%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV058^5 : 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 : 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 08:37:34 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV058^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.19 % Computer : n019.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Tue Sep 29 15:05:48 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.23 Running higher-order theorem proving
% 0.12/0.24 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
% 0.22/0.30 % (897099)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (897105)lrs+10_16_si=on:nwc=1.5:random_seed=3143629748:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.30 % (897105)Instruction limit reached!
% 0.22/0.30 % (897105)------------------------------
% 0.22/0.30 % (897105)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (897105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (897105)CaDiCaL version: 2.1.3
% 0.22/0.30 % (897105)Termination reason: Instruction limit
% 0.22/0.30 % (897105)Termination phase: Saturation
% 0.22/0.30 % (897105)Time elapsed: 0.007 s
% 0.22/0.30 % (897105)Peak memory usage: 12 MB
% 0.22/0.30 % (897105)Instructions burned: 22 (million)
% 0.22/0.30 % (897104)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=104748253:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (897106)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1698238726:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.30 % (897110)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.30 % (897110)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
% 0.22/0.30 % (897107)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=2834305756: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)
% 0.22/0.30 % (897106)Instruction limit reached!
% 0.22/0.30 % (897106)------------------------------
% 0.22/0.30 % (897106)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (897106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (897106)CaDiCaL version: 2.1.3
% 0.22/0.30 % (897106)Termination reason: Instruction limit
% 0.22/0.30 % (897106)Termination phase: Saturation
% 0.22/0.30 % (897106)Time elapsed: 0.002 s
% 0.22/0.30 % (897106)Peak memory usage: 12 MB
% 0.22/0.30 % (897106)Instructions burned: 3 (million)
% 0.22/0.30 % (897110)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=1221560016:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.30 % (897107) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-897099-897107"...
% 0.22/0.30 % (897104) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-897099-897104"...
% 0.22/0.30 % (897115)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4091009675:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.30 % (897109)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3109389318:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.30 % (897115)Instruction limit reached!
% 0.22/0.30 % (897115)------------------------------
% 0.22/0.30 % (897115)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (897115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (897115)CaDiCaL version: 2.1.3
% 0.22/0.30 % (897115)Termination reason: Instruction limit
% 0.22/0.30 % (897115)Termination phase: Saturation
% 0.22/0.30 % (897115)Time elapsed: 0.001 s
% 0.22/0.30 % (897115)Peak memory usage: 12 MB
% 0.22/0.30 % (897115)Instructions burned: 2 (million)
% 0.22/0.30 % (897104)...printing done.
% 0.22/0.30 % (897104)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% 0.22/0.30 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.30 thf(func_def_3, type, sP0: ((($i > $o) > ($i > $o) > $o) > $o)).
% 0.22/0.30 thf(func_def_4, type, sK1: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.22/0.30 thf(func_def_5, type, sK2: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.22/0.30 thf(func_def_6, type, sK3: ((($i > $o) > ($i > $o) > $o) > $i)).
% 0.22/0.30 thf(func_def_7, type, sK4: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.22/0.30 thf(func_def_8, type, sK5: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.22/0.30 thf(func_def_9, type, sK6: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.22/0.30 thf(func_def_10, type, sK7: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.22/0.30 thf(func_def_11, type, vNOT: ($o > $o)).
% 0.22/0.30 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.30 thf(func_def_13, type, db1: !>[X0: $tType]:(X0)).
% 0.22/0.30 thf(func_def_14, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.30 thf(func_def_15, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.30 thf(func_def_18, type, db2: !>[X0: $tType]:(X0)).
% 0.22/0.30 thf(f1,conjecture,(
% 0.22/0.30 ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X4 : ($i > $o)] : (X0 @ X4 @ X4) & ! [X2 : ($i > $o),X1 : ($i > $o)] : ((X0 @ X1 @ X2) => ! [X3 : $i] : ((X1 @ X3) => (X2 @ X3))) & ! [X5 : ($i > $o),X4 : ($i > $o),X3 : ($i > $o)] : (((X0 @ X5 @ X3) & (X0 @ X4 @ X5)) => (X0 @ X4 @ X3)))),
% 0.22/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM122_pme)).
% 0.22/0.30 thf(f2,negated_conjecture,(
% 0.22/0.30 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X4 : ($i > $o)] : (X0 @ X4 @ X4) & ! [X2 : ($i > $o),X1 : ($i > $o)] : ((X0 @ X1 @ X2) => ! [X3 : $i] : ((X1 @ X3) => (X2 @ X3))) & ! [X5 : ($i > $o),X4 : ($i > $o),X3 : ($i > $o)] : (((X0 @ X5 @ X3) & (X0 @ X4 @ X5)) => (X0 @ X4 @ X3)))),
% 0.22/0.30 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.30 thf(f3,plain,(
% 0.22/0.30 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o)] : (X0 @ X1 @ X1) & ! [X2 : ($i > $o),X3 : ($i > $o)] : ((X0 @ X3 @ X2) => ! [X4 : $i] : ((X3 @ X4) => (X2 @ X4))) & ! [X5 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o)] : (((X0 @ X5 @ X7) & (X0 @ X6 @ X5)) => (X0 @ X6 @ X7)))),
% 0.22/0.30 inference(rectify,[],[f2])).
% 0.22/0.30 thf(f4,plain,(
% 0.22/0.30 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o)] : (((X0 @ X1 @ X1)) = $true) & ! [X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : (((((X0 @ X6 @ X5)) = $true) & ($true = ((X0 @ X5 @ X7)))) => ($true = ((X0 @ X6 @ X7)))) & ! [X2 : ($i > $o),X3 : ($i > $o)] : ((((X0 @ X3 @ X2)) = $true) => ! [X4 : $i] : ((((X3 @ X4)) = $true) => (((X2 @ X4)) = $true))))),
% 0.22/0.30 inference(fool_elimination,[],[f3])).
% 0.22/0.30 thf(f5,plain,(
% 0.22/0.30 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o)] : (((X0 @ X1 @ X1)) != $true) | ? [X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : (($true != ((X0 @ X6 @ X7))) & ((((X0 @ X6 @ X5)) = $true) & ($true = ((X0 @ X5 @ X7))))) | ? [X3 : ($i > $o),X2 : ($i > $o)] : (? [X4 : $i] : ((((X3 @ X4)) = $true) & (((X2 @ X4)) != $true)) & (((X0 @ X3 @ X2)) = $true)))),
% 0.22/0.30 inference(ennf_transformation,[],[f4])).
% 0.22/0.30 thf(f6,plain,(
% 0.22/0.30 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o)] : (((X0 @ X1 @ X1)) != $true) | ? [X6 : ($i > $o),X5 : ($i > $o),X7 : ($i > $o)] : ((((X0 @ X6 @ X5)) = $true) & ($true != ((X0 @ X6 @ X7))) & ($true = ((X0 @ X5 @ X7)))) | ? [X3 : ($i > $o),X2 : ($i > $o)] : (? [X4 : $i] : ((((X3 @ X4)) = $true) & (((X2 @ X4)) != $true)) & (((X0 @ X3 @ X2)) = $true)))),
% 0.22/0.30 inference(flattening,[],[f5])).
% 0.22/0.30 thf(f7,definition,(
% 0.22/0.30 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X3 : ($i > $o),X2 : ($i > $o)] : (? [X4 : $i] : ((((X3 @ X4)) = $true) & (((X2 @ X4)) != $true)) & (((X0 @ X3 @ X2)) = $true)) | ~ (((sP0 @ X0)) = $true))),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.22/0.30 thf(f8,plain,(
% 0.22/0.30 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o)] : (((X0 @ X1 @ X1)) != $true) | ? [X6 : ($i > $o),X5 : ($i > $o),X7 : ($i > $o)] : ((((X0 @ X6 @ X5)) = $true) & ($true != ((X0 @ X6 @ X7))) & ($true = ((X0 @ X5 @ X7)))) | (((sP0 @ X0)) = $true))),
% 0.22/0.30 inference(definition_folding,[],[f6,f7])).
% 0.22/0.30 thf(f9,plain,(
% 0.22/0.30 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X3 : ($i > $o),X2 : ($i > $o)] : (? [X4 : $i] : ((((X3 @ X4)) = $true) & (((X2 @ X4)) != $true)) & (((X0 @ X3 @ X2)) = $true)) | (((sP0 @ X0)) != $true))),
% 0.22/0.30 inference(nnf_transformation,[],[f7])).
% 0.22/0.30 thf(f10,plain,(
% 0.22/0.30 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o),X2 : ($i > $o)] : (? [X3 : $i] : ((((X1 @ X3)) = $true) & (((X2 @ X3)) != $true)) & (((X0 @ X1 @ X2)) = $true)) | (((sP0 @ X0)) != $true))),
% 0.22/0.30 inference(rectify,[],[f9])).
% 0.22/0.30 thf(f11,plain,(
% 0.22/0.30 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (((($true = ((sK1 @ X0 @ (sK3 @ X0)))) & ($true != ((sK2 @ X0 @ (sK3 @ X0))))) & (((X0 @ (sK1 @ X0) @ (sK2 @ X0))) = $true)) | (((sP0 @ X0)) != $true))),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP]),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0)],[f10])).
% 0.22/0.30 thf(f12,plain,(
% 0.22/0.30 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o)] : (((X0 @ X1 @ X1)) != $true) | ? [X2 : ($i > $o),X3 : ($i > $o),X4 : ($i > $o)] : ((((X0 @ X2 @ X3)) = $true) & (((X0 @ X2 @ X4)) != $true) & (((X0 @ X3 @ X4)) = $true)) | (((sP0 @ X0)) = $true))),
% 0.22/0.30 inference(rectify,[],[f8])).
% 0.22/0.30 thf(f13,plain,(
% 0.22/0.30 ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (sK4 @ X0) @ (sK4 @ X0))) != $true) | ((((X0 @ (sK5 @ X0) @ (sK6 @ X0))) = $true) & (((X0 @ (sK5 @ X0) @ (sK7 @ X0))) != $true) & (((X0 @ (sK6 @ X0) @ (sK7 @ X0))) = $true)) | (((sP0 @ X0)) = $true))),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP]),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0)],[f12])).
% 0.22/0.30 thf(f14,plain,(
% 0.22/0.30 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((sP0 @ X0)) != $true) | (((X0 @ (sK1 @ X0) @ (sK2 @ X0))) = $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f11])).
% 0.22/0.30 thf(f15,plain,(
% 0.22/0.30 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true != ((sK2 @ X0 @ (sK3 @ X0)))) | (((sP0 @ X0)) != $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f11])).
% 0.22/0.30 thf(f16,plain,(
% 0.22/0.30 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((sP0 @ X0)) != $true) | ($true = ((sK1 @ X0 @ (sK3 @ X0))))) )),
% 0.22/0.30 inference(cnf_transformation,[],[f11])).
% 0.22/0.30 thf(f17,plain,(
% 0.22/0.30 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (sK4 @ X0) @ (sK4 @ X0))) != $true) | (((sP0 @ X0)) = $true) | (((X0 @ (sK6 @ X0) @ (sK7 @ X0))) = $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f13])).
% 0.22/0.30 thf(f18,plain,(
% 0.22/0.30 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (sK5 @ X0) @ (sK7 @ X0))) != $true) | (((sP0 @ X0)) = $true) | (((X0 @ (sK4 @ X0) @ (sK4 @ X0))) != $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f13])).
% 0.22/0.30 thf(f19,plain,(
% 0.22/0.30 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (sK4 @ X0) @ (sK4 @ X0))) != $true) | (((sP0 @ X0)) = $true) | (((X0 @ (sK5 @ X0) @ (sK6 @ X0))) = $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f13])).
% 0.22/0.30 thf(f22,plain,(
% 0.22/0.30 (((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))) = $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) = $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true)),
% 0.22/0.30 inference(primitive_instantiation,[],[f17])).
% 0.22/0.30 thf(f28,plain,(
% 0.22/0.30 (((sP0 @ =)) = $true) | ((((sK6 @ =) = (sK7 @ =))) = $true) | ((((sK4 @ =) = (sK4 @ =))) != $true)),
% 0.22/0.30 inference(beta-eta_normalization,[],[f22])).
% 0.22/0.30 thf(f29,plain,(
% 0.22/0.30 (((sK6 @ =)) = ((sK7 @ =))) | ((((sK4 @ =) = (sK4 @ =))) != $true) | (((sP0 @ =)) = $true)),
% 0.22/0.30 inference(equality_proxy_clausification,[],[f28])).
% 0.22/0.30 thf(f30,plain,(
% 0.22/0.30 (((sK6 @ =)) = ((sK7 @ =))) | (((sK4 @ =)) != ((sK4 @ =))) | (((sP0 @ =)) = $true)),
% 0.22/0.30 inference(equality_proxy_clausification,[],[f29])).
% 0.22/0.30 thf(f31,plain,(
% 0.22/0.30 (((sK6 @ =)) = ((sK7 @ =))) | (((sP0 @ =)) = $true)),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f30])).
% 0.22/0.30 thf(f44,definition,(
% 0.22/0.30 spl8_1 <=> (((sP0 @ =)) = $true)),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition])).
% 0.22/0.30 thf(f46,plain,(
% 0.22/0.30 (((sP0 @ =)) = $true) | ~spl8_1),
% 0.22/0.30 inference(avatar_component_clause,[],[f44])).
% 0.22/0.30 thf(f48,definition,(
% 0.22/0.30 spl8_2 <=> (((sK6 @ =)) = ((sK7 @ =)))),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition])).
% 0.22/0.30 thf(f50,plain,(
% 0.22/0.30 (((sK6 @ =)) = ((sK7 @ =))) | ~spl8_2),
% 0.22/0.30 inference(avatar_component_clause,[],[f48])).
% 0.22/0.30 thf(f51,plain,(
% 0.22/0.30 spl8_1 | spl8_2),
% 0.22/0.30 inference(avatar_split_clause,[],[f31,f48,f44])).
% 0.22/0.30 thf(f52,plain,(
% 0.22/0.30 ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true) | (((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))) = $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true)),
% 0.22/0.30 inference(primitive_instantiation,[],[f18])).
% 0.22/0.30 thf(f60,plain,(
% 0.22/0.30 ((((sK4 @ =) = (sK4 @ =))) != $true) | ($true != (((sK5 @ =) = (sK7 @ =)))) | (((sP0 @ =)) = $true)),
% 0.22/0.30 inference(beta-eta_normalization,[],[f52])).
% 0.22/0.30 thf(f61,plain,(
% 0.22/0.30 (((sP0 @ =)) = $true) | ($true != (((sK5 @ =) = (sK7 @ =)))) | (((sK4 @ =)) != ((sK4 @ =)))),
% 0.22/0.30 inference(equality_proxy_clausification,[],[f60])).
% 0.22/0.30 thf(f62,plain,(
% 0.22/0.30 (((sP0 @ =)) = $true) | (((sK4 @ =)) != ((sK4 @ =))) | (((sK5 @ =)) != ((sK7 @ =)))),
% 0.22/0.30 inference(equality_proxy_clausification,[],[f61])).
% 0.22/0.30 thf(f63,plain,(
% 0.22/0.30 (((sK5 @ =)) != ((sK7 @ =))) | (((sP0 @ =)) = $true)),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f62])).
% 0.22/0.30 thf(f79,definition,(
% 0.22/0.30 spl8_3 <=> (((sK5 @ =)) = ((sK7 @ =)))),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition])).
% 0.22/0.30 thf(f81,plain,(
% 0.22/0.30 (((sK5 @ =)) != ((sK7 @ =))) | spl8_3),
% 0.22/0.30 inference(avatar_component_clause,[],[f79])).
% 0.22/0.30 thf(f82,plain,(
% 0.22/0.30 spl8_1 | ~spl8_3),
% 0.22/0.30 inference(avatar_split_clause,[],[f63,f79,f44])).
% 0.22/0.30 thf(f113,plain,(
% 0.22/0.30 (((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))) = $true) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true)),
% 0.22/0.30 inference(primitive_instantiation,[],[f19])).
% 0.22/0.30 thf(f119,plain,(
% 0.22/0.30 (((sP0 @ =)) = $true) | ((((sK4 @ =) = (sK4 @ =))) != $true) | ($true = (((sK5 @ =) = (sK6 @ =))))),
% 0.22/0.30 inference(beta-eta_normalization,[],[f113])).
% 0.22/0.30 thf(f120,plain,(
% 0.22/0.30 (((sK4 @ =)) != ((sK4 @ =))) | (((sP0 @ =)) = $true) | ($true = (((sK5 @ =) = (sK6 @ =))))),
% 0.22/0.30 inference(equality_proxy_clausification,[],[f119])).
% 0.22/0.31 thf(f121,plain,(
% 0.22/0.31 (((sP0 @ =)) = $true) | (((sK6 @ =)) = ((sK5 @ =))) | (((sK4 @ =)) != ((sK4 @ =)))),
% 0.22/0.31 inference(equality_proxy_clausification,[],[f120])).
% 0.22/0.31 thf(f122,plain,(
% 0.22/0.31 (((sK6 @ =)) = ((sK5 @ =))) | (((sP0 @ =)) = $true)),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f121])).
% 0.22/0.31 thf(f134,plain,(
% 0.22/0.31 (((sK5 @ =)) = ((sK7 @ =))) | (((sP0 @ =)) = $true) | ~spl8_2),
% 0.22/0.31 inference(forward_demodulation,[],[f122,f50])).
% 0.22/0.31 thf(f135,plain,(
% 0.22/0.31 (((sP0 @ =)) = $true) | (~spl8_2 | spl8_3)),
% 0.22/0.31 inference(forward_subsumption_resolution,[],[f134,f81])).
% 0.22/0.31 thf(f136,plain,(
% 0.22/0.31 spl8_1 | ~spl8_2 | spl8_3),
% 0.22/0.31 inference(avatar_split_clause,[],[f135,f79,f48,f44])).
% 0.22/0.31 thf(f298,plain,(
% 0.22/0.31 (((sK1 @ = @ (sK3 @ =))) = $true) | ($true != $true) | ~spl8_1),
% 0.22/0.31 inference(constrained_superposition,[],[f16,f46])).
% 0.22/0.31 thf(f300,plain,(
% 0.22/0.31 (((sK1 @ = @ (sK3 @ =))) = $true) | ~spl8_1),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f298])).
% 0.22/0.31 thf(f302,plain,(
% 0.22/0.31 ($true != $true) | ((((sK1 @ =) = (sK2 @ =))) = $true) | ~spl8_1),
% 0.22/0.31 inference(constrained_superposition,[],[f14,f46])).
% 0.22/0.31 thf(f305,plain,(
% 0.22/0.31 ($true != $true) | (((sK1 @ =)) = ((sK2 @ =))) | ~spl8_1),
% 0.22/0.31 inference(equality_proxy_clausification,[],[f302])).
% 0.22/0.31 thf(f306,plain,(
% 0.22/0.31 (((sK1 @ =)) = ((sK2 @ =))) | ~spl8_1),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f305])).
% 0.22/0.31 thf(f307,plain,(
% 0.22/0.31 ( ! [X1 : $i] : ((((sK2 @ = @ X1)) = ((sK1 @ = @ X1)))) ) | ~spl8_1),
% 0.22/0.31 inference(argument_congruence,[],[f306])).
% 0.22/0.31 thf(f308,plain,(
% 0.22/0.31 ( ! [X1 : $i] : ((((sK2 @ = @ X1)) = $true) | ($false = ((sK1 @ = @ X1)))) ) | ~spl8_1),
% 0.22/0.31 inference(iff_proxy_clausification,[],[f307])).
% 0.22/0.31 thf(f310,plain,(
% 0.22/0.31 (((sK1 @ = @ (sK3 @ =))) = $false) | (((sP0 @ =)) != $true) | ($true != $true) | ~spl8_1),
% 0.22/0.31 inference(constrained_superposition,[],[f15,f308])).
% 0.22/0.31 thf(f311,plain,(
% 0.22/0.31 (((sP0 @ =)) != $true) | (((sK1 @ = @ (sK3 @ =))) = $false) | ~spl8_1),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f310])).
% 0.22/0.31 thf(f312,plain,(
% 0.22/0.31 (((sK1 @ = @ (sK3 @ =))) = $false) | ~spl8_1),
% 0.22/0.31 inference(forward_subsumption_resolution,[],[f311,f46])).
% 0.22/0.31 thf(f313,plain,(
% 0.22/0.31 ($true = $false) | ~spl8_1),
% 0.22/0.31 inference(forward_demodulation,[],[f312,f300])).
% 0.22/0.31 thf(f314,plain,(
% 0.22/0.31 $false | ~spl8_1),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f313])).
% 0.22/0.31 thf(f315,plain,(
% 0.22/0.31 ~spl8_1),
% 0.22/0.31 inference(avatar_contradiction_clause,[],[f314])).
% 0.22/0.31 cnf(s1, plain, spl8_1 | spl8_2, inference(sat_conversion,[],[f51])).
% 0.22/0.31 cnf(s2, plain, spl8_1 | ~spl8_3, inference(sat_conversion,[],[f82])).
% 0.22/0.31 cnf(s6, plain, spl8_1 | ~spl8_2 | spl8_3, inference(sat_conversion,[],[f136])).
% 0.22/0.31 cnf(s7, plain, ~spl8_1, inference(sat_conversion,[],[f315])).
% 0.22/0.31 cnf(s8, plain, ~spl8_2 | spl8_3, inference(rat,[],[s6,s7])).
% 0.22/0.31 cnf(s9, plain, ~spl8_3, inference(rat,[],[s2,s7])).
% 0.22/0.31 cnf(s10, plain, ~spl8_2, inference(rat,[],[s8,s9])).
% 0.22/0.31 cnf(s11, plain, $false, inference(rat,[],[s1,s10,s7])).
% 0.22/0.31 thf(f316,plain,(
% 0.22/0.31 $false),
% 0.22/0.31 inference(avatar_sat_refutation,[],[s11])).
% 0.22/0.31 % SZS output end Proof for theBenchmark
% 0.22/0.31 % (897104)------------------------------
% 0.22/0.31 % (897104)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (897104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (897104)CaDiCaL version: 2.1.3
% 0.22/0.31 % (897104)Termination reason: Refutation
% 0.22/0.31 % (897104)Time elapsed: 0.011 s
% 0.22/0.31 % (897104)Peak memory usage: 13 MB
% 0.22/0.31 % (897104)Instructions burned: 19 (million)
% 0.22/0.31 % (897099)Success in time 0.054 s
% 0.22/0.31 % Vampire exiting
%------------------------------------------------------------------------------