%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV260^5 : 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 : n013.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 08:38:08 AM UTC 2026
% Result : Theorem 0.23s 0.29s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV260^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.20 % Computer : n013.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % OS : Linux 6.8.0-71-generic
% 0.11/0.20 % CPULimit : 300
% 0.11/0.20 % WCLimit : 300
% 0.11/0.20 % DateTime : Tue Sep 29 15:27:51 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.23 Running higher-order theorem proving
% 0.11/0.25 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
% 0.23/0.29 % (2251002)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.29 % (2251008)lrs+10_16_si=on:nwc=1.5:random_seed=3621728386:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.29 % (2251007)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3735751447:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.29 % (2251010)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=670268246: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)
% 0.23/0.29 % (2251007) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2251002-2251007"...
% 0.23/0.29 % (2251008) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2251002-2251008"...
% 0.23/0.29 % (2251010)Refutation not found, incomplete strategy
% 0.23/0.29 % (2251010)------------------------------
% 0.23/0.29 % (2251010)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (2251010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (2251010)CaDiCaL version: 2.1.3
% 0.23/0.29 % (2251010)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.29 % (2251010)Time elapsed: 0.005 s
% 0.23/0.29 % (2251010)Peak memory usage: 12 MB
% 0.23/0.29 % (2251010)Instructions burned: 7 (million)
% 0.23/0.29 % (2251013)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.29 % (2251013)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
% 0.23/0.29 % (2251010)------------------------------
% 0.23/0.29 % (2251010)------------------------------
% 0.23/0.29 % (2251011)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4184906951:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.29 % (2251007)...printing done.
% 0.23/0.29 % (2251008)...printing done.
% 0.23/0.29 % (2251007)Refutation found. Thanks to Tanya!
% 0.23/0.29 % SZS status Theorem for theBenchmark
% 0.23/0.29 % SZS output start Proof for theBenchmark
% 0.23/0.29 thf(type_def_5, type, a: $tType).
% 0.23/0.29 thf(type_def_6, type, b: $tType).
% 0.23/0.29 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.29 thf(func_def_3, type, db0: !>[X0: $tType]:(X0)).
% 0.23/0.29 thf(func_def_4, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.23/0.29 thf(func_def_5, type, vNOT: ($o > $o)).
% 0.23/0.29 thf(func_def_6, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.23/0.29 thf(func_def_7, type, vAND: ($o > $o > $o)).
% 0.23/0.29 thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 0.23/0.29 thf(func_def_9, type, sK0: ((a > $o) > $o)).
% 0.23/0.29 thf(func_def_10, type, sK1: ((b > $o) > $o)).
% 0.23/0.29 thf(func_def_11, type, sK2: (a > b)).
% 0.23/0.29 thf(func_def_12, type, sK3: (b > $o)).
% 0.23/0.29 thf(func_def_13, type, sK4: (a > $o)).
% 0.23/0.29 thf(func_def_14, type, sK5: (a > $o)).
% 0.23/0.29 thf(func_def_15, type, sK6: (((a > $o) > $o) > a > $o)).
% 0.23/0.29 thf(func_def_16, type, sK7: (((b > $o) > $o) > b > $o)).
% 0.23/0.29 thf(f1,conjecture,(
% 0.23/0.29 ! [X0 : ((a > $o) > $o),X1 : ((b > $o) > $o),X2 : (a > b)] : ((! [X3 : (b > $o)] : (((^[X4 : b] : ($false)) = X3) => (X1 @ X3)) & ! [X3 : (a > $o)] : (((^[X4 : a] : ($false)) = X3) => (X0 @ X3)) & ! [X5 : ((b > $o) > $o),X3 : (b > $o)] : (((X3 = (^[X4 : b] : (? [X6 : (b > $o)] : ((X5 @ X6) & (X6 @ X4))))) & ! [X4 : (b > $o)] : ((X5 @ X4) => (X1 @ X4))) => (X1 @ X3)) & ! [X8 : (a > $o),X6 : (a > $o),X7 : (a > $o)] : (((X0 @ X7) & (X6 = (^[X4 : a] : ((X7 @ X4) & (X8 @ X4)))) & (X0 @ X8)) => (X0 @ X6)) & ! [X7 : (b > $o),X6 : (b > $o),X8 : (b > $o)] : ((((^[X4 : b] : ((X7 @ X4) & (X8 @ X4))) = X6) & (X1 @ X8) & (X1 @ X7)) => (X1 @ X6)) & ! [X3 : (a > $o)] : (((^[X4 : a] : (~$false)) = X3) => (X0 @ X3)) & ! [X5 : ((a > $o) > $o),X3 : (a > $o)] : ((! [X4 : (a > $o)] : ((X5 @ X4) => (X0 @ X4)) & (X3 = (^[X4 : a] : (? [X6 : (a > $o)] : ((X6 @ X4) & (X5 @ X6)))))) => (X0 @ X3)) & ! [X3 : (b > $o)] : ((X3 = (^[X4 : b] : (~$false))) => (X1 @ X3)) & ! [X9 : (b > $o)] : ((X1 @ X9) => ! [X7 : (a > $o)] : ((X7 = (^[X10 : a] : ((X9 @ (X2 @ X10))))) => (X0 @ X7)))) => ! [X9 : (b > $o)] : (! [X3 : (b > $o)] : ((X3 = (^[X4 : b] : (~(X9 @ X4)))) => (X1 @ X3)) => ! [X7 : (a > $o)] : ((X7 = (^[X10 : a] : ((X9 @ (X2 @ X10))))) => ! [X3 : (a > $o)] : ((X3 = (^[X4 : a] : (~(X7 @ X4)))) => (X0 @ X3)))))),
% 0.23/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCLOSED_THM1_pme)).
% 0.23/0.30 thf(f2,negated_conjecture,(
% 0.23/0.30 ~ ! [X0 : ((a > $o) > $o),X1 : ((b > $o) > $o),X2 : (a > b)] : ((! [X3 : (b > $o)] : (((^[X4 : b] : ($false)) = X3) => (X1 @ X3)) & ! [X3 : (a > $o)] : (((^[X4 : a] : ($false)) = X3) => (X0 @ X3)) & ! [X5 : ((b > $o) > $o),X3 : (b > $o)] : (((X3 = (^[X4 : b] : (? [X6 : (b > $o)] : ((X5 @ X6) & (X6 @ X4))))) & ! [X4 : (b > $o)] : ((X5 @ X4) => (X1 @ X4))) => (X1 @ X3)) & ! [X8 : (a > $o),X6 : (a > $o),X7 : (a > $o)] : (((X0 @ X7) & (X6 = (^[X4 : a] : ((X7 @ X4) & (X8 @ X4)))) & (X0 @ X8)) => (X0 @ X6)) & ! [X7 : (b > $o),X6 : (b > $o),X8 : (b > $o)] : ((((^[X4 : b] : ((X7 @ X4) & (X8 @ X4))) = X6) & (X1 @ X8) & (X1 @ X7)) => (X1 @ X6)) & ! [X3 : (a > $o)] : (((^[X4 : a] : (~$false)) = X3) => (X0 @ X3)) & ! [X5 : ((a > $o) > $o),X3 : (a > $o)] : ((! [X4 : (a > $o)] : ((X5 @ X4) => (X0 @ X4)) & (X3 = (^[X4 : a] : (? [X6 : (a > $o)] : ((X6 @ X4) & (X5 @ X6)))))) => (X0 @ X3)) & ! [X3 : (b > $o)] : ((X3 = (^[X4 : b] : (~$false))) => (X1 @ X3)) & ! [X9 : (b > $o)] : ((X1 @ X9) => ! [X7 : (a > $o)] : ((X7 = (^[X10 : a] : ((X9 @ (X2 @ X10))))) => (X0 @ X7)))) => ! [X9 : (b > $o)] : (! [X3 : (b > $o)] : ((X3 = (^[X4 : b] : (~(X9 @ X4)))) => (X1 @ X3)) => ! [X7 : (a > $o)] : ((X7 = (^[X10 : a] : ((X9 @ (X2 @ X10))))) => ! [X3 : (a > $o)] : ((X3 = (^[X4 : a] : (~(X7 @ X4)))) => (X0 @ X3)))))),
% 0.23/0.30 inference(negated_conjecture,[status(cth)],[f1])).
% 0.23/0.30 thf(f3,plain,(
% 0.23/0.30 ~ ! [X0 : ((a > $o) > $o),X1 : ((b > $o) > $o),X2 : (a > b)] : ((! [X3 : (b > $o)] : (((^[X4 : b] : ($false)) = X3) => (X1 @ X3)) & ! [X5 : (a > $o)] : (((^[X6 : a] : ($false)) = X5) => (X0 @ X5)) & ! [X7 : ((b > $o) > $o),X8 : (b > $o)] : (((X8 = (^[X9 : b] : (? [X10 : (b > $o)] : ((X7 @ X10) & (X10 @ X9))))) & ! [X11 : (b > $o)] : ((X7 @ X11) => (X1 @ X11))) => (X1 @ X8)) & ! [X12 : (a > $o),X13 : (a > $o),X14 : (a > $o)] : (((X0 @ X14) & (X13 = (^[X15 : a] : ((X14 @ X15) & (X12 @ X15)))) & (X0 @ X12)) => (X0 @ X13)) & ! [X16 : (b > $o),X17 : (b > $o),X18 : (b > $o)] : ((((^[X19 : b] : ((X16 @ X19) & (X18 @ X19))) = X17) & (X1 @ X18) & (X1 @ X16)) => (X1 @ X17)) & ! [X20 : (a > $o)] : (((^[X21 : a] : (~$false)) = X20) => (X0 @ X20)) & ! [X22 : ((a > $o) > $o),X23 : (a > $o)] : ((! [X24 : (a > $o)] : ((X22 @ X24) => (X0 @ X24)) & (X23 = (^[X25 : a] : (? [X26 : (a > $o)] : ((X26 @ X25) & (X22 @ X26)))))) => (X0 @ X23)) & ! [X27 : (b > $o)] : ((X27 = (^[X28 : b] : (~$false))) => (X1 @ X27)) & ! [X29 : (b > $o)] : ((X1 @ X29) => ! [X30 : (a > $o)] : ((X30 = (^[X31 : a] : ((X29 @ (X2 @ X31))))) => (X0 @ X30)))) => ! [X32 : (b > $o)] : (! [X33 : (b > $o)] : ((X33 = (^[X34 : b] : (~(X32 @ X34)))) => (X1 @ X33)) => ! [X35 : (a > $o)] : ((X35 = (^[X36 : a] : ((X32 @ (X2 @ X36))))) => ! [X37 : (a > $o)] : ((X37 = (^[X38 : a] : (~(X35 @ X38)))) => (X0 @ X37)))))),
% 0.23/0.30 inference(rectify,[],[f2])).
% 0.23/0.30 thf(f4,plain,(
% 0.23/0.30 ~ ! [X0 : ((a > $o) > $o),X1 : ((b > $o) > $o),X2 : (a > b)] : ((! [X3 : (b > $o)] : (((^[Y0 : b]: ($false)) = X3) => (((X1 @ X3)) = $true)) & ! [X5 : (a > $o)] : (((^[Y0 : a]: ($false)) = X5) => ($true = ((X0 @ X5)))) & ! [X7 : ((b > $o) > $o),X8 : (b > $o)] : ((((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y1 @ Y0) & (X7 @ Y1))))) = X8) & ! [X11 : (b > $o)] : ((((X7 @ X11)) = $true) => ($true = ((X1 @ X11))))) => (((X1 @ X8)) = $true)) & ! [X12 : (a > $o),X13 : (a > $o),X14 : (a > $o)] : (((((X0 @ X14)) = $true) & ((^[Y0 : a]: ((X12 @ Y0) & (X14 @ Y0))) = X13) & (((X0 @ X12)) = $true)) => (((X0 @ X13)) = $true)) & ! [X16 : (b > $o),X17 : (b > $o),X18 : (b > $o)] : ((((^[Y0 : b]: ((X18 @ Y0) & (X16 @ Y0))) = X17) & ($true = ((X1 @ X18))) & ($true = ((X1 @ X16)))) => (((X1 @ X17)) = $true)) & ! [X20 : (a > $o)] : (((^[Y0 : a]: (~ $false)) = X20) => ($true = ((X0 @ X20)))) & ! [X22 : ((a > $o) > $o),X23 : (a > $o)] : ((! [X24 : (a > $o)] : (($true = ((X22 @ X24))) => ($true = ((X0 @ X24)))) & ((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((X22 @ Y1) & (Y1 @ Y0))))) = X23)) => ($true = ((X0 @ X23)))) & ! [X27 : (b > $o)] : (((^[Y0 : b]: (~ $false)) = X27) => ($true = ((X1 @ X27)))) & ! [X29 : (b > $o)] : ((((X1 @ X29)) = $true) => ! [X30 : (a > $o)] : (((^[Y0 : a]: (X29 @ (X2 @ Y0))) = X30) => ($true = ((X0 @ X30)))))) => ! [X32 : (b > $o)] : (! [X33 : (b > $o)] : (((^[Y0 : b]: (~ (X32 @ Y0))) = X33) => ($true = ((X1 @ X33)))) => ! [X35 : (a > $o)] : (((^[Y0 : a]: (X32 @ (X2 @ Y0))) = X35) => ! [X37 : (a > $o)] : (((^[Y0 : a]: (~ (X35 @ Y0))) = X37) => (((X0 @ X37)) = $true)))))),
% 0.23/0.30 inference(fool_elimination,[],[f3])).
% 0.23/0.30 thf(f5,plain,(
% 0.23/0.30 ~ ! [X0 : ((a > $o) > $o),X1 : ((b > $o) > $o),X2 : (a > b)] : ((! [X15 : ((a > $o) > $o),X16 : (a > $o)] : ((! [X17 : (a > $o)] : (($true = ((X15 @ X17))) => ($true = ((X0 @ X17)))) & ((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((X15 @ Y1) & (Y1 @ Y0))))) = X16)) => (((X0 @ X16)) = $true)) & ! [X5 : ((b > $o) > $o),X6 : (b > $o)] : ((! [X7 : (b > $o)] : (($true = ((X5 @ X7))) => (((X1 @ X7)) = $true)) & ((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y1 @ Y0) & (X5 @ Y1))))) = X6)) => (((X1 @ X6)) = $true)) & ! [X11 : (b > $o),X12 : (b > $o),X13 : (b > $o)] : ((((^[Y0 : b]: ((X13 @ Y0) & (X11 @ Y0))) = X12) & (((X1 @ X13)) = $true) & ($true = ((X1 @ X11)))) => ($true = ((X1 @ X12)))) & ! [X3 : (b > $o)] : (((^[Y0 : b]: ($false)) = X3) => (((X1 @ X3)) = $true)) & ! [X14 : (a > $o)] : (((^[Y0 : a]: (~ $false)) = X14) => (((X0 @ X14)) = $true)) & ! [X18 : (b > $o)] : (((^[Y0 : b]: (~ $false)) = X18) => ($true = ((X1 @ X18)))) & ! [X4 : (a > $o)] : (((^[Y0 : a]: ($false)) = X4) => (((X0 @ X4)) = $true)) & ! [X19 : (b > $o)] : (($true = ((X1 @ X19))) => ! [X20 : (a > $o)] : (((^[Y0 : a]: (X19 @ (X2 @ Y0))) = X20) => ($true = ((X0 @ X20))))) & ! [X8 : (a > $o),X9 : (a > $o),X10 : (a > $o)] : ((($true = ((X0 @ X10))) & ((^[Y0 : a]: ((X8 @ Y0) & (X10 @ Y0))) = X9) & (((X0 @ X8)) = $true)) => (((X0 @ X9)) = $true))) => ! [X21 : (b > $o)] : (! [X22 : (b > $o)] : (((^[Y0 : b]: (~ (X21 @ Y0))) = X22) => ($true = ((X1 @ X22)))) => ! [X23 : (a > $o)] : (((^[Y0 : a]: (X21 @ (X2 @ Y0))) = X23) => ! [X24 : (a > $o)] : (((^[Y0 : a]: (~ (X23 @ Y0))) = X24) => ($true = ((X0 @ X24)))))))),
% 0.23/0.30 inference(rectify,[],[f4])).
% 0.23/0.30 thf(f6,plain,(
% 0.23/0.30 ? [X0 : ((a > $o) > $o),X1 : ((b > $o) > $o),X2 : (a > b)] : (? [X21 : (b > $o)] : (! [X22 : (b > $o)] : (($true = ((X1 @ X22))) | ((^[Y0 : b]: (~ (X21 @ Y0))) != X22)) & ? [X23 : (a > $o)] : (? [X24 : (a > $o)] : (($true != ((X0 @ X24))) & ((^[Y0 : a]: (~ (X23 @ Y0))) = X24)) & ((^[Y0 : a]: (X21 @ (X2 @ Y0))) = X23))) & (! [X15 : ((a > $o) > $o),X16 : (a > $o)] : ((((X0 @ X16)) = $true) | (? [X17 : (a > $o)] : (($true = ((X15 @ X17))) & ($true != ((X0 @ X17)))) | ((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((X15 @ Y1) & (Y1 @ Y0))))) != X16))) & ! [X5 : ((b > $o) > $o),X6 : (b > $o)] : ((((X1 @ X6)) = $true) | (? [X7 : (b > $o)] : ((((X1 @ X7)) != $true) & ($true = ((X5 @ X7)))) | ((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y1 @ Y0) & (X5 @ Y1))))) != X6))) & ! [X11 : (b > $o),X12 : (b > $o),X13 : (b > $o)] : (($true = ((X1 @ X12))) | (((^[Y0 : b]: ((X13 @ Y0) & (X11 @ Y0))) != X12) | (((X1 @ X13)) != $true) | ($true != ((X1 @ X11))))) & ! [X3 : (b > $o)] : ((((X1 @ X3)) = $true) | ((^[Y0 : b]: ($false)) != X3)) & ! [X14 : (a > $o)] : (((^[Y0 : a]: (~ $false)) != X14) | (((X0 @ X14)) = $true)) & ! [X18 : (b > $o)] : (((^[Y0 : b]: (~ $false)) != X18) | ($true = ((X1 @ X18)))) & ! [X4 : (a > $o)] : (((^[Y0 : a]: ($false)) != X4) | (((X0 @ X4)) = $true)) & ! [X19 : (b > $o)] : (! [X20 : (a > $o)] : (((^[Y0 : a]: (X19 @ (X2 @ Y0))) != X20) | ($true = ((X0 @ X20)))) | ($true != ((X1 @ X19)))) & ! [X8 : (a > $o),X9 : (a > $o),X10 : (a > $o)] : ((((X0 @ X9)) = $true) | (($true != ((X0 @ X10))) | ((^[Y0 : a]: ((X8 @ Y0) & (X10 @ Y0))) != X9) | (((X0 @ X8)) != $true)))))),
% 0.23/0.30 inference(ennf_transformation,[],[f5])).
% 0.23/0.30 thf(f7,plain,(
% 0.23/0.30 ? [X0 : ((a > $o) > $o),X1 : ((b > $o) > $o),X2 : (a > b)] : (? [X21 : (b > $o)] : (! [X22 : (b > $o)] : (($true = ((X1 @ X22))) | ((^[Y0 : b]: (~ (X21 @ Y0))) != X22)) & ? [X23 : (a > $o)] : (? [X24 : (a > $o)] : (($true != ((X0 @ X24))) & ((^[Y0 : a]: (~ (X23 @ Y0))) = X24)) & ((^[Y0 : a]: (X21 @ (X2 @ Y0))) = X23))) & ! [X16 : (a > $o),X15 : ((a > $o) > $o)] : (? [X17 : (a > $o)] : (($true = ((X15 @ X17))) & ($true != ((X0 @ X17)))) | (((X0 @ X16)) = $true) | ((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((X15 @ Y1) & (Y1 @ Y0))))) != X16)) & ! [X19 : (b > $o)] : (! [X20 : (a > $o)] : (((^[Y0 : a]: (X19 @ (X2 @ Y0))) != X20) | ($true = ((X0 @ X20)))) | ($true != ((X1 @ X19)))) & ! [X9 : (a > $o),X10 : (a > $o),X8 : (a > $o)] : ((((X0 @ X8)) != $true) | (((X0 @ X9)) = $true) | ((^[Y0 : a]: ((X8 @ Y0) & (X10 @ Y0))) != X9) | ($true != ((X0 @ X10)))) & ! [X4 : (a > $o)] : (((^[Y0 : a]: ($false)) != X4) | (((X0 @ X4)) = $true)) & ! [X14 : (a > $o)] : (((^[Y0 : a]: (~ $false)) != X14) | (((X0 @ X14)) = $true)) & ! [X12 : (b > $o),X13 : (b > $o),X11 : (b > $o)] : (($true = ((X1 @ X12))) | ((^[Y0 : b]: ((X13 @ Y0) & (X11 @ Y0))) != X12) | (((X1 @ X13)) != $true) | ($true != ((X1 @ X11)))) & ! [X3 : (b > $o)] : ((((X1 @ X3)) = $true) | ((^[Y0 : b]: ($false)) != X3)) & ! [X18 : (b > $o)] : (((^[Y0 : b]: (~ $false)) != X18) | ($true = ((X1 @ X18)))) & ! [X6 : (b > $o),X5 : ((b > $o) > $o)] : (((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y1 @ Y0) & (X5 @ Y1))))) != X6) | ? [X7 : (b > $o)] : ((((X1 @ X7)) != $true) & ($true = ((X5 @ X7)))) | (((X1 @ X6)) = $true)))),
% 0.23/0.30 inference(flattening,[],[f6])).
% 0.23/0.30 thf(f8,plain,(
% 0.23/0.30 ? [X0 : ((a > $o) > $o),X1 : ((b > $o) > $o),X2 : (a > b)] : (? [X3 : (b > $o)] : (! [X4 : (b > $o)] : ((((X1 @ X4)) = $true) | ((^[Y0 : b]: (~ (X3 @ Y0))) != X4)) & ? [X5 : (a > $o)] : (? [X6 : (a > $o)] : ((((X0 @ X6)) != $true) & ((^[Y0 : a]: (~ (X5 @ Y0))) = X6)) & ((^[Y0 : a]: (X3 @ (X2 @ Y0))) = X5))) & ! [X7 : (a > $o),X8 : ((a > $o) > $o)] : (? [X9 : (a > $o)] : (($true = ((X8 @ X9))) & (((X0 @ X9)) != $true)) | (((X0 @ X7)) = $true) | ((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((X8 @ Y1) & (Y1 @ Y0))))) != X7)) & ! [X10 : (b > $o)] : (! [X11 : (a > $o)] : (((^[Y0 : a]: (X10 @ (X2 @ Y0))) != X11) | (((X0 @ X11)) = $true)) | ($true != ((X1 @ X10)))) & ! [X12 : (a > $o),X13 : (a > $o),X14 : (a > $o)] : ((((X0 @ X14)) != $true) | (((X0 @ X12)) = $true) | ((^[Y0 : a]: ((X14 @ Y0) & (X13 @ Y0))) != X12) | (((X0 @ X13)) != $true)) & ! [X15 : (a > $o)] : (((^[Y0 : a]: ($false)) != X15) | ($true = ((X0 @ X15)))) & ! [X16 : (a > $o)] : (((^[Y0 : a]: (~ $false)) != X16) | (((X0 @ X16)) = $true)) & ! [X17 : (b > $o),X18 : (b > $o),X19 : (b > $o)] : ((((X1 @ X17)) = $true) | ((^[Y0 : b]: ((X18 @ Y0) & (X19 @ Y0))) != X17) | ($true != ((X1 @ X18))) | ($true != ((X1 @ X19)))) & ! [X20 : (b > $o)] : (($true = ((X1 @ X20))) | ((^[Y0 : b]: ($false)) != X20)) & ! [X21 : (b > $o)] : (((^[Y0 : b]: (~ $false)) != X21) | (((X1 @ X21)) = $true)) & ! [X22 : (b > $o),X23 : ((b > $o) > $o)] : (((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y1 @ Y0) & (X23 @ Y1))))) != X22) | ? [X24 : (b > $o)] : ((((X1 @ X24)) != $true) & (((X23 @ X24)) = $true)) | ($true = ((X1 @ X22)))))),
% 0.23/0.30 inference(rectify,[],[f7])).
% 0.23/0.30 thf(f9,plain,(
% 0.23/0.30 (! [X4 : (b > $o)] : (($true = ((sK1 @ X4))) | ((^[Y0 : b]: (~ (sK3 @ Y0))) != X4)) & (((((sK0 @ sK5)) != $true) & ((^[Y0 : a]: (~ (sK4 @ Y0))) = sK5)) & (sK4 = (^[Y0 : a]: (sK3 @ (sK2 @ Y0)))))) & ! [X7 : (a > $o),X8 : ((a > $o) > $o)] : (((((X8 @ (sK6 @ X8))) = $true) & ($true != ((sK0 @ (sK6 @ X8))))) | ($true = ((sK0 @ X7))) | ((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((X8 @ Y1) & (Y1 @ Y0))))) != X7)) & ! [X10 : (b > $o)] : (! [X11 : (a > $o)] : (((^[Y0 : a]: (X10 @ (sK2 @ Y0))) != X11) | ($true = ((sK0 @ X11)))) | (((sK1 @ X10)) != $true)) & ! [X12 : (a > $o),X13 : (a > $o),X14 : (a > $o)] : (($true != ((sK0 @ X14))) | ($true = ((sK0 @ X12))) | ((^[Y0 : a]: ((X14 @ Y0) & (X13 @ Y0))) != X12) | ($true != ((sK0 @ X13)))) & ! [X15 : (a > $o)] : (((^[Y0 : a]: ($false)) != X15) | (((sK0 @ X15)) = $true)) & ! [X16 : (a > $o)] : (((^[Y0 : a]: (~ $false)) != X16) | ($true = ((sK0 @ X16)))) & ! [X17 : (b > $o),X18 : (b > $o),X19 : (b > $o)] : (($true = ((sK1 @ X17))) | ((^[Y0 : b]: ((X18 @ Y0) & (X19 @ Y0))) != X17) | (((sK1 @ X18)) != $true) | ($true != ((sK1 @ X19)))) & ! [X20 : (b > $o)] : (($true = ((sK1 @ X20))) | ((^[Y0 : b]: ($false)) != X20)) & ! [X21 : (b > $o)] : (((^[Y0 : b]: (~ $false)) != X21) | ($true = ((sK1 @ X21)))) & ! [X22 : (b > $o),X23 : ((b > $o) > $o)] : (((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y1 @ Y0) & (X23 @ Y1))))) != X22) | (($true != ((sK1 @ (sK7 @ X23)))) & (((X23 @ (sK7 @ X23))) = $true)) | (((sK1 @ X22)) = $true))),
% 0.23/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X5,sK4),skolemize(X6,sK5),skolemize(X24,sK7 @ X23),skolemize(X24,sK7 @ X23)],[f8])).
% 0.23/0.30 thf(f18,plain,(
% 0.23/0.30 ( ! [X10 : (b > $o),X11 : (a > $o)] : (((^[Y0 : a]: (X10 @ (sK2 @ Y0))) != X11) | ($true = ((sK0 @ X11))) | (((sK1 @ X10)) != $true)) )),
% 0.23/0.30 inference(cnf_transformation,[],[f9])).
% 0.23/0.30 thf(f21,plain,(
% 0.23/0.30 (sK4 = (^[Y0 : a]: (sK3 @ (sK2 @ Y0))))),
% 0.23/0.30 inference(cnf_transformation,[],[f9])).
% 0.23/0.30 thf(f22,plain,(
% 0.23/0.30 ((^[Y0 : a]: (~ (sK4 @ Y0))) = sK5)),
% 0.23/0.30 inference(cnf_transformation,[],[f9])).
% 0.23/0.30 thf(f23,plain,(
% 0.23/0.30 (((sK0 @ sK5)) != $true)),
% 0.23/0.30 inference(cnf_transformation,[],[f9])).
% 0.23/0.30 thf(f24,plain,(
% 0.23/0.30 ( ! [X4 : (b > $o)] : (($true = ((sK1 @ X4))) | ((^[Y0 : b]: (~ (sK3 @ Y0))) != X4)) )),
% 0.23/0.30 inference(cnf_transformation,[],[f9])).
% 0.23/0.30 thf(f27,plain,(
% 0.23/0.30 ((^[Y0 : a]: (~ ((^[Y1 : a]: (sK3 @ (sK2 @ Y1))) @ Y0))) = sK5)),
% 0.23/0.30 inference(definition_unfolding,[],[f22,f21])).
% 0.23/0.30 thf(f28,plain,(
% 0.23/0.30 (((sK0 @ (^[Y0 : a]: (~ ((^[Y1 : a]: (sK3 @ (sK2 @ Y1))) @ Y0))))) != $true)),
% 0.23/0.30 inference(definition_unfolding,[],[f23,f27])).
% 0.23/0.30 thf(f29,plain,(
% 0.23/0.30 (((sK1 @ (^[Y0 : b]: (~ (sK3 @ Y0))))) = $true)),
% 0.23/0.30 inference(equality_resolution,[],[f24])).
% 0.23/0.30 thf(f32,plain,(
% 0.23/0.30 ( ! [X10 : (b > $o)] : ((((sK1 @ X10)) != $true) | ($true = ((sK0 @ (^[Y0 : a]: (X10 @ (sK2 @ Y0))))))) )),
% 0.23/0.30 inference(equality_resolution,[],[f18])).
% 0.23/0.30 thf(f41,plain,(
% 0.23/0.30 ($true != ((sK0 @ (^[Y0 : a]: (~ (sK3 @ (sK2 @ Y0)))))))),
% 0.23/0.30 inference(beta-eta_normalization,[],[f28])).
% 0.23/0.30 thf(f46,plain,(
% 0.23/0.30 ($true != $true) | ($true = ((sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (~ (sK3 @ Y1))) @ (sK2 @ Y0))))))),
% 0.23/0.30 inference(constrained_superposition,[],[f32,f29])).
% 0.23/0.30 thf(f49,plain,(
% 0.23/0.30 ($true = ((sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (~ (sK3 @ Y1))) @ (sK2 @ Y0))))))),
% 0.23/0.30 inference(trivial_inequality_removal,[],[f46])).
% 0.23/0.30 thf(f50,plain,(
% 0.23/0.30 ($true = ((sK0 @ (^[Y0 : a]: (~ (sK3 @ (sK2 @ Y0)))))))),
% 0.23/0.30 inference(beta-eta_normalization,[],[f49])).
% 0.23/0.30 thf(f53,plain,(
% 0.23/0.30 $false),
% 0.23/0.30 inference(forward_subsumption_resolution,[],[f50,f41])).
% 0.23/0.30 % SZS output end Proof for theBenchmark
% 0.23/0.30 % (2251007)------------------------------
% 0.23/0.30 % (2251007)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (2251007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (2251007)CaDiCaL version: 2.1.3
% 0.23/0.30 % (2251007)Termination reason: Refutation
% 0.23/0.30 % (2251007)Time elapsed: 0.006 s
% 0.23/0.30 % (2251007)Peak memory usage: 12 MB
% 0.23/0.30 % (2251007)Instructions burned: 9 (million)
% 0.23/0.30 % (2251002)Success in time 0.041 s
% 0.23/0.30 % Vampire exiting
%------------------------------------------------------------------------------