TSTP Solution File: SEV235^5 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEV235^5 : 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 : n005.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 04:15:29 EDT 2024
% Result : Theorem 0.15s 0.41s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15 % Problem : SEV235^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.17 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.38 % Computer : n005.cluster.edu
% 0.15/0.38 % Model : x86_64 x86_64
% 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38 % Memory : 8042.1875MB
% 0.15/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38 % CPULimit : 300
% 0.15/0.38 % WCLimit : 300
% 0.15/0.38 % DateTime : Sun May 19 19:05:23 EDT 2024
% 0.15/0.38 % CPUTime :
% 0.15/0.38 % (28140)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.40 % (28145)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.15/0.40 % (28147)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)
% 0.15/0.40 % (28146)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.15/0.40 % Exception at run slice level
% 0.15/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.40 % (28143)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)
% 0.15/0.40 % (28142)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.40 % (28143)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.40 % Exception at run slice level
% 0.15/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.41 % (28144)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.15/0.41 % (28144)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.41 % (28146)First to succeed.
% 0.15/0.41 % Exception at run slice level
% 0.15/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.41 % (28143)Also succeeded, but the first one will report.
% 0.15/0.41 % (28146)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-28140"
% 0.15/0.41 % (28146)Refutation found. Thanks to Tanya!
% 0.15/0.41 % SZS status Theorem for theBenchmark
% 0.15/0.41 % SZS output start Proof for theBenchmark
% 0.15/0.41 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.15/0.41 thf(func_def_0, type, cE: $i > $o).
% 0.15/0.41 thf(func_def_1, type, cD: $i > $o).
% 0.15/0.41 thf(func_def_5, type, sP0: ($i > $o) > $o).
% 0.15/0.41 thf(func_def_6, type, sK1: ($i > $o) > $i).
% 0.15/0.41 thf(func_def_7, type, sK2: ($i > $o) > $i).
% 0.15/0.41 thf(func_def_8, type, sK3: $i > $o).
% 0.15/0.41 thf(func_def_11, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)).
% 0.15/0.41 thf(func_def_12, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)).
% 0.15/0.41 thf(func_def_13, type, vAND: $o > $o > $o).
% 0.15/0.41 thf(func_def_14, type, vOR: $o > $o > $o).
% 0.15/0.41 thf(func_def_15, type, vIMP: $o > $o > $o).
% 0.15/0.41 thf(func_def_16, type, vNOT: $o > $o).
% 0.15/0.41 thf(func_def_17, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)).
% 0.15/0.41 thf(f242,plain,(
% 0.15/0.41 $false),
% 0.15/0.41 inference(avatar_sat_refutation,[],[f43,f48,f52,f56,f94,f102,f109,f120,f154,f164,f201,f241])).
% 0.15/0.41 thf(f241,plain,(
% 0.15/0.41 spl5_3 | ~spl5_5 | ~spl5_6 | ~spl5_7 | spl5_9),
% 0.15/0.41 inference(avatar_contradiction_clause,[],[f240])).
% 0.15/0.41 thf(f240,plain,(
% 0.15/0.41 $false | (spl5_3 | ~spl5_5 | ~spl5_6 | ~spl5_7 | spl5_9)),
% 0.15/0.41 inference(trivial_inequality_removal,[],[f239])).
% 0.15/0.41 thf(f239,plain,(
% 0.15/0.41 ($true = $false) | (spl5_3 | ~spl5_5 | ~spl5_6 | ~spl5_7 | spl5_9)),
% 0.15/0.41 inference(forward_demodulation,[],[f229,f203])).
% 0.15/0.41 thf(f203,plain,(
% 0.15/0.41 ($false = vAPP($i,$o,cD,vAPP(sTfun($i,$o),$i,sK2,sK3))) | spl5_9),
% 0.15/0.41 inference(trivial_inequality_removal,[],[f202])).
% 0.15/0.41 thf(f202,plain,(
% 0.15/0.41 ($true != $true) | ($false = vAPP($i,$o,cD,vAPP(sTfun($i,$o),$i,sK2,sK3))) | spl5_9),
% 0.15/0.41 inference(superposition,[],[f152,f4])).
% 0.15/0.41 thf(f4,plain,(
% 0.15/0.41 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.15/0.41 introduced(fool_axiom,[])).
% 0.15/0.41 thf(f152,plain,(
% 0.15/0.41 ($true != vAPP($i,$o,cD,vAPP(sTfun($i,$o),$i,sK2,sK3))) | spl5_9),
% 0.15/0.41 inference(avatar_component_clause,[],[f151])).
% 0.15/0.41 thf(f151,plain,(
% 0.15/0.41 spl5_9 <=> ($true = vAPP($i,$o,cD,vAPP(sTfun($i,$o),$i,sK2,sK3)))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl5_9])])).
% 0.15/0.41 thf(f229,plain,(
% 0.15/0.41 ($true = vAPP($i,$o,cD,vAPP(sTfun($i,$o),$i,sK2,sK3))) | (spl5_3 | ~spl5_5 | ~spl5_6 | ~spl5_7)),
% 0.15/0.41 inference(trivial_inequality_removal,[],[f228])).
% 0.15/0.41 thf(f228,plain,(
% 0.15/0.41 ($true != $true) | ($true = vAPP($i,$o,cD,vAPP(sTfun($i,$o),$i,sK2,sK3))) | (spl5_3 | ~spl5_5 | ~spl5_6 | ~spl5_7)),
% 0.15/0.41 inference(superposition,[],[f55,f198])).
% 0.15/0.41 thf(f198,plain,(
% 0.15/0.41 ($true = vAPP($i,$o,sK3,vAPP(sTfun($i,$o),$i,sK2,sK3))) | (spl5_3 | ~spl5_5 | ~spl5_7)),
% 0.15/0.41 inference(trivial_inequality_removal,[],[f197])).
% 0.15/0.41 thf(f197,plain,(
% 0.15/0.41 ($true = $false) | ($true = vAPP($i,$o,sK3,vAPP(sTfun($i,$o),$i,sK2,sK3))) | (spl5_3 | ~spl5_5 | ~spl5_7)),
% 0.15/0.41 inference(forward_demodulation,[],[f191,f122])).
% 0.15/0.41 thf(f122,plain,(
% 0.15/0.41 ($false = vAPP(sTfun($i,$o),$o,sP0,sK3)) | spl5_3),
% 0.15/0.41 inference(trivial_inequality_removal,[],[f121])).
% 0.15/0.41 thf(f121,plain,(
% 0.15/0.41 ($true != $true) | ($false = vAPP(sTfun($i,$o),$o,sP0,sK3)) | spl5_3),
% 0.15/0.41 inference(superposition,[],[f42,f4])).
% 0.15/0.41 thf(f42,plain,(
% 0.15/0.41 ($true != vAPP(sTfun($i,$o),$o,sP0,sK3)) | spl5_3),
% 0.15/0.41 inference(avatar_component_clause,[],[f40])).
% 0.15/0.41 thf(f40,plain,(
% 0.15/0.41 spl5_3 <=> ($true = vAPP(sTfun($i,$o),$o,sP0,sK3))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl5_3])])).
% 0.15/0.41 thf(f191,plain,(
% 0.15/0.41 ($true = vAPP(sTfun($i,$o),$o,sP0,sK3)) | ($true = vAPP($i,$o,sK3,vAPP(sTfun($i,$o),$i,sK2,sK3))) | (~spl5_5 | ~spl5_7)),
% 0.15/0.41 inference(trivial_inequality_removal,[],[f190])).
% 0.15/0.41 thf(f190,plain,(
% 0.15/0.41 ($true != $true) | ($true = vAPP(sTfun($i,$o),$o,sP0,sK3)) | ($true = vAPP($i,$o,sK3,vAPP(sTfun($i,$o),$i,sK2,sK3))) | (~spl5_5 | ~spl5_7)),
% 0.15/0.41 inference(superposition,[],[f25,f188])).
% 0.15/0.41 thf(f188,plain,(
% 0.15/0.41 ($true = vAPP($i,$o,cE,vAPP(sTfun($i,$o),$i,sK1,sK3))) | (~spl5_5 | ~spl5_7)),
% 0.15/0.41 inference(trivial_inequality_removal,[],[f185])).
% 0.15/0.41 thf(f185,plain,(
% 0.15/0.41 ($true != $true) | ($true = vAPP($i,$o,cE,vAPP(sTfun($i,$o),$i,sK1,sK3))) | (~spl5_5 | ~spl5_7)),
% 0.15/0.41 inference(superposition,[],[f51,f142])).
% 0.15/0.41 thf(f142,plain,(
% 0.15/0.41 ($true = vAPP($i,$o,sK3,vAPP(sTfun($i,$o),$i,sK1,sK3))) | ~spl5_7),
% 0.15/0.41 inference(avatar_component_clause,[],[f140])).
% 0.15/0.41 thf(f140,plain,(
% 0.15/0.41 spl5_7 <=> ($true = vAPP($i,$o,sK3,vAPP(sTfun($i,$o),$i,sK1,sK3)))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl5_7])])).
% 0.15/0.41 thf(f51,plain,(
% 0.15/0.41 ( ! [X2 : $i] : (($true != vAPP($i,$o,sK3,X2)) | ($true = vAPP($i,$o,cE,X2))) ) | ~spl5_5),
% 0.15/0.41 inference(avatar_component_clause,[],[f50])).
% 0.15/0.41 thf(f50,plain,(
% 0.15/0.41 spl5_5 <=> ! [X2] : (($true = vAPP($i,$o,cE,X2)) | ($true != vAPP($i,$o,sK3,X2)))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl5_5])])).
% 0.15/0.41 thf(f25,plain,(
% 0.15/0.41 ( ! [X0 : $i > $o] : (($true != vAPP($i,$o,cE,vAPP(sTfun($i,$o),$i,sK1,X0))) | ($true = vAPP(sTfun($i,$o),$o,sP0,X0)) | ($true = vAPP($i,$o,X0,vAPP(sTfun($i,$o),$i,sK2,X0)))) )),
% 0.15/0.41 inference(cnf_transformation,[],[f15])).
% 0.15/0.41 thf(f15,plain,(
% 0.15/0.41 ! [X0 : $i > $o] : ((($true = vAPP(sTfun($i,$o),$o,sP0,X0)) | (($true != vAPP($i,$o,cE,vAPP(sTfun($i,$o),$i,sK1,X0))) & ($true = vAPP($i,$o,X0,vAPP(sTfun($i,$o),$i,sK1,X0)))) | (($true != vAPP($i,$o,cD,vAPP(sTfun($i,$o),$i,sK2,X0))) & ($true = vAPP($i,$o,X0,vAPP(sTfun($i,$o),$i,sK2,X0))))) & ((! [X3] : (($true = vAPP($i,$o,cE,X3)) | ($true != vAPP($i,$o,X0,X3))) & ! [X4] : (($true = vAPP($i,$o,cD,X4)) | ($true != vAPP($i,$o,X0,X4)))) | ($true != vAPP(sTfun($i,$o),$o,sP0,X0))))),
% 0.15/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f12,f14,f13])).
% 0.15/0.41 thf(f13,plain,(
% 0.15/0.41 ! [X0 : $i > $o] : (? [X1] : ((vAPP($i,$o,cE,X1) != $true) & (vAPP($i,$o,X0,X1) = $true)) => (($true != vAPP($i,$o,cE,vAPP(sTfun($i,$o),$i,sK1,X0))) & ($true = vAPP($i,$o,X0,vAPP(sTfun($i,$o),$i,sK1,X0)))))),
% 0.15/0.41 introduced(choice_axiom,[])).
% 0.15/0.41 thf(f14,plain,(
% 0.15/0.41 ! [X0 : $i > $o] : (? [X2] : (($true != vAPP($i,$o,cD,X2)) & ($true = vAPP($i,$o,X0,X2))) => (($true != vAPP($i,$o,cD,vAPP(sTfun($i,$o),$i,sK2,X0))) & ($true = vAPP($i,$o,X0,vAPP(sTfun($i,$o),$i,sK2,X0)))))),
% 0.15/0.41 introduced(choice_axiom,[])).
% 0.15/0.41 thf(f12,plain,(
% 0.15/0.41 ! [X0 : $i > $o] : ((($true = vAPP(sTfun($i,$o),$o,sP0,X0)) | ? [X1] : ((vAPP($i,$o,cE,X1) != $true) & (vAPP($i,$o,X0,X1) = $true)) | ? [X2] : (($true != vAPP($i,$o,cD,X2)) & ($true = vAPP($i,$o,X0,X2)))) & ((! [X3] : (($true = vAPP($i,$o,cE,X3)) | ($true != vAPP($i,$o,X0,X3))) & ! [X4] : (($true = vAPP($i,$o,cD,X4)) | ($true != vAPP($i,$o,X0,X4)))) | ($true != vAPP(sTfun($i,$o),$o,sP0,X0))))),
% 0.15/0.41 inference(rectify,[],[f11])).
% 0.15/0.41 thf(f11,plain,(
% 0.15/0.41 ! [X0 : $i > $o] : ((($true = vAPP(sTfun($i,$o),$o,sP0,X0)) | ? [X2] : (($true != vAPP($i,$o,cE,X2)) & ($true = vAPP($i,$o,X0,X2))) | ? [X3] : (($true != vAPP($i,$o,cD,X3)) & ($true = vAPP($i,$o,X0,X3)))) & ((! [X2] : (($true = vAPP($i,$o,cE,X2)) | ($true != vAPP($i,$o,X0,X2))) & ! [X3] : (($true = vAPP($i,$o,cD,X3)) | ($true != vAPP($i,$o,X0,X3)))) | ($true != vAPP(sTfun($i,$o),$o,sP0,X0))))),
% 0.15/0.41 inference(flattening,[],[f10])).
% 0.15/0.41 thf(f10,plain,(
% 0.15/0.41 ! [X0 : $i > $o] : ((($true = vAPP(sTfun($i,$o),$o,sP0,X0)) | (? [X2] : (($true != vAPP($i,$o,cE,X2)) & ($true = vAPP($i,$o,X0,X2))) | ? [X3] : (($true != vAPP($i,$o,cD,X3)) & ($true = vAPP($i,$o,X0,X3))))) & ((! [X2] : (($true = vAPP($i,$o,cE,X2)) | ($true != vAPP($i,$o,X0,X2))) & ! [X3] : (($true = vAPP($i,$o,cD,X3)) | ($true != vAPP($i,$o,X0,X3)))) | ($true != vAPP(sTfun($i,$o),$o,sP0,X0))))),
% 0.15/0.41 inference(nnf_transformation,[],[f8])).
% 0.15/0.41 thf(f8,plain,(
% 0.15/0.41 ! [X0 : $i > $o] : (($true = vAPP(sTfun($i,$o),$o,sP0,X0)) <=> (! [X2] : (($true = vAPP($i,$o,cE,X2)) | ($true != vAPP($i,$o,X0,X2))) & ! [X3] : (($true = vAPP($i,$o,cD,X3)) | ($true != vAPP($i,$o,X0,X3)))))),
% 0.15/0.41 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 0.15/0.41 thf(f55,plain,(
% 0.15/0.41 ( ! [X2 : $i] : (($true != vAPP($i,$o,sK3,X2)) | ($true = vAPP($i,$o,cD,X2))) ) | ~spl5_6),
% 0.15/0.41 inference(avatar_component_clause,[],[f54])).
% 0.15/0.41 thf(f54,plain,(
% 0.15/0.41 spl5_6 <=> ! [X2] : (($true = vAPP($i,$o,cD,X2)) | ($true != vAPP($i,$o,sK3,X2)))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl5_6])])).
% 0.15/0.41 thf(f201,plain,(
% 0.15/0.41 ~spl5_9 | spl5_3 | ~spl5_5 | ~spl5_7),
% 0.15/0.41 inference(avatar_split_clause,[],[f200,f140,f50,f40,f151])).
% 0.15/0.41 thf(f200,plain,(
% 0.15/0.41 ($true != vAPP($i,$o,cD,vAPP(sTfun($i,$o),$i,sK2,sK3))) | (spl5_3 | ~spl5_5 | ~spl5_7)),
% 0.15/0.41 inference(trivial_inequality_removal,[],[f199])).
% 0.15/0.41 thf(f199,plain,(
% 0.15/0.41 ($true = $false) | ($true != vAPP($i,$o,cD,vAPP(sTfun($i,$o),$i,sK2,sK3))) | (spl5_3 | ~spl5_5 | ~spl5_7)),
% 0.15/0.41 inference(forward_demodulation,[],[f192,f122])).
% 0.15/0.41 thf(f192,plain,(
% 0.15/0.41 ($true = vAPP(sTfun($i,$o),$o,sP0,sK3)) | ($true != vAPP($i,$o,cD,vAPP(sTfun($i,$o),$i,sK2,sK3))) | (~spl5_5 | ~spl5_7)),
% 0.15/0.41 inference(trivial_inequality_removal,[],[f189])).
% 0.15/0.41 thf(f189,plain,(
% 0.15/0.41 ($true != $true) | ($true = vAPP(sTfun($i,$o),$o,sP0,sK3)) | ($true != vAPP($i,$o,cD,vAPP(sTfun($i,$o),$i,sK2,sK3))) | (~spl5_5 | ~spl5_7)),
% 0.15/0.41 inference(superposition,[],[f26,f188])).
% 0.15/0.41 thf(f26,plain,(
% 0.15/0.41 ( ! [X0 : $i > $o] : (($true != vAPP($i,$o,cE,vAPP(sTfun($i,$o),$i,sK1,X0))) | ($true = vAPP(sTfun($i,$o),$o,sP0,X0)) | ($true != vAPP($i,$o,cD,vAPP(sTfun($i,$o),$i,sK2,X0)))) )),
% 0.15/0.41 inference(cnf_transformation,[],[f15])).
% 0.15/0.41 thf(f164,plain,(
% 0.15/0.41 spl5_7 | spl5_3 | ~spl5_9),
% 0.15/0.41 inference(avatar_split_clause,[],[f163,f151,f40,f140])).
% 0.15/0.41 thf(f163,plain,(
% 0.15/0.41 ($true = vAPP($i,$o,sK3,vAPP(sTfun($i,$o),$i,sK1,sK3))) | (spl5_3 | ~spl5_9)),
% 0.15/0.41 inference(trivial_inequality_removal,[],[f162])).
% 0.15/0.41 thf(f162,plain,(
% 0.15/0.41 ($true = $false) | ($true = vAPP($i,$o,sK3,vAPP(sTfun($i,$o),$i,sK1,sK3))) | (spl5_3 | ~spl5_9)),
% 0.15/0.41 inference(forward_demodulation,[],[f161,f122])).
% 0.15/0.41 thf(f161,plain,(
% 0.15/0.41 ($true = vAPP($i,$o,sK3,vAPP(sTfun($i,$o),$i,sK1,sK3))) | ($true = vAPP(sTfun($i,$o),$o,sP0,sK3)) | ~spl5_9),
% 0.15/0.41 inference(trivial_inequality_removal,[],[f155])).
% 0.15/0.41 thf(f155,plain,(
% 0.15/0.41 ($true != $true) | ($true = vAPP($i,$o,sK3,vAPP(sTfun($i,$o),$i,sK1,sK3))) | ($true = vAPP(sTfun($i,$o),$o,sP0,sK3)) | ~spl5_9),
% 0.15/0.41 inference(superposition,[],[f24,f153])).
% 0.15/0.41 thf(f153,plain,(
% 0.15/0.41 ($true = vAPP($i,$o,cD,vAPP(sTfun($i,$o),$i,sK2,sK3))) | ~spl5_9),
% 0.15/0.41 inference(avatar_component_clause,[],[f151])).
% 0.15/0.41 thf(f24,plain,(
% 0.15/0.41 ( ! [X0 : $i > $o] : (($true != vAPP($i,$o,cD,vAPP(sTfun($i,$o),$i,sK2,X0))) | ($true = vAPP($i,$o,X0,vAPP(sTfun($i,$o),$i,sK1,X0))) | ($true = vAPP(sTfun($i,$o),$o,sP0,X0))) )),
% 0.15/0.41 inference(cnf_transformation,[],[f15])).
% 0.15/0.41 thf(f154,plain,(
% 0.15/0.41 spl5_7 | spl5_9 | spl5_3 | ~spl5_6),
% 0.15/0.41 inference(avatar_split_clause,[],[f149,f54,f40,f151,f140])).
% 0.15/0.41 thf(f149,plain,(
% 0.15/0.41 ($true = vAPP($i,$o,cD,vAPP(sTfun($i,$o),$i,sK2,sK3))) | ($true = vAPP($i,$o,sK3,vAPP(sTfun($i,$o),$i,sK1,sK3))) | (spl5_3 | ~spl5_6)),
% 0.15/0.41 inference(trivial_inequality_removal,[],[f148])).
% 0.15/0.41 thf(f148,plain,(
% 0.15/0.41 ($true = $false) | ($true = vAPP($i,$o,cD,vAPP(sTfun($i,$o),$i,sK2,sK3))) | ($true = vAPP($i,$o,sK3,vAPP(sTfun($i,$o),$i,sK1,sK3))) | (spl5_3 | ~spl5_6)),
% 0.15/0.41 inference(forward_demodulation,[],[f133,f122])).
% 0.15/0.41 thf(f133,plain,(
% 0.15/0.41 ($true = vAPP($i,$o,cD,vAPP(sTfun($i,$o),$i,sK2,sK3))) | ($true = vAPP($i,$o,sK3,vAPP(sTfun($i,$o),$i,sK1,sK3))) | ($true = vAPP(sTfun($i,$o),$o,sP0,sK3)) | ~spl5_6),
% 0.15/0.41 inference(trivial_inequality_removal,[],[f132])).
% 0.15/0.41 thf(f132,plain,(
% 0.15/0.41 ($true != $true) | ($true = vAPP($i,$o,cD,vAPP(sTfun($i,$o),$i,sK2,sK3))) | ($true = vAPP($i,$o,sK3,vAPP(sTfun($i,$o),$i,sK1,sK3))) | ($true = vAPP(sTfun($i,$o),$o,sP0,sK3)) | ~spl5_6),
% 0.15/0.41 inference(superposition,[],[f55,f23])).
% 0.15/0.41 thf(f23,plain,(
% 0.15/0.41 ( ! [X0 : $i > $o] : (($true = vAPP($i,$o,X0,vAPP(sTfun($i,$o),$i,sK2,X0))) | ($true = vAPP($i,$o,X0,vAPP(sTfun($i,$o),$i,sK1,X0))) | ($true = vAPP(sTfun($i,$o),$o,sP0,X0))) )),
% 0.15/0.41 inference(cnf_transformation,[],[f15])).
% 0.15/0.41 thf(f120,plain,(
% 0.15/0.41 spl5_2 | ~spl5_4 | ~spl5_5),
% 0.15/0.41 inference(avatar_split_clause,[],[f116,f50,f45,f36])).
% 0.15/0.41 thf(f36,plain,(
% 0.15/0.41 spl5_2 <=> ($true = vAPP($i,$o,cE,sK4))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl5_2])])).
% 0.15/0.41 thf(f45,plain,(
% 0.15/0.41 spl5_4 <=> ($true = vAPP($i,$o,sK3,sK4))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl5_4])])).
% 0.15/0.41 thf(f116,plain,(
% 0.15/0.41 ($true = vAPP($i,$o,cE,sK4)) | (~spl5_4 | ~spl5_5)),
% 0.15/0.41 inference(trivial_inequality_removal,[],[f113])).
% 0.15/0.41 thf(f113,plain,(
% 0.15/0.41 ($true != $true) | ($true = vAPP($i,$o,cE,sK4)) | (~spl5_4 | ~spl5_5)),
% 0.15/0.41 inference(superposition,[],[f51,f47])).
% 0.15/0.41 thf(f47,plain,(
% 0.15/0.41 ($true = vAPP($i,$o,sK3,sK4)) | ~spl5_4),
% 0.15/0.41 inference(avatar_component_clause,[],[f45])).
% 0.15/0.41 thf(f109,plain,(
% 0.15/0.41 spl5_5 | ~spl5_3),
% 0.15/0.41 inference(avatar_split_clause,[],[f108,f40,f50])).
% 0.15/0.41 thf(f108,plain,(
% 0.15/0.41 ( ! [X0 : $i] : (($true != vAPP($i,$o,sK3,X0)) | ($true = vAPP($i,$o,cE,X0))) ) | ~spl5_3),
% 0.15/0.41 inference(trivial_inequality_removal,[],[f105])).
% 0.15/0.41 thf(f105,plain,(
% 0.15/0.41 ( ! [X0 : $i] : (($true != $true) | ($true != vAPP($i,$o,sK3,X0)) | ($true = vAPP($i,$o,cE,X0))) ) | ~spl5_3),
% 0.15/0.41 inference(superposition,[],[f22,f41])).
% 0.15/0.41 thf(f41,plain,(
% 0.15/0.41 ($true = vAPP(sTfun($i,$o),$o,sP0,sK3)) | ~spl5_3),
% 0.15/0.41 inference(avatar_component_clause,[],[f40])).
% 0.15/0.41 thf(f22,plain,(
% 0.15/0.41 ( ! [X3 : $i,X0 : $i > $o] : (($true != vAPP(sTfun($i,$o),$o,sP0,X0)) | ($true != vAPP($i,$o,X0,X3)) | ($true = vAPP($i,$o,cE,X3))) )),
% 0.15/0.41 inference(cnf_transformation,[],[f15])).
% 0.15/0.41 thf(f102,plain,(
% 0.15/0.41 spl5_1 | ~spl5_4 | ~spl5_6),
% 0.15/0.41 inference(avatar_split_clause,[],[f98,f54,f45,f32])).
% 0.15/0.41 thf(f32,plain,(
% 0.15/0.41 spl5_1 <=> ($true = vAPP($i,$o,cD,sK4))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl5_1])])).
% 0.15/0.41 thf(f98,plain,(
% 0.15/0.41 ($true = vAPP($i,$o,cD,sK4)) | (~spl5_4 | ~spl5_6)),
% 0.15/0.41 inference(trivial_inequality_removal,[],[f95])).
% 0.15/0.41 thf(f95,plain,(
% 0.15/0.41 ($true != $true) | ($true = vAPP($i,$o,cD,sK4)) | (~spl5_4 | ~spl5_6)),
% 0.15/0.41 inference(superposition,[],[f55,f47])).
% 0.15/0.41 thf(f94,plain,(
% 0.15/0.41 spl5_6 | ~spl5_3),
% 0.15/0.41 inference(avatar_split_clause,[],[f93,f40,f54])).
% 0.15/0.41 thf(f93,plain,(
% 0.15/0.41 ( ! [X0 : $i] : (($true != vAPP($i,$o,sK3,X0)) | ($true = vAPP($i,$o,cD,X0))) ) | ~spl5_3),
% 0.15/0.41 inference(trivial_inequality_removal,[],[f90])).
% 0.15/0.41 thf(f90,plain,(
% 0.15/0.41 ( ! [X0 : $i] : (($true != $true) | ($true != vAPP($i,$o,sK3,X0)) | ($true = vAPP($i,$o,cD,X0))) ) | ~spl5_3),
% 0.15/0.41 inference(superposition,[],[f21,f41])).
% 0.15/0.41 thf(f21,plain,(
% 0.15/0.41 ( ! [X0 : $i > $o,X4 : $i] : (($true != vAPP(sTfun($i,$o),$o,sP0,X0)) | ($true != vAPP($i,$o,X0,X4)) | ($true = vAPP($i,$o,cD,X4))) )),
% 0.15/0.41 inference(cnf_transformation,[],[f15])).
% 0.15/0.41 thf(f56,plain,(
% 0.15/0.41 spl5_6 | spl5_3),
% 0.15/0.41 inference(avatar_split_clause,[],[f27,f40,f54])).
% 0.15/0.41 thf(f27,plain,(
% 0.15/0.41 ( ! [X2 : $i] : (($true = vAPP(sTfun($i,$o),$o,sP0,sK3)) | ($true = vAPP($i,$o,cD,X2)) | ($true != vAPP($i,$o,sK3,X2))) )),
% 0.15/0.41 inference(cnf_transformation,[],[f20])).
% 0.15/0.41 thf(f20,plain,(
% 0.15/0.41 (($true != vAPP(sTfun($i,$o),$o,sP0,sK3)) | ((($true != vAPP($i,$o,cE,sK4)) | ($true != vAPP($i,$o,cD,sK4))) & ($true = vAPP($i,$o,sK3,sK4)))) & (($true = vAPP(sTfun($i,$o),$o,sP0,sK3)) | ! [X2] : ((($true = vAPP($i,$o,cE,X2)) & ($true = vAPP($i,$o,cD,X2))) | ($true != vAPP($i,$o,sK3,X2))))),
% 0.15/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f17,f19,f18])).
% 0.15/0.41 thf(f18,plain,(
% 0.15/0.41 ? [X0 : $i > $o] : ((($true != vAPP(sTfun($i,$o),$o,sP0,X0)) | ? [X1] : (((vAPP($i,$o,cE,X1) != $true) | (vAPP($i,$o,cD,X1) != $true)) & (vAPP($i,$o,X0,X1) = $true))) & (($true = vAPP(sTfun($i,$o),$o,sP0,X0)) | ! [X2] : ((($true = vAPP($i,$o,cE,X2)) & ($true = vAPP($i,$o,cD,X2))) | ($true != vAPP($i,$o,X0,X2))))) => ((($true != vAPP(sTfun($i,$o),$o,sP0,sK3)) | ? [X1] : (((vAPP($i,$o,cE,X1) != $true) | (vAPP($i,$o,cD,X1) != $true)) & ($true = vAPP($i,$o,sK3,X1)))) & (($true = vAPP(sTfun($i,$o),$o,sP0,sK3)) | ! [X2] : ((($true = vAPP($i,$o,cE,X2)) & ($true = vAPP($i,$o,cD,X2))) | ($true != vAPP($i,$o,sK3,X2)))))),
% 0.15/0.41 introduced(choice_axiom,[])).
% 0.15/0.41 thf(f19,plain,(
% 0.15/0.41 ? [X1] : (((vAPP($i,$o,cE,X1) != $true) | (vAPP($i,$o,cD,X1) != $true)) & ($true = vAPP($i,$o,sK3,X1))) => ((($true != vAPP($i,$o,cE,sK4)) | ($true != vAPP($i,$o,cD,sK4))) & ($true = vAPP($i,$o,sK3,sK4)))),
% 0.15/0.41 introduced(choice_axiom,[])).
% 0.15/0.41 thf(f17,plain,(
% 0.15/0.41 ? [X0 : $i > $o] : ((($true != vAPP(sTfun($i,$o),$o,sP0,X0)) | ? [X1] : (((vAPP($i,$o,cE,X1) != $true) | (vAPP($i,$o,cD,X1) != $true)) & (vAPP($i,$o,X0,X1) = $true))) & (($true = vAPP(sTfun($i,$o),$o,sP0,X0)) | ! [X2] : ((($true = vAPP($i,$o,cE,X2)) & ($true = vAPP($i,$o,cD,X2))) | ($true != vAPP($i,$o,X0,X2)))))),
% 0.15/0.41 inference(rectify,[],[f16])).
% 0.15/0.41 thf(f16,plain,(
% 0.15/0.41 ? [X0 : $i > $o] : ((($true != vAPP(sTfun($i,$o),$o,sP0,X0)) | ? [X1] : (((vAPP($i,$o,cE,X1) != $true) | (vAPP($i,$o,cD,X1) != $true)) & (vAPP($i,$o,X0,X1) = $true))) & (($true = vAPP(sTfun($i,$o),$o,sP0,X0)) | ! [X1] : (((vAPP($i,$o,cE,X1) = $true) & (vAPP($i,$o,cD,X1) = $true)) | (vAPP($i,$o,X0,X1) != $true))))),
% 0.15/0.41 inference(nnf_transformation,[],[f9])).
% 0.15/0.41 thf(f9,plain,(
% 0.15/0.41 ? [X0 : $i > $o] : (! [X1] : (((vAPP($i,$o,cE,X1) = $true) & (vAPP($i,$o,cD,X1) = $true)) | (vAPP($i,$o,X0,X1) != $true)) <~> ($true = vAPP(sTfun($i,$o),$o,sP0,X0)))),
% 0.15/0.41 inference(definition_folding,[],[f7,f8])).
% 0.15/0.41 thf(f7,plain,(
% 0.15/0.41 ? [X0 : $i > $o] : (! [X1] : (((vAPP($i,$o,cE,X1) = $true) & (vAPP($i,$o,cD,X1) = $true)) | (vAPP($i,$o,X0,X1) != $true)) <~> (! [X2] : (($true = vAPP($i,$o,cE,X2)) | ($true != vAPP($i,$o,X0,X2))) & ! [X3] : (($true = vAPP($i,$o,cD,X3)) | ($true != vAPP($i,$o,X0,X3)))))),
% 0.15/0.41 inference(ennf_transformation,[],[f6])).
% 0.15/0.41 thf(f6,plain,(
% 0.15/0.41 ~! [X0 : $i > $o] : (! [X1] : ((vAPP($i,$o,X0,X1) = $true) => ((vAPP($i,$o,cE,X1) = $true) & (vAPP($i,$o,cD,X1) = $true))) <=> (! [X2] : (($true = vAPP($i,$o,X0,X2)) => ($true = vAPP($i,$o,cE,X2))) & ! [X3] : (($true = vAPP($i,$o,X0,X3)) => ($true = vAPP($i,$o,cD,X3)))))),
% 0.15/0.41 inference(fool_elimination,[],[f5])).
% 0.15/0.41 thf(f5,plain,(
% 0.15/0.41 ~! [X0 : $i > $o] : (! [X1] : (vAPP($i,$o,X0,X1) => (vAPP($i,$o,cE,X1) & vAPP($i,$o,cD,X1))) <=> (! [X2] : (vAPP($i,$o,X0,X2) => vAPP($i,$o,cE,X2)) & ! [X3] : (vAPP($i,$o,X0,X3) => vAPP($i,$o,cD,X3))))),
% 0.15/0.41 inference(rectify,[],[f2])).
% 0.15/0.41 thf(f2,negated_conjecture,(
% 0.15/0.41 ~! [X0 : $i > $o] : (! [X1] : (vAPP($i,$o,X0,X1) => (vAPP($i,$o,cE,X1) & vAPP($i,$o,cD,X1))) <=> (! [X1] : (vAPP($i,$o,X0,X1) => vAPP($i,$o,cE,X1)) & ! [X1] : (vAPP($i,$o,X0,X1) => vAPP($i,$o,cD,X1))))),
% 0.15/0.41 inference(negated_conjecture,[],[f1])).
% 0.15/0.41 thf(f1,conjecture,(
% 0.15/0.41 ! [X0 : $i > $o] : (! [X1] : (vAPP($i,$o,X0,X1) => (vAPP($i,$o,cE,X1) & vAPP($i,$o,cD,X1))) <=> (! [X1] : (vAPP($i,$o,X0,X1) => vAPP($i,$o,cE,X1)) & ! [X1] : (vAPP($i,$o,X0,X1) => vAPP($i,$o,cD,X1))))),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM46A_pme)).
% 0.15/0.41 thf(f52,plain,(
% 0.15/0.41 spl5_5 | spl5_3),
% 0.15/0.41 inference(avatar_split_clause,[],[f28,f40,f50])).
% 0.15/0.41 thf(f28,plain,(
% 0.15/0.41 ( ! [X2 : $i] : (($true = vAPP(sTfun($i,$o),$o,sP0,sK3)) | ($true = vAPP($i,$o,cE,X2)) | ($true != vAPP($i,$o,sK3,X2))) )),
% 0.15/0.41 inference(cnf_transformation,[],[f20])).
% 0.15/0.41 thf(f48,plain,(
% 0.15/0.41 spl5_4 | ~spl5_3),
% 0.15/0.41 inference(avatar_split_clause,[],[f29,f40,f45])).
% 0.15/0.41 thf(f29,plain,(
% 0.15/0.41 ($true != vAPP(sTfun($i,$o),$o,sP0,sK3)) | ($true = vAPP($i,$o,sK3,sK4))),
% 0.15/0.41 inference(cnf_transformation,[],[f20])).
% 0.15/0.41 thf(f43,plain,(
% 0.15/0.41 ~spl5_1 | ~spl5_2 | ~spl5_3),
% 0.15/0.41 inference(avatar_split_clause,[],[f30,f40,f36,f32])).
% 0.15/0.41 thf(f30,plain,(
% 0.15/0.41 ($true != vAPP(sTfun($i,$o),$o,sP0,sK3)) | ($true != vAPP($i,$o,cE,sK4)) | ($true != vAPP($i,$o,cD,sK4))),
% 0.15/0.41 inference(cnf_transformation,[],[f20])).
% 0.15/0.41 % SZS output end Proof for theBenchmark
% 0.15/0.41 % (28146)------------------------------
% 0.15/0.41 % (28146)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.41 % (28146)Termination reason: Refutation
% 0.15/0.41
% 0.15/0.41 % (28146)Memory used [KB]: 886
% 0.15/0.41 % (28146)Time elapsed: 0.010 s
% 0.15/0.41 % (28146)Instructions burned: 17 (million)
% 0.15/0.41 % (28140)Success in time 0.021 s
%------------------------------------------------------------------------------