%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV261^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:38:08 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
% 0.00/0.03 % Problem : SEV261^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n006.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 15:28:09 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.29 % (865282)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.29 % (865297)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3519652394:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.29 % (865297)Refutation not found, incomplete strategy
% 0.19/0.29 % (865297)------------------------------
% 0.19/0.29 % (865297)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (865297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (865297)CaDiCaL version: 2.1.3
% 0.19/0.29 % (865297)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.29 % (865297)Time elapsed: 0.002 s
% 0.19/0.29 % (865297)Peak memory usage: 12 MB
% 0.19/0.29 % (865297)Instructions burned: 3 (million)
% 0.19/0.29 % (865297)------------------------------
% 0.19/0.29 % (865297)------------------------------
% 0.19/0.29 % (865298)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3963054442:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.19/0.29 % (865295)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3825743636:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.29 % (865296)lrs+10_16_si=on:nwc=1.5:random_seed=1931776336:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.29 % (865298) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-865282-865298"...
% 0.19/0.29 % (865298)...printing done.
% 0.19/0.29 % (865295) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-865282-865295"...
% 0.19/0.29 % (865298)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) > $tType).
% 0.19/0.29 thf(func_def_1, type, vNOT: ($o > $o)).
% 0.19/0.29 thf(func_def_4, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.29 thf(func_def_5, type, vAND: ($o > $o > $o)).
% 0.19/0.29 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.29 thf(func_def_7, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 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, sK2: (a > $o)).
% 0.19/0.29 thf(func_def_12, type, sK3: ((a > $o) > $o)).
% 0.19/0.29 thf(func_def_13, type, sK4: (a > $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_19, type, sK10: (a > 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).
% 0.19/0.29 thf(func_def_27, type, sK18: a).
% 0.19/0.29 thf(f1,conjecture,(
% 0.19/0.29 ! [X0 : (a > $o)] : ((X0 = (^[X1 : a] : ($false))) => ((X0 = (^[X2 : a] : ($false))) | (X0 = (^[X2 : a] : (~$false))))) & ! [X3 : ((a > $o) > $o),X0 : (a > $o)] : ((! [X1 : (a > $o)] : ((X3 @ X1) => ((X1 = (^[X2 : a] : ($false))) | (X1 = (^[X2 : a] : (~$false))))) & (X0 = (^[X1 : a] : (? [X4 : (a > $o)] : ((X4 @ X1) & (X3 @ X4)))))) => ((X0 = (^[X2 : a] : (~$false))) | (X0 = (^[X2 : a] : ($false))))) & ! [X4 : (a > $o),X5 : (a > $o),X6 : (a > $o)] : ((((^[X1 : a] : ((X5 @ X1) & (X6 @ X1))) = X4) & (((^[X2 : a] : (~$false)) = X6) | ((^[X2 : a] : ($false)) = X6)) & (((^[X2 : a] : (~$false)) = X5) | ((^[X2 : a] : ($false)) = X5))) => ((X4 = (^[X2 : a] : ($false))) | ((^[X2 : a] : (~$false)) = X4))) & ! [X0 : (a > $o)] : ((X0 = (^[X1 : a] : (~$false))) => (((^[X2 : a] : ($false)) = X0) | (X0 = (^[X2 : a] : (~$false)))))),
% 0.19/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cINDISCRETE_TOPOLOGY_pme)).
% 0.19/0.29 thf(f2,negated_conjecture,(
% 0.19/0.29 ~(! [X0 : (a > $o)] : ((X0 = (^[X1 : a] : ($false))) => ((X0 = (^[X2 : a] : ($false))) | (X0 = (^[X2 : a] : (~$false))))) & ! [X3 : ((a > $o) > $o),X0 : (a > $o)] : ((! [X1 : (a > $o)] : ((X3 @ X1) => ((X1 = (^[X2 : a] : ($false))) | (X1 = (^[X2 : a] : (~$false))))) & (X0 = (^[X1 : a] : (? [X4 : (a > $o)] : ((X4 @ X1) & (X3 @ X4)))))) => ((X0 = (^[X2 : a] : (~$false))) | (X0 = (^[X2 : a] : ($false))))) & ! [X4 : (a > $o),X5 : (a > $o),X6 : (a > $o)] : ((((^[X1 : a] : ((X5 @ X1) & (X6 @ X1))) = X4) & (((^[X2 : a] : (~$false)) = X6) | ((^[X2 : a] : ($false)) = X6)) & (((^[X2 : a] : (~$false)) = X5) | ((^[X2 : a] : ($false)) = X5))) => ((X4 = (^[X2 : a] : ($false))) | ((^[X2 : a] : (~$false)) = X4))) & ! [X0 : (a > $o)] : ((X0 = (^[X1 : a] : (~$false))) => (((^[X2 : a] : ($false)) = X0) | (X0 = (^[X2 : a] : (~$false))))))),
% 0.19/0.29 inference(negated_conjecture,[status(cth)],[f1])).
% 0.19/0.29 thf(f3,plain,(
% 0.19/0.29 ~(! [X0 : (a > $o)] : ((X0 = (^[X1 : a] : ($false))) => ((X0 = (^[X2 : a] : ($false))) | (X0 = (^[X3 : a] : (~$false))))) & ! [X4 : ((a > $o) > $o),X5 : (a > $o)] : ((! [X6 : (a > $o)] : ((X4 @ X6) => ((X6 = (^[X7 : a] : ($false))) | (X6 = (^[X8 : a] : (~$false))))) & (X5 = (^[X9 : a] : (? [X10 : (a > $o)] : ((X10 @ X9) & (X4 @ X10)))))) => ((X5 = (^[X11 : a] : (~$false))) | (X5 = (^[X12 : a] : ($false))))) & ! [X13 : (a > $o),X14 : (a > $o),X15 : (a > $o)] : ((((^[X16 : a] : ((X14 @ X16) & (X15 @ X16))) = X13) & (((^[X17 : a] : (~$false)) = X15) | ((^[X18 : a] : ($false)) = X15)) & (((^[X19 : a] : (~$false)) = X14) | ((^[X20 : a] : ($false)) = X14))) => ((X13 = (^[X21 : a] : ($false))) | ((^[X22 : a] : (~$false)) = X13))) & ! [X23 : (a > $o)] : ((X23 = (^[X24 : a] : (~$false))) => (((^[X25 : a] : ($false)) = X23) | (X23 = (^[X26 : a] : (~$false))))))),
% 0.19/0.29 inference(rectify,[],[f2])).
% 0.19/0.29 thf(f4,plain,(
% 0.19/0.29 ~(! [X0 : (a > $o)] : (((^[Y0 : a]: ($false)) = X0) => (((^[Y0 : a]: (~ $false)) = X0) | ((^[Y0 : a]: ($false)) = X0))) & ! [X4 : ((a > $o) > $o),X5 : (a > $o)] : ((! [X6 : (a > $o)] : ((((X4 @ X6)) = $true) => (((^[Y0 : a]: ($false)) = X6) | ((^[Y0 : a]: (~ $false)) = X6))) & ((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((X4 @ Y1) & (Y1 @ Y0))))) = X5)) => (((^[Y0 : a]: (~ $false)) = X5) | ((^[Y0 : a]: ($false)) = X5))) & ! [X13 : (a > $o),X14 : (a > $o),X15 : (a > $o)] : ((((^[Y0 : a]: ((X15 @ Y0) & (X14 @ Y0))) = X13) & (((^[Y0 : a]: (~ $false)) = X15) | ((^[Y0 : a]: ($false)) = X15)) & (((^[Y0 : a]: (~ $false)) = X14) | ((^[Y0 : a]: ($false)) = X14))) => (((^[Y0 : a]: ($false)) = X13) | ((^[Y0 : a]: (~ $false)) = X13))) & ! [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 ~(! [X7 : (a > $o)] : (((^[Y0 : a]: (~ $false)) = X7) => (((^[Y0 : a]: ($false)) = X7) | ((^[Y0 : a]: (~ $false)) = X7))) & ! [X0 : (a > $o)] : (((^[Y0 : a]: ($false)) = X0) => (((^[Y0 : a]: (~ $false)) = X0) | ((^[Y0 : a]: ($false)) = X0))) & ! [X1 : ((a > $o) > $o),X2 : (a > $o)] : ((((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((X1 @ Y1) & (Y1 @ Y0))))) = X2) & ! [X3 : (a > $o)] : ((((X1 @ X3)) = $true) => (((^[Y0 : a]: ($false)) = X3) | ((^[Y0 : a]: (~ $false)) = X3)))) => (((^[Y0 : a]: (~ $false)) = X2) | ((^[Y0 : a]: ($false)) = X2))) & ! [X5 : (a > $o),X4 : (a > $o),X6 : (a > $o)] : (((((^[Y0 : a]: ($false)) = X6) | ((^[Y0 : a]: (~ $false)) = X6)) & (((^[Y0 : a]: ($false)) = X5) | ((^[Y0 : a]: (~ $false)) = X5)) & ((^[Y0 : a]: ((X6 @ Y0) & (X5 @ Y0))) = X4)) => (((^[Y0 : a]: ($false)) = X4) | ((^[Y0 : a]: (~ $false)) = X4))))),
% 0.19/0.29 inference(rectify,[],[f4])).
% 0.19/0.29 thf(f6,plain,(
% 0.19/0.29 ? [X7 : (a > $o)] : ((((^[Y0 : a]: ($false)) != X7) & ((^[Y0 : a]: (~ $false)) != X7)) & ((^[Y0 : a]: (~ $false)) = X7)) | ? [X0 : (a > $o)] : ((((^[Y0 : a]: (~ $false)) != X0) & ((^[Y0 : a]: ($false)) != X0)) & ((^[Y0 : a]: ($false)) = X0)) | ? [X1 : ((a > $o) > $o),X2 : (a > $o)] : ((((^[Y0 : a]: (~ $false)) != X2) & ((^[Y0 : a]: ($false)) != X2)) & (((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((X1 @ Y1) & (Y1 @ Y0))))) = X2) & ! [X3 : (a > $o)] : ((((^[Y0 : a]: ($false)) = X3) | ((^[Y0 : a]: (~ $false)) = X3)) | (((X1 @ X3)) != $true)))) | ? [X5 : (a > $o),X4 : (a > $o),X6 : (a > $o)] : ((((^[Y0 : a]: ($false)) != X4) & ((^[Y0 : a]: (~ $false)) != X4)) & ((((^[Y0 : a]: ($false)) = X6) | ((^[Y0 : a]: (~ $false)) = X6)) & (((^[Y0 : a]: ($false)) = X5) | ((^[Y0 : a]: (~ $false)) = X5)) & ((^[Y0 : a]: ((X6 @ Y0) & (X5 @ Y0))) = X4)))),
% 0.19/0.29 inference(ennf_transformation,[],[f5])).
% 0.19/0.29 thf(f7,plain,(
% 0.19/0.29 ? [X2 : (a > $o),X1 : ((a > $o) > $o)] : (((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((X1 @ Y1) & (Y1 @ Y0))))) = X2) & ! [X3 : (a > $o)] : ((((X1 @ X3)) != $true) | ((^[Y0 : a]: (~ $false)) = X3) | ((^[Y0 : a]: ($false)) = X3)) & ((^[Y0 : a]: ($false)) != X2) & ((^[Y0 : a]: (~ $false)) != X2)) | ? [X4 : (a > $o),X5 : (a > $o),X6 : (a > $o)] : (((^[Y0 : a]: (~ $false)) != X4) & (((^[Y0 : a]: ($false)) = X5) | ((^[Y0 : a]: (~ $false)) = X5)) & ((^[Y0 : a]: ((X6 @ Y0) & (X5 @ Y0))) = X4) & (((^[Y0 : a]: ($false)) = X6) | ((^[Y0 : a]: (~ $false)) = X6)) & ((^[Y0 : a]: ($false)) != X4)) | ? [X7 : (a > $o)] : (((^[Y0 : a]: (~ $false)) = X7) & ((^[Y0 : a]: (~ $false)) != X7) & ((^[Y0 : a]: ($false)) != X7)) | ? [X0 : (a > $o)] : (((^[Y0 : a]: ($false)) = X0) & ((^[Y0 : a]: ($false)) != X0) & ((^[Y0 : a]: (~ $false)) != X0))),
% 0.19/0.29 inference(flattening,[],[f6])).
% 0.19/0.29 thf(f8,definition,(
% 0.19/0.29 ? [X4 : (a > $o),X5 : (a > $o),X6 : (a > $o)] : (((^[Y0 : a]: (~ $false)) != X4) & (((^[Y0 : a]: ($false)) = X5) | ((^[Y0 : a]: (~ $false)) = X5)) & ((^[Y0 : a]: ((X6 @ Y0) & (X5 @ Y0))) = X4) & (((^[Y0 : a]: ($false)) = X6) | ((^[Y0 : a]: (~ $false)) = X6)) & ((^[Y0 : a]: ($false)) != X4)) | ~ (sP0 = $true)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.19/0.29 thf(f9,definition,(
% 0.19/0.29 ? [X2 : (a > $o),X1 : ((a > $o) > $o)] : (((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((X1 @ Y1) & (Y1 @ Y0))))) = X2) & ! [X3 : (a > $o)] : ((((X1 @ X3)) != $true) | ((^[Y0 : a]: (~ $false)) = X3) | ((^[Y0 : a]: ($false)) = X3)) & ((^[Y0 : a]: ($false)) != X2) & ((^[Y0 : a]: (~ $false)) != X2)) | ~ ($true = sP1)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.19/0.29 thf(f10,plain,(
% 0.19/0.29 ($true = sP1) | (sP0 = $true) | ? [X7 : (a > $o)] : (((^[Y0 : a]: (~ $false)) = X7) & ((^[Y0 : a]: (~ $false)) != X7) & ((^[Y0 : a]: ($false)) != X7)) | ? [X0 : (a > $o)] : (((^[Y0 : a]: ($false)) = X0) & ((^[Y0 : a]: ($false)) != X0) & ((^[Y0 : a]: (~ $false)) != X0))),
% 0.19/0.29 inference(definition_folding,[],[f7,f9,f8])).
% 0.19/0.29 thf(f11,plain,(
% 0.19/0.29 ? [X2 : (a > $o),X1 : ((a > $o) > $o)] : (((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((X1 @ Y1) & (Y1 @ Y0))))) = X2) & ! [X3 : (a > $o)] : ((((X1 @ X3)) != $true) | ((^[Y0 : a]: (~ $false)) = X3) | ((^[Y0 : a]: ($false)) = X3)) & ((^[Y0 : a]: ($false)) != X2) & ((^[Y0 : a]: (~ $false)) != X2)) | ($true != sP1)),
% 0.19/0.29 inference(nnf_transformation,[],[f9])).
% 0.19/0.29 thf(f12,plain,(
% 0.19/0.29 ? [X0 : (a > $o),X1 : ((a > $o) > $o)] : (((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((X1 @ Y1) & (Y1 @ Y0))))) = X0) & ! [X2 : (a > $o)] : ((((X1 @ X2)) != $true) | ((^[Y0 : a]: (~ $false)) = X2) | ((^[Y0 : a]: ($false)) = X2)) & ((^[Y0 : a]: ($false)) != X0) & ((^[Y0 : a]: (~ $false)) != X0)) | ($true != sP1)),
% 0.19/0.29 inference(rectify,[],[f11])).
% 0.19/0.29 thf(f13,plain,(
% 0.19/0.29 ((sK2 = (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((sK3 @ Y1) & (Y1 @ Y0)))))) & ! [X2 : (a > $o)] : ((((sK3 @ X2)) != $true) | ((^[Y0 : a]: (~ $false)) = X2) | ((^[Y0 : a]: ($false)) = X2)) & (sK2 != (^[Y0 : a]: ($false))) & (sK2 != (^[Y0 : a]: (~ $false)))) | ($true != sP1)),
% 0.19/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f12])).
% 0.19/0.29 thf(f14,plain,(
% 0.19/0.29 ? [X4 : (a > $o),X5 : (a > $o),X6 : (a > $o)] : (((^[Y0 : a]: (~ $false)) != X4) & (((^[Y0 : a]: ($false)) = X5) | ((^[Y0 : a]: (~ $false)) = X5)) & ((^[Y0 : a]: ((X6 @ Y0) & (X5 @ Y0))) = X4) & (((^[Y0 : a]: ($false)) = X6) | ((^[Y0 : a]: (~ $false)) = X6)) & ((^[Y0 : a]: ($false)) != X4)) | (sP0 != $true)),
% 0.19/0.29 inference(nnf_transformation,[],[f8])).
% 0.19/0.29 thf(f15,plain,(
% 0.19/0.29 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (((^[Y0 : a]: (~ $false)) != X0) & (((^[Y0 : a]: ($false)) = X1) | ((^[Y0 : a]: (~ $false)) = X1)) & ((^[Y0 : a]: ((X2 @ Y0) & (X1 @ Y0))) = X0) & (((^[Y0 : a]: ($false)) = X2) | ((^[Y0 : a]: (~ $false)) = X2)) & ((^[Y0 : a]: ($false)) != X0)) | (sP0 != $true)),
% 0.19/0.29 inference(rectify,[],[f14])).
% 0.19/0.29 thf(f16,plain,(
% 0.19/0.29 (((^[Y0 : a]: (~ $false)) != sK4) & (((^[Y0 : a]: ($false)) = sK5) | ((^[Y0 : a]: (~ $false)) = sK5)) & ((^[Y0 : a]: ((sK6 @ Y0) & (sK5 @ Y0))) = sK4) & ((sK6 = (^[Y0 : a]: ($false))) | (sK6 = (^[Y0 : a]: (~ $false)))) & ((^[Y0 : a]: ($false)) != sK4)) | (sP0 != $true)),
% 0.19/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6)],[f15])).
% 0.19/0.29 thf(f17,plain,(
% 0.19/0.29 ($true = sP1) | (sP0 = $true) | ? [X0 : (a > $o)] : (((^[Y0 : a]: (~ $false)) = X0) & ((^[Y0 : a]: (~ $false)) != X0) & ((^[Y0 : a]: ($false)) != X0)) | ? [X1 : (a > $o)] : (((^[Y0 : a]: ($false)) = X1) & ((^[Y0 : a]: ($false)) != X1) & ((^[Y0 : a]: (~ $false)) != X1))),
% 0.19/0.29 inference(rectify,[],[f10])).
% 0.19/0.29 thf(f18,plain,(
% 0.19/0.29 ($true = sP1) | (sP0 = $true) | (((^[Y0 : a]: (~ $false)) = sK7) & ((^[Y0 : a]: (~ $false)) != sK7) & ((^[Y0 : a]: ($false)) != sK7)) | (((^[Y0 : a]: ($false)) = sK8) & ((^[Y0 : a]: ($false)) != sK8) & ((^[Y0 : a]: (~ $false)) != sK8))),
% 0.19/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f17])).
% 0.19/0.29 thf(f19,plain,(
% 0.19/0.29 (sK2 != (^[Y0 : a]: (~ $false))) | ($true != sP1)),
% 0.19/0.29 inference(cnf_transformation,[],[f13])).
% 0.19/0.29 thf(f20,plain,(
% 0.19/0.29 (sK2 != (^[Y0 : a]: ($false))) | ($true != sP1)),
% 0.19/0.29 inference(cnf_transformation,[],[f13])).
% 0.19/0.29 thf(f21,plain,(
% 0.19/0.29 ( ! [X2 : (a > $o)] : (((^[Y0 : a]: ($false)) = X2) | (((sK3 @ X2)) != $true) | ((^[Y0 : a]: (~ $false)) = X2) | ($true != sP1)) )),
% 0.19/0.29 inference(cnf_transformation,[],[f13])).
% 0.19/0.29 thf(f22,plain,(
% 0.19/0.29 ($true != sP1) | (sK2 = (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((sK3 @ Y1) & (Y1 @ Y0))))))),
% 0.19/0.29 inference(cnf_transformation,[],[f13])).
% 0.19/0.29 thf(f23,plain,(
% 0.19/0.29 ((^[Y0 : a]: ($false)) != sK4) | (sP0 != $true)),
% 0.19/0.29 inference(cnf_transformation,[],[f16])).
% 0.19/0.29 thf(f24,plain,(
% 0.19/0.29 (sK6 = (^[Y0 : a]: (~ $false))) | (sK6 = (^[Y0 : a]: ($false))) | (sP0 != $true)),
% 0.19/0.29 inference(cnf_transformation,[],[f16])).
% 0.19/0.29 thf(f25,plain,(
% 0.19/0.29 ((^[Y0 : a]: ((sK6 @ Y0) & (sK5 @ Y0))) = sK4) | (sP0 != $true)),
% 0.19/0.29 inference(cnf_transformation,[],[f16])).
% 0.19/0.29 thf(f26,plain,(
% 0.19/0.29 ((^[Y0 : a]: ($false)) = sK5) | ((^[Y0 : a]: (~ $false)) = sK5) | (sP0 != $true)),
% 0.19/0.29 inference(cnf_transformation,[],[f16])).
% 0.19/0.29 thf(f27,plain,(
% 0.19/0.29 ((^[Y0 : a]: (~ $false)) != sK4) | (sP0 != $true)),
% 0.19/0.29 inference(cnf_transformation,[],[f16])).
% 0.19/0.29 thf(f32,plain,(
% 0.19/0.29 ($true = sP1) | ((^[Y0 : a]: (~ $false)) != sK7) | ((^[Y0 : a]: ($false)) != sK8) | (sP0 = $true)),
% 0.19/0.29 inference(cnf_transformation,[],[f18])).
% 0.19/0.29 thf(f33,plain,(
% 0.19/0.29 ((^[Y0 : a]: ($false)) = sK8) | ((^[Y0 : a]: (~ $false)) != sK7) | (sP0 = $true) | ($true = sP1)),
% 0.19/0.29 inference(cnf_transformation,[],[f18])).
% 0.19/0.29 thf(f35,plain,(
% 0.19/0.29 ((^[Y0 : a]: (~ $false)) = sK7) | (sP0 = $true) | ((^[Y0 : a]: ($false)) != sK8) | ($true = sP1)),
% 0.19/0.29 inference(cnf_transformation,[],[f18])).
% 0.19/0.29 thf(f36,plain,(
% 0.19/0.29 ((^[Y0 : a]: (~ $false)) = sK7) | ($true = sP1) | (sP0 = $true) | ((^[Y0 : a]: ($false)) = sK8)),
% 0.19/0.29 inference(cnf_transformation,[],[f18])).
% 0.19/0.29 thf(f38,plain,(
% 0.19/0.29 (sP0 != $true) | ((^[Y0 : a]: ($true)) != sK4)),
% 0.19/0.29 inference(boolean_simplification,[],[f27])).
% 0.19/0.29 thf(f39,plain,(
% 0.19/0.29 (sP0 != $true) | ((^[Y0 : a]: ($true)) = sK5) | ((^[Y0 : a]: ($false)) = sK5)),
% 0.19/0.29 inference(boolean_simplification,[],[f26])).
% 0.19/0.29 thf(f40,plain,(
% 0.19/0.29 ((^[Y0 : a]: ($false)) = sK8) | (sP0 = $true) | ((^[Y0 : a]: ($true)) != sK7) | ($true = sP1)),
% 0.19/0.29 inference(boolean_simplification,[],[f33])).
% 0.19/0.29 thf(f43,plain,(
% 0.19/0.29 ((^[Y0 : a]: ($true)) = sK7) | (sP0 = $true) | ($true = sP1) | ((^[Y0 : a]: ($false)) = sK8)),
% 0.19/0.29 inference(boolean_simplification,[],[f36])).
% 0.19/0.29 thf(f44,plain,(
% 0.19/0.29 (sP0 = $true) | ($true = sP1) | ((^[Y0 : a]: ($true)) = sK7) | ((^[Y0 : a]: ($false)) != sK8)),
% 0.19/0.29 inference(boolean_simplification,[],[f35])).
% 0.19/0.29 thf(f46,plain,(
% 0.19/0.29 ( ! [X2 : (a > $o)] : (((^[Y0 : a]: ($true)) = X2) | ((^[Y0 : a]: ($false)) = X2) | (((sK3 @ X2)) != $true) | ($true != sP1)) )),
% 0.19/0.29 inference(boolean_simplification,[],[f21])).
% 0.19/0.29 thf(f47,plain,(
% 0.19/0.29 (sP0 != $true) | (sK6 = (^[Y0 : a]: ($false))) | ((^[Y0 : a]: ($true)) = sK6)),
% 0.19/0.29 inference(boolean_simplification,[],[f24])).
% 0.19/0.29 thf(f48,plain,(
% 0.19/0.29 ($true != sP1) | ((^[Y0 : a]: ($true)) != sK2)),
% 0.19/0.29 inference(boolean_simplification,[],[f19])).
% 0.19/0.29 thf(f49,plain,(
% 0.19/0.29 ($true = sP1) | ((^[Y0 : a]: ($true)) != sK7) | ((^[Y0 : a]: ($false)) != sK8) | (sP0 = $true)),
% 0.19/0.29 inference(boolean_simplification,[],[f32])).
% 0.19/0.29 thf(f53,definition,(
% 0.19/0.29 spl9_1 <=> ((^[Y0 : a]: ($true)) = sK4)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition])).
% 0.19/0.29 thf(f57,definition,(
% 0.19/0.29 spl9_2 <=> (sP0 = $true)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition])).
% 0.19/0.29 thf(f60,plain,(
% 0.19/0.29 ~spl9_1 | ~spl9_2),
% 0.19/0.29 inference(avatar_split_clause,[],[f38,f57,f53])).
% 0.19/0.29 thf(f62,definition,(
% 0.19/0.29 spl9_3 <=> ($true = sP1)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition])).
% 0.19/0.29 thf(f64,plain,(
% 0.19/0.29 ($true != sP1) | spl9_3),
% 0.19/0.29 inference(avatar_component_clause,[],[f62])).
% 0.19/0.29 thf(f66,definition,(
% 0.19/0.29 spl9_4 <=> (sK2 = (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((sK3 @ Y1) & (Y1 @ Y0))))))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition])).
% 0.19/0.29 thf(f68,plain,(
% 0.19/0.29 (sK2 = (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((sK3 @ Y1) & (Y1 @ Y0)))))) | ~spl9_4),
% 0.19/0.29 inference(avatar_component_clause,[],[f66])).
% 0.19/0.29 thf(f69,plain,(
% 0.19/0.29 ~spl9_3 | spl9_4),
% 0.19/0.29 inference(avatar_split_clause,[],[f22,f66,f62])).
% 0.19/0.29 thf(f71,definition,(
% 0.19/0.29 spl9_5 <=> (sK2 = (^[Y0 : a]: ($false)))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition])).
% 0.19/0.29 thf(f73,plain,(
% 0.19/0.29 (sK2 != (^[Y0 : a]: ($false))) | spl9_5),
% 0.19/0.29 inference(avatar_component_clause,[],[f71])).
% 0.19/0.29 thf(f74,plain,(
% 0.19/0.29 ~spl9_3 | ~spl9_5),
% 0.19/0.29 inference(avatar_split_clause,[],[f20,f71,f62])).
% 0.19/0.29 thf(f80,definition,(
% 0.19/0.29 spl9_7 <=> ((^[Y0 : a]: ($false)) = sK8)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl9_7])],[avatar_definition])).
% 0.19/0.29 thf(f85,definition,(
% 0.19/0.29 spl9_8 <=> ((^[Y0 : a]: ($true)) = sK5)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl9_8])],[avatar_definition])).
% 0.19/0.29 thf(f89,definition,(
% 0.19/0.29 spl9_9 <=> ((^[Y0 : a]: ($false)) = sK5)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl9_9])],[avatar_definition])).
% 0.19/0.29 thf(f91,plain,(
% 0.19/0.29 ((^[Y0 : a]: ($false)) = sK5) | ~spl9_9),
% 0.19/0.29 inference(avatar_component_clause,[],[f89])).
% 0.19/0.29 thf(f92,plain,(
% 0.19/0.29 spl9_8 | spl9_9 | ~spl9_2),
% 0.19/0.29 inference(avatar_split_clause,[],[f39,f57,f89,f85])).
% 0.19/0.29 thf(f94,definition,(
% 0.19/0.29 spl9_10 <=> ((^[Y0 : a]: ($true)) = sK7)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl9_10])],[avatar_definition])).
% 0.19/0.29 thf(f97,plain,(
% 0.19/0.29 spl9_2 | spl9_7 | ~spl9_10 | spl9_3),
% 0.19/0.29 inference(avatar_split_clause,[],[f40,f62,f94,f80,f57])).
% 0.19/0.29 thf(f99,definition,(
% 0.19/0.29 spl9_11 <=> ((^[Y0 : a]: ($false)) = sK4)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl9_11])],[avatar_definition])).
% 0.19/0.29 thf(f101,plain,(
% 0.19/0.29 ((^[Y0 : a]: ($false)) != sK4) | spl9_11),
% 0.19/0.29 inference(avatar_component_clause,[],[f99])).
% 0.19/0.29 thf(f102,plain,(
% 0.19/0.29 ~spl9_2 | ~spl9_11),
% 0.19/0.29 inference(avatar_split_clause,[],[f23,f99,f57])).
% 0.19/0.29 thf(f109,definition,(
% 0.19/0.29 spl9_13 <=> ((^[Y0 : a]: ((sK6 @ Y0) & (sK5 @ Y0))) = sK4)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl9_13])],[avatar_definition])).
% 0.19/0.29 thf(f111,plain,(
% 0.19/0.29 ((^[Y0 : a]: ((sK6 @ Y0) & (sK5 @ Y0))) = sK4) | ~spl9_13),
% 0.19/0.29 inference(avatar_component_clause,[],[f109])).
% 0.19/0.29 thf(f112,plain,(
% 0.19/0.29 ~spl9_2 | spl9_13),
% 0.19/0.29 inference(avatar_split_clause,[],[f25,f109,f57])).
% 0.19/0.29 thf(f113,plain,(
% 0.19/0.29 spl9_3 | spl9_7 | spl9_2 | spl9_10),
% 0.19/0.29 inference(avatar_split_clause,[],[f43,f94,f57,f80,f62])).
% 0.19/0.29 thf(f114,plain,(
% 0.19/0.29 spl9_10 | ~spl9_7 | spl9_2 | spl9_3),
% 0.19/0.29 inference(avatar_split_clause,[],[f44,f62,f57,f80,f94])).
% 0.19/0.29 thf(f117,definition,(
% 0.19/0.29 spl9_14 <=> ! [X2 : (a > $o)] : (((^[Y0 : a]: ($true)) = X2) | (((sK3 @ X2)) != $true) | ((^[Y0 : a]: ($false)) = X2))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl9_14])],[avatar_definition])).
% 0.19/0.29 thf(f118,plain,(
% 0.19/0.29 ( ! [X2 : (a > $o)] : ((((sK3 @ X2)) != $true) | ((^[Y0 : a]: ($false)) = X2) | ((^[Y0 : a]: ($true)) = X2)) ) | ~spl9_14),
% 0.19/0.29 inference(avatar_component_clause,[],[f117])).
% 0.19/0.29 thf(f119,plain,(
% 0.19/0.29 spl9_14 | ~spl9_3),
% 0.19/0.29 inference(avatar_split_clause,[],[f46,f62,f117])).
% 0.19/0.29 thf(f121,definition,(
% 0.19/0.29 spl9_15 <=> (sK6 = (^[Y0 : a]: ($false)))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl9_15])],[avatar_definition])).
% 0.19/0.29 thf(f123,plain,(
% 0.19/0.29 (sK6 = (^[Y0 : a]: ($false))) | ~spl9_15),
% 0.19/0.29 inference(avatar_component_clause,[],[f121])).
% 0.19/0.29 thf(f125,definition,(
% 0.19/0.29 spl9_16 <=> ((^[Y0 : a]: ($true)) = sK6)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl9_16])],[avatar_definition])).
% 0.19/0.29 thf(f128,plain,(
% 0.19/0.29 spl9_15 | ~spl9_2 | spl9_16),
% 0.19/0.29 inference(avatar_split_clause,[],[f47,f125,f57,f121])).
% 0.19/0.29 thf(f130,definition,(
% 0.19/0.29 spl9_17 <=> ((^[Y0 : a]: ($true)) = sK2)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl9_17])],[avatar_definition])).
% 0.19/0.29 thf(f132,plain,(
% 0.19/0.29 ((^[Y0 : a]: ($true)) != sK2) | spl9_17),
% 0.19/0.29 inference(avatar_component_clause,[],[f130])).
% 0.19/0.29 thf(f133,plain,(
% 0.19/0.29 ~spl9_3 | ~spl9_17),
% 0.19/0.29 inference(avatar_split_clause,[],[f48,f130,f62])).
% 0.19/0.29 thf(f135,plain,(
% 0.19/0.29 ~spl9_7 | ~spl9_10 | spl9_2 | spl9_3),
% 0.19/0.29 inference(avatar_split_clause,[],[f49,f62,f57,f94,f80])).
% 0.19/0.29 thf(f138,plain,(
% 0.19/0.29 ( ! [X1 : a] : ((((sK2 @ X1)) = (((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((sK3 @ Y1) & (Y1 @ Y0))))) @ X1)))) ) | ~spl9_4),
% 0.19/0.29 inference(argument_congruence,[],[f68])).
% 0.19/0.29 thf(f139,plain,(
% 0.19/0.29 ( ! [X1 : a] : ((((sK2 @ X1)) = $true) | ($false = (((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((sK3 @ Y1) & (Y1 @ Y0))))) @ X1)))) ) | ~spl9_4),
% 0.19/0.29 inference(iff_proxy_clausification,[],[f138])).
% 0.19/0.29 thf(f140,plain,(
% 0.19/0.29 ( ! [X1 : a] : ((((sK2 @ X1)) = $false) | ($true = (((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((sK3 @ Y1) & (Y1 @ Y0))))) @ X1)))) ) | ~spl9_4),
% 0.19/0.29 inference(iff_proxy_clausification,[],[f138])).
% 0.19/0.29 thf(f141,plain,(
% 0.19/0.29 ( ! [X1 : a] : ((((?? @ (a > $o) @ (^[Y0 : a > $o]: ((sK3 @ Y0) & (Y0 @ X1))))) = $true) | (((sK2 @ X1)) = $false)) ) | ~spl9_4),
% 0.19/0.29 inference(beta-eta_normalization,[],[f140])).
% 0.19/0.29 thf(f142,plain,(
% 0.19/0.29 ( ! [X1 : a] : (((((^[Y0 : a > $o]: ((sK3 @ Y0) & (Y0 @ X1))) @ (sK10 @ X1))) = $true) | (((sK2 @ X1)) = $false)) ) | ~spl9_4),
% 0.19/0.29 inference(sigma_proxy_clausification,[],[f141])).
% 0.19/0.29 thf(f143,plain,(
% 0.19/0.29 ( ! [X1 : a] : (($true = (((sK3 @ (sK10 @ X1)) & (sK10 @ X1 @ X1)))) | (((sK2 @ X1)) = $false)) ) | ~spl9_4),
% 0.19/0.29 inference(beta-eta_normalization,[],[f142])).
% 0.19/0.29 thf(f144,plain,(
% 0.19/0.29 ( ! [X1 : a] : ((((sK10 @ X1 @ X1)) = $true) | (((sK2 @ X1)) = $false)) ) | ~spl9_4),
% 0.19/0.29 inference(and_proxy_clausification,[],[f143])).
% 0.19/0.29 thf(f145,plain,(
% 0.19/0.29 ( ! [X1 : a] : (($true = ((sK3 @ (sK10 @ X1)))) | (((sK2 @ X1)) = $false)) ) | ~spl9_4),
% 0.19/0.29 inference(and_proxy_clausification,[],[f143])).
% 0.19/0.29 thf(f146,plain,(
% 0.19/0.29 ( ! [X1 : a] : ((((sK2 @ X1)) = $true) | ($false = ((?? @ (a > $o) @ (^[Y0 : a > $o]: ((sK3 @ Y0) & (Y0 @ X1))))))) ) | ~spl9_4),
% 0.19/0.29 inference(beta-eta_normalization,[],[f139])).
% 0.19/0.29 thf(f147,plain,(
% 0.19/0.29 ( ! [X2 : (a > $o),X1 : a] : ((((sK2 @ X1)) = $true) | ((((^[Y0 : a > $o]: ((sK3 @ Y0) & (Y0 @ X1))) @ X2)) = $false)) ) | ~spl9_4),
% 0.19/0.29 inference(pi_proxy_clausification,[],[f146])).
% 0.19/0.29 thf(f148,plain,(
% 0.19/0.29 ( ! [X2 : (a > $o),X1 : a] : ((((sK2 @ X1)) = $true) | ($false = (((sK3 @ X2) & (X2 @ X1))))) ) | ~spl9_4),
% 0.19/0.29 inference(beta-eta_normalization,[],[f147])).
% 0.19/0.29 thf(f149,plain,(
% 0.19/0.29 ( ! [X2 : (a > $o),X1 : a] : ((((sK3 @ X2)) = $false) | (((X2 @ X1)) = $false) | (((sK2 @ X1)) = $true)) ) | ~spl9_4),
% 0.19/0.29 inference(and_proxy_clausification,[],[f148])).
% 0.19/0.29 thf(f150,plain,(
% 0.19/0.29 ( ! [X0 : a] : ((((sK10 @ X0)) = (^[Y0 : a]: ($false))) | ($false = ((sK2 @ X0))) | ($true != $true) | ((^[Y0 : a]: ($true)) = ((sK10 @ X0)))) ) | (~spl9_4 | ~spl9_14)),
% 0.19/0.29 inference(superposition,[],[f118,f145])).
% 0.19/0.29 thf(f151,plain,(
% 0.19/0.29 ( ! [X0 : a] : (((^[Y0 : a]: ($true)) = ((sK10 @ X0))) | ($false = ((sK2 @ X0))) | (((sK10 @ X0)) = (^[Y0 : a]: ($false)))) ) | (~spl9_4 | ~spl9_14)),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f150])).
% 0.19/0.29 thf(f162,plain,(
% 0.19/0.29 ( ! [X0 : a] : (($false = ((sK2 @ X0))) | (((sK3 @ (^[Y0 : a]: ($true)))) = $true) | ($false = ((sK2 @ X0))) | (((sK10 @ X0)) = (^[Y0 : a]: ($false)))) ) | (~spl9_4 | ~spl9_14)),
% 0.19/0.29 inference(superposition,[],[f145,f151])).
% 0.19/0.29 thf(f169,plain,(
% 0.19/0.29 ( ! [X0 : a] : ((((sK3 @ (^[Y0 : a]: ($true)))) = $true) | (((sK10 @ X0)) = (^[Y0 : a]: ($false))) | ($false = ((sK2 @ X0)))) ) | (~spl9_4 | ~spl9_14)),
% 0.19/0.29 inference(duplicate_literal_removal,[],[f162])).
% 0.19/0.29 thf(f171,definition,(
% 0.19/0.29 spl9_18 <=> ! [X0 : a] : (($false = ((sK2 @ X0))) | (((sK10 @ X0)) = (^[Y0 : a]: ($false))))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl9_18])],[avatar_definition])).
% 0.19/0.29 thf(f172,plain,(
% 0.19/0.29 ( ! [X0 : a] : ((((sK10 @ X0)) = (^[Y0 : a]: ($false))) | ($false = ((sK2 @ X0)))) ) | ~spl9_18),
% 0.19/0.29 inference(avatar_component_clause,[],[f171])).
% 0.19/0.29 thf(f179,definition,(
% 0.19/0.29 spl9_20 <=> (((sK3 @ (^[Y0 : a]: ($true)))) = $true)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl9_20])],[avatar_definition])).
% 0.19/0.29 thf(f181,plain,(
% 0.19/0.29 (((sK3 @ (^[Y0 : a]: ($true)))) = $true) | ~spl9_20),
% 0.19/0.29 inference(avatar_component_clause,[],[f179])).
% 0.19/0.29 thf(f182,plain,(
% 0.19/0.29 spl9_18 | spl9_20 | ~spl9_4 | ~spl9_14),
% 0.19/0.29 inference(avatar_split_clause,[],[f169,f117,f66,f179,f171])).
% 0.19/0.29 thf(f184,plain,(
% 0.19/0.29 ( ! [X0 : a] : (($false = (((^[Y0 : a]: ($true)) @ X0))) | ($true = ((sK2 @ X0))) | ($false = $true)) ) | (~spl9_4 | ~spl9_20)),
% 0.19/0.29 inference(superposition,[],[f149,f181])).
% 0.19/0.29 thf(f185,plain,(
% 0.19/0.29 ( ! [X0 : a] : (($true = ((sK2 @ X0))) | ($false = (((^[Y0 : a]: ($true)) @ X0)))) ) | (~spl9_4 | ~spl9_20)),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f184])).
% 0.19/0.29 thf(f186,plain,(
% 0.19/0.29 ( ! [X0 : a] : (($false = $true) | ($true = ((sK2 @ X0)))) ) | (~spl9_4 | ~spl9_20)),
% 0.19/0.29 inference(beta-eta_normalization,[],[f185])).
% 0.19/0.29 thf(f187,plain,(
% 0.19/0.29 ( ! [X0 : a] : (($true = ((sK2 @ X0)))) ) | (~spl9_4 | ~spl9_20)),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f186])).
% 0.19/0.29 thf(f201,plain,(
% 0.19/0.29 ((((^[Y0 : a]: ($false)) @ sK11)) != ((sK2 @ sK11))) | spl9_5),
% 0.19/0.29 inference(negative_extensionality,[],[f73])).
% 0.19/0.29 thf(f202,plain,(
% 0.19/0.29 ($true = ((sK2 @ sK11))) | ((((^[Y0 : a]: ($false)) @ sK11)) = $true) | spl9_5),
% 0.19/0.29 inference(xor_proxy_clausification,[],[f201])).
% 0.19/0.29 thf(f205,plain,(
% 0.19/0.29 ($true = ((sK2 @ sK11))) | ($false = $true) | spl9_5),
% 0.19/0.29 inference(beta-eta_normalization,[],[f202])).
% 0.19/0.29 thf(f206,plain,(
% 0.19/0.29 ($true = ((sK2 @ sK11))) | spl9_5),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f205])).
% 0.19/0.29 thf(f236,plain,(
% 0.19/0.29 ((((^[Y0 : a]: ($true)) @ sK12)) != ((sK2 @ sK12))) | spl9_17),
% 0.19/0.30 inference(negative_extensionality,[],[f132])).
% 0.19/0.30 thf(f238,plain,(
% 0.19/0.30 ((((^[Y0 : a]: ($true)) @ sK12)) = $false) | ($false = ((sK2 @ sK12))) | spl9_17),
% 0.19/0.30 inference(xor_proxy_clausification,[],[f236])).
% 0.19/0.30 thf(f239,plain,(
% 0.19/0.30 ($false = $true) | ($false = ((sK2 @ sK12))) | spl9_17),
% 0.19/0.30 inference(beta-eta_normalization,[],[f238])).
% 0.19/0.30 thf(f240,plain,(
% 0.19/0.30 ($false = ((sK2 @ sK12))) | spl9_17),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f239])).
% 0.19/0.30 thf(f242,plain,(
% 0.19/0.30 ($false = $true) | (~spl9_4 | spl9_17 | ~spl9_20)),
% 0.19/0.30 inference(forward_demodulation,[],[f240,f187])).
% 0.19/0.30 thf(f243,plain,(
% 0.19/0.30 $false | (~spl9_4 | spl9_17 | ~spl9_20)),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f242])).
% 0.19/0.30 thf(f244,plain,(
% 0.19/0.30 ~spl9_4 | spl9_17 | ~spl9_20),
% 0.19/0.30 inference(avatar_contradiction_clause,[],[f243])).
% 0.19/0.30 thf(f246,definition,(
% 0.19/0.30 spl9_24 <=> ($true = ((sK2 @ sK11)))),
% 0.19/0.30 introduced(definition,[new_symbols(definition,[spl9_24])],[avatar_definition])).
% 0.19/0.30 thf(f248,plain,(
% 0.19/0.30 ($true = ((sK2 @ sK11))) | ~spl9_24),
% 0.19/0.30 inference(avatar_component_clause,[],[f246])).
% 0.19/0.30 thf(f249,plain,(
% 0.19/0.30 spl9_24 | spl9_5),
% 0.19/0.30 inference(avatar_split_clause,[],[f206,f71,f246])).
% 0.19/0.30 thf(f263,definition,(
% 0.19/0.30 spl9_27 <=> ! [X0 : a] : ($false = ((sK2 @ X0)))),
% 0.19/0.30 introduced(definition,[new_symbols(definition,[spl9_27])],[avatar_definition])).
% 0.19/0.30 thf(f264,plain,(
% 0.19/0.30 ( ! [X0 : a] : (($false = ((sK2 @ X0)))) ) | ~spl9_27),
% 0.19/0.30 inference(avatar_component_clause,[],[f263])).
% 0.19/0.30 thf(f285,plain,(
% 0.19/0.30 ( ! [X0 : a,X1 : a] : (($false = ((sK2 @ X0))) | (((sK10 @ X0 @ X1)) = (((^[Y0 : a]: ($false)) @ X1)))) ) | ~spl9_18),
% 0.19/0.30 inference(argument_congruence,[],[f172])).
% 0.19/0.30 thf(f290,plain,(
% 0.19/0.30 ( ! [X0 : a,X1 : a] : (($false = ((sK2 @ X0))) | ($true = (((^[Y0 : a]: ($false)) @ X1))) | (((sK10 @ X0 @ X1)) = $false)) ) | ~spl9_18),
% 0.19/0.30 inference(iff_proxy_clausification,[],[f285])).
% 0.19/0.30 thf(f291,plain,(
% 0.19/0.30 ( ! [X0 : a,X1 : a] : ((((sK10 @ X0 @ X1)) = $false) | ($false = ((sK2 @ X0))) | ($false = $true)) ) | ~spl9_18),
% 0.19/0.30 inference(beta-eta_normalization,[],[f290])).
% 0.19/0.30 thf(f292,plain,(
% 0.19/0.30 ( ! [X0 : a,X1 : a] : ((((sK10 @ X0 @ X1)) = $false) | ($false = ((sK2 @ X0)))) ) | ~spl9_18),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f291])).
% 0.19/0.30 thf(f295,plain,(
% 0.19/0.30 ( ! [X0 : a] : (($false = $true) | ($false = ((sK2 @ X0))) | ($false = ((sK2 @ X0)))) ) | (~spl9_4 | ~spl9_18)),
% 0.19/0.30 inference(superposition,[],[f292,f144])).
% 0.19/0.30 thf(f297,plain,(
% 0.19/0.30 ( ! [X0 : a] : (($false = ((sK2 @ X0))) | ($false = $true)) ) | (~spl9_4 | ~spl9_18)),
% 0.19/0.30 inference(duplicate_literal_removal,[],[f295])).
% 0.19/0.30 thf(f298,plain,(
% 0.19/0.30 ( ! [X0 : a] : (($false = ((sK2 @ X0)))) ) | (~spl9_4 | ~spl9_18)),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f297])).
% 0.19/0.30 thf(f301,plain,(
% 0.19/0.30 spl9_27 | ~spl9_4 | ~spl9_18),
% 0.19/0.30 inference(avatar_split_clause,[],[f298,f171,f66,f263])).
% 0.19/0.30 thf(f302,plain,(
% 0.19/0.30 ($false = $true) | (~spl9_24 | ~spl9_27)),
% 0.19/0.30 inference(superposition,[],[f264,f248])).
% 0.19/0.30 thf(f306,plain,(
% 0.19/0.30 $false | (~spl9_24 | ~spl9_27)),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f302])).
% 0.19/0.30 thf(f307,plain,(
% 0.19/0.30 ~spl9_24 | ~spl9_27),
% 0.19/0.30 inference(avatar_contradiction_clause,[],[f306])).
% 0.19/0.30 thf(f311,plain,(
% 0.19/0.30 ($false = sP1) | ($true != $true) | spl9_3),
% 0.19/0.30 inference(fool_paramodulation,[],[f64])).
% 0.19/0.30 thf(f312,plain,(
% 0.19/0.30 ($false = sP1) | spl9_3),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f311])).
% 0.19/0.30 thf(f314,definition,(
% 0.19/0.30 spl9_28 <=> ($false = sP1)),
% 0.19/0.30 introduced(definition,[new_symbols(definition,[spl9_28])],[avatar_definition])).
% 0.19/0.30 thf(f317,plain,(
% 0.19/0.30 spl9_28 | spl9_3),
% 0.19/0.30 inference(avatar_split_clause,[],[f312,f62,f314])).
% 0.19/0.30 thf(f333,plain,(
% 0.19/0.30 ( ! [X1 : a] : ((((sK6 @ X1)) = (((^[Y0 : a]: ($false)) @ X1)))) ) | ~spl9_15),
% 0.19/0.30 inference(argument_congruence,[],[f123])).
% 0.19/0.30 thf(f335,plain,(
% 0.19/0.30 ( ! [X1 : a] : (($true = (((^[Y0 : a]: ($false)) @ X1))) | ($false = ((sK6 @ X1)))) ) | ~spl9_15),
% 0.19/0.30 inference(iff_proxy_clausification,[],[f333])).
% 0.19/0.30 thf(f336,plain,(
% 0.19/0.30 ( ! [X1 : a] : (($false = $true) | ($false = ((sK6 @ X1)))) ) | ~spl9_15),
% 0.19/0.30 inference(beta-eta_normalization,[],[f335])).
% 0.19/0.30 thf(f337,plain,(
% 0.19/0.30 ( ! [X1 : a] : (($false = ((sK6 @ X1)))) ) | ~spl9_15),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f336])).
% 0.19/0.30 thf(f341,definition,(
% 0.19/0.30 spl9_29 <=> (sK5 = sK4)),
% 0.19/0.30 introduced(definition,[new_symbols(definition,[spl9_29])],[avatar_definition])).
% 0.19/0.30 thf(f343,plain,(
% 0.19/0.30 (sK5 != sK4) | spl9_29),
% 0.19/0.30 inference(avatar_component_clause,[],[f341])).
% 0.19/0.30 thf(f354,plain,(
% 0.19/0.30 ( ! [X1 : a] : (((((^[Y0 : a]: ((sK6 @ Y0) & (sK5 @ Y0))) @ X1)) = ((sK4 @ X1)))) ) | ~spl9_13),
% 0.19/0.30 inference(argument_congruence,[],[f111])).
% 0.19/0.30 thf(f355,plain,(
% 0.19/0.30 ( ! [X1 : a] : (((((^[Y0 : a]: ((sK6 @ Y0) & (sK5 @ Y0))) @ X1)) = $true) | (((sK4 @ X1)) = $false)) ) | ~spl9_13),
% 0.19/0.30 inference(iff_proxy_clausification,[],[f354])).
% 0.19/0.30 thf(f356,plain,(
% 0.19/0.30 ( ! [X1 : a] : ((((sK4 @ X1)) = $true) | ((((^[Y0 : a]: ((sK6 @ Y0) & (sK5 @ Y0))) @ X1)) = $false)) ) | ~spl9_13),
% 0.19/0.30 inference(iff_proxy_clausification,[],[f354])).
% 0.19/0.30 thf(f357,plain,(
% 0.19/0.30 ( ! [X1 : a] : (((((sK6 @ X1) & (sK5 @ X1))) = $false) | (((sK4 @ X1)) = $true)) ) | ~spl9_13),
% 0.19/0.30 inference(beta-eta_normalization,[],[f356])).
% 0.19/0.30 thf(f358,plain,(
% 0.19/0.30 ( ! [X1 : a] : (($false = ((sK6 @ X1))) | ($false = ((sK5 @ X1))) | (((sK4 @ X1)) = $true)) ) | ~spl9_13),
% 0.19/0.30 inference(and_proxy_clausification,[],[f357])).
% 0.19/0.30 thf(f359,plain,(
% 0.19/0.30 ( ! [X1 : a] : ((((sK4 @ X1)) = $false) | ((((sK6 @ X1) & (sK5 @ X1))) = $true)) ) | ~spl9_13),
% 0.19/0.30 inference(beta-eta_normalization,[],[f355])).
% 0.19/0.30 thf(f360,plain,(
% 0.19/0.30 ( ! [X1 : a] : (($true = ((sK5 @ X1))) | (((sK4 @ X1)) = $false)) ) | ~spl9_13),
% 0.19/0.30 inference(and_proxy_clausification,[],[f359])).
% 0.19/0.30 thf(f361,plain,(
% 0.19/0.30 ( ! [X1 : a] : (($true = ((sK6 @ X1))) | (((sK4 @ X1)) = $false)) ) | ~spl9_13),
% 0.19/0.30 inference(and_proxy_clausification,[],[f359])).
% 0.19/0.30 thf(f362,plain,(
% 0.19/0.30 ( ! [X1 : a] : (($false = $true) | (((sK4 @ X1)) = $false)) ) | (~spl9_13 | ~spl9_15)),
% 0.19/0.30 inference(forward_demodulation,[],[f361,f337])).
% 0.19/0.30 thf(f363,plain,(
% 0.19/0.30 ( ! [X1 : a] : ((((sK4 @ X1)) = $false)) ) | (~spl9_13 | ~spl9_15)),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f362])).
% 0.19/0.30 thf(f364,plain,(
% 0.19/0.30 (((sK5 @ sK14)) != ((sK4 @ sK14))) | spl9_29),
% 0.19/0.30 inference(negative_extensionality,[],[f343])).
% 0.19/0.30 thf(f365,plain,(
% 0.19/0.30 (((sK5 @ sK14)) = $true) | (((sK4 @ sK14)) = $true) | spl9_29),
% 0.19/0.30 inference(xor_proxy_clausification,[],[f364])).
% 0.19/0.30 thf(f366,plain,(
% 0.19/0.30 (((sK5 @ sK14)) = $false) | (((sK4 @ sK14)) = $false) | spl9_29),
% 0.19/0.30 inference(xor_proxy_clausification,[],[f364])).
% 0.19/0.30 thf(f379,plain,(
% 0.19/0.30 (sK6 != sK4) | (spl9_11 | ~spl9_15)),
% 0.19/0.30 inference(forward_demodulation,[],[f101,f123])).
% 0.19/0.30 thf(f381,definition,(
% 0.19/0.30 spl9_32 <=> (sK6 = sK4)),
% 0.19/0.30 introduced(definition,[new_symbols(definition,[spl9_32])],[avatar_definition])).
% 0.19/0.30 thf(f383,plain,(
% 0.19/0.30 (sK6 != sK4) | spl9_32),
% 0.19/0.30 inference(avatar_component_clause,[],[f381])).
% 0.19/0.30 thf(f384,plain,(
% 0.19/0.30 ~spl9_32 | spl9_11 | ~spl9_15),
% 0.19/0.30 inference(avatar_split_clause,[],[f379,f121,f99,f381])).
% 0.19/0.30 thf(f385,plain,(
% 0.19/0.30 (((sK6 @ sK15)) != ((sK4 @ sK15))) | spl9_32),
% 0.19/0.30 inference(negative_extensionality,[],[f383])).
% 0.19/0.30 thf(f386,plain,(
% 0.19/0.30 (((sK4 @ sK15)) = $true) | (((sK6 @ sK15)) = $true) | spl9_32),
% 0.19/0.30 inference(xor_proxy_clausification,[],[f385])).
% 0.19/0.30 thf(f387,plain,(
% 0.19/0.30 (((sK4 @ sK15)) = $false) | (((sK6 @ sK15)) = $false) | spl9_32),
% 0.19/0.30 inference(xor_proxy_clausification,[],[f385])).
% 0.19/0.30 thf(f388,plain,(
% 0.19/0.30 ($false = $true) | (((sK4 @ sK15)) = $true) | (~spl9_15 | spl9_32)),
% 0.19/0.30 inference(forward_demodulation,[],[f386,f337])).
% 0.19/0.30 thf(f389,plain,(
% 0.19/0.30 (((sK4 @ sK15)) = $true) | (~spl9_15 | spl9_32)),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f388])).
% 0.19/0.30 thf(f390,plain,(
% 0.19/0.30 ($false = $true) | (~spl9_13 | ~spl9_15 | spl9_32)),
% 0.19/0.30 inference(forward_demodulation,[],[f389,f363])).
% 0.19/0.30 thf(f391,plain,(
% 0.19/0.30 $false | (~spl9_13 | ~spl9_15 | spl9_32)),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f390])).
% 0.19/0.30 thf(f392,plain,(
% 0.19/0.30 ~spl9_13 | ~spl9_15 | spl9_32),
% 0.19/0.30 inference(avatar_contradiction_clause,[],[f391])).
% 0.19/0.30 thf(f394,definition,(
% 0.19/0.30 spl9_33 <=> (((sK4 @ sK15)) = $true)),
% 0.19/0.30 introduced(definition,[new_symbols(definition,[spl9_33])],[avatar_definition])).
% 0.19/0.30 thf(f398,definition,(
% 0.19/0.30 spl9_34 <=> (((sK6 @ sK15)) = $true)),
% 0.19/0.30 introduced(definition,[new_symbols(definition,[spl9_34])],[avatar_definition])).
% 0.19/0.30 thf(f400,plain,(
% 0.19/0.30 (((sK6 @ sK15)) = $true) | ~spl9_34),
% 0.19/0.30 inference(avatar_component_clause,[],[f398])).
% 0.19/0.30 thf(f401,plain,(
% 0.19/0.30 spl9_33 | spl9_34 | spl9_32),
% 0.19/0.30 inference(avatar_split_clause,[],[f386,f381,f398,f394])).
% 0.19/0.30 thf(f403,definition,(
% 0.19/0.30 spl9_35 <=> (((sK4 @ sK15)) = $false)),
% 0.19/0.30 introduced(definition,[new_symbols(definition,[spl9_35])],[avatar_definition])).
% 0.19/0.30 thf(f407,definition,(
% 0.19/0.30 spl9_36 <=> (((sK6 @ sK15)) = $false)),
% 0.19/0.30 introduced(definition,[new_symbols(definition,[spl9_36])],[avatar_definition])).
% 0.19/0.30 thf(f409,plain,(
% 0.19/0.30 (((sK6 @ sK15)) = $false) | ~spl9_36),
% 0.19/0.30 inference(avatar_component_clause,[],[f407])).
% 0.19/0.30 thf(f410,plain,(
% 0.19/0.30 spl9_35 | spl9_36 | spl9_32),
% 0.19/0.30 inference(avatar_split_clause,[],[f387,f381,f407,f403])).
% 0.19/0.30 thf(f417,definition,(
% 0.19/0.30 spl9_37 <=> (((sK4 @ sK14)) = $false)),
% 0.19/0.30 introduced(definition,[new_symbols(definition,[spl9_37])],[avatar_definition])).
% 0.19/0.30 thf(f430,definition,(
% 0.19/0.30 spl9_39 <=> (((sK5 @ sK14)) = $false)),
% 0.19/0.30 introduced(definition,[new_symbols(definition,[spl9_39])],[avatar_definition])).
% 0.19/0.30 thf(f432,plain,(
% 0.19/0.30 (((sK5 @ sK14)) = $false) | ~spl9_39),
% 0.19/0.30 inference(avatar_component_clause,[],[f430])).
% 0.19/0.30 thf(f433,plain,(
% 0.19/0.30 spl9_39 | spl9_37 | spl9_29),
% 0.19/0.30 inference(avatar_split_clause,[],[f366,f341,f417,f430])).
% 0.19/0.30 thf(f435,definition,(
% 0.19/0.30 spl9_40 <=> (((sK5 @ sK14)) = $true)),
% 0.19/0.30 introduced(definition,[new_symbols(definition,[spl9_40])],[avatar_definition])).
% 0.19/0.30 thf(f437,plain,(
% 0.19/0.30 (((sK5 @ sK14)) = $true) | ~spl9_40),
% 0.19/0.30 inference(avatar_component_clause,[],[f435])).
% 0.19/0.30 thf(f439,definition,(
% 0.19/0.30 spl9_41 <=> (((sK4 @ sK14)) = $true)),
% 0.19/0.30 introduced(definition,[new_symbols(definition,[spl9_41])],[avatar_definition])).
% 0.19/0.30 thf(f442,plain,(
% 0.19/0.30 spl9_40 | spl9_41 | spl9_29),
% 0.19/0.30 inference(avatar_split_clause,[],[f365,f341,f439,f435])).
% 0.19/0.30 thf(f476,plain,(
% 0.19/0.30 ($false = $true) | (((sK4 @ sK14)) = $false) | (~spl9_13 | ~spl9_39)),
% 0.19/0.30 inference(superposition,[],[f360,f432])).
% 0.19/0.30 thf(f482,plain,(
% 0.19/0.30 (((sK4 @ sK14)) = $false) | (~spl9_13 | ~spl9_39)),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f476])).
% 0.19/0.30 thf(f488,plain,(
% 0.19/0.30 spl9_37 | ~spl9_13 | ~spl9_39),
% 0.19/0.30 inference(avatar_split_clause,[],[f482,f430,f109,f417])).
% 0.19/0.30 thf(f499,definition,(
% 0.19/0.30 ($false != sP1) | (((sK4 @ sK14)) != $false) | (((sK4 @ sK14)) != $true) | ($true = sP1)),
% 0.19/0.30 introduced(theory,[theory_tautology_sat_conflict])).
% 0.19/0.30 thf(f502,definition,(
% 0.19/0.30 ((^[Y0 : a]: ($false)) != sK5) | (sK5 != sK4) | ((^[Y0 : a]: ($false)) = sK4)),
% 0.19/0.30 introduced(theory,[theory_tautology_sat_conflict])).
% 0.19/0.30 thf(f506,plain,(
% 0.19/0.30 (((sK4 @ sK15)) = $false) | ($false = $true) | (~spl9_13 | ~spl9_36)),
% 0.19/0.30 inference(superposition,[],[f361,f409])).
% 0.19/0.30 thf(f510,plain,(
% 0.19/0.30 (((sK4 @ sK15)) = $false) | (~spl9_13 | ~spl9_36)),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f506])).
% 0.19/0.30 thf(f512,plain,(
% 0.19/0.30 spl9_35 | ~spl9_13 | ~spl9_36),
% 0.19/0.30 inference(avatar_split_clause,[],[f510,f407,f109,f403])).
% 0.19/0.30 thf(f513,definition,(
% 0.19/0.30 ($false != sP1) | (((sK4 @ sK15)) != $false) | (((sK4 @ sK15)) != $true) | ($true = sP1)),
% 0.19/0.30 introduced(theory,[theory_tautology_sat_conflict])).
% 0.19/0.30 thf(f516,definition,(
% 0.19/0.30 (sK6 != sK4) | ((^[Y0 : a]: ($true)) != sK6) | ((^[Y0 : a]: ($true)) = sK4)),
% 0.19/0.30 introduced(theory,[theory_tautology_sat_conflict])).
% 0.19/0.30 thf(f520,plain,(
% 0.19/0.30 (((sK5 @ sK15)) = $false) | (((sK4 @ sK15)) = $true) | ($false = $true) | (~spl9_13 | ~spl9_34)),
% 0.19/0.30 inference(superposition,[],[f400,f358])).
% 0.19/0.30 thf(f523,plain,(
% 0.19/0.30 (((sK5 @ sK15)) = $false) | (((sK4 @ sK15)) = $true) | (~spl9_13 | ~spl9_34)),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f520])).
% 0.19/0.30 thf(f525,definition,(
% 0.19/0.30 spl9_47 <=> (((sK5 @ sK15)) = $false)),
% 0.19/0.30 introduced(definition,[new_symbols(definition,[spl9_47])],[avatar_definition])).
% 0.19/0.30 thf(f529,plain,(
% 0.19/0.30 spl9_33 | spl9_47 | ~spl9_13 | ~spl9_34),
% 0.19/0.30 inference(avatar_split_clause,[],[f523,f398,f109,f525,f394])).
% 0.19/0.30 thf(f534,plain,(
% 0.19/0.30 ( ! [X1 : a] : (((((^[Y0 : a]: ($false)) @ X1)) = ((sK5 @ X1)))) ) | ~spl9_9),
% 0.19/0.30 inference(argument_congruence,[],[f91])).
% 0.19/0.30 thf(f535,plain,(
% 0.19/0.30 ( ! [X1 : a] : (($false = ((sK5 @ X1))) | ($true = (((^[Y0 : a]: ($false)) @ X1)))) ) | ~spl9_9),
% 0.19/0.30 inference(iff_proxy_clausification,[],[f534])).
% 0.19/0.30 thf(f538,plain,(
% 0.19/0.30 ( ! [X1 : a] : (($false = ((sK5 @ X1))) | ($false = $true)) ) | ~spl9_9),
% 0.19/0.30 inference(beta-eta_normalization,[],[f535])).
% 0.19/0.30 thf(f539,plain,(
% 0.19/0.30 ( ! [X1 : a] : (($false = ((sK5 @ X1)))) ) | ~spl9_9),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f538])).
% 0.19/0.30 thf(f542,plain,(
% 0.19/0.30 ($false = $true) | (~spl9_9 | ~spl9_40)),
% 0.19/0.30 inference(superposition,[],[f539,f437])).
% 0.19/0.30 thf(f549,plain,(
% 0.19/0.30 $false | (~spl9_9 | ~spl9_40)),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f542])).
% 0.19/0.30 thf(f550,plain,(
% 0.19/0.30 ~spl9_9 | ~spl9_40),
% 0.19/0.30 inference(avatar_contradiction_clause,[],[f549])).
% 0.19/0.30 thf(f552,definition,(
% 0.19/0.30 ((^[Y0 : a]: ($true)) != sK6) | (((sK6 @ sK15)) != $true) | (((sK5 @ sK15)) != $false) | ((^[Y0 : a]: ($true)) != sK5) | ((^[Y0 : a]: ($false)) = sK5)),
% 0.19/0.30 introduced(theory,[theory_tautology_sat_conflict])).
% 0.19/0.30 cnf(s1, plain, ~spl9_1 | ~spl9_2, inference(sat_conversion,[],[f60])).
% 0.19/0.30 cnf(s2, plain, ~spl9_3 | spl9_4, inference(sat_conversion,[],[f69])).
% 0.19/0.30 cnf(s3, plain, ~spl9_3 | ~spl9_5, inference(sat_conversion,[],[f74])).
% 0.19/0.30 cnf(s5, plain, ~spl9_2 | spl9_8 | spl9_9, inference(sat_conversion,[],[f92])).
% 0.19/0.30 cnf(s6, plain, spl9_2 | spl9_3 | spl9_7 | ~spl9_10, inference(sat_conversion,[],[f97])).
% 0.19/0.30 cnf(s7, plain, ~spl9_2 | ~spl9_11, inference(sat_conversion,[],[f102])).
% 0.19/0.30 cnf(s9, plain, ~spl9_2 | spl9_13, inference(sat_conversion,[],[f112])).
% 0.19/0.30 cnf(s10, plain, spl9_2 | spl9_3 | spl9_7 | spl9_10, inference(sat_conversion,[],[f113])).
% 0.19/0.30 cnf(s11, plain, spl9_2 | spl9_3 | ~spl9_7 | spl9_10, inference(sat_conversion,[],[f114])).
% 0.19/0.30 cnf(s13, plain, ~spl9_3 | spl9_14, inference(sat_conversion,[],[f119])).
% 0.19/0.30 cnf(s14, plain, ~spl9_2 | spl9_15 | spl9_16, inference(sat_conversion,[],[f128])).
% 0.19/0.30 cnf(s15, plain, ~spl9_3 | ~spl9_17, inference(sat_conversion,[],[f133])).
% 0.19/0.30 cnf(s17, plain, spl9_2 | spl9_3 | ~spl9_7 | ~spl9_10, inference(sat_conversion,[],[f135])).
% 0.19/0.30 cnf(s20, plain, ~spl9_4 | ~spl9_14 | spl9_18 | spl9_20, inference(sat_conversion,[],[f182])).
% 0.19/0.30 cnf(s25, plain, ~spl9_4 | spl9_17 | ~spl9_20, inference(sat_conversion,[],[f244])).
% 0.19/0.30 cnf(s26, plain, spl9_5 | spl9_24, inference(sat_conversion,[],[f249])).
% 0.19/0.30 cnf(s32, plain, ~spl9_4 | ~spl9_18 | spl9_27, inference(sat_conversion,[],[f301])).
% 0.19/0.30 cnf(s35, plain, ~spl9_24 | ~spl9_27, inference(sat_conversion,[],[f307])).
% 0.19/0.30 cnf(s38, plain, spl9_3 | spl9_28, inference(sat_conversion,[],[f317])).
% 0.19/0.30 cnf(s44, plain, spl9_11 | ~spl9_15 | ~spl9_32, inference(sat_conversion,[],[f384])).
% 0.19/0.30 cnf(s45, plain, ~spl9_13 | ~spl9_15 | spl9_32, inference(sat_conversion,[],[f392])).
% 0.19/0.30 cnf(s46, plain, spl9_32 | spl9_33 | spl9_34, inference(sat_conversion,[],[f401])).
% 0.19/0.30 cnf(s47, plain, spl9_32 | spl9_35 | spl9_36, inference(sat_conversion,[],[f410])).
% 0.19/0.30 cnf(s53, plain, spl9_29 | spl9_37 | spl9_39, inference(sat_conversion,[],[f433])).
% 0.19/0.30 cnf(s54, plain, spl9_29 | spl9_40 | spl9_41, inference(sat_conversion,[],[f442])).
% 0.19/0.30 cnf(s59, plain, ~spl9_13 | spl9_37 | ~spl9_39, inference(sat_conversion,[],[f488])).
% 0.19/0.30 cnf(s65, plain, spl9_3 | ~spl9_28 | ~spl9_37 | ~spl9_41, inference(sat_conversion,[],[f499])).
% 0.19/0.30 cnf(s68, plain, ~spl9_9 | spl9_11 | ~spl9_29, inference(sat_conversion,[],[f502])).
% 0.19/0.30 cnf(s72, plain, ~spl9_13 | spl9_35 | ~spl9_36, inference(sat_conversion,[],[f512])).
% 0.19/0.30 cnf(s74, plain, spl9_3 | ~spl9_28 | ~spl9_33 | ~spl9_35, inference(sat_conversion,[],[f513])).
% 0.19/0.30 cnf(s77, plain, spl9_1 | ~spl9_16 | ~spl9_32, inference(sat_conversion,[],[f516])).
% 0.19/0.30 cnf(s82, plain, ~spl9_13 | spl9_33 | ~spl9_34 | spl9_47, inference(sat_conversion,[],[f529])).
% 0.19/0.30 cnf(s84, plain, ~spl9_9 | ~spl9_40, inference(sat_conversion,[],[f550])).
% 0.19/0.30 cnf(s86, plain, ~spl9_8 | spl9_9 | ~spl9_16 | ~spl9_34 | ~spl9_47, inference(sat_conversion,[],[f552])).
% 0.19/0.30 cnf(s91, plain, spl9_7 | spl9_3 | spl9_2, inference(rat,[],[s6,s10])).
% 0.19/0.30 cnf(s92, plain, ~spl9_7 | spl9_3 | spl9_2, inference(rat,[],[s11,s17])).
% 0.19/0.30 cnf(s93, plain, spl9_3 | spl9_2, inference(rat,[],[s92,s91])).
% 0.19/0.30 cnf(s94, plain, ~spl9_3, inference(rat,[],[s32,s35,s20,s25,s26,s2,s3,s13,s15])).
% 0.19/0.30 cnf(s95, plain, spl9_28, inference(rat,[],[s38,s94])).
% 0.19/0.30 cnf(s96, plain, spl9_2, inference(rat,[],[s93,s94])).
% 0.19/0.30 cnf(s97, plain, spl9_13, inference(rat,[],[s9,s96])).
% 0.19/0.30 cnf(s98, plain, ~spl9_11, inference(rat,[],[s7,s96])).
% 0.19/0.30 cnf(s99, plain, spl9_29 | spl9_40, inference(rat,[],[s53,s59,s65,s54,s95,s94,s97])).
% 0.19/0.30 cnf(s100, plain, ~spl9_9, inference(rat,[],[s99,s68,s84,s98])).
% 0.19/0.30 cnf(s101, plain, spl9_8, inference(rat,[],[s5,s96,s100])).
% 0.19/0.30 cnf(s102, plain, spl9_33 | spl9_32 | ~spl9_16, inference(rat,[],[s86,s82,s46,s100,s101,s97])).
% 0.19/0.30 cnf(s103, plain, spl9_35 | spl9_32, inference(rat,[],[s47,s72,s97])).
% 0.19/0.30 cnf(s104, plain, spl9_32 | ~spl9_16, inference(rat,[],[s74,s103,s102,s95,s94])).
% 0.19/0.30 cnf(s105, plain, ~spl9_16 | spl9_1, inference(rat,[],[s104,s77])).
% 0.19/0.30 cnf(s106, plain, ~spl9_15, inference(rat,[],[s44,s45,s98,s97])).
% 0.19/0.30 cnf(s107, plain, ~spl9_1, inference(rat,[],[s1,s96])).
% 0.19/0.30 cnf(s109, plain, spl9_16, inference(rat,[],[s14,s96,s106])).
% 0.19/0.30 cnf(s111, plain, $false, inference(rat,[],[s105,s107,s109])).
% 0.19/0.30 thf(f557,plain,(
% 0.19/0.30 $false),
% 0.19/0.30 inference(avatar_sat_refutation,[],[s111])).
% 0.19/0.30 % SZS output end Proof for theBenchmark
% 0.19/0.30 % (865298)------------------------------
% 0.19/0.30 % (865298)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (865298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (865298)CaDiCaL version: 2.1.3
% 0.19/0.30 % (865298)Termination reason: Refutation
% 0.19/0.30 % (865298)Time elapsed: 0.019 s
% 0.19/0.30 % (865298)Peak memory usage: 13 MB
% 0.19/0.30 % (865298)Instructions burned: 27 (million)
% 0.19/0.30 % (865282)Success in time 0.056 s
% 0.19/0.30 % Vampire exiting
%------------------------------------------------------------------------------