%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV052^5 : 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 : n009.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 08:37:33 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 : SEV052^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n009.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 15:05:31 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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 % (4113502)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (4113508)lrs+10_16_si=on:nwc=1.5:random_seed=2986990173:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.28 % (4113513)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 % (4113513)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 % (4113508)Instruction limit reached!
% 0.20/0.28 % (4113508)------------------------------
% 0.20/0.28 % (4113508)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (4113508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (4113508)CaDiCaL version: 2.1.3
% 0.20/0.28 % (4113508)Termination reason: Instruction limit
% 0.20/0.28 % (4113508)Termination phase: Saturation
% 0.20/0.28 % (4113508)Time elapsed: 0.006 s
% 0.20/0.28 % (4113508)Peak memory usage: 12 MB
% 0.20/0.28 % (4113508)Instructions burned: 20 (million)
% 0.20/0.28 % (4113507)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4141186890:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28 % (4113509)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=783085877:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.28 % (4113512)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=645778561:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.28 % (4113511)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4173952996:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.28 % (4113510)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=2511267941: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 % (4113513)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=2037862121:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.28 % (4113509)Instruction limit reached!
% 0.20/0.28 % (4113509)------------------------------
% 0.20/0.28 % (4113509)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (4113509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (4113509)CaDiCaL version: 2.1.3
% 0.20/0.28 % (4113509)Termination reason: Instruction limit
% 0.20/0.28 % (4113509)Termination phase: Saturation
% 0.20/0.28 % (4113509)Time elapsed: 0.003 s
% 0.20/0.28 % (4113509)Peak memory usage: 12 MB
% 0.20/0.28 % (4113509)Instructions burned: 5 (million)
% 0.20/0.28 % (4113507) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4113502-4113507"...
% 0.20/0.28 % (4113513)Refutation not found, incomplete strategy
% 0.20/0.28 % (4113513)------------------------------
% 0.20/0.28 % (4113513)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (4113513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (4113513)CaDiCaL version: 2.1.3
% 0.20/0.28 % (4113513)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.28 % (4113513)Time elapsed: 0.003 s
% 0.20/0.28 % (4113513)Peak memory usage: 12 MB
% 0.20/0.28 % (4113513)Instructions burned: 4 (million)
% 0.20/0.28 % (4113511) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4113502-4113511"...
% 0.20/0.28 % (4113510) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4113502-4113510"...
% 0.20/0.28 % (4113513)------------------------------
% 0.20/0.28 % (4113513)------------------------------
% 0.20/0.28 % (4113511)...printing done.
% 0.20/0.28 % (4113507)...printing done.
% 0.20/0.28 % (4113510)...printing done.
% 0.20/0.28 % (4113511)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, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.28 thf(func_def_4, type, sK0: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.20/0.28 thf(func_def_5, type, sK1: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.20/0.28 thf(func_def_6, type, sK2: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.20/0.28 thf(func_def_7, type, sK3: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.20/0.28 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.20/0.28 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.28 thf(func_def_10, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.28 thf(func_def_11, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.28 thf(f1,conjecture,(
% 0.20/0.28 ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o),X3 : ($i > $o),X2 : ($i > $o)] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3)) & ! [X1 : ($i > $o)] : (X0 @ X1 @ X1) & ~(X0 @ (^[X1 : $i] : ($true)) @ (^[X1 : $i] : ($false))))),
% 0.20/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM120B_pme)).
% 0.20/0.28 thf(f2,negated_conjecture,(
% 0.20/0.28 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o),X3 : ($i > $o),X2 : ($i > $o)] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3)) & ! [X1 : ($i > $o)] : (X0 @ X1 @ X1) & ~(X0 @ (^[X1 : $i] : ($true)) @ (^[X1 : $i] : ($false))))),
% 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 > $o),X3 : ($i > $o)] : (((X0 @ X1 @ X3) & (X0 @ X3 @ X2)) => (X0 @ X1 @ X2)) & ! [X4 : ($i > $o)] : (X0 @ X4 @ X4) & ~(X0 @ (^[X5 : $i] : ($true)) @ (^[X6 : $i] : ($false))))),
% 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 > $o),X3 : ($i > $o),X1 : ($i > $o)] : ((($true = ((X0 @ X3 @ X2))) & (((X0 @ X1 @ X3)) = $true)) => (((X0 @ X1 @ X2)) = $true)) & ! [X4 : ($i > $o)] : (((X0 @ X4 @ X4)) = $true) & ~ (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true))),
% 0.20/0.28 inference(fool_elimination,[],[f3])).
% 0.20/0.28 thf(f5,plain,(
% 0.20/0.28 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) != $true) & ! [X2 : ($i > $o),X3 : ($i > $o),X1 : ($i > $o)] : ((($true = ((X0 @ X3 @ X2))) & (((X0 @ X1 @ X3)) = $true)) => (((X0 @ X1 @ X2)) = $true)) & ! [X4 : ($i > $o)] : (((X0 @ X4 @ X4)) = $true))),
% 0.20/0.28 inference(flattening,[],[f4])).
% 0.20/0.28 thf(f6,plain,(
% 0.20/0.28 ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true) | ? [X2 : ($i > $o),X3 : ($i > $o),X1 : ($i > $o)] : ((((X0 @ X1 @ X2)) != $true) & (($true = ((X0 @ X3 @ X2))) & (((X0 @ X1 @ X3)) = $true))) | ? [X4 : ($i > $o)] : (((X0 @ X4 @ X4)) != $true))),
% 0.20/0.28 inference(ennf_transformation,[],[f5])).
% 0.20/0.28 thf(f7,plain,(
% 0.20/0.28 ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true) | ? [X1 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : ((((X0 @ X1 @ X3)) = $true) & (((X0 @ X1 @ X2)) != $true) & ($true = ((X0 @ X3 @ X2)))) | ? [X4 : ($i > $o)] : (((X0 @ X4 @ X4)) != $true))),
% 0.20/0.28 inference(flattening,[],[f6])).
% 0.20/0.28 thf(f8,plain,(
% 0.20/0.28 ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true) | (($true = ((X0 @ (sK0 @ X0) @ (sK2 @ X0)))) & (((X0 @ (sK0 @ X0) @ (sK1 @ X0))) != $true) & ($true = ((X0 @ (sK2 @ X0) @ (sK1 @ X0))))) | (((X0 @ (sK3 @ X0) @ (sK3 @ X0))) != $true))),
% 0.20/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP]),skolemize(X4,sK3 @ X0),skolemize(X4,sK3 @ X0),skolemize(X4,sK3 @ X0),skolemize(X4,sK3 @ X0)],[f7])).
% 0.20/0.28 thf(f9,plain,(
% 0.20/0.28 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true = ((X0 @ (sK2 @ X0) @ (sK1 @ X0)))) | (((X0 @ (sK3 @ X0) @ (sK3 @ X0))) != $true) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true)) )),
% 0.20/0.28 inference(cnf_transformation,[],[f8])).
% 0.20/0.28 thf(f10,plain,(
% 0.20/0.28 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (sK0 @ X0) @ (sK1 @ X0))) != $true) | (((X0 @ (sK3 @ X0) @ (sK3 @ X0))) != $true) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true)) )),
% 0.20/0.28 inference(cnf_transformation,[],[f8])).
% 0.20/0.28 thf(f11,plain,(
% 0.20/0.28 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true = ((X0 @ (sK0 @ X0) @ (sK2 @ X0)))) | (((X0 @ (sK3 @ X0) @ (sK3 @ X0))) != $true) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true)) )),
% 0.20/0.28 inference(cnf_transformation,[],[f8])).
% 0.20/0.28 thf(f13,plain,(
% 0.20/0.28 ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK3 @ (^[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)))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true)),
% 0.20/0.28 inference(primitive_instantiation,[],[f9])).
% 0.20/0.28 thf(f29,plain,(
% 0.20/0.28 ((((sK2 @ =) = (sK1 @ =))) = $true) | ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true) | ((((sK3 @ =) = (sK3 @ =))) != $true)),
% 0.20/0.28 inference(beta-eta_normalization,[],[f13])).
% 0.20/0.28 thf(f30,plain,(
% 0.20/0.28 ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true) | ((((sK3 @ =) = (sK3 @ =))) != $true) | (((sK1 @ =)) = ((sK2 @ =)))),
% 0.20/0.28 inference(equality_proxy_clausification,[],[f29])).
% 0.20/0.28 thf(f31,plain,(
% 0.20/0.28 (((sK1 @ =)) = ((sK2 @ =))) | ((((sK3 @ =) = (sK3 @ =))) != $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
% 0.20/0.28 inference(equality_proxy_clausification,[],[f30])).
% 0.20/0.28 thf(f32,plain,(
% 0.20/0.28 (((sK3 @ =)) != ((sK3 @ =))) | (((sK1 @ =)) = ((sK2 @ =))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
% 0.20/0.28 inference(equality_proxy_clausification,[],[f31])).
% 0.20/0.28 thf(f33,plain,(
% 0.20/0.28 (((sK1 @ =)) = ((sK2 @ =))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f32])).
% 0.20/0.28 thf(f53,plain,(
% 0.20/0.28 ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true)),
% 0.20/0.28 inference(primitive_instantiation,[],[f10])).
% 0.20/0.28 thf(f59,plain,(
% 0.20/0.28 ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true) | ((((sK3 @ =) = (sK3 @ =))) != $true) | ($true != (((sK0 @ =) = (sK1 @ =))))),
% 0.20/0.28 inference(beta-eta_normalization,[],[f53])).
% 0.20/0.28 thf(f60,plain,(
% 0.20/0.28 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true != (((sK0 @ =) = (sK1 @ =)))) | ((((sK3 @ =) = (sK3 @ =))) != $true)),
% 0.20/0.28 inference(equality_proxy_clausification,[],[f59])).
% 0.20/0.28 thf(f61,plain,(
% 0.20/0.28 (((sK1 @ =)) != ((sK0 @ =))) | ((((sK3 @ =) = (sK3 @ =))) != $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
% 0.20/0.28 inference(equality_proxy_clausification,[],[f60])).
% 0.20/0.28 thf(f62,plain,(
% 0.20/0.28 (((sK1 @ =)) != ((sK0 @ =))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((sK3 @ =)) != ((sK3 @ =)))),
% 0.20/0.28 inference(equality_proxy_clausification,[],[f61])).
% 0.20/0.28 thf(f63,plain,(
% 0.20/0.28 (((sK1 @ =)) != ((sK0 @ =))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f62])).
% 0.20/0.28 thf(f95,plain,(
% 0.20/0.28 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true = (((sK0 @ =) = (sK1 @ =)))) | ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true) | ((((sK3 @ =) = (sK3 @ =))) != $true)),
% 0.20/0.28 inference(superposition,[],[f11,f33])).
% 0.20/0.28 thf(f109,plain,(
% 0.20/0.28 (((sK1 @ =)) = ((sK0 @ =))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true) | ((((sK3 @ =) = (sK3 @ =))) != $true)),
% 0.20/0.28 inference(equality_proxy_clausification,[],[f95])).
% 0.20/0.28 thf(f110,plain,(
% 0.20/0.28 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ((((sK3 @ =) = (sK3 @ =))) != $true) | (((sK1 @ =)) = ((sK0 @ =))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
% 0.20/0.28 inference(equality_proxy_clausification,[],[f109])).
% 0.20/0.28 thf(f111,plain,(
% 0.20/0.28 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((sK3 @ =)) != ((sK3 @ =))) | (((sK1 @ =)) = ((sK0 @ =)))),
% 0.20/0.28 inference(equality_proxy_clausification,[],[f110])).
% 0.20/0.28 thf(f112,plain,(
% 0.20/0.28 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((sK1 @ =)) = ((sK0 @ =))) | (((sK3 @ =)) != ((sK3 @ =)))),
% 0.20/0.28 inference(duplicate_literal_removal,[],[f111])).
% 0.20/0.28 thf(f113,plain,(
% 0.20/0.28 (((sK1 @ =)) = ((sK0 @ =))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f112])).
% 0.20/0.28 thf(f121,plain,(
% 0.20/0.28 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
% 0.20/0.28 inference(forward_subsumption_resolution,[],[f113,f63])).
% 0.20/0.28 thf(f122,plain,(
% 0.20/0.28 ( ! [X1 : $i] : (((((^[Y0 : $i]: ($false)) @ X1)) = (((^[Y0 : $i]: ($true)) @ X1)))) )),
% 0.20/0.28 inference(argument_congruence,[],[f121])).
% 0.20/0.28 thf(f123,plain,(
% 0.20/0.28 ( ! [X1 : $i] : (((((^[Y0 : $i]: ($false)) @ X1)) = $true) | ($false = (((^[Y0 : $i]: ($true)) @ X1)))) )),
% 0.20/0.28 inference(iff_proxy_clausification,[],[f122])).
% 0.20/0.28 thf(f126,plain,(
% 0.20/0.28 ($true = $false) | ($true = $false)),
% 0.20/0.28 inference(beta-eta_normalization,[],[f123])).
% 0.20/0.28 thf(f127,plain,(
% 0.20/0.28 ($true = $false)),
% 0.20/0.28 inference(duplicate_literal_removal,[],[f126])).
% 0.20/0.28 thf(f128,plain,(
% 0.20/0.28 $false),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f127])).
% 0.20/0.28 % SZS output end Proof for theBenchmark
% 0.20/0.28 % (4113511)------------------------------
% 0.20/0.28 % (4113511)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (4113511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (4113511)CaDiCaL version: 2.1.3
% 0.20/0.28 % (4113511)Termination reason: Refutation
% 0.20/0.28 % (4113511)Time elapsed: 0.005 s
% 0.20/0.28 % (4113511)Peak memory usage: 12 MB
% 0.20/0.28 % (4113511)Instructions burned: 9 (million)
% 0.20/0.28 % (4113502)Success in time 0.041 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------