%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO331^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:47:27 AM UTC 2026
% Result : Theorem 0.31s 0.39s
% Output : Refutation 0.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYO331^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.26 % Computer : n007.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Tue Sep 29 16:44:26 UTC 2026
% 0.10/0.27 % CPUTime :
% 0.10/0.27 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.32 Running higher-order theorem proving
% 0.25/0.33 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.31/0.39 % (3621721)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.31/0.39 % (3621727)lrs+10_16_si=on:nwc=1.5:random_seed=2894651786:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.31/0.39 % (3621732)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.31/0.39 % (3621732)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
% 0.31/0.39 % (3621727)Instruction limit reached!
% 0.31/0.39 % (3621727)------------------------------
% 0.31/0.39 % (3621727)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.39 % (3621727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.39 % (3621727)CaDiCaL version: 2.1.3
% 0.31/0.39 % (3621727)Termination reason: Instruction limit
% 0.31/0.39 % (3621727)Termination phase: Saturation
% 0.31/0.39 % (3621727)Time elapsed: 0.010 s
% 0.31/0.39 % (3621727)Peak memory usage: 12 MB
% 0.31/0.39 % (3621727)Instructions burned: 19 (million)
% 0.31/0.39 % (3621728)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2837287881:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.31/0.39 % (3621730)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=327894884:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.31/0.39 % (3621731)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2711284164:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.31/0.39 % (3621729)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=1790229123: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)
% 0.31/0.39 % (3621732)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=2190111600:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.31/0.39 % (3621726)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=532332029:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.31/0.39 % (3621728)Instruction limit reached!
% 0.31/0.39 % (3621728)------------------------------
% 0.31/0.39 % (3621728)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.39 % (3621728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.39 % (3621728)CaDiCaL version: 2.1.3
% 0.31/0.39 % (3621728)Termination reason: Instruction limit
% 0.31/0.39 % (3621728)Termination phase: Saturation
% 0.31/0.39 % (3621728)Time elapsed: 0.004 s
% 0.31/0.39 % (3621728)Peak memory usage: 12 MB
% 0.31/0.39 % (3621728)Instructions burned: 3 (million)
% 0.31/0.39 % (3621730) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3621721-3621730"...
% 0.31/0.39 % (3621730)...printing done.
% 0.31/0.39 % (3621730)Refutation found. Thanks to Tanya!
% 0.31/0.39 % SZS status Theorem for theBenchmark
% 0.31/0.39 % SZS output start Proof for theBenchmark
% 0.31/0.39 thf(type_def_5, type, a: $tType).
% 0.31/0.39 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.31/0.40 thf(func_def_0, type, cK: ((a > $o) > a > $o)).
% 0.31/0.40 thf(func_def_4, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.31/0.40 thf(func_def_5, type, vAND: ($o > $o > $o)).
% 0.31/0.40 thf(func_def_6, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.31/0.40 thf(func_def_7, type, vIMP: ($o > $o > $o)).
% 0.31/0.40 thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 0.31/0.40 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.31/0.40 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.31/0.40 thf(func_def_11, type, sK0: a).
% 0.31/0.40 thf(func_def_12, type, sK1: (a > $o)).
% 0.31/0.40 thf(func_def_13, type, sK2: ((a > $o) > a)).
% 0.31/0.40 thf(func_def_14, type, sK3: ((a > $o) > a)).
% 0.31/0.40 thf(func_def_15, type, vNOT: ($o > $o)).
% 0.31/0.40 thf(func_def_16, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.31/0.40 thf(func_def_17, type, sK4: ((a > $o) > a)).
% 0.31/0.40 thf(func_def_18, type, sK5: ((a > $o) > a)).
% 0.31/0.40 thf(func_def_19, type, sK6: ((a > $o) > a)).
% 0.31/0.40 thf(f1,conjecture,(
% 0.31/0.40 ! [X0 : (a > $o)] : (! [X1 : a] : ((X0 @ X1) => ? [X2 : (a > $o)] : ((X2 @ X1) & ! [X3 : a] : ((X2 @ X3) => (cK @ X2 @ X3)))) => ! [X1 : a] : ((cK @ X0 @ X1) => (cK @ (^[X3 : a] : (? [X2 : (a > $o)] : ((X2 @ X3) & ! [X4 : a] : ((X2 @ X4) => (cK @ X2 @ X4))))) @ X1))) => ! [X1 : a] : (? [X2 : (a > $o)] : (! [X3 : a] : ((X2 @ X3) => (cK @ X2 @ X3)) & (X2 @ X1)) => (cK @ (^[X3 : a] : (? [X2 : (a > $o)] : ((X2 @ X3) & ! [X4 : a] : ((X2 @ X4) => (cK @ X2 @ X4))))) @ X1))),
% 0.31/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM116_2SS_pme)).
% 0.31/0.40 thf(f2,negated_conjecture,(
% 0.31/0.40 ~(! [X0 : (a > $o)] : (! [X1 : a] : ((X0 @ X1) => ? [X2 : (a > $o)] : ((X2 @ X1) & ! [X3 : a] : ((X2 @ X3) => (cK @ X2 @ X3)))) => ! [X1 : a] : ((cK @ X0 @ X1) => (cK @ (^[X3 : a] : (? [X2 : (a > $o)] : ((X2 @ X3) & ! [X4 : a] : ((X2 @ X4) => (cK @ X2 @ X4))))) @ X1))) => ! [X1 : a] : (? [X2 : (a > $o)] : (! [X3 : a] : ((X2 @ X3) => (cK @ X2 @ X3)) & (X2 @ X1)) => (cK @ (^[X3 : a] : (? [X2 : (a > $o)] : ((X2 @ X3) & ! [X4 : a] : ((X2 @ X4) => (cK @ X2 @ X4))))) @ X1)))),
% 0.31/0.40 inference(negated_conjecture,[status(cth)],[f1])).
% 0.31/0.40 thf(f3,plain,(
% 0.31/0.40 ~(! [X0 : (a > $o)] : (! [X1 : a] : ((X0 @ X1) => ? [X2 : (a > $o)] : ((X2 @ X1) & ! [X3 : a] : ((X2 @ X3) => (cK @ X2 @ X3)))) => ! [X4 : a] : ((cK @ X0 @ X4) => (cK @ (^[X5 : a] : (? [X6 : (a > $o)] : ((X6 @ X5) & ! [X7 : a] : ((X6 @ X7) => (cK @ X6 @ X7))))) @ X4))) => ! [X8 : a] : (? [X9 : (a > $o)] : (! [X10 : a] : ((X9 @ X10) => (cK @ X9 @ X10)) & (X9 @ X8)) => (cK @ (^[X11 : a] : (? [X12 : (a > $o)] : ((X12 @ X11) & ! [X13 : a] : ((X12 @ X13) => (cK @ X12 @ X13))))) @ X8)))),
% 0.31/0.40 inference(rectify,[],[f2])).
% 0.31/0.40 thf(f4,plain,(
% 0.31/0.40 ~(! [X0 : (a > $o)] : (! [X1 : a] : ((((X0 @ X1)) = $true) => ? [X2 : (a > $o)] : ((((X2 @ X1)) = $true) & ! [X3 : a] : ((((X2 @ X3)) = $true) => (((cK @ X2 @ X3)) = $true)))) => ! [X4 : a] : (($true = ((cK @ X0 @ X4))) => (((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4)) = $true))) => ! [X8 : a] : (? [X9 : (a > $o)] : (! [X10 : a] : (($true = ((X9 @ X10))) => ($true = ((cK @ X9 @ X10)))) & (((X9 @ X8)) = $true)) => (((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X8)) = $true)))),
% 0.31/0.40 inference(fool_elimination,[],[f3])).
% 0.31/0.40 thf(f5,plain,(
% 0.31/0.40 ~(! [X0 : (a > $o)] : (! [X1 : a] : ((((X0 @ X1)) = $true) => ? [X2 : (a > $o)] : ((((X2 @ X1)) = $true) & ! [X3 : a] : ((((X2 @ X3)) = $true) => (((cK @ X2 @ X3)) = $true)))) => ! [X4 : a] : (($true = ((cK @ X0 @ X4))) => (((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4)) = $true))) => ! [X5 : a] : (? [X6 : (a > $o)] : (! [X7 : a] : (($true = ((X6 @ X7))) => ($true = ((cK @ X6 @ X7)))) & (((X6 @ X5)) = $true)) => ($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X5)))))),
% 0.31/0.40 inference(rectify,[],[f4])).
% 0.31/0.40 thf(f6,plain,(
% 0.31/0.40 ? [X5 : a] : (? [X6 : (a > $o)] : (! [X7 : a] : (($true = ((cK @ X6 @ X7))) | ($true != ((X6 @ X7)))) & (((X6 @ X5)) = $true)) & ($true != ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X5)))) & ! [X0 : (a > $o)] : (? [X1 : a] : (! [X2 : (a > $o)] : ((((X2 @ X1)) != $true) | ? [X3 : a] : ((((X2 @ X3)) = $true) & (((cK @ X2 @ X3)) != $true))) & (((X0 @ X1)) = $true)) | ! [X4 : a] : (($true != ((cK @ X0 @ X4))) | (((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4)) = $true)))),
% 0.31/0.40 inference(ennf_transformation,[],[f5])).
% 0.31/0.40 thf(f7,plain,(
% 0.31/0.40 ? [X0 : a] : (? [X1 : (a > $o)] : (! [X2 : a] : (($true = ((cK @ X1 @ X2))) | ($true != ((X1 @ X2)))) & (((X1 @ X0)) = $true)) & ($true != ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X0)))) & ! [X3 : (a > $o)] : (? [X4 : a] : (! [X5 : (a > $o)] : (($true != ((X5 @ X4))) | ? [X6 : a] : ((((X5 @ X6)) = $true) & ($true != ((cK @ X5 @ X6))))) & (((X3 @ X4)) = $true)) | ! [X7 : a] : (($true != ((cK @ X3 @ X7))) | (((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X7)) = $true)))),
% 0.31/0.40 inference(rectify,[],[f6])).
% 0.31/0.40 thf(f8,plain,(
% 0.31/0.40 ((! [X2 : a] : (($true = ((cK @ sK1 @ X2))) | (((sK1 @ X2)) != $true)) & ($true = ((sK1 @ sK0)))) & ($true != ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK0)))) & ! [X3 : (a > $o)] : ((! [X5 : (a > $o)] : ((((X5 @ (sK2 @ X3))) != $true) | (($true = ((X5 @ (sK3 @ X5)))) & ($true != ((cK @ X5 @ (sK3 @ X5)))))) & (((X3 @ (sK2 @ X3))) = $true)) | ! [X7 : a] : (($true != ((cK @ X3 @ X7))) | (((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X7)) = $true)))),
% 0.31/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X6,sK3 @ X5),skolemize(X6,sK3 @ X5)],[f7])).
% 0.31/0.40 thf(f9,plain,(
% 0.31/0.40 ( ! [X3 : (a > $o),X7 : a] : (($true != ((cK @ X3 @ X7))) | (((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X7)) = $true) | (((X3 @ (sK2 @ X3))) = $true)) )),
% 0.31/0.40 inference(cnf_transformation,[],[f8])).
% 0.31/0.40 thf(f10,plain,(
% 0.31/0.40 ( ! [X3 : (a > $o),X7 : a,X5 : (a > $o)] : (($true != ((cK @ X5 @ (sK3 @ X5)))) | (((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X7)) = $true) | (((X5 @ (sK2 @ X3))) != $true) | ($true != ((cK @ X3 @ X7)))) )),
% 0.31/0.40 inference(cnf_transformation,[],[f8])).
% 0.31/0.40 thf(f11,plain,(
% 0.31/0.40 ( ! [X3 : (a > $o),X7 : a,X5 : (a > $o)] : (($true != ((cK @ X3 @ X7))) | (((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X7)) = $true) | ($true = ((X5 @ (sK3 @ X5)))) | (((X5 @ (sK2 @ X3))) != $true)) )),
% 0.31/0.40 inference(cnf_transformation,[],[f8])).
% 0.31/0.40 thf(f12,plain,(
% 0.31/0.40 ($true != ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK0)))),
% 0.31/0.40 inference(cnf_transformation,[],[f8])).
% 0.31/0.40 thf(f13,plain,(
% 0.31/0.40 ($true = ((sK1 @ sK0)))),
% 0.31/0.40 inference(cnf_transformation,[],[f8])).
% 0.31/0.40 thf(f14,plain,(
% 0.31/0.40 ( ! [X2 : a] : (($true = ((cK @ sK1 @ X2))) | (((sK1 @ X2)) != $true)) )),
% 0.31/0.40 inference(cnf_transformation,[],[f8])).
% 0.31/0.40 thf(f16,plain,(
% 0.31/0.40 ( ! [X0 : a] : (($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X0))) | ($true != $true) | (((sK1 @ X0)) != $true) | (((sK1 @ (sK2 @ sK1))) = $true)) )),
% 0.31/0.40 inference(superposition,[],[f9,f14])).
% 0.31/0.40 thf(f17,plain,(
% 0.31/0.40 ( ! [X0 : a] : (($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X0))) | (((sK1 @ X0)) != $true) | (((sK1 @ (sK2 @ sK1))) = $true)) )),
% 0.31/0.40 inference(trivial_inequality_removal,[],[f16])).
% 0.31/0.40 thf(f46,plain,(
% 0.31/0.40 ( ! [X0 : a,X1 : (a > $o)] : (($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X0))) | ($true != ((sK1 @ (sK2 @ X1)))) | (((cK @ X1 @ X0)) != $true) | (((sK1 @ (sK3 @ sK1))) != $true) | ($true != $true)) )),
% 0.31/0.40 inference(superposition,[],[f10,f14])).
% 0.31/0.40 thf(f49,plain,(
% 0.31/0.40 ( ! [X0 : a,X1 : (a > $o)] : ((((sK1 @ (sK3 @ sK1))) != $true) | (((cK @ X1 @ X0)) != $true) | ($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X0))) | ($true != ((sK1 @ (sK2 @ X1))))) )),
% 0.31/0.40 inference(trivial_inequality_removal,[],[f46])).
% 0.31/0.40 thf(f68,plain,(
% 0.31/0.40 ( ! [X0 : a,X1 : (a > $o)] : ((((cK @ X1 @ X0)) != $true) | ($true != ((sK1 @ (sK2 @ X1)))) | ($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X0)))) )),
% 0.31/0.40 inference(forward_subsumption_resolution,[],[f49,f11])).
% 0.31/0.40 thf(f69,plain,(
% 0.31/0.40 ( ! [X0 : a] : (($true != $true) | (((sK1 @ (sK2 @ sK1))) != $true) | ($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X0))) | (((sK1 @ X0)) != $true)) )),
% 0.31/0.40 inference(superposition,[],[f68,f14])).
% 0.31/0.40 thf(f70,plain,(
% 0.31/0.40 ( ! [X0 : a] : ((((sK1 @ (sK2 @ sK1))) != $true) | ($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X0))) | (((sK1 @ X0)) != $true)) )),
% 0.31/0.40 inference(trivial_inequality_removal,[],[f69])).
% 0.31/0.40 thf(f71,plain,(
% 0.31/0.40 ( ! [X0 : a] : (($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X0))) | (((sK1 @ X0)) != $true)) )),
% 0.31/0.40 inference(forward_subsumption_resolution,[],[f70,f17])).
% 0.31/0.40 thf(f73,plain,(
% 0.31/0.40 ($true != $true) | ($true != ((sK1 @ sK0)))),
% 0.31/0.40 inference(superposition,[],[f12,f71])).
% 0.31/0.40 thf(f84,plain,(
% 0.31/0.40 ($true != ((sK1 @ sK0)))),
% 0.31/0.40 inference(trivial_inequality_removal,[],[f73])).
% 0.31/0.40 thf(f86,plain,(
% 0.31/0.40 $false),
% 0.31/0.40 inference(forward_subsumption_resolution,[],[f84,f13])).
% 0.31/0.40 % SZS output end Proof for theBenchmark
% 0.31/0.40 % (3621730)------------------------------
% 0.31/0.40 % (3621730)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.40 % (3621730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.40 % (3621730)CaDiCaL version: 2.1.3
% 0.31/0.40 % (3621730)Termination reason: Refutation
% 0.31/0.40 % (3621730)Time elapsed: 0.013 s
% 0.31/0.40 % (3621730)Peak memory usage: 12 MB
% 0.31/0.40 % (3621730)Instructions burned: 13 (million)
% 0.31/0.40 % (3621721)Success in time 0.051 s
% 0.31/0.40 % Vampire exiting
%------------------------------------------------------------------------------