%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV101^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:39:00 AM UTC 2026
% Result : Theorem 0.19s 0.29s
% Output : Refutation 0.19s
% 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/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n019.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 15:10:33 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.29 % (903181)Will run a generic schedule for satisfiability detection.
% 0.19/0.29 % (903187)% WARNING: option uhcvi not known.
% 0.19/0.29 % (903187)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=661601303:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.29 % (903187)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.29 % (903187)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.29 % (903188)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3685305039:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.29 % (903186)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3534677821_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.29 % Exception at run slice level
% 0.19/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.29 % (903190)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=895358449:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.29 % (903190)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.29 % (903196)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=803758185:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.29 % Exception at run slice level
% 0.19/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.29 % (903187) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-903181-903187"...
% 0.19/0.29 % (903187)...printing done.
% 0.19/0.29 % (903187)Refutation found. Thanks to Tanya!
% 0.19/0.29 % SZS status Theorem for theBenchmark
% 0.19/0.29 % SZS output start Proof for theBenchmark
% 0.19/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.29 thf(func_def_0, type, p: $o).
% 0.19/0.29 thf(func_def_4, type, vOR: ($o > $o > $o)).
% 0.19/0.29 thf(func_def_5, type, vNOT: ($o > $o)).
% 0.19/0.29 thf(func_def_6, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.29 thf(func_def_7, type, vAND: ($o > $o > $o)).
% 0.19/0.29 thf(func_def_8, type, sK0: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 0.19/0.29 thf(func_def_9, type, sK1: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 0.19/0.29 thf(func_def_10, type, sK2: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 0.19/0.29 thf(func_def_11, type, sK3: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i)).
% 0.19/0.29 thf(func_def_12, type, sK4: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 0.19/0.29 thf(func_def_13, type, sK5: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i)).
% 0.19/0.29 thf(func_def_14, type, db1: !>[X0: $tType]:(X0)).
% 0.19/0.29 thf(func_def_15, type, db2: !>[X0: $tType]:(X0)).
% 0.19/0.29 thf(func_def_16, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.19/0.29 thf(func_def_17, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.29 thf(func_def_20, type, sK8: ((($i > $o) > ($i > $o) > $i > $o) > $i)).
% 0.19/0.29 thf(func_def_21, type, sK9: ((($i > $o) > ($i > $o) > $i > $o) > $i)).
% 0.19/0.29 thf(f1,conjecture,(
% 0.19/0.29 ? [X0 : (($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 : $i] : (~p & p)) @ X3)) & ! [X2 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : ((! [X3 : $i] : ((X0 @ X4 @ X5 @ X3) | (X1 @ X4 @ X5 @ X3)) & ! [X3 : $i] : ((X0 @ X2 @ X4 @ X3) | (X1 @ X2 @ X4 @ X3))) => ! [X3 : $i] : ((X0 @ X2 @ X5 @ X3) | (X1 @ X2 @ X5 @ X3))) & ! [X2 : ($i > $o),X3 : $i] : ((X0 @ X2 @ X2 @ X3) | (X1 @ X2 @ X2 @ X3)))),
% 0.19/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM120E_pme)).
% 0.19/0.29 thf(f2,negated_conjecture,(
% 0.19/0.29 ~ ? [X0 : (($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 : $i] : (~p & p)) @ X3)) & ! [X2 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : ((! [X3 : $i] : ((X0 @ X4 @ X5 @ X3) | (X1 @ X4 @ X5 @ X3)) & ! [X3 : $i] : ((X0 @ X2 @ X4 @ X3) | (X1 @ X2 @ X4 @ X3))) => ! [X3 : $i] : ((X0 @ X2 @ X5 @ X3) | (X1 @ X2 @ X5 @ X3))) & ! [X2 : ($i > $o),X3 : $i] : ((X0 @ X2 @ X2 @ X3) | (X1 @ X2 @ X2 @ X3)))),
% 0.19/0.29 inference(negated_conjecture,[status(cth)],[f1])).
% 0.19/0.29 thf(f3,plain,(
% 0.19/0.29 ~ ? [X0 : (($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 @ X9 @ X10) | (X1 @ X8 @ X9 @ X10)) & ! [X11 : $i] : ((X0 @ X7 @ X8 @ X11) | (X1 @ X7 @ X8 @ X11))) => ! [X12 : $i] : ((X0 @ X7 @ X9 @ X12) | (X1 @ X7 @ X9 @ X12))) & ! [X13 : ($i > $o),X14 : $i] : ((X0 @ X13 @ X13 @ X14) | (X1 @ X13 @ X13 @ X14)))),
% 0.19/0.29 inference(rectify,[],[f2])).
% 0.19/0.29 thf(f4,plain,(
% 0.19/0.29 ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X2 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2)))) & ! [X7 : ($i > $o),X8 : ($i > $o),X9 : ($i > $o)] : ((! [X10 : $i] : ((((X0 @ X8 @ X9 @ X10)) = $true) | (((X1 @ X8 @ X9 @ X10)) = $true)) & ! [X11 : $i] : ((((X0 @ X7 @ X8 @ X11)) = $true) | (((X1 @ X7 @ X8 @ X11)) = $true))) => ! [X12 : $i] : ((((X0 @ X7 @ X9 @ X12)) = $true) | (((X1 @ X7 @ X9 @ X12)) = $true))) & ! [X13 : ($i > $o),X14 : $i] : ((((X0 @ X13 @ X13 @ X14)) = $true) | (((X1 @ X13 @ X13 @ X14)) = $true)))),
% 0.19/0.29 inference(fool_elimination,[],[f3])).
% 0.19/0.29 thf(f5,plain,(
% 0.19/0.29 ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X2 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2)))) & ! [X3 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : ((! [X6 : $i] : (($true = ((X0 @ X4 @ X5 @ X6))) | ($true = ((X1 @ X4 @ X5 @ X6)))) & ! [X7 : $i] : (($true = ((X0 @ X3 @ X4 @ X7))) | ($true = ((X1 @ X3 @ X4 @ X7))))) => ! [X8 : $i] : (($true = ((X0 @ X3 @ X5 @ X8))) | ($true = ((X1 @ X3 @ X5 @ X8))))) & ! [X9 : ($i > $o),X10 : $i] : (($true = ((X0 @ X9 @ X9 @ X10))) | ($true = ((X1 @ X9 @ X9 @ X10)))))),
% 0.19/0.29 inference(rectify,[],[f4])).
% 0.19/0.29 thf(f6,plain,(
% 0.19/0.29 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2)))) | ? [X3 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : (? [X8 : $i] : (($true != ((X0 @ X3 @ X5 @ X8))) & ($true != ((X1 @ X3 @ X5 @ X8)))) & (! [X6 : $i] : (($true = ((X0 @ X4 @ X5 @ X6))) | ($true = ((X1 @ X4 @ X5 @ X6)))) & ! [X7 : $i] : (($true = ((X0 @ X3 @ X4 @ X7))) | ($true = ((X1 @ X3 @ X4 @ X7)))))) | ? [X9 : ($i > $o),X10 : $i] : (($true != ((X0 @ X9 @ X9 @ X10))) & ($true != ((X1 @ X9 @ X9 @ X10)))))),
% 0.19/0.29 inference(ennf_transformation,[],[f5])).
% 0.19/0.29 thf(f7,plain,(
% 0.19/0.29 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2)))) | ? [X3 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : (? [X8 : $i] : (($true != ((X0 @ X3 @ X5 @ X8))) & ($true != ((X1 @ X3 @ X5 @ X8)))) & ! [X6 : $i] : (($true = ((X0 @ X4 @ X5 @ X6))) | ($true = ((X1 @ X4 @ X5 @ X6)))) & ! [X7 : $i] : (($true = ((X0 @ X3 @ X4 @ X7))) | ($true = ((X1 @ X3 @ X4 @ X7))))) | ? [X9 : ($i > $o),X10 : $i] : (($true != ((X0 @ X9 @ X9 @ X10))) & ($true != ((X1 @ X9 @ X9 @ X10)))))),
% 0.19/0.29 inference(flattening,[],[f6])).
% 0.19/0.29 thf(f8,plain,(
% 0.19/0.29 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2)))) | ? [X3 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : (? [X6 : $i] : (($true != ((X0 @ X3 @ X5 @ X6))) & ($true != ((X1 @ X3 @ X5 @ X6)))) & ! [X7 : $i] : (($true = ((X0 @ X4 @ X5 @ X7))) | ($true = ((X1 @ X4 @ X5 @ X7)))) & ! [X8 : $i] : (($true = ((X0 @ X3 @ X4 @ X8))) | ($true = ((X1 @ X3 @ X4 @ X8))))) | ? [X9 : ($i > $o),X10 : $i] : (($true != ((X0 @ X9 @ X9 @ X10))) & ($true != ((X1 @ X9 @ X9 @ X10)))))),
% 0.19/0.29 inference(rectify,[],[f7])).
% 0.19/0.29 thf(f9,plain,(
% 0.19/0.29 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2)))) | ((($true != ((X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)))) & ($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0))))) & ! [X7 : $i] : (($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) | ($true = ((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7)))) & ! [X8 : $i] : (($true = ((X0 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X8))) | ($true = ((X1 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X8))))) | (($true != ((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) & ($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))))))),
% 0.19/0.29 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])).
% 0.19/0.29 thf(f10,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true = ((X0 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X8))) | ($true = ((X1 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X8))) | ($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))))) )),
% 0.19/0.29 inference(cnf_transformation,[],[f9])).
% 0.19/0.29 thf(f12,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) | ($true = ((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) | ($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))))) )),
% 0.19/0.29 inference(cnf_transformation,[],[f9])).
% 0.19/0.29 thf(f14,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)))) | ($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))))) )),
% 0.19/0.29 inference(cnf_transformation,[],[f9])).
% 0.19/0.29 thf(f19,definition,(
% 0.19/0.29 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.19/0.29 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.19/0.29 thf(f20,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true = ((X0 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X8))) | ($true = ((X1 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X8))) | ($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))))) )),
% 0.19/0.29 inference(boolean_simplification,[],[f10])).
% 0.19/0.29 thf(f21,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true = ((X0 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X8))) | ($true = ((X1 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X8))) | ($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))))) )),
% 0.19/0.29 inference(boolean_simplification,[],[f20])).
% 0.19/0.29 thf(f22,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X8))) | ($true = ((X1 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X8))) | ($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))))) )),
% 0.19/0.29 inference(boolean_simplification,[],[f21])).
% 0.19/0.29 thf(f23,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X8))) | ($true = ((X1 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X8))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 0.19/0.29 inference(boolean_simplification,[],[f22])).
% 0.19/0.29 thf(f28,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) | ($true = ((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) | ($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))))) )),
% 0.19/0.29 inference(boolean_simplification,[],[f12])).
% 0.19/0.29 thf(f29,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) | ($true = ((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) | ($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))))) )),
% 0.19/0.29 inference(boolean_simplification,[],[f28])).
% 0.19/0.29 thf(f30,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) | ($true = ((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) | ($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))))) )),
% 0.19/0.29 inference(boolean_simplification,[],[f29])).
% 0.19/0.29 thf(f31,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : (($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) | ($true = ((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 0.19/0.29 inference(boolean_simplification,[],[f30])).
% 0.19/0.29 thf(f36,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)))) | ($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))))) )),
% 0.19/0.29 inference(boolean_simplification,[],[f14])).
% 0.19/0.29 thf(f37,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)))) | ($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))))) )),
% 0.19/0.29 inference(boolean_simplification,[],[f36])).
% 0.19/0.29 thf(f38,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)))) | ($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))))) )),
% 0.19/0.29 inference(boolean_simplification,[],[f37])).
% 0.19/0.29 thf(f39,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 0.19/0.29 inference(boolean_simplification,[],[f38])).
% 0.19/0.29 thf(f65,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != $true) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true != ((X0 @ (sK0 @ X0 @ X1) @ (sK2 @ X0 @ X1) @ (sK3 @ X0 @ X1)))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($false = ((X0 @ (sK4 @ X0 @ X1) @ (sK4 @ X0 @ X1) @ (sK5 @ X0 @ X1))))) )),
% 0.19/0.29 inference(constrained_superposition,[],[f39,f19])).
% 0.19/0.29 thf(f68,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != ((X0 @ (sK0 @ X0 @ X1) @ (sK2 @ X0 @ X1) @ (sK3 @ X0 @ X1)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($false = ((X0 @ (sK4 @ X0 @ X1) @ (sK4 @ X0 @ X1) @ (sK5 @ X0 @ X1))))) )),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f65])).
% 0.19/0.29 thf(f94,definition,(
% 0.19/0.29 spl6_2 <=> ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition])).
% 0.19/0.29 thf(f95,plain,(
% 0.19/0.29 ((^[Y0 : $i]: ($false)) != (^[Y0 : $i]: ($true))) | spl6_2),
% 0.19/0.29 inference(avatar_component_clause,[],[f94])).
% 0.19/0.29 thf(f96,plain,(
% 0.19/0.29 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ~spl6_2),
% 0.19/0.29 inference(avatar_component_clause,[],[f94])).
% 0.19/0.29 thf(f159,plain,(
% 0.19/0.29 ( ! [X1 : $i] : (((((^[Y0 : $i]: ($false)) @ X1)) = (((^[Y0 : $i]: ($true)) @ X1)))) ) | ~spl6_2),
% 0.19/0.29 inference(argument_congruence,[],[f96])).
% 0.19/0.29 thf(f160,plain,(
% 0.19/0.29 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ($false)) @ X1))) | ($false = (((^[Y0 : $i]: ($true)) @ X1)))) ) | ~spl6_2),
% 0.19/0.29 inference(iff_proxy_clausification,[],[f159])).
% 0.19/0.29 thf(f163,plain,(
% 0.19/0.29 ($true = $false) | ($true = $false) | ~spl6_2),
% 0.19/0.29 inference(beta-eta_normalization,[],[f160])).
% 0.19/0.29 thf(f164,plain,(
% 0.19/0.29 ($true = $false) | ~spl6_2),
% 0.19/0.29 inference(duplicate_literal_removal,[],[f163])).
% 0.19/0.29 thf(f165,plain,(
% 0.19/0.29 $false | ~spl6_2),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f164])).
% 0.19/0.29 thf(f166,plain,(
% 0.19/0.29 ~spl6_2),
% 0.19/0.29 inference(avatar_contradiction_clause,[],[f165])).
% 0.19/0.29 thf(f207,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($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 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X8))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X8))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 0.19/0.29 inference(primitive_instantiation,[],[f23])).
% 0.19/0.29 thf(f235,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true != (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X8))) | ($true = (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 0.19/0.29 inference(beta-eta_normalization,[],[f207])).
% 0.19/0.29 thf(f236,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : ((((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X8))) | ($true = (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 0.19/0.29 inference(equality_proxy_clausification,[],[f235])).
% 0.19/0.29 thf(f237,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $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))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X8))) | ($true = (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 0.19/0.29 inference(equality_proxy_clausification,[],[f236])).
% 0.19/0.29 thf(f238,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $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))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X8))) | (((sK0 @ (^[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)) @ X2)))) )),
% 0.19/0.29 inference(equality_proxy_clausification,[],[f237])).
% 0.19/0.29 thf(f239,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X8))) | (((sK0 @ (^[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)) @ X2)))) )),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f238])).
% 0.19/0.29 thf(f240,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X8 : $i] : (($true = ((X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X8))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) ) | spl6_2),
% 0.19/0.29 inference(forward_subsumption_resolution,[],[f239,f95])).
% 0.19/0.29 thf(f275,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : (($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 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK1 @ (^[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)))))) @ (sK1 @ (^[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 = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 0.19/0.29 inference(primitive_instantiation,[],[f31])).
% 0.19/0.29 thf(f303,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : (($true != (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = ((X0 @ (sK1 @ (^[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 = (((sK1 @ (^[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 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 0.19/0.29 inference(beta-eta_normalization,[],[f275])).
% 0.19/0.29 thf(f304,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : ((((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = ((X0 @ (sK1 @ (^[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 = (((sK1 @ (^[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 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 0.19/0.29 inference(equality_proxy_clausification,[],[f303])).
% 0.19/0.29 thf(f305,plain,(
% 0.19/0.29 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),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))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true = ((X0 @ (sK1 @ (^[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 = (((sK1 @ (^[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 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 0.19/0.30 inference(equality_proxy_clausification,[],[f304])).
% 0.19/0.30 thf(f306,plain,(
% 0.19/0.30 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),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))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true = ((X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[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)) @ X2)))) )),
% 0.19/0.30 inference(equality_proxy_clausification,[],[f305])).
% 0.19/0.30 thf(f307,plain,(
% 0.19/0.30 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true = ((X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK2 @ (^[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)) @ X2)))) )),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f306])).
% 0.19/0.30 thf(f308,plain,(
% 0.19/0.30 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X7 : $i] : (($true = ((X0 @ (sK1 @ (^[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 = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | (((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_2),
% 0.19/0.30 inference(forward_subsumption_resolution,[],[f307,f95])).
% 0.19/0.30 thf(f490,plain,(
% 0.19/0.30 ( ! [X2 : $i,X8 : $i] : (($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ X8))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) ) | spl6_2),
% 0.19/0.30 inference(primitive_instantiation,[],[f240])).
% 0.19/0.30 thf(f645,plain,(
% 0.19/0.30 ($true = $false) | ($true = $false) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | spl6_2),
% 0.19/0.30 inference(beta-eta_normalization,[],[f490])).
% 0.19/0.30 thf(f646,plain,(
% 0.19/0.30 ($true = $false) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | spl6_2),
% 0.19/0.30 inference(duplicate_literal_removal,[],[f645])).
% 0.19/0.30 thf(f647,plain,(
% 0.19/0.30 (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | spl6_2),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f646])).
% 0.19/0.30 thf(f975,plain,(
% 0.19/0.30 ( ! [X2 : $i,X7 : $i] : (($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ X7))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) ) | spl6_2),
% 0.19/0.30 inference(primitive_instantiation,[],[f308])).
% 0.19/0.30 thf(f1134,plain,(
% 0.19/0.30 ($true = $false) | ($true = $false) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | spl6_2),
% 0.19/0.30 inference(beta-eta_normalization,[],[f975])).
% 0.19/0.30 thf(f1135,plain,(
% 0.19/0.30 ($true = $false) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | spl6_2),
% 0.19/0.30 inference(duplicate_literal_removal,[],[f1134])).
% 0.19/0.30 thf(f1136,plain,(
% 0.19/0.30 (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | spl6_2),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f1135])).
% 0.19/0.30 thf(f1195,plain,(
% 0.19/0.30 (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | spl6_2),
% 0.19/0.30 inference(forward_demodulation,[],[f1136,f647])).
% 0.19/0.30 thf(f1202,plain,(
% 0.19/0.30 ( ! [X0 : $i] : (($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X0))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X0))) | ($false = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))))) ) | spl6_2),
% 0.19/0.30 inference(constrained_superposition,[],[f68,f1195])).
% 0.19/0.30 thf(f1218,plain,(
% 0.19/0.30 ($true != (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = $false) | ($false = (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) | spl6_2),
% 0.19/0.30 inference(beta-eta_normalization,[],[f1202])).
% 0.19/0.30 thf(f1219,plain,(
% 0.19/0.30 (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) != ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = $false) | ($false = (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) | spl6_2),
% 0.19/0.30 inference(equality_proxy_clausification,[],[f1218])).
% 0.19/0.30 thf(f1220,plain,(
% 0.19/0.30 (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) != ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true = $false) | ($false = (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) | spl6_2),
% 0.19/0.30 inference(equality_proxy_clausification,[],[f1219])).
% 0.19/0.30 thf(f1221,plain,(
% 0.19/0.30 (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) != ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true = $false) | (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) != ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | spl6_2),
% 0.19/0.30 inference(equality_proxy_clausification,[],[f1220])).
% 0.19/0.30 thf(f1222,plain,(
% 0.19/0.30 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | spl6_2),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f1221])).
% 0.19/0.30 thf(f1230,plain,(
% 0.19/0.30 $false | spl6_2),
% 0.19/0.30 inference(forward_subsumption_resolution,[],[f1222,f95])).
% 0.19/0.30 thf(f1231,plain,(
% 0.19/0.30 spl6_2),
% 0.19/0.30 inference(avatar_contradiction_clause,[],[f1230])).
% 0.19/0.30 cnf(s5, plain, ~spl6_2, inference(sat_conversion,[],[f166])).
% 0.19/0.30 cnf(s62, plain, spl6_2, inference(sat_conversion,[],[f1231])).
% 0.19/0.30 cnf(s63, plain, $false, inference(rat,[],[s5,s62])).
% 0.19/0.30 thf(f1232,plain,(
% 0.19/0.30 $false),
% 0.19/0.30 inference(avatar_sat_refutation,[],[s63])).
% 0.19/0.30 % SZS output end Proof for theBenchmark
% 0.19/0.30 % (903187)------------------------------
% 0.19/0.30 % (903187)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (903187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (903187)CaDiCaL version: 2.1.3
% 0.19/0.30 % (903187)Termination reason: Refutation
% 0.19/0.30 % (903187)Time elapsed: 0.037 s
% 0.19/0.30 % (903187)Peak memory usage: 13 MB
% 0.19/0.30 % (903187)Instructions burned: 154 (million)
% 0.19/0.30 % (903181)Success in time 0.073 s
% 0.19/0.30 % Vampire exiting
%------------------------------------------------------------------------------