%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV064^5 : 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 : n016.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 08:37:34 AM UTC 2026
% Result : Theorem 0.23s 0.30s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV064^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n016.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 15:10:50 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 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
% 0.23/0.30 % (466512)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.30 % (466517)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1699746778:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.30 % (466523)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.30 % (466523)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
% 0.23/0.30 % (466518)lrs+10_16_si=on:nwc=1.5:random_seed=1181337189:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.30 % (466519)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2127288462:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.30 % (466523)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=3510603063:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.30 % (466520)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=2035887708: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)
% 0.23/0.30 % (466521)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3378017663:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.30 % (466522)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2633317969:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.30 % (466519)Instruction limit reached!
% 0.23/0.30 % (466519)------------------------------
% 0.23/0.30 % (466519)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (466519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (466519)CaDiCaL version: 2.1.3
% 0.23/0.30 % (466519)Termination reason: Instruction limit
% 0.23/0.30 % (466519)Termination phase: Saturation
% 0.23/0.30 % (466519)Time elapsed: 0.002 s
% 0.23/0.30 % (466519)Peak memory usage: 11 MB
% 0.23/0.30 % (466519)Instructions burned: 3 (million)
% 0.23/0.30 % (466517) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-466512-466517"...
% 0.23/0.30 % (466518)Instruction limit reached!
% 0.23/0.30 % (466518)------------------------------
% 0.23/0.30 % (466518)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (466518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (466518)CaDiCaL version: 2.1.3
% 0.23/0.30 % (466518)Termination reason: Instruction limit
% 0.23/0.30 % (466518)Termination phase: Saturation
% 0.23/0.30 % (466518)Time elapsed: 0.009 s
% 0.23/0.30 % (466518)Peak memory usage: 12 MB
% 0.23/0.30 % (466518)Instructions burned: 18 (million)
% 0.23/0.30 % (466517)...printing done.
% 0.23/0.30 % (466517)Refutation found. Thanks to Tanya!
% 0.23/0.30 % SZS status Theorem for theBenchmark
% 0.23/0.30 % SZS output start Proof for theBenchmark
% 0.23/0.30 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.30 thf(func_def_3, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.23/0.30 thf(func_def_4, type, sK0: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 0.23/0.30 thf(func_def_5, type, sK1: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i)).
% 0.23/0.30 thf(func_def_6, type, sK2: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 0.23/0.30 thf(func_def_7, type, sK3: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 0.23/0.30 thf(func_def_8, type, sK4: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 0.23/0.30 thf(func_def_9, type, sK5: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i)).
% 0.23/0.30 thf(func_def_10, type, vNOT: ($o > $o)).
% 0.23/0.30 thf(func_def_11, type, db1: !>[X0: $tType]:(X0)).
% 0.23/0.30 thf(func_def_12, type, db2: !>[X0: $tType]:(X0)).
% 0.23/0.30 thf(func_def_13, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.23/0.30 thf(func_def_14, type, db0: !>[X0: $tType]:(X0)).
% 0.23/0.30 thf(func_def_17, type, sK8: ((($i > $o) > ($i > $o) > $i > $o) > $i)).
% 0.23/0.30 thf(func_def_18, type, sK9: ((($i > $o) > ($i > $o) > $i > $o) > $i)).
% 0.23/0.30 thf(f1,conjecture,(
% 0.23/0.30 ? [X1 : (($i > $o) > ($i > $o) > $i > $o),X0 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : $i,X3 : ($i > $o)] : ((X1 @ X3 @ X3 @ X2) | (X0 @ X3 @ X3 @ X2)) & ~ ! [X2 : $i] : ((X0 @ (^[X3 : $i] : ($true)) @ (^[X3 : $i] : ($false)) @ X2) | (X1 @ (^[X3 : $i] : ($true)) @ (^[X3 : $i] : ($false)) @ X2)) & ! [X4 : ($i > $o),X3 : ($i > $o),X5 : ($i > $o)] : ((! [X2 : $i] : ((X0 @ X4 @ X5 @ X2) | (X1 @ X4 @ X5 @ X2)) & ! [X2 : $i] : ((X0 @ X3 @ X4 @ X2) | (X1 @ X3 @ X4 @ X2))) => ! [X2 : $i] : ((X1 @ X3 @ X5 @ X2) | (X0 @ X3 @ X5 @ X2))))),
% 0.23/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM120C_pme)).
% 0.23/0.30 thf(f2,negated_conjecture,(
% 0.23/0.30 ~ ? [X1 : (($i > $o) > ($i > $o) > $i > $o),X0 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : $i,X3 : ($i > $o)] : ((X1 @ X3 @ X3 @ X2) | (X0 @ X3 @ X3 @ X2)) & ~ ! [X2 : $i] : ((X0 @ (^[X3 : $i] : ($true)) @ (^[X3 : $i] : ($false)) @ X2) | (X1 @ (^[X3 : $i] : ($true)) @ (^[X3 : $i] : ($false)) @ X2)) & ! [X4 : ($i > $o),X3 : ($i > $o),X5 : ($i > $o)] : ((! [X2 : $i] : ((X0 @ X4 @ X5 @ X2) | (X1 @ X4 @ X5 @ X2)) & ! [X2 : $i] : ((X0 @ X3 @ X4 @ X2) | (X1 @ X3 @ X4 @ X2))) => ! [X2 : $i] : ((X1 @ X3 @ X5 @ X2) | (X0 @ X3 @ X5 @ X2))))),
% 0.23/0.30 inference(negated_conjecture,[status(cth)],[f1])).
% 0.23/0.30 thf(f3,plain,(
% 0.23/0.30 ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : $i,X3 : ($i > $o)] : ((X0 @ X3 @ X3 @ X2) | (X1 @ X3 @ X3 @ X2)) & ~ ! [X4 : $i] : ((X1 @ (^[X5 : $i] : ($true)) @ (^[X6 : $i] : ($false)) @ X4) | (X0 @ (^[X7 : $i] : ($true)) @ (^[X8 : $i] : ($false)) @ X4)) & ! [X9 : ($i > $o),X10 : ($i > $o),X11 : ($i > $o)] : ((! [X12 : $i] : ((X1 @ X9 @ X11 @ X12) | (X0 @ X9 @ X11 @ X12)) & ! [X13 : $i] : ((X1 @ X10 @ X9 @ X13) | (X0 @ X10 @ X9 @ X13))) => ! [X14 : $i] : ((X0 @ X10 @ X11 @ X14) | (X1 @ X10 @ X11 @ X14))))),
% 0.23/0.30 inference(rectify,[],[f2])).
% 0.23/0.30 thf(f4,plain,(
% 0.23/0.30 ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X3 : ($i > $o),X2 : $i] : ((((X0 @ X3 @ X3 @ X2)) = $true) | (((X1 @ X3 @ X3 @ X2)) = $true)) & ~ ! [X4 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4)))) & ! [X9 : ($i > $o),X10 : ($i > $o),X11 : ($i > $o)] : ((! [X12 : $i] : (($true = ((X1 @ X9 @ X11 @ X12))) | ($true = ((X0 @ X9 @ X11 @ X12)))) & ! [X13 : $i] : (($true = ((X1 @ X10 @ X9 @ X13))) | ($true = ((X0 @ X10 @ X9 @ X13))))) => ! [X14 : $i] : (($true = ((X0 @ X10 @ X11 @ X14))) | ($true = ((X1 @ X10 @ X11 @ X14))))))),
% 0.23/0.30 inference(fool_elimination,[],[f3])).
% 0.23/0.30 thf(f5,plain,(
% 0.23/0.30 ~ ? [X1 : (($i > $o) > ($i > $o) > $i > $o),X0 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X7 : ($i > $o),X5 : ($i > $o),X6 : ($i > $o)] : ((! [X9 : $i] : ((((X1 @ X6 @ X5 @ X9)) = $true) | (((X0 @ X6 @ X5 @ X9)) = $true)) & ! [X8 : $i] : (($true = ((X1 @ X5 @ X7 @ X8))) | ($true = ((X0 @ X5 @ X7 @ X8))))) => ! [X10 : $i] : (($true = ((X0 @ X6 @ X7 @ X10))) | ($true = ((X1 @ X6 @ X7 @ X10))))) & ~ ! [X4 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4)))) & ! [X3 : ($i > $o),X2 : $i] : ((((X0 @ X3 @ X3 @ X2)) = $true) | (((X1 @ X3 @ X3 @ X2)) = $true)))),
% 0.23/0.30 inference(rectify,[],[f4])).
% 0.23/0.30 thf(f6,plain,(
% 0.23/0.30 ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X0 : (($i > $o) > ($i > $o) > $i > $o)] : (? [X7 : ($i > $o),X5 : ($i > $o),X6 : ($i > $o)] : (? [X10 : $i] : (($true != ((X0 @ X6 @ X7 @ X10))) & ($true != ((X1 @ X6 @ X7 @ X10)))) & (! [X9 : $i] : ((((X1 @ X6 @ X5 @ X9)) = $true) | (((X0 @ X6 @ X5 @ X9)) = $true)) & ! [X8 : $i] : (($true = ((X1 @ X5 @ X7 @ X8))) | ($true = ((X0 @ X5 @ X7 @ X8)))))) | ! [X4 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4)))) | ? [X3 : ($i > $o),X2 : $i] : ((((X1 @ X3 @ X3 @ X2)) != $true) & (((X0 @ X3 @ X3 @ X2)) != $true)))),
% 0.23/0.30 inference(ennf_transformation,[],[f5])).
% 0.23/0.30 thf(f7,plain,(
% 0.23/0.30 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (? [X3 : ($i > $o),X2 : $i] : ((((X1 @ X3 @ X3 @ X2)) != $true) & (((X0 @ X3 @ X3 @ X2)) != $true)) | ! [X4 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4)))) | ? [X6 : ($i > $o),X5 : ($i > $o),X7 : ($i > $o)] : (! [X8 : $i] : (($true = ((X1 @ X5 @ X7 @ X8))) | ($true = ((X0 @ X5 @ X7 @ X8)))) & ! [X9 : $i] : ((((X1 @ X6 @ X5 @ X9)) = $true) | (((X0 @ X6 @ X5 @ X9)) = $true)) & ? [X10 : $i] : (($true != ((X0 @ X6 @ X7 @ X10))) & ($true != ((X1 @ X6 @ X7 @ X10))))))),
% 0.23/0.30 inference(flattening,[],[f6])).
% 0.23/0.30 thf(f8,plain,(
% 0.23/0.30 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (? [X2 : ($i > $o),X3 : $i] : (($true != ((X1 @ X2 @ X2 @ X3))) & ($true != ((X0 @ X2 @ X2 @ X3)))) | ! [X4 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4)))) | ? [X5 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o)] : (! [X8 : $i] : (($true = ((X1 @ X6 @ X7 @ X8))) | ($true = ((X0 @ X6 @ X7 @ X8)))) & ! [X9 : $i] : (($true = ((X1 @ X5 @ X6 @ X9))) | ($true = ((X0 @ X5 @ X6 @ X9)))) & ? [X10 : $i] : (($true != ((X0 @ X5 @ X7 @ X10))) & ($true != ((X1 @ X5 @ X7 @ X10))))))),
% 0.23/0.30 inference(rectify,[],[f7])).
% 0.23/0.30 thf(f9,plain,(
% 0.23/0.30 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : ((($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0)))) & (((X0 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0))) != $true)) | ! [X4 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4)))) | (! [X8 : $i] : (($true = ((X1 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X8))) | ($true = ((X0 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X8)))) & ! [X9 : $i] : (($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X9))) | ($true = ((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X9)))) & ((((X0 @ (sK2 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) != $true) & ($true != ((X1 @ (sK2 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))))))),
% 0.23/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X10,sK5 @ X1 @ X0),skolemize(X10,sK5 @ X1 @ X0),skolemize(X10,sK5 @ X1 @ X0),skolemize(X10,sK5 @ X1 @ X0),skolemize(X10,sK5 @ X1 @ X0),skolemize(X10,sK5 @ X1 @ X0)],[f8])).
% 0.23/0.30 thf(f11,plain,(
% 0.23/0.30 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X4 : $i] : ((((X0 @ (sK2 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) != $true) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4))) | (((X0 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0))) != $true) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4)))) )),
% 0.23/0.30 inference(cnf_transformation,[],[f9])).
% 0.23/0.30 thf(f12,plain,(
% 0.23/0.30 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i,X4 : $i] : ((((X0 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0))) != $true) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4))) | ($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X9))) | ($true = ((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X9)))) )),
% 0.23/0.30 inference(cnf_transformation,[],[f9])).
% 0.23/0.30 thf(f13,plain,(
% 0.23/0.30 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X4 : $i] : ((((X0 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0))) != $true) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4))) | ($true = ((X1 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X8))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4))) | ($true = ((X0 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X8)))) )),
% 0.23/0.30 inference(cnf_transformation,[],[f9])).
% 0.23/0.30 thf(f44,definition,(
% 0.23/0.30 spl6_2 <=> ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 0.23/0.30 introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition])).
% 0.23/0.30 thf(f45,plain,(
% 0.23/0.30 ((^[Y0 : $i]: ($true)) != (^[Y0 : $i]: ($false))) | spl6_2),
% 0.23/0.30 inference(avatar_component_clause,[],[f44])).
% 0.23/0.30 thf(f46,plain,(
% 0.23/0.30 ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ~spl6_2),
% 0.23/0.30 inference(avatar_component_clause,[],[f44])).
% 0.23/0.30 thf(f82,plain,(
% 0.23/0.30 ( ! [X1 : $i] : (((((^[Y0 : $i]: ($true)) @ X1)) = (((^[Y0 : $i]: ($false)) @ X1)))) ) | ~spl6_2),
% 0.23/0.30 inference(argument_congruence,[],[f46])).
% 0.23/0.30 thf(f84,plain,(
% 0.23/0.30 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ($true)) @ X1))) | ($true = (((^[Y0 : $i]: ($false)) @ X1)))) ) | ~spl6_2),
% 0.23/0.30 inference(iff_proxy_clausification,[],[f82])).
% 0.23/0.30 thf(f85,plain,(
% 0.23/0.30 ($true = $false) | ($true = $false) | ~spl6_2),
% 0.23/0.30 inference(beta-eta_normalization,[],[f84])).
% 0.23/0.30 thf(f86,plain,(
% 0.23/0.30 ($true = $false) | ~spl6_2),
% 0.23/0.30 inference(duplicate_literal_removal,[],[f85])).
% 0.23/0.30 thf(f87,plain,(
% 0.23/0.30 $false | ~spl6_2),
% 0.23/0.30 inference(trivial_inequality_removal,[],[f86])).
% 0.23/0.30 thf(f88,plain,(
% 0.23/0.30 ~spl6_2),
% 0.23/0.30 inference(avatar_contradiction_clause,[],[f87])).
% 0.23/0.30 thf(f330,plain,(
% 0.23/0.30 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i,X4 : $i] : (($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X9))) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | ($true = ((X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X9))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4)))) )),
% 0.23/0.30 inference(primitive_instantiation,[],[f12])).
% 0.23/0.30 thf(f349,plain,(
% 0.23/0.30 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i,X4 : $i] : (($true = (((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | ($true = ((X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X9))) | ((((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) != $true) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4)))) )),
% 0.23/0.30 inference(beta-eta_normalization,[],[f330])).
% 0.23/0.30 thf(f350,plain,(
% 0.23/0.30 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i,X4 : $i] : (($true = ((X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X9))) | (((sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4))) | ((((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) != $true) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))))) )),
% 0.23/0.30 inference(equality_proxy_clausification,[],[f349])).
% 0.23/0.30 thf(f351,plain,(
% 0.23/0.30 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i,X4 : $i] : ((((sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4))) | ($true = ((X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X9))) | (((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) )),
% 0.23/0.30 inference(equality_proxy_clausification,[],[f350])).
% 0.23/0.30 thf(f352,plain,(
% 0.23/0.30 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i,X4 : $i] : (($true = ((X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X9))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4))) | (((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | (((sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) )),
% 0.23/0.30 inference(equality_proxy_clausification,[],[f351])).
% 0.23/0.30 thf(f353,plain,(
% 0.23/0.30 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i,X4 : $i] : (($true = ((X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X9))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4))) | (((sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) )),
% 0.23/0.30 inference(trivial_inequality_removal,[],[f352])).
% 0.23/0.30 thf(f358,plain,(
% 0.23/0.30 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i,X4 : $i] : (($true = ((X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X9))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4))) | (((sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) ) | spl6_2),
% 0.23/0.30 inference(forward_subsumption_resolution,[],[f353,f45])).
% 0.23/0.30 thf(f359,plain,(
% 0.23/0.30 ( ! [X9 : $i,X4 : $i] : (($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))))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X9))) | (((sK3 @ (^[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 > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4)))) ) | spl6_2),
% 0.23/0.30 inference(primitive_instantiation,[],[f358])).
% 0.23/0.30 thf(f371,plain,(
% 0.23/0.30 ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | (((sK3 @ (^[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 = (((sK2 @ (^[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 : $i]: (Y0 = Y1)))))))))) | spl6_2),
% 0.23/0.30 inference(beta-eta_normalization,[],[f359])).
% 0.23/0.30 thf(f372,plain,(
% 0.23/0.30 ($true = (((sK2 @ (^[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)))))))))) | (((sK3 @ (^[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 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | spl6_2),
% 0.23/0.30 inference(equality_proxy_clausification,[],[f371])).
% 0.23/0.30 thf(f373,plain,(
% 0.23/0.30 (((sK3 @ (^[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))))))))) | (((sK3 @ (^[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 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | spl6_2),
% 0.23/0.30 inference(equality_proxy_clausification,[],[f372])).
% 0.23/0.30 thf(f374,plain,(
% 0.23/0.30 ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | (((sK3 @ (^[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_2),
% 0.23/0.30 inference(duplicate_literal_removal,[],[f373])).
% 0.23/0.30 thf(f403,plain,(
% 0.23/0.30 (((sK3 @ (^[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_2),
% 0.23/0.30 inference(forward_subsumption_resolution,[],[f374,f45])).
% 0.23/0.30 thf(f450,plain,(
% 0.23/0.30 ( ! [X0 : $i] : (($true != (((^[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))))))) @ (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 > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X0))) | ($true != (((^[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))))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK5 @ (^[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)) @ X0)))) ) | spl6_2),
% 0.23/0.30 inference(constrained_superposition,[],[f11,f403])).
% 0.23/0.30 thf(f455,plain,(
% 0.23/0.30 ( ! [X0 : $i] : (($true != (((^[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))))))) @ (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 > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X0))) | ($true != (((^[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))))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))))) ) | spl6_2),
% 0.23/0.30 inference(duplicate_literal_removal,[],[f450])).
% 0.23/0.30 thf(f456,plain,(
% 0.23/0.30 ($true != (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK4 @ (^[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 != (((sK0 @ (^[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 : $i]: (Y0 = Y1)))))))))) | spl6_2),
% 0.23/0.30 inference(beta-eta_normalization,[],[f455])).
% 0.23/0.30 thf(f457,plain,(
% 0.23/0.30 ($true != (((sK0 @ (^[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)))))))))) | (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK4 @ (^[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_2),
% 0.23/0.30 inference(equality_proxy_clausification,[],[f456])).
% 0.23/0.30 thf(f458,plain,(
% 0.23/0.30 (((sK0 @ (^[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))))) | (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | spl6_2),
% 0.23/0.30 inference(equality_proxy_clausification,[],[f457])).
% 0.23/0.30 thf(f459,plain,(
% 0.23/0.30 (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((^[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)))))))) != ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | spl6_2),
% 0.23/0.30 inference(equality_proxy_clausification,[],[f458])).
% 0.23/0.30 thf(f460,plain,(
% 0.23/0.30 (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | spl6_2),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f459])).
% 0.23/0.31 thf(f475,plain,(
% 0.23/0.31 (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | spl6_2),
% 0.23/0.31 inference(forward_subsumption_resolution,[],[f460,f45])).
% 0.23/0.31 thf(f528,plain,(
% 0.23/0.31 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X4 : $i] : (($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X8))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4))) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | (((X1 @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X8)) = $true)) )),
% 0.23/0.31 inference(primitive_instantiation,[],[f13])).
% 0.23/0.31 thf(f538,plain,(
% 0.23/0.31 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X4 : $i] : (((((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) != $true) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = (((sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | (((X1 @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X8)) = $true) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4)))) )),
% 0.23/0.31 inference(beta-eta_normalization,[],[f528])).
% 0.23/0.31 thf(f539,plain,(
% 0.23/0.31 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X4 : $i] : ((((X1 @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X8)) = $true) | ($true = (((sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | (((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))))) )),
% 0.23/0.31 inference(equality_proxy_clausification,[],[f538])).
% 0.23/0.31 thf(f540,plain,(
% 0.23/0.31 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X4 : $i] : (($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4))) | (((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | (((sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | (((X1 @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X8)) = $true) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))))) )),
% 0.23/0.31 inference(equality_proxy_clausification,[],[f539])).
% 0.23/0.31 thf(f541,plain,(
% 0.23/0.31 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X4 : $i] : (($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4))) | (((sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | (((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | (((X1 @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X8)) = $true) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) )),
% 0.23/0.31 inference(equality_proxy_clausification,[],[f540])).
% 0.23/0.31 thf(f542,plain,(
% 0.23/0.31 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X4 : $i] : ((((X1 @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X8)) = $true) | (((sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) )),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f541])).
% 0.23/0.31 thf(f556,plain,(
% 0.23/0.31 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X4 : $i] : ((((X1 @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X8)) = $true) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4))) | (((sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) ) | spl6_2),
% 0.23/0.31 inference(forward_subsumption_resolution,[],[f542,f45])).
% 0.23/0.31 thf(f591,plain,(
% 0.23/0.31 ( ! [X8 : $i,X4 : $i] : ((((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK4 @ (^[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)) @ X4))) | ($true = (((^[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))))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X8)))) ) | spl6_2),
% 0.23/0.31 inference(primitive_instantiation,[],[f556])).
% 0.23/0.31 thf(f626,plain,(
% 0.23/0.31 ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ($true = (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | spl6_2),
% 0.23/0.31 inference(beta-eta_normalization,[],[f591])).
% 0.23/0.31 thf(f627,plain,(
% 0.23/0.31 (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ($true = (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | spl6_2),
% 0.23/0.31 inference(equality_proxy_clausification,[],[f626])).
% 0.23/0.31 thf(f628,plain,(
% 0.23/0.31 ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK4 @ (^[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)))))))) = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | spl6_2),
% 0.23/0.31 inference(equality_proxy_clausification,[],[f627])).
% 0.23/0.31 thf(f629,plain,(
% 0.23/0.31 (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | spl6_2),
% 0.23/0.31 inference(duplicate_literal_removal,[],[f628])).
% 0.23/0.31 thf(f635,plain,(
% 0.23/0.31 ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | spl6_2),
% 0.23/0.31 inference(forward_subsumption_resolution,[],[f629,f475])).
% 0.23/0.31 thf(f638,plain,(
% 0.23/0.31 $false | spl6_2),
% 0.23/0.31 inference(forward_subsumption_resolution,[],[f635,f45])).
% 0.23/0.31 thf(f639,plain,(
% 0.23/0.31 spl6_2),
% 0.23/0.31 inference(avatar_contradiction_clause,[],[f638])).
% 0.23/0.31 cnf(s3, plain, ~spl6_2, inference(sat_conversion,[],[f88])).
% 0.23/0.31 cnf(s18, plain, spl6_2, inference(sat_conversion,[],[f639])).
% 0.23/0.31 cnf(s19, plain, $false, inference(rat,[],[s3,s18])).
% 0.23/0.31 thf(f640,plain,(
% 0.23/0.31 $false),
% 0.23/0.31 inference(avatar_sat_refutation,[],[s19])).
% 0.23/0.31 % SZS output end Proof for theBenchmark
% 0.23/0.31 % (466517)------------------------------
% 0.23/0.31 % (466517)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (466517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (466517)CaDiCaL version: 2.1.3
% 0.23/0.31 % (466517)Termination reason: Refutation
% 0.23/0.31 % (466517)Time elapsed: 0.019 s
% 0.23/0.31 % (466517)Peak memory usage: 13 MB
% 0.23/0.31 % (466517)Instructions burned: 68 (million)
% 0.23/0.31 % (466512)Success in time 0.043 s
% 0.23/0.31 % Vampire exiting
%------------------------------------------------------------------------------