%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV107^5 : 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 : n018.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 08:37:39 AM UTC 2026
% Result : Theorem 0.47s 0.39s
% Output : Refutation 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV107^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 % Computer : n018.cluster.edu
% 0.09/0.25 % Model : x86_64 x86_64
% 0.09/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.25 % Memory : 8046.5625MB
% 0.09/0.25 % OS : Linux 6.8.0-71-generic
% 0.09/0.25 % CPULimit : 300
% 0.09/0.25 % WCLimit : 300
% 0.09/0.25 % DateTime : Tue Sep 29 15:12:56 UTC 2026
% 0.09/0.25 % CPUTime :
% 0.09/0.25 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.31 Running higher-order theorem proving
% 0.25/0.32 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
% 0.47/0.39 % (203493)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.47/0.39 % (203501)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=2820367034: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)
% 0.47/0.39 % (203504)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.47/0.39 % (203504)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
% 0.47/0.39 % (203498)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3187283321:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.47/0.39 % (203500)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=704185428:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.47/0.39 % (203502)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3572787329:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.47/0.39 % (203499)lrs+10_16_si=on:nwc=1.5:random_seed=4006963058:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.47/0.39 % (203503)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2563923716:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.47/0.39 % (203504)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=121472052:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.47/0.39 % (203500)Instruction limit reached!
% 0.47/0.39 % (203500)------------------------------
% 0.47/0.39 % (203500)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.39 % (203500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.39 % (203500)CaDiCaL version: 2.1.3
% 0.47/0.39 % (203500)Termination reason: Instruction limit
% 0.47/0.39 % (203500)Termination phase: Saturation
% 0.47/0.39 % (203500)Time elapsed: 0.004 s
% 0.47/0.39 % (203500)Peak memory usage: 12 MB
% 0.47/0.39 % (203500)Instructions burned: 3 (million)
% 0.47/0.39 % (203498) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-203493-203498"...
% 0.47/0.39 % (203502) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-203493-203502"...
% 0.47/0.39 % (203499) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-203493-203499"...
% 0.47/0.39 % (203502)...printing done.
% 0.47/0.39 % (203498)...printing done.
% 0.47/0.39 % (203502)Refutation found. Thanks to Tanya!
% 0.47/0.39 % SZS status Theorem for theBenchmark
% 0.47/0.39 % SZS output start Proof for theBenchmark
% 0.47/0.39 thf(type_def_5, type, a: $tType).
% 0.47/0.39 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.47/0.39 thf(func_def_0, type, z: a).
% 0.47/0.39 thf(func_def_1, type, cR: (a > a > $o)).
% 0.47/0.39 thf(func_def_2, type, f: (a > $i > $o)).
% 0.47/0.39 thf(func_def_3, type, cS: ($i > $i > $o)).
% 0.47/0.39 thf(func_def_7, type, sP0: $o).
% 0.47/0.39 thf(func_def_9, type, sK2: a).
% 0.47/0.39 thf(func_def_10, type, sK3: a).
% 0.47/0.39 thf(func_def_11, type, sK4: a).
% 0.47/0.39 thf(func_def_12, type, sK5: ($i > a)).
% 0.47/0.39 thf(func_def_14, type, sK7: (a > a)).
% 0.47/0.39 thf(func_def_15, type, sK8: (a > $i)).
% 0.47/0.39 thf(f1,conjecture,(
% 0.47/0.39 (! [X3 : a] : (cR @ X3 @ X3) & ! [X1 : a,X0 : a,X2 : a] : (((cR @ X2 @ X1) & (cR @ X0 @ X1)) => (cR @ X0 @ X2))) => ((! [X8 : a,X7 : a,X4 : $i] : (((f @ X7 @ X4) & (f @ X8 @ X4)) => (cR @ X7 @ X8)) & ! [X3 : a] : ? [X4 : $i] : (f @ X3 @ X4) & ! [X3 : a,X5 : $i,X6 : $i] : (((f @ X3 @ X5) & (f @ X3 @ X6)) => (cS @ X5 @ X6))) => (! [X8 : a,X4 : $i,X7 : a] : ((! [X2 : a] : (((cR @ X8 @ z) & ~(f @ X2 @ X4)) | (f @ X8 @ X4)) & ! [X2 : a] : ((~(f @ X2 @ X4) & (cR @ X7 @ z)) | (f @ X7 @ X4))) => (cR @ X7 @ X8)) & ! [X3 : a] : ? [X4 : $i] : ! [X2 : a] : (((cR @ X3 @ z) & ~(f @ X2 @ X4)) | (f @ X3 @ X4)) & ! [X4 : $i] : ? [X3 : a] : ! [X2 : a] : (((cR @ X3 @ z) & ~(f @ X2 @ X4)) | (f @ X3 @ X4))))),
% 0.47/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM552B_pme)).
% 0.47/0.39 thf(f2,negated_conjecture,(
% 0.47/0.39 ~((! [X3 : a] : (cR @ X3 @ X3) & ! [X1 : a,X0 : a,X2 : a] : (((cR @ X2 @ X1) & (cR @ X0 @ X1)) => (cR @ X0 @ X2))) => ((! [X8 : a,X7 : a,X4 : $i] : (((f @ X7 @ X4) & (f @ X8 @ X4)) => (cR @ X7 @ X8)) & ! [X3 : a] : ? [X4 : $i] : (f @ X3 @ X4) & ! [X3 : a,X5 : $i,X6 : $i] : (((f @ X3 @ X5) & (f @ X3 @ X6)) => (cS @ X5 @ X6))) => (! [X8 : a,X4 : $i,X7 : a] : ((! [X2 : a] : (((cR @ X8 @ z) & ~(f @ X2 @ X4)) | (f @ X8 @ X4)) & ! [X2 : a] : ((~(f @ X2 @ X4) & (cR @ X7 @ z)) | (f @ X7 @ X4))) => (cR @ X7 @ X8)) & ! [X3 : a] : ? [X4 : $i] : ! [X2 : a] : (((cR @ X3 @ z) & ~(f @ X2 @ X4)) | (f @ X3 @ X4)) & ! [X4 : $i] : ? [X3 : a] : ! [X2 : a] : (((cR @ X3 @ z) & ~(f @ X2 @ X4)) | (f @ X3 @ X4)))))),
% 0.47/0.39 inference(negated_conjecture,[status(cth)],[f1])).
% 0.47/0.39 thf(f3,plain,(
% 0.47/0.39 ~((! [X0 : a] : (cR @ X0 @ X0) & ! [X1 : a,X2 : a,X3 : a] : (((cR @ X3 @ X1) & (cR @ X2 @ X1)) => (cR @ X2 @ X3))) => ((! [X4 : a,X5 : a,X6 : $i] : (((f @ X5 @ X6) & (f @ X4 @ X6)) => (cR @ X5 @ X4)) & ! [X7 : a] : ? [X8 : $i] : (f @ X7 @ X8) & ! [X9 : a,X10 : $i,X11 : $i] : (((f @ X9 @ X10) & (f @ X9 @ X11)) => (cS @ X10 @ X11))) => (! [X12 : a,X13 : $i,X14 : a] : ((! [X15 : a] : (((cR @ X12 @ z) & ~(f @ X15 @ X13)) | (f @ X12 @ X13)) & ! [X16 : a] : ((~(f @ X16 @ X13) & (cR @ X14 @ z)) | (f @ X14 @ X13))) => (cR @ X14 @ X12)) & ! [X17 : a] : ? [X18 : $i] : ! [X19 : a] : (((cR @ X17 @ z) & ~(f @ X19 @ X18)) | (f @ X17 @ X18)) & ! [X20 : $i] : ? [X21 : a] : ! [X22 : a] : (((cR @ X21 @ z) & ~(f @ X22 @ X20)) | (f @ X21 @ X20)))))),
% 0.47/0.39 inference(rectify,[],[f2])).
% 0.47/0.39 thf(f4,plain,(
% 0.47/0.39 ~((! [X3 : a,X2 : a,X1 : a] : (((((cR @ X2 @ X1)) = $true) & ($true = ((cR @ X3 @ X1)))) => ($true = ((cR @ X2 @ X3)))) & ! [X0 : a] : ($true = ((cR @ X0 @ X0)))) => ((! [X10 : $i,X9 : a,X11 : $i] : ((($true = ((f @ X9 @ X10))) & ($true = ((f @ X9 @ X11)))) => ($true = ((cS @ X10 @ X11)))) & ! [X7 : a] : ? [X8 : $i] : ($true = ((f @ X7 @ X8))) & ! [X5 : a,X4 : a,X6 : $i] : ((($true = ((f @ X5 @ X6))) & ($true = ((f @ X4 @ X6)))) => ($true = ((cR @ X5 @ X4))))) => (! [X12 : a,X13 : $i,X14 : a] : ((! [X15 : a] : ((($true = ((cR @ X12 @ z))) & ~ ($true = ((f @ X15 @ X13)))) | ($true = ((f @ X12 @ X13)))) & ! [X16 : a] : ((~ ($true = ((f @ X16 @ X13))) & ($true = ((cR @ X14 @ z)))) | ($true = ((f @ X14 @ X13))))) => ($true = ((cR @ X14 @ X12)))) & ! [X17 : a] : ? [X18 : $i] : ! [X19 : a] : ((($true = ((cR @ X17 @ z))) & ~ ($true = ((f @ X19 @ X18)))) | ($true = ((f @ X17 @ X18)))) & ! [X20 : $i] : ? [X21 : a] : ! [X22 : a] : ((($true = ((cR @ X21 @ z))) & ~ ($true = ((f @ X22 @ X20)))) | ($true = ((f @ X21 @ X20)))))))),
% 0.47/0.39 inference(fool_elimination,[],[f3])).
% 0.47/0.39 thf(f5,plain,(
% 0.47/0.39 ~((! [X3 : a,X2 : a,X1 : a] : (((((cR @ X2 @ X1)) = $true) & ($true = ((cR @ X3 @ X1)))) => ($true = ((cR @ X2 @ X3)))) & ! [X0 : a] : ($true = ((cR @ X0 @ X0)))) => ((! [X10 : $i,X9 : a,X11 : $i] : ((($true = ((f @ X9 @ X10))) & ($true = ((f @ X9 @ X11)))) => ($true = ((cS @ X10 @ X11)))) & ! [X7 : a] : ? [X8 : $i] : ($true = ((f @ X7 @ X8))) & ! [X5 : a,X4 : a,X6 : $i] : ((($true = ((f @ X5 @ X6))) & ($true = ((f @ X4 @ X6)))) => ($true = ((cR @ X5 @ X4))))) => (! [X14 : a,X13 : $i,X12 : a] : ((! [X15 : a] : (($true = ((f @ X12 @ X13))) | (($true != ((f @ X15 @ X13))) & ($true = ((cR @ X12 @ z))))) & ! [X16 : a] : ((($true != ((f @ X16 @ X13))) & ($true = ((cR @ X14 @ z)))) | ($true = ((f @ X14 @ X13))))) => ($true = ((cR @ X14 @ X12)))) & ! [X20 : $i] : ? [X21 : a] : ! [X22 : a] : (($true = ((f @ X21 @ X20))) | (($true != ((f @ X22 @ X20))) & ($true = ((cR @ X21 @ z))))) & ! [X17 : a] : ? [X18 : $i] : ! [X19 : a] : (($true = ((f @ X17 @ X18))) | (($true != ((f @ X19 @ X18))) & ($true = ((cR @ X17 @ z))))))))),
% 0.47/0.39 inference(flattening,[],[f4])).
% 0.47/0.39 thf(f6,plain,(
% 0.47/0.39 ((? [X14 : a,X13 : $i,X12 : a] : (($true != ((cR @ X14 @ X12))) & (! [X15 : a] : (($true = ((f @ X12 @ X13))) | (($true != ((f @ X15 @ X13))) & ($true = ((cR @ X12 @ z))))) & ! [X16 : a] : ((($true != ((f @ X16 @ X13))) & ($true = ((cR @ X14 @ z)))) | ($true = ((f @ X14 @ X13)))))) | ? [X20 : $i] : ! [X21 : a] : ? [X22 : a] : ((($true = ((f @ X22 @ X20))) | ($true != ((cR @ X21 @ z)))) & ($true != ((f @ X21 @ X20)))) | ? [X17 : a] : ! [X18 : $i] : ? [X19 : a] : (($true != ((f @ X17 @ X18))) & (($true != ((cR @ X17 @ z))) | ($true = ((f @ X19 @ X18)))))) & (! [X10 : $i,X9 : a,X11 : $i] : (($true = ((cS @ X10 @ X11))) | (($true != ((f @ X9 @ X10))) | ($true != ((f @ X9 @ X11))))) & ! [X7 : a] : ? [X8 : $i] : ($true = ((f @ X7 @ X8))) & ! [X5 : a,X4 : a,X6 : $i] : (($true = ((cR @ X5 @ X4))) | (($true != ((f @ X5 @ X6))) | ($true != ((f @ X4 @ X6))))))) & (! [X3 : a,X2 : a,X1 : a] : (($true = ((cR @ X2 @ X3))) | ((((cR @ X2 @ X1)) != $true) | ($true != ((cR @ X3 @ X1))))) & ! [X0 : a] : ($true = ((cR @ X0 @ X0))))),
% 0.47/0.39 inference(ennf_transformation,[],[f5])).
% 0.47/0.39 thf(f7,plain,(
% 0.47/0.39 ! [X2 : a,X3 : a,X1 : a] : ((((cR @ X2 @ X1)) != $true) | ($true != ((cR @ X3 @ X1))) | ($true = ((cR @ X2 @ X3)))) & ! [X0 : a] : ($true = ((cR @ X0 @ X0))) & ! [X9 : a,X11 : $i,X10 : $i] : (($true != ((f @ X9 @ X10))) | ($true = ((cS @ X10 @ X11))) | ($true != ((f @ X9 @ X11)))) & ! [X4 : a,X5 : a,X6 : $i] : (($true != ((f @ X4 @ X6))) | ($true != ((f @ X5 @ X6))) | ($true = ((cR @ X5 @ X4)))) & (? [X17 : a] : ! [X18 : $i] : ? [X19 : a] : (($true != ((f @ X17 @ X18))) & (($true != ((cR @ X17 @ z))) | ($true = ((f @ X19 @ X18))))) | ? [X20 : $i] : ! [X21 : a] : ? [X22 : a] : ((($true = ((f @ X22 @ X20))) | ($true != ((cR @ X21 @ z)))) & ($true != ((f @ X21 @ X20)))) | ? [X13 : $i,X14 : a,X12 : a] : (! [X16 : a] : ((($true != ((f @ X16 @ X13))) & ($true = ((cR @ X14 @ z)))) | ($true = ((f @ X14 @ X13)))) & ! [X15 : a] : (($true = ((f @ X12 @ X13))) | (($true != ((f @ X15 @ X13))) & ($true = ((cR @ X12 @ z))))) & ($true != ((cR @ X14 @ X12))))) & ! [X7 : a] : ? [X8 : $i] : ($true = ((f @ X7 @ X8)))),
% 0.47/0.39 inference(flattening,[],[f6])).
% 0.47/0.39 thf(f8,definition,(
% 0.47/0.39 ? [X13 : $i,X14 : a,X12 : a] : (! [X16 : a] : ((($true != ((f @ X16 @ X13))) & ($true = ((cR @ X14 @ z)))) | ($true = ((f @ X14 @ X13)))) & ! [X15 : a] : (($true = ((f @ X12 @ X13))) | (($true != ((f @ X15 @ X13))) & ($true = ((cR @ X12 @ z))))) & ($true != ((cR @ X14 @ X12)))) | ~ ($true = sP0)),
% 0.47/0.39 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.47/0.39 thf(f9,plain,(
% 0.47/0.39 ! [X2 : a,X3 : a,X1 : a] : ((((cR @ X2 @ X1)) != $true) | ($true != ((cR @ X3 @ X1))) | ($true = ((cR @ X2 @ X3)))) & ! [X0 : a] : ($true = ((cR @ X0 @ X0))) & ! [X9 : a,X11 : $i,X10 : $i] : (($true != ((f @ X9 @ X10))) | ($true = ((cS @ X10 @ X11))) | ($true != ((f @ X9 @ X11)))) & ! [X4 : a,X5 : a,X6 : $i] : (($true != ((f @ X4 @ X6))) | ($true != ((f @ X5 @ X6))) | ($true = ((cR @ X5 @ X4)))) & (? [X17 : a] : ! [X18 : $i] : ? [X19 : a] : (($true != ((f @ X17 @ X18))) & (($true != ((cR @ X17 @ z))) | ($true = ((f @ X19 @ X18))))) | ? [X20 : $i] : ! [X21 : a] : ? [X22 : a] : ((($true = ((f @ X22 @ X20))) | ($true != ((cR @ X21 @ z)))) & ($true != ((f @ X21 @ X20)))) | ($true = sP0)) & ! [X7 : a] : ? [X8 : $i] : ($true = ((f @ X7 @ X8)))),
% 0.47/0.39 inference(definition_folding,[],[f7,f8])).
% 0.47/0.39 thf(f10,plain,(
% 0.47/0.39 ? [X13 : $i,X14 : a,X12 : a] : (! [X16 : a] : ((($true != ((f @ X16 @ X13))) & ($true = ((cR @ X14 @ z)))) | ($true = ((f @ X14 @ X13)))) & ! [X15 : a] : (($true = ((f @ X12 @ X13))) | (($true != ((f @ X15 @ X13))) & ($true = ((cR @ X12 @ z))))) & ($true != ((cR @ X14 @ X12)))) | ($true != sP0)),
% 0.47/0.39 inference(nnf_transformation,[],[f8])).
% 0.47/0.39 thf(f11,plain,(
% 0.47/0.39 ? [X0 : $i,X1 : a,X2 : a] : (! [X3 : a] : ((($true != ((f @ X3 @ X0))) & ($true = ((cR @ X1 @ z)))) | ($true = ((f @ X1 @ X0)))) & ! [X4 : a] : (($true = ((f @ X2 @ X0))) | (($true != ((f @ X4 @ X0))) & ($true = ((cR @ X2 @ z))))) & ($true != ((cR @ X1 @ X2)))) | ($true != sP0)),
% 0.47/0.39 inference(rectify,[],[f10])).
% 0.47/0.39 thf(f12,plain,(
% 0.47/0.39 (! [X3 : a] : ((($true != ((f @ X3 @ sK1))) & ($true = ((cR @ sK2 @ z)))) | ($true = ((f @ sK2 @ sK1)))) & ! [X4 : a] : (($true = ((f @ sK3 @ sK1))) | (($true != ((f @ X4 @ sK1))) & ($true = ((cR @ sK3 @ z))))) & ($true != ((cR @ sK2 @ sK3)))) | ($true != sP0)),
% 0.47/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f11])).
% 0.47/0.39 thf(f13,plain,(
% 0.47/0.39 ! [X0 : a,X1 : a,X2 : a] : ((((cR @ X0 @ X2)) != $true) | ($true != ((cR @ X1 @ X2))) | (((cR @ X0 @ X1)) = $true)) & ! [X3 : a] : (((cR @ X3 @ X3)) = $true) & ! [X4 : a,X5 : $i,X6 : $i] : (($true != ((f @ X4 @ X6))) | ($true = ((cS @ X6 @ X5))) | ($true != ((f @ X4 @ X5)))) & ! [X7 : a,X8 : a,X9 : $i] : ((((f @ X7 @ X9)) != $true) | ($true != ((f @ X8 @ X9))) | ($true = ((cR @ X8 @ X7)))) & (? [X10 : a] : ! [X11 : $i] : ? [X12 : a] : (($true != ((f @ X10 @ X11))) & (($true != ((cR @ X10 @ z))) | ($true = ((f @ X12 @ X11))))) | ? [X13 : $i] : ! [X14 : a] : ? [X15 : a] : ((($true = ((f @ X15 @ X13))) | ($true != ((cR @ X14 @ z)))) & ($true != ((f @ X14 @ X13)))) | ($true = sP0)) & ! [X16 : a] : ? [X17 : $i] : ($true = ((f @ X16 @ X17)))),
% 0.47/0.39 inference(rectify,[],[f9])).
% 0.47/0.39 thf(f14,plain,(
% 0.47/0.39 ! [X0 : a,X1 : a,X2 : a] : ((((cR @ X0 @ X2)) != $true) | ($true != ((cR @ X1 @ X2))) | (((cR @ X0 @ X1)) = $true)) & ! [X3 : a] : (((cR @ X3 @ X3)) = $true) & ! [X4 : a,X5 : $i,X6 : $i] : (($true != ((f @ X4 @ X6))) | ($true = ((cS @ X6 @ X5))) | ($true != ((f @ X4 @ X5)))) & ! [X7 : a,X8 : a,X9 : $i] : ((((f @ X7 @ X9)) != $true) | ($true != ((f @ X8 @ X9))) | ($true = ((cR @ X8 @ X7)))) & (! [X11 : $i] : (($true != ((f @ sK4 @ X11))) & (($true != ((cR @ sK4 @ z))) | ($true = ((f @ (sK5 @ X11) @ X11))))) | ! [X14 : a] : ((($true = ((f @ (sK7 @ X14) @ sK6))) | ($true != ((cR @ X14 @ z)))) & ($true != ((f @ X14 @ sK6)))) | ($true = sP0)) & ! [X16 : a] : ($true = ((f @ X16 @ (sK8 @ X16))))),
% 0.47/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK4,vAPP,sK6,vAPP,vAPP]),skolemize(X10,sK4),skolemize(X17,sK8 @ X16),skolemize(X13,sK6),skolemize(X17,sK8 @ X16),skolemize(X17,sK8 @ X16)],[f13])).
% 0.47/0.39 thf(f15,plain,(
% 0.47/0.39 ($true != sP0) | ($true != ((cR @ sK2 @ sK3)))),
% 0.47/0.39 inference(cnf_transformation,[],[f12])).
% 0.47/0.39 thf(f16,plain,(
% 0.47/0.39 ($true != sP0) | ($true = ((cR @ sK3 @ z))) | ($true = ((f @ sK3 @ sK1)))),
% 0.47/0.39 inference(cnf_transformation,[],[f12])).
% 0.47/0.39 thf(f17,plain,(
% 0.47/0.39 ( ! [X4 : a] : (($true != sP0) | ($true = ((f @ sK3 @ sK1))) | ($true != ((f @ X4 @ sK1)))) )),
% 0.47/0.39 inference(cnf_transformation,[],[f12])).
% 0.47/0.39 thf(f18,plain,(
% 0.47/0.39 ($true = ((cR @ sK2 @ z))) | ($true = ((f @ sK2 @ sK1))) | ($true != sP0)),
% 0.47/0.39 inference(cnf_transformation,[],[f12])).
% 0.47/0.39 thf(f19,plain,(
% 0.47/0.39 ( ! [X3 : a] : (($true != ((f @ X3 @ sK1))) | ($true != sP0) | ($true = ((f @ sK2 @ sK1)))) )),
% 0.47/0.39 inference(cnf_transformation,[],[f12])).
% 0.47/0.39 thf(f20,plain,(
% 0.47/0.39 ( ! [X16 : a] : (($true = ((f @ X16 @ (sK8 @ X16))))) )),
% 0.47/0.39 inference(cnf_transformation,[],[f14])).
% 0.47/0.39 thf(f23,plain,(
% 0.47/0.39 ( ! [X11 : $i,X14 : a] : (($true != ((f @ X14 @ sK6))) | ($true = sP0) | ($true != ((f @ sK4 @ X11)))) )),
% 0.47/0.39 inference(cnf_transformation,[],[f14])).
% 0.47/0.39 thf(f24,plain,(
% 0.47/0.39 ( ! [X11 : $i,X14 : a] : (($true = sP0) | ($true != ((f @ sK4 @ X11))) | ($true = ((f @ (sK7 @ X14) @ sK6))) | ($true != ((cR @ X14 @ z)))) )),
% 0.47/0.39 inference(cnf_transformation,[],[f14])).
% 0.47/0.39 thf(f25,plain,(
% 0.47/0.39 ( ! [X8 : a,X9 : $i,X7 : a] : ((((f @ X7 @ X9)) != $true) | ($true != ((f @ X8 @ X9))) | ($true = ((cR @ X8 @ X7)))) )),
% 0.47/0.39 inference(cnf_transformation,[],[f14])).
% 0.47/0.39 thf(f27,plain,(
% 0.47/0.39 ( ! [X3 : a] : ((((cR @ X3 @ X3)) = $true)) )),
% 0.47/0.39 inference(cnf_transformation,[],[f14])).
% 0.47/0.39 thf(f28,plain,(
% 0.47/0.39 ( ! [X2 : a,X0 : a,X1 : a] : ((((cR @ X0 @ X2)) != $true) | ($true != ((cR @ X1 @ X2))) | (((cR @ X0 @ X1)) = $true)) )),
% 0.47/0.39 inference(cnf_transformation,[],[f14])).
% 0.47/0.39 thf(f36,plain,(
% 0.47/0.39 ( ! [X0 : a,X1 : a] : (($true != $true) | (((cR @ X0 @ X1)) = $true) | ($true != ((cR @ X1 @ X0)))) )),
% 0.47/0.39 inference(superposition,[],[f28,f27])).
% 0.47/0.39 thf(f37,plain,(
% 0.47/0.39 ( ! [X0 : a,X1 : a] : (($true != ((cR @ X1 @ X0))) | (((cR @ X0 @ X1)) = $true)) )),
% 0.47/0.39 inference(trivial_inequality_removal,[],[f36])).
% 0.47/0.39 thf(f38,plain,(
% 0.47/0.39 ( ! [X11 : $i,X14 : a] : (($true != ((f @ sK4 @ X11))) | ($true != ((cR @ X14 @ z))) | ($true = sP0)) )),
% 0.47/0.39 inference(forward_subsumption_resolution,[],[f24,f23])).
% 0.47/0.39 thf(f39,plain,(
% 0.47/0.39 ( ! [X0 : a] : (($true = sP0) | ($true != ((cR @ X0 @ z))) | ($true != $true)) )),
% 0.47/0.39 inference(superposition,[],[f38,f20])).
% 0.47/0.39 thf(f40,plain,(
% 0.47/0.39 ( ! [X0 : a] : (($true != ((cR @ X0 @ z))) | ($true = sP0)) )),
% 0.47/0.39 inference(trivial_inequality_removal,[],[f39])).
% 0.47/0.39 thf(f41,plain,(
% 0.47/0.39 ($true != $true) | ($true = sP0)),
% 0.47/0.39 inference(superposition,[],[f40,f27])).
% 0.47/0.39 thf(f42,plain,(
% 0.47/0.39 ($true = sP0)),
% 0.47/0.39 inference(trivial_inequality_removal,[],[f41])).
% 0.47/0.39 thf(f44,plain,(
% 0.47/0.39 ($true != ((cR @ sK2 @ sK3)))),
% 0.47/0.39 inference(forward_subsumption_resolution,[],[f15,f42])).
% 0.47/0.39 thf(f45,plain,(
% 0.47/0.39 ($true = ((f @ sK3 @ sK1))) | ($true = ((cR @ sK3 @ z)))),
% 0.47/0.39 inference(forward_subsumption_resolution,[],[f16,f42])).
% 0.47/0.39 thf(f47,plain,(
% 0.47/0.39 ( ! [X0 : a] : (($true = ((cR @ X0 @ sK3))) | ($true != $true) | ($true != ((f @ X0 @ sK1))) | ($true = ((cR @ sK3 @ z)))) )),
% 0.47/0.39 inference(superposition,[],[f25,f45])).
% 0.47/0.39 thf(f48,plain,(
% 0.47/0.39 ( ! [X0 : a] : (($true != ((f @ X0 @ sK1))) | ($true = ((cR @ sK3 @ z))) | ($true = ((cR @ X0 @ sK3)))) )),
% 0.47/0.39 inference(trivial_inequality_removal,[],[f47])).
% 0.47/0.39 thf(f53,plain,(
% 0.47/0.39 ( ! [X4 : a] : (($true != ((f @ X4 @ sK1))) | ($true = ((f @ sK3 @ sK1)))) )),
% 0.47/0.39 inference(forward_subsumption_resolution,[],[f17,f42])).
% 0.47/0.39 thf(f54,plain,(
% 0.47/0.39 ($true = ((f @ sK2 @ sK1))) | ($true = ((cR @ sK2 @ z)))),
% 0.47/0.39 inference(forward_subsumption_resolution,[],[f18,f42])).
% 0.47/0.39 thf(f55,plain,(
% 0.47/0.39 ($true = ((f @ sK3 @ sK1))) | ($true != $true) | ($true = ((cR @ sK2 @ z)))),
% 0.47/0.39 inference(superposition,[],[f53,f54])).
% 0.47/0.39 thf(f58,plain,(
% 0.47/0.39 ( ! [X0 : a] : (($true = ((cR @ sK2 @ z))) | ($true != ((f @ X0 @ sK1))) | ($true = ((cR @ X0 @ sK2))) | ($true != $true)) )),
% 0.47/0.39 inference(superposition,[],[f25,f54])).
% 0.47/0.39 thf(f59,plain,(
% 0.47/0.39 ( ! [X0 : a] : (($true != ((f @ X0 @ sK1))) | ($true = ((cR @ sK2 @ z))) | ($true = ((cR @ X0 @ sK2)))) )),
% 0.47/0.39 inference(trivial_inequality_removal,[],[f58])).
% 0.47/0.39 thf(f60,plain,(
% 0.47/0.39 ($true = ((f @ sK3 @ sK1))) | ($true = ((cR @ sK2 @ z)))),
% 0.47/0.39 inference(trivial_inequality_removal,[],[f55])).
% 0.47/0.39 thf(f64,plain,(
% 0.47/0.39 ( ! [X3 : a] : (($true != ((f @ X3 @ sK1))) | ($true = ((f @ sK2 @ sK1)))) )),
% 0.47/0.39 inference(forward_subsumption_resolution,[],[f19,f42])).
% 0.47/0.39 thf(f65,plain,(
% 0.47/0.39 ($true = ((cR @ sK3 @ z))) | ($true = ((f @ sK2 @ sK1))) | ($true != $true)),
% 0.47/0.39 inference(superposition,[],[f64,f45])).
% 0.47/0.39 thf(f66,plain,(
% 0.47/0.39 ($true = ((f @ sK2 @ sK1))) | ($true = ((cR @ sK3 @ z)))),
% 0.47/0.39 inference(trivial_inequality_removal,[],[f65])).
% 0.47/0.39 thf(f76,plain,(
% 0.47/0.39 ($true != $true) | ($true = ((cR @ sK3 @ z))) | ($true = ((cR @ sK3 @ z))) | ($true = ((cR @ sK2 @ sK3)))),
% 0.47/0.39 inference(superposition,[],[f48,f66])).
% 0.47/0.39 thf(f80,plain,(
% 0.47/0.39 ($true = ((cR @ sK3 @ z))) | ($true = ((cR @ sK2 @ sK3))) | ($true != $true)),
% 0.47/0.39 inference(duplicate_literal_removal,[],[f76])).
% 0.47/0.39 thf(f81,plain,(
% 0.47/0.39 ($true = ((cR @ sK3 @ z))) | ($true = ((cR @ sK2 @ sK3)))),
% 0.47/0.39 inference(trivial_inequality_removal,[],[f80])).
% 0.47/0.39 thf(f84,plain,(
% 0.47/0.39 ($true = ((cR @ sK3 @ z)))),
% 0.47/0.39 inference(forward_subsumption_resolution,[],[f81,f44])).
% 0.47/0.39 thf(f87,plain,(
% 0.47/0.39 ( ! [X0 : a] : ((((cR @ sK3 @ X0)) = $true) | ($true != $true) | ($true != ((cR @ X0 @ z)))) )),
% 0.47/0.39 inference(superposition,[],[f28,f84])).
% 0.47/0.39 thf(f88,plain,(
% 0.47/0.39 ( ! [X0 : a] : (($true != ((cR @ X0 @ z))) | (((cR @ sK3 @ X0)) = $true)) )),
% 0.47/0.39 inference(trivial_inequality_removal,[],[f87])).
% 0.47/0.39 thf(f91,plain,(
% 0.47/0.39 ($true = ((cR @ sK2 @ z))) | ($true != $true) | ($true = ((cR @ sK2 @ z))) | ($true = ((cR @ sK3 @ sK2)))),
% 0.47/0.39 inference(superposition,[],[f59,f60])).
% 0.47/0.39 thf(f99,plain,(
% 0.47/0.39 ($true != $true) | ($true = ((cR @ sK3 @ sK2))) | ($true = ((cR @ sK2 @ z)))),
% 0.47/0.39 inference(duplicate_literal_removal,[],[f91])).
% 0.47/0.39 thf(f100,plain,(
% 0.47/0.39 ($true = ((cR @ sK3 @ sK2))) | ($true = ((cR @ sK2 @ z)))),
% 0.47/0.39 inference(trivial_inequality_removal,[],[f99])).
% 0.47/0.39 thf(f105,plain,(
% 0.47/0.39 ($true = ((cR @ sK2 @ sK3))) | ($true != $true) | ($true = ((cR @ sK2 @ z)))),
% 0.47/0.39 inference(superposition,[],[f37,f100])).
% 0.47/0.39 thf(f107,plain,(
% 0.47/0.39 ($true = ((cR @ sK2 @ z))) | ($true = ((cR @ sK2 @ sK3)))),
% 0.47/0.39 inference(trivial_inequality_removal,[],[f105])).
% 0.47/0.39 thf(f109,plain,(
% 0.47/0.39 ($true = ((cR @ sK2 @ z)))),
% 0.47/0.39 inference(forward_subsumption_resolution,[],[f107,f44])).
% 0.47/0.39 thf(f121,plain,(
% 0.47/0.39 ($true != $true) | ($true = ((cR @ sK3 @ sK2)))),
% 0.47/0.39 inference(superposition,[],[f88,f109])).
% 0.47/0.39 thf(f124,plain,(
% 0.47/0.39 ($true = ((cR @ sK3 @ sK2)))),
% 0.47/0.39 inference(trivial_inequality_removal,[],[f121])).
% 0.47/0.39 thf(f126,plain,(
% 0.47/0.39 ($true = ((cR @ sK2 @ sK3))) | ($true != $true)),
% 0.47/0.39 inference(superposition,[],[f37,f124])).
% 0.47/0.39 thf(f129,plain,(
% 0.47/0.39 ($true = ((cR @ sK2 @ sK3)))),
% 0.47/0.39 inference(trivial_inequality_removal,[],[f126])).
% 0.47/0.39 thf(f130,plain,(
% 0.47/0.39 $false),
% 0.47/0.39 inference(forward_subsumption_resolution,[],[f129,f44])).
% 0.47/0.39 % SZS output end Proof for theBenchmark
% 0.47/0.39 % (203502)------------------------------
% 0.47/0.39 % (203502)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.39 % (203502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.39 % (203502)CaDiCaL version: 2.1.3
% 0.47/0.39 % (203502)Termination reason: Refutation
% 0.47/0.39 % (203502)Time elapsed: 0.015 s
% 0.47/0.39 % (203502)Peak memory usage: 12 MB
% 0.47/0.39 % (203502)Instructions burned: 15 (million)
% 0.47/0.39 % (203493)Success in time 0.054 s
% 0.47/0.39 % Vampire exiting
%------------------------------------------------------------------------------