%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV261^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:39:14 AM UTC 2026
% Result : Theorem 0.19s 0.29s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV261^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.19 % Computer : n004.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Tue Sep 29 15:28:22 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.22 Running first-order model finding
% 0.06/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.29 % (1429339)Will run a generic schedule for satisfiability detection.
% 0.19/0.29 % (1429346)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2676808754:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.29 % (1429345)% WARNING: option uhcvi not known.
% 0.19/0.29 % (1429345)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=956378649:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.29 % (1429349)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2804472228:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.29 % (1429347)dis+10_1_sil=32000:sp=arity:random_seed=1524404168:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.29 % (1429348)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3657969926:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.29 % (1429345)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.29 % (1429348)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.29 % (1429345)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.29 % (1429344)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3901851985_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.29 % (1429350)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2713892252:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.29 % (1429349) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1429339-1429349"...
% 0.19/0.29 % Exception at run slice level
% 0.19/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.29 % (1429349)...printing done.
% 0.19/0.29 % (1429349)Refutation found. Thanks to Tanya!
% 0.19/0.29 % SZS status Theorem for theBenchmark
% 0.19/0.29 % SZS output start Proof for theBenchmark
% 0.19/0.29 thf(type_def_5, type, a: $tType).
% 0.19/0.29 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.29 thf(func_def_3, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.29 thf(func_def_4, type, vNOT: ($o > $o)).
% 0.19/0.29 thf(func_def_5, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.19/0.29 thf(func_def_6, type, vAND: ($o > $o > $o)).
% 0.19/0.29 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.29 thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 0.19/0.29 thf(func_def_9, type, sP0: $o).
% 0.19/0.29 thf(func_def_10, type, sP1: $o).
% 0.19/0.29 thf(func_def_11, type, sP2: $o).
% 0.19/0.29 thf(func_def_12, type, sK3: (a > $o)).
% 0.19/0.29 thf(func_def_13, type, sK4: ((a > $o) > $o)).
% 0.19/0.29 thf(func_def_14, type, sK5: (a > $o)).
% 0.19/0.29 thf(func_def_15, type, sK6: (a > $o)).
% 0.19/0.29 thf(func_def_16, type, sK7: (a > $o)).
% 0.19/0.29 thf(func_def_17, type, sK8: (a > $o)).
% 0.19/0.29 thf(func_def_18, type, sK9: (a > $o)).
% 0.19/0.29 thf(func_def_20, type, sK11: a).
% 0.19/0.29 thf(func_def_21, type, sK12: a).
% 0.19/0.29 thf(func_def_22, type, sK13: a).
% 0.19/0.29 thf(func_def_23, type, sK14: a).
% 0.19/0.29 thf(func_def_24, type, sK15: a).
% 0.19/0.29 thf(func_def_25, type, sK16: a).
% 0.19/0.29 thf(func_def_26, type, sK17: (a > a > $o)).
% 0.19/0.29 thf(func_def_27, type, sK18: a).
% 0.19/0.29 thf(func_def_28, type, sK19: (a > $o)).
% 0.19/0.29 thf(func_def_29, type, sK20: a).
% 0.19/0.29 thf(func_def_30, type, sK21: (a > $o)).
% 0.19/0.29 thf(f1,conjecture,(
% 0.19/0.29 ! [X5 : (a > $o),X6 : (a > $o),X4 : (a > $o)] : (((X4 = (^[X1 : a] : ((X6 @ X1) & (X5 @ X1)))) & ((X6 = (^[X2 : a] : (~$false))) | (X6 = (^[X2 : a] : ($false)))) & ((X5 = (^[X2 : a] : (~$false))) | (X5 = (^[X2 : a] : ($false))))) => ((X4 = (^[X2 : a] : (~$false))) | (X4 = (^[X2 : a] : ($false))))) & ! [X3 : ((a > $o) > $o),X0 : (a > $o)] : (((X0 = (^[X1 : a] : (? [X4 : (a > $o)] : ((X4 @ X1) & (X3 @ X4))))) & ! [X1 : (a > $o)] : ((X3 @ X1) => ((X1 = (^[X2 : a] : (~$false))) | (X1 = (^[X2 : a] : ($false)))))) => ((X0 = (^[X2 : a] : (~$false))) | (X0 = (^[X2 : a] : ($false))))) & ! [X0 : (a > $o)] : ((X0 = (^[X1 : a] : (~$false))) => ((X0 = (^[X2 : a] : (~$false))) | (X0 = (^[X2 : a] : ($false))))) & ! [X0 : (a > $o)] : ((X0 = (^[X1 : a] : ($false))) => ((X0 = (^[X2 : a] : (~$false))) | (X0 = (^[X2 : a] : ($false)))))),
% 0.19/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cINDISCRETE_TOPOLOGY_pme)).
% 0.19/0.29 thf(f2,negated_conjecture,(
% 0.19/0.29 ~(! [X5 : (a > $o),X6 : (a > $o),X4 : (a > $o)] : (((X4 = (^[X1 : a] : ((X6 @ X1) & (X5 @ X1)))) & ((X6 = (^[X2 : a] : (~$false))) | (X6 = (^[X2 : a] : ($false)))) & ((X5 = (^[X2 : a] : (~$false))) | (X5 = (^[X2 : a] : ($false))))) => ((X4 = (^[X2 : a] : (~$false))) | (X4 = (^[X2 : a] : ($false))))) & ! [X3 : ((a > $o) > $o),X0 : (a > $o)] : (((X0 = (^[X1 : a] : (? [X4 : (a > $o)] : ((X4 @ X1) & (X3 @ X4))))) & ! [X1 : (a > $o)] : ((X3 @ X1) => ((X1 = (^[X2 : a] : (~$false))) | (X1 = (^[X2 : a] : ($false)))))) => ((X0 = (^[X2 : a] : (~$false))) | (X0 = (^[X2 : a] : ($false))))) & ! [X0 : (a > $o)] : ((X0 = (^[X1 : a] : (~$false))) => ((X0 = (^[X2 : a] : (~$false))) | (X0 = (^[X2 : a] : ($false))))) & ! [X0 : (a > $o)] : ((X0 = (^[X1 : a] : ($false))) => ((X0 = (^[X2 : a] : (~$false))) | (X0 = (^[X2 : a] : ($false))))))),
% 0.19/0.29 inference(negated_conjecture,[status(cth)],[f1])).
% 0.19/0.29 thf(f3,plain,(
% 0.19/0.29 ~(! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (((X2 = (^[X3 : a] : ((X1 @ X3) & (X0 @ X3)))) & ((X1 = (^[X4 : a] : (~$false))) | (X1 = (^[X5 : a] : ($false)))) & ((X0 = (^[X6 : a] : (~$false))) | (X0 = (^[X7 : a] : ($false))))) => ((X2 = (^[X8 : a] : (~$false))) | (X2 = (^[X9 : a] : ($false))))) & ! [X10 : ((a > $o) > $o),X11 : (a > $o)] : (((X11 = (^[X12 : a] : (? [X13 : (a > $o)] : ((X13 @ X12) & (X10 @ X13))))) & ! [X14 : (a > $o)] : ((X10 @ X14) => ((X14 = (^[X15 : a] : (~$false))) | (X14 = (^[X16 : a] : ($false)))))) => ((X11 = (^[X17 : a] : (~$false))) | (X11 = (^[X18 : a] : ($false))))) & ! [X19 : (a > $o)] : ((X19 = (^[X20 : a] : (~$false))) => ((X19 = (^[X21 : a] : (~$false))) | (X19 = (^[X22 : a] : ($false))))) & ! [X23 : (a > $o)] : ((X23 = (^[X24 : a] : ($false))) => ((X23 = (^[X25 : a] : (~$false))) | (X23 = (^[X26 : a] : ($false))))))),
% 0.19/0.29 inference(rectify,[],[f2])).
% 0.19/0.29 thf(f4,plain,(
% 0.19/0.29 ~(! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) = X2) & (((^[Y0 : a]: (~ $false)) = X1) | ((^[Y0 : a]: ($false)) = X1)) & (((^[Y0 : a]: (~ $false)) = X0) | ((^[Y0 : a]: ($false)) = X0))) => (((^[Y0 : a]: (~ $false)) = X2) | ((^[Y0 : a]: ($false)) = X2))) & ! [X10 : ((a > $o) > $o),X11 : (a > $o)] : ((((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((X10 @ Y1) & (Y1 @ Y0))))) = X11) & ! [X14 : (a > $o)] : ((((X10 @ X14)) = $true) => (((^[Y0 : a]: (~ $false)) = X14) | ((^[Y0 : a]: ($false)) = X14)))) => (((^[Y0 : a]: (~ $false)) = X11) | ((^[Y0 : a]: ($false)) = X11))) & ! [X19 : (a > $o)] : (((^[Y0 : a]: (~ $false)) = X19) => (((^[Y0 : a]: (~ $false)) = X19) | ((^[Y0 : a]: ($false)) = X19))) & ! [X23 : (a > $o)] : (((^[Y0 : a]: ($false)) = X23) => (((^[Y0 : a]: (~ $false)) = X23) | ((^[Y0 : a]: ($false)) = X23))))),
% 0.19/0.29 inference(fool_elimination,[],[f3])).
% 0.19/0.29 thf(f5,plain,(
% 0.19/0.29 ~(! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) = X2) & (((^[Y0 : a]: (~ $false)) = X1) | ((^[Y0 : a]: ($false)) = X1)) & (((^[Y0 : a]: (~ $false)) = X0) | ((^[Y0 : a]: ($false)) = X0))) => (((^[Y0 : a]: (~ $false)) = X2) | ((^[Y0 : a]: ($false)) = X2))) & ! [X3 : ((a > $o) > $o),X4 : (a > $o)] : ((((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((X3 @ Y1) & (Y1 @ Y0))))) = X4) & ! [X5 : (a > $o)] : (($true = ((X3 @ X5))) => (((^[Y0 : a]: (~ $false)) = X5) | ((^[Y0 : a]: ($false)) = X5)))) => (((^[Y0 : a]: (~ $false)) = X4) | ((^[Y0 : a]: ($false)) = X4))) & ! [X6 : (a > $o)] : (((^[Y0 : a]: (~ $false)) = X6) => (((^[Y0 : a]: (~ $false)) = X6) | ((^[Y0 : a]: ($false)) = X6))) & ! [X7 : (a > $o)] : (((^[Y0 : a]: ($false)) = X7) => (((^[Y0 : a]: (~ $false)) = X7) | ((^[Y0 : a]: ($false)) = X7))))),
% 0.19/0.29 inference(rectify,[],[f4])).
% 0.19/0.29 thf(f6,plain,(
% 0.19/0.29 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((((^[Y0 : a]: (~ $false)) != X2) & ((^[Y0 : a]: ($false)) != X2)) & (((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) = X2) & (((^[Y0 : a]: (~ $false)) = X1) | ((^[Y0 : a]: ($false)) = X1)) & (((^[Y0 : a]: (~ $false)) = X0) | ((^[Y0 : a]: ($false)) = X0)))) | ? [X3 : ((a > $o) > $o),X4 : (a > $o)] : ((((^[Y0 : a]: (~ $false)) != X4) & ((^[Y0 : a]: ($false)) != X4)) & (((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((X3 @ Y1) & (Y1 @ Y0))))) = X4) & ! [X5 : (a > $o)] : ((((^[Y0 : a]: (~ $false)) = X5) | ((^[Y0 : a]: ($false)) = X5)) | ($true != ((X3 @ X5)))))) | ? [X6 : (a > $o)] : ((((^[Y0 : a]: (~ $false)) != X6) & ((^[Y0 : a]: ($false)) != X6)) & ((^[Y0 : a]: (~ $false)) = X6)) | ? [X7 : (a > $o)] : ((((^[Y0 : a]: (~ $false)) != X7) & ((^[Y0 : a]: ($false)) != X7)) & ((^[Y0 : a]: ($false)) = X7))),
% 0.19/0.29 inference(ennf_transformation,[],[f5])).
% 0.19/0.29 thf(f7,plain,(
% 0.19/0.29 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (((^[Y0 : a]: (~ $false)) != X2) & ((^[Y0 : a]: ($false)) != X2) & ((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) = X2) & (((^[Y0 : a]: (~ $false)) = X1) | ((^[Y0 : a]: ($false)) = X1)) & (((^[Y0 : a]: (~ $false)) = X0) | ((^[Y0 : a]: ($false)) = X0))) | ? [X3 : ((a > $o) > $o),X4 : (a > $o)] : (((^[Y0 : a]: (~ $false)) != X4) & ((^[Y0 : a]: ($false)) != X4) & ((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((X3 @ Y1) & (Y1 @ Y0))))) = X4) & ! [X5 : (a > $o)] : (((^[Y0 : a]: (~ $false)) = X5) | ((^[Y0 : a]: ($false)) = X5) | ($true != ((X3 @ X5))))) | ? [X6 : (a > $o)] : (((^[Y0 : a]: (~ $false)) != X6) & ((^[Y0 : a]: ($false)) != X6) & ((^[Y0 : a]: (~ $false)) = X6)) | ? [X7 : (a > $o)] : (((^[Y0 : a]: (~ $false)) != X7) & ((^[Y0 : a]: ($false)) != X7) & ((^[Y0 : a]: ($false)) = X7))),
% 0.19/0.29 inference(flattening,[],[f6])).
% 0.19/0.29 thf(f8,definition,(
% 0.19/0.29 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (((^[Y0 : a]: (~ $false)) != X2) & ((^[Y0 : a]: ($false)) != X2) & ((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) = X2) & (((^[Y0 : a]: (~ $false)) = X1) | ((^[Y0 : a]: ($false)) = X1)) & (((^[Y0 : a]: (~ $false)) = X0) | ((^[Y0 : a]: ($false)) = X0))) | ~ ($true = sP0)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.19/0.29 thf(f9,definition,(
% 0.19/0.29 ? [X3 : ((a > $o) > $o),X4 : (a > $o)] : (((^[Y0 : a]: (~ $false)) != X4) & ((^[Y0 : a]: ($false)) != X4) & ((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((X3 @ Y1) & (Y1 @ Y0))))) = X4) & ! [X5 : (a > $o)] : (((^[Y0 : a]: (~ $false)) = X5) | ((^[Y0 : a]: ($false)) = X5) | ($true != ((X3 @ X5))))) | ~ ($true = sP1)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.19/0.29 thf(f10,definition,(
% 0.19/0.29 ? [X7 : (a > $o)] : (((^[Y0 : a]: (~ $false)) != X7) & ((^[Y0 : a]: ($false)) != X7) & ((^[Y0 : a]: ($false)) = X7)) | ~ ($true = sP2)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.19/0.29 thf(f11,plain,(
% 0.19/0.29 ($true = sP0) | ($true = sP1) | ? [X6 : (a > $o)] : (((^[Y0 : a]: (~ $false)) != X6) & ((^[Y0 : a]: ($false)) != X6) & ((^[Y0 : a]: (~ $false)) = X6)) | ($true = sP2)),
% 0.19/0.29 inference(definition_folding,[],[f7,f10,f9,f8])).
% 0.19/0.29 thf(f12,plain,(
% 0.19/0.29 ? [X7 : (a > $o)] : (((^[Y0 : a]: (~ $false)) != X7) & ((^[Y0 : a]: ($false)) != X7) & ((^[Y0 : a]: ($false)) = X7)) | ($true != sP2)),
% 0.19/0.29 inference(nnf_transformation,[],[f10])).
% 0.19/0.29 thf(f13,plain,(
% 0.19/0.29 ? [X0 : (a > $o)] : (((^[Y0 : a]: (~ $false)) != X0) & ((^[Y0 : a]: ($false)) != X0) & ((^[Y0 : a]: ($false)) = X0)) | ($true != sP2)),
% 0.19/0.29 inference(rectify,[],[f12])).
% 0.19/0.29 thf(f14,plain,(
% 0.19/0.29 (((^[Y0 : a]: (~ $false)) != sK3) & ((^[Y0 : a]: ($false)) != sK3) & ((^[Y0 : a]: ($false)) = sK3)) | ($true != sP2)),
% 0.19/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f13])).
% 0.19/0.29 thf(f15,plain,(
% 0.19/0.29 ? [X3 : ((a > $o) > $o),X4 : (a > $o)] : (((^[Y0 : a]: (~ $false)) != X4) & ((^[Y0 : a]: ($false)) != X4) & ((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((X3 @ Y1) & (Y1 @ Y0))))) = X4) & ! [X5 : (a > $o)] : (((^[Y0 : a]: (~ $false)) = X5) | ((^[Y0 : a]: ($false)) = X5) | ($true != ((X3 @ X5))))) | ($true != sP1)),
% 0.19/0.29 inference(nnf_transformation,[],[f9])).
% 0.19/0.29 thf(f16,plain,(
% 0.19/0.29 ? [X0 : ((a > $o) > $o),X1 : (a > $o)] : (((^[Y0 : a]: (~ $false)) != X1) & ((^[Y0 : a]: ($false)) != X1) & ((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((X0 @ Y1) & (Y1 @ Y0))))) = X1) & ! [X2 : (a > $o)] : (((^[Y0 : a]: (~ $false)) = X2) | ((^[Y0 : a]: ($false)) = X2) | ($true != ((X0 @ X2))))) | ($true != sP1)),
% 0.19/0.29 inference(rectify,[],[f15])).
% 0.19/0.29 thf(f17,plain,(
% 0.19/0.29 (((^[Y0 : a]: (~ $false)) != sK5) & ((^[Y0 : a]: ($false)) != sK5) & (sK5 = (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((sK4 @ Y1) & (Y1 @ Y0)))))) & ! [X2 : (a > $o)] : (((^[Y0 : a]: (~ $false)) = X2) | ((^[Y0 : a]: ($false)) = X2) | ($true != ((sK4 @ X2))))) | ($true != sP1)),
% 0.19/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f16])).
% 0.19/0.29 thf(f18,plain,(
% 0.19/0.29 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (((^[Y0 : a]: (~ $false)) != X2) & ((^[Y0 : a]: ($false)) != X2) & ((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) = X2) & (((^[Y0 : a]: (~ $false)) = X1) | ((^[Y0 : a]: ($false)) = X1)) & (((^[Y0 : a]: (~ $false)) = X0) | ((^[Y0 : a]: ($false)) = X0))) | ($true != sP0)),
% 0.19/0.29 inference(nnf_transformation,[],[f8])).
% 0.19/0.29 thf(f19,plain,(
% 0.19/0.29 (((^[Y0 : a]: (~ $false)) != sK8) & ((^[Y0 : a]: ($false)) != sK8) & (sK8 = (^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0)))) & (((^[Y0 : a]: (~ $false)) = sK7) | ((^[Y0 : a]: ($false)) = sK7)) & (((^[Y0 : a]: (~ $false)) = sK6) | ((^[Y0 : a]: ($false)) = sK6))) | ($true != sP0)),
% 0.19/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8)],[f18])).
% 0.19/0.29 thf(f20,plain,(
% 0.19/0.29 ($true = sP0) | ($true = sP1) | ? [X0 : (a > $o)] : (((^[Y0 : a]: (~ $false)) != X0) & ((^[Y0 : a]: ($false)) != X0) & ((^[Y0 : a]: (~ $false)) = X0)) | ($true = sP2)),
% 0.19/0.29 inference(rectify,[],[f11])).
% 0.19/0.29 thf(f21,plain,(
% 0.19/0.29 ($true = sP0) | ($true = sP1) | (((^[Y0 : a]: (~ $false)) != sK9) & ((^[Y0 : a]: ($false)) != sK9) & ((^[Y0 : a]: (~ $false)) = sK9)) | ($true = sP2)),
% 0.19/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X0,sK9)],[f20])).
% 0.19/0.29 thf(f22,plain,(
% 0.19/0.29 ((^[Y0 : a]: ($false)) = sK3) | ($true != sP2)),
% 0.19/0.29 inference(cnf_transformation,[],[f14])).
% 0.19/0.29 thf(f23,plain,(
% 0.19/0.29 ((^[Y0 : a]: ($false)) != sK3) | ($true != sP2)),
% 0.19/0.29 inference(cnf_transformation,[],[f14])).
% 0.19/0.29 thf(f25,plain,(
% 0.19/0.29 ( ! [X2 : (a > $o)] : (((^[Y0 : a]: (~ $false)) = X2) | ((^[Y0 : a]: ($false)) = X2) | ($true != ((sK4 @ X2))) | ($true != sP1)) )),
% 0.19/0.29 inference(cnf_transformation,[],[f17])).
% 0.19/0.29 thf(f26,plain,(
% 0.19/0.29 (sK5 = (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((sK4 @ Y1) & (Y1 @ Y0)))))) | ($true != sP1)),
% 0.19/0.29 inference(cnf_transformation,[],[f17])).
% 0.19/0.29 thf(f27,plain,(
% 0.19/0.29 ((^[Y0 : a]: ($false)) != sK5) | ($true != sP1)),
% 0.19/0.29 inference(cnf_transformation,[],[f17])).
% 0.19/0.29 thf(f28,plain,(
% 0.19/0.29 ((^[Y0 : a]: (~ $false)) != sK5) | ($true != sP1)),
% 0.19/0.29 inference(cnf_transformation,[],[f17])).
% 0.19/0.29 thf(f29,plain,(
% 0.19/0.29 ((^[Y0 : a]: (~ $false)) = sK6) | ((^[Y0 : a]: ($false)) = sK6) | ($true != sP0)),
% 0.19/0.29 inference(cnf_transformation,[],[f19])).
% 0.19/0.29 thf(f30,plain,(
% 0.19/0.29 ((^[Y0 : a]: (~ $false)) = sK7) | ((^[Y0 : a]: ($false)) = sK7) | ($true != sP0)),
% 0.19/0.29 inference(cnf_transformation,[],[f19])).
% 0.19/0.29 thf(f31,plain,(
% 0.19/0.29 (sK8 = (^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0)))) | ($true != sP0)),
% 0.19/0.29 inference(cnf_transformation,[],[f19])).
% 0.19/0.29 thf(f32,plain,(
% 0.19/0.29 ((^[Y0 : a]: ($false)) != sK8) | ($true != sP0)),
% 0.19/0.29 inference(cnf_transformation,[],[f19])).
% 0.19/0.29 thf(f33,plain,(
% 0.19/0.29 ((^[Y0 : a]: (~ $false)) != sK8) | ($true != sP0)),
% 0.19/0.29 inference(cnf_transformation,[],[f19])).
% 0.19/0.29 thf(f34,plain,(
% 0.19/0.29 ($true = sP0) | ($true = sP1) | ((^[Y0 : a]: (~ $false)) = sK9) | ($true = sP2)),
% 0.19/0.29 inference(cnf_transformation,[],[f21])).
% 0.19/0.29 thf(f36,plain,(
% 0.19/0.29 ($true = sP0) | ($true = sP1) | ((^[Y0 : a]: (~ $false)) != sK9) | ($true = sP2)),
% 0.19/0.29 inference(cnf_transformation,[],[f21])).
% 0.19/0.29 thf(f37,definition,(
% 0.19/0.29 ($false != $true)),
% 0.19/0.29 introduced(theory,[fool_distinctness_axiom])).
% 0.19/0.29 thf(f39,plain,(
% 0.19/0.29 ($true = sP0) | ($true = sP1) | (sK9 = (^[Y0 : a]: ($true))) | ($true = sP2)),
% 0.19/0.29 inference(boolean_simplification,[],[f34])).
% 0.19/0.29 thf(f40,plain,(
% 0.19/0.29 ($true = sP0) | ($true = sP1) | (sK9 != (^[Y0 : a]: ($true))) | ($true = sP2)),
% 0.19/0.29 inference(boolean_simplification,[],[f36])).
% 0.19/0.29 thf(f41,plain,(
% 0.19/0.29 (sK6 = (^[Y0 : a]: ($true))) | ((^[Y0 : a]: ($false)) = sK6) | ($true != sP0)),
% 0.19/0.29 inference(boolean_simplification,[],[f29])).
% 0.19/0.29 thf(f42,plain,(
% 0.19/0.29 (sK7 = (^[Y0 : a]: ($true))) | ((^[Y0 : a]: ($false)) = sK7) | ($true != sP0)),
% 0.19/0.29 inference(boolean_simplification,[],[f30])).
% 0.19/0.29 thf(f43,plain,(
% 0.19/0.29 (sK8 != (^[Y0 : a]: ($true))) | ($true != sP0)),
% 0.19/0.29 inference(boolean_simplification,[],[f33])).
% 0.19/0.29 thf(f44,plain,(
% 0.19/0.29 ( ! [X2 : (a > $o)] : (((^[Y0 : a]: ($true)) = X2) | ((^[Y0 : a]: ($false)) = X2) | ($true != ((sK4 @ X2))) | ($true != sP1)) )),
% 0.19/0.29 inference(boolean_simplification,[],[f25])).
% 0.19/0.29 thf(f45,plain,(
% 0.19/0.29 (sK5 != (^[Y0 : a]: ($true))) | ($true != sP1)),
% 0.19/0.29 inference(boolean_simplification,[],[f28])).
% 0.19/0.29 thf(f48,definition,(
% 0.19/0.29 spl10_1 <=> ($true = sP2)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition])).
% 0.19/0.29 thf(f52,definition,(
% 0.19/0.29 spl10_2 <=> (sK9 = (^[Y0 : a]: ($true)))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition])).
% 0.19/0.29 thf(f56,definition,(
% 0.19/0.29 spl10_3 <=> ($true = sP1)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition])).
% 0.19/0.29 thf(f60,definition,(
% 0.19/0.29 spl10_4 <=> ($true = sP0)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition])).
% 0.19/0.29 thf(f63,plain,(
% 0.19/0.29 spl10_1 | spl10_2 | spl10_3 | spl10_4),
% 0.19/0.29 inference(avatar_split_clause,[],[f39,f60,f56,f52,f48])).
% 0.19/0.29 thf(f69,plain,(
% 0.19/0.29 spl10_1 | ~spl10_2 | spl10_3 | spl10_4),
% 0.19/0.29 inference(avatar_split_clause,[],[f40,f60,f56,f52,f48])).
% 0.19/0.29 thf(f71,definition,(
% 0.19/0.29 spl10_6 <=> ((^[Y0 : a]: ($false)) = sK6)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition])).
% 0.19/0.29 thf(f73,plain,(
% 0.19/0.29 ((^[Y0 : a]: ($false)) = sK6) | ~spl10_6),
% 0.19/0.29 inference(avatar_component_clause,[],[f71])).
% 0.19/0.29 thf(f75,definition,(
% 0.19/0.29 spl10_7 <=> (sK6 = (^[Y0 : a]: ($true)))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl10_7])],[avatar_definition])).
% 0.19/0.29 thf(f77,plain,(
% 0.19/0.29 (sK6 = (^[Y0 : a]: ($true))) | ~spl10_7),
% 0.19/0.29 inference(avatar_component_clause,[],[f75])).
% 0.19/0.29 thf(f78,plain,(
% 0.19/0.29 ~spl10_4 | spl10_6 | spl10_7),
% 0.19/0.29 inference(avatar_split_clause,[],[f41,f75,f71,f60])).
% 0.19/0.29 thf(f80,definition,(
% 0.19/0.29 spl10_8 <=> ((^[Y0 : a]: ($false)) = sK7)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl10_8])],[avatar_definition])).
% 0.19/0.29 thf(f82,plain,(
% 0.19/0.29 ((^[Y0 : a]: ($false)) = sK7) | ~spl10_8),
% 0.19/0.29 inference(avatar_component_clause,[],[f80])).
% 0.19/0.29 thf(f84,definition,(
% 0.19/0.29 spl10_9 <=> (sK7 = (^[Y0 : a]: ($true)))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl10_9])],[avatar_definition])).
% 0.19/0.29 thf(f86,plain,(
% 0.19/0.29 (sK7 = (^[Y0 : a]: ($true))) | ~spl10_9),
% 0.19/0.29 inference(avatar_component_clause,[],[f84])).
% 0.19/0.29 thf(f87,plain,(
% 0.19/0.29 ~spl10_4 | spl10_8 | spl10_9),
% 0.19/0.29 inference(avatar_split_clause,[],[f42,f84,f80,f60])).
% 0.19/0.29 thf(f89,definition,(
% 0.19/0.29 spl10_10 <=> (sK8 = (^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0))))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl10_10])],[avatar_definition])).
% 0.19/0.29 thf(f91,plain,(
% 0.19/0.29 (sK8 = (^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0)))) | ~spl10_10),
% 0.19/0.29 inference(avatar_component_clause,[],[f89])).
% 0.19/0.29 thf(f92,plain,(
% 0.19/0.29 ~spl10_4 | spl10_10),
% 0.19/0.29 inference(avatar_split_clause,[],[f31,f89,f60])).
% 0.19/0.29 thf(f94,definition,(
% 0.19/0.29 spl10_11 <=> ((^[Y0 : a]: ($false)) = sK8)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl10_11])],[avatar_definition])).
% 0.19/0.29 thf(f96,plain,(
% 0.19/0.29 ((^[Y0 : a]: ($false)) != sK8) | spl10_11),
% 0.19/0.29 inference(avatar_component_clause,[],[f94])).
% 0.19/0.29 thf(f97,plain,(
% 0.19/0.29 ~spl10_4 | ~spl10_11),
% 0.19/0.29 inference(avatar_split_clause,[],[f32,f94,f60])).
% 0.19/0.29 thf(f99,definition,(
% 0.19/0.29 spl10_12 <=> (sK8 = (^[Y0 : a]: ($true)))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl10_12])],[avatar_definition])).
% 0.19/0.29 thf(f101,plain,(
% 0.19/0.29 (sK8 != (^[Y0 : a]: ($true))) | spl10_12),
% 0.19/0.29 inference(avatar_component_clause,[],[f99])).
% 0.19/0.29 thf(f102,plain,(
% 0.19/0.29 ~spl10_4 | ~spl10_12),
% 0.19/0.29 inference(avatar_split_clause,[],[f43,f99,f60])).
% 0.19/0.29 thf(f104,definition,(
% 0.19/0.29 spl10_13 <=> ! [X2 : (a > $o)] : (((^[Y0 : a]: ($true)) = X2) | ($true != ((sK4 @ X2))) | ((^[Y0 : a]: ($false)) = X2))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl10_13])],[avatar_definition])).
% 0.19/0.29 thf(f105,plain,(
% 0.19/0.29 ( ! [X2 : (a > $o)] : (($true != ((sK4 @ X2))) | ((^[Y0 : a]: ($true)) = X2) | ((^[Y0 : a]: ($false)) = X2)) ) | ~spl10_13),
% 0.19/0.29 inference(avatar_component_clause,[],[f104])).
% 0.19/0.29 thf(f106,plain,(
% 0.19/0.29 ~spl10_3 | spl10_13),
% 0.19/0.29 inference(avatar_split_clause,[],[f44,f104,f56])).
% 0.19/0.29 thf(f108,definition,(
% 0.19/0.29 spl10_14 <=> (sK5 = (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((sK4 @ Y1) & (Y1 @ Y0))))))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl10_14])],[avatar_definition])).
% 0.19/0.29 thf(f110,plain,(
% 0.19/0.29 (sK5 = (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((sK4 @ Y1) & (Y1 @ Y0)))))) | ~spl10_14),
% 0.19/0.29 inference(avatar_component_clause,[],[f108])).
% 0.19/0.29 thf(f111,plain,(
% 0.19/0.29 ~spl10_3 | spl10_14),
% 0.19/0.29 inference(avatar_split_clause,[],[f26,f108,f56])).
% 0.19/0.29 thf(f113,definition,(
% 0.19/0.29 spl10_15 <=> ((^[Y0 : a]: ($false)) = sK5)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl10_15])],[avatar_definition])).
% 0.19/0.29 thf(f115,plain,(
% 0.19/0.29 ((^[Y0 : a]: ($false)) != sK5) | spl10_15),
% 0.19/0.29 inference(avatar_component_clause,[],[f113])).
% 0.19/0.29 thf(f116,plain,(
% 0.19/0.29 ~spl10_3 | ~spl10_15),
% 0.19/0.29 inference(avatar_split_clause,[],[f27,f113,f56])).
% 0.19/0.29 thf(f118,definition,(
% 0.19/0.29 spl10_16 <=> (sK5 = (^[Y0 : a]: ($true)))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl10_16])],[avatar_definition])).
% 0.19/0.29 thf(f120,plain,(
% 0.19/0.29 (sK5 != (^[Y0 : a]: ($true))) | spl10_16),
% 0.19/0.29 inference(avatar_component_clause,[],[f118])).
% 0.19/0.29 thf(f121,plain,(
% 0.19/0.29 ~spl10_3 | ~spl10_16),
% 0.19/0.29 inference(avatar_split_clause,[],[f45,f118,f56])).
% 0.19/0.29 thf(f123,definition,(
% 0.19/0.29 spl10_17 <=> ((^[Y0 : a]: ($false)) = sK3)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl10_17])],[avatar_definition])).
% 0.19/0.29 thf(f126,plain,(
% 0.19/0.29 ~spl10_1 | spl10_17),
% 0.19/0.29 inference(avatar_split_clause,[],[f22,f123,f48])).
% 0.19/0.29 thf(f127,plain,(
% 0.19/0.29 ~spl10_1 | ~spl10_17),
% 0.19/0.29 inference(avatar_split_clause,[],[f23,f123,f48])).
% 0.19/0.29 thf(f133,plain,(
% 0.19/0.29 ((^[Y0 : a]: ($false)) != (^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0)))) | (~spl10_10 | spl10_11)),
% 0.19/0.29 inference(forward_demodulation,[],[f96,f91])).
% 0.19/0.29 thf(f134,plain,(
% 0.19/0.29 ((^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0))) != (^[Y0 : a]: ($true))) | (~spl10_10 | spl10_12)),
% 0.19/0.29 inference(forward_demodulation,[],[f101,f91])).
% 0.19/0.29 thf(f146,plain,(
% 0.19/0.29 ( ! [X1 : a] : (((((^[Y0 : a]: ($false)) @ X1)) = ((sK6 @ X1)))) ) | ~spl10_6),
% 0.19/0.29 inference(argument_congruence,[],[f73])).
% 0.19/0.29 thf(f147,plain,(
% 0.19/0.29 ( ! [X1 : a] : (($true = (((^[Y0 : a]: ($false)) @ X1))) | ($false = ((sK6 @ X1)))) ) | ~spl10_6),
% 0.19/0.29 inference(iff_proxy_clausification,[],[f146])).
% 0.19/0.29 thf(f150,plain,(
% 0.19/0.29 ( ! [X1 : a] : (($false = $true) | ($false = ((sK6 @ X1)))) ) | ~spl10_6),
% 0.19/0.29 inference(beta-eta_normalization,[],[f147])).
% 0.19/0.29 thf(f151,plain,(
% 0.19/0.29 ( ! [X1 : a] : (($false = ((sK6 @ X1)))) ) | ~spl10_6),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f150])).
% 0.19/0.29 thf(f155,plain,(
% 0.19/0.29 ( ! [X1 : a] : ((((sK7 @ X1)) = (((^[Y0 : a]: ($true)) @ X1)))) ) | ~spl10_9),
% 0.19/0.29 inference(argument_congruence,[],[f86])).
% 0.19/0.29 thf(f156,plain,(
% 0.19/0.29 ( ! [X1 : a] : (($true = ((sK7 @ X1))) | ($false = (((^[Y0 : a]: ($true)) @ X1)))) ) | ~spl10_9),
% 0.19/0.29 inference(iff_proxy_clausification,[],[f155])).
% 0.19/0.29 thf(f159,plain,(
% 0.19/0.29 ( ! [X1 : a] : (($true = ((sK7 @ X1))) | ($false = $true)) ) | ~spl10_9),
% 0.19/0.29 inference(beta-eta_normalization,[],[f156])).
% 0.19/0.29 thf(f160,plain,(
% 0.19/0.29 ( ! [X1 : a] : (($true = ((sK7 @ X1)))) ) | ~spl10_9),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f159])).
% 0.19/0.29 thf(f176,plain,(
% 0.19/0.29 ((((^[Y0 : a]: ($false)) @ sK11)) != (((^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0))) @ sK11))) | (~spl10_10 | spl10_11)),
% 0.19/0.29 inference(negative_extensionality,[],[f133])).
% 0.19/0.29 thf(f177,plain,(
% 0.19/0.29 ($true = (((^[Y0 : a]: ($false)) @ sK11))) | ($true = (((^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0))) @ sK11))) | (~spl10_10 | spl10_11)),
% 0.19/0.29 inference(xor_proxy_clausification,[],[f176])).
% 0.19/0.29 thf(f181,plain,(
% 0.19/0.29 ($false = $true) | ($true = (((sK6 @ sK11) & (sK7 @ sK11)))) | (~spl10_10 | spl10_11)),
% 0.19/0.29 inference(beta-eta_normalization,[],[f177])).
% 0.19/0.29 thf(f182,plain,(
% 0.19/0.29 ($false = $true) | ($true = ((sK7 @ sK11))) | (~spl10_10 | spl10_11)),
% 0.19/0.29 inference(and_proxy_clausification,[],[f181])).
% 0.19/0.29 thf(f183,plain,(
% 0.19/0.29 ($false = $true) | ($true = ((sK6 @ sK11))) | (~spl10_10 | spl10_11)),
% 0.19/0.29 inference(and_proxy_clausification,[],[f181])).
% 0.19/0.29 thf(f184,plain,(
% 0.19/0.29 ($true = ((sK6 @ sK11))) | (~spl10_10 | spl10_11)),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f183])).
% 0.19/0.29 thf(f185,plain,(
% 0.19/0.29 ($true = ((sK7 @ sK11))) | (~spl10_10 | spl10_11)),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f182])).
% 0.19/0.29 thf(f186,plain,(
% 0.19/0.29 ($false = $true) | (~spl10_6 | ~spl10_10 | spl10_11)),
% 0.19/0.29 inference(forward_demodulation,[],[f184,f151])).
% 0.19/0.29 thf(f187,plain,(
% 0.19/0.29 $false | (~spl10_6 | ~spl10_10 | spl10_11)),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f186])).
% 0.19/0.29 thf(f188,plain,(
% 0.19/0.29 ~spl10_6 | ~spl10_10 | spl10_11),
% 0.19/0.29 inference(avatar_contradiction_clause,[],[f187])).
% 0.19/0.29 thf(f197,plain,(
% 0.19/0.29 ( ! [X1 : a] : ((((sK6 @ X1)) = (((^[Y0 : a]: ($true)) @ X1)))) ) | ~spl10_7),
% 0.19/0.29 inference(argument_congruence,[],[f77])).
% 0.19/0.29 thf(f199,plain,(
% 0.19/0.29 ( ! [X1 : a] : (($true = ((sK6 @ X1))) | ($false = (((^[Y0 : a]: ($true)) @ X1)))) ) | ~spl10_7),
% 0.19/0.29 inference(iff_proxy_clausification,[],[f197])).
% 0.19/0.29 thf(f202,plain,(
% 0.19/0.29 ( ! [X1 : a] : (($true = ((sK6 @ X1))) | ($false = $true)) ) | ~spl10_7),
% 0.19/0.29 inference(beta-eta_normalization,[],[f199])).
% 0.19/0.29 thf(f203,plain,(
% 0.19/0.29 ( ! [X1 : a] : (($true = ((sK6 @ X1)))) ) | ~spl10_7),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f202])).
% 0.19/0.29 thf(f204,plain,(
% 0.19/0.29 ((((^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0))) @ sK13)) != (((^[Y0 : a]: ($true)) @ sK13))) | (~spl10_10 | spl10_12)),
% 0.19/0.29 inference(negative_extensionality,[],[f134])).
% 0.19/0.29 thf(f206,plain,(
% 0.19/0.29 ($false = (((^[Y0 : a]: ((sK6 @ Y0) & (sK7 @ Y0))) @ sK13))) | ($false = (((^[Y0 : a]: ($true)) @ sK13))) | (~spl10_10 | spl10_12)),
% 0.19/0.29 inference(xor_proxy_clausification,[],[f204])).
% 0.19/0.29 thf(f207,plain,(
% 0.19/0.29 ($false = (((sK6 @ sK13) & (sK7 @ sK13)))) | ($false = $true) | (~spl10_10 | spl10_12)),
% 0.19/0.29 inference(beta-eta_normalization,[],[f206])).
% 0.19/0.29 thf(f208,plain,(
% 0.19/0.29 ($false = ((sK7 @ sK13))) | ($false = $true) | ($false = ((sK6 @ sK13))) | (~spl10_10 | spl10_12)),
% 0.19/0.29 inference(and_proxy_clausification,[],[f207])).
% 0.19/0.29 thf(f209,plain,(
% 0.19/0.29 ($false = ((sK7 @ sK13))) | ($false = ((sK6 @ sK13))) | (~spl10_10 | spl10_12)),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f208])).
% 0.19/0.29 thf(f213,plain,(
% 0.19/0.29 ($false = $true) | ($false = ((sK6 @ sK13))) | (~spl10_9 | ~spl10_10 | spl10_12)),
% 0.19/0.29 inference(forward_demodulation,[],[f209,f160])).
% 0.19/0.29 thf(f214,plain,(
% 0.19/0.29 ($false = ((sK6 @ sK13))) | (~spl10_9 | ~spl10_10 | spl10_12)),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f213])).
% 0.19/0.29 thf(f215,plain,(
% 0.19/0.29 ($false = $true) | (~spl10_7 | ~spl10_9 | ~spl10_10 | spl10_12)),
% 0.19/0.29 inference(forward_demodulation,[],[f214,f203])).
% 0.19/0.29 thf(f216,plain,(
% 0.19/0.29 $false | (~spl10_7 | ~spl10_9 | ~spl10_10 | spl10_12)),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f215])).
% 0.19/0.29 thf(f217,plain,(
% 0.19/0.29 ~spl10_7 | ~spl10_9 | ~spl10_10 | spl10_12),
% 0.19/0.29 inference(avatar_contradiction_clause,[],[f216])).
% 0.19/0.29 thf(f225,plain,(
% 0.19/0.29 ( ! [X1 : a] : (((((^[Y0 : a]: ($false)) @ X1)) = ((sK7 @ X1)))) ) | ~spl10_8),
% 0.19/0.29 inference(argument_congruence,[],[f82])).
% 0.19/0.29 thf(f226,plain,(
% 0.19/0.29 ( ! [X1 : a] : (($true = (((^[Y0 : a]: ($false)) @ X1))) | ($false = ((sK7 @ X1)))) ) | ~spl10_8),
% 0.19/0.29 inference(iff_proxy_clausification,[],[f225])).
% 0.19/0.29 thf(f229,plain,(
% 0.19/0.29 ( ! [X1 : a] : (($false = $true) | ($false = ((sK7 @ X1)))) ) | ~spl10_8),
% 0.19/0.29 inference(beta-eta_normalization,[],[f226])).
% 0.19/0.29 thf(f230,plain,(
% 0.19/0.29 ( ! [X1 : a] : (($false = ((sK7 @ X1)))) ) | ~spl10_8),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f229])).
% 0.19/0.29 thf(f238,plain,(
% 0.19/0.29 ($false = $true) | (~spl10_8 | ~spl10_10 | spl10_11)),
% 0.19/0.29 inference(constrained_superposition,[],[f185,f230])).
% 0.19/0.29 thf(f242,plain,(
% 0.19/0.29 $false | (~spl10_8 | ~spl10_10 | spl10_11)),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f238])).
% 0.19/0.29 thf(f243,plain,(
% 0.19/0.29 ~spl10_8 | ~spl10_10 | spl10_11),
% 0.19/0.29 inference(avatar_contradiction_clause,[],[f242])).
% 0.19/0.29 thf(f244,plain,(
% 0.19/0.29 ((^[Y0 : a]: ($false)) != (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((sK4 @ Y1) & (Y1 @ Y0)))))) | (~spl10_14 | spl10_15)),
% 0.19/0.29 inference(forward_demodulation,[],[f115,f110])).
% 0.19/0.29 thf(f245,plain,(
% 0.19/0.29 ((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((sK4 @ Y1) & (Y1 @ Y0))))) != (^[Y0 : a]: ($true))) | (~spl10_14 | spl10_16)),
% 0.19/0.29 inference(forward_demodulation,[],[f120,f110])).
% 0.19/0.29 thf(f290,plain,(
% 0.19/0.29 ((((^[Y0 : a]: ($false)) @ sK18)) != (((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((sK4 @ Y1) & (Y1 @ Y0))))) @ sK18))) | (~spl10_14 | spl10_15)),
% 0.19/0.29 inference(negative_extensionality,[],[f244])).
% 0.19/0.29 thf(f291,plain,(
% 0.19/0.29 ($true = (((^[Y0 : a]: ($false)) @ sK18))) | ($true = (((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((sK4 @ Y1) & (Y1 @ Y0))))) @ sK18))) | (~spl10_14 | spl10_15)),
% 0.19/0.29 inference(xor_proxy_clausification,[],[f290])).
% 0.19/0.29 thf(f295,plain,(
% 0.19/0.29 ($false = $true) | ($true = ((?? @ (a > $o) @ (^[Y0 : a > $o]: ((sK4 @ Y0) & (Y0 @ sK18)))))) | (~spl10_14 | spl10_15)),
% 0.19/0.29 inference(beta-eta_normalization,[],[f291])).
% 0.19/0.29 thf(f296,plain,(
% 0.19/0.29 ($false = $true) | ($true = (((^[Y0 : a > $o]: ((sK4 @ Y0) & (Y0 @ sK18))) @ sK19))) | (~spl10_14 | spl10_15)),
% 0.19/0.29 inference(sigma_proxy_clausification,[],[f295])).
% 0.19/0.29 thf(f297,plain,(
% 0.19/0.29 ($true = (((^[Y0 : a > $o]: ((sK4 @ Y0) & (Y0 @ sK18))) @ sK19))) | (~spl10_14 | spl10_15)),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f296])).
% 0.19/0.29 thf(f298,plain,(
% 0.19/0.29 ($true = (((sK4 @ sK19) & (sK19 @ sK18)))) | (~spl10_14 | spl10_15)),
% 0.19/0.29 inference(beta-eta_normalization,[],[f297])).
% 0.19/0.29 thf(f299,plain,(
% 0.19/0.29 ($true = ((sK19 @ sK18))) | (~spl10_14 | spl10_15)),
% 0.19/0.29 inference(and_proxy_clausification,[],[f298])).
% 0.19/0.29 thf(f300,plain,(
% 0.19/0.29 ($true = ((sK4 @ sK19))) | (~spl10_14 | spl10_15)),
% 0.19/0.29 inference(and_proxy_clausification,[],[f298])).
% 0.19/0.29 thf(f301,plain,(
% 0.19/0.29 ((((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((sK4 @ Y1) & (Y1 @ Y0))))) @ sK20)) != (((^[Y0 : a]: ($true)) @ sK20))) | (~spl10_14 | spl10_16)),
% 0.19/0.29 inference(negative_extensionality,[],[f245])).
% 0.19/0.29 thf(f303,plain,(
% 0.19/0.29 ($false = (((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((sK4 @ Y1) & (Y1 @ Y0))))) @ sK20))) | ($false = (((^[Y0 : a]: ($true)) @ sK20))) | (~spl10_14 | spl10_16)),
% 0.19/0.29 inference(xor_proxy_clausification,[],[f301])).
% 0.19/0.29 thf(f304,plain,(
% 0.19/0.29 ($false = ((?? @ (a > $o) @ (^[Y0 : a > $o]: ((sK4 @ Y0) & (Y0 @ sK20)))))) | ($false = $true) | (~spl10_14 | spl10_16)),
% 0.19/0.29 inference(beta-eta_normalization,[],[f303])).
% 0.19/0.29 thf(f305,plain,(
% 0.19/0.29 ( ! [X1 : (a > $o)] : (($false = (((^[Y0 : a > $o]: ((sK4 @ Y0) & (Y0 @ sK20))) @ X1))) | ($false = $true)) ) | (~spl10_14 | spl10_16)),
% 0.19/0.29 inference(pi_proxy_clausification,[],[f304])).
% 0.19/0.29 thf(f306,plain,(
% 0.19/0.29 ( ! [X1 : (a > $o)] : (($false = (((^[Y0 : a > $o]: ((sK4 @ Y0) & (Y0 @ sK20))) @ X1)))) ) | (~spl10_14 | spl10_16)),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f305])).
% 0.19/0.29 thf(f307,plain,(
% 0.19/0.29 ( ! [X1 : (a > $o)] : (($false = (((sK4 @ X1) & (X1 @ sK20))))) ) | (~spl10_14 | spl10_16)),
% 0.19/0.29 inference(beta-eta_normalization,[],[f306])).
% 0.19/0.29 thf(f308,plain,(
% 0.19/0.29 ( ! [X1 : (a > $o)] : (($false = ((X1 @ sK20))) | ($false = ((sK4 @ X1)))) ) | (~spl10_14 | spl10_16)),
% 0.19/0.29 inference(and_proxy_clausification,[],[f307])).
% 0.19/0.29 thf(f311,plain,(
% 0.19/0.29 ($true != $true) | ((^[Y0 : a]: ($true)) = sK19) | ((^[Y0 : a]: ($false)) = sK19) | (~spl10_13 | ~spl10_14 | spl10_15)),
% 0.19/0.29 inference(constrained_superposition,[],[f105,f300])).
% 0.19/0.29 thf(f312,plain,(
% 0.19/0.29 ((^[Y0 : a]: ($true)) = sK19) | ((^[Y0 : a]: ($false)) = sK19) | (~spl10_13 | ~spl10_14 | spl10_15)),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f311])).
% 0.19/0.29 thf(f314,definition,(
% 0.19/0.29 spl10_21 <=> ((^[Y0 : a]: ($false)) = sK19)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl10_21])],[avatar_definition])).
% 0.19/0.29 thf(f316,plain,(
% 0.19/0.29 ((^[Y0 : a]: ($false)) = sK19) | ~spl10_21),
% 0.19/0.29 inference(avatar_component_clause,[],[f314])).
% 0.19/0.29 thf(f318,definition,(
% 0.19/0.29 spl10_22 <=> ((^[Y0 : a]: ($true)) = sK19)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl10_22])],[avatar_definition])).
% 0.19/0.29 thf(f320,plain,(
% 0.19/0.29 ((^[Y0 : a]: ($true)) = sK19) | ~spl10_22),
% 0.19/0.29 inference(avatar_component_clause,[],[f318])).
% 0.19/0.29 thf(f321,plain,(
% 0.19/0.29 spl10_21 | spl10_22 | ~spl10_13 | ~spl10_14 | spl10_15),
% 0.19/0.29 inference(avatar_split_clause,[],[f312,f113,f108,f104,f318,f314])).
% 0.19/0.29 thf(f331,plain,(
% 0.19/0.29 ($true = ((sK4 @ (^[Y0 : a]: ($true))))) | (~spl10_14 | spl10_15 | ~spl10_22)),
% 0.19/0.29 inference(constrained_superposition,[],[f300,f320])).
% 0.19/0.29 thf(f358,plain,(
% 0.19/0.29 ($false != $false) | ($false = ((sK4 @ (^[Y0 : a]: ($true))))) | (~spl10_14 | spl10_16)),
% 0.19/0.29 inference(constrained_superposition,[],[f37,f308])).
% 0.19/0.29 thf(f377,plain,(
% 0.19/0.29 ($false = ((sK4 @ (^[Y0 : a]: ($true))))) | (~spl10_14 | spl10_16)),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f358])).
% 0.19/0.29 thf(f599,plain,(
% 0.19/0.29 ($false = $true) | (~spl10_14 | spl10_15 | spl10_16 | ~spl10_22)),
% 0.19/0.29 inference(constrained_superposition,[],[f331,f377])).
% 0.19/0.29 thf(f606,plain,(
% 0.19/0.29 $false | (~spl10_14 | spl10_15 | spl10_16 | ~spl10_22)),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f599])).
% 0.19/0.29 thf(f607,plain,(
% 0.19/0.29 ~spl10_14 | spl10_15 | spl10_16 | ~spl10_22),
% 0.19/0.29 inference(avatar_contradiction_clause,[],[f606])).
% 0.19/0.29 thf(f646,plain,(
% 0.19/0.29 ( ! [X1 : a] : (((((^[Y0 : a]: ($false)) @ X1)) = ((sK19 @ X1)))) ) | ~spl10_21),
% 0.19/0.29 inference(argument_congruence,[],[f316])).
% 0.19/0.29 thf(f648,plain,(
% 0.19/0.29 ( ! [X1 : a] : (($true = (((^[Y0 : a]: ($false)) @ X1))) | ($false = ((sK19 @ X1)))) ) | ~spl10_21),
% 0.19/0.29 inference(iff_proxy_clausification,[],[f646])).
% 0.19/0.29 thf(f651,plain,(
% 0.19/0.29 ( ! [X1 : a] : (($false = $true) | ($false = ((sK19 @ X1)))) ) | ~spl10_21),
% 0.19/0.29 inference(beta-eta_normalization,[],[f648])).
% 0.19/0.29 thf(f652,plain,(
% 0.19/0.29 ( ! [X1 : a] : (($false = ((sK19 @ X1)))) ) | ~spl10_21),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f651])).
% 0.19/0.29 thf(f657,plain,(
% 0.19/0.29 ($false = $true) | (~spl10_14 | spl10_15 | ~spl10_21)),
% 0.19/0.29 inference(constrained_superposition,[],[f652,f299])).
% 0.19/0.29 thf(f661,plain,(
% 0.19/0.29 $false | (~spl10_14 | spl10_15 | ~spl10_21)),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f657])).
% 0.19/0.29 thf(f662,plain,(
% 0.19/0.29 ~spl10_14 | spl10_15 | ~spl10_21),
% 0.19/0.29 inference(avatar_contradiction_clause,[],[f661])).
% 0.19/0.29 cnf(s1, plain, spl10_1 | spl10_2 | spl10_3 | spl10_4, inference(sat_conversion,[],[f63])).
% 0.19/0.29 cnf(s3, plain, spl10_1 | ~spl10_2 | spl10_3 | spl10_4, inference(sat_conversion,[],[f69])).
% 0.19/0.29 cnf(s4, plain, ~spl10_4 | spl10_6 | spl10_7, inference(sat_conversion,[],[f78])).
% 0.19/0.29 cnf(s5, plain, ~spl10_4 | spl10_8 | spl10_9, inference(sat_conversion,[],[f87])).
% 0.19/0.29 cnf(s6, plain, ~spl10_4 | spl10_10, inference(sat_conversion,[],[f92])).
% 0.19/0.29 cnf(s7, plain, ~spl10_4 | ~spl10_11, inference(sat_conversion,[],[f97])).
% 0.19/0.29 cnf(s8, plain, ~spl10_4 | ~spl10_12, inference(sat_conversion,[],[f102])).
% 0.19/0.29 cnf(s9, plain, ~spl10_3 | spl10_13, inference(sat_conversion,[],[f106])).
% 0.19/0.29 cnf(s10, plain, ~spl10_3 | spl10_14, inference(sat_conversion,[],[f111])).
% 0.19/0.29 cnf(s11, plain, ~spl10_3 | ~spl10_15, inference(sat_conversion,[],[f116])).
% 0.19/0.29 cnf(s12, plain, ~spl10_3 | ~spl10_16, inference(sat_conversion,[],[f121])).
% 0.19/0.29 cnf(s13, plain, ~spl10_1 | spl10_17, inference(sat_conversion,[],[f126])).
% 0.19/0.29 cnf(s14, plain, ~spl10_1 | ~spl10_17, inference(sat_conversion,[],[f127])).
% 0.19/0.29 cnf(s16, plain, ~spl10_6 | ~spl10_10 | spl10_11, inference(sat_conversion,[],[f188])).
% 0.19/0.29 cnf(s17, plain, ~spl10_7 | ~spl10_9 | ~spl10_10 | spl10_12, inference(sat_conversion,[],[f217])).
% 0.19/0.29 cnf(s19, plain, ~spl10_8 | ~spl10_10 | spl10_11, inference(sat_conversion,[],[f243])).
% 0.19/0.29 cnf(s21, plain, ~spl10_13 | ~spl10_14 | spl10_15 | spl10_21 | spl10_22, inference(sat_conversion,[],[f321])).
% 0.19/0.29 cnf(s31, plain, ~spl10_14 | spl10_15 | spl10_16 | ~spl10_22, inference(sat_conversion,[],[f607])).
% 0.19/0.29 cnf(s37, plain, ~spl10_14 | spl10_15 | ~spl10_21, inference(sat_conversion,[],[f662])).
% 0.19/0.29 cnf(s38, plain, ~spl10_4, inference(rat,[],[s17,s4,s5,s16,s19,s6,s7,s8])).
% 0.19/0.29 cnf(s39, plain, ~spl10_3, inference(rat,[],[s21,s31,s37,s9,s10,s11,s12])).
% 0.19/0.29 cnf(s40, plain, spl10_1, inference(rat,[],[s3,s1,s39,s38])).
% 0.19/0.29 cnf(s42, plain, ~spl10_17, inference(rat,[],[s14,s40])).
% 0.19/0.29 cnf(s43, plain, $false, inference(rat,[],[s13,s42,s40])).
% 0.19/0.29 thf(f664,plain,(
% 0.19/0.29 $false),
% 0.19/0.29 inference(avatar_sat_refutation,[],[s43])).
% 0.19/0.29 % SZS output end Proof for theBenchmark
% 0.19/0.29 % (1429349)------------------------------
% 0.19/0.29 % (1429349)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (1429349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (1429349)CaDiCaL version: 2.1.3
% 0.19/0.29 % (1429349)Termination reason: Refutation
% 0.19/0.29 % (1429349)Time elapsed: 0.023 s
% 0.19/0.29 % (1429349)Peak memory usage: 13 MB
% 0.19/0.29 % (1429349)Instructions burned: 38 (million)
% 0.19/0.29 % (1429339)Success in time 0.06 s
% 0.19/0.29 % Vampire exiting
%------------------------------------------------------------------------------