%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV100^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:37:38 AM UTC 2026
% Result : Theorem 0.64s 0.39s
% Output : Refutation 0.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV100^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.23 % Computer : n018.cluster.edu
% 0.11/0.23 % Model : x86_64 x86_64
% 0.11/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.23 % Memory : 8046.5625MB
% 0.11/0.23 % OS : Linux 6.8.0-71-generic
% 0.11/0.23 % CPULimit : 300
% 0.11/0.23 % WCLimit : 300
% 0.11/0.23 % DateTime : Tue Sep 29 15:12:11 UTC 2026
% 0.11/0.23 % CPUTime :
% 0.11/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.28 Running higher-order theorem proving
% 0.25/0.30 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.64/0.39 % (201090)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.64/0.39 % (201097)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3105299348:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.64/0.39 % (201096)lrs+10_16_si=on:nwc=1.5:random_seed=822032935:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.64/0.39 % (201097)Instruction limit reached!
% 0.64/0.39 % (201097)------------------------------
% 0.64/0.39 % (201097)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.39 % (201097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.39 % (201097)CaDiCaL version: 2.1.3
% 0.64/0.39 % (201097)Termination reason: Instruction limit
% 0.64/0.39 % (201097)Termination phase: Saturation
% 0.64/0.39 % (201097)Time elapsed: 0.002 s
% 0.64/0.39 % (201097)Peak memory usage: 11 MB
% 0.64/0.39 % (201097)Instructions burned: 4 (million)
% 0.64/0.39 % (201101)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.64/0.39 % (201101)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
% 0.64/0.39 % (201096)Instruction limit reached!
% 0.64/0.39 % (201096)------------------------------
% 0.64/0.39 % (201096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.39 % (201096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.39 % (201096)CaDiCaL version: 2.1.3
% 0.64/0.39 % (201096)Termination reason: Instruction limit
% 0.64/0.39 % (201096)Termination phase: Saturation
% 0.64/0.39 % (201096)Time elapsed: 0.010 s
% 0.64/0.39 % (201096)Peak memory usage: 12 MB
% 0.64/0.39 % (201096)Instructions burned: 18 (million)
% 0.64/0.39 % (201095)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3628375441:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.64/0.39 % (201099)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2367710691:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.64/0.39 % (201100)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=753374585:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.64/0.39 % (201098)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=3910510111: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)
% 0.64/0.39 % (201101)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=4068733113:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.64/0.39 % (201108)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3268313673:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.64/0.39 % (201108)Instruction limit reached!
% 0.64/0.39 % (201108)------------------------------
% 0.64/0.39 % (201108)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.39 % (201104)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1823740700:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.64/0.39 % (201108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.39 % (201108)CaDiCaL version: 2.1.3
% 0.64/0.39 % (201108)Termination reason: Instruction limit
% 0.64/0.39 % (201108)Termination phase: Saturation
% 0.64/0.39 % (201108)Time elapsed: 0.003 s
% 0.64/0.39 % (201108)Peak memory usage: 11 MB
% 0.64/0.39 % (201108)Instructions burned: 7 (million)
% 0.64/0.39 % (201099)Instruction limit reached!
% 0.64/0.39 % (201099)------------------------------
% 0.64/0.39 % (201099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.39 % (201099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.39 % (201099)CaDiCaL version: 2.1.3
% 0.64/0.39 % (201099)Termination reason: Instruction limit
% 0.64/0.39 % (201099)Termination phase: Saturation
% 0.64/0.39 % (201099)Time elapsed: 0.022 s
% 0.64/0.39 % (201099)Peak memory usage: 11 MB
% 0.64/0.39 % (201099)Instructions burned: 25 (million)
% 0.64/0.39 % (201104)Instruction limit reached!
% 0.64/0.39 % (201104)------------------------------
% 0.64/0.39 % (201104)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.39 % (201104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.39 % (201104)CaDiCaL version: 2.1.3
% 0.64/0.39 % (201104)Termination reason: Instruction limit
% 0.64/0.39 % (201104)Termination phase: Property scanning
% 0.64/0.39 % (201104)Time elapsed: 0.002 s
% 0.64/0.39 % (201104)Peak memory usage: 10 MB
% 0.64/0.39 % (201104)Instructions burned: 2 (million)
% 0.64/0.39 % (201098) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-201090-201098"...
% 0.64/0.39 % (201113)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.64/0.39 % (201113)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3226446675:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.64/0.39 % (201113)Instruction limit reached!
% 0.64/0.39 % (201113)------------------------------
% 0.64/0.39 % (201113)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.39 % (201113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.39 % (201113)CaDiCaL version: 2.1.3
% 0.64/0.39 % (201113)Termination reason: Instruction limit
% 0.64/0.39 % (201113)Termination phase: Saturation
% 0.64/0.39 % (201113)Time elapsed: 0.004 s
% 0.64/0.39 % (201113)Peak memory usage: 12 MB
% 0.64/0.39 % (201113)Instructions burned: 8 (million)
% 0.64/0.39 % (201098)...printing done.
% 0.64/0.39 % (201098)Refutation found. Thanks to Tanya!
% 0.64/0.39 % SZS status Theorem for theBenchmark
% 0.64/0.39 % SZS output start Proof for theBenchmark
% 0.64/0.39 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.64/0.39 thf(func_def_0, type, p: $o).
% 0.64/0.39 thf(func_def_4, type, vOR: ($o > $o > $o)).
% 0.64/0.39 thf(func_def_5, type, vNOT: ($o > $o)).
% 0.64/0.39 thf(func_def_6, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.64/0.39 thf(func_def_7, type, vAND: ($o > $o > $o)).
% 0.64/0.39 thf(func_def_8, type, sK0: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 0.64/0.39 thf(func_def_9, type, sK1: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 0.64/0.39 thf(func_def_10, type, sK2: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 0.64/0.39 thf(func_def_11, type, sK3: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i)).
% 0.64/0.39 thf(func_def_12, type, sK4: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 0.64/0.39 thf(func_def_13, type, sK5: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i)).
% 0.64/0.39 thf(func_def_14, type, db1: !>[X0: $tType]:(X0)).
% 0.64/0.39 thf(func_def_15, type, db2: !>[X0: $tType]:(X0)).
% 0.64/0.39 thf(func_def_16, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.64/0.39 thf(func_def_17, type, db0: !>[X0: $tType]:(X0)).
% 0.64/0.39 thf(func_def_19, type, sK7: ((($i > $o) > ($i > $o) > $i > $o) > $i)).
% 0.64/0.39 thf(func_def_20, type, sK8: ((($i > $o) > ($i > $o) > $i > $o) > $i)).
% 0.64/0.39 thf(f1,conjecture,(
% 0.64/0.39 ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : ($i > $o),X5 : $i] : ((X1 @ X2 @ X2 @ X5) | (X0 @ X2 @ X2 @ X5)) & ~ ! [X5 : $i] : ((X1 @ (^[X2 : $i] : (p | ~p)) @ (^[X2 : $i] : (~p & p)) @ X5) | (X0 @ (^[X2 : $i] : (p | ~p)) @ (^[X2 : $i] : (p & ~p)) @ X5)) & ! [X3 : ($i > $o),X4 : ($i > $o),X2 : ($i > $o)] : ((! [X5 : $i] : ((X0 @ X3 @ X4 @ X5) | (X1 @ X3 @ X4 @ X5)) & ! [X5 : $i] : ((X0 @ X2 @ X3 @ X5) | (X1 @ X2 @ X3 @ X5))) => ! [X5 : $i] : ((X1 @ X2 @ X4 @ X5) | (X0 @ X2 @ X4 @ X5))))),
% 0.64/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM120F_pme)).
% 0.64/0.39 thf(f2,negated_conjecture,(
% 0.64/0.39 ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : ($i > $o),X5 : $i] : ((X1 @ X2 @ X2 @ X5) | (X0 @ X2 @ X2 @ X5)) & ~ ! [X5 : $i] : ((X1 @ (^[X2 : $i] : (p | ~p)) @ (^[X2 : $i] : (~p & p)) @ X5) | (X0 @ (^[X2 : $i] : (p | ~p)) @ (^[X2 : $i] : (p & ~p)) @ X5)) & ! [X3 : ($i > $o),X4 : ($i > $o),X2 : ($i > $o)] : ((! [X5 : $i] : ((X0 @ X3 @ X4 @ X5) | (X1 @ X3 @ X4 @ X5)) & ! [X5 : $i] : ((X0 @ X2 @ X3 @ X5) | (X1 @ X2 @ X3 @ X5))) => ! [X5 : $i] : ((X1 @ X2 @ X4 @ X5) | (X0 @ X2 @ X4 @ X5))))),
% 0.64/0.39 inference(negated_conjecture,[status(cth)],[f1])).
% 0.64/0.39 thf(f3,plain,(
% 0.64/0.39 ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : ($i > $o),X3 : $i] : ((X1 @ X2 @ X2 @ X3) | (X0 @ X2 @ X2 @ X3)) & ~ ! [X4 : $i] : ((X1 @ (^[X5 : $i] : (p | ~p)) @ (^[X6 : $i] : (~p & p)) @ X4) | (X0 @ (^[X7 : $i] : (p | ~p)) @ (^[X8 : $i] : (p & ~p)) @ X4)) & ! [X9 : ($i > $o),X10 : ($i > $o),X11 : ($i > $o)] : ((! [X12 : $i] : ((X0 @ X9 @ X10 @ X12) | (X1 @ X9 @ X10 @ X12)) & ! [X13 : $i] : ((X0 @ X11 @ X9 @ X13) | (X1 @ X11 @ X9 @ X13))) => ! [X14 : $i] : ((X1 @ X11 @ X10 @ X14) | (X0 @ X11 @ X10 @ X14))))),
% 0.64/0.39 inference(rectify,[],[f2])).
% 0.64/0.39 thf(f4,plain,(
% 0.64/0.39 ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X3 : $i,X2 : ($i > $o)] : (($true = ((X1 @ X2 @ X2 @ X3))) | ($true = ((X0 @ X2 @ X2 @ X3)))) & ~ ! [X4 : $i] : (($true = ((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X4))) | (((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ((~ p) & p)) @ X4)) = $true)) & ! [X9 : ($i > $o),X10 : ($i > $o),X11 : ($i > $o)] : ((! [X12 : $i] : ((((X0 @ X9 @ X10 @ X12)) = $true) | ($true = ((X1 @ X9 @ X10 @ X12)))) & ! [X13 : $i] : ((((X0 @ X11 @ X9 @ X13)) = $true) | ($true = ((X1 @ X11 @ X9 @ X13))))) => ! [X14 : $i] : (($true = ((X1 @ X11 @ X10 @ X14))) | ($true = ((X0 @ X11 @ X10 @ X14))))))),
% 0.64/0.39 inference(fool_elimination,[],[f3])).
% 0.64/0.39 thf(f5,plain,(
% 0.64/0.39 ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X4 : $i] : (($true = ((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X4))) | (((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ((~ p) & p)) @ X4)) = $true)) & ! [X3 : $i,X2 : ($i > $o)] : (($true = ((X1 @ X2 @ X2 @ X3))) | ($true = ((X0 @ X2 @ X2 @ X3)))) & ! [X6 : ($i > $o),X5 : ($i > $o),X7 : ($i > $o)] : ((! [X9 : $i] : ((((X1 @ X7 @ X5 @ X9)) = $true) | (((X0 @ X7 @ X5 @ X9)) = $true)) & ! [X8 : $i] : (($true = ((X0 @ X5 @ X6 @ X8))) | ($true = ((X1 @ X5 @ X6 @ X8))))) => ! [X10 : $i] : (($true = ((X1 @ X7 @ X6 @ X10))) | ($true = ((X0 @ X7 @ X6 @ X10))))))),
% 0.64/0.39 inference(rectify,[],[f4])).
% 0.64/0.39 thf(f6,plain,(
% 0.64/0.39 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X4 : $i] : (($true = ((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X4))) | (((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ((~ p) & p)) @ X4)) = $true)) | ? [X2 : ($i > $o),X3 : $i] : (($true != ((X0 @ X2 @ X2 @ X3))) & ($true != ((X1 @ X2 @ X2 @ X3)))) | ? [X6 : ($i > $o),X5 : ($i > $o),X7 : ($i > $o)] : (? [X10 : $i] : (($true != ((X1 @ X7 @ X6 @ X10))) & ($true != ((X0 @ X7 @ X6 @ X10)))) & (! [X9 : $i] : ((((X1 @ X7 @ X5 @ X9)) = $true) | (((X0 @ X7 @ X5 @ X9)) = $true)) & ! [X8 : $i] : (($true = ((X0 @ X5 @ X6 @ X8))) | ($true = ((X1 @ X5 @ X6 @ X8)))))))),
% 0.64/0.39 inference(ennf_transformation,[],[f5])).
% 0.64/0.39 thf(f7,plain,(
% 0.64/0.39 ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X0 : (($i > $o) > ($i > $o) > $i > $o)] : (? [X5 : ($i > $o),X7 : ($i > $o),X6 : ($i > $o)] : (! [X9 : $i] : ((((X1 @ X7 @ X5 @ X9)) = $true) | (((X0 @ X7 @ X5 @ X9)) = $true)) & ? [X10 : $i] : (($true != ((X1 @ X7 @ X6 @ X10))) & ($true != ((X0 @ X7 @ X6 @ X10)))) & ! [X8 : $i] : (($true = ((X0 @ X5 @ X6 @ X8))) | ($true = ((X1 @ X5 @ X6 @ X8))))) | ! [X4 : $i] : (($true = ((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X4))) | (((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ((~ p) & p)) @ X4)) = $true)) | ? [X2 : ($i > $o),X3 : $i] : (($true != ((X0 @ X2 @ X2 @ X3))) & ($true != ((X1 @ X2 @ X2 @ X3)))))),
% 0.64/0.39 inference(flattening,[],[f6])).
% 0.64/0.39 thf(f8,plain,(
% 0.64/0.39 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (? [X2 : ($i > $o),X3 : ($i > $o),X4 : ($i > $o)] : (! [X5 : $i] : (($true = ((X0 @ X3 @ X2 @ X5))) | ($true = ((X1 @ X3 @ X2 @ X5)))) & ? [X6 : $i] : (($true != ((X0 @ X3 @ X4 @ X6))) & ($true != ((X1 @ X3 @ X4 @ X6)))) & ! [X7 : $i] : (($true = ((X1 @ X2 @ X4 @ X7))) | ($true = ((X0 @ X2 @ X4 @ X7))))) | ! [X8 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X8))) | (((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ((~ p) & p)) @ X8)) = $true)) | ? [X9 : ($i > $o),X10 : $i] : ((((X1 @ X9 @ X9 @ X10)) != $true) & (((X0 @ X9 @ X9 @ X10)) != $true)))),
% 0.64/0.39 inference(rectify,[],[f7])).
% 0.64/0.39 thf(f9,plain,(
% 0.64/0.39 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : ((! [X5 : $i] : (($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X5))) | (((X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X5)) = $true)) & (($true != ((X0 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)))) & (((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0))) != $true)) & ! [X7 : $i] : (($true = ((X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) | (((X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7)) = $true))) | ! [X8 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X8))) | (((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ((~ p) & p)) @ X8)) = $true)) | ((((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) != $true) & ($true != ((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))))))),
% 0.64/0.39 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])).
% 0.64/0.39 thf(f11,plain,(
% 0.64/0.39 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : (($true = ((X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) | (((X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7)) = $true) | (((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) != $true) | ($true = ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X8))) | (((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ((~ p) & p)) @ X8)) = $true)) )),
% 0.64/0.39 inference(cnf_transformation,[],[f9])).
% 0.64/0.39 thf(f12,plain,(
% 0.64/0.39 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : ((((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ((~ p) & p)) @ X8)) = $true) | (((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0))) != $true) | ($true = ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X8))) | ($true != ((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))))) )),
% 0.64/0.39 inference(cnf_transformation,[],[f9])).
% 0.64/0.39 thf(f16,plain,(
% 0.64/0.39 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X5 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X8))) | (((X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X5)) = $true) | (((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ((~ p) & p)) @ X8)) = $true) | ($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X5))) | ($true != ((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))))) )),
% 0.64/0.39 inference(cnf_transformation,[],[f9])).
% 0.64/0.39 thf(f19,plain,(
% 0.64/0.39 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X5 : $i] : ((((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ($true != ((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | (((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ((~ p) & p)) @ X8)) = $true) | ($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X5))) | (((X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X5)) = $true)) )),
% 0.64/0.39 inference(boolean_simplification,[],[f16])).
% 0.64/0.39 thf(f20,plain,(
% 0.64/0.39 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X5 : $i] : ((((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ((~ p) & p)) @ X8)) = $true) | ($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X5))) | ($true != ((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | (((X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X5)) = $true) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true)) )),
% 0.64/0.39 inference(boolean_simplification,[],[f19])).
% 0.64/0.39 thf(f21,plain,(
% 0.64/0.39 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X5 : $i] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X5))) | (((X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X5)) = $true) | (((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ($true != ((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))))) )),
% 0.64/0.39 inference(boolean_simplification,[],[f20])).
% 0.64/0.39 thf(f22,plain,(
% 0.64/0.39 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X5 : $i] : (($true != ((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X5))) | (((X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X5)) = $true) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true)) )),
% 0.64/0.39 inference(boolean_simplification,[],[f21])).
% 0.64/0.39 thf(f23,plain,(
% 0.64/0.39 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : ((((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ((~ p) & p)) @ X8)) = $true) | ($true = ((X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) | (((X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7)) = $true) | (((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) != $true) | (((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true)) )),
% 0.64/0.39 inference(boolean_simplification,[],[f11])).
% 0.64/0.39 thf(f24,plain,(
% 0.64/0.39 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : (($true = ((X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) | (((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) != $true) | (((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7)) = $true)) )),
% 0.64/0.39 inference(boolean_simplification,[],[f23])).
% 0.64/0.39 thf(f25,plain,(
% 0.64/0.39 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : ((((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7)) = $true) | ($true = ((X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) | (((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) != $true) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true)) )),
% 0.64/0.39 inference(boolean_simplification,[],[f24])).
% 0.64/0.39 thf(f26,plain,(
% 0.64/0.39 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : ((((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) != $true) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ($true = ((X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7)) = $true)) )),
% 0.64/0.39 inference(boolean_simplification,[],[f25])).
% 0.64/0.39 thf(f43,plain,(
% 0.64/0.39 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X8))) | (((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0))) != $true) | ($true != ((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))))) )),
% 0.64/0.39 inference(boolean_simplification,[],[f12])).
% 0.64/0.39 thf(f44,plain,(
% 0.64/0.39 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : ((((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0))) != $true) | (((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ($true != ((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))))) )),
% 0.64/0.39 inference(boolean_simplification,[],[f43])).
% 0.64/0.39 thf(f45,plain,(
% 0.64/0.39 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true != ((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | (((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0))) != $true)) )),
% 0.64/0.39 inference(boolean_simplification,[],[f44])).
% 0.64/0.39 thf(f46,plain,(
% 0.64/0.39 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true != ((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | (((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0))) != $true) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true)) )),
% 0.64/0.39 inference(boolean_simplification,[],[f45])).
% 0.64/0.39 thf(f75,definition,(
% 0.64/0.39 spl6_2 <=> ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
% 0.64/0.39 introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition])).
% 0.64/0.39 thf(f76,plain,(
% 0.64/0.39 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ~spl6_2),
% 0.64/0.39 inference(avatar_component_clause,[],[f75])).
% 0.64/0.39 thf(f77,plain,(
% 0.64/0.39 ((^[Y0 : $i]: ($false)) != (^[Y0 : $i]: ($true))) | spl6_2),
% 0.64/0.39 inference(avatar_component_clause,[],[f75])).
% 0.64/0.39 thf(f115,plain,(
% 0.64/0.39 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8))) | (((X1 @ (sK1 @ X1 @ (^[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))))))))) != $true) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))))) )),
% 0.64/0.39 inference(primitive_instantiation,[],[f46])).
% 0.64/0.39 thf(f127,plain,(
% 0.64/0.39 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : ((((X1 @ (sK1 @ X1 @ (^[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))))))))) != $true) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ($true != (((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true)) )),
% 0.64/0.39 inference(beta-eta_normalization,[],[f115])).
% 0.64/0.39 thf(f128,plain,(
% 0.64/0.39 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : ((((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true) | (((X1 @ (sK1 @ X1 @ (^[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))))))))) != $true) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true)) )),
% 0.64/0.39 inference(equality_proxy_clausification,[],[f127])).
% 0.64/0.39 thf(f129,plain,(
% 0.64/0.39 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : ((((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | (((X1 @ (sK1 @ X1 @ (^[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))))))))) != $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true)) )),
% 0.64/0.39 inference(equality_proxy_clausification,[],[f128])).
% 0.64/0.39 thf(f130,plain,(
% 0.64/0.39 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((X1 @ (sK1 @ X1 @ (^[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))))))))) != $true) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true)) )),
% 0.64/0.39 inference(trivial_inequality_removal,[],[f129])).
% 0.64/0.39 thf(f137,definition,(
% 0.64/0.39 spl6_5 <=> ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : ((((X1 @ (sK1 @ X1 @ (^[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))))))))) != $true) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true))),
% 0.64/0.39 introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition])).
% 0.64/0.39 thf(f138,plain,(
% 0.64/0.39 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : ((((X1 @ (sK1 @ X1 @ (^[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))))))))) != $true) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true)) ) | ~spl6_5),
% 0.64/0.39 inference(avatar_component_clause,[],[f137])).
% 0.64/0.39 thf(f139,plain,(
% 0.64/0.39 spl6_5 | spl6_2),
% 0.64/0.39 inference(avatar_split_clause,[],[f130,f75,f137])).
% 0.64/0.39 thf(f172,plain,(
% 0.64/0.39 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X5 : $i] : (($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8))) | ($true = ((X1 @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X5))) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X5))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true)) )),
% 0.64/0.39 inference(primitive_instantiation,[],[f22])).
% 0.64/0.39 thf(f188,plain,(
% 0.64/0.39 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X5 : $i] : (((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ((((sK1 @ 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 = ((X1 @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X5))) | ($true != (((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))))) )),
% 0.64/0.39 inference(beta-eta_normalization,[],[f172])).
% 0.64/0.39 thf(f189,plain,(
% 0.64/0.39 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X5 : $i] : (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true = ((X1 @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X5))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ($true != (((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | ((((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) = $true)) )),
% 0.64/0.39 inference(equality_proxy_clausification,[],[f188])).
% 0.64/0.39 thf(f190,plain,(
% 0.64/0.39 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X5 : $i] : ((((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true = ((X1 @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X5))) | ((((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) = $true) | (((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) )),
% 0.64/0.39 inference(equality_proxy_clausification,[],[f189])).
% 0.64/0.39 thf(f191,plain,(
% 0.64/0.39 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X5 : $i] : ((((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 @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X5))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) )),
% 0.64/0.39 inference(equality_proxy_clausification,[],[f190])).
% 0.64/0.39 thf(f192,plain,(
% 0.64/0.39 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X5 : $i] : ((((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true = ((X1 @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X5))) | (((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) )),
% 0.64/0.39 inference(trivial_inequality_removal,[],[f191])).
% 0.64/0.39 thf(f201,definition,(
% 0.64/0.39 spl6_7 <=> ! [X5 : $i,X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : ((((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((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 @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X5))))),
% 0.64/0.39 introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition])).
% 0.64/0.39 thf(f202,plain,(
% 0.64/0.39 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X5 : $i] : (($true = ((X1 @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X5))) | (((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 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true)) ) | ~spl6_7),
% 0.64/0.39 inference(avatar_component_clause,[],[f201])).
% 0.64/0.39 thf(f203,plain,(
% 0.64/0.39 spl6_2 | spl6_7),
% 0.64/0.39 inference(avatar_split_clause,[],[f192,f201,f75])).
% 0.64/0.39 thf(f204,plain,(
% 0.64/0.39 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8))) | ($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))))) )),
% 0.64/0.39 inference(primitive_instantiation,[],[f26])).
% 0.64/0.39 thf(f221,plain,(
% 0.64/0.39 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : (($true = (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ($true != (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true) | ($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7)))) )),
% 0.64/0.39 inference(beta-eta_normalization,[],[f204])).
% 0.64/0.39 thf(f222,plain,(
% 0.64/0.39 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | ($true != (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true)) )),
% 0.64/0.39 inference(equality_proxy_clausification,[],[f221])).
% 0.64/0.39 thf(f223,plain,(
% 0.64/0.39 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true) | ($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7)))) )),
% 0.64/0.39 inference(equality_proxy_clausification,[],[f222])).
% 0.64/0.39 thf(f224,plain,(
% 0.64/0.39 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : ((((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) )),
% 0.64/0.39 inference(equality_proxy_clausification,[],[f223])).
% 0.64/0.39 thf(f225,plain,(
% 0.64/0.39 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) )),
% 0.64/0.39 inference(trivial_inequality_removal,[],[f224])).
% 0.64/0.39 thf(f233,definition,(
% 0.64/0.39 spl6_8 <=> ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))))),
% 0.64/0.39 introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition])).
% 0.64/0.39 thf(f234,plain,(
% 0.64/0.39 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : (($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true)) ) | ~spl6_8),
% 0.64/0.39 inference(avatar_component_clause,[],[f233])).
% 0.64/0.39 thf(f235,plain,(
% 0.64/0.39 spl6_8 | spl6_2),
% 0.64/0.39 inference(avatar_split_clause,[],[f225,f75,f233])).
% 0.64/0.39 thf(f300,plain,(
% 0.64/0.39 ( ! [X1 : $i] : (((((^[Y0 : $i]: ($false)) @ X1)) = (((^[Y0 : $i]: ($true)) @ X1)))) ) | ~spl6_2),
% 0.64/0.39 inference(argument_congruence,[],[f76])).
% 0.64/0.39 thf(f301,plain,(
% 0.64/0.39 ( ! [X1 : $i] : (((((^[Y0 : $i]: ($true)) @ X1)) = $false) | ((((^[Y0 : $i]: ($false)) @ X1)) = $true)) ) | ~spl6_2),
% 0.64/0.39 inference(iff_proxy_clausification,[],[f300])).
% 0.64/0.39 thf(f304,plain,(
% 0.64/0.39 ($true = $false) | ($true = $false) | ~spl6_2),
% 0.64/0.39 inference(beta-eta_normalization,[],[f301])).
% 0.64/0.39 thf(f305,plain,(
% 0.64/0.39 ($true = $false) | ~spl6_2),
% 0.64/0.39 inference(duplicate_literal_removal,[],[f304])).
% 0.64/0.39 thf(f306,plain,(
% 0.64/0.39 $false | ~spl6_2),
% 0.64/0.39 inference(trivial_inequality_removal,[],[f305])).
% 0.64/0.39 thf(f307,plain,(
% 0.64/0.39 ~spl6_2),
% 0.64/0.39 inference(avatar_contradiction_clause,[],[f306])).
% 0.64/0.39 thf(f314,plain,(
% 0.64/0.39 ( ! [X8 : $i] : (($true != (((^[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))))))) @ (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 : $i]: (Y0 = Y1)))))))))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)))) ) | ~spl6_5),
% 0.64/0.39 inference(primitive_instantiation,[],[f138])).
% 0.64/0.39 thf(f323,plain,(
% 0.64/0.39 ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true) | ((((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) | ~spl6_5),
% 0.64/0.39 inference(beta-eta_normalization,[],[f314])).
% 0.64/0.39 thf(f324,plain,(
% 0.64/0.39 ((^[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))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) != $true) | ~spl6_5),
% 0.64/0.39 inference(equality_proxy_clausification,[],[f323])).
% 0.64/0.39 thf(f325,plain,(
% 0.64/0.39 (((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))))))))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ~spl6_5),
% 0.64/0.39 inference(equality_proxy_clausification,[],[f324])).
% 0.64/0.39 thf(f335,definition,(
% 0.64/0.39 spl6_11 <=> (((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)))))))))),
% 0.64/0.39 introduced(definition,[new_symbols(definition,[spl6_11])],[avatar_definition])).
% 0.64/0.39 thf(f338,plain,(
% 0.64/0.39 ~spl6_11 | spl6_2 | ~spl6_5),
% 0.64/0.39 inference(avatar_split_clause,[],[f325,f137,f75,f335])).
% 0.64/0.39 thf(f349,plain,(
% 0.64/0.39 ( ! [X8 : $i,X5 : $i] : (($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8))) | ($true = (((^[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))))))) @ X5))) | (((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_7),
% 0.64/0.39 inference(primitive_instantiation,[],[f202])).
% 0.64/0.39 thf(f357,plain,(
% 0.64/0.39 ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $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))))))))) = $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_7),
% 0.64/0.39 inference(beta-eta_normalization,[],[f349])).
% 0.64/0.39 thf(f358,plain,(
% 0.64/0.39 ((((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) | (((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_7),
% 0.64/0.39 inference(equality_proxy_clausification,[],[f357])).
% 0.64/0.39 thf(f359,plain,(
% 0.64/0.39 (((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))))))))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ~spl6_7),
% 0.64/0.39 inference(equality_proxy_clausification,[],[f358])).
% 0.64/0.39 thf(f360,plain,(
% 0.64/0.39 ((^[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_7),
% 0.64/0.39 inference(duplicate_literal_removal,[],[f359])).
% 0.64/0.39 thf(f371,plain,(
% 0.64/0.39 (((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_2 | ~spl6_7)),
% 0.64/0.39 inference(forward_subsumption_resolution,[],[f360,f77])).
% 0.64/0.39 thf(f378,definition,(
% 0.64/0.39 spl6_14 <=> (((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)))))))))),
% 0.64/0.39 introduced(definition,[new_symbols(definition,[spl6_14])],[avatar_definition])).
% 0.64/0.39 thf(f381,plain,(
% 0.64/0.39 spl6_14 | spl6_2 | ~spl6_7),
% 0.64/0.39 inference(avatar_split_clause,[],[f371,f201,f75,f378])).
% 0.64/0.39 thf(f403,plain,(
% 0.64/0.39 ( ! [X8 : $i,X7 : $i] : (($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8))) | (((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)))))) @ (sK0 @ (^[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))))))) @ X7)))) ) | ~spl6_8),
% 0.64/0.39 inference(primitive_instantiation,[],[f234])).
% 0.64/0.39 thf(f408,plain,(
% 0.64/0.39 (((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 = (((sK0 @ (^[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)))) = $true) | ~spl6_8),
% 0.64/0.39 inference(beta-eta_normalization,[],[f403])).
% 0.64/0.39 thf(f409,plain,(
% 0.64/0.39 (((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 : $i]: ($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_8),
% 0.64/0.39 inference(equality_proxy_clausification,[],[f408])).
% 0.64/0.39 thf(f410,plain,(
% 0.64/0.39 (((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_8),
% 0.64/0.39 inference(equality_proxy_clausification,[],[f409])).
% 0.64/0.39 thf(f411,plain,(
% 0.64/0.39 (((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_8),
% 0.64/0.39 inference(duplicate_literal_removal,[],[f410])).
% 0.64/0.39 thf(f425,plain,(
% 0.64/0.39 (((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_2 | ~spl6_8)),
% 0.64/0.39 inference(forward_subsumption_resolution,[],[f411,f77])).
% 0.64/0.39 thf(f432,definition,(
% 0.64/0.39 spl6_20 <=> (((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)))))))))),
% 0.64/0.39 introduced(definition,[new_symbols(definition,[spl6_20])],[avatar_definition])).
% 0.64/0.39 thf(f435,plain,(
% 0.64/0.39 spl6_20 | spl6_2 | ~spl6_8),
% 0.64/0.39 inference(avatar_split_clause,[],[f425,f233,f75,f432])).
% 0.64/0.39 thf(f436,definition,(
% 0.64/0.39 (((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))))))))) | (((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))))))))) | (((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)))))))))),
% 0.64/0.39 introduced(theory,[theory_tautology_sat_conflict])).
% 0.64/0.39 cnf(s4, plain, spl6_2 | spl6_5, inference(sat_conversion,[],[f139])).
% 0.64/0.39 cnf(s6, plain, spl6_2 | spl6_7, inference(sat_conversion,[],[f203])).
% 0.64/0.39 cnf(s7, plain, spl6_2 | spl6_8, inference(sat_conversion,[],[f235])).
% 0.64/0.39 cnf(s10, plain, ~spl6_2, inference(sat_conversion,[],[f307])).
% 0.64/0.39 cnf(s11, plain, spl6_2 | ~spl6_5 | ~spl6_11, inference(sat_conversion,[],[f338])).
% 0.64/0.39 cnf(s14, plain, spl6_2 | ~spl6_7 | spl6_14, inference(sat_conversion,[],[f381])).
% 0.64/0.39 cnf(s18, plain, spl6_2 | ~spl6_8 | spl6_20, inference(sat_conversion,[],[f435])).
% 0.64/0.39 cnf(s19, plain, spl6_11 | ~spl6_14 | ~spl6_20, inference(sat_conversion,[],[f436])).
% 0.64/0.39 cnf(s22, plain, spl6_8, inference(rat,[],[s7,s10])).
% 0.64/0.39 cnf(s23, plain, spl6_20, inference(rat,[],[s18,s10,s22])).
% 0.64/0.39 cnf(s25, plain, spl6_7, inference(rat,[],[s6,s10])).
% 0.64/0.39 cnf(s26, plain, spl6_14, inference(rat,[],[s14,s10,s25])).
% 0.64/0.39 cnf(s28, plain, spl6_11, inference(rat,[],[s19,s23,s26])).
% 0.64/0.39 cnf(s29, plain, ~spl6_5, inference(rat,[],[s11,s10,s28])).
% 0.64/0.39 cnf(s31, plain, $false, inference(rat,[],[s4,s29,s10])).
% 0.64/0.39 thf(f437,plain,(
% 0.64/0.39 $false),
% 0.64/0.39 inference(avatar_sat_refutation,[],[s31])).
% 0.64/0.39 % SZS output end Proof for theBenchmark
% 0.64/0.39 % (201098)------------------------------
% 0.64/0.39 % (201098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.39 % (201098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.39 % (201098)CaDiCaL version: 2.1.3
% 0.64/0.39 % (201098)Termination reason: Refutation
% 0.64/0.39 % (201098)Time elapsed: 0.044 s
% 0.64/0.39 % (201098)Peak memory usage: 13 MB
% 0.64/0.39 % (201098)Instructions burned: 49 (million)
% 0.64/0.39 % (201090)Success in time 0.083 s
% 0.64/0.39 % Vampire exiting
%------------------------------------------------------------------------------