.11/0.35 inference(avatar_split_clause,[],[f109,f102,f62,f175])).
% 0.11/0.35 thf(f109,plain,(
% 0.11/0.35 ($false = vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knight)) | (~spl0_2 | spl0_5)),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f108])).
% 0.11/0.35 thf(f108,plain,(
% 0.11/0.35 ($true != $true) | ($false = vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knight)) | (~spl0_2 | spl0_5)),
% 0.11/0.35 inference(superposition,[],[f104,f63])).
% 0.11/0.35 thf(f104,plain,(
% 0.11/0.35 ($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knight)) | spl0_5),
% 0.11/0.35 inference(avatar_component_clause,[],[f102])).
% 0.11/0.35 thf(f158,plain,(
% 0.11/0.35 spl0_13),
% 0.11/0.35 inference(avatar_split_clause,[],[f51,f156])).
% 0.11/0.35 thf(f156,plain,(
% 0.11/0.35 spl0_13 <=> ! [X0] : (($true != vAPP($o,$o,vAPP($i,sTfun($o,$o),says,X0),$true)) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knave) != $true))),
% 0.11/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_13])])).
% 0.11/0.35 thf(f51,plain,(
% 0.11/0.35 ( ! [X0 : $i] : (($true != vAPP($o,$o,vAPP($i,sTfun($o,$o),says,X0),$true)) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knave) != $true)) )),
% 0.11/0.35 inference(equality_resolution,[],[f40])).
% 0.11/0.35 thf(f40,plain,(
% 0.11/0.35 ( ! [X0 : $i,X1 : $o] : (($true != X1) | (vAPP($o,$o,vAPP($i,sTfun($o,$o),says,X0),X1) != $true) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knave) != $true)) )),
% 0.11/0.35 inference(cnf_transformation,[],[f30])).
% 0.11/0.35 thf(f30,plain,(
% 0.11/0.35 ! [X0] : (! [X1 : $o] : (($true != X1) | (vAPP($o,$o,vAPP($i,sTfun($o,$o),says,X0),X1) != $true)) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knave) != $true))),
% 0.11/0.35 inference(ennf_transformation,[],[f25])).
% 0.11/0.35 thf(f25,plain,(
% 0.11/0.35 ! [X0] : ((vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knave) = $true) => ! [X1 : $o] : ((vAPP($o,$o,vAPP($i,sTfun($o,$o),says,X0),X1) = $true) => ($true != X1)))),
% 0.11/0.35 inference(flattening,[],[f20])).
% 0.11/0.35 thf(f20,plain,(
% 0.11/0.35 ! [X0] : ((vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knave) = $true) => ! [X1 : $o] : ((vAPP($o,$o,vAPP($i,sTfun($o,$o),says,X0),X1) = $true) => ~($true = X1)))),
% 0.11/0.35 inference(fool_elimination,[],[f19])).
% 0.11/0.35 thf(f19,plain,(
% 0.11/0.35 ! [X0] : (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knave) => ! [X1 : $o] : (vAPP($o,$o,vAPP($i,sTfun($o,$o),says,X0),X1) => ~X1))),
% 0.11/0.35 inference(rectify,[],[f3])).
% 0.11/0.35 thf(f3,axiom,(
% 0.11/0.35 ! [X0] : (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,X0),knave) => ! [X1 : $o] : (vAPP($o,$o,vAPP($i,sTfun($o,$o),says,X0),X1) => ~X1))),
% 0.11/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kk_6_3)).
% 0.11/0.35 thf(f148,plain,(
% 0.11/0.35 spl0_12 | ~spl0_2 | spl0_6 | ~spl0_11),
% 0.11/0.35 inference(avatar_split_clause,[],[f143,f139,f111,f62,f145])).
% 0.11/0.35 thf(f139,plain,(
% 0.11/0.35 spl0_11 <=> (vAPP($o,$o,vAPP($i,sTfun($o,$o),says,zoey),vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave)) = $true)),
% 0.11/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_11])])).
% 0.11/0.35 thf(f143,plain,(
% 0.11/0.35 ($true = vAPP($o,$o,vAPP($i,sTfun($o,$o),says,zoey),$false)) | (~spl0_2 | spl0_6 | ~spl0_11)),
% 0.11/0.35 inference(forward_demodulation,[],[f141,f120])).
% 0.11/0.35 thf(f141,plain,(
% 0.11/0.35 (vAPP($o,$o,vAPP($i,sTfun($o,$o),says,zoey),vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave)) = $true) | ~spl0_11),
% 0.11/0.35 inference(avatar_component_clause,[],[f139])).
% 0.11/0.35 thf(f142,plain,(
% 0.11/0.35 spl0_11),
% 0.11/0.35 inference(avatar_split_clause,[],[f41,f139])).
% 0.11/0.35 thf(f41,plain,(
% 0.11/0.35 (vAPP($o,$o,vAPP($i,sTfun($o,$o),says,zoey),vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave)) = $true)),
% 0.11/0.35 inference(cnf_transformation,[],[f22])).
% 0.11/0.35 thf(f22,plain,(
% 0.11/0.35 (vAPP($o,$o,vAPP($i,sTfun($o,$o),says,zoey),vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave)) = $true)),
% 0.11/0.35 inference(fool_elimination,[],[f21])).
% 0.11/0.35 thf(f21,plain,(
% 0.11/0.35 vAPP($o,$o,vAPP($i,sTfun($o,$o),says,zoey),vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave))),
% 0.11/0.35 inference(rectify,[],[f5])).
% 0.11/0.35 thf(f5,axiom,(
% 0.11/0.35 vAPP($o,$o,vAPP($i,sTfun($o,$o),says,zoey),vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave))),
% 0.11/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kk_6_5)).
% 0.11/0.35 thf(f137,plain,(
% 0.11/0.35 spl0_10),
% 0.11/0.35 inference(avatar_split_clause,[],[f37,f134])).
% 0.11/0.35 thf(f37,plain,(
% 0.11/0.35 (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),islander) = $true)),
% 0.11/0.35 inference(cnf_transformation,[],[f14])).
% 0.11/0.35 thf(f14,plain,(
% 0.11/0.35 (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),islander) = $true) & (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),islander) = $true)),
% 0.11/0.35 inference(fool_elimination,[],[f13])).
% 0.11/0.35 thf(f13,plain,(
% 0.11/0.35 vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),islander) & vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),islander)),
% 0.11/0.35 inference(rectify,[],[f4])).
% 0.11/0.35 thf(f4,axiom,(
% 0.11/0.35 vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),islander) & vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),islander)),
% 0.11/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kk_6_4)).
% 0.11/0.35 thf(f132,plain,(
% 0.11/0.35 spl0_9 | ~spl0_2 | spl0_4),
% 0.11/0.35 inference(avatar_split_clause,[],[f107,f98,f62,f129])).
% 0.11/0.35 thf(f107,plain,(
% 0.11/0.35 ($false = vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knight)) | (~spl0_2 | spl0_4)),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f106])).
% 0.11/0.35 thf(f106,plain,(
% 0.11/0.35 ($true != $true) | ($false = vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knight)) | (~spl0_2 | spl0_4)),
% 0.11/0.35 inference(superposition,[],[f100,f63])).
% 0.11/0.35 thf(f100,plain,(
% 0.11/0.35 ($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knight)) | spl0_4),
% 0.11/0.35 inference(avatar_component_clause,[],[f98])).
% 0.11/0.35 thf(f127,plain,(
% 0.11/0.35 spl0_8),
% 0.11/0.35 inference(avatar_split_clause,[],[f36,f124])).
% 0.11/0.35 thf(f36,plain,(
% 0.11/0.35 (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),islander) = $true)),
% 0.11/0.35 inference(cnf_transformation,[],[f14])).
% 0.11/0.35 thf(f118,plain,(
% 0.11/0.35 spl0_3 | ~spl0_6 | ~spl0_7),
% 0.11/0.35 inference(avatar_split_clause,[],[f55,f115,f111,f94])).
% 0.11/0.35 thf(f55,plain,(
% 0.11/0.35 (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knave) != $true) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave) != $true) | (knight = knave)),
% 0.11/0.35 inference(duplicate_literal_removal,[],[f44])).
% 0.11/0.35 thf(f44,plain,(
% 0.11/0.35 (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knave) != $true) | (vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knave) != $true) | (knight = knave) | (knight = knave)),
% 0.11/0.35 inference(equality_resolution,[],[f43])).
% 0.11/0.35 thf(f43,plain,(
% 0.11/0.35 ( ! [X0 : $i] : ((vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knave) != $true) | ($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),X0)) | (knight = knave) | (knight = X0) | (knave != X0)) )),
% 0.11/0.35 inference(equality_resolution,[],[f35])).
% 0.11/0.35 thf(f35,plain,(
% 0.11/0.35 ( ! [X0 : $i,X1 : $i] : (($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),X1)) | ($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),X0)) | (knight = X1) | (knave != X1) | (knight = X0) | (knave != X0)) )),
% 0.11/0.35 inference(cnf_transformation,[],[f31])).
% 0.11/0.35 thf(f105,plain,(
% 0.11/0.35 spl0_3 | ~spl0_4 | ~spl0_5),
% 0.11/0.35 inference(avatar_split_clause,[],[f52,f102,f98,f94])).
% 0.11/0.35 thf(f52,plain,(
% 0.11/0.35 ($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knight)) | ($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knight)) | (knight = knave)),
% 0.11/0.35 inference(duplicate_literal_removal,[],[f50])).
% 0.11/0.35 thf(f50,plain,(
% 0.11/0.35 ($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knight)) | ($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),knight)) | (knight = knave) | (knight = knave)),
% 0.11/0.35 inference(equality_resolution,[],[f49])).
% 0.11/0.35 thf(f49,plain,(
% 0.11/0.35 ( ! [X0 : $i] : (($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),knight)) | ($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),X0)) | (knight = knave) | (knave = X0) | (knight != X0)) )),
% 0.11/0.35 inference(equality_resolution,[],[f32])).
% 0.11/0.35 thf(f32,plain,(
% 0.11/0.35 ( ! [X0 : $i,X1 : $i] : (($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,zoey),X1)) | ($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),is_a,mel),X0)) | (knave = X1) | (knight != X1) | (knave = X0) | (knight != X0)) )),
% 0.11/0.35 inference(cnf_transformation,[],[f31])).
% 0.11/0.35 thf(f64,plain,(
% 0.11/0.35 spl0_2),
% 0.11/0.35 inference(avatar_split_clause,[],[f10,f62])).
% 0.11/0.35 thf(f10,plain,(
% 0.11/0.35 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.11/0.35 introduced(fool_axiom,[])).
% 0.11/0.35 thf(f60,plain,(
% 0.11/0.35 ~spl0_1),
% 0.11/0.35 inference(avatar_split_clause,[],[f9,f57])).
% 0.11/0.35 thf(f57,plain,(
% 0.11/0.35 spl0_1 <=> ($true = $false)),
% 0.11/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.11/0.35 thf(f9,plain,(
% 0.11/0.35 ($true != $false)),
% 0.11/0.35 introduced(fool_axiom,[])).
% 0.11/0.35 % SZS output end Proof for theBenchmark
% 0.11/0.35 % (15560)------------------------------
% 0.11/0.35 % (15560)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.11/0.35 % (15560)Termination reason: Refutation
% 0.11/0.35
% 0.11/0.35 % (15560)Memory used [KB]: 909
% 0.11/0.35 % (15560)Time elapsed: 0.011 s
% 0.11/0.35 % (15560)Instructions burned: 22 (million)
% 0.11/0.35 % (15555)Success in time 0.026 s
%------------------------------------------------------------------------------