%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV066^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 08:37:35 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV066^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/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 15:05:40 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.28 % (840564)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (840569)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=456383740:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (840575)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.28 % (840575)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.28 % (840570)lrs+10_16_si=on:nwc=1.5:random_seed=2110806809:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.28 % (840571)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=268262552:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.28 % (840574)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=200516928:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.28 % (840573)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3508755604:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.28 % (840572)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=1852166813: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)
% 0.21/0.28 % (840575)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2489954985:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.28 % (840571)Instruction limit reached!
% 0.21/0.28 % (840571)------------------------------
% 0.21/0.28 % (840571)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (840571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (840571)CaDiCaL version: 2.1.3
% 0.21/0.28 % (840571)Termination reason: Instruction limit
% 0.21/0.28 % (840571)Termination phase: Saturation
% 0.21/0.28 % (840571)Time elapsed: 0.002 s
% 0.21/0.28 % (840571)Peak memory usage: 11 MB
% 0.21/0.28 % (840571)Instructions burned: 3 (million)
% 0.21/0.28 % (840570)Instruction limit reached!
% 0.21/0.28 % (840570)------------------------------
% 0.21/0.28 % (840570)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (840570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (840570)CaDiCaL version: 2.1.3
% 0.21/0.28 % (840570)Termination reason: Instruction limit
% 0.21/0.28 % (840570)Termination phase: Saturation
% 0.21/0.28 % (840570)Time elapsed: 0.009 s
% 0.21/0.28 % (840570)Peak memory usage: 12 MB
% 0.21/0.28 % (840570)Instructions burned: 18 (million)
% 0.21/0.28 % (840569) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-840564-840569"...
% 0.21/0.28 % (840573)Instruction limit reached!
% 0.21/0.28 % (840573)------------------------------
% 0.21/0.28 % (840573)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (840573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (840573)CaDiCaL version: 2.1.3
% 0.21/0.28 % (840573)Termination reason: Instruction limit
% 0.21/0.28 % (840573)Termination phase: Saturation
% 0.21/0.28 % (840573)Time elapsed: 0.012 s
% 0.21/0.28 % (840573)Peak memory usage: 12 MB
% 0.21/0.28 % (840573)Instructions burned: 25 (million)
% 0.21/0.28 % (840569)...printing done.
% 0.21/0.28 % (840569)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% 0.21/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.28 thf(func_def_3, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.28 thf(func_def_4, type, sK0: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 0.21/0.28 thf(func_def_5, type, sK1: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 0.21/0.28 thf(func_def_6, type, sK2: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 0.21/0.28 thf(func_def_7, type, sK3: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i)).
% 0.21/0.28 thf(func_def_8, type, sK4: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i)).
% 0.21/0.28 thf(func_def_9, type, sK5: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 0.21/0.28 thf(func_def_10, type, vNOT: ($o > $o)).
% 0.21/0.28 thf(func_def_11, type, db1: !>[X0: $tType]:(X0)).
% 0.21/0.28 thf(func_def_12, type, db2: !>[X0: $tType]:(X0)).
% 0.21/0.28 thf(func_def_13, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.28 thf(func_def_14, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.28 thf(func_def_17, type, sK8: ((($i > $o) > ($i > $o) > $i > $o) > $i)).
% 0.21/0.28 thf(func_def_19, type, sK10: ((($i > $o) > ($i > $o) > $i > $o) > $i)).
% 0.21/0.28 thf(func_def_21, type, sK12: ((($i > $o) > ($i > $o) > $i > $o) > $i)).
% 0.21/0.28 thf(func_def_22, type, sK13: ((($i > $o) > ($i > $o) > $i > $o) > $i)).
% 0.21/0.28 thf(f1,conjecture,(
% 0.21/0.28 ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X3 : $i] : ((X1 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X3) | (X0 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X3)) & ! [X2 : ($i > $o),X3 : $i] : ((X1 @ X2 @ X2 @ X3) | (X0 @ X2 @ X2 @ X3)) & ! [X5 : ($i > $o),X2 : ($i > $o),X4 : ($i > $o)] : ((! [X3 : $i] : ((X1 @ X2 @ X4 @ X3) | (X0 @ X2 @ X4 @ X3)) & ! [X3 : $i] : ((X1 @ X4 @ X5 @ X3) | (X0 @ X4 @ X5 @ X3))) => ! [X3 : $i] : ((X0 @ X2 @ X5 @ X3) | (X1 @ X2 @ X5 @ X3))))),
% 0.21/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM120D_pme)).
% 0.21/0.28 thf(f2,negated_conjecture,(
% 0.21/0.28 ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X3 : $i] : ((X1 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X3) | (X0 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X3)) & ! [X2 : ($i > $o),X3 : $i] : ((X1 @ X2 @ X2 @ X3) | (X0 @ X2 @ X2 @ X3)) & ! [X5 : ($i > $o),X2 : ($i > $o),X4 : ($i > $o)] : ((! [X3 : $i] : ((X1 @ X2 @ X4 @ X3) | (X0 @ X2 @ X4 @ X3)) & ! [X3 : $i] : ((X1 @ X4 @ X5 @ X3) | (X0 @ X4 @ X5 @ X3))) => ! [X3 : $i] : ((X0 @ X2 @ X5 @ X3) | (X1 @ X2 @ X5 @ X3))))),
% 0.21/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.28 thf(f3,plain,(
% 0.21/0.28 ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X2 : $i] : ((X1 @ (^[X3 : $i] : ($true)) @ (^[X4 : $i] : ($false)) @ X2) | (X0 @ (^[X5 : $i] : ($true)) @ (^[X6 : $i] : ($false)) @ X2)) & ! [X7 : ($i > $o),X8 : $i] : ((X1 @ X7 @ X7 @ X8) | (X0 @ X7 @ X7 @ X8)) & ! [X9 : ($i > $o),X10 : ($i > $o),X11 : ($i > $o)] : ((! [X12 : $i] : ((X1 @ X10 @ X11 @ X12) | (X0 @ X10 @ X11 @ X12)) & ! [X13 : $i] : ((X1 @ X11 @ X9 @ X13) | (X0 @ X11 @ X9 @ X13))) => ! [X14 : $i] : ((X0 @ X10 @ X9 @ X14) | (X1 @ X10 @ X9 @ X14))))),
% 0.21/0.28 inference(rectify,[],[f2])).
% 0.21/0.28 thf(f4,plain,(
% 0.21/0.28 ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X2 : $i] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) = $true) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) = $true)) & ! [X7 : ($i > $o),X8 : $i] : ((((X1 @ X7 @ X7 @ X8)) = $true) | (((X0 @ X7 @ X7 @ X8)) = $true)) & ! [X9 : ($i > $o),X10 : ($i > $o),X11 : ($i > $o)] : ((! [X12 : $i] : ((((X1 @ X10 @ X11 @ X12)) = $true) | (((X0 @ X10 @ X11 @ X12)) = $true)) & ! [X13 : $i] : (($true = ((X1 @ X11 @ X9 @ X13))) | (((X0 @ X11 @ X9 @ X13)) = $true))) => ! [X14 : $i] : (($true = ((X0 @ X10 @ X9 @ X14))) | (((X1 @ X10 @ X9 @ X14)) = $true))))),
% 0.21/0.28 inference(fool_elimination,[],[f3])).
% 0.21/0.28 thf(f5,plain,(
% 0.21/0.28 ~ ? [X1 : (($i > $o) > ($i > $o) > $i > $o),X0 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X2 : $i] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) = $true) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) = $true)) & ! [X7 : ($i > $o),X5 : ($i > $o),X6 : ($i > $o)] : ((! [X9 : $i] : ((((X1 @ X7 @ X5 @ X9)) = $true) | ($true = ((X0 @ X7 @ X5 @ X9)))) & ! [X8 : $i] : (($true = ((X1 @ X6 @ X7 @ X8))) | (((X0 @ X6 @ X7 @ X8)) = $true))) => ! [X10 : $i] : ((((X0 @ X6 @ X5 @ X10)) = $true) | (((X1 @ X6 @ X5 @ X10)) = $true))) & ! [X4 : $i,X3 : ($i > $o)] : (($true = ((X1 @ X3 @ X3 @ X4))) | ($true = ((X0 @ X3 @ X3 @ X4)))))),
% 0.21/0.28 inference(rectify,[],[f4])).
% 0.21/0.28 thf(f6,plain,(
% 0.21/0.28 ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X0 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : $i] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) = $true) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) = $true)) | ? [X7 : ($i > $o),X5 : ($i > $o),X6 : ($i > $o)] : (? [X10 : $i] : ((((X0 @ X6 @ X5 @ X10)) != $true) & (((X1 @ X6 @ X5 @ X10)) != $true)) & (! [X9 : $i] : ((((X1 @ X7 @ X5 @ X9)) = $true) | ($true = ((X0 @ X7 @ X5 @ X9)))) & ! [X8 : $i] : (($true = ((X1 @ X6 @ X7 @ X8))) | (((X0 @ X6 @ X7 @ X8)) = $true)))) | ? [X4 : $i,X3 : ($i > $o)] : (($true != ((X0 @ X3 @ X3 @ X4))) & ($true != ((X1 @ X3 @ X3 @ X4)))))),
% 0.21/0.28 inference(ennf_transformation,[],[f5])).
% 0.21/0.28 thf(f7,plain,(
% 0.21/0.28 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (? [X7 : ($i > $o),X5 : ($i > $o),X6 : ($i > $o)] : (? [X10 : $i] : ((((X0 @ X6 @ X5 @ X10)) != $true) & (((X1 @ X6 @ X5 @ X10)) != $true)) & ! [X8 : $i] : (($true = ((X1 @ X6 @ X7 @ X8))) | (((X0 @ X6 @ X7 @ X8)) = $true)) & ! [X9 : $i] : ((((X1 @ X7 @ X5 @ X9)) = $true) | ($true = ((X0 @ X7 @ X5 @ X9))))) | ? [X4 : $i,X3 : ($i > $o)] : (($true != ((X0 @ X3 @ X3 @ X4))) & ($true != ((X1 @ X3 @ X3 @ X4)))) | ! [X2 : $i] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) = $true) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) = $true)))),
% 0.21/0.28 inference(flattening,[],[f6])).
% 0.21/0.28 thf(f8,plain,(
% 0.21/0.28 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (? [X2 : ($i > $o),X3 : ($i > $o),X4 : ($i > $o)] : (? [X5 : $i] : ((((X0 @ X4 @ X3 @ X5)) != $true) & ($true != ((X1 @ X4 @ X3 @ X5)))) & ! [X6 : $i] : (($true = ((X1 @ X4 @ X2 @ X6))) | ($true = ((X0 @ X4 @ X2 @ X6)))) & ! [X7 : $i] : ((((X1 @ X2 @ X3 @ X7)) = $true) | ($true = ((X0 @ X2 @ X3 @ X7))))) | ? [X8 : $i,X9 : ($i > $o)] : ((((X0 @ X9 @ X9 @ X8)) != $true) & ($true != ((X1 @ X9 @ X9 @ X8)))) | ! [X10 : $i] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)))))),
% 0.21/0.28 inference(rectify,[],[f7])).
% 0.21/0.28 thf(f9,plain,(
% 0.21/0.28 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (((($true != ((X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0)))) & ($true != ((X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0))))) & ! [X6 : $i] : ((((X1 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6)) = $true) | (((X0 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6)) = $true)) & ! [X7 : $i] : (($true = ((X1 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7))) | ($true = ((X0 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7))))) | ((((X0 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0))) != $true) & ($true != ((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0))))) | ! [X10 : $i] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)))))),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X9,sK5 @ X1 @ X0),skolemize(X9,sK5 @ X1 @ X0),skolemize(X9,sK5 @ X1 @ X0),skolemize(X9,sK5 @ X1 @ X0),skolemize(X9,sK5 @ X1 @ X0),skolemize(X9,sK5 @ X1 @ X0)],[f8])).
% 0.21/0.28 thf(f10,plain,(
% 0.21/0.28 ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : (($true != ((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)))) | ($true = ((X1 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7))) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ($true = ((X0 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7)))) )),
% 0.21/0.28 inference(cnf_transformation,[],[f9])).
% 0.21/0.28 thf(f12,plain,(
% 0.21/0.28 ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X6 : $i] : (($true != ((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)))) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true) | (((X1 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6)) = $true) | (((X0 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6)) = $true) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)))) )),
% 0.21/0.28 inference(cnf_transformation,[],[f9])).
% 0.21/0.28 thf(f16,plain,(
% 0.21/0.28 ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != ((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)))) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true) | ($true != ((X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0)))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)))) )),
% 0.21/0.28 inference(cnf_transformation,[],[f9])).
% 0.21/0.28 thf(f49,definition,(
% 0.21/0.28 spl6_1 <=> ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
% 0.21/0.28 thf(f50,plain,(
% 0.21/0.28 ((^[Y0 : $i]: ($false)) != (^[Y0 : $i]: ($true))) | spl6_1),
% 0.21/0.28 inference(avatar_component_clause,[],[f49])).
% 0.21/0.28 thf(f51,plain,(
% 0.21/0.28 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ~spl6_1),
% 0.21/0.28 inference(avatar_component_clause,[],[f49])).
% 0.21/0.28 thf(f143,plain,(
% 0.21/0.28 ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o)] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true) | (((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true)) )),
% 0.21/0.28 inference(primitive_instantiation,[],[f16])).
% 0.21/0.28 thf(f160,plain,(
% 0.21/0.28 ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o)] : ((((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ((((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true)) )),
% 0.21/0.28 inference(beta-eta_normalization,[],[f143])).
% 0.21/0.28 thf(f161,plain,(
% 0.21/0.28 ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o)] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ((((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true) | (((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true)) )),
% 0.21/0.28 inference(equality_proxy_clausification,[],[f160])).
% 0.21/0.28 thf(f162,plain,(
% 0.21/0.28 ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o)] : ((((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true) | (((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) )),
% 0.21/0.28 inference(equality_proxy_clausification,[],[f161])).
% 0.21/0.28 thf(f163,plain,(
% 0.21/0.28 ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o)] : (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true)) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f162])).
% 0.21/0.28 thf(f299,plain,(
% 0.21/0.28 ( ! [X1 : $i] : (((((^[Y0 : $i]: ($true)) @ X1)) = (((^[Y0 : $i]: ($false)) @ X1)))) ) | ~spl6_1),
% 0.21/0.28 inference(argument_congruence,[],[f51])).
% 0.21/0.28 thf(f301,plain,(
% 0.21/0.28 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ($false)) @ X1))) | ((((^[Y0 : $i]: ($true)) @ X1)) = $false)) ) | ~spl6_1),
% 0.21/0.28 inference(iff_proxy_clausification,[],[f299])).
% 0.21/0.28 thf(f302,plain,(
% 0.21/0.28 ($true = $false) | ($true = $false) | ~spl6_1),
% 0.21/0.28 inference(beta-eta_normalization,[],[f301])).
% 0.21/0.28 thf(f303,plain,(
% 0.21/0.28 ($true = $false) | ~spl6_1),
% 0.21/0.28 inference(duplicate_literal_removal,[],[f302])).
% 0.21/0.28 thf(f304,plain,(
% 0.21/0.28 $false | ~spl6_1),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f303])).
% 0.21/0.28 thf(f305,plain,(
% 0.21/0.28 ~spl6_1),
% 0.21/0.28 inference(avatar_contradiction_clause,[],[f304])).
% 0.21/0.28 thf(f325,definition,(
% 0.21/0.28 spl6_23 <=> ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X10 : $i] : ((((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true))),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl6_23])],[avatar_definition])).
% 0.21/0.28 thf(f326,plain,(
% 0.21/0.28 ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o)] : ((((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true)) ) | ~spl6_23),
% 0.21/0.28 inference(avatar_component_clause,[],[f325])).
% 0.21/0.28 thf(f327,plain,(
% 0.21/0.28 spl6_1 | spl6_23),
% 0.21/0.28 inference(avatar_split_clause,[],[f163,f325,f49])).
% 0.21/0.28 thf(f450,plain,(
% 0.21/0.28 ( ! [X10 : $i] : (($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) != $true)) ) | ~spl6_23),
% 0.21/0.28 inference(primitive_instantiation,[],[f326])).
% 0.21/0.28 thf(f467,plain,(
% 0.21/0.28 ($true != (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ~spl6_23),
% 0.21/0.28 inference(beta-eta_normalization,[],[f450])).
% 0.21/0.28 thf(f468,plain,(
% 0.21/0.28 (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ~spl6_23),
% 0.21/0.28 inference(equality_proxy_clausification,[],[f467])).
% 0.21/0.28 thf(f469,plain,(
% 0.21/0.28 (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ~spl6_23),
% 0.21/0.28 inference(equality_proxy_clausification,[],[f468])).
% 0.21/0.28 thf(f470,plain,(
% 0.21/0.28 (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | (spl6_1 | ~spl6_23)),
% 0.21/0.28 inference(forward_subsumption_resolution,[],[f469,f50])).
% 0.21/0.28 thf(f492,plain,(
% 0.21/0.28 ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : (((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7)) = $true) | ($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)))) )),
% 0.21/0.28 inference(primitive_instantiation,[],[f10])).
% 0.21/0.28 thf(f504,plain,(
% 0.21/0.28 ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : (($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true) | ((((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true) | ($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7)))) )),
% 0.21/0.28 inference(beta-eta_normalization,[],[f492])).
% 0.21/0.28 thf(f505,plain,(
% 0.21/0.28 ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ((((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true) | ($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | ($true = (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))))) )),
% 0.21/0.28 inference(equality_proxy_clausification,[],[f504])).
% 0.21/0.28 thf(f506,plain,(
% 0.21/0.28 ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true) | (((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7)))) )),
% 0.21/0.28 inference(equality_proxy_clausification,[],[f505])).
% 0.21/0.28 thf(f507,plain,(
% 0.21/0.28 ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : (($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | (((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) )),
% 0.21/0.28 inference(equality_proxy_clausification,[],[f506])).
% 0.21/0.28 thf(f508,plain,(
% 0.21/0.28 ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : (($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true)) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f507])).
% 0.21/0.28 thf(f520,plain,(
% 0.21/0.28 ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : (($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) ) | spl6_1),
% 0.21/0.28 inference(forward_subsumption_resolution,[],[f508,f50])).
% 0.21/0.28 thf(f526,plain,(
% 0.21/0.28 ( ! [X10 : $i,X7 : $i] : ((((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X7)) = $true) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)))) ) | spl6_1),
% 0.21/0.28 inference(primitive_instantiation,[],[f520])).
% 0.21/0.28 thf(f541,plain,(
% 0.21/0.28 (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ((((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) = $true) | spl6_1),
% 0.21/0.28 inference(beta-eta_normalization,[],[f526])).
% 0.21/0.28 thf(f542,plain,(
% 0.21/0.28 ((((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) = $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | spl6_1),
% 0.21/0.28 inference(equality_proxy_clausification,[],[f541])).
% 0.21/0.28 thf(f543,plain,(
% 0.21/0.28 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | spl6_1),
% 0.21/0.28 inference(equality_proxy_clausification,[],[f542])).
% 0.21/0.28 thf(f544,plain,(
% 0.21/0.28 (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | spl6_1),
% 0.21/0.28 inference(duplicate_literal_removal,[],[f543])).
% 0.21/0.28 thf(f565,plain,(
% 0.21/0.28 (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | spl6_1),
% 0.21/0.28 inference(forward_subsumption_resolution,[],[f544,f50])).
% 0.21/0.28 thf(f650,plain,(
% 0.21/0.28 ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X6 : $i] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X6)) = $true) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X6)))) )),
% 0.21/0.28 inference(primitive_instantiation,[],[f12])).
% 0.21/0.28 thf(f669,plain,(
% 0.21/0.28 ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X6 : $i] : (($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ((((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) = $true) | ((((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true) | ($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X6)))) )),
% 0.21/0.28 inference(beta-eta_normalization,[],[f650])).
% 0.21/0.28 thf(f670,plain,(
% 0.21/0.28 ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X6 : $i] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X6))) | ((((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true) | ((((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) = $true)) )),
% 0.21/0.28 inference(equality_proxy_clausification,[],[f669])).
% 0.21/0.28 thf(f671,plain,(
% 0.21/0.28 ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X6 : $i] : (($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X6))) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ((((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) = $true) | (((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) )),
% 0.21/0.28 inference(equality_proxy_clausification,[],[f670])).
% 0.21/0.28 thf(f672,plain,(
% 0.21/0.28 ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X6 : $i] : (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X6))) | (((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) )),
% 0.21/0.28 inference(equality_proxy_clausification,[],[f671])).
% 0.21/0.28 thf(f673,plain,(
% 0.21/0.28 ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X6 : $i] : ((((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true) | ($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X6)))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f672])).
% 0.21/0.28 thf(f678,plain,(
% 0.21/0.28 ( ! [X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X6 : $i] : (($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X6))) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) = $true) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) ) | spl6_1),
% 0.21/0.28 inference(forward_subsumption_resolution,[],[f673,f50])).
% 0.21/0.28 thf(f679,plain,(
% 0.21/0.28 ( ! [X10 : $i,X6 : $i] : (($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X6))) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)))) ) | spl6_1),
% 0.21/0.28 inference(primitive_instantiation,[],[f678])).
% 0.21/0.28 thf(f708,plain,(
% 0.21/0.28 (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | spl6_1),
% 0.21/0.28 inference(beta-eta_normalization,[],[f679])).
% 0.21/0.28 thf(f709,plain,(
% 0.21/0.28 (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ($true = (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | spl6_1),
% 0.21/0.28 inference(equality_proxy_clausification,[],[f708])).
% 0.21/0.28 thf(f710,plain,(
% 0.21/0.28 (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | spl6_1),
% 0.21/0.28 inference(equality_proxy_clausification,[],[f709])).
% 0.21/0.28 thf(f711,plain,(
% 0.21/0.28 (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | spl6_1),
% 0.21/0.28 inference(duplicate_literal_removal,[],[f710])).
% 0.21/0.28 thf(f725,plain,(
% 0.21/0.28 (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | spl6_1),
% 0.21/0.28 inference(forward_subsumption_resolution,[],[f711,f50])).
% 0.21/0.28 thf(f728,plain,(
% 0.21/0.28 (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | spl6_1),
% 0.21/0.28 inference(forward_demodulation,[],[f725,f565])).
% 0.21/0.28 thf(f731,plain,(
% 0.21/0.28 $false | (spl6_1 | ~spl6_23)),
% 0.21/0.28 inference(forward_subsumption_resolution,[],[f728,f470])).
% 0.21/0.28 thf(f732,plain,(
% 0.21/0.28 spl6_1 | ~spl6_23),
% 0.21/0.28 inference(avatar_contradiction_clause,[],[f731])).
% 0.21/0.28 cnf(s12, plain, ~spl6_1, inference(sat_conversion,[],[f305])).
% 0.21/0.28 cnf(s18, plain, spl6_1 | spl6_23, inference(sat_conversion,[],[f327])).
% 0.21/0.28 cnf(s27, plain, spl6_1 | ~spl6_23, inference(sat_conversion,[],[f732])).
% 0.21/0.28 cnf(s28, plain, ~spl6_23, inference(rat,[],[s27,s12])).
% 0.21/0.28 cnf(s29, plain, $false, inference(rat,[],[s18,s28,s12])).
% 0.21/0.28 thf(f733,plain,(
% 0.21/0.28 $false),
% 0.21/0.28 inference(avatar_sat_refutation,[],[s29])).
% 0.21/0.28 % SZS output end Proof for theBenchmark
% 0.21/0.28 % (840569)------------------------------
% 0.21/0.28 % (840569)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (840569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (840569)CaDiCaL version: 2.1.3
% 0.21/0.28 % (840569)Termination reason: Refutation
% 0.21/0.28 % (840569)Time elapsed: 0.022 s
% 0.21/0.28 % (840569)Peak memory usage: 14 MB
% 0.21/0.28 % (840569)Instructions burned: 81 (million)
% 0.21/0.28 % (840564)Success in time 0.052 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------