%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV101^5 : 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 : n011.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 0.22s 0.35s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV101^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n011.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 15:10:16 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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
% 0.22/0.35 % (199934)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.35 % (199939)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2828627489:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.35 % (199941)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1536418156:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.35 % (199941)Instruction limit reached!
% 0.22/0.35 % (199941)------------------------------
% 0.22/0.35 % (199941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (199941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (199941)CaDiCaL version: 2.1.3
% 0.22/0.35 % (199941)Termination reason: Instruction limit
% 0.22/0.35 % (199941)Termination phase: Saturation
% 0.22/0.35 % (199941)Time elapsed: 0.003 s
% 0.22/0.35 % (199941)Peak memory usage: 11 MB
% 0.22/0.35 % (199941)Instructions burned: 3 (million)
% 0.22/0.35 % (199939) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-199934-199939"...
% 0.22/0.35 % (199945)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.35 % (199945)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
% 0.22/0.35 % (199943)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=793637589:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.35 % (199940)lrs+10_16_si=on:nwc=1.5:random_seed=3997320074:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.35 % (199945)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=1718851031:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.35 % (199942)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=502316417: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)
% 0.22/0.35 % (199944)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4151120531:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.35 % (199939)...printing done.
% 0.22/0.35 % (199939)Refutation found. Thanks to Tanya!
% 0.22/0.35 % SZS status Theorem for theBenchmark
% 0.22/0.35 % SZS output start Proof for theBenchmark
% 0.22/0.35 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.35 thf(func_def_0, type, p: $o).
% 0.22/0.35 thf(func_def_4, type, vOR: ($o > $o > $o)).
% 0.22/0.35 thf(func_def_5, type, vNOT: ($o > $o)).
% 0.22/0.35 thf(func_def_6, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.35 thf(func_def_7, type, vAND: ($o > $o > $o)).
% 0.22/0.35 thf(func_def_8, type, sK0: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 0.22/0.35 thf(func_def_9, type, sK1: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 0.22/0.35 thf(func_def_10, type, sK2: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 0.22/0.35 thf(func_def_11, type, sK3: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i)).
% 0.22/0.35 thf(func_def_12, type, sK4: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i)).
% 0.22/0.35 thf(func_def_13, type, sK5: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 0.22/0.35 thf(func_def_14, type, db1: !>[X0: $tType]:(X0)).
% 0.22/0.35 thf(func_def_15, type, db2: !>[X0: $tType]:(X0)).
% 0.22/0.35 thf(func_def_16, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.35 thf(func_def_17, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.35 thf(func_def_20, type, sK8: ((($i > $o) > ($i > $o) > $i > $o) > $i)).
% 0.22/0.35 thf(func_def_21, type, sK9: ((($i > $o) > ($i > $o) > $i > $o) > $i)).
% 0.22/0.35 thf(func_def_23, type, sK11: ((($i > $o) > ($i > $o) > $i > $o) > $i)).
% 0.22/0.35 thf(func_def_24, type, sK12: ((($i > $o) > ($i > $o) > $i > $o) > $i)).
% 0.22/0.35 thf(f1,conjecture,(
% 0.22/0.35 ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X3 : $i] : ((X0 @ (^[X2 : $i] : (~p | p)) @ (^[X2 : $i] : (p & ~p)) @ X3) | (X1 @ (^[X2 : $i] : (p | ~p)) @ (^[X2 : $i] : (~p & p)) @ X3)) & ! [X5 : ($i > $o),X4 : ($i > $o),X2 : ($i > $o)] : ((! [X3 : $i] : ((X0 @ X4 @ X5 @ X3) | (X1 @ X4 @ X5 @ X3)) & ! [X3 : $i] : ((X0 @ X2 @ X4 @ X3) | (X1 @ X2 @ X4 @ X3))) => ! [X3 : $i] : ((X1 @ X2 @ X5 @ X3) | (X0 @ X2 @ X5 @ X3))) & ! [X3 : $i,X2 : ($i > $o)] : ((X0 @ X2 @ X2 @ X3) | (X1 @ X2 @ X2 @ X3)))),
% 0.22/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM120E_pme)).
% 0.22/0.35 thf(f2,negated_conjecture,(
% 0.22/0.35 ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X3 : $i] : ((X0 @ (^[X2 : $i] : (~p | p)) @ (^[X2 : $i] : (p & ~p)) @ X3) | (X1 @ (^[X2 : $i] : (p | ~p)) @ (^[X2 : $i] : (~p & p)) @ X3)) & ! [X5 : ($i > $o),X4 : ($i > $o),X2 : ($i > $o)] : ((! [X3 : $i] : ((X0 @ X4 @ X5 @ X3) | (X1 @ X4 @ X5 @ X3)) & ! [X3 : $i] : ((X0 @ X2 @ X4 @ X3) | (X1 @ X2 @ X4 @ X3))) => ! [X3 : $i] : ((X1 @ X2 @ X5 @ X3) | (X0 @ X2 @ X5 @ X3))) & ! [X3 : $i,X2 : ($i > $o)] : ((X0 @ X2 @ X2 @ X3) | (X1 @ X2 @ X2 @ X3)))),
% 0.22/0.35 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.35 thf(f3,plain,(
% 0.22/0.35 ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X2 : $i] : ((X0 @ (^[X3 : $i] : (~p | p)) @ (^[X4 : $i] : (p & ~p)) @ X2) | (X1 @ (^[X5 : $i] : (p | ~p)) @ (^[X6 : $i] : (~p & p)) @ X2)) & ! [X7 : ($i > $o),X8 : ($i > $o),X9 : ($i > $o)] : ((! [X10 : $i] : ((X0 @ X8 @ X7 @ X10) | (X1 @ X8 @ X7 @ X10)) & ! [X11 : $i] : ((X0 @ X9 @ X8 @ X11) | (X1 @ X9 @ X8 @ X11))) => ! [X12 : $i] : ((X1 @ X9 @ X7 @ X12) | (X0 @ X9 @ X7 @ X12))) & ! [X13 : $i,X14 : ($i > $o)] : ((X0 @ X14 @ X14 @ X13) | (X1 @ X14 @ X14 @ X13)))),
% 0.22/0.35 inference(rectify,[],[f2])).
% 0.22/0.35 thf(f4,plain,(
% 0.22/0.35 ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X2 : $i] : ((((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2)) = $true) | ($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ((~ p) & p)) @ X2)))) & ! [X7 : ($i > $o),X8 : ($i > $o),X9 : ($i > $o)] : ((! [X10 : $i] : (($true = ((X0 @ X8 @ X7 @ X10))) | ($true = ((X1 @ X8 @ X7 @ X10)))) & ! [X11 : $i] : (($true = ((X0 @ X9 @ X8 @ X11))) | (((X1 @ X9 @ X8 @ X11)) = $true))) => ! [X12 : $i] : (($true = ((X1 @ X9 @ X7 @ X12))) | ($true = ((X0 @ X9 @ X7 @ X12))))) & ! [X13 : $i,X14 : ($i > $o)] : (($true = ((X0 @ X14 @ X14 @ X13))) | ($true = ((X1 @ X14 @ X14 @ X13)))))),
% 0.22/0.35 inference(fool_elimination,[],[f3])).
% 0.22/0.35 thf(f5,plain,(
% 0.22/0.35 ~ ? [X1 : (($i > $o) > ($i > $o) > $i > $o),X0 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X2 : $i] : ((((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2)) = $true) | ($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ((~ p) & p)) @ X2)))) & ! [X9 : $i,X10 : ($i > $o)] : (($true = ((X1 @ X10 @ X10 @ X9))) | ($true = ((X0 @ X10 @ X10 @ X9)))) & ! [X4 : ($i > $o),X5 : ($i > $o),X3 : ($i > $o)] : ((! [X7 : $i] : (($true = ((X0 @ X5 @ X4 @ X7))) | ($true = ((X1 @ X5 @ X4 @ X7)))) & ! [X6 : $i] : (($true = ((X0 @ X4 @ X3 @ X6))) | ($true = ((X1 @ X4 @ X3 @ X6))))) => ! [X8 : $i] : (($true = ((X1 @ X5 @ X3 @ X8))) | ($true = ((X0 @ X5 @ X3 @ X8))))))),
% 0.22/0.35 inference(rectify,[],[f4])).
% 0.22/0.35 thf(f6,plain,(
% 0.22/0.35 ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X0 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : $i] : ((((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2)) = $true) | ($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ((~ p) & p)) @ X2)))) | ? [X9 : $i,X10 : ($i > $o)] : (($true != ((X0 @ X10 @ X10 @ X9))) & ($true != ((X1 @ X10 @ X10 @ X9)))) | ? [X4 : ($i > $o),X5 : ($i > $o),X3 : ($i > $o)] : (? [X8 : $i] : (($true != ((X1 @ X5 @ X3 @ X8))) & ($true != ((X0 @ X5 @ X3 @ X8)))) & (! [X7 : $i] : (($true = ((X0 @ X5 @ X4 @ X7))) | ($true = ((X1 @ X5 @ X4 @ X7)))) & ! [X6 : $i] : (($true = ((X0 @ X4 @ X3 @ X6))) | ($true = ((X1 @ X4 @ X3 @ X6)))))))),
% 0.22/0.35 inference(ennf_transformation,[],[f5])).
% 0.22/0.35 thf(f7,plain,(
% 0.22/0.35 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (? [X3 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : (? [X8 : $i] : (($true != ((X1 @ X5 @ X3 @ X8))) & ($true != ((X0 @ X5 @ X3 @ X8)))) & ! [X6 : $i] : (($true = ((X0 @ X4 @ X3 @ X6))) | ($true = ((X1 @ X4 @ X3 @ X6)))) & ! [X7 : $i] : (($true = ((X0 @ X5 @ X4 @ X7))) | ($true = ((X1 @ X5 @ X4 @ X7))))) | ! [X2 : $i] : ((((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2)) = $true) | ($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ((~ p) & p)) @ X2)))) | ? [X9 : $i,X10 : ($i > $o)] : (($true != ((X0 @ X10 @ X10 @ X9))) & ($true != ((X1 @ X10 @ X10 @ X9)))))),
% 0.22/0.35 inference(flattening,[],[f6])).
% 0.22/0.35 thf(f8,plain,(
% 0.22/0.35 ! [X0 : (($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 != ((X1 @ X4 @ X2 @ X5))) & ($true != ((X0 @ X4 @ X2 @ X5)))) & ! [X6 : $i] : (($true = ((X0 @ X3 @ X2 @ X6))) | ($true = ((X1 @ X3 @ X2 @ X6)))) & ! [X7 : $i] : (($true = ((X0 @ X4 @ X3 @ X7))) | ($true = ((X1 @ X4 @ X3 @ X7))))) | ! [X8 : $i] : (($true = ((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X8))) | ($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ((~ p) & p)) @ X8)))) | ? [X9 : $i,X10 : ($i > $o)] : (($true != ((X0 @ X10 @ X10 @ X9))) & ($true != ((X1 @ X10 @ X10 @ X9)))))),
% 0.22/0.35 inference(rectify,[],[f7])).
% 0.22/0.35 thf(f9,plain,(
% 0.22/0.35 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (((($true != ((X1 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK3 @ X1 @ X0)))) & ($true != ((X0 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK3 @ X1 @ X0))))) & ! [X6 : $i] : (($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6))) | ($true = ((X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6)))) & ! [X7 : $i] : (($true = ((X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7))) | ($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7))))) | ! [X8 : $i] : (($true = ((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X8))) | ($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ((~ p) & p)) @ X8)))) | (($true != ((X0 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)))) & (((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0))) != $true)))),
% 0.22/0.35 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X10,sK5 @ X1 @ X0),skolemize(X10,sK5 @ X1 @ X0),skolemize(X10,sK5 @ X1 @ X0),skolemize(X10,sK5 @ X1 @ X0),skolemize(X10,sK5 @ X1 @ X0),skolemize(X10,sK5 @ X1 @ X0)],[f8])).
% 0.22/0.35 thf(f10,plain,(
% 0.22/0.35 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ((~ p) & p)) @ X8))) | ($true = ((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X8))) | ($true = ((X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7))) | (((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0))) != $true) | ($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7)))) )),
% 0.22/0.35 inference(cnf_transformation,[],[f9])).
% 0.22/0.35 thf(f13,plain,(
% 0.22/0.35 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X6 : $i] : (($true != ((X0 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ((~ p) & p)) @ X8))) | ($true = ((X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6))) | ($true = ((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X8))) | ($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6)))) )),
% 0.22/0.35 inference(cnf_transformation,[],[f9])).
% 0.22/0.35 thf(f15,plain,(
% 0.22/0.35 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ((~ p) & p)) @ X8))) | ($true != ((X0 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)))) | ($true = ((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X8))) | ($true != ((X0 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK3 @ X1 @ X0))))) )),
% 0.22/0.35 inference(cnf_transformation,[],[f9])).
% 0.22/0.35 thf(f20,plain,(
% 0.22/0.35 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X6 : $i] : (($true = ((X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6))) | ($true = ((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X8))) | ($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6))) | ($true != ((X0 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X8)))) )),
% 0.22/0.35 inference(boolean_simplification,[],[f13])).
% 0.22/0.35 thf(f21,plain,(
% 0.22/0.35 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X6 : $i] : (($true = ((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X8))) | ($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6))) | ($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X8))) | ($true != ((X0 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)))) | ($true = ((X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6)))) )),
% 0.22/0.35 inference(boolean_simplification,[],[f20])).
% 0.22/0.35 thf(f22,plain,(
% 0.22/0.35 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X6 : $i] : (($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6))) | ($true != ((X0 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ($true = ((X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6))) | ($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X8)))) )),
% 0.22/0.35 inference(boolean_simplification,[],[f21])).
% 0.22/0.35 thf(f23,plain,(
% 0.22/0.35 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X6 : $i] : (($true != ((X0 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8))) | ($true = ((X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6))) | ($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6)))) )),
% 0.22/0.35 inference(boolean_simplification,[],[f22])).
% 0.22/0.35 thf(f24,plain,(
% 0.22/0.35 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : (($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7))) | (((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0))) != $true) | ($true = ((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X8))) | ($true = ((X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7))) | ($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X8)))) )),
% 0.22/0.35 inference(boolean_simplification,[],[f10])).
% 0.22/0.35 thf(f25,plain,(
% 0.22/0.35 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : ((((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0))) != $true) | ($true = ((X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7))) | ($true = ((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X8))) | ($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X8))) | ($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7)))) )),
% 0.22/0.35 inference(boolean_simplification,[],[f24])).
% 0.22/0.35 thf(f26,plain,(
% 0.22/0.35 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X8))) | ($true = ((X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7))) | ($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7))) | (((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0))) != $true) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true)) )),
% 0.22/0.35 inference(boolean_simplification,[],[f25])).
% 0.22/0.35 thf(f27,plain,(
% 0.22/0.35 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : ((((X1 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0))) != $true) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8))) | ($true = ((X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7))) | ($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7)))) )),
% 0.22/0.35 inference(boolean_simplification,[],[f26])).
% 0.22/0.35 thf(f36,plain,(
% 0.22/0.35 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true = ((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X8))) | ($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X8))) | ($true != ((X0 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)))) | ($true != ((X0 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK3 @ X1 @ X0))))) )),
% 0.22/0.35 inference(boolean_simplification,[],[f15])).
% 0.22/0.35 thf(f37,plain,(
% 0.22/0.35 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true = ((X1 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X8))) | ($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X8))) | ($true != ((X0 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)))) | ($true != ((X0 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK3 @ X1 @ X0))))) )),
% 0.22/0.35 inference(boolean_simplification,[],[f36])).
% 0.22/0.35 thf(f38,plain,(
% 0.22/0.35 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true != ((X0 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ($true != ((X0 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK3 @ X1 @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X8)))) )),
% 0.22/0.35 inference(boolean_simplification,[],[f37])).
% 0.22/0.35 thf(f39,plain,(
% 0.22/0.35 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true != ((X0 @ (sK5 @ X1 @ X0) @ (sK5 @ X1 @ X0) @ (sK4 @ X1 @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ($true != ((X0 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK3 @ X1 @ X0))))) )),
% 0.22/0.35 inference(boolean_simplification,[],[f38])).
% 0.22/0.35 thf(f73,definition,(
% 0.22/0.35 spl6_1 <=> ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 0.22/0.35 introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
% 0.22/0.35 thf(f74,plain,(
% 0.22/0.35 ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ~spl6_1),
% 0.22/0.35 inference(avatar_component_clause,[],[f73])).
% 0.22/0.35 thf(f75,plain,(
% 0.22/0.35 ((^[Y0 : $i]: ($true)) != (^[Y0 : $i]: ($false))) | spl6_1),
% 0.22/0.35 inference(avatar_component_clause,[],[f73])).
% 0.22/0.35 thf(f84,plain,(
% 0.22/0.35 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : ((((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK2 @ 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 : $i]: (Y0 = Y1)))))))))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)))) )),
% 0.22/0.35 inference(primitive_instantiation,[],[f39])).
% 0.22/0.35 thf(f105,plain,(
% 0.22/0.35 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : ((((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ($true != (((sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | ($true != (((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))))) )),
% 0.22/0.35 inference(beta-eta_normalization,[],[f84])).
% 0.22/0.35 thf(f106,plain,(
% 0.22/0.35 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true != (((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((sK5 @ 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 : $i]: ($true)) = (^[Y0 : $i]: ($false)))))) )),
% 0.22/0.35 inference(equality_proxy_clausification,[],[f105])).
% 0.22/0.35 thf(f107,plain,(
% 0.22/0.35 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | (((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | (((sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true)) )),
% 0.22/0.35 inference(equality_proxy_clausification,[],[f106])).
% 0.22/0.35 thf(f108,plain,(
% 0.22/0.35 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : ((((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | (((sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) )),
% 0.22/0.35 inference(equality_proxy_clausification,[],[f107])).
% 0.22/0.35 thf(f109,plain,(
% 0.22/0.35 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : ((((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | (((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) )),
% 0.22/0.35 inference(trivial_inequality_removal,[],[f108])).
% 0.22/0.35 thf(f277,plain,(
% 0.22/0.35 ( ! [X1 : $i] : (((((^[Y0 : $i]: ($true)) @ X1)) = (((^[Y0 : $i]: ($false)) @ X1)))) ) | ~spl6_1),
% 0.22/0.35 inference(argument_congruence,[],[f74])).
% 0.22/0.35 thf(f279,plain,(
% 0.22/0.35 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ($false)) @ X1))) | ((((^[Y0 : $i]: ($true)) @ X1)) = $false)) ) | ~spl6_1),
% 0.22/0.35 inference(iff_proxy_clausification,[],[f277])).
% 0.22/0.35 thf(f280,plain,(
% 0.22/0.35 ($true = $false) | ($true = $false) | ~spl6_1),
% 0.22/0.35 inference(beta-eta_normalization,[],[f279])).
% 0.22/0.35 thf(f281,plain,(
% 0.22/0.35 ($true = $false) | ~spl6_1),
% 0.22/0.35 inference(duplicate_literal_removal,[],[f280])).
% 0.22/0.35 thf(f282,plain,(
% 0.22/0.35 $false | ~spl6_1),
% 0.22/0.35 inference(trivial_inequality_removal,[],[f281])).
% 0.22/0.35 thf(f283,plain,(
% 0.22/0.35 ~spl6_1),
% 0.22/0.35 inference(avatar_contradiction_clause,[],[f282])).
% 0.22/0.35 thf(f286,plain,(
% 0.22/0.35 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : ((((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true)) ) | spl6_1),
% 0.22/0.35 inference(forward_subsumption_resolution,[],[f109,f75])).
% 0.22/0.35 thf(f425,plain,(
% 0.22/0.35 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X6 : $i] : (($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK5 @ 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 @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) @ X6))) | ($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))))))) @ X6))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)))) )),
% 0.22/0.35 inference(primitive_instantiation,[],[f23])).
% 0.22/0.35 thf(f435,plain,(
% 0.22/0.35 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X6 : $i] : (($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))))))) @ X6))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ($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 = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true != (((sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))))) )),
% 0.22/0.35 inference(beta-eta_normalization,[],[f425])).
% 0.22/0.35 thf(f436,plain,(
% 0.22/0.35 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X6 : $i] : (($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | (((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 != (((sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK5 @ 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))))))) @ X6))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true)) )),
% 0.22/0.35 inference(equality_proxy_clausification,[],[f435])).
% 0.22/0.35 thf(f437,plain,(
% 0.22/0.35 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X6 : $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))))))))) | (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) = $true) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ($true != (((sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK5 @ 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 : $i]: (Y0 = Y1))))))) @ X6)))) )),
% 0.22/0.35 inference(equality_proxy_clausification,[],[f436])).
% 0.22/0.35 thf(f438,plain,(
% 0.22/0.35 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X6 : $i] : (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ($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))))))) @ X6))) | (((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) | (((sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) != ((sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) )),
% 0.22/0.35 inference(equality_proxy_clausification,[],[f437])).
% 0.22/0.35 thf(f439,plain,(
% 0.22/0.35 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X6 : $i] : (($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))))))) @ X6))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | (((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)) = $true)) )),
% 0.22/0.35 inference(trivial_inequality_removal,[],[f438])).
% 0.22/0.35 thf(f453,plain,(
% 0.22/0.35 ( ! [X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X6 : $i] : (($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))))))) @ X6))) | (((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)))))))))) ) | spl6_1),
% 0.22/0.35 inference(forward_subsumption_resolution,[],[f439,f75])).
% 0.22/0.35 thf(f459,plain,(
% 0.22/0.35 ( ! [X8 : $i,X6 : $i] : (($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8))) | (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (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))))))) @ X6)) = $true)) ) | spl6_1),
% 0.22/0.35 inference(primitive_instantiation,[],[f453])).
% 0.22/0.35 thf(f474,plain,(
% 0.22/0.35 ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ((((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_1),
% 0.22/0.35 inference(beta-eta_normalization,[],[f459])).
% 0.22/0.35 thf(f475,plain,(
% 0.22/0.35 (((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))))))))) = $true) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | spl6_1),
% 0.22/0.35 inference(equality_proxy_clausification,[],[f474])).
% 0.22/0.35 thf(f476,plain,(
% 0.22/0.35 (((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 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | spl6_1),
% 0.22/0.35 inference(equality_proxy_clausification,[],[f475])).
% 0.22/0.35 thf(f477,plain,(
% 0.22/0.35 (((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 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | spl6_1),
% 0.22/0.35 inference(duplicate_literal_removal,[],[f476])).
% 0.22/0.35 thf(f498,plain,(
% 0.22/0.35 (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | spl6_1),
% 0.22/0.35 inference(forward_subsumption_resolution,[],[f477,f75])).
% 0.22/0.35 thf(f550,plain,(
% 0.22/0.35 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : (($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) != $true) | ($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)))) )),
% 0.22/0.35 inference(primitive_instantiation,[],[f27])).
% 0.22/0.35 thf(f558,plain,(
% 0.22/0.35 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : (($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true != (((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8))) | ($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7)))) )),
% 0.22/0.35 inference(beta-eta_normalization,[],[f550])).
% 0.22/0.35 thf(f559,plain,(
% 0.22/0.35 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : (($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | ($true != (((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) )),
% 0.22/0.35 inference(equality_proxy_clausification,[],[f558])).
% 0.22/0.35 thf(f560,plain,(
% 0.22/0.35 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : (($true = (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | (((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) )),
% 0.22/0.35 inference(equality_proxy_clausification,[],[f559])).
% 0.22/0.35 thf(f561,plain,(
% 0.22/0.35 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | (((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)))) )),
% 0.22/0.35 inference(equality_proxy_clausification,[],[f560])).
% 0.22/0.35 thf(f562,plain,(
% 0.22/0.35 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : (($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) )),
% 0.22/0.35 inference(trivial_inequality_removal,[],[f561])).
% 0.22/0.35 thf(f578,plain,(
% 0.22/0.35 ( ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i,X7 : $i] : (($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X7))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8))) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) ) | spl6_1),
% 0.22/0.35 inference(forward_subsumption_resolution,[],[f562,f75])).
% 0.22/0.35 thf(f583,plain,(
% 0.22/0.35 ( ! [X0 : $i] : (($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X0))) | (((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 : $i]: (Y0 = Y1)))))))))) ) | spl6_1),
% 0.22/0.35 inference(constrained_superposition,[],[f286,f498])).
% 0.22/0.35 thf(f584,plain,(
% 0.22/0.35 ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | (((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))))))))) | spl6_1),
% 0.22/0.35 inference(beta-eta_normalization,[],[f583])).
% 0.22/0.35 thf(f585,plain,(
% 0.22/0.35 (((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 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | spl6_1),
% 0.22/0.35 inference(equality_proxy_clausification,[],[f584])).
% 0.22/0.35 thf(f606,plain,(
% 0.22/0.35 (((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))))))))) | spl6_1),
% 0.22/0.35 inference(forward_subsumption_resolution,[],[f585,f75])).
% 0.22/0.35 thf(f673,plain,(
% 0.22/0.35 ( ! [X8 : $i,X7 : $i] : (($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)))))) @ (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))))))) @ X7))) | (((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)))))))))) ) | spl6_1),
% 0.22/0.35 inference(primitive_instantiation,[],[f578])).
% 0.22/0.35 thf(f697,plain,(
% 0.22/0.35 (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))) = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | spl6_1),
% 0.22/0.35 inference(beta-eta_normalization,[],[f673])).
% 0.22/0.35 thf(f698,plain,(
% 0.22/0.35 (((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 : $i]: ($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))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))))))) | spl6_1),
% 0.22/0.35 inference(equality_proxy_clausification,[],[f697])).
% 0.22/0.35 thf(f699,plain,(
% 0.22/0.35 (((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 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | (((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))))))))) | spl6_1),
% 0.22/0.35 inference(equality_proxy_clausification,[],[f698])).
% 0.22/0.35 thf(f700,plain,(
% 0.22/0.35 ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | (((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))))))))) | spl6_1),
% 0.22/0.35 inference(duplicate_literal_removal,[],[f699])).
% 0.22/0.35 thf(f713,plain,(
% 0.22/0.35 (((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))))))))) | spl6_1),
% 0.22/0.35 inference(forward_subsumption_resolution,[],[f700,f75])).
% 0.22/0.35 thf(f716,plain,(
% 0.22/0.35 $false | spl6_1),
% 0.22/0.35 inference(forward_subsumption_resolution,[],[f713,f606])).
% 0.22/0.35 thf(f717,plain,(
% 0.22/0.35 spl6_1),
% 0.22/0.35 inference(avatar_contradiction_clause,[],[f716])).
% 0.22/0.35 cnf(s8, plain, ~spl6_1, inference(sat_conversion,[],[f283])).
% 0.22/0.35 cnf(s19, plain, spl6_1, inference(sat_conversion,[],[f717])).
% 0.22/0.35 cnf(s20, plain, $false, inference(rat,[],[s8,s19])).
% 0.22/0.35 thf(f718,plain,(
% 0.22/0.35 $false),
% 0.22/0.35 inference(avatar_sat_refutation,[],[s20])).
% 0.22/0.35 % SZS output end Proof for theBenchmark
% 0.22/0.35 % (199939)------------------------------
% 0.22/0.35 % (199939)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (199939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (199939)CaDiCaL version: 2.1.3
% 0.22/0.35 % (199939)Termination reason: Refutation
% 0.22/0.35 % (199939)Time elapsed: 0.055 s
% 0.22/0.35 % (199939)Peak memory usage: 13 MB
% 0.22/0.35 % (199939)Instructions burned: 82 (million)
% 0.22/0.35 % (199934)Success in time 0.102 s
% 0.22/0.35 % Vampire exiting
%------------------------------------------------------------------------------