%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV085^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:37:36 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV085^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n016.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 15:11:49 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 Running higher-order theorem proving
% 0.10/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.28 % (467832)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (467841)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=631229288:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.28 % (467839)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=948635042:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.28 % (467841)Instruction limit reached!
% 0.20/0.28 % (467841)------------------------------
% 0.20/0.28 % (467841)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (467841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (467841)CaDiCaL version: 2.1.3
% 0.20/0.28 % (467838)lrs+10_16_si=on:nwc=1.5:random_seed=3714178771:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.28 % (467841)Termination reason: Instruction limit
% 0.20/0.28 % (467841)Termination phase: Saturation
% 0.20/0.28 % (467841)Time elapsed: 0.007 s
% 0.20/0.28 % (467841)Peak memory usage: 12 MB
% 0.20/0.28 % (467841)Instructions burned: 26 (million)
% 0.20/0.28 % (467837)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=309256618:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28 % (467840)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=99921958: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)
% 0.20/0.28 % (467839)Instruction limit reached!
% 0.20/0.28 % (467839)------------------------------
% 0.20/0.28 % (467839)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (467839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (467843)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.28 % (467839)CaDiCaL version: 2.1.3
% 0.20/0.28 % (467839)Termination reason: Instruction limit
% 0.20/0.28 % (467839)Termination phase: Saturation
% 0.20/0.28 % (467839)Time elapsed: 0.002 s
% 0.20/0.28 % (467839)Peak memory usage: 12 MB
% 0.20/0.28 % (467839)Instructions burned: 3 (million)
% 0.20/0.28 % (467843)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
% 0.20/0.28 % (467842)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1414929636:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.28 % (467843)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=263737712:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.28 % (467837) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-467832-467837"...
% 0.20/0.28 % (467840) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-467832-467840"...
% 0.20/0.28 % (467837)...printing done.
% 0.20/0.28 % (467840)...printing done.
% 0.20/0.28 % (467837)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% 0.20/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.28 thf(func_def_3, type, sK0: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.20/0.28 thf(func_def_4, type, sK1: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.20/0.28 thf(func_def_5, type, sK2: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.20/0.28 thf(func_def_6, type, sK3: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.20/0.28 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.20/0.28 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.28 thf(func_def_9, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.28 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.28 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.28 thf(f1,conjecture,(
% 0.20/0.28 ? [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X2 : ($i > $o),X1 : ($i > $o)] : (X0 @ X1 @ X2) & ! [X7 : ($i > $o),X6 : ($i > $o),X5 : ($i > $o)] : (((X0 @ X5 @ X6) & (X0 @ X6 @ X7)) => (X0 @ X5 @ X7)) & ! [X5 : ($i > $o)] : (X0 @ X5 @ X5) & ? [X3 : ($i > $o),X4 : ($i > $o)] : ~(X0 @ X3 @ X4))),
% 0.20/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM120_2_pme)).
% 0.20/0.28 thf(f2,negated_conjecture,(
% 0.20/0.28 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X2 : ($i > $o),X1 : ($i > $o)] : (X0 @ X1 @ X2) & ! [X7 : ($i > $o),X6 : ($i > $o),X5 : ($i > $o)] : (((X0 @ X5 @ X6) & (X0 @ X6 @ X7)) => (X0 @ X5 @ X7)) & ! [X5 : ($i > $o)] : (X0 @ X5 @ X5) & ? [X3 : ($i > $o),X4 : ($i > $o)] : ~(X0 @ X3 @ X4))),
% 0.20/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.28 thf(f3,plain,(
% 0.20/0.28 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o),X2 : ($i > $o)] : (X0 @ X2 @ X1) & ! [X3 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : (((X0 @ X5 @ X4) & (X0 @ X4 @ X3)) => (X0 @ X5 @ X3)) & ! [X6 : ($i > $o)] : (X0 @ X6 @ X6) & ? [X7 : ($i > $o),X8 : ($i > $o)] : ~(X0 @ X7 @ X8))),
% 0.20/0.28 inference(rectify,[],[f2])).
% 0.20/0.28 thf(f4,plain,(
% 0.20/0.28 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X2 : ($i > $o),X1 : ($i > $o)] : (((X0 @ X2 @ X1)) = $true) & ! [X3 : ($i > $o),X5 : ($i > $o),X4 : ($i > $o)] : (((((X0 @ X4 @ X3)) = $true) & ($true = ((X0 @ X5 @ X4)))) => ($true = ((X0 @ X5 @ X3)))) & ! [X6 : ($i > $o)] : ($true = ((X0 @ X6 @ X6))) & ? [X7 : ($i > $o),X8 : ($i > $o)] : ~ ($true = ((X0 @ X7 @ X8))))),
% 0.20/0.28 inference(fool_elimination,[],[f3])).
% 0.20/0.28 thf(f5,plain,(
% 0.20/0.28 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X2 : ($i > $o),X1 : ($i > $o)] : (((X0 @ X2 @ X1)) = $true) & ! [X3 : ($i > $o),X5 : ($i > $o),X4 : ($i > $o)] : (((((X0 @ X4 @ X3)) = $true) & ($true = ((X0 @ X5 @ X4)))) => ($true = ((X0 @ X5 @ X3)))) & ? [X7 : ($i > $o),X8 : ($i > $o)] : ($true != ((X0 @ X7 @ X8))) & ! [X6 : ($i > $o)] : ($true = ((X0 @ X6 @ X6))))),
% 0.20/0.28 inference(flattening,[],[f4])).
% 0.20/0.28 thf(f6,plain,(
% 0.20/0.28 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X2 : ($i > $o),X1 : ($i > $o)] : (((X0 @ X2 @ X1)) != $true) | ? [X3 : ($i > $o),X5 : ($i > $o),X4 : ($i > $o)] : (($true != ((X0 @ X5 @ X3))) & ((((X0 @ X4 @ X3)) = $true) & ($true = ((X0 @ X5 @ X4))))) | ! [X7 : ($i > $o),X8 : ($i > $o)] : ($true = ((X0 @ X7 @ X8))) | ? [X6 : ($i > $o)] : ($true != ((X0 @ X6 @ X6))))),
% 0.20/0.28 inference(ennf_transformation,[],[f5])).
% 0.20/0.28 thf(f7,plain,(
% 0.20/0.28 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X7 : ($i > $o),X8 : ($i > $o)] : ($true = ((X0 @ X7 @ X8))) | ? [X6 : ($i > $o)] : ($true != ((X0 @ X6 @ X6))) | ? [X5 : ($i > $o),X3 : ($i > $o),X4 : ($i > $o)] : (($true != ((X0 @ X5 @ X3))) & ($true = ((X0 @ X5 @ X4))) & (((X0 @ X4 @ X3)) = $true)) | ! [X2 : ($i > $o),X1 : ($i > $o)] : (((X0 @ X2 @ X1)) != $true))),
% 0.20/0.28 inference(flattening,[],[f6])).
% 0.20/0.28 thf(f8,plain,(
% 0.20/0.28 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o),X2 : ($i > $o)] : (((X0 @ X1 @ X2)) = $true) | ? [X3 : ($i > $o)] : ($true != ((X0 @ X3 @ X3))) | ? [X4 : ($i > $o),X5 : ($i > $o),X6 : ($i > $o)] : ((((X0 @ X4 @ X5)) != $true) & ($true = ((X0 @ X4 @ X6))) & ($true = ((X0 @ X6 @ X5)))) | ! [X7 : ($i > $o),X8 : ($i > $o)] : ($true != ((X0 @ X7 @ X8))))),
% 0.20/0.28 inference(rectify,[],[f7])).
% 0.20/0.28 thf(f9,plain,(
% 0.20/0.28 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o),X2 : ($i > $o)] : (((X0 @ X1 @ X2)) = $true) | (((X0 @ (sK0 @ X0) @ (sK0 @ X0))) != $true) | ((((X0 @ (sK1 @ X0) @ (sK2 @ X0))) != $true) & ($true = ((X0 @ (sK1 @ X0) @ (sK3 @ X0)))) & ($true = ((X0 @ (sK3 @ X0) @ (sK2 @ X0))))) | ! [X7 : ($i > $o),X8 : ($i > $o)] : ($true != ((X0 @ X7 @ X8))))),
% 0.20/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP]),skolemize(X6,sK3 @ X0),skolemize(X6,sK3 @ X0),skolemize(X6,sK3 @ X0),skolemize(X6,sK3 @ X0)],[f8])).
% 0.20/0.28 thf(f10,plain,(
% 0.20/0.28 ( ! [X2 : ($i > $o),X0 : (($i > $o) > ($i > $o) > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((((X0 @ (sK0 @ X0) @ (sK0 @ X0))) != $true) | (((X0 @ X1 @ X2)) = $true) | ($true != ((X0 @ X7 @ X8))) | ($true = ((X0 @ (sK3 @ X0) @ (sK2 @ X0))))) )),
% 0.20/0.28 inference(cnf_transformation,[],[f9])).
% 0.20/0.28 thf(f11,plain,(
% 0.20/0.28 ( ! [X2 : ($i > $o),X0 : (($i > $o) > ($i > $o) > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((((X0 @ (sK0 @ X0) @ (sK0 @ X0))) != $true) | (((X0 @ X1 @ X2)) = $true) | ($true != ((X0 @ X7 @ X8))) | ($true = ((X0 @ (sK1 @ X0) @ (sK3 @ X0))))) )),
% 0.20/0.28 inference(cnf_transformation,[],[f9])).
% 0.20/0.28 thf(f12,plain,(
% 0.20/0.28 ( ! [X2 : ($i > $o),X0 : (($i > $o) > ($i > $o) > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((((X0 @ (sK1 @ X0) @ (sK2 @ X0))) != $true) | (((X0 @ X1 @ X2)) = $true) | (((X0 @ (sK0 @ X0) @ (sK0 @ X0))) != $true) | ($true != ((X0 @ X7 @ X8)))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f9])).
% 0.20/0.29 thf(f15,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : (($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ X1 @ X2))) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ X7 @ X8))) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) = $true)) )),
% 0.20/0.29 inference(primitive_instantiation,[],[f10])).
% 0.20/0.29 thf(f21,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : (((((sK3 @ =) = (sK2 @ =))) = $true) | ($true = ((X1 = X2))) | (((X7 = X8)) != $true) | ($true != (((sK0 @ =) = (sK0 @ =))))) )),
% 0.20/0.29 inference(beta-eta_normalization,[],[f15])).
% 0.20/0.29 thf(f22,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : (($true = ((X1 = X2))) | (((sK2 @ =)) = ((sK3 @ =))) | (((X7 = X8)) != $true) | ($true != (((sK0 @ =) = (sK0 @ =))))) )),
% 0.20/0.29 inference(equality_proxy_clausification,[],[f21])).
% 0.20/0.29 thf(f23,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((X1 = X2) | (((sK2 @ =)) = ((sK3 @ =))) | (((X7 = X8)) != $true) | ($true != (((sK0 @ =) = (sK0 @ =))))) )),
% 0.20/0.29 inference(equality_proxy_clausification,[],[f22])).
% 0.20/0.29 thf(f24,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((X7 != X8) | (((sK2 @ =)) = ((sK3 @ =))) | ($true != (((sK0 @ =) = (sK0 @ =)))) | (X1 = X2)) )),
% 0.20/0.29 inference(equality_proxy_clausification,[],[f23])).
% 0.20/0.29 thf(f25,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((X7 != X8) | (((sK0 @ =)) != ((sK0 @ =))) | (((sK2 @ =)) = ((sK3 @ =))) | (X1 = X2)) )),
% 0.20/0.29 inference(equality_proxy_clausification,[],[f24])).
% 0.20/0.29 thf(f26,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((X7 != X8) | (((sK2 @ =)) = ((sK3 @ =))) | (X1 = X2)) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f25])).
% 0.20/0.29 thf(f48,definition,(
% 0.20/0.29 spl4_1 <=> (((sK2 @ =)) = ((sK3 @ =)))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.20/0.29 thf(f50,plain,(
% 0.20/0.29 (((sK2 @ =)) = ((sK3 @ =))) | ~spl4_1),
% 0.20/0.29 inference(avatar_component_clause,[],[f48])).
% 0.20/0.29 thf(f52,definition,(
% 0.20/0.29 spl4_2 <=> ! [X8 : ($i > $o),X7 : ($i > $o)] : (X7 != X8)),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.20/0.29 thf(f53,plain,(
% 0.20/0.29 ( ! [X8 : ($i > $o),X7 : ($i > $o)] : ((X7 != X8)) ) | ~spl4_2),
% 0.20/0.29 inference(avatar_component_clause,[],[f52])).
% 0.20/0.29 thf(f55,definition,(
% 0.20/0.29 spl4_3 <=> ! [X2 : ($i > $o),X1 : ($i > $o)] : (X1 = X2)),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition])).
% 0.20/0.29 thf(f56,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X1 : ($i > $o)] : ((X1 = X2)) ) | ~spl4_3),
% 0.20/0.29 inference(avatar_component_clause,[],[f55])).
% 0.20/0.29 thf(f57,plain,(
% 0.20/0.29 spl4_1 | spl4_2 | spl4_3),
% 0.20/0.29 inference(avatar_split_clause,[],[f26,f55,f52,f48])).
% 0.20/0.29 thf(f58,plain,(
% 0.20/0.29 $false | ~spl4_2),
% 0.20/0.29 inference(flex-flex_simplification,[],[f53])).
% 0.20/0.29 thf(f59,plain,(
% 0.20/0.29 ~spl4_2),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f58])).
% 0.20/0.29 thf(f60,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : (((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ X1 @ X2))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ X7 @ X8)))) )),
% 0.20/0.29 inference(primitive_instantiation,[],[f11])).
% 0.20/0.29 thf(f68,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : (($true = ((X1 = X2))) | (((X7 = X8)) != $true) | ($true != (((sK0 @ =) = (sK0 @ =)))) | ($true = (((sK1 @ =) = (sK3 @ =))))) )),
% 0.20/0.29 inference(beta-eta_normalization,[],[f60])).
% 0.20/0.29 thf(f69,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : (($true = (((sK1 @ =) = (sK3 @ =)))) | (X1 = X2) | ($true != (((sK0 @ =) = (sK0 @ =)))) | (((X7 = X8)) != $true)) )),
% 0.20/0.29 inference(equality_proxy_clausification,[],[f68])).
% 0.20/0.29 thf(f70,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : (($true != (((sK0 @ =) = (sK0 @ =)))) | (((X7 = X8)) != $true) | (((sK1 @ =)) = ((sK3 @ =))) | (X1 = X2)) )),
% 0.20/0.29 inference(equality_proxy_clausification,[],[f69])).
% 0.20/0.29 thf(f71,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((X1 = X2) | (((sK1 @ =)) = ((sK3 @ =))) | (((X7 = X8)) != $true) | (((sK0 @ =)) != ((sK0 @ =)))) )),
% 0.20/0.29 inference(equality_proxy_clausification,[],[f70])).
% 0.20/0.29 thf(f72,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((X7 != X8) | (((sK0 @ =)) != ((sK0 @ =))) | (X1 = X2) | (((sK1 @ =)) = ((sK3 @ =)))) )),
% 0.20/0.29 inference(equality_proxy_clausification,[],[f71])).
% 0.20/0.29 thf(f73,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((((sK1 @ =)) = ((sK3 @ =))) | (X7 != X8) | (X1 = X2)) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f72])).
% 0.20/0.29 thf(f92,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o)] : ((((X1 @ X3)) = ((X2 @ X3)))) ) | ~spl4_3),
% 0.20/0.29 inference(argument_congruence,[],[f56])).
% 0.20/0.29 thf(f98,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o)] : (($false = ((X1 @ X3))) | ($true = ((X2 @ X3)))) ) | ~spl4_3),
% 0.20/0.29 inference(iff_proxy_clausification,[],[f92])).
% 0.20/0.29 thf(f99,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X3 : $i] : (($false = (((^[Y0 : $i]: ($true)) @ X3))) | ($true = ((X2 @ X3)))) ) | ~spl4_3),
% 0.20/0.29 inference(primitive_instantiation,[],[f98])).
% 0.20/0.29 thf(f104,plain,(
% 0.20/0.29 ( ! [X3 : $i,X1 : ($i > $o),X4 : ($i > $o)] : (((((^[Y0 : $i]: (~ (X4 @ Y0))) @ X3)) = $true) | ($false = ((X1 @ X3)))) ) | ~spl4_3),
% 0.20/0.29 inference(primitive_instantiation,[],[f98])).
% 0.20/0.29 thf(f108,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X3 : $i] : (($true = ((X2 @ X3))) | ($false = $true)) ) | ~spl4_3),
% 0.20/0.29 inference(beta-eta_normalization,[],[f99])).
% 0.20/0.29 thf(f109,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X3 : $i] : (($true = ((X2 @ X3)))) ) | ~spl4_3),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f108])).
% 0.20/0.29 thf(f115,plain,(
% 0.20/0.29 ( ! [X3 : $i,X1 : ($i > $o),X4 : ($i > $o)] : (($true = ((~ (X4 @ X3)))) | ($false = ((X1 @ X3)))) ) | ~spl4_3),
% 0.20/0.29 inference(beta-eta_normalization,[],[f104])).
% 0.20/0.29 thf(f116,plain,(
% 0.20/0.29 ( ! [X3 : $i,X1 : ($i > $o),X4 : ($i > $o)] : (($false = ((X4 @ X3))) | ($false = ((X1 @ X3)))) ) | ~spl4_3),
% 0.20/0.29 inference(not_proxy_clausification,[],[f115])).
% 0.20/0.29 thf(f123,plain,(
% 0.20/0.29 ( ! [X3 : $i,X1 : ($i > $o)] : (($false = ((X1 @ X3))) | ($false = $true)) ) | ~spl4_3),
% 0.20/0.29 inference(forward_demodulation,[],[f116,f109])).
% 0.20/0.29 thf(f124,plain,(
% 0.20/0.29 ( ! [X3 : $i,X1 : ($i > $o)] : (($false = ((X1 @ X3)))) ) | ~spl4_3),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f123])).
% 0.20/0.29 thf(f125,plain,(
% 0.20/0.29 ($false = $true) | ~spl4_3),
% 0.20/0.29 inference(forward_demodulation,[],[f124,f109])).
% 0.20/0.29 thf(f126,plain,(
% 0.20/0.29 $false | ~spl4_3),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f125])).
% 0.20/0.29 thf(f127,plain,(
% 0.20/0.29 ~spl4_3),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f126])).
% 0.20/0.29 thf(f129,definition,(
% 0.20/0.29 spl4_4 <=> (((sK1 @ =)) = ((sK3 @ =)))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition])).
% 0.20/0.29 thf(f131,plain,(
% 0.20/0.29 (((sK1 @ =)) = ((sK3 @ =))) | ~spl4_4),
% 0.20/0.29 inference(avatar_component_clause,[],[f129])).
% 0.20/0.29 thf(f132,plain,(
% 0.20/0.29 spl4_2 | spl4_3 | spl4_4),
% 0.20/0.29 inference(avatar_split_clause,[],[f73,f129,f55,f52])).
% 0.20/0.29 thf(f143,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : (((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ X1 @ X2))) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ X7 @ X8)))) )),
% 0.20/0.29 inference(primitive_instantiation,[],[f12])).
% 0.20/0.29 thf(f156,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : (($true = ((X1 = X2))) | (((X7 = X8)) != $true) | ($true != (((sK0 @ =) = (sK0 @ =)))) | ($true != (((sK1 @ =) = (sK2 @ =))))) )),
% 0.20/0.29 inference(beta-eta_normalization,[],[f143])).
% 0.20/0.29 thf(f157,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((X1 = X2) | ($true != (((sK1 @ =) = (sK2 @ =)))) | ($true != (((sK0 @ =) = (sK0 @ =)))) | (((X7 = X8)) != $true)) )),
% 0.20/0.29 inference(equality_proxy_clausification,[],[f156])).
% 0.20/0.29 thf(f158,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : (($true != (((sK0 @ =) = (sK0 @ =)))) | (X1 = X2) | (((sK2 @ =)) != ((sK1 @ =))) | (((X7 = X8)) != $true)) )),
% 0.20/0.29 inference(equality_proxy_clausification,[],[f157])).
% 0.20/0.29 thf(f159,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((((sK0 @ =)) != ((sK0 @ =))) | (X1 = X2) | (((X7 = X8)) != $true) | (((sK2 @ =)) != ((sK1 @ =)))) )),
% 0.20/0.29 inference(equality_proxy_clausification,[],[f158])).
% 0.20/0.29 thf(f160,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((X1 = X2) | (X7 != X8) | (((sK2 @ =)) != ((sK1 @ =))) | (((sK0 @ =)) != ((sK0 @ =)))) )),
% 0.20/0.29 inference(equality_proxy_clausification,[],[f159])).
% 0.20/0.29 thf(f161,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((X1 = X2) | (((sK2 @ =)) != ((sK1 @ =))) | (X7 != X8)) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f160])).
% 0.20/0.29 thf(f188,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((X7 != X8) | (((sK2 @ =)) != ((sK3 @ =))) | (X1 = X2)) ) | ~spl4_4),
% 0.20/0.29 inference(forward_demodulation,[],[f161,f131])).
% 0.20/0.29 thf(f191,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X1 : ($i > $o),X8 : ($i > $o),X7 : ($i > $o)] : ((X7 != X8) | (X1 = X2)) ) | (~spl4_1 | ~spl4_4)),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f188,f50])).
% 0.20/0.29 thf(f193,plain,(
% 0.20/0.29 spl4_2 | spl4_3 | ~spl4_1 | ~spl4_4),
% 0.20/0.29 inference(avatar_split_clause,[],[f191,f129,f48,f55,f52])).
% 0.20/0.29 cnf(s1, plain, spl4_1 | spl4_2 | spl4_3, inference(sat_conversion,[],[f57])).
% 0.20/0.29 cnf(s2, plain, ~spl4_2, inference(sat_conversion,[],[f59])).
% 0.20/0.29 cnf(s4, plain, ~spl4_3, inference(sat_conversion,[],[f127])).
% 0.20/0.29 cnf(s5, plain, spl4_2 | spl4_3 | spl4_4, inference(sat_conversion,[],[f132])).
% 0.20/0.29 cnf(s8, plain, ~spl4_1 | spl4_2 | spl4_3 | ~spl4_4, inference(sat_conversion,[],[f193])).
% 0.20/0.29 cnf(s9, plain, spl4_4, inference(rat,[],[s5,s4,s2])).
% 0.20/0.29 cnf(s10, plain, ~spl4_1, inference(rat,[],[s8,s2,s4,s9])).
% 0.20/0.29 cnf(s11, plain, $false, inference(rat,[],[s1,s4,s2,s10])).
% 0.20/0.29 thf(f194,plain,(
% 0.20/0.29 $false),
% 0.20/0.29 inference(avatar_sat_refutation,[],[s11])).
% 0.20/0.29 % SZS output end Proof for theBenchmark
% 0.20/0.29 % (467837)------------------------------
% 0.20/0.29 % (467837)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (467837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (467837)CaDiCaL version: 2.1.3
% 0.20/0.29 % (467837)Termination reason: Refutation
% 0.20/0.29 % (467837)Time elapsed: 0.008 s
% 0.20/0.29 % (467837)Peak memory usage: 13 MB
% 0.20/0.29 % (467837)Instructions burned: 12 (million)
% 0.20/0.29 % (467832)Success in time 0.057 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------