%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV086^5 : 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 : n015.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 08:37:37 AM UTC 2026
% Result : Theorem 0.26s 0.34s
% Output : Refutation 0.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV086^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n015.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 15:10:18 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.28 Running higher-order theorem proving
% 0.26/0.29 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
% 0.26/0.34 % (3642796)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.26/0.34 % (3642805)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3378321029:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.26/0.34 % (3642802)lrs+10_16_si=on:nwc=1.5:random_seed=1535704393:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.26/0.34 % (3642807)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.26/0.34 % (3642807)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
% 0.26/0.34 % (3642805) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3642796-3642805"...
% 0.26/0.34 % (3642801)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2954750467:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.26/0.34 % (3642806)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1791122292:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.26/0.34 % (3642804)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=1345864781: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)
% 0.26/0.34 % (3642805)...printing done.
% 0.26/0.34 % (3642803)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2383298616:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.26/0.34 % (3642807)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=2938999990:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.26/0.34 % (3642802)Instruction limit reached!
% 0.26/0.34 % (3642802)------------------------------
% 0.26/0.34 % (3642802)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.34 % (3642802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.34 % (3642802)CaDiCaL version: 2.1.3
% 0.26/0.34 % (3642802)Termination reason: Instruction limit
% 0.26/0.34 % (3642802)Termination phase: Saturation
% 0.26/0.34 % (3642802)Time elapsed: 0.012 s
% 0.26/0.34 % (3642802)Peak memory usage: 12 MB
% 0.26/0.34 % (3642802)Instructions burned: 20 (million)
% 0.26/0.34 % (3642805)Refutation found. Thanks to Tanya!
% 0.26/0.34 % SZS status Theorem for theBenchmark
% 0.26/0.34 % SZS output start Proof for theBenchmark
% 0.26/0.34 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.26/0.34 thf(func_def_3, type, sP0: ((($i > $o) > ($i > $o) > $o) > $o)).
% 0.26/0.34 thf(func_def_4, type, sK1: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.26/0.34 thf(func_def_5, type, sK2: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.26/0.34 thf(func_def_6, type, sK3: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.26/0.34 thf(func_def_7, type, sK4: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.26/0.34 thf(func_def_8, type, sK5: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.26/0.34 thf(func_def_9, type, sK6: ((($i > $o) > ($i > $o) > $o) > $i)).
% 0.26/0.34 thf(func_def_10, type, sK7: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.26/0.34 thf(func_def_11, type, vNOT: ($o > $o)).
% 0.26/0.34 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.26/0.34 thf(func_def_13, type, db1: !>[X0: $tType]:(X0)).
% 0.26/0.34 thf(func_def_14, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.26/0.34 thf(func_def_15, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.26/0.34 thf(func_def_17, type, db2: !>[X0: $tType]:(X0)).
% 0.26/0.34 thf(f1,conjecture,(
% 0.26/0.34 ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o)] : (X0 @ X1 @ X1) & ! [X1 : ($i > $o),X3 : ($i > $o),X2 : ($i > $o)] : (((X0 @ X2 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X1 @ X3)) & ! [X5 : ($i > $o),X4 : ($i > $o)] : (((X0 @ X5 @ X4) & (X0 @ X4 @ X5)) => ! [X1 : $i] : ((X5 @ X1) <=> (X4 @ X1))))),
% 0.26/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM120I_pme)).
% 0.26/0.34 thf(f2,negated_conjecture,(
% 0.26/0.34 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o)] : (X0 @ X1 @ X1) & ! [X1 : ($i > $o),X3 : ($i > $o),X2 : ($i > $o)] : (((X0 @ X2 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X1 @ X3)) & ! [X5 : ($i > $o),X4 : ($i > $o)] : (((X0 @ X5 @ X4) & (X0 @ X4 @ X5)) => ! [X1 : $i] : ((X5 @ X1) <=> (X4 @ X1))))),
% 0.26/0.34 inference(negated_conjecture,[status(cth)],[f1])).
% 0.26/0.34 thf(f3,plain,(
% 0.26/0.34 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o)] : (X0 @ X1 @ X1) & ! [X2 : ($i > $o),X3 : ($i > $o),X4 : ($i > $o)] : (((X0 @ X4 @ X3) & (X0 @ X2 @ X4)) => (X0 @ X2 @ X3)) & ! [X5 : ($i > $o),X6 : ($i > $o)] : (((X0 @ X5 @ X6) & (X0 @ X6 @ X5)) => ! [X7 : $i] : ((X5 @ X7) <=> (X6 @ X7))))),
% 0.26/0.34 inference(rectify,[],[f2])).
% 0.26/0.34 thf(f4,plain,(
% 0.26/0.34 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X6 : ($i > $o),X5 : ($i > $o)] : (((((X0 @ X6 @ X5)) = $true) & ($true = ((X0 @ X5 @ X6)))) => ! [X7 : $i] : (((X6 @ X7)) = ((X5 @ X7)))) & ! [X1 : ($i > $o)] : (((X0 @ X1 @ X1)) = $true) & ! [X2 : ($i > $o),X4 : ($i > $o),X3 : ($i > $o)] : ((($true = ((X0 @ X4 @ X3))) & ($true = ((X0 @ X2 @ X4)))) => (((X0 @ X2 @ X3)) = $true)))),
% 0.26/0.34 inference(fool_elimination,[],[f3])).
% 0.26/0.34 thf(f5,plain,(
% 0.26/0.34 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X6 : ($i > $o),X5 : ($i > $o)] : (? [X7 : $i] : (((X6 @ X7)) != ((X5 @ X7))) & ((((X0 @ X6 @ X5)) = $true) & ($true = ((X0 @ X5 @ X6))))) | ? [X1 : ($i > $o)] : (((X0 @ X1 @ X1)) != $true) | ? [X2 : ($i > $o),X4 : ($i > $o),X3 : ($i > $o)] : ((((X0 @ X2 @ X3)) != $true) & (($true = ((X0 @ X4 @ X3))) & ($true = ((X0 @ X2 @ X4))))))),
% 0.26/0.34 inference(ennf_transformation,[],[f4])).
% 0.26/0.34 thf(f6,plain,(
% 0.26/0.34 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X6 : ($i > $o),X5 : ($i > $o)] : (? [X7 : $i] : (((X6 @ X7)) != ((X5 @ X7))) & ($true = ((X0 @ X5 @ X6))) & (((X0 @ X6 @ X5)) = $true)) | ? [X2 : ($i > $o),X4 : ($i > $o),X3 : ($i > $o)] : ((((X0 @ X2 @ X3)) != $true) & ($true = ((X0 @ X4 @ X3))) & ($true = ((X0 @ X2 @ X4)))) | ? [X1 : ($i > $o)] : (((X0 @ X1 @ X1)) != $true))),
% 0.26/0.34 inference(flattening,[],[f5])).
% 0.26/0.34 thf(f7,definition,(
% 0.26/0.34 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X2 : ($i > $o),X4 : ($i > $o),X3 : ($i > $o)] : ((((X0 @ X2 @ X3)) != $true) & ($true = ((X0 @ X4 @ X3))) & ($true = ((X0 @ X2 @ X4)))) | ~ ($true = ((sP0 @ X0))))),
% 0.26/0.34 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.26/0.34 thf(f8,plain,(
% 0.26/0.34 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X6 : ($i > $o),X5 : ($i > $o)] : (? [X7 : $i] : (((X6 @ X7)) != ((X5 @ X7))) & ($true = ((X0 @ X5 @ X6))) & (((X0 @ X6 @ X5)) = $true)) | ($true = ((sP0 @ X0))) | ? [X1 : ($i > $o)] : (((X0 @ X1 @ X1)) != $true))),
% 0.26/0.34 inference(definition_folding,[],[f6,f7])).
% 0.26/0.34 thf(f9,plain,(
% 0.26/0.34 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X2 : ($i > $o),X4 : ($i > $o),X3 : ($i > $o)] : ((((X0 @ X2 @ X3)) != $true) & ($true = ((X0 @ X4 @ X3))) & ($true = ((X0 @ X2 @ X4)))) | ($true != ((sP0 @ X0))))),
% 0.26/0.34 inference(nnf_transformation,[],[f7])).
% 0.26/0.34 thf(f10,plain,(
% 0.26/0.34 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : ((((X0 @ X1 @ X3)) != $true) & (((X0 @ X2 @ X3)) = $true) & (((X0 @ X1 @ X2)) = $true)) | ($true != ((sP0 @ X0))))),
% 0.26/0.34 inference(rectify,[],[f9])).
% 0.26/0.34 thf(f11,plain,(
% 0.26/0.34 ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((($true != ((X0 @ (sK1 @ X0) @ (sK3 @ X0)))) & ($true = ((X0 @ (sK2 @ X0) @ (sK3 @ X0)))) & ($true = ((X0 @ (sK1 @ X0) @ (sK2 @ X0))))) | ($true != ((sP0 @ X0))))),
% 0.26/0.34 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP]),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0)],[f10])).
% 0.26/0.34 thf(f12,plain,(
% 0.26/0.34 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o),X2 : ($i > $o)] : (? [X3 : $i] : (((X2 @ X3)) != ((X1 @ X3))) & ($true = ((X0 @ X2 @ X1))) & (((X0 @ X1 @ X2)) = $true)) | ($true = ((sP0 @ X0))) | ? [X4 : ($i > $o)] : ($true != ((X0 @ X4 @ X4))))),
% 0.26/0.34 inference(rectify,[],[f8])).
% 0.26/0.34 thf(f13,plain,(
% 0.26/0.34 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (((((sK4 @ X0 @ (sK6 @ X0))) != ((sK5 @ X0 @ (sK6 @ X0)))) & ($true = ((X0 @ (sK5 @ X0) @ (sK4 @ X0)))) & ($true = ((X0 @ (sK4 @ X0) @ (sK5 @ X0))))) | ($true = ((sP0 @ X0))) | ($true != ((X0 @ (sK7 @ X0) @ (sK7 @ X0)))))),
% 0.26/0.34 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP]),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0)],[f12])).
% 0.26/0.34 thf(f14,plain,(
% 0.26/0.34 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true = ((X0 @ (sK1 @ X0) @ (sK2 @ X0)))) | ($true != ((sP0 @ X0)))) )),
% 0.26/0.34 inference(cnf_transformation,[],[f11])).
% 0.26/0.34 thf(f15,plain,(
% 0.26/0.34 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true = ((X0 @ (sK2 @ X0) @ (sK3 @ X0)))) | ($true != ((sP0 @ X0)))) )),
% 0.26/0.34 inference(cnf_transformation,[],[f11])).
% 0.26/0.34 thf(f16,plain,(
% 0.26/0.34 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true != ((X0 @ (sK1 @ X0) @ (sK3 @ X0)))) | ($true != ((sP0 @ X0)))) )),
% 0.26/0.34 inference(cnf_transformation,[],[f11])).
% 0.26/0.34 thf(f17,plain,(
% 0.26/0.34 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true = ((X0 @ (sK4 @ X0) @ (sK5 @ X0)))) | ($true != ((X0 @ (sK7 @ X0) @ (sK7 @ X0)))) | ($true = ((sP0 @ X0)))) )),
% 0.26/0.34 inference(cnf_transformation,[],[f13])).
% 0.26/0.34 thf(f19,plain,(
% 0.26/0.34 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true = ((sP0 @ X0))) | ($true != ((X0 @ (sK7 @ X0) @ (sK7 @ X0)))) | (((sK4 @ X0 @ (sK6 @ X0))) != ((sK5 @ X0 @ (sK6 @ X0))))) )),
% 0.26/0.34 inference(cnf_transformation,[],[f13])).
% 0.26/0.34 thf(f21,plain,(
% 0.26/0.34 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true != ((X0 @ (sK7 @ X0) @ (sK7 @ X0)))) | ($true = ((sK5 @ X0 @ (sK6 @ X0)))) | ($true = ((sK4 @ X0 @ (sK6 @ X0)))) | ($true = ((sP0 @ X0)))) )),
% 0.26/0.34 inference(xor_proxy_clausification,[],[f19])).
% 0.26/0.34 thf(f22,plain,(
% 0.26/0.34 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true != ((X0 @ (sK7 @ X0) @ (sK7 @ X0)))) | ($true = ((sP0 @ X0))) | (((sK4 @ X0 @ (sK6 @ X0))) = $false) | ($false = ((sK5 @ X0 @ (sK6 @ X0))))) )),
% 0.26/0.34 inference(xor_proxy_clausification,[],[f19])).
% 0.26/0.34 thf(f23,plain,(
% 0.26/0.34 ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | (((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))) = $true) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))))),
% 0.26/0.34 inference(primitive_instantiation,[],[f17])).
% 0.26/0.34 thf(f28,plain,(
% 0.26/0.34 ($true = ((sP0 @ =))) | ($true = (((sK4 @ =) = (sK5 @ =)))) | ($true != (((sK7 @ =) = (sK7 @ =))))),
% 0.26/0.34 inference(beta-eta_normalization,[],[f23])).
% 0.26/0.34 thf(f29,plain,(
% 0.26/0.34 ($true = ((sP0 @ =))) | (((sK4 @ =)) = ((sK5 @ =))) | ($true != (((sK7 @ =) = (sK7 @ =))))),
% 0.26/0.34 inference(equality_proxy_clausification,[],[f28])).
% 0.26/0.34 thf(f30,plain,(
% 0.26/0.34 (((sK4 @ =)) = ((sK5 @ =))) | ($true = ((sP0 @ =))) | (((sK7 @ =)) != ((sK7 @ =)))),
% 0.26/0.34 inference(equality_proxy_clausification,[],[f29])).
% 0.26/0.34 thf(f31,plain,(
% 0.26/0.34 (((sK4 @ =)) = ((sK5 @ =))) | ($true = ((sP0 @ =)))),
% 0.26/0.34 inference(trivial_inequality_removal,[],[f30])).
% 0.26/0.34 thf(f42,plain,(
% 0.26/0.34 ( ! [X1 : $i] : (($true = ((sP0 @ =))) | (((sK5 @ = @ X1)) = ((sK4 @ = @ X1)))) )),
% 0.26/0.34 inference(argument_congruence,[],[f31])).
% 0.26/0.34 thf(f44,plain,(
% 0.26/0.34 ( ! [X1 : $i] : ((((sK5 @ = @ X1)) = $true) | ($false = ((sK4 @ = @ X1))) | ($true = ((sP0 @ =)))) )),
% 0.26/0.34 inference(iff_proxy_clausification,[],[f42])).
% 0.26/0.34 thf(f45,plain,(
% 0.26/0.34 ( ! [X1 : $i] : ((((sK5 @ = @ X1)) = $false) | ($true = ((sP0 @ =))) | ($true = ((sK4 @ = @ X1)))) )),
% 0.26/0.34 inference(iff_proxy_clausification,[],[f42])).
% 0.26/0.34 thf(f79,plain,(
% 0.26/0.34 (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) = $true) | (((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))) = $true) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ($true = ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))))),
% 0.26/0.34 inference(primitive_instantiation,[],[f21])).
% 0.26/0.34 thf(f93,plain,(
% 0.26/0.34 ($true = ((sK4 @ = @ (sK6 @ =)))) | ($true = ((sK5 @ = @ (sK6 @ =)))) | ($true != (((sK7 @ =) = (sK7 @ =)))) | ($true = ((sP0 @ =)))),
% 0.26/0.34 inference(beta-eta_normalization,[],[f79])).
% 0.26/0.34 thf(f94,plain,(
% 0.26/0.34 ($true = ((sK4 @ = @ (sK6 @ =)))) | ($true = ((sP0 @ =))) | ($true = ((sK5 @ = @ (sK6 @ =)))) | (((sK7 @ =)) != ((sK7 @ =)))),
% 0.26/0.34 inference(equality_proxy_clausification,[],[f93])).
% 0.26/0.34 thf(f95,plain,(
% 0.26/0.34 ($true = ((sK5 @ = @ (sK6 @ =)))) | ($true = ((sP0 @ =))) | ($true = ((sK4 @ = @ (sK6 @ =))))),
% 0.26/0.34 inference(trivial_inequality_removal,[],[f94])).
% 0.26/0.34 thf(f98,plain,(
% 0.26/0.34 ($true = ((sK4 @ = @ (sK6 @ =)))) | ($true = ((sP0 @ =))) | ($true = ((sP0 @ =))) | ($true = ((sK4 @ = @ (sK6 @ =)))) | ($true = $false)),
% 0.26/0.34 inference(superposition,[],[f95,f45])).
% 0.26/0.34 thf(f100,plain,(
% 0.26/0.34 ($true = $false) | ($true = ((sK4 @ = @ (sK6 @ =)))) | ($true = ((sP0 @ =)))),
% 0.26/0.34 inference(duplicate_literal_removal,[],[f98])).
% 0.26/0.34 thf(f101,plain,(
% 0.26/0.34 ($true = ((sK4 @ = @ (sK6 @ =)))) | ($true = ((sP0 @ =)))),
% 0.26/0.34 inference(trivial_inequality_removal,[],[f100])).
% 0.26/0.34 thf(f104,plain,(
% 0.26/0.34 ($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)))))))) | (((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))) != $true)),
% 0.26/0.34 inference(primitive_instantiation,[],[f14])).
% 0.26/0.34 thf(f116,plain,(
% 0.26/0.34 ($true = (((sK1 @ =) = (sK2 @ =)))) | ($true != ((sP0 @ =)))),
% 0.26/0.34 inference(beta-eta_normalization,[],[f104])).
% 0.26/0.34 thf(f117,plain,(
% 0.26/0.34 ($true != ((sP0 @ =))) | (((sK1 @ =)) = ((sK2 @ =)))),
% 0.26/0.34 inference(equality_proxy_clausification,[],[f116])).
% 0.26/0.34 thf(f119,plain,(
% 0.26/0.34 ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) = $false) | (((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))) = $true) | (((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) = $false)),
% 0.26/0.34 inference(primitive_instantiation,[],[f22])).
% 0.26/0.34 thf(f125,plain,(
% 0.26/0.34 ($true != (((sK7 @ =) = (sK7 @ =)))) | ($false = ((sK5 @ = @ (sK6 @ =)))) | ($true = ((sP0 @ =))) | ($false = ((sK4 @ = @ (sK6 @ =))))),
% 0.26/0.34 inference(beta-eta_normalization,[],[f119])).
% 0.26/0.34 thf(f126,plain,(
% 0.26/0.34 ($false = ((sK4 @ = @ (sK6 @ =)))) | ($true = ((sP0 @ =))) | ($false = ((sK5 @ = @ (sK6 @ =)))) | (((sK7 @ =)) != ((sK7 @ =)))),
% 0.26/0.34 inference(equality_proxy_clausification,[],[f125])).
% 0.26/0.34 thf(f127,plain,(
% 0.26/0.34 ($false = ((sK5 @ = @ (sK6 @ =)))) | ($true = ((sP0 @ =))) | ($false = ((sK4 @ = @ (sK6 @ =))))),
% 0.26/0.34 inference(trivial_inequality_removal,[],[f126])).
% 0.26/0.34 thf(f139,plain,(
% 0.26/0.34 ($false = ((sK4 @ = @ (sK6 @ =)))) | ($true = ((sP0 @ =))) | ($true = ((sP0 @ =))) | ($false = ((sK4 @ = @ (sK6 @ =)))) | ($true = $false)),
% 0.26/0.34 inference(superposition,[],[f127,f44])).
% 0.26/0.34 thf(f144,plain,(
% 0.26/0.34 ($true = ((sP0 @ =))) | ($false = ((sK4 @ = @ (sK6 @ =)))) | ($true = $false)),
% 0.26/0.34 inference(duplicate_literal_removal,[],[f139])).
% 0.26/0.34 thf(f145,plain,(
% 0.26/0.34 ($false = ((sK4 @ = @ (sK6 @ =)))) | ($true = ((sP0 @ =)))),
% 0.26/0.34 inference(trivial_inequality_removal,[],[f144])).
% 0.26/0.34 thf(f152,plain,(
% 0.26/0.34 ($true = $false) | ($true = ((sP0 @ =))) | ($true = ((sP0 @ =)))),
% 0.26/0.34 inference(superposition,[],[f101,f145])).
% 0.26/0.34 thf(f153,plain,(
% 0.26/0.34 ($true = ((sP0 @ =))) | ($true = $false)),
% 0.26/0.34 inference(duplicate_literal_removal,[],[f152])).
% 0.26/0.34 thf(f154,plain,(
% 0.26/0.34 ($true = ((sP0 @ =)))),
% 0.26/0.34 inference(trivial_inequality_removal,[],[f153])).
% 0.26/0.34 thf(f159,plain,(
% 0.26/0.34 (((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))) != $true) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))))),
% 0.26/0.34 inference(primitive_instantiation,[],[f15])).
% 0.26/0.34 thf(f172,plain,(
% 0.26/0.34 ($true != ((sP0 @ =))) | ((((sK2 @ =) = (sK3 @ =))) = $true)),
% 0.26/0.34 inference(beta-eta_normalization,[],[f159])).
% 0.26/0.34 thf(f173,plain,(
% 0.26/0.34 (((sK3 @ =)) = ((sK2 @ =))) | ($true != ((sP0 @ =)))),
% 0.26/0.34 inference(equality_proxy_clausification,[],[f172])).
% 0.26/0.34 thf(f174,plain,(
% 0.26/0.34 (((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))) != $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))))))) != $true)),
% 0.26/0.34 inference(primitive_instantiation,[],[f16])).
% 0.26/0.34 thf(f190,plain,(
% 0.26/0.34 ($true != ((sP0 @ =))) | ($true != (((sK1 @ =) = (sK3 @ =))))),
% 0.26/0.34 inference(beta-eta_normalization,[],[f174])).
% 0.26/0.34 thf(f191,plain,(
% 0.26/0.34 (((sK1 @ =)) != ((sK3 @ =))) | ($true != ((sP0 @ =)))),
% 0.26/0.34 inference(equality_proxy_clausification,[],[f190])).
% 0.26/0.34 thf(f192,plain,(
% 0.26/0.34 (((sK1 @ =)) != ((sK3 @ =)))),
% 0.26/0.34 inference(forward_subsumption_resolution,[],[f191,f154])).
% 0.26/0.34 thf(f345,plain,(
% 0.26/0.34 (((sK1 @ =)) = ((sK2 @ =)))),
% 0.26/0.34 inference(forward_subsumption_resolution,[],[f117,f154])).
% 0.26/0.34 thf(f347,plain,(
% 0.26/0.34 (((sK3 @ =)) != ((sK2 @ =)))),
% 0.26/0.34 inference(superposition,[],[f192,f345])).
% 0.26/0.34 thf(f362,plain,(
% 0.26/0.34 ($true != ((sP0 @ =)))),
% 0.26/0.34 inference(forward_subsumption_resolution,[],[f173,f347])).
% 0.26/0.34 thf(f363,plain,(
% 0.26/0.34 $false),
% 0.26/0.34 inference(forward_subsumption_resolution,[],[f362,f154])).
% 0.26/0.34 % SZS output end Proof for theBenchmark
% 0.26/0.34 % (3642805)------------------------------
% 0.26/0.34 % (3642805)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.34 % (3642805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.34 % (3642805)CaDiCaL version: 2.1.3
% 0.26/0.34 % (3642805)Termination reason: Refutation
% 0.26/0.34 % (3642805)Time elapsed: 0.013 s
% 0.26/0.34 % (3642805)Peak memory usage: 12 MB
% 0.26/0.34 % (3642805)Instructions burned: 26 (million)
% 0.26/0.34 % (3642796)Success in time 0.037 s
% 0.26/0.34 % Vampire exiting
%------------------------------------------------------------------------------