%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV238^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 08:39:12 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV238^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n015.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 15:30:07 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.29 % (3658903)Will run a generic schedule for satisfiability detection.
% 0.20/0.29 % (3658909)% WARNING: option uhcvi not known.
% 0.20/0.29 % (3658909)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1434072694:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.29 % (3658909)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.29 % (3658909)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.29 % (3658908)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3955935303_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.29 % (3658910)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3227174781:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.29 % (3658911)dis+10_1_sil=32000:sp=arity:random_seed=2924676823:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.29 % (3658912)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1387271688:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.29 % (3658912)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.29 % Exception at run slice level
% 0.20/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.29 % (3658913)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2160339318:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.29 % (3658914)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2778397209:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.29 % (3658909) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3658903-3658909"...
% 0.20/0.29 % (3658920)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1382923485:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.29 % (3658909)...printing done.
% 0.20/0.29 % Exception at run slice level
% 0.20/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.29 % (3658909)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% 0.20/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.29 thf(func_def_3, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.29 thf(func_def_4, type, vAND: ($o > $o > $o)).
% 0.20/0.29 thf(func_def_5, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.29 thf(func_def_6, type, vIMP: ($o > $o > $o)).
% 0.20/0.29 thf(func_def_7, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.29 thf(func_def_10, type, sK0: (($i > $o) > $i > $o)).
% 0.20/0.29 thf(func_def_14, type, sK4: ($i > $o)).
% 0.20/0.29 thf(func_def_15, type, sK5: (($i > $o) > $i)).
% 0.20/0.29 thf(func_def_16, type, sK6: (($i > $o) > $i)).
% 0.20/0.29 thf(func_def_17, type, vNOT: ($o > $o)).
% 0.20/0.29 thf(func_def_19, type, sK8: ($i > $o)).
% 0.20/0.29 thf(func_def_20, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.29 thf(func_def_21, type, sK9: (($i > $o) > $i)).
% 0.20/0.29 thf(func_def_22, type, sK10: (($i > $o) > $i)).
% 0.20/0.29 thf(f1,conjecture,(
% 0.20/0.29 ! [X0 : (($i > $o) > $i > $o)] : (((! [X1 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X1) & ! [X2 : $i] : ((X3 @ X2) => (X0 @ X3 @ X2))) => (X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4))))) @ X1)) => ! [X1 : $i] : ((X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4))))) @ X1) => (X0 @ (X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)))))) @ X1))) & ! [X1 : ($i > $o)] : (! [X2 : $i] : ((X1 @ X2) => ? [X3 : ($i > $o)] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)))) => ! [X2 : $i] : ((X0 @ X1 @ X2) => (X0 @ (^[X4 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X4) & ! [X5 : $i] : ((X3 @ X5) => (X0 @ X3 @ X5))))) @ X2)))) => ! [X1 : $i] : ((X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4))))) @ X1) <=> ((X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4))))) @ X1) & ! [X2 : $i] : ((X0 @ (^[X4 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X4) & ! [X5 : $i] : ((X3 @ X5) => (X0 @ X3 @ X5))))) @ X2) => (X0 @ (X0 @ (^[X4 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X4) & ! [X5 : $i] : ((X3 @ X5) => (X0 @ X3 @ X5)))))) @ X2)))))),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM2D_pme)).
% 0.20/0.29 thf(f2,negated_conjecture,(
% 0.20/0.29 ~ ! [X0 : (($i > $o) > $i > $o)] : (((! [X1 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X1) & ! [X2 : $i] : ((X3 @ X2) => (X0 @ X3 @ X2))) => (X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4))))) @ X1)) => ! [X1 : $i] : ((X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4))))) @ X1) => (X0 @ (X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)))))) @ X1))) & ! [X1 : ($i > $o)] : (! [X2 : $i] : ((X1 @ X2) => ? [X3 : ($i > $o)] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)))) => ! [X2 : $i] : ((X0 @ X1 @ X2) => (X0 @ (^[X4 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X4) & ! [X5 : $i] : ((X3 @ X5) => (X0 @ X3 @ X5))))) @ X2)))) => ! [X1 : $i] : ((X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4))))) @ X1) <=> ((X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4))))) @ X1) & ! [X2 : $i] : ((X0 @ (^[X4 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X4) & ! [X5 : $i] : ((X3 @ X5) => (X0 @ X3 @ X5))))) @ X2) => (X0 @ (X0 @ (^[X4 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X4) & ! [X5 : $i] : ((X3 @ X5) => (X0 @ X3 @ X5)))))) @ X2)))))),
% 0.20/0.29 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.29 thf(f3,plain,(
% 0.20/0.29 ~ ! [X0 : (($i > $o) > $i > $o)] : (((! [X1 : $i] : (? [X2 : ($i > $o)] : ((X2 @ X1) & ! [X3 : $i] : ((X2 @ X3) => (X0 @ X2 @ X3))) => (X0 @ (^[X4 : $i] : (? [X5 : ($i > $o)] : ((X5 @ X4) & ! [X6 : $i] : ((X5 @ X6) => (X0 @ X5 @ X6))))) @ X1)) => ! [X7 : $i] : ((X0 @ (^[X8 : $i] : (? [X9 : ($i > $o)] : ((X9 @ X8) & ! [X10 : $i] : ((X9 @ X10) => (X0 @ X9 @ X10))))) @ X7) => (X0 @ (X0 @ (^[X11 : $i] : (? [X12 : ($i > $o)] : ((X12 @ X11) & ! [X13 : $i] : ((X12 @ X13) => (X0 @ X12 @ X13)))))) @ X7))) & ! [X14 : ($i > $o)] : (! [X15 : $i] : ((X14 @ X15) => ? [X16 : ($i > $o)] : ((X16 @ X15) & ! [X17 : $i] : ((X16 @ X17) => (X0 @ X16 @ X17)))) => ! [X18 : $i] : ((X0 @ X14 @ X18) => (X0 @ (^[X19 : $i] : (? [X20 : ($i > $o)] : ((X20 @ X19) & ! [X21 : $i] : ((X20 @ X21) => (X0 @ X20 @ X21))))) @ X18)))) => ! [X22 : $i] : ((X0 @ (^[X23 : $i] : (? [X24 : ($i > $o)] : ((X24 @ X23) & ! [X25 : $i] : ((X24 @ X25) => (X0 @ X24 @ X25))))) @ X22) <=> ((X0 @ (^[X26 : $i] : (? [X27 : ($i > $o)] : ((X27 @ X26) & ! [X28 : $i] : ((X27 @ X28) => (X0 @ X27 @ X28))))) @ X22) & ! [X29 : $i] : ((X0 @ (^[X30 : $i] : (? [X31 : ($i > $o)] : ((X31 @ X30) & ! [X32 : $i] : ((X31 @ X32) => (X0 @ X31 @ X32))))) @ X29) => (X0 @ (X0 @ (^[X33 : $i] : (? [X34 : ($i > $o)] : ((X34 @ X33) & ! [X35 : $i] : ((X34 @ X35) => (X0 @ X34 @ X35)))))) @ X29)))))),
% 0.20/0.29 inference(rectify,[],[f2])).
% 0.20/0.29 thf(f4,plain,(
% 0.20/0.29 ~ ! [X0 : (($i > $o) > $i > $o)] : (((! [X1 : $i] : (? [X2 : ($i > $o)] : ((((X2 @ X1)) = $true) & ! [X3 : $i] : ((((X2 @ X3)) = $true) => (((X0 @ X2 @ X3)) = $true))) => ($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1)))) => ! [X7 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X7))) => ($true = ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X7))))) & ! [X14 : ($i > $o)] : (! [X15 : $i] : ((((X14 @ X15)) = $true) => ? [X16 : ($i > $o)] : ((((X16 @ X15)) = $true) & ! [X17 : $i] : ((((X16 @ X17)) = $true) => (((X0 @ X16 @ X17)) = $true)))) => ! [X18 : $i] : ((((X0 @ X14 @ X18)) = $true) => ($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X18)))))) => ! [X22 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X22))) <=> (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X22))) & ! [X29 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X29))) => ($true = ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X29)))))))),
% 0.20/0.29 inference(fool_elimination,[],[f3])).
% 0.20/0.29 thf(f5,plain,(
% 0.20/0.29 ~ ! [X0 : (($i > $o) > $i > $o)] : (((! [X1 : $i] : (? [X2 : ($i > $o)] : ((((X2 @ X1)) = $true) & ! [X3 : $i] : ((((X2 @ X3)) = $true) => (((X0 @ X2 @ X3)) = $true))) => ($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1)))) => ! [X4 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4))) => ($true = ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X4))))) & ! [X5 : ($i > $o)] : (! [X6 : $i] : ((((X5 @ X6)) = $true) => ? [X7 : ($i > $o)] : (($true = ((X7 @ X6))) & ! [X8 : $i] : (($true = ((X7 @ X8))) => ($true = ((X0 @ X7 @ X8)))))) => ! [X9 : $i] : (($true = ((X0 @ X5 @ X9))) => ($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X9)))))) => ! [X10 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X10))) <=> (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X10))) & ! [X11 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X11))) => ($true = ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X11)))))))),
% 0.20/0.29 inference(rectify,[],[f4])).
% 0.20/0.29 thf(f6,plain,(
% 0.20/0.29 ? [X0 : (($i > $o) > $i > $o)] : (? [X10 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X10))) <~> (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X10))) & ! [X11 : $i] : (($true = ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X11))) | ($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X11)))))) & ((! [X4 : $i] : (($true = ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X4))) | ($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4)))) | ? [X1 : $i] : (($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1))) & ? [X2 : ($i > $o)] : ((((X2 @ X1)) = $true) & ! [X3 : $i] : ((((X0 @ X2 @ X3)) = $true) | (((X2 @ X3)) != $true))))) & ! [X5 : ($i > $o)] : (! [X9 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X9))) | ($true != ((X0 @ X5 @ X9)))) | ? [X6 : $i] : (! [X7 : ($i > $o)] : (($true != ((X7 @ X6))) | ? [X8 : $i] : (($true != ((X0 @ X7 @ X8))) & ($true = ((X7 @ X8))))) & (((X5 @ X6)) = $true)))))),
% 0.20/0.29 inference(ennf_transformation,[],[f5])).
% 0.20/0.29 thf(f7,plain,(
% 0.20/0.29 ? [X0 : (($i > $o) > $i > $o)] : (? [X10 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X10))) <~> (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X10))) & ! [X11 : $i] : (($true = ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X11))) | ($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X11)))))) & (! [X4 : $i] : (($true = ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X4))) | ($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4)))) | ? [X1 : $i] : (($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1))) & ? [X2 : ($i > $o)] : ((((X2 @ X1)) = $true) & ! [X3 : $i] : ((((X0 @ X2 @ X3)) = $true) | (((X2 @ X3)) != $true))))) & ! [X5 : ($i > $o)] : (! [X9 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X9))) | ($true != ((X0 @ X5 @ X9)))) | ? [X6 : $i] : (! [X7 : ($i > $o)] : (($true != ((X7 @ X6))) | ? [X8 : $i] : (($true != ((X0 @ X7 @ X8))) & ($true = ((X7 @ X8))))) & (((X5 @ X6)) = $true))))),
% 0.20/0.29 inference(flattening,[],[f6])).
% 0.20/0.29 thf(f8,plain,(
% 0.20/0.29 ? [X0 : (($i > $o) > $i > $o)] : (? [X10 : $i] : (((($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X10))) | ? [X11 : $i] : (($true != ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X11))) & ($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X11))))) | ($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X10)))) & ((($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X10))) & ! [X11 : $i] : (($true = ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X11))) | ($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X11))))) | ($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X10))))) & (! [X4 : $i] : (($true = ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X4))) | ($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4)))) | ? [X1 : $i] : (($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1))) & ? [X2 : ($i > $o)] : ((((X2 @ X1)) = $true) & ! [X3 : $i] : ((((X0 @ X2 @ X3)) = $true) | (((X2 @ X3)) != $true))))) & ! [X5 : ($i > $o)] : (! [X9 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X9))) | ($true != ((X0 @ X5 @ X9)))) | ? [X6 : $i] : (! [X7 : ($i > $o)] : (($true != ((X7 @ X6))) | ? [X8 : $i] : (($true != ((X0 @ X7 @ X8))) & ($true = ((X7 @ X8))))) & (((X5 @ X6)) = $true))))),
% 0.20/0.29 inference(nnf_transformation,[],[f7])).
% 0.20/0.29 thf(f9,plain,(
% 0.20/0.29 ? [X0 : (($i > $o) > $i > $o)] : (? [X10 : $i] : ((($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X10))) | ? [X11 : $i] : (($true != ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X11))) & ($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X11)))) | ($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X10)))) & ((($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X10))) & ! [X11 : $i] : (($true = ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X11))) | ($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X11))))) | ($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X10))))) & (! [X4 : $i] : (($true = ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X4))) | ($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4)))) | ? [X1 : $i] : (($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1))) & ? [X2 : ($i > $o)] : ((((X2 @ X1)) = $true) & ! [X3 : $i] : ((((X0 @ X2 @ X3)) = $true) | (((X2 @ X3)) != $true))))) & ! [X5 : ($i > $o)] : (! [X9 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X9))) | ($true != ((X0 @ X5 @ X9)))) | ? [X6 : $i] : (! [X7 : ($i > $o)] : (($true != ((X7 @ X6))) | ? [X8 : $i] : (($true != ((X0 @ X7 @ X8))) & ($true = ((X7 @ X8))))) & (((X5 @ X6)) = $true))))),
% 0.20/0.29 inference(flattening,[],[f8])).
% 0.20/0.29 thf(f10,plain,(
% 0.20/0.29 ? [X0 : (($i > $o) > $i > $o)] : (? [X1 : $i] : ((($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1))) | ? [X2 : $i] : (($true != ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X2))) & ($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X2)))) | ($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1)))) & ((($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1))) & ! [X3 : $i] : (($true = ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X3))) | ($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X3))))) | ($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1))))) & (! [X4 : $i] : (($true = ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X4))) | ($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4)))) | ? [X5 : $i] : (($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X5))) & ? [X6 : ($i > $o)] : (($true = ((X6 @ X5))) & ! [X7 : $i] : (($true = ((X0 @ X6 @ X7))) | ($true != ((X6 @ X7))))))) & ! [X8 : ($i > $o)] : (! [X9 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X9))) | ($true != ((X0 @ X8 @ X9)))) | ? [X10 : $i] : (! [X11 : ($i > $o)] : (($true != ((X11 @ X10))) | ? [X12 : $i] : (($true != ((X0 @ X11 @ X12))) & ($true = ((X11 @ X12))))) & ($true = ((X8 @ X10))))))),
% 0.20/0.29 inference(rectify,[],[f9])).
% 0.20/0.29 thf(f11,plain,(
% 0.20/0.29 ((($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1))) | (($true != ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ sK2))) & ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK2)))) | ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1)))) & ((($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1))) & ! [X3 : $i] : (($true = ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X3))) | ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X3))))) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1))))) & (! [X4 : $i] : (($true = ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X4))) | ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4)))) | (($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK3))) & (($true = ((sK4 @ sK3))) & ! [X7 : $i] : (($true = ((sK0 @ sK4 @ X7))) | ($true != ((sK4 @ X7))))))) & ! [X8 : ($i > $o)] : (! [X9 : $i] : (($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X9))) | ($true != ((sK0 @ X8 @ X9)))) | (! [X11 : ($i > $o)] : (($true != ((X11 @ (sK5 @ X8)))) | (($true != ((sK0 @ X11 @ (sK6 @ X11)))) & ($true = ((X11 @ (sK6 @ X11)))))) & ($true = ((X8 @ (sK5 @ X8))))))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X5,sK3),skolemize(X6,sK4),skolemize(X12,sK6 @ X11),skolemize(X12,sK6 @ X11)],[f10])).
% 0.20/0.29 thf(f12,plain,(
% 0.20/0.29 ( ! [X8 : ($i > $o),X9 : $i] : (($true != ((sK0 @ X8 @ X9))) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X9))) | ($true = ((X8 @ (sK5 @ X8))))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f11])).
% 0.20/0.29 thf(f13,plain,(
% 0.20/0.29 ( ! [X11 : ($i > $o),X8 : ($i > $o),X9 : $i] : (($true != ((sK0 @ X8 @ X9))) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X9))) | ($true != ((X11 @ (sK5 @ X8)))) | ($true = ((X11 @ (sK6 @ X11))))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f11])).
% 0.20/0.29 thf(f14,plain,(
% 0.20/0.29 ( ! [X11 : ($i > $o),X8 : ($i > $o),X9 : $i] : (($true != ((sK0 @ X11 @ (sK6 @ X11)))) | ($true != ((sK0 @ X8 @ X9))) | ($true != ((X11 @ (sK5 @ X8)))) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X9)))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f11])).
% 0.20/0.29 thf(f15,plain,(
% 0.20/0.29 ( ! [X7 : $i,X4 : $i] : (($true = ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X4))) | ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4))) | ($true = ((sK0 @ sK4 @ X7))) | ($true != ((sK4 @ X7)))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f11])).
% 0.20/0.29 thf(f16,plain,(
% 0.20/0.29 ( ! [X4 : $i] : (($true = ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X4))) | ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4))) | ($true = ((sK4 @ sK3)))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f11])).
% 0.20/0.29 thf(f17,plain,(
% 0.20/0.29 ( ! [X4 : $i] : (($true = ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X4))) | ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4))) | ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK3)))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f11])).
% 0.20/0.29 thf(f19,plain,(
% 0.20/0.29 ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1))) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1)))),
% 0.20/0.29 inference(cnf_transformation,[],[f11])).
% 0.20/0.29 thf(f20,plain,(
% 0.20/0.29 ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1))) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK2))) | ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1)))),
% 0.20/0.29 inference(cnf_transformation,[],[f11])).
% 0.20/0.29 thf(f21,plain,(
% 0.20/0.29 ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1))) | ($true != ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ sK2))) | ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1)))),
% 0.20/0.29 inference(cnf_transformation,[],[f11])).
% 0.20/0.29 thf(f23,definition,(
% 0.20/0.29 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.29 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.29 thf(f24,plain,(
% 0.20/0.29 ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1)))),
% 0.20/0.29 inference(duplicate_literal_removal,[],[f19])).
% 0.20/0.29 thf(f25,plain,(
% 0.20/0.29 ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1))) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK2)))),
% 0.20/0.29 inference(duplicate_literal_removal,[],[f20])).
% 0.20/0.29 thf(f26,plain,(
% 0.20/0.29 ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1))) | ($true != ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ sK2)))),
% 0.20/0.29 inference(duplicate_literal_removal,[],[f21])).
% 0.20/0.29 thf(f28,definition,(
% 0.20/0.29 spl7_1 <=> ! [X7 : $i] : (($true = ((sK0 @ sK4 @ X7))) | ($true != ((sK4 @ X7))))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition])).
% 0.20/0.29 thf(f29,plain,(
% 0.20/0.29 ( ! [X7 : $i] : (($true != ((sK4 @ X7))) | ($true = ((sK0 @ sK4 @ X7)))) ) | ~spl7_1),
% 0.20/0.29 inference(avatar_component_clause,[],[f28])).
% 0.20/0.29 thf(f31,definition,(
% 0.20/0.29 spl7_2 <=> ! [X4 : $i] : (($true = ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X4))) | ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4))))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition])).
% 0.20/0.29 thf(f32,plain,(
% 0.20/0.29 ( ! [X4 : $i] : (($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4))) | ($true = ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X4)))) ) | ~spl7_2),
% 0.20/0.29 inference(avatar_component_clause,[],[f31])).
% 0.20/0.29 thf(f33,plain,(
% 0.20/0.29 spl7_1 | spl7_2),
% 0.20/0.29 inference(avatar_split_clause,[],[f15,f31,f28])).
% 0.20/0.29 thf(f35,definition,(
% 0.20/0.29 spl7_3 <=> ($true = ((sK4 @ sK3)))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition])).
% 0.20/0.29 thf(f37,plain,(
% 0.20/0.29 ($true = ((sK4 @ sK3))) | ~spl7_3),
% 0.20/0.29 inference(avatar_component_clause,[],[f35])).
% 0.20/0.29 thf(f38,plain,(
% 0.20/0.29 spl7_3 | spl7_2),
% 0.20/0.29 inference(avatar_split_clause,[],[f16,f31,f35])).
% 0.20/0.29 thf(f40,definition,(
% 0.20/0.29 spl7_4 <=> ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK3)))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition])).
% 0.20/0.29 thf(f42,plain,(
% 0.20/0.29 ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK3))) | spl7_4),
% 0.20/0.29 inference(avatar_component_clause,[],[f40])).
% 0.20/0.29 thf(f43,plain,(
% 0.20/0.29 ~spl7_4 | spl7_2),
% 0.20/0.29 inference(avatar_split_clause,[],[f17,f31,f40])).
% 0.20/0.29 thf(f45,definition,(
% 0.20/0.29 spl7_5 <=> ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1)))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition])).
% 0.20/0.29 thf(f49,plain,(
% 0.20/0.29 spl7_5),
% 0.20/0.29 inference(avatar_split_clause,[],[f24,f45])).
% 0.20/0.29 thf(f51,definition,(
% 0.20/0.29 spl7_6 <=> ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK2)))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition])).
% 0.20/0.29 thf(f53,plain,(
% 0.20/0.29 ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK2))) | ~spl7_6),
% 0.20/0.29 inference(avatar_component_clause,[],[f51])).
% 0.20/0.29 thf(f54,plain,(
% 0.20/0.29 spl7_6 | ~spl7_5),
% 0.20/0.29 inference(avatar_split_clause,[],[f25,f45,f51])).
% 0.20/0.29 thf(f56,definition,(
% 0.20/0.29 spl7_7 <=> ($true = ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ sK2)))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition])).
% 0.20/0.29 thf(f58,plain,(
% 0.20/0.29 ($true != ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ sK2))) | spl7_7),
% 0.20/0.29 inference(avatar_component_clause,[],[f56])).
% 0.20/0.29 thf(f59,plain,(
% 0.20/0.29 ~spl7_7 | ~spl7_5),
% 0.20/0.29 inference(avatar_split_clause,[],[f26,f45,f56])).
% 0.20/0.29 thf(f194,plain,(
% 0.20/0.29 ($true != $true) | ($true = ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ sK2))) | (~spl7_2 | ~spl7_6)),
% 0.20/0.29 inference(constrained_superposition,[],[f32,f53])).
% 0.20/0.29 thf(f202,plain,(
% 0.20/0.29 ($true = ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ sK2))) | (~spl7_2 | ~spl7_6)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f194])).
% 0.20/0.29 thf(f205,plain,(
% 0.20/0.29 $false | (~spl7_2 | ~spl7_6 | spl7_7)),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f202,f58])).
% 0.20/0.29 thf(f206,plain,(
% 0.20/0.29 ~spl7_2 | ~spl7_6 | spl7_7),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f205])).
% 0.20/0.29 thf(f207,plain,(
% 0.20/0.29 ( ! [X0 : $i] : (($true != $true) | ($true = ((sK0 @ sK4 @ X0))) | ($false = ((sK4 @ X0)))) ) | ~spl7_1),
% 0.20/0.29 inference(constrained_superposition,[],[f29,f23])).
% 0.20/0.29 thf(f209,plain,(
% 0.20/0.29 ($true != $true) | ($true = ((sK0 @ sK4 @ sK3))) | (~spl7_1 | ~spl7_3)),
% 0.20/0.29 inference(constrained_superposition,[],[f29,f37])).
% 0.20/0.29 thf(f210,plain,(
% 0.20/0.29 ($true = ((sK0 @ sK4 @ sK3))) | (~spl7_1 | ~spl7_3)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f209])).
% 0.20/0.29 thf(f212,plain,(
% 0.20/0.29 ( ! [X0 : $i] : (($true = ((sK0 @ sK4 @ X0))) | ($false = ((sK4 @ X0)))) ) | ~spl7_1),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f207])).
% 0.20/0.29 thf(f213,plain,(
% 0.20/0.29 ( ! [X0 : ($i > $o)] : (($true != $true) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK3))) | ($true != ((X0 @ (sK5 @ sK4)))) | ($true = ((X0 @ (sK6 @ X0))))) ) | (~spl7_1 | ~spl7_3)),
% 0.20/0.29 inference(constrained_superposition,[],[f13,f210])).
% 0.20/0.29 thf(f214,plain,(
% 0.20/0.29 ($true != $true) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK3))) | ($true = ((sK4 @ (sK5 @ sK4)))) | (~spl7_1 | ~spl7_3)),
% 0.20/0.29 inference(constrained_superposition,[],[f12,f210])).
% 0.20/0.29 thf(f215,plain,(
% 0.20/0.29 ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK3))) | ($true = ((sK4 @ (sK5 @ sK4)))) | (~spl7_1 | ~spl7_3)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f214])).
% 0.20/0.29 thf(f216,plain,(
% 0.20/0.29 ( ! [X0 : ($i > $o)] : (($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK3))) | ($true != ((X0 @ (sK5 @ sK4)))) | ($true = ((X0 @ (sK6 @ X0))))) ) | (~spl7_1 | ~spl7_3)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f213])).
% 0.20/0.29 thf(f218,definition,(
% 0.20/0.29 spl7_14 <=> ($true = ((sK4 @ (sK5 @ sK4))))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl7_14])],[avatar_definition])).
% 0.20/0.29 thf(f220,plain,(
% 0.20/0.29 ($true = ((sK4 @ (sK5 @ sK4)))) | ~spl7_14),
% 0.20/0.29 inference(avatar_component_clause,[],[f218])).
% 0.20/0.29 thf(f221,plain,(
% 0.20/0.29 spl7_14 | spl7_4 | ~spl7_1 | ~spl7_3),
% 0.20/0.29 inference(avatar_split_clause,[],[f215,f35,f28,f40,f218])).
% 0.20/0.29 thf(f223,definition,(
% 0.20/0.29 spl7_15 <=> ! [X0 : ($i > $o)] : (($true != ((X0 @ (sK5 @ sK4)))) | ($true = ((X0 @ (sK6 @ X0)))))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl7_15])],[avatar_definition])).
% 0.20/0.29 thf(f224,plain,(
% 0.20/0.29 ( ! [X0 : ($i > $o)] : (($true != ((X0 @ (sK5 @ sK4)))) | ($true = ((X0 @ (sK6 @ X0))))) ) | ~spl7_15),
% 0.20/0.29 inference(avatar_component_clause,[],[f223])).
% 0.20/0.29 thf(f225,plain,(
% 0.20/0.29 spl7_15 | spl7_4 | ~spl7_1 | ~spl7_3),
% 0.20/0.29 inference(avatar_split_clause,[],[f216,f35,f28,f40,f223])).
% 0.20/0.29 thf(f237,plain,(
% 0.20/0.29 ( ! [X0 : ($i > $o),X1 : $i] : (($true != $true) | ($true != ((sK0 @ X0 @ X1))) | ($true != ((sK4 @ (sK5 @ X0)))) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1))) | ($false = ((sK4 @ (sK6 @ sK4))))) ) | ~spl7_1),
% 0.20/0.29 inference(constrained_superposition,[],[f14,f212])).
% 0.20/0.29 thf(f238,plain,(
% 0.20/0.29 ( ! [X0 : ($i > $o),X1 : $i] : (($true != ((sK0 @ X0 @ X1))) | ($true != ((sK4 @ (sK5 @ X0)))) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1))) | ($false = ((sK4 @ (sK6 @ sK4))))) ) | ~spl7_1),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f237])).
% 0.20/0.29 thf(f242,definition,(
% 0.20/0.29 spl7_16 <=> ($false = ((sK4 @ (sK6 @ sK4))))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl7_16])],[avatar_definition])).
% 0.20/0.29 thf(f244,plain,(
% 0.20/0.29 ($false = ((sK4 @ (sK6 @ sK4)))) | ~spl7_16),
% 0.20/0.29 inference(avatar_component_clause,[],[f242])).
% 0.20/0.29 thf(f246,definition,(
% 0.20/0.29 spl7_17 <=> ! [X0 : ($i > $o),X1 : $i] : (($true != ((sK0 @ X0 @ X1))) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1))) | ($true != ((sK4 @ (sK5 @ X0)))))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl7_17])],[avatar_definition])).
% 0.20/0.29 thf(f247,plain,(
% 0.20/0.29 ( ! [X0 : ($i > $o),X1 : $i] : (($true != ((sK0 @ X0 @ X1))) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1))) | ($true != ((sK4 @ (sK5 @ X0))))) ) | ~spl7_17),
% 0.20/0.29 inference(avatar_component_clause,[],[f246])).
% 0.20/0.29 thf(f248,plain,(
% 0.20/0.29 spl7_16 | spl7_17 | ~spl7_1),
% 0.20/0.29 inference(avatar_split_clause,[],[f238,f28,f246,f242])).
% 0.20/0.29 thf(f409,plain,(
% 0.20/0.29 ($true != $true) | ($true = (((^[Y0 : $i]: (sK4 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK6 @ (^[Y0 : $i]: (sK4 @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) | (~spl7_14 | ~spl7_15)),
% 0.20/0.29 inference(constrained_superposition,[],[f224,f220])).
% 0.20/0.29 thf(f417,plain,(
% 0.20/0.29 ($true = (((^[Y0 : $i]: (sK4 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK6 @ (^[Y0 : $i]: (sK4 @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) | (~spl7_14 | ~spl7_15)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f409])).
% 0.20/0.29 thf(f418,plain,(
% 0.20/0.29 ($true = ((sK4 @ (sK6 @ sK4)))) | (~spl7_14 | ~spl7_15)),
% 0.20/0.29 inference(beta-eta_normalization,[],[f417])).
% 0.20/0.29 thf(f447,plain,(
% 0.20/0.29 ($true = $false) | (~spl7_14 | ~spl7_15 | ~spl7_16)),
% 0.20/0.29 inference(forward_demodulation,[],[f418,f244])).
% 0.20/0.29 thf(f448,plain,(
% 0.20/0.29 $false | (~spl7_14 | ~spl7_15 | ~spl7_16)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f447])).
% 0.20/0.29 thf(f449,plain,(
% 0.20/0.29 ~spl7_14 | ~spl7_15 | ~spl7_16),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f448])).
% 0.20/0.29 thf(f894,plain,(
% 0.20/0.29 ($true != $true) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK3))) | ($true != ((sK4 @ (sK5 @ sK4)))) | (~spl7_1 | ~spl7_3 | ~spl7_17)),
% 0.20/0.29 inference(constrained_superposition,[],[f247,f210])).
% 0.20/0.29 thf(f901,plain,(
% 0.20/0.29 ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK3))) | ($true != ((sK4 @ (sK5 @ sK4)))) | (~spl7_1 | ~spl7_3 | ~spl7_17)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f894])).
% 0.20/0.29 thf(f905,plain,(
% 0.20/0.29 ($true != ((sK4 @ (sK5 @ sK4)))) | (~spl7_1 | ~spl7_3 | spl7_4 | ~spl7_17)),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f901,f42])).
% 0.20/0.29 thf(f907,plain,(
% 0.20/0.29 $false | (~spl7_1 | ~spl7_3 | spl7_4 | ~spl7_14 | ~spl7_17)),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f905,f220])).
% 0.20/0.29 thf(f908,plain,(
% 0.20/0.29 ~spl7_1 | ~spl7_3 | spl7_4 | ~spl7_14 | ~spl7_17),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f907])).
% 0.20/0.29 cnf(s1, plain, spl7_1 | spl7_2, inference(sat_conversion,[],[f33])).
% 0.20/0.29 cnf(s2, plain, spl7_2 | spl7_3, inference(sat_conversion,[],[f38])).
% 0.20/0.29 cnf(s3, plain, spl7_2 | ~spl7_4, inference(sat_conversion,[],[f43])).
% 0.20/0.29 cnf(s5, plain, spl7_5, inference(sat_conversion,[],[f49])).
% 0.20/0.29 cnf(s6, plain, ~spl7_5 | spl7_6, inference(sat_conversion,[],[f54])).
% 0.20/0.29 cnf(s7, plain, ~spl7_5 | ~spl7_7, inference(sat_conversion,[],[f59])).
% 0.20/0.29 cnf(s12, plain, ~spl7_2 | ~spl7_6 | spl7_7, inference(sat_conversion,[],[f206])).
% 0.20/0.29 cnf(s13, plain, ~spl7_1 | ~spl7_3 | spl7_4 | spl7_14, inference(sat_conversion,[],[f221])).
% 0.20/0.29 cnf(s14, plain, ~spl7_1 | ~spl7_3 | spl7_4 | spl7_15, inference(sat_conversion,[],[f225])).
% 0.20/0.29 cnf(s15, plain, ~spl7_1 | spl7_16 | spl7_17, inference(sat_conversion,[],[f248])).
% 0.20/0.29 cnf(s25, plain, ~spl7_14 | ~spl7_15 | ~spl7_16, inference(sat_conversion,[],[f449])).
% 0.20/0.29 cnf(s53, plain, ~spl7_1 | ~spl7_3 | spl7_4 | ~spl7_14 | ~spl7_17, inference(sat_conversion,[],[f908])).
% 0.20/0.29 cnf(s55, plain, ~spl7_7, inference(rat,[],[s7,s5])).
% 0.20/0.29 cnf(s56, plain, spl7_6, inference(rat,[],[s6,s5])).
% 0.20/0.29 cnf(s57, plain, ~spl7_2, inference(rat,[],[s12,s55,s56])).
% 0.20/0.29 cnf(s58, plain, ~spl7_4, inference(rat,[],[s3,s57])).
% 0.20/0.29 cnf(s59, plain, spl7_3, inference(rat,[],[s2,s57])).
% 0.20/0.29 cnf(s60, plain, spl7_1, inference(rat,[],[s1,s57])).
% 0.20/0.29 cnf(s63, plain, spl7_15, inference(rat,[],[s14,s59,s58,s60])).
% 0.20/0.29 cnf(s64, plain, spl7_14, inference(rat,[],[s13,s59,s58,s60])).
% 0.20/0.29 cnf(s69, plain, ~spl7_16, inference(rat,[],[s25,s63,s64])).
% 0.20/0.29 cnf(s70, plain, ~spl7_17, inference(rat,[],[s53,s60,s59,s58,s64])).
% 0.20/0.29 cnf(s71, plain, $false, inference(rat,[],[s15,s60,s70,s69])).
% 0.20/0.29 thf(f909,plain,(
% 0.20/0.29 $false),
% 0.20/0.29 inference(avatar_sat_refutation,[],[s71])).
% 0.20/0.29 % SZS output end Proof for theBenchmark
% 0.20/0.29 % (3658909)------------------------------
% 0.20/0.29 % (3658909)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (3658909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (3658909)CaDiCaL version: 2.1.3
% 0.20/0.29 % (3658909)Termination reason: Refutation
% 0.20/0.29 % (3658909)Time elapsed: 0.030 s
% 0.20/0.29 % (3658909)Peak memory usage: 13 MB
% 0.20/0.29 % (3658909)Instructions burned: 111 (million)
% 0.20/0.29 % (3658903)Success in time 0.056 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------