TSTP Solution File: ITP019^2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP019^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 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 : Sun May 5 06:59:06 EDT 2024
% Result : Theorem 0.21s 0.40s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP019^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 19:06:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (7395)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.37 % (7399)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.37 % (7398)WARNING: value z3 for option sas not known
% 0.21/0.37 % (7396)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.37 % (7398)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)
% 0.21/0.37 % (7397)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.37 % (7401)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)
% 0.21/0.37 % (7402)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)
% 0.21/0.37 % (7400)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)
% 0.21/0.37 % Exception at run slice level
% 0.21/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.38 % (7402)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.38 % Exception at run slice level
% 0.21/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.38 % Exception at run slice level
% 0.21/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.39 % (7403)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.39 % (7403)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 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 % (7404)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.21/0.39 % (7405)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.21/0.39 % (7400)First to succeed.
% 0.21/0.40 % (7404)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.40 % (7400)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-7395"
% 0.21/0.40 % (7400)Refutation found. Thanks to Tanya!
% 0.21/0.40 % SZS status Theorem for theBenchmark
% 0.21/0.40 % SZS output start Proof for theBenchmark
% 0.21/0.40 thf(type_def_5, type, del: $tType).
% 0.21/0.40 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.40 thf(type_def_7, type, tp__ty_2Enum_2Enum: $tType).
% 0.21/0.40 thf(type_def_8, type, tp__ty_2Erealax_2Ereal: $tType).
% 0.21/0.40 thf(type_def_9, type, tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal: $tType).
% 0.21/0.40 thf(func_def_0, type, del: $tType).
% 0.21/0.40 thf(func_def_1, type, bool: del).
% 0.21/0.40 thf(func_def_2, type, ind: del).
% 0.21/0.40 thf(func_def_3, type, arr: del > del > del).
% 0.21/0.40 thf(func_def_4, type, mem: $i > del > $o).
% 0.21/0.40 thf(func_def_5, type, ap: $i > $i > $i).
% 0.21/0.40 thf(func_def_6, type, lam: del > ($i > $i) > $i).
% 0.21/0.40 thf(func_def_7, type, p: $i > $o).
% 0.21/0.40 thf(func_def_8, type, inj__o: $o > $i).
% 0.21/0.40 thf(func_def_15, type, ty_2Enum_2Enum: del).
% 0.21/0.40 thf(func_def_16, type, tp__ty_2Enum_2Enum: $tType).
% 0.21/0.40 thf(func_def_17, type, inj__ty_2Enum_2Enum: tp__ty_2Enum_2Enum > $i).
% 0.21/0.40 thf(func_def_18, type, surj__ty_2Enum_2Enum: $i > tp__ty_2Enum_2Enum).
% 0.21/0.40 thf(func_def_20, type, fo__c_2Enum_2E0: tp__ty_2Enum_2Enum).
% 0.21/0.40 thf(func_def_21, type, ty_2Erealax_2Ereal: del).
% 0.21/0.40 thf(func_def_22, type, tp__ty_2Erealax_2Ereal: $tType).
% 0.21/0.40 thf(func_def_23, type, inj__ty_2Erealax_2Ereal: tp__ty_2Erealax_2Ereal > $i).
% 0.21/0.40 thf(func_def_24, type, surj__ty_2Erealax_2Ereal: $i > tp__ty_2Erealax_2Ereal).
% 0.21/0.40 thf(func_def_25, type, ty_2Epair_2Eprod: del > del > del).
% 0.21/0.40 thf(func_def_26, type, tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal: $tType).
% 0.21/0.40 thf(func_def_27, type, inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal > $i).
% 0.21/0.40 thf(func_def_28, type, surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal: $i > tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal).
% 0.21/0.40 thf(func_def_31, type, c_2Emin_2E_3D: del > $i).
% 0.21/0.40 thf(func_def_32, type, c_2Ebool_2E_21: del > $i).
% 0.21/0.40 thf(func_def_35, type, sP0: $i > $o).
% 0.21/0.40 thf(func_def_36, type, sK1: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal).
% 0.21/0.40 thf(func_def_37, type, sK2: $i > del > $i).
% 0.21/0.40 thf(func_def_38, type, sK3: $i > del > $i).
% 0.21/0.40 thf(func_def_39, type, sK4: ($i > $i) > del > del > $i).
% 0.21/0.40 thf(func_def_40, type, sK5: $i > $i > del > $i).
% 0.21/0.40 thf(func_def_42, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)).
% 0.21/0.40 thf(func_def_43, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)).
% 0.21/0.40 thf(func_def_44, type, vAND: $o > $o > $o).
% 0.21/0.40 thf(func_def_45, type, vOR: $o > $o > $o).
% 0.21/0.40 thf(func_def_46, type, vIMP: $o > $o > $o).
% 0.21/0.40 thf(func_def_47, type, vNOT: $o > $o).
% 0.21/0.40 thf(func_def_48, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)).
% 0.21/0.40 thf(f612,plain,(
% 0.21/0.40 $false),
% 0.21/0.40 inference(avatar_sat_refutation,[],[f223,f228,f234,f238,f271,f276,f281,f288,f294,f298,f302,f306,f312,f317,f322,f327,f332,f338,f342,f346,f351,f355,f360,f373,f377,f381,f388,f413,f418,f423,f428,f432,f440,f444,f448,f452,f469,f473,f478,f492,f496,f561,f565,f572,f592,f596,f600,f604,f608,f611])).
% 0.21/0.40 thf(f611,plain,(
% 0.21/0.40 spl6_3 | ~spl6_9 | ~spl6_43),
% 0.21/0.40 inference(avatar_split_clause,[],[f568,f563,f291,f231])).
% 0.21/0.40 thf(f231,plain,(
% 0.21/0.40 spl6_3 <=> (sK1 = vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),c_2Enum_2E0)))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_3])])).
% 0.21/0.40 thf(f291,plain,(
% 0.21/0.40 spl6_9 <=> (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,sK1))) = vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),c_2Enum_2E0)))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_9])])).
% 0.21/0.40 thf(f563,plain,(
% 0.21/0.40 spl6_43 <=> ! [X0 : tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X0))) != vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),c_2Enum_2E0))) | (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),c_2Enum_2E0)) = X0))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_43])])).
% 0.21/0.40 thf(f568,plain,(
% 0.21/0.40 (sK1 = vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),c_2Enum_2E0))) | (~spl6_9 | ~spl6_43)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f566])).
% 0.21/0.40 thf(f566,plain,(
% 0.21/0.40 (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),c_2Enum_2E0)) != vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),c_2Enum_2E0))) | (sK1 = vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),c_2Enum_2E0))) | (~spl6_9 | ~spl6_43)),
% 0.21/0.40 inference(superposition,[],[f564,f293])).
% 0.21/0.40 thf(f293,plain,(
% 0.21/0.40 (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,sK1))) = vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),c_2Enum_2E0))) | ~spl6_9),
% 0.21/0.40 inference(avatar_component_clause,[],[f291])).
% 0.21/0.40 thf(f564,plain,(
% 0.21/0.40 ( ! [X0 : tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X0))) != vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),c_2Enum_2E0))) | (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),c_2Enum_2E0)) = X0)) ) | ~spl6_43),
% 0.21/0.40 inference(avatar_component_clause,[],[f563])).
% 0.21/0.40 thf(f608,plain,(
% 0.21/0.40 spl6_49),
% 0.21/0.40 inference(avatar_split_clause,[],[f191,f606])).
% 0.21/0.40 thf(f606,plain,(
% 0.21/0.40 spl6_49 <=> ! [X2,X0 : del,X1] : ((X1 = X2) | ($true != vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP(del,$i,c_2Emin_2E_3D,X0)),X1)),X2))) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),X0)) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),X0)))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_49])])).
% 0.21/0.40 thf(f191,plain,(
% 0.21/0.40 ( ! [X2 : $i,X0 : del,X1 : $i] : ((X1 = X2) | ($true != vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP(del,$i,c_2Emin_2E_3D,X0)),X1)),X2))) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),X0)) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),X0))) )),
% 0.21/0.40 inference(cnf_transformation,[],[f145])).
% 0.21/0.40 thf(f145,plain,(
% 0.21/0.40 ! [X0 : del,X1] : (! [X2] : (((($true = vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP(del,$i,c_2Emin_2E_3D,X0)),X1)),X2))) | (X1 != X2)) & ((X1 = X2) | ($true != vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP(del,$i,c_2Emin_2E_3D,X0)),X1)),X2))))) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),X0))) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),X0)))),
% 0.21/0.40 inference(nnf_transformation,[],[f121])).
% 0.21/0.40 thf(f121,plain,(
% 0.21/0.40 ! [X0 : del,X1] : (! [X2] : ((($true = vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP(del,$i,c_2Emin_2E_3D,X0)),X1)),X2))) <=> (X1 = X2)) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),X0))) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),X0)))),
% 0.21/0.40 inference(ennf_transformation,[],[f76])).
% 0.21/0.40 thf(f76,plain,(
% 0.21/0.40 ! [X0 : del,X1] : (($true = vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),X0)) => ! [X2] : (($true = vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),X0)) => (($true = vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP(del,$i,c_2Emin_2E_3D,X0)),X1)),X2))) <=> (X1 = X2))))),
% 0.21/0.40 inference(fool_elimination,[],[f75])).
% 0.21/0.40 thf(f75,plain,(
% 0.21/0.40 ! [X0 : del,X1] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),X0) => ! [X2] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),X0) => (vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP(del,$i,c_2Emin_2E_3D,X0)),X1)),X2)) <=> (X1 = X2))))),
% 0.21/0.40 inference(rectify,[],[f32])).
% 0.21/0.40 thf(f32,axiom,(
% 0.21/0.40 ! [X1 : del,X0] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),X1) => ! [X8] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X8),X1) => (vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP(del,$i,c_2Emin_2E_3D,X1)),X0)),X8)) <=> (X0 = X8))))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_eq_p)).
% 0.21/0.40 thf(f604,plain,(
% 0.21/0.40 spl6_48),
% 0.21/0.40 inference(avatar_split_clause,[],[f178,f602])).
% 0.21/0.40 thf(f602,plain,(
% 0.21/0.40 spl6_48 <=> ! [X0,X1] : (($true = vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Emin_2E_3D_3D_3E),X0)),X1))) | ($true != vAPP($i,$o,p,X1)) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),bool)) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_48])])).
% 0.21/0.40 thf(f178,plain,(
% 0.21/0.40 ( ! [X0 : $i,X1 : $i] : (($true = vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Emin_2E_3D_3D_3E),X0)),X1))) | ($true != vAPP($i,$o,p,X1)) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),bool)) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true)) )),
% 0.21/0.40 inference(cnf_transformation,[],[f139])).
% 0.21/0.40 thf(f139,plain,(
% 0.21/0.40 ! [X0] : (! [X1] : (((($true = vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Emin_2E_3D_3D_3E),X0)),X1))) | (($true != vAPP($i,$o,p,X1)) & (vAPP($i,$o,p,X0) = $true))) & (($true = vAPP($i,$o,p,X1)) | (vAPP($i,$o,p,X0) != $true) | ($true != vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Emin_2E_3D_3D_3E),X0)),X1))))) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),bool))) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true))),
% 0.21/0.40 inference(flattening,[],[f138])).
% 0.21/0.40 thf(f138,plain,(
% 0.21/0.40 ! [X0] : (! [X1] : (((($true = vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Emin_2E_3D_3D_3E),X0)),X1))) | (($true != vAPP($i,$o,p,X1)) & (vAPP($i,$o,p,X0) = $true))) & ((($true = vAPP($i,$o,p,X1)) | (vAPP($i,$o,p,X0) != $true)) | ($true != vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Emin_2E_3D_3D_3E),X0)),X1))))) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),bool))) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true))),
% 0.21/0.40 inference(nnf_transformation,[],[f118])).
% 0.21/0.40 thf(f118,plain,(
% 0.21/0.40 ! [X0] : (! [X1] : ((($true = vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Emin_2E_3D_3D_3E),X0)),X1))) <=> (($true = vAPP($i,$o,p,X1)) | (vAPP($i,$o,p,X0) != $true))) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),bool))) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true))),
% 0.21/0.40 inference(ennf_transformation,[],[f58])).
% 0.21/0.40 thf(f58,plain,(
% 0.21/0.40 ! [X0] : ((vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) = $true) => ! [X1] : (($true = vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),bool)) => (($true = vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Emin_2E_3D_3D_3E),X0)),X1))) <=> ((vAPP($i,$o,p,X0) = $true) => ($true = vAPP($i,$o,p,X1))))))),
% 0.21/0.40 inference(fool_elimination,[],[f57])).
% 0.21/0.40 thf(f57,plain,(
% 0.21/0.40 ! [X0] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) => ! [X1] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),bool) => (vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Emin_2E_3D_3D_3E),X0)),X1)) <=> (vAPP($i,$o,p,X0) => vAPP($i,$o,p,X1)))))),
% 0.21/0.40 inference(rectify,[],[f15])).
% 0.21/0.40 thf(f15,axiom,(
% 0.21/0.40 ! [X5] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X5),bool) => ! [X6] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X6),bool) => (vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Emin_2E_3D_3D_3E),X5)),X6)) <=> (vAPP($i,$o,p,X5) => vAPP($i,$o,p,X6)))))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_imp_p)).
% 0.21/0.40 thf(f600,plain,(
% 0.21/0.40 spl6_47),
% 0.21/0.40 inference(avatar_split_clause,[],[f177,f598])).
% 0.21/0.40 thf(f598,plain,(
% 0.21/0.40 spl6_47 <=> ! [X0,X1] : (($true = vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Emin_2E_3D_3D_3E),X0)),X1))) | (vAPP($i,$o,p,X0) = $true) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),bool)) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_47])])).
% 0.21/0.40 thf(f177,plain,(
% 0.21/0.40 ( ! [X0 : $i,X1 : $i] : (($true = vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Emin_2E_3D_3D_3E),X0)),X1))) | (vAPP($i,$o,p,X0) = $true) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),bool)) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true)) )),
% 0.21/0.40 inference(cnf_transformation,[],[f139])).
% 0.21/0.40 thf(f596,plain,(
% 0.21/0.40 spl6_46),
% 0.21/0.40 inference(avatar_split_clause,[],[f174,f594])).
% 0.21/0.40 thf(f594,plain,(
% 0.21/0.40 spl6_46 <=> ! [X0,X1] : (($true = vAPP($i,$o,p,X1)) | ($true != vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ebool_2E_2F_5C),X0)),X1))) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),bool)) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_46])])).
% 0.21/0.40 thf(f174,plain,(
% 0.21/0.40 ( ! [X0 : $i,X1 : $i] : (($true = vAPP($i,$o,p,X1)) | ($true != vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ebool_2E_2F_5C),X0)),X1))) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),bool)) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true)) )),
% 0.21/0.40 inference(cnf_transformation,[],[f137])).
% 0.21/0.40 thf(f137,plain,(
% 0.21/0.40 ! [X0] : (! [X1] : (((($true = vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ebool_2E_2F_5C),X0)),X1))) | ($true != vAPP($i,$o,p,X1)) | (vAPP($i,$o,p,X0) != $true)) & ((($true = vAPP($i,$o,p,X1)) & (vAPP($i,$o,p,X0) = $true)) | ($true != vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ebool_2E_2F_5C),X0)),X1))))) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),bool))) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true))),
% 0.21/0.40 inference(flattening,[],[f136])).
% 0.21/0.40 thf(f136,plain,(
% 0.21/0.40 ! [X0] : (! [X1] : (((($true = vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ebool_2E_2F_5C),X0)),X1))) | (($true != vAPP($i,$o,p,X1)) | (vAPP($i,$o,p,X0) != $true))) & ((($true = vAPP($i,$o,p,X1)) & (vAPP($i,$o,p,X0) = $true)) | ($true != vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ebool_2E_2F_5C),X0)),X1))))) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),bool))) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true))),
% 0.21/0.40 inference(nnf_transformation,[],[f117])).
% 0.21/0.40 thf(f117,plain,(
% 0.21/0.40 ! [X0] : (! [X1] : ((($true = vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ebool_2E_2F_5C),X0)),X1))) <=> (($true = vAPP($i,$o,p,X1)) & (vAPP($i,$o,p,X0) = $true))) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),bool))) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true))),
% 0.21/0.40 inference(ennf_transformation,[],[f56])).
% 0.21/0.40 thf(f56,plain,(
% 0.21/0.40 ! [X0] : ((vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) = $true) => ! [X1] : (($true = vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),bool)) => (($true = vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ebool_2E_2F_5C),X0)),X1))) <=> (($true = vAPP($i,$o,p,X1)) & (vAPP($i,$o,p,X0) = $true)))))),
% 0.21/0.40 inference(fool_elimination,[],[f55])).
% 0.21/0.40 thf(f55,plain,(
% 0.21/0.40 ! [X0] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) => ! [X1] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),bool) => (vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ebool_2E_2F_5C),X0)),X1)) <=> (vAPP($i,$o,p,X1) & vAPP($i,$o,p,X0)))))),
% 0.21/0.40 inference(rectify,[],[f17])).
% 0.21/0.40 thf(f17,axiom,(
% 0.21/0.40 ! [X5] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X5),bool) => ! [X6] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X6),bool) => (vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ebool_2E_2F_5C),X5)),X6)) <=> (vAPP($i,$o,p,X6) & vAPP($i,$o,p,X5)))))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_and_p)).
% 0.21/0.40 thf(f592,plain,(
% 0.21/0.40 spl6_45),
% 0.21/0.40 inference(avatar_split_clause,[],[f173,f590])).
% 0.21/0.40 thf(f590,plain,(
% 0.21/0.40 spl6_45 <=> ! [X0,X1] : ((vAPP($i,$o,p,X0) = $true) | ($true != vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ebool_2E_2F_5C),X0)),X1))) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),bool)) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_45])])).
% 0.21/0.40 thf(f173,plain,(
% 0.21/0.40 ( ! [X0 : $i,X1 : $i] : ((vAPP($i,$o,p,X0) = $true) | ($true != vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ebool_2E_2F_5C),X0)),X1))) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),bool)) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true)) )),
% 0.21/0.40 inference(cnf_transformation,[],[f137])).
% 0.21/0.40 thf(f572,plain,(
% 0.21/0.40 spl6_44),
% 0.21/0.40 inference(avatar_split_clause,[],[f199,f570])).
% 0.21/0.40 thf(f570,plain,(
% 0.21/0.40 spl6_44 <=> ! [X0 : del,X3,X2,X1 : del] : (($true = vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,X2),X3)),X1)) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X3),X0)) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),vAPP(del,del,vAPP(del,sTfun(del,del),arr,X0),X1))))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_44])])).
% 0.21/0.40 thf(f199,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X0 : del,X1 : del] : (($true = vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,X2),X3)),X1)) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X3),X0)) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),vAPP(del,del,vAPP(del,sTfun(del,del),arr,X0),X1)))) )),
% 0.21/0.40 inference(cnf_transformation,[],[f125])).
% 0.21/0.40 thf(f125,plain,(
% 0.21/0.40 ! [X0 : del,X1 : del,X2] : (! [X3] : (($true = vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,X2),X3)),X1)) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X3),X0))) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),vAPP(del,del,vAPP(del,sTfun(del,del),arr,X0),X1))))),
% 0.21/0.40 inference(ennf_transformation,[],[f84])).
% 0.21/0.40 thf(f84,plain,(
% 0.21/0.40 ! [X0 : del,X1 : del,X2] : (($true = vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),vAPP(del,del,vAPP(del,sTfun(del,del),arr,X0),X1))) => ! [X3] : (($true = vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X3),X0)) => ($true = vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,X2),X3)),X1))))),
% 0.21/0.40 inference(fool_elimination,[],[f83])).
% 0.21/0.40 thf(f83,plain,(
% 0.21/0.40 ! [X0 : del,X1 : del,X2] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),vAPP(del,del,vAPP(del,sTfun(del,del),arr,X0),X1)) => ! [X3] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X3),X0) => vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,X2),X3)),X1)))),
% 0.21/0.40 inference(rectify,[],[f4])).
% 0.21/0.40 thf(f4,axiom,(
% 0.21/0.40 ! [X1 : del,X2 : del,X3] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X3),vAPP(del,del,vAPP(del,sTfun(del,del),arr,X1),X2)) => ! [X0] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),X1) => vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,X3),X0)),X2)))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_tp)).
% 0.21/0.40 thf(f565,plain,(
% 0.21/0.40 spl6_43),
% 0.21/0.40 inference(avatar_split_clause,[],[f218,f563])).
% 0.21/0.40 thf(f218,plain,(
% 0.21/0.40 ( ! [X0 : tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X0))) != vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),c_2Enum_2E0))) | (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),c_2Enum_2E0)) = X0)) )),
% 0.21/0.40 inference(forward_demodulation,[],[f217,f156])).
% 0.21/0.40 thf(f156,plain,(
% 0.21/0.40 (c_2Enum_2E0 = vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))),
% 0.21/0.40 inference(cnf_transformation,[],[f22])).
% 0.21/0.40 thf(f22,axiom,(
% 0.21/0.40 (c_2Enum_2E0 = vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Enum_2E0)).
% 0.21/0.40 thf(f217,plain,(
% 0.21/0.40 ( ! [X0 : tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),c_2Enum_2E0)) = X0) | (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) != vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X0))))) )),
% 0.21/0.40 inference(forward_demodulation,[],[f180,f156])).
% 0.21/0.40 thf(f180,plain,(
% 0.21/0.40 ( ! [X0 : tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) = X0) | (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) != vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X0))))) )),
% 0.21/0.40 inference(cnf_transformation,[],[f140])).
% 0.21/0.40 thf(f140,plain,(
% 0.21/0.40 ! [X0 : tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (((vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) = vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X0)))) | (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) != X0)) & ((vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) = X0) | (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) != vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X0))))))),
% 0.21/0.40 inference(nnf_transformation,[],[f110])).
% 0.21/0.40 thf(f110,plain,(
% 0.21/0.40 ! [X0 : tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) = vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X0)))) <=> (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) = X0))),
% 0.21/0.40 inference(rectify,[],[f38])).
% 0.21/0.40 thf(f38,axiom,(
% 0.21/0.40 ! [X11 : tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X11))) = vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0)))) <=> (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) = X11))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0)).
% 0.21/0.40 thf(f561,plain,(
% 0.21/0.40 spl6_42 | ~spl6_15 | ~spl6_23),
% 0.21/0.40 inference(avatar_split_clause,[],[f368,f358,f319,f558])).
% 0.21/0.40 thf(f558,plain,(
% 0.21/0.40 spl6_42 <=> ($true = vAPP($i,$o,sP0,c_2Ebool_2ET))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_42])])).
% 0.21/0.40 thf(f319,plain,(
% 0.21/0.40 spl6_15 <=> (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ebool_2ET),bool) = $true)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_15])])).
% 0.21/0.40 thf(f358,plain,(
% 0.21/0.40 spl6_23 <=> ! [X0] : (($true = vAPP($i,$o,sP0,X0)) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_23])])).
% 0.21/0.40 thf(f368,plain,(
% 0.21/0.40 ($true = vAPP($i,$o,sP0,c_2Ebool_2ET)) | (~spl6_15 | ~spl6_23)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f361])).
% 0.21/0.40 thf(f361,plain,(
% 0.21/0.40 ($true != $true) | ($true = vAPP($i,$o,sP0,c_2Ebool_2ET)) | (~spl6_15 | ~spl6_23)),
% 0.21/0.40 inference(superposition,[],[f359,f321])).
% 0.21/0.40 thf(f321,plain,(
% 0.21/0.40 (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ebool_2ET),bool) = $true) | ~spl6_15),
% 0.21/0.40 inference(avatar_component_clause,[],[f319])).
% 0.21/0.40 thf(f359,plain,(
% 0.21/0.40 ( ! [X0 : $i] : ((vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true) | ($true = vAPP($i,$o,sP0,X0))) ) | ~spl6_23),
% 0.21/0.40 inference(avatar_component_clause,[],[f358])).
% 0.21/0.40 thf(f496,plain,(
% 0.21/0.40 spl6_41),
% 0.21/0.40 inference(avatar_split_clause,[],[f213,f494])).
% 0.21/0.40 thf(f494,plain,(
% 0.21/0.40 spl6_41 <=> ! [X2,X0 : del] : (($true = vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP(del,$i,c_2Emin_2E_3D,X0)),X2)),X2))) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),X0)))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_41])])).
% 0.21/0.40 thf(f213,plain,(
% 0.21/0.40 ( ! [X2 : $i,X0 : del] : (($true = vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP(del,$i,c_2Emin_2E_3D,X0)),X2)),X2))) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),X0))) )),
% 0.21/0.40 inference(duplicate_literal_removal,[],[f212])).
% 0.21/0.40 thf(f212,plain,(
% 0.21/0.40 ( ! [X2 : $i,X0 : del] : (($true = vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP(del,$i,c_2Emin_2E_3D,X0)),X2)),X2))) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),X0)) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),X0))) )),
% 0.21/0.40 inference(equality_resolution,[],[f192])).
% 0.21/0.40 thf(f192,plain,(
% 0.21/0.40 ( ! [X2 : $i,X0 : del,X1 : $i] : (($true = vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP(del,$i,c_2Emin_2E_3D,X0)),X1)),X2))) | (X1 != X2) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),X0)) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),X0))) )),
% 0.21/0.40 inference(cnf_transformation,[],[f145])).
% 0.21/0.40 thf(f492,plain,(
% 0.21/0.40 spl6_40),
% 0.21/0.40 inference(avatar_split_clause,[],[f198,f490])).
% 0.21/0.40 thf(f490,plain,(
% 0.21/0.40 spl6_40 <=> ! [X2,X0 : del,X1 : $i > $i] : ((vAPP($i,$i,X1,X2) = vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP(sTfun($i,$i),$i,vAPP(del,sTfun(sTfun($i,$i),$i),lam,X0),X1)),X2)) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),X0)))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_40])])).
% 0.21/0.40 thf(f198,plain,(
% 0.21/0.40 ( ! [X2 : $i,X0 : del,X1 : $i > $i] : ((vAPP($i,$i,X1,X2) = vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP(sTfun($i,$i),$i,vAPP(del,sTfun(sTfun($i,$i),$i),lam,X0),X1)),X2)) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),X0))) )),
% 0.21/0.40 inference(cnf_transformation,[],[f124])).
% 0.21/0.40 thf(f124,plain,(
% 0.21/0.40 ! [X0 : del,X1 : $i > $i,X2] : ((vAPP($i,$i,X1,X2) = vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP(sTfun($i,$i),$i,vAPP(del,sTfun(sTfun($i,$i),$i),lam,X0),X1)),X2)) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),X0)))),
% 0.21/0.40 inference(ennf_transformation,[],[f82])).
% 0.21/0.40 thf(f82,plain,(
% 0.21/0.40 ! [X0 : del,X1 : $i > $i,X2] : (($true = vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),X0)) => (vAPP($i,$i,X1,X2) = vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP(sTfun($i,$i),$i,vAPP(del,sTfun(sTfun($i,$i),$i),lam,X0),X1)),X2)))),
% 0.21/0.40 inference(fool_elimination,[],[f81])).
% 0.21/0.40 thf(f81,plain,(
% 0.21/0.40 ! [X0 : del,X1 : $i > $i,X2] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),X0) => (vAPP($i,$i,X1,X2) = vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP(sTfun($i,$i),$i,vAPP(del,sTfun(sTfun($i,$i),$i),lam,X0),X1)),X2)))),
% 0.21/0.40 inference(rectify,[],[f7])).
% 0.21/0.40 thf(f7,axiom,(
% 0.21/0.40 ! [X1 : del,X3 : $i > $i,X0] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),X1) => (vAPP($i,$i,X3,X0) = vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,vAPP(sTfun($i,$i),$i,vAPP(del,sTfun(sTfun($i,$i),$i),lam,X1),X3)),X0)))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta)).
% 0.21/0.40 thf(f478,plain,(
% 0.21/0.40 spl6_39),
% 0.21/0.40 inference(avatar_split_clause,[],[f210,f475])).
% 0.21/0.40 thf(f475,plain,(
% 0.21/0.40 spl6_39 <=> (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ecomplex_2Ecomplex__inv),vAPP(del,del,vAPP(del,sTfun(del,del),arr,vAPP(del,del,vAPP(del,sTfun(del,del),ty_2Epair_2Eprod,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal)),vAPP(del,del,vAPP(del,sTfun(del,del),ty_2Epair_2Eprod,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal))) = $true)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_39])])).
% 0.21/0.40 thf(f210,plain,(
% 0.21/0.40 (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ecomplex_2Ecomplex__inv),vAPP(del,del,vAPP(del,sTfun(del,del),arr,vAPP(del,del,vAPP(del,sTfun(del,del),ty_2Epair_2Eprod,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal)),vAPP(del,del,vAPP(del,sTfun(del,del),ty_2Epair_2Eprod,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal))) = $true)),
% 0.21/0.40 inference(cnf_transformation,[],[f104])).
% 0.21/0.40 thf(f104,plain,(
% 0.21/0.40 (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ecomplex_2Ecomplex__inv),vAPP(del,del,vAPP(del,sTfun(del,del),arr,vAPP(del,del,vAPP(del,sTfun(del,del),ty_2Epair_2Eprod,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal)),vAPP(del,del,vAPP(del,sTfun(del,del),ty_2Epair_2Eprod,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal))) = $true)),
% 0.21/0.40 inference(fool_elimination,[],[f103])).
% 0.21/0.40 thf(f103,plain,(
% 0.21/0.40 vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ecomplex_2Ecomplex__inv),vAPP(del,del,vAPP(del,sTfun(del,del),arr,vAPP(del,del,vAPP(del,sTfun(del,del),ty_2Epair_2Eprod,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal)),vAPP(del,del,vAPP(del,sTfun(del,del),ty_2Epair_2Eprod,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal)))),
% 0.21/0.40 inference(rectify,[],[f30])).
% 0.21/0.40 thf(f30,axiom,(
% 0.21/0.40 vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ecomplex_2Ecomplex__inv),vAPP(del,del,vAPP(del,sTfun(del,del),arr,vAPP(del,del,vAPP(del,sTfun(del,del),ty_2Epair_2Eprod,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal)),vAPP(del,del,vAPP(del,sTfun(del,del),ty_2Epair_2Eprod,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal)))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ecomplex_2Ecomplex__inv)).
% 0.21/0.40 thf(f473,plain,(
% 0.21/0.40 spl6_38),
% 0.21/0.40 inference(avatar_split_clause,[],[f188,f471])).
% 0.21/0.40 thf(f471,plain,(
% 0.21/0.40 spl6_38 <=> ! [X0 : del,X1] : (($true = vAPP($i,$o,p,X1)) | ($true = vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(del,$i,vAPP($i,sTfun(del,$i),sK2,X1),X0)),X0)) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),bool)))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_38])])).
% 0.21/0.40 thf(f188,plain,(
% 0.21/0.40 ( ! [X0 : del,X1 : $i] : (($true = vAPP($i,$o,p,X1)) | ($true = vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(del,$i,vAPP($i,sTfun(del,$i),sK2,X1),X0)),X0)) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),bool))) )),
% 0.21/0.40 inference(cnf_transformation,[],[f144])).
% 0.21/0.40 thf(f144,plain,(
% 0.21/0.40 ! [X0 : del,X1] : (((! [X2] : (($true = vAPP($i,$o,p,X1)) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),X0))) | ($true != vAPP($i,$o,p,X1))) & (($true = vAPP($i,$o,p,X1)) | (($true != vAPP($i,$o,p,X1)) & ($true = vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(del,$i,vAPP($i,sTfun(del,$i),sK2,X1),X0)),X0))))) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),bool)))),
% 0.21/0.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f142,f143])).
% 0.21/0.40 thf(f143,plain,(
% 0.21/0.40 ! [X0 : del,X1] : (? [X3] : (($true != vAPP($i,$o,p,X1)) & ($true = vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X3),X0))) => (($true != vAPP($i,$o,p,X1)) & ($true = vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(del,$i,vAPP($i,sTfun(del,$i),sK2,X1),X0)),X0))))),
% 0.21/0.40 introduced(choice_axiom,[])).
% 0.21/0.40 thf(f142,plain,(
% 0.21/0.40 ! [X0 : del,X1] : (((! [X2] : (($true = vAPP($i,$o,p,X1)) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),X0))) | ($true != vAPP($i,$o,p,X1))) & (($true = vAPP($i,$o,p,X1)) | ? [X3] : (($true != vAPP($i,$o,p,X1)) & ($true = vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X3),X0))))) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),bool)))),
% 0.21/0.40 inference(rectify,[],[f141])).
% 0.21/0.40 thf(f141,plain,(
% 0.21/0.40 ! [X0 : del,X1] : (((! [X2] : (($true = vAPP($i,$o,p,X1)) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),X0))) | ($true != vAPP($i,$o,p,X1))) & (($true = vAPP($i,$o,p,X1)) | ? [X2] : (($true != vAPP($i,$o,p,X1)) & ($true = vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),X0))))) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),bool)))),
% 0.21/0.40 inference(nnf_transformation,[],[f120])).
% 0.21/0.40 thf(f120,plain,(
% 0.21/0.40 ! [X0 : del,X1] : ((! [X2] : (($true = vAPP($i,$o,p,X1)) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),X0))) <=> ($true = vAPP($i,$o,p,X1))) | ($true != vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),bool)))),
% 0.21/0.40 inference(ennf_transformation,[],[f74])).
% 0.21/0.40 thf(f74,plain,(
% 0.21/0.40 ! [X0 : del,X1] : (($true = vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),bool)) => (! [X2] : (($true = vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),X0)) => ($true = vAPP($i,$o,p,X1))) <=> ($true = vAPP($i,$o,p,X1))))),
% 0.21/0.40 inference(fool_elimination,[],[f73])).
% 0.21/0.40 thf(f73,plain,(
% 0.21/0.40 ! [X0 : del,X1] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X1),bool) => (! [X2] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X2),X0) => vAPP($i,$o,p,X1)) <=> vAPP($i,$o,p,X1)))),
% 0.21/0.40 inference(rectify,[],[f36])).
% 0.21/0.40 thf(f36,axiom,(
% 0.21/0.40 ! [X7 : del,X9] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X9),bool) => (! [X10] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X10),X7) => vAPP($i,$o,p,X9)) <=> vAPP($i,$o,p,X9)))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EFORALL__SIMP)).
% 0.21/0.40 thf(f469,plain,(
% 0.21/0.40 spl6_37 | ~spl6_16 | ~spl6_23),
% 0.21/0.40 inference(avatar_split_clause,[],[f367,f358,f324,f466])).
% 0.21/0.40 thf(f466,plain,(
% 0.21/0.40 spl6_37 <=> ($true = vAPP($i,$o,sP0,c_2Ebool_2EF))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_37])])).
% 0.21/0.40 thf(f324,plain,(
% 0.21/0.40 spl6_16 <=> (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ebool_2EF),bool) = $true)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_16])])).
% 0.21/0.40 thf(f367,plain,(
% 0.21/0.40 ($true = vAPP($i,$o,sP0,c_2Ebool_2EF)) | (~spl6_16 | ~spl6_23)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f362])).
% 0.21/0.40 thf(f362,plain,(
% 0.21/0.40 ($true != $true) | ($true = vAPP($i,$o,sP0,c_2Ebool_2EF)) | (~spl6_16 | ~spl6_23)),
% 0.21/0.40 inference(superposition,[],[f359,f326])).
% 0.21/0.40 thf(f326,plain,(
% 0.21/0.40 (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ebool_2EF),bool) = $true) | ~spl6_16),
% 0.21/0.40 inference(avatar_component_clause,[],[f324])).
% 0.21/0.40 thf(f452,plain,(
% 0.21/0.40 spl6_36),
% 0.21/0.40 inference(avatar_split_clause,[],[f187,f450])).
% 0.21/0.40 thf(f450,plain,(
% 0.21/0.40 spl6_36 <=> ! [X0 : del] : ($true = vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(del,$i,c_2Emin_2E_3D,X0)),vAPP(del,del,vAPP(del,sTfun(del,del),arr,X0),vAPP(del,del,vAPP(del,sTfun(del,del),arr,X0),bool))))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_36])])).
% 0.21/0.40 thf(f187,plain,(
% 0.21/0.40 ( ! [X0 : del] : (($true = vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(del,$i,c_2Emin_2E_3D,X0)),vAPP(del,del,vAPP(del,sTfun(del,del),arr,X0),vAPP(del,del,vAPP(del,sTfun(del,del),arr,X0),bool))))) )),
% 0.21/0.40 inference(cnf_transformation,[],[f72])).
% 0.21/0.40 thf(f72,plain,(
% 0.21/0.40 ! [X0 : del] : ($true = vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(del,$i,c_2Emin_2E_3D,X0)),vAPP(del,del,vAPP(del,sTfun(del,del),arr,X0),vAPP(del,del,vAPP(del,sTfun(del,del),arr,X0),bool))))),
% 0.21/0.40 inference(fool_elimination,[],[f71])).
% 0.21/0.40 thf(f71,plain,(
% 0.21/0.40 ! [X0 : del] : vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(del,$i,c_2Emin_2E_3D,X0)),vAPP(del,del,vAPP(del,sTfun(del,del),arr,X0),vAPP(del,del,vAPP(del,sTfun(del,del),arr,X0),bool)))),
% 0.21/0.40 inference(rectify,[],[f31])).
% 0.21/0.40 thf(f31,axiom,(
% 0.21/0.40 ! [X7 : del] : vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(del,$i,c_2Emin_2E_3D,X7)),vAPP(del,del,vAPP(del,sTfun(del,del),arr,X7),vAPP(del,del,vAPP(del,sTfun(del,del),arr,X7),bool)))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Emin_2E_3D)).
% 0.21/0.40 thf(f448,plain,(
% 0.21/0.40 spl6_35),
% 0.21/0.40 inference(avatar_split_clause,[],[f186,f446])).
% 0.21/0.40 thf(f446,plain,(
% 0.21/0.40 spl6_35 <=> ! [X0 : del] : ($true = vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(del,$i,c_2Ebool_2E_21,X0)),vAPP(del,del,vAPP(del,sTfun(del,del),arr,vAPP(del,del,vAPP(del,sTfun(del,del),arr,X0),bool)),bool)))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_35])])).
% 0.21/0.40 thf(f186,plain,(
% 0.21/0.40 ( ! [X0 : del] : (($true = vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(del,$i,c_2Ebool_2E_21,X0)),vAPP(del,del,vAPP(del,sTfun(del,del),arr,vAPP(del,del,vAPP(del,sTfun(del,del),arr,X0),bool)),bool)))) )),
% 0.21/0.40 inference(cnf_transformation,[],[f70])).
% 0.21/0.40 thf(f70,plain,(
% 0.21/0.40 ! [X0 : del] : ($true = vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(del,$i,c_2Ebool_2E_21,X0)),vAPP(del,del,vAPP(del,sTfun(del,del),arr,vAPP(del,del,vAPP(del,sTfun(del,del),arr,X0),bool)),bool)))),
% 0.21/0.40 inference(fool_elimination,[],[f69])).
% 0.21/0.40 thf(f69,plain,(
% 0.21/0.40 ! [X0 : del] : vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(del,$i,c_2Ebool_2E_21,X0)),vAPP(del,del,vAPP(del,sTfun(del,del),arr,vAPP(del,del,vAPP(del,sTfun(del,del),arr,X0),bool)),bool))),
% 0.21/0.40 inference(rectify,[],[f33])).
% 0.21/0.40 thf(f33,axiom,(
% 0.21/0.40 ! [X7 : del] : vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(del,$i,c_2Ebool_2E_21,X7)),vAPP(del,del,vAPP(del,sTfun(del,del),arr,vAPP(del,del,vAPP(del,sTfun(del,del),arr,X7),bool)),bool))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_21)).
% 0.21/0.40 thf(f444,plain,(
% 0.21/0.40 spl6_34),
% 0.21/0.40 inference(avatar_split_clause,[],[f172,f442])).
% 0.21/0.40 thf(f442,plain,(
% 0.21/0.40 spl6_34 <=> ! [X0] : (($true = vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ebool_2E_7E),X0))) | (vAPP($i,$o,p,X0) = $true) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_34])])).
% 0.21/0.40 thf(f172,plain,(
% 0.21/0.40 ( ! [X0 : $i] : (($true = vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ebool_2E_7E),X0))) | (vAPP($i,$o,p,X0) = $true) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true)) )),
% 0.21/0.40 inference(cnf_transformation,[],[f135])).
% 0.21/0.40 thf(f135,plain,(
% 0.21/0.40 ! [X0] : (((($true = vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ebool_2E_7E),X0))) | (vAPP($i,$o,p,X0) = $true)) & ((vAPP($i,$o,p,X0) != $true) | ($true != vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ebool_2E_7E),X0))))) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true))),
% 0.21/0.40 inference(nnf_transformation,[],[f116])).
% 0.21/0.40 thf(f116,plain,(
% 0.21/0.40 ! [X0] : ((($true = vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ebool_2E_7E),X0))) <=> (vAPP($i,$o,p,X0) != $true)) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true))),
% 0.21/0.40 inference(ennf_transformation,[],[f109])).
% 0.21/0.40 thf(f109,plain,(
% 0.21/0.40 ! [X0] : ((vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) = $true) => (($true = vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ebool_2E_7E),X0))) <=> (vAPP($i,$o,p,X0) != $true)))),
% 0.21/0.40 inference(flattening,[],[f54])).
% 0.21/0.40 thf(f54,plain,(
% 0.21/0.40 ! [X0] : ((vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) = $true) => (($true = vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ebool_2E_7E),X0))) <=> ~(vAPP($i,$o,p,X0) = $true)))),
% 0.21/0.40 inference(fool_elimination,[],[f53])).
% 0.21/0.40 thf(f53,plain,(
% 0.21/0.40 ! [X0] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) => (vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ebool_2E_7E),X0)) <=> ~vAPP($i,$o,p,X0)))),
% 0.21/0.40 inference(rectify,[],[f9])).
% 0.21/0.40 thf(f9,axiom,(
% 0.21/0.40 ! [X5] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X5),bool) => (vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ebool_2E_7E),X5)) <=> ~vAPP($i,$o,p,X5)))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_neg_p)).
% 0.21/0.40 thf(f440,plain,(
% 0.21/0.40 spl6_33),
% 0.21/0.40 inference(avatar_split_clause,[],[f171,f438])).
% 0.21/0.40 thf(f438,plain,(
% 0.21/0.40 spl6_33 <=> ! [X0] : ((vAPP($i,$o,p,X0) != $true) | ($true != vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ebool_2E_7E),X0))) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_33])])).
% 0.21/0.40 thf(f171,plain,(
% 0.21/0.40 ( ! [X0 : $i] : ((vAPP($i,$o,p,X0) != $true) | ($true != vAPP($i,$o,p,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ebool_2E_7E),X0))) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true)) )),
% 0.21/0.40 inference(cnf_transformation,[],[f135])).
% 0.21/0.40 thf(f432,plain,(
% 0.21/0.40 spl6_32),
% 0.21/0.40 inference(avatar_split_clause,[],[f179,f430])).
% 0.21/0.40 thf(f430,plain,(
% 0.21/0.40 spl6_32 <=> ! [X0] : ((vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X0)) = X0) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),vAPP(del,del,vAPP(del,sTfun(del,del),ty_2Epair_2Eprod,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal)) != $true))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_32])])).
% 0.21/0.40 thf(f179,plain,(
% 0.21/0.40 ( ! [X0 : $i] : ((vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X0)) = X0) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),vAPP(del,del,vAPP(del,sTfun(del,del),ty_2Epair_2Eprod,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal)) != $true)) )),
% 0.21/0.40 inference(cnf_transformation,[],[f119])).
% 0.21/0.40 thf(f119,plain,(
% 0.21/0.40 ! [X0] : ((vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X0)) = X0) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),vAPP(del,del,vAPP(del,sTfun(del,del),ty_2Epair_2Eprod,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal)) != $true))),
% 0.21/0.40 inference(ennf_transformation,[],[f60])).
% 0.21/0.40 thf(f60,plain,(
% 0.21/0.40 ! [X0] : ((vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),vAPP(del,del,vAPP(del,sTfun(del,del),ty_2Epair_2Eprod,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal)) = $true) => (vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X0)) = X0))),
% 0.21/0.40 inference(fool_elimination,[],[f59])).
% 0.21/0.40 thf(f59,plain,(
% 0.21/0.40 ! [X0] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),vAPP(del,del,vAPP(del,sTfun(del,del),ty_2Epair_2Eprod,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal)) => (vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X0)) = X0))),
% 0.21/0.40 inference(rectify,[],[f28])).
% 0.21/0.40 thf(f28,axiom,(
% 0.21/0.40 ! [X0] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),vAPP(del,del,vAPP(del,sTfun(del,del),ty_2Epair_2Eprod,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal)) => (vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X0)) = X0))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_iso_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)).
% 0.21/0.40 thf(f428,plain,(
% 0.21/0.40 spl6_31),
% 0.21/0.40 inference(avatar_split_clause,[],[f209,f425])).
% 0.21/0.40 thf(f425,plain,(
% 0.21/0.40 spl6_31 <=> (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ecomplex_2Ecomplex__of__num),vAPP(del,del,vAPP(del,sTfun(del,del),arr,ty_2Enum_2Enum),vAPP(del,del,vAPP(del,sTfun(del,del),ty_2Epair_2Eprod,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal))) = $true)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_31])])).
% 0.21/0.40 thf(f209,plain,(
% 0.21/0.40 (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ecomplex_2Ecomplex__of__num),vAPP(del,del,vAPP(del,sTfun(del,del),arr,ty_2Enum_2Enum),vAPP(del,del,vAPP(del,sTfun(del,del),ty_2Epair_2Eprod,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal))) = $true)),
% 0.21/0.40 inference(cnf_transformation,[],[f102])).
% 0.21/0.40 thf(f102,plain,(
% 0.21/0.40 (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ecomplex_2Ecomplex__of__num),vAPP(del,del,vAPP(del,sTfun(del,del),arr,ty_2Enum_2Enum),vAPP(del,del,vAPP(del,sTfun(del,del),ty_2Epair_2Eprod,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal))) = $true)),
% 0.21/0.40 inference(fool_elimination,[],[f101])).
% 0.21/0.40 thf(f101,plain,(
% 0.21/0.40 vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ecomplex_2Ecomplex__of__num),vAPP(del,del,vAPP(del,sTfun(del,del),arr,ty_2Enum_2Enum),vAPP(del,del,vAPP(del,sTfun(del,del),ty_2Epair_2Eprod,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal)))),
% 0.21/0.40 inference(rectify,[],[f29])).
% 0.21/0.40 thf(f29,axiom,(
% 0.21/0.40 vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ecomplex_2Ecomplex__of__num),vAPP(del,del,vAPP(del,sTfun(del,del),arr,ty_2Enum_2Enum),vAPP(del,del,vAPP(del,sTfun(del,del),ty_2Epair_2Eprod,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal)))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ecomplex_2Ecomplex__of__num)).
% 0.21/0.40 thf(f423,plain,(
% 0.21/0.40 spl6_30),
% 0.21/0.40 inference(avatar_split_clause,[],[f208,f420])).
% 0.21/0.40 thf(f420,plain,(
% 0.21/0.40 spl6_30 <=> (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Emin_2E_3D_3D_3E),vAPP(del,del,vAPP(del,sTfun(del,del),arr,bool),vAPP(del,del,vAPP(del,sTfun(del,del),arr,bool),bool))) = $true)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_30])])).
% 0.21/0.40 thf(f208,plain,(
% 0.21/0.40 (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Emin_2E_3D_3D_3E),vAPP(del,del,vAPP(del,sTfun(del,del),arr,bool),vAPP(del,del,vAPP(del,sTfun(del,del),arr,bool),bool))) = $true)),
% 0.21/0.40 inference(cnf_transformation,[],[f100])).
% 0.21/0.40 thf(f100,plain,(
% 0.21/0.40 (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Emin_2E_3D_3D_3E),vAPP(del,del,vAPP(del,sTfun(del,del),arr,bool),vAPP(del,del,vAPP(del,sTfun(del,del),arr,bool),bool))) = $true)),
% 0.21/0.40 inference(fool_elimination,[],[f99])).
% 0.21/0.40 thf(f99,plain,(
% 0.21/0.40 vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Emin_2E_3D_3D_3E),vAPP(del,del,vAPP(del,sTfun(del,del),arr,bool),vAPP(del,del,vAPP(del,sTfun(del,del),arr,bool),bool)))),
% 0.21/0.40 inference(rectify,[],[f14])).
% 0.21/0.40 thf(f14,axiom,(
% 0.21/0.40 vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Emin_2E_3D_3D_3E),vAPP(del,del,vAPP(del,sTfun(del,del),arr,bool),vAPP(del,del,vAPP(del,sTfun(del,del),arr,bool),bool)))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Emin_2E_3D_3D_3E)).
% 0.21/0.40 thf(f418,plain,(
% 0.21/0.40 spl6_29),
% 0.21/0.40 inference(avatar_split_clause,[],[f207,f415])).
% 0.21/0.40 thf(f415,plain,(
% 0.21/0.40 spl6_29 <=> (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ebool_2E_2F_5C),vAPP(del,del,vAPP(del,sTfun(del,del),arr,bool),vAPP(del,del,vAPP(del,sTfun(del,del),arr,bool),bool))) = $true)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_29])])).
% 0.21/0.40 thf(f207,plain,(
% 0.21/0.40 (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ebool_2E_2F_5C),vAPP(del,del,vAPP(del,sTfun(del,del),arr,bool),vAPP(del,del,vAPP(del,sTfun(del,del),arr,bool),bool))) = $true)),
% 0.21/0.40 inference(cnf_transformation,[],[f98])).
% 0.21/0.40 thf(f98,plain,(
% 0.21/0.40 (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ebool_2E_2F_5C),vAPP(del,del,vAPP(del,sTfun(del,del),arr,bool),vAPP(del,del,vAPP(del,sTfun(del,del),arr,bool),bool))) = $true)),
% 0.21/0.40 inference(fool_elimination,[],[f97])).
% 0.21/0.40 thf(f97,plain,(
% 0.21/0.40 vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ebool_2E_2F_5C),vAPP(del,del,vAPP(del,sTfun(del,del),arr,bool),vAPP(del,del,vAPP(del,sTfun(del,del),arr,bool),bool)))),
% 0.21/0.40 inference(rectify,[],[f16])).
% 0.21/0.40 thf(f16,axiom,(
% 0.21/0.40 vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ebool_2E_2F_5C),vAPP(del,del,vAPP(del,sTfun(del,del),arr,bool),vAPP(del,del,vAPP(del,sTfun(del,del),arr,bool),bool)))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_2F_5C)).
% 0.21/0.40 thf(f413,plain,(
% 0.21/0.40 spl6_28),
% 0.21/0.40 inference(avatar_split_clause,[],[f185,f411])).
% 0.21/0.40 thf(f411,plain,(
% 0.21/0.40 spl6_28 <=> ! [X0 : tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X0)),vAPP(del,del,vAPP(del,sTfun(del,del),ty_2Epair_2Eprod,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal)) = $true)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_28])])).
% 0.21/0.40 thf(f185,plain,(
% 0.21/0.40 ( ! [X0 : tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X0)),vAPP(del,del,vAPP(del,sTfun(del,del),ty_2Epair_2Eprod,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal)) = $true)) )),
% 0.21/0.40 inference(cnf_transformation,[],[f68])).
% 0.21/0.40 thf(f68,plain,(
% 0.21/0.40 ! [X0 : tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X0)),vAPP(del,del,vAPP(del,sTfun(del,del),ty_2Epair_2Eprod,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal)) = $true)),
% 0.21/0.40 inference(fool_elimination,[],[f67])).
% 0.21/0.40 thf(f67,plain,(
% 0.21/0.40 ! [X0 : tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X0)),vAPP(del,del,vAPP(del,sTfun(del,del),ty_2Epair_2Eprod,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal))),
% 0.21/0.40 inference(rectify,[],[f27])).
% 0.21/0.40 thf(f27,axiom,(
% 0.21/0.40 ! [X0 : tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X0)),vAPP(del,del,vAPP(del,sTfun(del,del),ty_2Epair_2Eprod,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)).
% 0.21/0.40 thf(f388,plain,(
% 0.21/0.40 spl6_27),
% 0.21/0.40 inference(avatar_split_clause,[],[f164,f386])).
% 0.21/0.40 thf(f386,plain,(
% 0.21/0.40 spl6_27 <=> ! [X0] : ((vAPP($o,$i,inj__o,vAPP($i,$o,p,X0)) = X0) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_27])])).
% 0.21/0.40 thf(f164,plain,(
% 0.21/0.40 ( ! [X0 : $i] : ((vAPP($o,$i,inj__o,vAPP($i,$o,p,X0)) = X0) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true)) )),
% 0.21/0.40 inference(cnf_transformation,[],[f114])).
% 0.21/0.40 thf(f114,plain,(
% 0.21/0.40 ! [X0] : ((vAPP($o,$i,inj__o,vAPP($i,$o,p,X0)) = X0) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true))),
% 0.21/0.40 inference(ennf_transformation,[],[f50])).
% 0.21/0.40 thf(f50,plain,(
% 0.21/0.40 ! [X0] : ((vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) = $true) => (vAPP($o,$i,inj__o,vAPP($i,$o,p,X0)) = X0))),
% 0.21/0.40 inference(fool_elimination,[],[f49])).
% 0.21/0.40 thf(f49,plain,(
% 0.21/0.40 ! [X0] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) => (vAPP($o,$i,inj__o,vAPP($i,$o,p,X0)) = X0))),
% 0.21/0.40 inference(rectify,[],[f3])).
% 0.21/0.40 thf(f3,axiom,(
% 0.21/0.40 ! [X0] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) => (vAPP($o,$i,inj__o,vAPP($i,$o,p,X0)) = X0))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_iso_mem_o)).
% 0.21/0.40 thf(f381,plain,(
% 0.21/0.40 spl6_26),
% 0.21/0.40 inference(avatar_split_clause,[],[f163,f379])).
% 0.21/0.40 thf(f379,plain,(
% 0.21/0.40 spl6_26 <=> ! [X0] : ((vAPP(tp__ty_2Erealax_2Ereal,$i,inj__ty_2Erealax_2Ereal,vAPP($i,tp__ty_2Erealax_2Ereal,surj__ty_2Erealax_2Ereal,X0)) = X0) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),ty_2Erealax_2Ereal) != $true))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_26])])).
% 0.21/0.40 thf(f163,plain,(
% 0.21/0.40 ( ! [X0 : $i] : ((vAPP(tp__ty_2Erealax_2Ereal,$i,inj__ty_2Erealax_2Ereal,vAPP($i,tp__ty_2Erealax_2Ereal,surj__ty_2Erealax_2Ereal,X0)) = X0) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),ty_2Erealax_2Ereal) != $true)) )),
% 0.21/0.40 inference(cnf_transformation,[],[f113])).
% 0.21/0.40 thf(f113,plain,(
% 0.21/0.40 ! [X0] : ((vAPP(tp__ty_2Erealax_2Ereal,$i,inj__ty_2Erealax_2Ereal,vAPP($i,tp__ty_2Erealax_2Ereal,surj__ty_2Erealax_2Ereal,X0)) = X0) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),ty_2Erealax_2Ereal) != $true))),
% 0.21/0.40 inference(ennf_transformation,[],[f48])).
% 0.21/0.40 thf(f48,plain,(
% 0.21/0.40 ! [X0] : ((vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),ty_2Erealax_2Ereal) = $true) => (vAPP(tp__ty_2Erealax_2Ereal,$i,inj__ty_2Erealax_2Ereal,vAPP($i,tp__ty_2Erealax_2Ereal,surj__ty_2Erealax_2Ereal,X0)) = X0))),
% 0.21/0.40 inference(fool_elimination,[],[f47])).
% 0.21/0.40 thf(f47,plain,(
% 0.21/0.40 ! [X0] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),ty_2Erealax_2Ereal) => (vAPP(tp__ty_2Erealax_2Ereal,$i,inj__ty_2Erealax_2Ereal,vAPP($i,tp__ty_2Erealax_2Ereal,surj__ty_2Erealax_2Ereal,X0)) = X0))),
% 0.21/0.40 inference(rectify,[],[f25])).
% 0.21/0.40 thf(f25,axiom,(
% 0.21/0.40 ! [X0] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),ty_2Erealax_2Ereal) => (vAPP(tp__ty_2Erealax_2Ereal,$i,inj__ty_2Erealax_2Ereal,vAPP($i,tp__ty_2Erealax_2Ereal,surj__ty_2Erealax_2Ereal,X0)) = X0))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_iso_mem_ty_2Erealax_2Ereal)).
% 0.21/0.40 thf(f377,plain,(
% 0.21/0.40 spl6_25),
% 0.21/0.40 inference(avatar_split_clause,[],[f162,f375])).
% 0.21/0.40 thf(f375,plain,(
% 0.21/0.40 spl6_25 <=> ! [X0] : ((vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,vAPP($i,tp__ty_2Enum_2Enum,surj__ty_2Enum_2Enum,X0)) = X0) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),ty_2Enum_2Enum) != $true))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_25])])).
% 0.21/0.40 thf(f162,plain,(
% 0.21/0.40 ( ! [X0 : $i] : ((vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,vAPP($i,tp__ty_2Enum_2Enum,surj__ty_2Enum_2Enum,X0)) = X0) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),ty_2Enum_2Enum) != $true)) )),
% 0.21/0.40 inference(cnf_transformation,[],[f112])).
% 0.21/0.40 thf(f112,plain,(
% 0.21/0.40 ! [X0] : ((vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,vAPP($i,tp__ty_2Enum_2Enum,surj__ty_2Enum_2Enum,X0)) = X0) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),ty_2Enum_2Enum) != $true))),
% 0.21/0.40 inference(ennf_transformation,[],[f46])).
% 0.21/0.40 thf(f46,plain,(
% 0.21/0.40 ! [X0] : ((vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),ty_2Enum_2Enum) = $true) => (vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,vAPP($i,tp__ty_2Enum_2Enum,surj__ty_2Enum_2Enum,X0)) = X0))),
% 0.21/0.40 inference(fool_elimination,[],[f45])).
% 0.21/0.40 thf(f45,plain,(
% 0.21/0.40 ! [X0] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),ty_2Enum_2Enum) => (vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,vAPP($i,tp__ty_2Enum_2Enum,surj__ty_2Enum_2Enum,X0)) = X0))),
% 0.21/0.40 inference(rectify,[],[f20])).
% 0.21/0.40 thf(f20,axiom,(
% 0.21/0.40 ! [X0] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),ty_2Enum_2Enum) => (vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,vAPP($i,tp__ty_2Enum_2Enum,surj__ty_2Enum_2Enum,X0)) = X0))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_iso_mem_ty_2Enum_2Enum)).
% 0.21/0.40 thf(f373,plain,(
% 0.21/0.40 spl6_24),
% 0.21/0.40 inference(avatar_split_clause,[],[f206,f370])).
% 0.21/0.40 thf(f370,plain,(
% 0.21/0.40 spl6_24 <=> (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ebool_2E_7E),vAPP(del,del,vAPP(del,sTfun(del,del),arr,bool),bool)) = $true)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl6_24])])).
% 0.21/0.40 thf(f206,plain,(
% 0.21/0.40 (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ebool_2E_7E),vAPP(del,del,vAPP(del,sTfun(del,del),arr,bool),bool)) = $true)),
% 0.21/0.40 inference(cnf_transformation,[],[f96])).
% 0.21/0.40 thf(f96,plain,(
% 0.21/0.40 (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ebool_2E_7E),vAPP(del,del,vAPP(del,sTfun(del,del),arr,bool),bool)) = $true)),
% 0.21/0.40 inference(fool_elimination,[],[f95])).
% 0.21/0.40 thf(f95,plain,(
% 0.21/0.40 vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ebool_2E_7E),vAPP(del,del,vAPP(del,sTfun(del,del),arr,bool),bool))),
% 0.21/0.40 inference(rectify,[],[f8])).
% 0.21/0.40 thf(f8,axiom,(
% 0.21/0.40 vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ebool_2E_7E),vAPP(del,del,vAPP(del,sTfun(del,del),arr,bool),bool))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_7E)).
% 0.21/0.40 thf(f360,plain,(
% 0.21/0.40 spl6_23),
% 0.21/0.40 inference(avatar_split_clause,[],[f167,f358])).
% 0.21/0.40 thf(f167,plain,(
% 0.21/0.40 ( ! [X0 : $i] : (($true = vAPP($i,$o,sP0,X0)) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true)) )),
% 0.21/0.40 inference(cnf_transformation,[],[f134])).
% 0.21/0.40 thf(f134,plain,(
% 0.21/0.40 ! [X0] : ((((vAPP($i,$o,p,X0) != $true) | (vAPP($i,$o,p,X0) = $true)) & ((vAPP($i,$o,p,X0) != $true) | (vAPP($i,$o,p,X0) = $true)) & ((vAPP($i,$o,p,X0) = $true) | (vAPP($i,$o,p,X0) != $true)) & ($true = vAPP($i,$o,sP0,X0))) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true))),
% 0.21/0.41 inference(flattening,[],[f133])).
% 0.21/0.41 thf(f133,plain,(
% 0.21/0.41 ! [X0] : (((((vAPP($i,$o,p,X0) != $true) | (vAPP($i,$o,p,X0) = $true)) & ((vAPP($i,$o,p,X0) != $true) | (vAPP($i,$o,p,X0) = $true))) & ((vAPP($i,$o,p,X0) = $true) | (vAPP($i,$o,p,X0) != $true)) & ($true = vAPP($i,$o,sP0,X0))) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true))),
% 0.21/0.41 inference(nnf_transformation,[],[f129])).
% 0.21/0.41 thf(f129,plain,(
% 0.21/0.41 ! [X0] : ((((vAPP($i,$o,p,X0) != $true) <=> (vAPP($i,$o,p,X0) != $true)) & ((vAPP($i,$o,p,X0) = $true) | (vAPP($i,$o,p,X0) != $true)) & ($true = vAPP($i,$o,sP0,X0))) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true))),
% 0.21/0.41 inference(definition_folding,[],[f115,f128])).
% 0.21/0.41 thf(f128,plain,(
% 0.21/0.41 ! [X0] : (((vAPP($i,$o,p,X0) = $true) <=> (vAPP($i,$o,p,X0) = $true)) | ~($true = vAPP($i,$o,sP0,X0)))),
% 0.21/0.41 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 0.21/0.41 thf(f115,plain,(
% 0.21/0.41 ! [X0] : ((((vAPP($i,$o,p,X0) != $true) <=> (vAPP($i,$o,p,X0) != $true)) & ((vAPP($i,$o,p,X0) = $true) | (vAPP($i,$o,p,X0) != $true)) & ((vAPP($i,$o,p,X0) = $true) <=> (vAPP($i,$o,p,X0) = $true))) | (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) != $true))),
% 0.21/0.41 inference(ennf_transformation,[],[f108])).
% 0.21/0.41 thf(f108,plain,(
% 0.21/0.41 ! [X0] : ((vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) = $true) => (((vAPP($i,$o,p,X0) != $true) <=> (vAPP($i,$o,p,X0) != $true)) & ((vAPP($i,$o,p,X0) = $true) => (vAPP($i,$o,p,X0) = $true)) & ((vAPP($i,$o,p,X0) = $true) <=> (vAPP($i,$o,p,X0) = $true))))),
% 0.21/0.41 inference(flattening,[],[f107])).
% 0.21/0.41 thf(f107,plain,(
% 0.21/0.41 ! [X0] : ((vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) = $true) => ((~(vAPP($i,$o,p,X0) = $true) <=> ~(vAPP($i,$o,p,X0) = $true)) & ((vAPP($i,$o,p,X0) = $true) => (vAPP($i,$o,p,X0) = $true)) & ((vAPP($i,$o,p,X0) = $true) <=> (vAPP($i,$o,p,X0) = $true))))),
% 0.21/0.41 inference(true_and_false_elimination,[],[f52])).
% 0.21/0.41 thf(f52,plain,(
% 0.21/0.41 ! [X0] : ((vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) = $true) => ((((vAPP($i,$o,p,X0) = $true) => $false) <=> ~(vAPP($i,$o,p,X0) = $true)) & (((vAPP($i,$o,p,X0) = $true) => (vAPP($i,$o,p,X0) = $true)) <=> $true) & (($false => (vAPP($i,$o,p,X0) = $true)) <=> $true) & (((vAPP($i,$o,p,X0) = $true) => $true) <=> $true) & (($true => (vAPP($i,$o,p,X0) = $true)) <=> (vAPP($i,$o,p,X0) = $true))))),
% 0.21/0.41 inference(fool_elimination,[],[f51])).
% 0.21/0.41 thf(f51,plain,(
% 0.21/0.41 ! [X0] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X0),bool) => (((vAPP($i,$o,p,X0) => $false) <=> ~vAPP($i,$o,p,X0)) & ((vAPP($i,$o,p,X0) => vAPP($i,$o,p,X0)) <=> $true) & (($false => vAPP($i,$o,p,X0)) <=> $true) & ((vAPP($i,$o,p,X0) => $true) <=> $true) & (($true => vAPP($i,$o,p,X0)) <=> vAPP($i,$o,p,X0))))),
% 0.21/0.41 inference(rectify,[],[f37])).
% 0.21/0.41 thf(f37,axiom,(
% 0.21/0.41 ! [X9] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,X9),bool) => (((vAPP($i,$o,p,X9) => $false) <=> ~vAPP($i,$o,p,X9)) & ((vAPP($i,$o,p,X9) => vAPP($i,$o,p,X9)) <=> $true) & (($false => vAPP($i,$o,p,X9)) <=> $true) & ((vAPP($i,$o,p,X9) => $true) <=> $true) & (($true => vAPP($i,$o,p,X9)) <=> vAPP($i,$o,p,X9))))),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EIMP__CLAUSES)).
% 0.21/0.41 thf(f355,plain,(
% 0.21/0.41 spl6_22),
% 0.21/0.41 inference(avatar_split_clause,[],[f184,f353])).
% 0.21/0.41 thf(f353,plain,(
% 0.21/0.41 spl6_22 <=> ! [X0 : $o] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP($o,$i,inj__o,X0)),bool) = $true)),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl6_22])])).
% 0.21/0.41 thf(f184,plain,(
% 0.21/0.41 ( ! [X0 : $o] : ((vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP($o,$i,inj__o,X0)),bool) = $true)) )),
% 0.21/0.41 inference(cnf_transformation,[],[f66])).
% 0.21/0.41 thf(f66,plain,(
% 0.21/0.41 ! [X0 : $o] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP($o,$i,inj__o,X0)),bool) = $true)),
% 0.21/0.41 inference(fool_elimination,[],[f65])).
% 0.21/0.41 thf(f65,plain,(
% 0.21/0.41 ! [X0 : $o] : vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP($o,$i,inj__o,X0)),bool)),
% 0.21/0.41 inference(rectify,[],[f2])).
% 0.21/0.41 thf(f2,axiom,(
% 0.21/0.41 ! [X0 : $o] : vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP($o,$i,inj__o,X0)),bool)),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_o)).
% 0.21/0.41 thf(f351,plain,(
% 0.21/0.41 spl6_21 | ~spl6_5 | ~spl6_11),
% 0.21/0.41 inference(avatar_split_clause,[],[f307,f300,f268,f348])).
% 0.21/0.41 thf(f348,plain,(
% 0.21/0.41 spl6_21 <=> (fo__c_2Enum_2E0 = vAPP($i,tp__ty_2Enum_2Enum,surj__ty_2Enum_2Enum,c_2Enum_2E0))),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl6_21])])).
% 0.21/0.41 thf(f268,plain,(
% 0.21/0.41 spl6_5 <=> (c_2Enum_2E0 = vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl6_5])])).
% 0.21/0.41 thf(f300,plain,(
% 0.21/0.41 spl6_11 <=> ! [X0 : tp__ty_2Enum_2Enum] : (vAPP($i,tp__ty_2Enum_2Enum,surj__ty_2Enum_2Enum,vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,X0)) = X0)),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl6_11])])).
% 0.21/0.41 thf(f307,plain,(
% 0.21/0.41 (fo__c_2Enum_2E0 = vAPP($i,tp__ty_2Enum_2Enum,surj__ty_2Enum_2Enum,c_2Enum_2E0)) | (~spl6_5 | ~spl6_11)),
% 0.21/0.41 inference(superposition,[],[f301,f270])).
% 0.21/0.41 thf(f270,plain,(
% 0.21/0.41 (c_2Enum_2E0 = vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0)) | ~spl6_5),
% 0.21/0.41 inference(avatar_component_clause,[],[f268])).
% 0.21/0.41 thf(f301,plain,(
% 0.21/0.41 ( ! [X0 : tp__ty_2Enum_2Enum] : ((vAPP($i,tp__ty_2Enum_2Enum,surj__ty_2Enum_2Enum,vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,X0)) = X0)) ) | ~spl6_11),
% 0.21/0.41 inference(avatar_component_clause,[],[f300])).
% 0.21/0.41 thf(f346,plain,(
% 0.21/0.41 spl6_20),
% 0.21/0.41 inference(avatar_split_clause,[],[f183,f344])).
% 0.21/0.41 thf(f344,plain,(
% 0.21/0.41 spl6_20 <=> ! [X0 : tp__ty_2Enum_2Enum] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,X0)),ty_2Enum_2Enum) = $true)),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl6_20])])).
% 0.21/0.41 thf(f183,plain,(
% 0.21/0.41 ( ! [X0 : tp__ty_2Enum_2Enum] : ((vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,X0)),ty_2Enum_2Enum) = $true)) )),
% 0.21/0.41 inference(cnf_transformation,[],[f64])).
% 0.21/0.41 thf(f64,plain,(
% 0.21/0.41 ! [X0 : tp__ty_2Enum_2Enum] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,X0)),ty_2Enum_2Enum) = $true)),
% 0.21/0.41 inference(fool_elimination,[],[f63])).
% 0.21/0.41 thf(f63,plain,(
% 0.21/0.41 ! [X0 : tp__ty_2Enum_2Enum] : vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,X0)),ty_2Enum_2Enum)),
% 0.21/0.41 inference(rectify,[],[f19])).
% 0.21/0.41 thf(f19,axiom,(
% 0.21/0.41 ! [X0 : tp__ty_2Enum_2Enum] : vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,X0)),ty_2Enum_2Enum)),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_ty_2Enum_2Enum)).
% 0.21/0.41 thf(f342,plain,(
% 0.21/0.41 spl6_19),
% 0.21/0.41 inference(avatar_split_clause,[],[f182,f340])).
% 0.21/0.41 thf(f340,plain,(
% 0.21/0.41 spl6_19 <=> ! [X0 : tp__ty_2Erealax_2Ereal] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(tp__ty_2Erealax_2Ereal,$i,inj__ty_2Erealax_2Ereal,X0)),ty_2Erealax_2Ereal) = $true)),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl6_19])])).
% 0.21/0.41 thf(f182,plain,(
% 0.21/0.41 ( ! [X0 : tp__ty_2Erealax_2Ereal] : ((vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(tp__ty_2Erealax_2Ereal,$i,inj__ty_2Erealax_2Ereal,X0)),ty_2Erealax_2Ereal) = $true)) )),
% 0.21/0.41 inference(cnf_transformation,[],[f62])).
% 0.21/0.41 thf(f62,plain,(
% 0.21/0.41 ! [X0 : tp__ty_2Erealax_2Ereal] : (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(tp__ty_2Erealax_2Ereal,$i,inj__ty_2Erealax_2Ereal,X0)),ty_2Erealax_2Ereal) = $true)),
% 0.21/0.41 inference(fool_elimination,[],[f61])).
% 0.21/0.41 thf(f61,plain,(
% 0.21/0.41 ! [X0 : tp__ty_2Erealax_2Ereal] : vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(tp__ty_2Erealax_2Ereal,$i,inj__ty_2Erealax_2Ereal,X0)),ty_2Erealax_2Ereal)),
% 0.21/0.41 inference(rectify,[],[f24])).
% 0.21/0.41 thf(f24,axiom,(
% 0.21/0.41 ! [X0 : tp__ty_2Erealax_2Ereal] : vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,vAPP(tp__ty_2Erealax_2Ereal,$i,inj__ty_2Erealax_2Ereal,X0)),ty_2Erealax_2Ereal)),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_ty_2Erealax_2Ereal)).
% 0.21/0.41 thf(f338,plain,(
% 0.21/0.41 spl6_18 | ~spl6_9 | ~spl6_17),
% 0.21/0.41 inference(avatar_split_clause,[],[f333,f329,f291,f335])).
% 0.21/0.41 thf(f335,plain,(
% 0.21/0.41 spl6_18 <=> (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),c_2Enum_2E0)) = vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),c_2Enum_2E0))))))),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl6_18])])).
% 0.21/0.41 thf(f329,plain,(
% 0.21/0.41 spl6_17 <=> (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,sK1))) = vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,sK1)))))))),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl6_17])])).
% 0.21/0.41 thf(f333,plain,(
% 0.21/0.41 (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),c_2Enum_2E0)) = vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),c_2Enum_2E0)))))) | (~spl6_9 | ~spl6_17)),
% 0.21/0.41 inference(forward_demodulation,[],[f331,f293])).
% 0.21/0.41 thf(f331,plain,(
% 0.21/0.41 (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,sK1))) = vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,sK1))))))) | ~spl6_17),
% 0.21/0.41 inference(avatar_component_clause,[],[f329])).
% 0.21/0.41 thf(f332,plain,(
% 0.21/0.41 spl6_17),
% 0.21/0.41 inference(avatar_split_clause,[],[f216,f329])).
% 0.21/0.41 thf(f216,plain,(
% 0.21/0.41 (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,sK1))) = vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,sK1)))))))),
% 0.21/0.41 inference(forward_demodulation,[],[f211,f155])).
% 0.21/0.41 thf(f155,plain,(
% 0.21/0.41 (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) = vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,sK1))))),
% 0.21/0.41 inference(cnf_transformation,[],[f131])).
% 0.21/0.41 thf(f131,plain,(
% 0.21/0.41 (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) = vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,sK1)))) & (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) != sK1)),
% 0.21/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f111,f130])).
% 0.21/0.41 thf(f130,plain,(
% 0.21/0.41 ? [X0 : tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) = vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X0)))) & (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) != X0)) => ((vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) = vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,sK1)))) & (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) != sK1))),
% 0.21/0.41 introduced(choice_axiom,[])).
% 0.21/0.41 thf(f111,plain,(
% 0.21/0.41 ? [X0 : tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) = vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X0)))) & (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) != X0))),
% 0.21/0.41 inference(ennf_transformation,[],[f105])).
% 0.21/0.41 thf(f105,plain,(
% 0.21/0.41 ~! [X0 : tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) != X0) => (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) != vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X0)))))),
% 0.21/0.41 inference(rectify,[],[f40])).
% 0.21/0.41 thf(f40,negated_conjecture,(
% 0.21/0.41 ~! [X11 : tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) != X11) => (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X11))) != vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0)))))),
% 0.21/0.41 inference(negated_conjecture,[],[f39])).
% 0.21/0.41 thf(f39,conjecture,(
% 0.21/0.41 ! [X11 : tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) != X11) => (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X11))) != vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0)))))),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ)).
% 0.21/0.41 thf(f211,plain,(
% 0.21/0.41 (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) = vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0)))))))),
% 0.21/0.41 inference(equality_resolution,[],[f181])).
% 0.21/0.41 thf(f181,plain,(
% 0.21/0.41 ( ! [X0 : tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) = vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X0)))) | (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) != X0)) )),
% 0.21/0.41 inference(cnf_transformation,[],[f140])).
% 0.21/0.41 thf(f327,plain,(
% 0.21/0.41 spl6_16),
% 0.21/0.41 inference(avatar_split_clause,[],[f205,f324])).
% 0.21/0.41 thf(f205,plain,(
% 0.21/0.41 (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ebool_2EF),bool) = $true)),
% 0.21/0.41 inference(cnf_transformation,[],[f94])).
% 0.21/0.41 thf(f94,plain,(
% 0.21/0.41 (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ebool_2EF),bool) = $true)),
% 0.21/0.41 inference(fool_elimination,[],[f93])).
% 0.21/0.41 thf(f93,plain,(
% 0.21/0.41 vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ebool_2EF),bool)),
% 0.21/0.41 inference(rectify,[],[f10])).
% 0.21/0.41 thf(f10,axiom,(
% 0.21/0.41 vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ebool_2EF),bool)),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2EF)).
% 0.21/0.41 thf(f322,plain,(
% 0.21/0.41 spl6_15),
% 0.21/0.41 inference(avatar_split_clause,[],[f204,f319])).
% 0.21/0.41 thf(f204,plain,(
% 0.21/0.41 (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ebool_2ET),bool) = $true)),
% 0.21/0.41 inference(cnf_transformation,[],[f92])).
% 0.21/0.41 thf(f92,plain,(
% 0.21/0.41 (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ebool_2ET),bool) = $true)),
% 0.21/0.41 inference(fool_elimination,[],[f91])).
% 0.21/0.41 thf(f91,plain,(
% 0.21/0.41 vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ebool_2ET),bool)),
% 0.21/0.41 inference(rectify,[],[f12])).
% 0.21/0.41 thf(f12,axiom,(
% 0.21/0.41 vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Ebool_2ET),bool)),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2ET)).
% 0.21/0.41 thf(f317,plain,(
% 0.21/0.41 spl6_14 | ~spl6_4 | spl6_6),
% 0.21/0.41 inference(avatar_split_clause,[],[f283,f273,f236,f314])).
% 0.21/0.41 thf(f314,plain,(
% 0.21/0.41 spl6_14 <=> (vAPP($i,$o,p,c_2Ebool_2EF) = $false)),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl6_14])])).
% 0.21/0.41 thf(f236,plain,(
% 0.21/0.41 spl6_4 <=> ! [X0 : $o] : (($true = X0) | ($false = X0))),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl6_4])])).
% 0.21/0.41 thf(f273,plain,(
% 0.21/0.41 spl6_6 <=> (vAPP($i,$o,p,c_2Ebool_2EF) = $true)),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl6_6])])).
% 0.21/0.41 thf(f283,plain,(
% 0.21/0.41 (vAPP($i,$o,p,c_2Ebool_2EF) = $false) | (~spl6_4 | spl6_6)),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f282])).
% 0.21/0.41 thf(f282,plain,(
% 0.21/0.41 ($true != $true) | (vAPP($i,$o,p,c_2Ebool_2EF) = $false) | (~spl6_4 | spl6_6)),
% 0.21/0.41 inference(superposition,[],[f275,f237])).
% 0.21/0.41 thf(f237,plain,(
% 0.21/0.41 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) ) | ~spl6_4),
% 0.21/0.41 inference(avatar_component_clause,[],[f236])).
% 0.21/0.41 thf(f275,plain,(
% 0.21/0.41 (vAPP($i,$o,p,c_2Ebool_2EF) != $true) | spl6_6),
% 0.21/0.41 inference(avatar_component_clause,[],[f273])).
% 0.21/0.41 thf(f312,plain,(
% 0.21/0.41 spl6_13),
% 0.21/0.41 inference(avatar_split_clause,[],[f203,f309])).
% 0.21/0.41 thf(f309,plain,(
% 0.21/0.41 spl6_13 <=> (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Enum_2E0),ty_2Enum_2Enum) = $true)),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl6_13])])).
% 0.21/0.41 thf(f203,plain,(
% 0.21/0.41 (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Enum_2E0),ty_2Enum_2Enum) = $true)),
% 0.21/0.41 inference(cnf_transformation,[],[f90])).
% 0.21/0.41 thf(f90,plain,(
% 0.21/0.41 (vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Enum_2E0),ty_2Enum_2Enum) = $true)),
% 0.21/0.41 inference(fool_elimination,[],[f89])).
% 0.21/0.41 thf(f89,plain,(
% 0.21/0.41 vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Enum_2E0),ty_2Enum_2Enum)),
% 0.21/0.41 inference(rectify,[],[f21])).
% 0.21/0.41 thf(f21,axiom,(
% 0.21/0.41 vAPP(del,$o,vAPP($i,sTfun(del,$o),mem,c_2Enum_2E0),ty_2Enum_2Enum)),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Enum_2E0)).
% 0.21/0.41 thf(f306,plain,(
% 0.21/0.41 spl6_12),
% 0.21/0.41 inference(avatar_split_clause,[],[f160,f304])).
% 0.21/0.41 thf(f304,plain,(
% 0.21/0.41 spl6_12 <=> ! [X0 : tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X0)) = X0)),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl6_12])])).
% 0.21/0.41 thf(f160,plain,(
% 0.21/0.41 ( ! [X0 : tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ((vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X0)) = X0)) )),
% 0.21/0.41 inference(cnf_transformation,[],[f26])).
% 0.21/0.41 thf(f26,axiom,(
% 0.21/0.41 ! [X0 : tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,X0)) = X0)),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)).
% 0.21/0.41 thf(f302,plain,(
% 0.21/0.41 spl6_11),
% 0.21/0.41 inference(avatar_split_clause,[],[f159,f300])).
% 0.21/0.41 thf(f159,plain,(
% 0.21/0.41 ( ! [X0 : tp__ty_2Enum_2Enum] : ((vAPP($i,tp__ty_2Enum_2Enum,surj__ty_2Enum_2Enum,vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,X0)) = X0)) )),
% 0.21/0.41 inference(cnf_transformation,[],[f18])).
% 0.21/0.41 thf(f18,axiom,(
% 0.21/0.41 ! [X0 : tp__ty_2Enum_2Enum] : (vAPP($i,tp__ty_2Enum_2Enum,surj__ty_2Enum_2Enum,vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,X0)) = X0)),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_ty_2Enum_2Enum)).
% 0.21/0.41 thf(f298,plain,(
% 0.21/0.41 spl6_10),
% 0.21/0.41 inference(avatar_split_clause,[],[f158,f296])).
% 0.21/0.41 thf(f296,plain,(
% 0.21/0.41 spl6_10 <=> ! [X0 : tp__ty_2Erealax_2Ereal] : (vAPP($i,tp__ty_2Erealax_2Ereal,surj__ty_2Erealax_2Ereal,vAPP(tp__ty_2Erealax_2Ereal,$i,inj__ty_2Erealax_2Ereal,X0)) = X0)),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl6_10])])).
% 0.21/0.41 thf(f158,plain,(
% 0.21/0.41 ( ! [X0 : tp__ty_2Erealax_2Ereal] : ((vAPP($i,tp__ty_2Erealax_2Ereal,surj__ty_2Erealax_2Ereal,vAPP(tp__ty_2Erealax_2Ereal,$i,inj__ty_2Erealax_2Ereal,X0)) = X0)) )),
% 0.21/0.41 inference(cnf_transformation,[],[f23])).
% 0.21/0.41 thf(f23,axiom,(
% 0.21/0.41 ! [X0 : tp__ty_2Erealax_2Ereal] : (vAPP($i,tp__ty_2Erealax_2Ereal,surj__ty_2Erealax_2Ereal,vAPP(tp__ty_2Erealax_2Ereal,$i,inj__ty_2Erealax_2Ereal,X0)) = X0)),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_ty_2Erealax_2Ereal)).
% 0.21/0.41 thf(f294,plain,(
% 0.21/0.41 spl6_9 | ~spl6_5 | ~spl6_8),
% 0.21/0.41 inference(avatar_split_clause,[],[f289,f285,f268,f291])).
% 0.21/0.41 thf(f285,plain,(
% 0.21/0.41 spl6_8 <=> (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) = vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,sK1))))),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl6_8])])).
% 0.21/0.41 thf(f289,plain,(
% 0.21/0.41 (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,sK1))) = vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),c_2Enum_2E0))) | (~spl6_5 | ~spl6_8)),
% 0.21/0.41 inference(forward_demodulation,[],[f287,f270])).
% 0.21/0.41 thf(f287,plain,(
% 0.21/0.41 (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) = vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__inv),vAPP(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,$i,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,sK1)))) | ~spl6_8),
% 0.21/0.41 inference(avatar_component_clause,[],[f285])).
% 0.21/0.41 thf(f288,plain,(
% 0.21/0.41 spl6_8),
% 0.21/0.41 inference(avatar_split_clause,[],[f155,f285])).
% 0.21/0.41 thf(f281,plain,(
% 0.21/0.41 spl6_7),
% 0.21/0.41 inference(avatar_split_clause,[],[f202,f278])).
% 0.21/0.41 thf(f278,plain,(
% 0.21/0.41 spl6_7 <=> (vAPP($i,$o,p,c_2Ebool_2ET) = $true)),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl6_7])])).
% 0.21/0.41 thf(f202,plain,(
% 0.21/0.41 (vAPP($i,$o,p,c_2Ebool_2ET) = $true)),
% 0.21/0.41 inference(cnf_transformation,[],[f88])).
% 0.21/0.41 thf(f88,plain,(
% 0.21/0.41 (vAPP($i,$o,p,c_2Ebool_2ET) = $true)),
% 0.21/0.41 inference(fool_elimination,[],[f87])).
% 0.21/0.41 thf(f87,plain,(
% 0.21/0.41 vAPP($i,$o,p,c_2Ebool_2ET)),
% 0.21/0.41 inference(rectify,[],[f13])).
% 0.21/0.41 thf(f13,axiom,(
% 0.21/0.41 vAPP($i,$o,p,c_2Ebool_2ET)),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_true_p)).
% 0.21/0.41 thf(f276,plain,(
% 0.21/0.41 ~spl6_6),
% 0.21/0.41 inference(avatar_split_clause,[],[f157,f273])).
% 0.21/0.41 thf(f157,plain,(
% 0.21/0.41 (vAPP($i,$o,p,c_2Ebool_2EF) != $true)),
% 0.21/0.41 inference(cnf_transformation,[],[f106])).
% 0.21/0.41 thf(f106,plain,(
% 0.21/0.41 (vAPP($i,$o,p,c_2Ebool_2EF) != $true)),
% 0.21/0.41 inference(flattening,[],[f44])).
% 0.21/0.41 thf(f44,plain,(
% 0.21/0.41 ~(vAPP($i,$o,p,c_2Ebool_2EF) = $true)),
% 0.21/0.41 inference(fool_elimination,[],[f43])).
% 0.21/0.41 thf(f43,plain,(
% 0.21/0.41 ~vAPP($i,$o,p,c_2Ebool_2EF)),
% 0.21/0.41 inference(rectify,[],[f11])).
% 0.21/0.41 thf(f11,axiom,(
% 0.21/0.41 ~vAPP($i,$o,p,c_2Ebool_2EF)),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_false_p)).
% 0.21/0.41 thf(f271,plain,(
% 0.21/0.41 spl6_5),
% 0.21/0.41 inference(avatar_split_clause,[],[f156,f268])).
% 0.21/0.41 thf(f238,plain,(
% 0.21/0.41 spl6_4),
% 0.21/0.41 inference(avatar_split_clause,[],[f42,f236])).
% 0.21/0.41 thf(f42,plain,(
% 0.21/0.41 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.21/0.41 introduced(fool_axiom,[])).
% 0.21/0.41 thf(f234,plain,(
% 0.21/0.41 ~spl6_3 | spl6_2),
% 0.21/0.41 inference(avatar_split_clause,[],[f229,f225,f231])).
% 0.21/0.41 thf(f225,plain,(
% 0.21/0.41 spl6_2 <=> (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) = sK1)),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl6_2])])).
% 0.21/0.41 thf(f229,plain,(
% 0.21/0.41 (sK1 != vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),c_2Enum_2E0))) | spl6_2),
% 0.21/0.41 inference(forward_demodulation,[],[f227,f156])).
% 0.21/0.41 thf(f227,plain,(
% 0.21/0.41 (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) != sK1) | spl6_2),
% 0.21/0.41 inference(avatar_component_clause,[],[f225])).
% 0.21/0.41 thf(f228,plain,(
% 0.21/0.41 ~spl6_2),
% 0.21/0.41 inference(avatar_split_clause,[],[f154,f225])).
% 0.21/0.41 thf(f154,plain,(
% 0.21/0.41 (vAPP($i,tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,vAPP($i,$i,vAPP($i,sTfun($i,$i),ap,c_2Ecomplex_2Ecomplex__of__num),vAPP(tp__ty_2Enum_2Enum,$i,inj__ty_2Enum_2Enum,fo__c_2Enum_2E0))) != sK1)),
% 0.21/0.41 inference(cnf_transformation,[],[f131])).
% 0.21/0.41 thf(f223,plain,(
% 0.21/0.41 ~spl6_1),
% 0.21/0.41 inference(avatar_split_clause,[],[f41,f220])).
% 0.21/0.41 thf(f220,plain,(
% 0.21/0.41 spl6_1 <=> ($true = $false)),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl6_1])])).
% 0.21/0.41 thf(f41,plain,(
% 0.21/0.41 ($true != $false)),
% 0.21/0.41 introduced(fool_axiom,[])).
% 0.21/0.41 % SZS output end Proof for theBenchmark
% 0.21/0.41 % (7400)------------------------------
% 0.21/0.41 % (7400)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.41 % (7400)Termination reason: Refutation
% 0.21/0.41
% 0.21/0.41 % (7400)Memory used [KB]: 1092
% 0.21/0.41 % (7400)Time elapsed: 0.030 s
% 0.21/0.41 % (7400)Instructions burned: 55 (million)
% 0.21/0.41 % (7395)Success in time 0.048 s
%------------------------------------------------------------------------------