TSTP Solution File: SEV512^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEV512^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 04:15:56 EDT 2024
% Result : Theorem 0.22s 0.52s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV512^1 : TPTP v8.2.0. Released v7.0.0.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n029.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun May 19 18:36:08 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (28984)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (28988)WARNING: value z3 for option sas not known
% 0.15/0.38 % (28990)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (28986)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (28987)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (28988)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)
% 0.15/0.38 % (28991)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)
% 0.15/0.38 % (28992)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)
% 0.15/0.38 % (28993)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)
% 0.15/0.38 % (28993)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.38 % Exception at run slice level% Exception at run slice level
% 0.15/0.38
% 0.15/0.38 User error: User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructsFinite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.38
% 0.15/0.38 % Exception at run slice level
% 0.15/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.40 % (28999)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.15/0.40 % (29001)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)
% 0.15/0.40 % (29000)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)
% 0.15/0.40 % (28999)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.40 % (29000)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.40 % Exception at run slice level
% 0.15/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.41 % (29008)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.22/0.52 % (29000)First to succeed.
% 0.22/0.52 % (29000)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-28984"
% 0.22/0.52 % (29000)Refutation found. Thanks to Tanya!
% 0.22/0.52 % SZS status Theorem for theBenchmark
% 0.22/0.52 % SZS output start Proof for theBenchmark
% 0.22/0.52 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.52 thf(type_def_6, type, 'type/nums/num': $tType).
% 0.22/0.52 thf(type_def_7, type, 'type/realax/real': $tType).
% 0.22/0.52 thf(type_def_8, type, sK1: $tType).
% 0.22/0.52 thf(type_def_9, type, sK2: $tType).
% 0.22/0.52 thf(func_def_0, type, 'type/realax/real': $tType).
% 0.22/0.52 thf(func_def_1, type, 'type/nums/num': $tType).
% 0.22/0.52 thf(func_def_2, type, 'const/trivia/o': !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X2) > (X1 > X0) > X1 > X2)).
% 0.22/0.52 thf(func_def_3, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 0.22/0.52 thf(func_def_4, type, 'const/sets/IMAGE': !>[X0: $tType, X1: $tType]:((X0 > X1) > (X0 > $o) > X1 > $o)).
% 0.22/0.52 thf(func_def_5, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 0.22/0.52 thf(func_def_6, type, 'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real').
% 0.22/0.52 thf(func_def_7, type, 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real').
% 0.22/0.52 thf(func_def_8, type, 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num').
% 0.22/0.52 thf(func_def_9, type, 'const/nums/_0': 'type/nums/num').
% 0.22/0.52 thf(func_def_10, type, 'const/iterate/sum': !>[X0: $tType]:((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real')).
% 0.22/0.52 thf(func_def_11, type, 'const/iterate/neutral': !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 0.22/0.52 thf(func_def_12, type, 'const/iterate/monoidal': !>[X0: $tType]:((X0 > X0 > X0) > $o)).
% 0.22/0.52 thf(func_def_13, type, 'const/iterate/iterate': !>[X0: $tType, X1: $tType]:((X1 > X1 > X1) > (X0 > $o) > (X0 > X1) > X1)).
% 0.22/0.52 thf(func_def_17, type, sP0: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > $o) > (X1 > X0) > (X2 > X1) > (X0 > X0 > X0) > $o)).
% 0.22/0.52 thf(func_def_18, type, sK3: sK2 > 'type/realax/real').
% 0.22/0.52 thf(func_def_19, type, sK4: sK1 > sK2).
% 0.22/0.52 thf(func_def_20, type, sK5: sK1 > $o).
% 0.22/0.52 thf(func_def_21, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > $o) > (X1 > X0) > (X2 > X1) > (X0 > X0 > X0) > X2)).
% 0.22/0.52 thf(func_def_22, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > $o) > (X1 > X0) > (X2 > X1) > (X0 > X0 > X0) > X2)).
% 0.22/0.52 thf(func_def_23, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)).
% 0.22/0.52 thf(func_def_24, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)).
% 0.22/0.52 thf(func_def_25, type, vAND: $o > $o > $o).
% 0.22/0.52 thf(func_def_26, type, vOR: $o > $o > $o).
% 0.22/0.52 thf(func_def_27, type, vIMP: $o > $o > $o).
% 0.22/0.52 thf(func_def_28, type, vNOT: $o > $o).
% 0.22/0.52 thf(func_def_29, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)).
% 0.22/0.52 thf(f1309,plain,(
% 0.22/0.52 $false),
% 0.22/0.52 inference(subsumption_resolution,[],[f1308,f389])).
% 0.22/0.52 thf(f389,plain,(
% 0.22/0.52 (vAPP(sK1,sK2,sK4,vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1,vAPP(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1),vAPP(sTfun(sK2,'type/realax/real'),sTfun(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1)),vAPP(sTfun(sK1,$o),sTfun(sTfun(sK2,'type/realax/real'),sTfun(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1))),sK6('type/realax/real',sK2,sK1),sK5),sK3),sK4),'const/realax/real_add')) = vAPP(sK1,sK2,sK4,vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1,vAPP(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1),vAPP(sTfun(sK2,'type/realax/real'),sTfun(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1)),vAPP(sTfun(sK1,$o),sTfun(sTfun(sK2,'type/realax/real'),sTfun(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1))),sK7('type/realax/real',sK2,sK1),sK5),sK3),sK4),'const/realax/real_add')))),
% 0.22/0.52 inference(unit_resulting_resolution,[],[f384,f36])).
% 0.22/0.52 thf(f36,plain,(
% 0.22/0.52 ( ! [X4 : $tType,X1 : $tType,X3 : $tType,X2 : X4 > X3,X0 : X1 > X1 > X1,X6 : X4 > $o,X5 : X3 > X1] : (($true != vAPP(sTfun(X1,sTfun(X1,X1)),$o,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),$o),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),$o)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),$o))),sP0(X1,X3,X4),X6),X5),X2),X0)) | (vAPP(X4,X3,X2,vAPP(sTfun(X1,sTfun(X1,X1)),X4,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4))),sK6(X1,X3,X4),X6),X5),X2),X0)) = vAPP(X4,X3,X2,vAPP(sTfun(X1,sTfun(X1,X1)),X4,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4))),sK7(X1,X3,X4),X6),X5),X2),X0)))) )),
% 0.22/0.52 inference(cnf_transformation,[],[f27])).
% 0.22/0.52 thf(f27,plain,(
% 0.22/0.52 ! [X0 : X1 > X1 > X1,X1 : $tType,X2 : X4 > X3,X3 : $tType,X4 : $tType,X5 : X3 > X1,X6 : X4 > $o] : (((vAPP(sTfun(X1,sTfun(X1,X1)),X1,'const/iterate/neutral'(X1),X0) != vAPP(X3,X1,X5,vAPP(X4,X3,X2,vAPP(sTfun(X1,sTfun(X1,X1)),X4,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4))),sK6(X1,X3,X4),X6),X5),X2),X0)))) & (vAPP(X4,X3,X2,vAPP(sTfun(X1,sTfun(X1,X1)),X4,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4))),sK6(X1,X3,X4),X6),X5),X2),X0)) = vAPP(X4,X3,X2,vAPP(sTfun(X1,sTfun(X1,X1)),X4,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4))),sK7(X1,X3,X4),X6),X5),X2),X0))) & (vAPP(sTfun(X1,sTfun(X1,X1)),X4,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4))),sK6(X1,X3,X4),X6),X5),X2),X0) != vAPP(sTfun(X1,sTfun(X1,X1)),X4,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4))),sK7(X1,X3,X4),X6),X5),X2),X0)) & ($true = vAPP(sTfun(X4,$o),$o,vAPP(X4,sTfun(sTfun(X4,$o),$o),'const/sets/IN'(X4),vAPP(sTfun(X1,sTfun(X1,X1)),X4,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4))),sK7(X1,X3,X4),X6),X5),X2),X0)),X6)) & ($true = vAPP(sTfun(X4,$o),$o,vAPP(X4,sTfun(sTfun(X4,$o),$o),'const/sets/IN'(X4),vAPP(sTfun(X1,sTfun(X1,X1)),X4,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4))),sK6(X1,X3,X4),X6),X5),X2),X0)),X6))) | ($true != vAPP(sTfun(X1,sTfun(X1,X1)),$o,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),$o),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),$o)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),$o))),sP0(X1,X3,X4),X6),X5),X2),X0)))),
% 0.22/0.52 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f25,f26])).
% 0.22/0.52 thf(f26,plain,(
% 0.22/0.52 ! [X4 : $tType,X3 : $tType,X1 : $tType,X0 : X1 > X1 > X1,X2 : X4 > X3,X5 : X3 > X1,X6 : X4 > $o] : (? [X7 : X4,X8 : X4] : ((vAPP(X3,X1,X5,vAPP(X4,X3,X2,X7)) != vAPP(sTfun(X1,sTfun(X1,X1)),X1,'const/iterate/neutral'(X1),X0)) & (vAPP(X4,X3,X2,X7) = vAPP(X4,X3,X2,X8)) & (X7 != X8) & ($true = vAPP(sTfun(X4,$o),$o,vAPP(X4,sTfun(sTfun(X4,$o),$o),'const/sets/IN'(X4),X8),X6)) & ($true = vAPP(sTfun(X4,$o),$o,vAPP(X4,sTfun(sTfun(X4,$o),$o),'const/sets/IN'(X4),X7),X6))) => ((vAPP(sTfun(X1,sTfun(X1,X1)),X1,'const/iterate/neutral'(X1),X0) != vAPP(X3,X1,X5,vAPP(X4,X3,X2,vAPP(sTfun(X1,sTfun(X1,X1)),X4,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4))),sK6(X1,X3,X4),X6),X5),X2),X0)))) & (vAPP(X4,X3,X2,vAPP(sTfun(X1,sTfun(X1,X1)),X4,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4))),sK6(X1,X3,X4),X6),X5),X2),X0)) = vAPP(X4,X3,X2,vAPP(sTfun(X1,sTfun(X1,X1)),X4,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4))),sK7(X1,X3,X4),X6),X5),X2),X0))) & (vAPP(sTfun(X1,sTfun(X1,X1)),X4,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4))),sK6(X1,X3,X4),X6),X5),X2),X0) != vAPP(sTfun(X1,sTfun(X1,X1)),X4,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4))),sK7(X1,X3,X4),X6),X5),X2),X0)) & ($true = vAPP(sTfun(X4,$o),$o,vAPP(X4,sTfun(sTfun(X4,$o),$o),'const/sets/IN'(X4),vAPP(sTfun(X1,sTfun(X1,X1)),X4,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4))),sK7(X1,X3,X4),X6),X5),X2),X0)),X6)) & ($true = vAPP(sTfun(X4,$o),$o,vAPP(X4,sTfun(sTfun(X4,$o),$o),'const/sets/IN'(X4),vAPP(sTfun(X1,sTfun(X1,X1)),X4,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4))),sK6(X1,X3,X4),X6),X5),X2),X0)),X6))))),
% 0.22/0.52 introduced(choice_axiom,[])).
% 0.22/0.52 thf(f25,plain,(
% 0.22/0.52 ! [X0 : X1 > X1 > X1,X1 : $tType,X2 : X4 > X3,X3 : $tType,X4 : $tType,X5 : X3 > X1,X6 : X4 > $o] : (? [X7 : X4,X8 : X4] : ((vAPP(X3,X1,X5,vAPP(X4,X3,X2,X7)) != vAPP(sTfun(X1,sTfun(X1,X1)),X1,'const/iterate/neutral'(X1),X0)) & (vAPP(X4,X3,X2,X7) = vAPP(X4,X3,X2,X8)) & (X7 != X8) & ($true = vAPP(sTfun(X4,$o),$o,vAPP(X4,sTfun(sTfun(X4,$o),$o),'const/sets/IN'(X4),X8),X6)) & ($true = vAPP(sTfun(X4,$o),$o,vAPP(X4,sTfun(sTfun(X4,$o),$o),'const/sets/IN'(X4),X7),X6))) | ($true != vAPP(sTfun(X1,sTfun(X1,X1)),$o,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),$o),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),$o)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),$o))),sP0(X1,X3,X4),X6),X5),X2),X0)))),
% 0.22/0.52 inference(rectify,[],[f24])).
% 0.22/0.52 thf(f24,plain,(
% 0.22/0.52 ! [X3 : X0 > X0 > X0,X0 : $tType,X5 : X1 > X2,X2 : $tType,X1 : $tType,X4 : X2 > X0,X6 : X1 > $o] : (? [X7 : X1,X8 : X1] : ((vAPP(X2,X0,X4,vAPP(X1,X2,X5,X7)) != vAPP(sTfun(X0,sTfun(X0,X0)),X0,'const/iterate/neutral'(X0),X3)) & (vAPP(X1,X2,X5,X7) = vAPP(X1,X2,X5,X8)) & (X7 != X8) & (vAPP(sTfun(X1,$o),$o,vAPP(X1,sTfun(sTfun(X1,$o),$o),'const/sets/IN'(X1),X8),X6) = $true) & (vAPP(sTfun(X1,$o),$o,vAPP(X1,sTfun(sTfun(X1,$o),$o),'const/sets/IN'(X1),X7),X6) = $true)) | ($true != vAPP(sTfun(X0,sTfun(X0,X0)),$o,vAPP(sTfun(X1,X2),sTfun(sTfun(X0,sTfun(X0,X0)),$o),vAPP(sTfun(X2,X0),sTfun(sTfun(X1,X2),sTfun(sTfun(X0,sTfun(X0,X0)),$o)),vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X0),sTfun(sTfun(X1,X2),sTfun(sTfun(X0,sTfun(X0,X0)),$o))),sP0(X0,X2,X1),X6),X4),X5),X3)))),
% 0.22/0.52 inference(nnf_transformation,[],[f20])).
% 0.22/0.52 thf(f20,plain,(
% 0.22/0.52 ! [X3 : X0 > X0 > X0,X0 : $tType,X5 : X1 > X2,X2 : $tType,X1 : $tType,X4 : X2 > X0,X6 : X1 > $o] : (? [X7 : X1,X8 : X1] : ((vAPP(X2,X0,X4,vAPP(X1,X2,X5,X7)) != vAPP(sTfun(X0,sTfun(X0,X0)),X0,'const/iterate/neutral'(X0),X3)) & (vAPP(X1,X2,X5,X7) = vAPP(X1,X2,X5,X8)) & (X7 != X8) & (vAPP(sTfun(X1,$o),$o,vAPP(X1,sTfun(sTfun(X1,$o),$o),'const/sets/IN'(X1),X8),X6) = $true) & (vAPP(sTfun(X1,$o),$o,vAPP(X1,sTfun(sTfun(X1,$o),$o),'const/sets/IN'(X1),X7),X6) = $true)) | ~($true = vAPP(sTfun(X0,sTfun(X0,X0)),$o,vAPP(sTfun(X1,X2),sTfun(sTfun(X0,sTfun(X0,X0)),$o),vAPP(sTfun(X2,X0),sTfun(sTfun(X1,X2),sTfun(sTfun(X0,sTfun(X0,X0)),$o)),vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X0),sTfun(sTfun(X1,X2),sTfun(sTfun(X0,sTfun(X0,X0)),$o))),sP0(X0,X2,X1),X6),X4),X5),X3)))),
% 0.22/0.52 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 0.22/0.52 thf(f384,plain,(
% 0.22/0.52 ($true = vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),$o,vAPP(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),$o),vAPP(sTfun(sK2,'type/realax/real'),sTfun(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),$o)),vAPP(sTfun(sK1,$o),sTfun(sTfun(sK2,'type/realax/real'),sTfun(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),$o))),sP0('type/realax/real',sK2,sK1),sK5),sK3),sK4),'const/realax/real_add'))),
% 0.22/0.52 inference(unit_resulting_resolution,[],[f28,f39,f40,f38])).
% 0.22/0.52 thf(f38,plain,(
% 0.22/0.52 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0 > X0 > X0,X6 : X1 > $o,X4 : X2 > X0,X5 : X1 > X2] : ((vAPP(sTfun(X1,$o),$o,'const/sets/FINITE'(X1),X6) != $true) | ($true = vAPP(sTfun(X0,sTfun(X0,X0)),$o,vAPP(sTfun(X1,X2),sTfun(sTfun(X0,sTfun(X0,X0)),$o),vAPP(sTfun(X2,X0),sTfun(sTfun(X1,X2),sTfun(sTfun(X0,sTfun(X0,X0)),$o)),vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X0),sTfun(sTfun(X1,X2),sTfun(sTfun(X0,sTfun(X0,X0)),$o))),sP0(X0,X2,X1),X6),X4),X5),X3)) | (vAPP(sTfun(X2,X0),X0,vAPP(sTfun(X2,$o),sTfun(sTfun(X2,X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun(X2,$o),sTfun(sTfun(X2,X0),X0)),'const/iterate/iterate'(X2,X0),X3),vAPP(sTfun(X1,$o),sTfun(X2,$o),vAPP(sTfun(X1,X2),sTfun(sTfun(X1,$o),sTfun(X2,$o)),'const/sets/IMAGE'(X1,X2),X5),X6)),X4) = vAPP(sTfun(X1,X0),X0,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun(X1,$o),sTfun(sTfun(X1,X0),X0)),'const/iterate/iterate'(X1,X0),X3),X6),vAPP(sTfun(X1,X2),sTfun(X1,X0),vAPP(sTfun(X2,X0),sTfun(sTfun(X1,X2),sTfun(X1,X0)),'const/trivia/o'(X2,X1,X0),X4),X5))) | ($true != vAPP(sTfun(X0,sTfun(X0,X0)),$o,'const/iterate/monoidal'(X0),X3))) )),
% 0.22/0.52 inference(cnf_transformation,[],[f21])).
% 0.22/0.52 thf(f21,plain,(
% 0.22/0.52 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0 > X0 > X0] : (! [X4 : X2 > X0,X5 : X1 > X2,X6 : X1 > $o] : ((vAPP(sTfun(X2,X0),X0,vAPP(sTfun(X2,$o),sTfun(sTfun(X2,X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun(X2,$o),sTfun(sTfun(X2,X0),X0)),'const/iterate/iterate'(X2,X0),X3),vAPP(sTfun(X1,$o),sTfun(X2,$o),vAPP(sTfun(X1,X2),sTfun(sTfun(X1,$o),sTfun(X2,$o)),'const/sets/IMAGE'(X1,X2),X5),X6)),X4) = vAPP(sTfun(X1,X0),X0,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun(X1,$o),sTfun(sTfun(X1,X0),X0)),'const/iterate/iterate'(X1,X0),X3),X6),vAPP(sTfun(X1,X2),sTfun(X1,X0),vAPP(sTfun(X2,X0),sTfun(sTfun(X1,X2),sTfun(X1,X0)),'const/trivia/o'(X2,X1,X0),X4),X5))) | ($true = vAPP(sTfun(X0,sTfun(X0,X0)),$o,vAPP(sTfun(X1,X2),sTfun(sTfun(X0,sTfun(X0,X0)),$o),vAPP(sTfun(X2,X0),sTfun(sTfun(X1,X2),sTfun(sTfun(X0,sTfun(X0,X0)),$o)),vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X0),sTfun(sTfun(X1,X2),sTfun(sTfun(X0,sTfun(X0,X0)),$o))),sP0(X0,X2,X1),X6),X4),X5),X3)) | (vAPP(sTfun(X1,$o),$o,'const/sets/FINITE'(X1),X6) != $true)) | ($true != vAPP(sTfun(X0,sTfun(X0,X0)),$o,'const/iterate/monoidal'(X0),X3)))),
% 0.22/0.52 inference(definition_folding,[],[f19,f20])).
% 0.22/0.52 thf(f19,plain,(
% 0.22/0.52 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0 > X0 > X0] : (! [X4 : X2 > X0,X5 : X1 > X2,X6 : X1 > $o] : ((vAPP(sTfun(X2,X0),X0,vAPP(sTfun(X2,$o),sTfun(sTfun(X2,X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun(X2,$o),sTfun(sTfun(X2,X0),X0)),'const/iterate/iterate'(X2,X0),X3),vAPP(sTfun(X1,$o),sTfun(X2,$o),vAPP(sTfun(X1,X2),sTfun(sTfun(X1,$o),sTfun(X2,$o)),'const/sets/IMAGE'(X1,X2),X5),X6)),X4) = vAPP(sTfun(X1,X0),X0,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun(X1,$o),sTfun(sTfun(X1,X0),X0)),'const/iterate/iterate'(X1,X0),X3),X6),vAPP(sTfun(X1,X2),sTfun(X1,X0),vAPP(sTfun(X2,X0),sTfun(sTfun(X1,X2),sTfun(X1,X0)),'const/trivia/o'(X2,X1,X0),X4),X5))) | ? [X7 : X1,X8 : X1] : ((vAPP(X2,X0,X4,vAPP(X1,X2,X5,X7)) != vAPP(sTfun(X0,sTfun(X0,X0)),X0,'const/iterate/neutral'(X0),X3)) & (vAPP(X1,X2,X5,X7) = vAPP(X1,X2,X5,X8)) & (X7 != X8) & (vAPP(sTfun(X1,$o),$o,vAPP(X1,sTfun(sTfun(X1,$o),$o),'const/sets/IN'(X1),X8),X6) = $true) & (vAPP(sTfun(X1,$o),$o,vAPP(X1,sTfun(sTfun(X1,$o),$o),'const/sets/IN'(X1),X7),X6) = $true)) | (vAPP(sTfun(X1,$o),$o,'const/sets/FINITE'(X1),X6) != $true)) | ($true != vAPP(sTfun(X0,sTfun(X0,X0)),$o,'const/iterate/monoidal'(X0),X3)))),
% 0.22/0.52 inference(flattening,[],[f18])).
% 0.22/0.52 thf(f18,plain,(
% 0.22/0.52 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0 > X0 > X0] : (! [X4 : X2 > X0,X5 : X1 > X2,X6 : X1 > $o] : ((vAPP(sTfun(X2,X0),X0,vAPP(sTfun(X2,$o),sTfun(sTfun(X2,X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun(X2,$o),sTfun(sTfun(X2,X0),X0)),'const/iterate/iterate'(X2,X0),X3),vAPP(sTfun(X1,$o),sTfun(X2,$o),vAPP(sTfun(X1,X2),sTfun(sTfun(X1,$o),sTfun(X2,$o)),'const/sets/IMAGE'(X1,X2),X5),X6)),X4) = vAPP(sTfun(X1,X0),X0,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun(X1,$o),sTfun(sTfun(X1,X0),X0)),'const/iterate/iterate'(X1,X0),X3),X6),vAPP(sTfun(X1,X2),sTfun(X1,X0),vAPP(sTfun(X2,X0),sTfun(sTfun(X1,X2),sTfun(X1,X0)),'const/trivia/o'(X2,X1,X0),X4),X5))) | (? [X7 : X1,X8 : X1] : ((vAPP(X2,X0,X4,vAPP(X1,X2,X5,X7)) != vAPP(sTfun(X0,sTfun(X0,X0)),X0,'const/iterate/neutral'(X0),X3)) & ((vAPP(X1,X2,X5,X7) = vAPP(X1,X2,X5,X8)) & (X7 != X8) & (vAPP(sTfun(X1,$o),$o,vAPP(X1,sTfun(sTfun(X1,$o),$o),'const/sets/IN'(X1),X8),X6) = $true) & (vAPP(sTfun(X1,$o),$o,vAPP(X1,sTfun(sTfun(X1,$o),$o),'const/sets/IN'(X1),X7),X6) = $true))) | (vAPP(sTfun(X1,$o),$o,'const/sets/FINITE'(X1),X6) != $true))) | ($true != vAPP(sTfun(X0,sTfun(X0,X0)),$o,'const/iterate/monoidal'(X0),X3)))),
% 0.22/0.52 inference(ennf_transformation,[],[f12])).
% 0.22/0.52 thf(f12,plain,(
% 0.22/0.52 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0 > X0 > X0] : (($true = vAPP(sTfun(X0,sTfun(X0,X0)),$o,'const/iterate/monoidal'(X0),X3)) => ! [X4 : X2 > X0,X5 : X1 > X2,X6 : X1 > $o] : ((! [X7 : X1,X8 : X1] : (((vAPP(X1,X2,X5,X7) = vAPP(X1,X2,X5,X8)) & (X7 != X8) & (vAPP(sTfun(X1,$o),$o,vAPP(X1,sTfun(sTfun(X1,$o),$o),'const/sets/IN'(X1),X8),X6) = $true) & (vAPP(sTfun(X1,$o),$o,vAPP(X1,sTfun(sTfun(X1,$o),$o),'const/sets/IN'(X1),X7),X6) = $true)) => (vAPP(X2,X0,X4,vAPP(X1,X2,X5,X7)) = vAPP(sTfun(X0,sTfun(X0,X0)),X0,'const/iterate/neutral'(X0),X3))) & (vAPP(sTfun(X1,$o),$o,'const/sets/FINITE'(X1),X6) = $true)) => (vAPP(sTfun(X2,X0),X0,vAPP(sTfun(X2,$o),sTfun(sTfun(X2,X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun(X2,$o),sTfun(sTfun(X2,X0),X0)),'const/iterate/iterate'(X2,X0),X3),vAPP(sTfun(X1,$o),sTfun(X2,$o),vAPP(sTfun(X1,X2),sTfun(sTfun(X1,$o),sTfun(X2,$o)),'const/sets/IMAGE'(X1,X2),X5),X6)),X4) = vAPP(sTfun(X1,X0),X0,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun(X1,$o),sTfun(sTfun(X1,X0),X0)),'const/iterate/iterate'(X1,X0),X3),X6),vAPP(sTfun(X1,X2),sTfun(X1,X0),vAPP(sTfun(X2,X0),sTfun(sTfun(X1,X2),sTfun(X1,X0)),'const/trivia/o'(X2,X1,X0),X4),X5)))))),
% 0.22/0.52 inference(fool_elimination,[],[f11])).
% 0.22/0.52 thf(f11,plain,(
% 0.22/0.52 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0 > X0 > X0] : (vAPP(sTfun(X0,sTfun(X0,X0)),$o,'const/iterate/monoidal'(X0),X3) => ! [X4 : X2 > X0,X5 : X1 > X2,X6 : X1 > $o] : ((! [X7 : X1,X8 : X1] : (((vAPP(X1,X2,X5,X7) = vAPP(X1,X2,X5,X8)) & (X7 != X8) & vAPP(sTfun(X1,$o),$o,vAPP(X1,sTfun(sTfun(X1,$o),$o),'const/sets/IN'(X1),X8),X6) & vAPP(sTfun(X1,$o),$o,vAPP(X1,sTfun(sTfun(X1,$o),$o),'const/sets/IN'(X1),X7),X6)) => (vAPP(X2,X0,X4,vAPP(X1,X2,X5,X7)) = vAPP(sTfun(X0,sTfun(X0,X0)),X0,'const/iterate/neutral'(X0),X3))) & vAPP(sTfun(X1,$o),$o,'const/sets/FINITE'(X1),X6)) => (vAPP(sTfun(X2,X0),X0,vAPP(sTfun(X2,$o),sTfun(sTfun(X2,X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun(X2,$o),sTfun(sTfun(X2,X0),X0)),'const/iterate/iterate'(X2,X0),X3),vAPP(sTfun(X1,$o),sTfun(X2,$o),vAPP(sTfun(X1,X2),sTfun(sTfun(X1,$o),sTfun(X2,$o)),'const/sets/IMAGE'(X1,X2),X5),X6)),X4) = vAPP(sTfun(X1,X0),X0,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun(X1,$o),sTfun(sTfun(X1,X0),X0)),'const/iterate/iterate'(X1,X0),X3),X6),vAPP(sTfun(X1,X2),sTfun(X1,X0),vAPP(sTfun(X2,X0),sTfun(sTfun(X1,X2),sTfun(X1,X0)),'const/trivia/o'(X2,X1,X0),X4),X5)))))),
% 0.22/0.52 inference(rectify,[],[f1])).
% 0.22/0.52 thf(f1,axiom,(
% 0.22/0.52 ! [X2 : $tType,X1 : $tType,X0 : $tType,X3 : X2 > X2 > X2] : (vAPP(sTfun(X2,sTfun(X2,X2)),$o,'const/iterate/monoidal'(X2),X3) => ! [X4 : X0 > X2,X5 : X1 > X0,X6 : X1 > $o] : ((! [X7 : X1,X8 : X1] : (((vAPP(X1,X0,X5,X7) = vAPP(X1,X0,X5,X8)) & (X7 != X8) & vAPP(sTfun(X1,$o),$o,vAPP(X1,sTfun(sTfun(X1,$o),$o),'const/sets/IN'(X1),X8),X6) & vAPP(sTfun(X1,$o),$o,vAPP(X1,sTfun(sTfun(X1,$o),$o),'const/sets/IN'(X1),X7),X6)) => (vAPP(X0,X2,X4,vAPP(X1,X0,X5,X7)) = vAPP(sTfun(X2,sTfun(X2,X2)),X2,'const/iterate/neutral'(X2),X3))) & vAPP(sTfun(X1,$o),$o,'const/sets/FINITE'(X1),X6)) => (vAPP(sTfun(X0,X2),X2,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X2),vAPP(sTfun(X2,sTfun(X2,X2)),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,X2),X2)),'const/iterate/iterate'(X0,X2),X3),vAPP(sTfun(X1,$o),sTfun(X0,$o),vAPP(sTfun(X1,X0),sTfun(sTfun(X1,$o),sTfun(X0,$o)),'const/sets/IMAGE'(X1,X0),X5),X6)),X4) = vAPP(sTfun(X1,X2),X2,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X2),X2),vAPP(sTfun(X2,sTfun(X2,X2)),sTfun(sTfun(X1,$o),sTfun(sTfun(X1,X2),X2)),'const/iterate/iterate'(X1,X2),X3),X6),vAPP(sTfun(X1,X0),sTfun(X1,X2),vAPP(sTfun(X0,X2),sTfun(sTfun(X1,X0),sTfun(X1,X2)),'const/trivia/o'(X0,X1,X2),X4),X5)))))),
% 0.22/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/ITERATE_IMAGE_NONZERO_')).
% 0.22/0.52 thf(f40,plain,(
% 0.22/0.52 (vAPP(sTfun(sK2,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK2,$o),sTfun(sTfun(sK2,'type/realax/real'),'type/realax/real'),vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sTfun(sTfun(sK2,$o),sTfun(sTfun(sK2,'type/realax/real'),'type/realax/real')),'const/iterate/iterate'(sK2,'type/realax/real'),'const/realax/real_add'),vAPP(sTfun(sK1,$o),sTfun(sK2,$o),vAPP(sTfun(sK1,sK2),sTfun(sTfun(sK1,$o),sTfun(sK2,$o)),'const/sets/IMAGE'(sK1,sK2),sK4),sK5)),sK3) != vAPP(sTfun(sK1,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK1,$o),sTfun(sTfun(sK1,'type/realax/real'),'type/realax/real'),vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sTfun(sTfun(sK1,$o),sTfun(sTfun(sK1,'type/realax/real'),'type/realax/real')),'const/iterate/iterate'(sK1,'type/realax/real'),'const/realax/real_add'),sK5),vAPP(sTfun(sK1,sK2),sTfun(sK1,'type/realax/real'),vAPP(sTfun(sK2,'type/realax/real'),sTfun(sTfun(sK1,sK2),sTfun(sK1,'type/realax/real')),'const/trivia/o'(sK2,sK1,'type/realax/real'),sK3),sK4)))),
% 0.22/0.52 inference(definition_unfolding,[],[f30,f32,f32])).
% 0.22/0.52 thf(f32,plain,(
% 0.22/0.52 ( ! [X0 : $tType] : (('const/iterate/sum'(X0) = vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real')),'const/iterate/iterate'(X0,'type/realax/real'),'const/realax/real_add'))) )),
% 0.22/0.52 inference(cnf_transformation,[],[f15])).
% 0.22/0.52 thf(f15,plain,(
% 0.22/0.52 ! [X0 : $tType] : ('const/iterate/sum'(X0) = vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real')),'const/iterate/iterate'(X0,'type/realax/real'),'const/realax/real_add'))),
% 0.22/0.52 inference(rectify,[],[f3])).
% 0.22/0.52 thf(f3,axiom,(
% 0.22/0.52 ! [X1 : $tType] : ('const/iterate/sum'(X1) = vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sTfun(sTfun(X1,$o),sTfun(sTfun(X1,'type/realax/real'),'type/realax/real')),'const/iterate/iterate'(X1,'type/realax/real'),'const/realax/real_add'))),
% 0.22/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/sum_')).
% 0.22/0.52 thf(f30,plain,(
% 0.22/0.52 (vAPP(sTfun(sK2,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK2,$o),sTfun(sTfun(sK2,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK2),vAPP(sTfun(sK1,$o),sTfun(sK2,$o),vAPP(sTfun(sK1,sK2),sTfun(sTfun(sK1,$o),sTfun(sK2,$o)),'const/sets/IMAGE'(sK1,sK2),sK4),sK5)),sK3) != vAPP(sTfun(sK1,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK1,$o),sTfun(sTfun(sK1,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK1),sK5),vAPP(sTfun(sK1,sK2),sTfun(sK1,'type/realax/real'),vAPP(sTfun(sK2,'type/realax/real'),sTfun(sTfun(sK1,sK2),sTfun(sK1,'type/realax/real')),'const/trivia/o'(sK2,sK1,'type/realax/real'),sK3),sK4)))),
% 0.22/0.52 inference(cnf_transformation,[],[f23])).
% 0.22/0.52 thf(f23,plain,(
% 0.22/0.52 (vAPP(sTfun(sK2,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK2,$o),sTfun(sTfun(sK2,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK2),vAPP(sTfun(sK1,$o),sTfun(sK2,$o),vAPP(sTfun(sK1,sK2),sTfun(sTfun(sK1,$o),sTfun(sK2,$o)),'const/sets/IMAGE'(sK1,sK2),sK4),sK5)),sK3) != vAPP(sTfun(sK1,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK1,$o),sTfun(sTfun(sK1,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK1),sK5),vAPP(sTfun(sK1,sK2),sTfun(sK1,'type/realax/real'),vAPP(sTfun(sK2,'type/realax/real'),sTfun(sTfun(sK1,sK2),sTfun(sK1,'type/realax/real')),'const/trivia/o'(sK2,sK1,'type/realax/real'),sK3),sK4))) & ! [X5 : sK1,X6 : sK1] : ((vAPP('type/nums/num','type/realax/real','const/realax/real_of_num',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')) = vAPP(sK2,'type/realax/real',sK3,vAPP(sK1,sK2,sK4,X5))) | (vAPP(sK1,sK2,sK4,X5) != vAPP(sK1,sK2,sK4,X6)) | (X5 = X6) | ($true != vAPP(sTfun(sK1,$o),$o,vAPP(sK1,sTfun(sTfun(sK1,$o),$o),'const/sets/IN'(sK1),X6),sK5)) | ($true != vAPP(sTfun(sK1,$o),$o,vAPP(sK1,sTfun(sTfun(sK1,$o),$o),'const/sets/IN'(sK1),X5),sK5))) & ($true = vAPP(sTfun(sK1,$o),$o,'const/sets/FINITE'(sK1),sK5))),
% 0.22/0.52 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5])],[f17,f22])).
% 0.22/0.52 thf(f22,plain,(
% 0.22/0.52 ( ! [X0 : $tType] : (? [X0 : $tType,X1 : $tType,X2 : X1 > 'type/realax/real',X3 : X0 > X1,X4 : X0 > $o] : ((vAPP(sTfun(X1,'type/realax/real'),'type/realax/real',vAPP(sTfun(X1,$o),sTfun(sTfun(X1,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X1),vAPP(sTfun(X0,$o),sTfun(X1,$o),vAPP(sTfun(X0,X1),sTfun(sTfun(X0,$o),sTfun(X1,$o)),'const/sets/IMAGE'(X0,X1),X3),X4)),X2) != vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X4),vAPP(sTfun(X0,X1),sTfun(X0,'type/realax/real'),vAPP(sTfun(X1,'type/realax/real'),sTfun(sTfun(X0,X1),sTfun(X0,'type/realax/real')),'const/trivia/o'(X1,X0,'type/realax/real'),X2),X3))) & ! [X5 : X0,X6 : X0] : ((vAPP('type/nums/num','type/realax/real','const/realax/real_of_num',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')) = vAPP(X1,'type/realax/real',X2,vAPP(X0,X1,X3,X5))) | (vAPP(X0,X1,X3,X5) != vAPP(X0,X1,X3,X6)) | (X5 = X6) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),'const/sets/IN'(X0),X6),X4)) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),'const/sets/IN'(X0),X5),X4))) & ($true = vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X4))) => ((vAPP(sTfun(sK2,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK2,$o),sTfun(sTfun(sK2,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK2),vAPP(sTfun(sK1,$o),sTfun(sK2,$o),vAPP(sTfun(sK1,sK2),sTfun(sTfun(sK1,$o),sTfun(sK2,$o)),'const/sets/IMAGE'(sK1,sK2),sK4),sK5)),sK3) != vAPP(sTfun(sK1,'type/realax/real'),'type/realax/real',vAPP(sTfun(sK1,$o),sTfun(sTfun(sK1,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(sK1),sK5),vAPP(sTfun(sK1,sK2),sTfun(sK1,'type/realax/real'),vAPP(sTfun(sK2,'type/realax/real'),sTfun(sTfun(sK1,sK2),sTfun(sK1,'type/realax/real')),'const/trivia/o'(sK2,sK1,'type/realax/real'),sK3),sK4))) & ! [X6 : sK1,X5 : sK1] : ((vAPP('type/nums/num','type/realax/real','const/realax/real_of_num',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')) = vAPP(sK2,'type/realax/real',sK3,vAPP(sK1,sK2,sK4,X5))) | (vAPP(sK1,sK2,sK4,X5) != vAPP(sK1,sK2,sK4,X6)) | (X5 = X6) | ($true != vAPP(sTfun(sK1,$o),$o,vAPP(sK1,sTfun(sTfun(sK1,$o),$o),'const/sets/IN'(sK1),X6),sK5)) | ($true != vAPP(sTfun(sK1,$o),$o,vAPP(sK1,sTfun(sTfun(sK1,$o),$o),'const/sets/IN'(sK1),X5),sK5))) & ($true = vAPP(sTfun(sK1,$o),$o,'const/sets/FINITE'(sK1),sK5)))) )),
% 0.22/0.52 introduced(choice_axiom,[])).
% 0.22/0.52 thf(f17,plain,(
% 0.22/0.52 ? [X0 : $tType,X1 : $tType,X2 : X1 > 'type/realax/real',X3 : X0 > X1,X4 : X0 > $o] : ((vAPP(sTfun(X1,'type/realax/real'),'type/realax/real',vAPP(sTfun(X1,$o),sTfun(sTfun(X1,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X1),vAPP(sTfun(X0,$o),sTfun(X1,$o),vAPP(sTfun(X0,X1),sTfun(sTfun(X0,$o),sTfun(X1,$o)),'const/sets/IMAGE'(X0,X1),X3),X4)),X2) != vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X4),vAPP(sTfun(X0,X1),sTfun(X0,'type/realax/real'),vAPP(sTfun(X1,'type/realax/real'),sTfun(sTfun(X0,X1),sTfun(X0,'type/realax/real')),'const/trivia/o'(X1,X0,'type/realax/real'),X2),X3))) & ! [X5 : X0,X6 : X0] : ((vAPP('type/nums/num','type/realax/real','const/realax/real_of_num',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')) = vAPP(X1,'type/realax/real',X2,vAPP(X0,X1,X3,X5))) | (vAPP(X0,X1,X3,X5) != vAPP(X0,X1,X3,X6)) | (X5 = X6) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),'const/sets/IN'(X0),X6),X4)) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),'const/sets/IN'(X0),X5),X4))) & ($true = vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X4)))),
% 0.22/0.52 inference(flattening,[],[f16])).
% 0.22/0.52 thf(f16,plain,(
% 0.22/0.52 ? [X0 : $tType,X1 : $tType,X2 : X1 > 'type/realax/real',X3 : X0 > X1,X4 : X0 > $o] : ((vAPP(sTfun(X1,'type/realax/real'),'type/realax/real',vAPP(sTfun(X1,$o),sTfun(sTfun(X1,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X1),vAPP(sTfun(X0,$o),sTfun(X1,$o),vAPP(sTfun(X0,X1),sTfun(sTfun(X0,$o),sTfun(X1,$o)),'const/sets/IMAGE'(X0,X1),X3),X4)),X2) != vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X4),vAPP(sTfun(X0,X1),sTfun(X0,'type/realax/real'),vAPP(sTfun(X1,'type/realax/real'),sTfun(sTfun(X0,X1),sTfun(X0,'type/realax/real')),'const/trivia/o'(X1,X0,'type/realax/real'),X2),X3))) & (! [X5 : X0,X6 : X0] : ((vAPP('type/nums/num','type/realax/real','const/realax/real_of_num',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')) = vAPP(X1,'type/realax/real',X2,vAPP(X0,X1,X3,X5))) | ((vAPP(X0,X1,X3,X5) != vAPP(X0,X1,X3,X6)) | (X5 = X6) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),'const/sets/IN'(X0),X6),X4)) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),'const/sets/IN'(X0),X5),X4)))) & ($true = vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X4))))),
% 0.22/0.52 inference(ennf_transformation,[],[f10])).
% 0.22/0.52 thf(f10,plain,(
% 0.22/0.52 ~! [X0 : $tType,X1 : $tType,X2 : X1 > 'type/realax/real',X3 : X0 > X1,X4 : X0 > $o] : ((! [X5 : X0,X6 : X0] : (((vAPP(X0,X1,X3,X5) = vAPP(X0,X1,X3,X6)) & (X5 != X6) & ($true = vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),'const/sets/IN'(X0),X6),X4)) & ($true = vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),'const/sets/IN'(X0),X5),X4))) => (vAPP('type/nums/num','type/realax/real','const/realax/real_of_num',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')) = vAPP(X1,'type/realax/real',X2,vAPP(X0,X1,X3,X5)))) & ($true = vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X4))) => (vAPP(sTfun(X1,'type/realax/real'),'type/realax/real',vAPP(sTfun(X1,$o),sTfun(sTfun(X1,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X1),vAPP(sTfun(X0,$o),sTfun(X1,$o),vAPP(sTfun(X0,X1),sTfun(sTfun(X0,$o),sTfun(X1,$o)),'const/sets/IMAGE'(X0,X1),X3),X4)),X2) = vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X4),vAPP(sTfun(X0,X1),sTfun(X0,'type/realax/real'),vAPP(sTfun(X1,'type/realax/real'),sTfun(sTfun(X0,X1),sTfun(X0,'type/realax/real')),'const/trivia/o'(X1,X0,'type/realax/real'),X2),X3))))),
% 0.22/0.52 inference(fool_elimination,[],[f9])).
% 0.22/0.52 thf(f9,plain,(
% 0.22/0.52 ~! [X0 : $tType,X1 : $tType,X2 : X1 > 'type/realax/real',X3 : X0 > X1,X4 : X0 > $o] : ((! [X5 : X0,X6 : X0] : (((vAPP(X0,X1,X3,X5) = vAPP(X0,X1,X3,X6)) & (X5 != X6) & vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),'const/sets/IN'(X0),X6),X4) & vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),'const/sets/IN'(X0),X5),X4)) => (vAPP('type/nums/num','type/realax/real','const/realax/real_of_num',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')) = vAPP(X1,'type/realax/real',X2,vAPP(X0,X1,X3,X5)))) & vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X4)) => (vAPP(sTfun(X1,'type/realax/real'),'type/realax/real',vAPP(sTfun(X1,$o),sTfun(sTfun(X1,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X1),vAPP(sTfun(X0,$o),sTfun(X1,$o),vAPP(sTfun(X0,X1),sTfun(sTfun(X0,$o),sTfun(X1,$o)),'const/sets/IMAGE'(X0,X1),X3),X4)),X2) = vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X4),vAPP(sTfun(X0,X1),sTfun(X0,'type/realax/real'),vAPP(sTfun(X1,'type/realax/real'),sTfun(sTfun(X0,X1),sTfun(X0,'type/realax/real')),'const/trivia/o'(X1,X0,'type/realax/real'),X2),X3))))),
% 0.22/0.52 inference(rectify,[],[f6])).
% 0.22/0.52 thf(f6,negated_conjecture,(
% 0.22/0.52 ~! [X1 : $tType,X0 : $tType,X3 : X0 > 'type/realax/real',X4 : X1 > X0,X5 : X1 > $o] : ((! [X6 : X1,X7 : X1] : (((vAPP(X1,X0,X4,X6) = vAPP(X1,X0,X4,X7)) & (X6 != X7) & vAPP(sTfun(X1,$o),$o,vAPP(X1,sTfun(sTfun(X1,$o),$o),'const/sets/IN'(X1),X7),X5) & vAPP(sTfun(X1,$o),$o,vAPP(X1,sTfun(sTfun(X1,$o),$o),'const/sets/IN'(X1),X6),X5)) => (vAPP('type/nums/num','type/realax/real','const/realax/real_of_num',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')) = vAPP(X0,'type/realax/real',X3,vAPP(X1,X0,X4,X6)))) & vAPP(sTfun(X1,$o),$o,'const/sets/FINITE'(X1),X5)) => (vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),vAPP(sTfun(X1,$o),sTfun(X0,$o),vAPP(sTfun(X1,X0),sTfun(sTfun(X1,$o),sTfun(X0,$o)),'const/sets/IMAGE'(X1,X0),X4),X5)),X3) = vAPP(sTfun(X1,'type/realax/real'),'type/realax/real',vAPP(sTfun(X1,$o),sTfun(sTfun(X1,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X1),X5),vAPP(sTfun(X1,X0),sTfun(X1,'type/realax/real'),vAPP(sTfun(X0,'type/realax/real'),sTfun(sTfun(X1,X0),sTfun(X1,'type/realax/real')),'const/trivia/o'(X0,X1,'type/realax/real'),X3),X4))))),
% 0.22/0.52 inference(negated_conjecture,[],[f5])).
% 0.22/0.52 thf(f5,conjecture,(
% 0.22/0.52 ! [X1 : $tType,X0 : $tType,X3 : X0 > 'type/realax/real',X4 : X1 > X0,X5 : X1 > $o] : ((! [X6 : X1,X7 : X1] : (((vAPP(X1,X0,X4,X6) = vAPP(X1,X0,X4,X7)) & (X6 != X7) & vAPP(sTfun(X1,$o),$o,vAPP(X1,sTfun(sTfun(X1,$o),$o),'const/sets/IN'(X1),X7),X5) & vAPP(sTfun(X1,$o),$o,vAPP(X1,sTfun(sTfun(X1,$o),$o),'const/sets/IN'(X1),X6),X5)) => (vAPP('type/nums/num','type/realax/real','const/realax/real_of_num',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')) = vAPP(X0,'type/realax/real',X3,vAPP(X1,X0,X4,X6)))) & vAPP(sTfun(X1,$o),$o,'const/sets/FINITE'(X1),X5)) => (vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),vAPP(sTfun(X1,$o),sTfun(X0,$o),vAPP(sTfun(X1,X0),sTfun(sTfun(X1,$o),sTfun(X0,$o)),'const/sets/IMAGE'(X1,X0),X4),X5)),X3) = vAPP(sTfun(X1,'type/realax/real'),'type/realax/real',vAPP(sTfun(X1,$o),sTfun(sTfun(X1,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X1),X5),vAPP(sTfun(X1,X0),sTfun(X1,'type/realax/real'),vAPP(sTfun(X0,'type/realax/real'),sTfun(sTfun(X1,X0),sTfun(X1,'type/realax/real')),'const/trivia/o'(X0,X1,'type/realax/real'),X3),X4))))),
% 0.22/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_IMAGE_NONZERO_')).
% 0.22/0.52 thf(f39,plain,(
% 0.22/0.52 (vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),$o,'const/iterate/monoidal'('type/realax/real'),'const/realax/real_add') = $true)),
% 0.22/0.52 inference(cnf_transformation,[],[f14])).
% 0.22/0.52 thf(f14,plain,(
% 0.22/0.52 (vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),$o,'const/iterate/monoidal'('type/realax/real'),'const/realax/real_add') = $true)),
% 0.22/0.52 inference(fool_elimination,[],[f13])).
% 0.22/0.52 thf(f13,plain,(
% 0.22/0.52 vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),$o,'const/iterate/monoidal'('type/realax/real'),'const/realax/real_add')),
% 0.22/0.52 inference(rectify,[],[f2])).
% 0.22/0.52 thf(f2,axiom,(
% 0.22/0.52 vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),$o,'const/iterate/monoidal'('type/realax/real'),'const/realax/real_add')),
% 0.22/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/MONOIDAL_REAL_ADD_')).
% 0.22/0.52 thf(f28,plain,(
% 0.22/0.52 ($true = vAPP(sTfun(sK1,$o),$o,'const/sets/FINITE'(sK1),sK5))),
% 0.22/0.52 inference(cnf_transformation,[],[f23])).
% 0.22/0.52 thf(f1308,plain,(
% 0.22/0.52 (vAPP(sK1,sK2,sK4,vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1,vAPP(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1),vAPP(sTfun(sK2,'type/realax/real'),sTfun(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1)),vAPP(sTfun(sK1,$o),sTfun(sTfun(sK2,'type/realax/real'),sTfun(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1))),sK6('type/realax/real',sK2,sK1),sK5),sK3),sK4),'const/realax/real_add')) != vAPP(sK1,sK2,sK4,vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1,vAPP(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1),vAPP(sTfun(sK2,'type/realax/real'),sTfun(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1)),vAPP(sTfun(sK1,$o),sTfun(sTfun(sK2,'type/realax/real'),sTfun(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1))),sK7('type/realax/real',sK2,sK1),sK5),sK3),sK4),'const/realax/real_add')))),
% 0.22/0.52 inference(unit_resulting_resolution,[],[f393,f392,f405,f390,f29])).
% 0.22/0.52 thf(f29,plain,(
% 0.22/0.52 ( ! [X6 : sK1,X5 : sK1] : ((vAPP(sK1,sK2,sK4,X5) != vAPP(sK1,sK2,sK4,X6)) | (vAPP('type/nums/num','type/realax/real','const/realax/real_of_num',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')) = vAPP(sK2,'type/realax/real',sK3,vAPP(sK1,sK2,sK4,X5))) | (X5 = X6) | ($true != vAPP(sTfun(sK1,$o),$o,vAPP(sK1,sTfun(sTfun(sK1,$o),$o),'const/sets/IN'(sK1),X6),sK5)) | ($true != vAPP(sTfun(sK1,$o),$o,vAPP(sK1,sTfun(sTfun(sK1,$o),$o),'const/sets/IN'(sK1),X5),sK5))) )),
% 0.22/0.52 inference(cnf_transformation,[],[f23])).
% 0.22/0.52 thf(f390,plain,(
% 0.22/0.52 (vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1,vAPP(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1),vAPP(sTfun(sK2,'type/realax/real'),sTfun(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1)),vAPP(sTfun(sK1,$o),sTfun(sTfun(sK2,'type/realax/real'),sTfun(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1))),sK6('type/realax/real',sK2,sK1),sK5),sK3),sK4),'const/realax/real_add') != vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1,vAPP(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1),vAPP(sTfun(sK2,'type/realax/real'),sTfun(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1)),vAPP(sTfun(sK1,$o),sTfun(sTfun(sK2,'type/realax/real'),sTfun(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1))),sK7('type/realax/real',sK2,sK1),sK5),sK3),sK4),'const/realax/real_add'))),
% 0.22/0.52 inference(unit_resulting_resolution,[],[f384,f35])).
% 0.22/0.52 thf(f35,plain,(
% 0.22/0.52 ( ! [X4 : $tType,X1 : $tType,X3 : $tType,X2 : X4 > X3,X0 : X1 > X1 > X1,X6 : X4 > $o,X5 : X3 > X1] : ((vAPP(sTfun(X1,sTfun(X1,X1)),X4,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4))),sK6(X1,X3,X4),X6),X5),X2),X0) != vAPP(sTfun(X1,sTfun(X1,X1)),X4,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4))),sK7(X1,X3,X4),X6),X5),X2),X0)) | ($true != vAPP(sTfun(X1,sTfun(X1,X1)),$o,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),$o),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),$o)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),$o))),sP0(X1,X3,X4),X6),X5),X2),X0))) )),
% 0.22/0.52 inference(cnf_transformation,[],[f27])).
% 0.22/0.52 thf(f405,plain,(
% 0.22/0.52 (vAPP('type/nums/num','type/realax/real','const/realax/real_of_num',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')) != vAPP(sK2,'type/realax/real',sK3,vAPP(sK1,sK2,sK4,vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1,vAPP(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1),vAPP(sTfun(sK2,'type/realax/real'),sTfun(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1)),vAPP(sTfun(sK1,$o),sTfun(sTfun(sK2,'type/realax/real'),sTfun(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1))),sK6('type/realax/real',sK2,sK1),sK5),sK3),sK4),'const/realax/real_add'))))),
% 0.22/0.52 inference(forward_demodulation,[],[f391,f31])).
% 0.22/0.52 thf(f31,plain,(
% 0.22/0.52 (vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),'type/realax/real','const/iterate/neutral'('type/realax/real'),'const/realax/real_add') = vAPP('type/nums/num','type/realax/real','const/realax/real_of_num',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')))),
% 0.22/0.52 inference(cnf_transformation,[],[f4])).
% 0.22/0.52 thf(f4,axiom,(
% 0.22/0.52 (vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),'type/realax/real','const/iterate/neutral'('type/realax/real'),'const/realax/real_add') = vAPP('type/nums/num','type/realax/real','const/realax/real_of_num',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')))),
% 0.22/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/NEUTRAL_REAL_ADD_')).
% 0.22/0.52 thf(f391,plain,(
% 0.22/0.52 (vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),'type/realax/real','const/iterate/neutral'('type/realax/real'),'const/realax/real_add') != vAPP(sK2,'type/realax/real',sK3,vAPP(sK1,sK2,sK4,vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1,vAPP(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1),vAPP(sTfun(sK2,'type/realax/real'),sTfun(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1)),vAPP(sTfun(sK1,$o),sTfun(sTfun(sK2,'type/realax/real'),sTfun(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1))),sK6('type/realax/real',sK2,sK1),sK5),sK3),sK4),'const/realax/real_add'))))),
% 0.22/0.52 inference(unit_resulting_resolution,[],[f384,f37])).
% 0.22/0.52 thf(f37,plain,(
% 0.22/0.52 ( ! [X4 : $tType,X1 : $tType,X3 : $tType,X2 : X4 > X3,X0 : X1 > X1 > X1,X6 : X4 > $o,X5 : X3 > X1] : ((vAPP(sTfun(X1,sTfun(X1,X1)),X1,'const/iterate/neutral'(X1),X0) != vAPP(X3,X1,X5,vAPP(X4,X3,X2,vAPP(sTfun(X1,sTfun(X1,X1)),X4,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4))),sK6(X1,X3,X4),X6),X5),X2),X0)))) | ($true != vAPP(sTfun(X1,sTfun(X1,X1)),$o,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),$o),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),$o)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),$o))),sP0(X1,X3,X4),X6),X5),X2),X0))) )),
% 0.22/0.52 inference(cnf_transformation,[],[f27])).
% 0.22/0.52 thf(f392,plain,(
% 0.22/0.52 ($true = vAPP(sTfun(sK1,$o),$o,vAPP(sK1,sTfun(sTfun(sK1,$o),$o),'const/sets/IN'(sK1),vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1,vAPP(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1),vAPP(sTfun(sK2,'type/realax/real'),sTfun(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1)),vAPP(sTfun(sK1,$o),sTfun(sTfun(sK2,'type/realax/real'),sTfun(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1))),sK7('type/realax/real',sK2,sK1),sK5),sK3),sK4),'const/realax/real_add')),sK5))),
% 0.22/0.52 inference(unit_resulting_resolution,[],[f384,f34])).
% 0.22/0.52 thf(f34,plain,(
% 0.22/0.52 ( ! [X4 : $tType,X1 : $tType,X3 : $tType,X2 : X4 > X3,X0 : X1 > X1 > X1,X6 : X4 > $o,X5 : X3 > X1] : (($true != vAPP(sTfun(X1,sTfun(X1,X1)),$o,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),$o),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),$o)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),$o))),sP0(X1,X3,X4),X6),X5),X2),X0)) | ($true = vAPP(sTfun(X4,$o),$o,vAPP(X4,sTfun(sTfun(X4,$o),$o),'const/sets/IN'(X4),vAPP(sTfun(X1,sTfun(X1,X1)),X4,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4))),sK7(X1,X3,X4),X6),X5),X2),X0)),X6))) )),
% 0.22/0.52 inference(cnf_transformation,[],[f27])).
% 0.22/0.52 thf(f393,plain,(
% 0.22/0.52 ($true = vAPP(sTfun(sK1,$o),$o,vAPP(sK1,sTfun(sTfun(sK1,$o),$o),'const/sets/IN'(sK1),vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1,vAPP(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1),vAPP(sTfun(sK2,'type/realax/real'),sTfun(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1)),vAPP(sTfun(sK1,$o),sTfun(sTfun(sK2,'type/realax/real'),sTfun(sTfun(sK1,sK2),sTfun(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sK1))),sK6('type/realax/real',sK2,sK1),sK5),sK3),sK4),'const/realax/real_add')),sK5))),
% 0.22/0.52 inference(unit_resulting_resolution,[],[f384,f33])).
% 0.22/0.52 thf(f33,plain,(
% 0.22/0.52 ( ! [X4 : $tType,X1 : $tType,X3 : $tType,X2 : X4 > X3,X0 : X1 > X1 > X1,X6 : X4 > $o,X5 : X3 > X1] : (($true != vAPP(sTfun(X1,sTfun(X1,X1)),$o,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),$o),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),$o)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),$o))),sP0(X1,X3,X4),X6),X5),X2),X0)) | ($true = vAPP(sTfun(X4,$o),$o,vAPP(X4,sTfun(sTfun(X4,$o),$o),'const/sets/IN'(X4),vAPP(sTfun(X1,sTfun(X1,X1)),X4,vAPP(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4),vAPP(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4)),vAPP(sTfun(X4,$o),sTfun(sTfun(X3,X1),sTfun(sTfun(X4,X3),sTfun(sTfun(X1,sTfun(X1,X1)),X4))),sK6(X1,X3,X4),X6),X5),X2),X0)),X6))) )),
% 0.22/0.52 inference(cnf_transformation,[],[f27])).
% 0.22/0.52 % SZS output end Proof for theBenchmark
% 0.22/0.52 % (29000)------------------------------
% 0.22/0.52 % (29000)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.52 % (29000)Termination reason: Refutation
% 0.22/0.52
% 0.22/0.52 % (29000)Memory used [KB]: 1715
% 0.22/0.52 % (29000)Time elapsed: 0.130 s
% 0.22/0.52 % (29000)Instructions burned: 318 (million)
% 0.22/0.52 % (28984)Success in time 0.162 s
%------------------------------------------------------------------------------