%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV123^5 : 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 : n008.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 08:37:51 AM UTC 2026
% Result : Theorem 0.20s 0.32s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV123^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n008.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 15:12:54 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
% 0.20/0.32 % (3283432)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.32 % (3283442)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=705590161:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.32 % (3283443)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.32 % (3283443)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
% 0.20/0.32 % (3283438)lrs+10_16_si=on:nwc=1.5:random_seed=2930758023:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.32 % (3283437)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2547792837:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.32 % (3283439)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1185561642:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.32 % (3283441)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2733326933:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.32 % (3283440)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=259166051: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)
% 0.20/0.32 % (3283443)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=379083984:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.32 % (3283439)Instruction limit reached!
% 0.20/0.32 % (3283439)------------------------------
% 0.20/0.32 % (3283439)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (3283439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (3283439)CaDiCaL version: 2.1.3
% 0.20/0.32 % (3283439)Termination reason: Instruction limit
% 0.20/0.32 % (3283439)Termination phase: Saturation
% 0.20/0.32 % (3283439)Time elapsed: 0.003 s
% 0.20/0.32 % (3283439)Peak memory usage: 12 MB
% 0.20/0.32 % (3283439)Instructions burned: 4 (million)
% 0.20/0.32 % (3283438)Instruction limit reached!
% 0.20/0.32 % (3283438)------------------------------
% 0.20/0.32 % (3283438)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (3283438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (3283438)CaDiCaL version: 2.1.3
% 0.20/0.32 % (3283438)Termination reason: Instruction limit
% 0.20/0.32 % (3283438)Termination phase: Saturation
% 0.20/0.32 % (3283438)Time elapsed: 0.011 s
% 0.20/0.32 % (3283438)Peak memory usage: 12 MB
% 0.20/0.32 % (3283438)Instructions burned: 19 (million)
% 0.20/0.32 % (3283441)Instruction limit reached!
% 0.20/0.32 % (3283441)------------------------------
% 0.20/0.32 % (3283441)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (3283441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (3283441)CaDiCaL version: 2.1.3
% 0.20/0.32 % (3283441)Termination reason: Instruction limit
% 0.20/0.32 % (3283441)Termination phase: Saturation
% 0.20/0.32 % (3283441)Time elapsed: 0.014 s
% 0.20/0.32 % (3283441)Peak memory usage: 12 MB
% 0.20/0.32 % (3283441)Instructions burned: 25 (million)
% 0.20/0.32 % (3283442)Instruction limit reached!
% 0.20/0.32 % (3283442)------------------------------
% 0.20/0.32 % (3283442)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (3283442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (3283442)CaDiCaL version: 2.1.3
% 0.20/0.32 % (3283442)Termination reason: Instruction limit
% 0.20/0.32 % (3283442)Termination phase: Saturation
% 0.20/0.32 % (3283442)Time elapsed: 0.024 s
% 0.20/0.32 % (3283442)Peak memory usage: 13 MB
% 0.20/0.32 % (3283442)Instructions burned: 75 (million)
% 0.20/0.32 % (3283451)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=611134830:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.32 % (3283451)Instruction limit reached!
% 0.20/0.32 % (3283451)------------------------------
% 0.20/0.32 % (3283451)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (3283451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (3283451)CaDiCaL version: 2.1.3
% 0.20/0.32 % (3283451)Termination reason: Instruction limit
% 0.20/0.32 % (3283451)Termination phase: Saturation
% 0.20/0.32 % (3283451)Time elapsed: 0.003 s
% 0.20/0.32 % (3283451)Peak memory usage: 12 MB
% 0.20/0.32 % (3283451)Instructions burned: 4 (million)
% 0.20/0.32 % (3283437) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3283432-3283437"...
% 0.20/0.32 % (3283454)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2220471394:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/0.32 % (3283440) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3283432-3283440"...
% 0.20/0.32 % (3283453)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.32 % (3283437)...printing done.
% 0.20/0.32 % (3283437)Refutation found. Thanks to Tanya!
% 0.20/0.32 % SZS status Theorem for theBenchmark
% 0.20/0.32 % SZS output start Proof for theBenchmark
% 0.20/0.32 thf(type_def_5, type, a: $tType).
% 0.20/0.32 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.32 thf(func_def_3, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.32 thf(func_def_4, type, vIMP: ($o > $o > $o)).
% 0.20/0.32 thf(func_def_5, type, vAND: ($o > $o > $o)).
% 0.20/0.32 thf(func_def_6, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.32 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.32 thf(func_def_8, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.32 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.32 thf(func_def_10, type, sK0: a).
% 0.20/0.32 thf(func_def_11, type, sK1: ((a > a > $o) > $o)).
% 0.20/0.32 thf(func_def_12, type, sK2: ((a > a > $o) > $o)).
% 0.20/0.32 thf(func_def_13, type, sK3: a).
% 0.20/0.32 thf(func_def_14, type, sK4: (a > a > $o)).
% 0.20/0.32 thf(func_def_15, type, sK5: ((a > a > $o) > a)).
% 0.20/0.32 thf(func_def_16, type, sK6: ((a > a > $o) > a)).
% 0.20/0.32 thf(func_def_17, type, sK7: ((a > a > $o) > a > a > $o)).
% 0.20/0.32 thf(func_def_18, type, sK8: ((a > a > $o) > a > a > $o)).
% 0.20/0.32 thf(func_def_19, type, vNOT: ($o > $o)).
% 0.20/0.32 thf(func_def_20, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.32 thf(func_def_22, type, sK10: (a > a > a > a > $o)).
% 0.20/0.32 thf(func_def_23, type, sK11: ((a > a > $o) > a)).
% 0.20/0.32 thf(func_def_24, type, sK12: ((a > a > $o) > a)).
% 0.20/0.32 thf(f1,conjecture,(
% 0.20/0.32 ! [X2 : a,X3 : a,X0 : ((a > a > $o) > $o),X1 : ((a > a > $o) > $o)] : (! [X4 : (a > a > $o)] : (((X0 @ X4) & ! [X5 : a,X6 : a] : (? [X7 : (a > a > $o)] : ((X7 @ X5 @ X6) & ? [X8 : (a > a > $o)] : (((^[X9 : a, X10 : a] : (! [X11 : (a > a > $o)] : (((X0 @ X11) & ! [X13 : a,X12 : a] : ((X8 @ X12 @ X13) => (X11 @ X12 @ X13))) => (X11 @ X9 @ X10)))) = X7) & (X1 @ X8))) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3)) => ! [X4 : (a > a > $o)] : ((! [X5 : a,X6 : a] : (? [X7 : (a > a > $o)] : ((X1 @ X7) & (X7 @ X5 @ X6)) => (X4 @ X5 @ X6)) & (X0 @ X4)) => (X4 @ X2 @ X3)))),
% 0.20/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM254_B_pme)).
% 0.20/0.32 thf(f2,negated_conjecture,(
% 0.20/0.32 ~ ! [X2 : a,X3 : a,X0 : ((a > a > $o) > $o),X1 : ((a > a > $o) > $o)] : (! [X4 : (a > a > $o)] : (((X0 @ X4) & ! [X5 : a,X6 : a] : (? [X7 : (a > a > $o)] : ((X7 @ X5 @ X6) & ? [X8 : (a > a > $o)] : (((^[X9 : a, X10 : a] : (! [X11 : (a > a > $o)] : (((X0 @ X11) & ! [X13 : a,X12 : a] : ((X8 @ X12 @ X13) => (X11 @ X12 @ X13))) => (X11 @ X9 @ X10)))) = X7) & (X1 @ X8))) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3)) => ! [X4 : (a > a > $o)] : ((! [X5 : a,X6 : a] : (? [X7 : (a > a > $o)] : ((X1 @ X7) & (X7 @ X5 @ X6)) => (X4 @ X5 @ X6)) & (X0 @ X4)) => (X4 @ X2 @ X3)))),
% 0.20/0.32 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.32 thf(f3,plain,(
% 0.20/0.32 ~ ! [X0 : a,X1 : a,X2 : ((a > a > $o) > $o),X3 : ((a > a > $o) > $o)] : (! [X4 : (a > a > $o)] : (((X2 @ X4) & ! [X5 : a,X6 : a] : (? [X7 : (a > a > $o)] : ((X7 @ X5 @ X6) & ? [X8 : (a > a > $o)] : (((^[X9 : a, X10 : a] : (! [X11 : (a > a > $o)] : (((X2 @ X11) & ! [X12 : a,X13 : a] : ((X8 @ X13 @ X12) => (X11 @ X13 @ X12))) => (X11 @ X9 @ X10)))) = X7) & (X3 @ X8))) => (X4 @ X5 @ X6))) => (X4 @ X0 @ X1)) => ! [X14 : (a > a > $o)] : ((! [X15 : a,X16 : a] : (? [X17 : (a > a > $o)] : ((X3 @ X17) & (X17 @ X15 @ X16)) => (X14 @ X15 @ X16)) & (X2 @ X14)) => (X14 @ X0 @ X1)))),
% 0.20/0.32 inference(rectify,[],[f2])).
% 0.20/0.32 thf(f4,plain,(
% 0.20/0.32 ~ ! [X0 : a,X1 : a,X2 : ((a > a > $o) > $o),X3 : ((a > a > $o) > $o)] : (! [X4 : (a > a > $o)] : (((((X2 @ X4)) = $true) & ! [X5 : a,X6 : a] : (? [X7 : (a > a > $o)] : ((((X7 @ X5 @ X6)) = $true) & ? [X8 : (a > a > $o)] : ((((X3 @ X8)) = $true) & ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X8 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (X2 @ Y2)) => (Y2 @ Y0 @ Y1))))))) = X7))) => (((X4 @ X5 @ X6)) = $true))) => ($true = ((X4 @ X0 @ X1)))) => ! [X14 : (a > a > $o)] : ((! [X15 : a,X16 : a] : (? [X17 : (a > a > $o)] : ((((X3 @ X17)) = $true) & (((X17 @ X15 @ X16)) = $true)) => (((X14 @ X15 @ X16)) = $true)) & (((X2 @ X14)) = $true)) => (((X14 @ X0 @ X1)) = $true)))),
% 0.20/0.32 inference(fool_elimination,[],[f3])).
% 0.20/0.32 thf(f5,plain,(
% 0.20/0.32 ~ ! [X3 : ((a > a > $o) > $o),X1 : a,X2 : ((a > a > $o) > $o),X0 : a] : (! [X4 : (a > a > $o)] : (((((X2 @ X4)) = $true) & ! [X5 : a,X6 : a] : (? [X7 : (a > a > $o)] : ((((X7 @ X5 @ X6)) = $true) & ? [X8 : (a > a > $o)] : ((((X3 @ X8)) = $true) & ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X8 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (X2 @ Y2)) => (Y2 @ Y0 @ Y1))))))) = X7))) => (((X4 @ X5 @ X6)) = $true))) => ($true = ((X4 @ X0 @ X1)))) => ! [X9 : (a > a > $o)] : ((! [X11 : a,X10 : a] : (? [X12 : (a > a > $o)] : (($true = ((X12 @ X10 @ X11))) & (((X3 @ X12)) = $true)) => (((X9 @ X10 @ X11)) = $true)) & ($true = ((X2 @ X9)))) => (((X9 @ X0 @ X1)) = $true)))),
% 0.20/0.32 inference(rectify,[],[f4])).
% 0.20/0.32 thf(f6,plain,(
% 0.20/0.32 ? [X3 : ((a > a > $o) > $o),X1 : a,X2 : ((a > a > $o) > $o),X0 : a] : (? [X9 : (a > a > $o)] : ((((X9 @ X0 @ X1)) != $true) & (! [X10 : a,X11 : a] : ((((X9 @ X10 @ X11)) = $true) | ! [X12 : (a > a > $o)] : (($true != ((X12 @ X10 @ X11))) | (((X3 @ X12)) != $true))) & ($true = ((X2 @ X9))))) & ! [X4 : (a > a > $o)] : (($true = ((X4 @ X0 @ X1))) | ((((X2 @ X4)) != $true) | ? [X5 : a,X6 : a] : (? [X7 : (a > a > $o)] : ((((X7 @ X5 @ X6)) = $true) & ? [X8 : (a > a > $o)] : ((((X3 @ X8)) = $true) & ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X8 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (X2 @ Y2)) => (Y2 @ Y0 @ Y1))))))) = X7))) & (((X4 @ X5 @ X6)) != $true)))))),
% 0.20/0.32 inference(ennf_transformation,[],[f5])).
% 0.20/0.32 thf(f7,plain,(
% 0.20/0.32 ? [X0 : a,X2 : ((a > a > $o) > $o),X3 : ((a > a > $o) > $o),X1 : a] : (? [X9 : (a > a > $o)] : (($true = ((X2 @ X9))) & ! [X10 : a,X11 : a] : ((((X9 @ X10 @ X11)) = $true) | ! [X12 : (a > a > $o)] : (($true != ((X12 @ X10 @ X11))) | (((X3 @ X12)) != $true))) & (((X9 @ X0 @ X1)) != $true)) & ! [X4 : (a > a > $o)] : ((((X2 @ X4)) != $true) | ? [X5 : a,X6 : a] : (? [X7 : (a > a > $o)] : ((((X7 @ X5 @ X6)) = $true) & ? [X8 : (a > a > $o)] : ((((X3 @ X8)) = $true) & ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X8 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (X2 @ Y2)) => (Y2 @ Y0 @ Y1))))))) = X7))) & (((X4 @ X5 @ X6)) != $true)) | ($true = ((X4 @ X0 @ X1)))))),
% 0.20/0.32 inference(flattening,[],[f6])).
% 0.20/0.32 thf(f8,plain,(
% 0.20/0.32 ? [X0 : a,X1 : ((a > a > $o) > $o),X2 : ((a > a > $o) > $o),X3 : a] : (? [X4 : (a > a > $o)] : ((((X1 @ X4)) = $true) & ! [X5 : a,X6 : a] : ((((X4 @ X5 @ X6)) = $true) | ! [X7 : (a > a > $o)] : ((((X7 @ X5 @ X6)) != $true) | ($true != ((X2 @ X7))))) & (((X4 @ X0 @ X3)) != $true)) & ! [X8 : (a > a > $o)] : ((((X1 @ X8)) != $true) | ? [X9 : a,X10 : a] : (? [X11 : (a > a > $o)] : ((((X11 @ X9 @ X10)) = $true) & ? [X12 : (a > a > $o)] : ((((X2 @ X12)) = $true) & ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X12 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (X1 @ Y2)) => (Y2 @ Y0 @ Y1))))))) = X11))) & (((X8 @ X9 @ X10)) != $true)) | (((X8 @ X0 @ X3)) = $true)))),
% 0.20/0.32 inference(rectify,[],[f7])).
% 0.20/0.32 thf(f9,plain,(
% 0.20/0.32 (($true = ((sK1 @ sK4))) & ! [X5 : a,X6 : a] : ((((sK4 @ X5 @ X6)) = $true) | ! [X7 : (a > a > $o)] : ((((X7 @ X5 @ X6)) != $true) | (((sK2 @ X7)) != $true))) & (((sK4 @ sK0 @ sK3)) != $true)) & ! [X8 : (a > a > $o)] : ((((sK1 @ X8)) != $true) | (((((sK7 @ X8 @ (sK5 @ X8) @ (sK6 @ X8))) = $true) & ((((sK2 @ (sK8 @ X8))) = $true) & ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK8 @ X8 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK1 @ Y2)) => (Y2 @ Y0 @ Y1))))))) = ((sK7 @ X8))))) & ($true != ((X8 @ (sK5 @ X8) @ (sK6 @ X8))))) | ($true = ((X8 @ sK0 @ sK3))))),
% 0.20/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X12,sK8 @ X8),skolemize(X12,sK8 @ X8),skolemize(X12,sK8 @ X8),skolemize(X12,sK8 @ X8)],[f8])).
% 0.20/0.32 thf(f10,plain,(
% 0.20/0.32 ( ! [X8 : (a > a > $o)] : (($true != ((X8 @ (sK5 @ X8) @ (sK6 @ X8)))) | ($true = ((X8 @ sK0 @ sK3))) | (((sK1 @ X8)) != $true)) )),
% 0.20/0.32 inference(cnf_transformation,[],[f9])).
% 0.20/0.32 thf(f11,plain,(
% 0.20/0.32 ( ! [X8 : (a > a > $o)] : ((((sK1 @ X8)) != $true) | ($true = ((X8 @ sK0 @ sK3))) | ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK8 @ X8 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK1 @ Y2)) => (Y2 @ Y0 @ Y1))))))) = ((sK7 @ X8)))) )),
% 0.20/0.32 inference(cnf_transformation,[],[f9])).
% 0.20/0.32 thf(f12,plain,(
% 0.20/0.32 ( ! [X8 : (a > a > $o)] : ((((sK1 @ X8)) != $true) | (((sK2 @ (sK8 @ X8))) = $true) | ($true = ((X8 @ sK0 @ sK3)))) )),
% 0.20/0.32 inference(cnf_transformation,[],[f9])).
% 0.20/0.32 thf(f13,plain,(
% 0.20/0.32 ( ! [X8 : (a > a > $o)] : ((((sK1 @ X8)) != $true) | (((sK7 @ X8 @ (sK5 @ X8) @ (sK6 @ X8))) = $true) | ($true = ((X8 @ sK0 @ sK3)))) )),
% 0.20/0.32 inference(cnf_transformation,[],[f9])).
% 0.20/0.32 thf(f14,plain,(
% 0.20/0.32 (((sK4 @ sK0 @ sK3)) != $true)),
% 0.20/0.32 inference(cnf_transformation,[],[f9])).
% 0.20/0.32 thf(f15,plain,(
% 0.20/0.32 ( ! [X6 : a,X7 : (a > a > $o),X5 : a] : ((((X7 @ X5 @ X6)) != $true) | (((sK4 @ X5 @ X6)) = $true) | (((sK2 @ X7)) != $true)) )),
% 0.20/0.32 inference(cnf_transformation,[],[f9])).
% 0.20/0.32 thf(f16,plain,(
% 0.20/0.32 ($true = ((sK1 @ sK4)))),
% 0.20/0.32 inference(cnf_transformation,[],[f9])).
% 0.20/0.32 thf(f62,plain,(
% 0.20/0.32 (((sK4 @ sK0 @ sK3)) = $true) | ($true != $true) | (((sK2 @ (sK8 @ sK4))) = $true)),
% 0.20/0.32 inference(constrained_superposition,[],[f12,f16])).
% 0.20/0.32 thf(f63,plain,(
% 0.20/0.32 (((sK4 @ sK0 @ sK3)) = $true) | (((sK2 @ (sK8 @ sK4))) = $true)),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f62])).
% 0.20/0.32 thf(f64,plain,(
% 0.20/0.32 (((sK2 @ (sK8 @ sK4))) = $true)),
% 0.20/0.32 inference(forward_subsumption_resolution,[],[f63,f14])).
% 0.20/0.32 thf(f107,plain,(
% 0.20/0.32 (((sK4 @ sK0 @ sK3)) = $true) | ($true = ((sK7 @ sK4 @ (sK5 @ sK4) @ (sK6 @ sK4)))) | ($true != $true)),
% 0.20/0.32 inference(constrained_superposition,[],[f13,f16])).
% 0.20/0.32 thf(f108,plain,(
% 0.20/0.32 (((sK4 @ sK0 @ sK3)) = $true) | ($true = ((sK7 @ sK4 @ (sK5 @ sK4) @ (sK6 @ sK4))))),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f107])).
% 0.20/0.32 thf(f109,plain,(
% 0.20/0.32 ($true = ((sK7 @ sK4 @ (sK5 @ sK4) @ (sK6 @ sK4))))),
% 0.20/0.32 inference(forward_subsumption_resolution,[],[f108,f14])).
% 0.20/0.32 thf(f117,definition,(
% 0.20/0.32 spl9_13 <=> (((sK4 @ (sK5 @ sK4) @ (sK6 @ sK4))) = $true)),
% 0.20/0.32 introduced(definition,[new_symbols(definition,[spl9_13])],[avatar_definition])).
% 0.20/0.32 thf(f118,plain,(
% 0.20/0.32 (((sK4 @ (sK5 @ sK4) @ (sK6 @ sK4))) != $true) | spl9_13),
% 0.20/0.32 inference(avatar_component_clause,[],[f117])).
% 0.20/0.32 thf(f119,plain,(
% 0.20/0.32 (((sK4 @ (sK5 @ sK4) @ (sK6 @ sK4))) = $true) | ~spl9_13),
% 0.20/0.32 inference(avatar_component_clause,[],[f117])).
% 0.20/0.32 thf(f121,plain,(
% 0.20/0.32 (((sK7 @ sK4)) = (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK8 @ sK4 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK1 @ Y2)) => (Y2 @ Y0 @ Y1)))))))) | (((sK4 @ sK0 @ sK3)) = $true) | ($true != $true)),
% 0.20/0.32 inference(constrained_superposition,[],[f11,f16])).
% 0.20/0.32 thf(f122,plain,(
% 0.20/0.32 (((sK4 @ sK0 @ sK3)) = $true) | (((sK7 @ sK4)) = (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK8 @ sK4 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK1 @ Y2)) => (Y2 @ Y0 @ Y1))))))))),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f121])).
% 0.20/0.32 thf(f123,plain,(
% 0.20/0.32 (((sK7 @ sK4)) = (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK8 @ sK4 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK1 @ Y2)) => (Y2 @ Y0 @ Y1))))))))),
% 0.20/0.32 inference(forward_subsumption_resolution,[],[f122,f14])).
% 0.20/0.32 thf(f124,plain,(
% 0.20/0.32 ( ! [X1 : a] : ((((sK7 @ sK4 @ X1)) = (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK8 @ sK4 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK1 @ Y2)) => (Y2 @ Y0 @ Y1))))))) @ X1)))) )),
% 0.20/0.32 inference(argument_congruence,[],[f123])).
% 0.20/0.32 thf(f125,plain,(
% 0.20/0.32 ( ! [X1 : a] : (((^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK8 @ sK4 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (sK1 @ Y1)) => (Y1 @ X1 @ Y0))))) = ((sK7 @ sK4 @ X1)))) )),
% 0.20/0.32 inference(beta-eta_normalization,[],[f124])).
% 0.20/0.32 thf(f126,plain,(
% 0.20/0.32 ( ! [X2 : a,X1 : a] : (((((^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK8 @ sK4 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (sK1 @ Y1)) => (Y1 @ X1 @ Y0))))) @ X2)) = ((sK7 @ sK4 @ X1 @ X2)))) )),
% 0.20/0.32 inference(argument_congruence,[],[f125])).
% 0.20/0.32 thf(f127,plain,(
% 0.20/0.32 ( ! [X2 : a,X1 : a] : (((((^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK8 @ sK4 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (sK1 @ Y1)) => (Y1 @ X1 @ Y0))))) @ X2)) = $true) | ($false = ((sK7 @ sK4 @ X1 @ X2)))) )),
% 0.20/0.32 inference(iff_proxy_clausification,[],[f126])).
% 0.20/0.32 thf(f141,plain,(
% 0.20/0.32 ( ! [X2 : a,X1 : a] : (($false = ((sK7 @ sK4 @ X1 @ X2))) | (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK8 @ sK4 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (sK1 @ Y0)) => (Y0 @ X1 @ X2))))) = $true)) )),
% 0.20/0.32 inference(beta-eta_normalization,[],[f127])).
% 0.20/0.32 thf(f142,plain,(
% 0.20/0.32 ( ! [X2 : a,X3 : (a > a > $o),X1 : a] : (((((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK8 @ sK4 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (sK1 @ Y0)) => (Y0 @ X1 @ X2))) @ X3)) = $true) | ($false = ((sK7 @ sK4 @ X1 @ X2)))) )),
% 0.20/0.32 inference(pi_proxy_clausification,[],[f141])).
% 0.20/0.32 thf(f143,plain,(
% 0.20/0.32 ( ! [X2 : a,X3 : (a > a > $o),X1 : a] : (($false = ((sK7 @ sK4 @ X1 @ X2))) | ($true = ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK8 @ sK4 @ Y0 @ Y1) => (X3 @ Y0 @ Y1)))))) & (sK1 @ X3)) => (X3 @ X1 @ X2))))) )),
% 0.20/0.32 inference(beta-eta_normalization,[],[f142])).
% 0.20/0.32 thf(f144,plain,(
% 0.20/0.32 ( ! [X2 : a,X3 : (a > a > $o),X1 : a] : (($false = ((sK7 @ sK4 @ X1 @ X2))) | ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK8 @ sK4 @ Y0 @ Y1) => (X3 @ Y0 @ Y1)))))) & (sK1 @ X3))) = $false) | (((X3 @ X1 @ X2)) = $true)) )),
% 0.20/0.32 inference(imp_proxy_clausification,[],[f143])).
% 0.20/0.32 thf(f145,plain,(
% 0.20/0.32 ( ! [X2 : a,X3 : (a > a > $o),X1 : a] : (($false = ((sK7 @ sK4 @ X1 @ X2))) | (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK8 @ sK4 @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))) = $false) | ($false = ((sK1 @ X3))) | (((X3 @ X1 @ X2)) = $true)) )),
% 0.20/0.32 inference(and_proxy_clausification,[],[f144])).
% 0.20/0.32 thf(f146,plain,(
% 0.20/0.32 ( ! [X2 : a,X3 : (a > a > $o),X1 : a] : ((((X3 @ X1 @ X2)) = $true) | ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK8 @ sK4 @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))) @ (sK11 @ X3))) = $false) | ($false = ((sK1 @ X3))) | ($false = ((sK7 @ sK4 @ X1 @ X2)))) )),
% 0.20/0.32 inference(sigma_proxy_clausification,[],[f145])).
% 0.20/0.32 thf(f147,plain,(
% 0.20/0.32 ( ! [X2 : a,X3 : (a > a > $o),X1 : a] : ((((X3 @ X1 @ X2)) = $true) | ($false = ((sK1 @ X3))) | ($false = ((sK7 @ sK4 @ X1 @ X2))) | (((!! @ a @ (^[Y0 : a]: ((sK8 @ sK4 @ (sK11 @ X3) @ Y0) => (X3 @ (sK11 @ X3) @ Y0))))) = $false)) )),
% 0.20/0.32 inference(beta-eta_normalization,[],[f146])).
% 0.20/0.32 thf(f148,plain,(
% 0.20/0.32 ( ! [X2 : a,X3 : (a > a > $o),X1 : a] : (($false = ((sK1 @ X3))) | ($false = (((^[Y0 : a]: ((sK8 @ sK4 @ (sK11 @ X3) @ Y0) => (X3 @ (sK11 @ X3) @ Y0))) @ (sK12 @ X3)))) | ($false = ((sK7 @ sK4 @ X1 @ X2))) | (((X3 @ X1 @ X2)) = $true)) )),
% 0.20/0.32 inference(sigma_proxy_clausification,[],[f147])).
% 0.20/0.32 thf(f149,plain,(
% 0.20/0.32 ( ! [X2 : a,X3 : (a > a > $o),X1 : a] : (($false = (((sK8 @ sK4 @ (sK11 @ X3) @ (sK12 @ X3)) => (X3 @ (sK11 @ X3) @ (sK12 @ X3))))) | ($false = ((sK1 @ X3))) | (((X3 @ X1 @ X2)) = $true) | ($false = ((sK7 @ sK4 @ X1 @ X2)))) )),
% 0.20/0.32 inference(beta-eta_normalization,[],[f148])).
% 0.20/0.32 thf(f150,plain,(
% 0.20/0.32 ( ! [X2 : a,X3 : (a > a > $o),X1 : a] : (($false = ((X3 @ (sK11 @ X3) @ (sK12 @ X3)))) | ($false = ((sK7 @ sK4 @ X1 @ X2))) | (((X3 @ X1 @ X2)) = $true) | ($false = ((sK1 @ X3)))) )),
% 0.20/0.32 inference(imp_proxy_clausification,[],[f149])).
% 0.20/0.32 thf(f151,plain,(
% 0.20/0.32 ( ! [X2 : a,X3 : (a > a > $o),X1 : a] : ((((sK8 @ sK4 @ (sK11 @ X3) @ (sK12 @ X3))) = $true) | ($false = ((sK7 @ sK4 @ X1 @ X2))) | (((X3 @ X1 @ X2)) = $true) | ($false = ((sK1 @ X3)))) )),
% 0.20/0.32 inference(imp_proxy_clausification,[],[f149])).
% 0.20/0.32 thf(f170,plain,(
% 0.20/0.32 ( ! [X0 : (a > a > $o)] : ((((X0 @ (sK11 @ X0) @ (sK12 @ X0))) = $false) | ($false = ((sK1 @ X0))) | ($true = $false) | (((X0 @ (sK5 @ sK4) @ (sK6 @ sK4))) = $true)) )),
% 0.20/0.32 inference(constrained_superposition,[],[f150,f109])).
% 0.20/0.32 thf(f180,plain,(
% 0.20/0.32 ( ! [X0 : (a > a > $o)] : ((((X0 @ (sK11 @ X0) @ (sK12 @ X0))) = $false) | (((X0 @ (sK5 @ sK4) @ (sK6 @ sK4))) = $true) | ($false = ((sK1 @ X0)))) )),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f170])).
% 0.20/0.32 thf(f268,plain,(
% 0.20/0.32 ($true != $true) | ($true != ((sK1 @ sK4))) | (((sK4 @ sK0 @ sK3)) = $true) | ~spl9_13),
% 0.20/0.32 inference(constrained_superposition,[],[f10,f119])).
% 0.20/0.32 thf(f269,plain,(
% 0.20/0.32 (((sK4 @ sK0 @ sK3)) = $true) | ($true != ((sK1 @ sK4))) | ~spl9_13),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f268])).
% 0.20/0.32 thf(f270,plain,(
% 0.20/0.32 ($true != ((sK1 @ sK4))) | ~spl9_13),
% 0.20/0.32 inference(forward_subsumption_resolution,[],[f269,f14])).
% 0.20/0.32 thf(f271,plain,(
% 0.20/0.32 $false | ~spl9_13),
% 0.20/0.32 inference(forward_subsumption_resolution,[],[f270,f16])).
% 0.20/0.32 thf(f272,plain,(
% 0.20/0.32 ~spl9_13),
% 0.20/0.32 inference(avatar_contradiction_clause,[],[f271])).
% 0.20/0.32 thf(f437,plain,(
% 0.20/0.32 ( ! [X0 : (a > a > $o)] : ((((X0 @ (sK5 @ sK4) @ (sK6 @ sK4))) = $true) | ($true = $false) | ($false = ((sK1 @ X0))) | (((sK8 @ sK4 @ (sK11 @ X0) @ (sK12 @ X0))) = $true)) )),
% 0.20/0.32 inference(constrained_superposition,[],[f151,f109])).
% 0.20/0.32 thf(f503,plain,(
% 0.20/0.32 ( ! [X0 : (a > a > $o)] : ((((sK8 @ sK4 @ (sK11 @ X0) @ (sK12 @ X0))) = $true) | (((X0 @ (sK5 @ sK4) @ (sK6 @ sK4))) = $true) | ($false = ((sK1 @ X0)))) )),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f437])).
% 0.20/0.32 thf(f596,plain,(
% 0.20/0.32 ( ! [X0 : (a > a > $o)] : (($false = ((sK1 @ X0))) | (((sK2 @ (sK8 @ sK4))) != $true) | (((X0 @ (sK5 @ sK4) @ (sK6 @ sK4))) = $true) | (((sK4 @ (sK11 @ X0) @ (sK12 @ X0))) = $true) | ($true != $true)) )),
% 0.20/0.32 inference(constrained_superposition,[],[f15,f503])).
% 0.20/0.32 thf(f603,plain,(
% 0.20/0.32 ( ! [X0 : (a > a > $o)] : (($false = ((sK1 @ X0))) | (((sK4 @ (sK11 @ X0) @ (sK12 @ X0))) = $true) | (((X0 @ (sK5 @ sK4) @ (sK6 @ sK4))) = $true) | (((sK2 @ (sK8 @ sK4))) != $true)) )),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f596])).
% 0.20/0.32 thf(f667,plain,(
% 0.20/0.32 ( ! [X0 : (a > a > $o)] : ((((sK4 @ (sK11 @ X0) @ (sK12 @ X0))) = $true) | (((X0 @ (sK5 @ sK4) @ (sK6 @ sK4))) = $true) | ($false = ((sK1 @ X0)))) )),
% 0.20/0.32 inference(forward_subsumption_resolution,[],[f603,f64])).
% 0.20/0.32 thf(f675,plain,(
% 0.20/0.32 (((sK4 @ (sK5 @ sK4) @ (sK6 @ sK4))) = $true) | ($false = ((sK1 @ sK4))) | (((sK4 @ (sK5 @ sK4) @ (sK6 @ sK4))) = $true) | ($true = $false) | ($false = ((sK1 @ sK4)))),
% 0.20/0.32 inference(constrained_superposition,[],[f667,f180])).
% 0.20/0.32 thf(f685,plain,(
% 0.20/0.32 (((sK4 @ (sK5 @ sK4) @ (sK6 @ sK4))) = $true) | ($true = $false) | ($false = ((sK1 @ sK4)))),
% 0.20/0.32 inference(duplicate_literal_removal,[],[f675])).
% 0.20/0.32 thf(f686,plain,(
% 0.20/0.32 ($false = ((sK1 @ sK4))) | (((sK4 @ (sK5 @ sK4) @ (sK6 @ sK4))) = $true)),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f685])).
% 0.20/0.32 thf(f706,plain,(
% 0.20/0.32 ($false = ((sK1 @ sK4))) | spl9_13),
% 0.20/0.32 inference(forward_subsumption_resolution,[],[f686,f118])).
% 0.20/0.32 thf(f716,plain,(
% 0.20/0.32 ($true = $false) | spl9_13),
% 0.20/0.32 inference(forward_demodulation,[],[f706,f16])).
% 0.20/0.32 thf(f717,plain,(
% 0.20/0.32 $false | spl9_13),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f716])).
% 0.20/0.32 thf(f718,plain,(
% 0.20/0.32 spl9_13),
% 0.20/0.32 inference(avatar_contradiction_clause,[],[f717])).
% 0.20/0.32 cnf(s16, plain, ~spl9_13, inference(sat_conversion,[],[f272])).
% 0.20/0.32 cnf(s35, plain, spl9_13, inference(sat_conversion,[],[f718])).
% 0.20/0.32 cnf(s40, plain, $false, inference(rat,[],[s16,s35])).
% 0.20/0.32 thf(f727,plain,(
% 0.20/0.32 $false),
% 0.20/0.32 inference(avatar_sat_refutation,[],[s40])).
% 0.20/0.32 % SZS output end Proof for theBenchmark
% 0.20/0.32 % (3283437)------------------------------
% 0.20/0.32 % (3283437)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (3283437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (3283437)CaDiCaL version: 2.1.3
% 0.20/0.32 % (3283437)Termination reason: Refutation
% 0.20/0.32 % (3283437)Time elapsed: 0.031 s
% 0.20/0.32 % (3283437)Peak memory usage: 13 MB
% 0.20/0.32 % (3283437)Instructions burned: 53 (million)
% 0.20/0.32 % (3283432)Success in time 0.08 s
% 0.20/0.32 % Vampire exiting
%------------------------------------------------------------------------------