%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV259^5 : 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 08:38:08 AM UTC 2026
% Result : Theorem 0.10s 0.25s
% Output : Refutation 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV259^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n008.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 15:29:09 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 Running higher-order theorem proving
% 0.10/0.21 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
% 0.10/0.25 % (3298393)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.10/0.25 % (3298399)lrs+10_16_si=on:nwc=1.5:random_seed=247905082:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.10/0.25 % (3298398)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2413489544:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.10/0.25 % (3298402)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=956162747:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.10/0.25 % (3298402) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3298393-3298402"...
% 0.10/0.25 % (3298398) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3298393-3298398"...
% 0.10/0.25 % (3298399) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3298393-3298399"...
% 0.10/0.25 % (3298400)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3494886931:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.10/0.25 % (3298402)...printing done.
% 0.10/0.25 % (3298402)Refutation found. Thanks to Tanya!
% 0.10/0.25 % SZS status Theorem for theBenchmark
% 0.10/0.25 % SZS output start Proof for theBenchmark
% 0.10/0.25 thf(type_def_5, type, b: $tType).
% 0.10/0.25 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.10/0.25 thf(func_def_1, type, vNOT: ($o > $o)).
% 0.10/0.25 thf(func_def_4, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.10/0.25 thf(func_def_5, type, vAND: ($o > $o > $o)).
% 0.10/0.25 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.10/0.25 thf(func_def_7, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.10/0.25 thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 0.10/0.25 thf(func_def_9, type, sK0: ((b > $o) > $o)).
% 0.10/0.25 thf(func_def_10, type, sK1: b).
% 0.10/0.25 thf(func_def_11, type, sK2: (b > $o)).
% 0.10/0.25 thf(func_def_12, type, sK3: (b > $o)).
% 0.10/0.25 thf(func_def_13, type, sK4: (((b > $o) > $o) > b > $o)).
% 0.10/0.25 thf(f1,conjecture,(
% 0.10/0.25 ! [X0 : ((b > $o) > $o)] : ((! [X1 : (b > $o)] : (((^[X2 : b] : ($false)) = X1) => (X0 @ X1)) & ! [X3 : ((b > $o) > $o),X1 : (b > $o)] : ((! [X2 : (b > $o)] : ((X3 @ X2) => (X0 @ X2)) & (X1 = (^[X2 : b] : (? [X4 : (b > $o)] : ((X3 @ X4) & (X4 @ X2)))))) => (X0 @ X1)) & ! [X5 : (b > $o),X4 : (b > $o),X6 : (b > $o)] : (((X0 @ X6) & (X0 @ X5) & (X4 = (^[X2 : b] : ((X5 @ X2) & (X6 @ X2))))) => (X0 @ X4)) & ! [X1 : (b > $o)] : (((^[X2 : b] : (~$false)) = X1) => (X0 @ X1))) => ! [X2 : b,X7 : (b > $o)] : ((X7 @ X2) => ! [X4 : (b > $o)] : ((! [X8 : b] : ((X7 @ X8) => (X4 @ X8)) & ! [X1 : (b > $o)] : (((^[X8 : b] : (~(X4 @ X8))) = X1) => (X0 @ X1))) => (X4 @ X2))))),
% 0.10/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCLOSURE_THM0_pme)).
% 0.10/0.25 thf(f2,negated_conjecture,(
% 0.10/0.25 ~ ! [X0 : ((b > $o) > $o)] : ((! [X1 : (b > $o)] : (((^[X2 : b] : ($false)) = X1) => (X0 @ X1)) & ! [X3 : ((b > $o) > $o),X1 : (b > $o)] : ((! [X2 : (b > $o)] : ((X3 @ X2) => (X0 @ X2)) & (X1 = (^[X2 : b] : (? [X4 : (b > $o)] : ((X3 @ X4) & (X4 @ X2)))))) => (X0 @ X1)) & ! [X5 : (b > $o),X4 : (b > $o),X6 : (b > $o)] : (((X0 @ X6) & (X0 @ X5) & (X4 = (^[X2 : b] : ((X5 @ X2) & (X6 @ X2))))) => (X0 @ X4)) & ! [X1 : (b > $o)] : (((^[X2 : b] : (~$false)) = X1) => (X0 @ X1))) => ! [X2 : b,X7 : (b > $o)] : ((X7 @ X2) => ! [X4 : (b > $o)] : ((! [X8 : b] : ((X7 @ X8) => (X4 @ X8)) & ! [X1 : (b > $o)] : (((^[X8 : b] : (~(X4 @ X8))) = X1) => (X0 @ X1))) => (X4 @ X2))))),
% 0.10/0.25 inference(negated_conjecture,[status(cth)],[f1])).
% 0.10/0.25 thf(f3,plain,(
% 0.10/0.25 ~ ! [X0 : ((b > $o) > $o)] : ((! [X1 : (b > $o)] : (((^[X2 : b] : ($false)) = X1) => (X0 @ X1)) & ! [X3 : ((b > $o) > $o),X4 : (b > $o)] : ((! [X5 : (b > $o)] : ((X3 @ X5) => (X0 @ X5)) & (X4 = (^[X6 : b] : (? [X7 : (b > $o)] : ((X3 @ X7) & (X7 @ X6)))))) => (X0 @ X4)) & ! [X8 : (b > $o),X9 : (b > $o),X10 : (b > $o)] : (((X0 @ X10) & (X0 @ X8) & (X9 = (^[X11 : b] : ((X8 @ X11) & (X10 @ X11))))) => (X0 @ X9)) & ! [X12 : (b > $o)] : (((^[X13 : b] : (~$false)) = X12) => (X0 @ X12))) => ! [X14 : b,X15 : (b > $o)] : ((X15 @ X14) => ! [X16 : (b > $o)] : ((! [X17 : b] : ((X15 @ X17) => (X16 @ X17)) & ! [X18 : (b > $o)] : (((^[X19 : b] : (~(X16 @ X19))) = X18) => (X0 @ X18))) => (X16 @ X14))))),
% 0.10/0.25 inference(rectify,[],[f2])).
% 0.10/0.25 thf(f4,plain,(
% 0.10/0.25 ~ ! [X0 : ((b > $o) > $o)] : ((! [X1 : (b > $o)] : (((^[Y0 : b]: ($false)) = X1) => (((X0 @ X1)) = $true)) & ! [X3 : ((b > $o) > $o),X4 : (b > $o)] : ((! [X5 : (b > $o)] : (($true = ((X3 @ X5))) => (((X0 @ X5)) = $true)) & ((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y1 @ Y0) & (X3 @ Y1))))) = X4)) => (((X0 @ X4)) = $true)) & ! [X8 : (b > $o),X9 : (b > $o),X10 : (b > $o)] : ((($true = ((X0 @ X10))) & ($true = ((X0 @ X8))) & ((^[Y0 : b]: ((X10 @ Y0) & (X8 @ Y0))) = X9)) => ($true = ((X0 @ X9)))) & ! [X12 : (b > $o)] : (((^[Y0 : b]: (~ $false)) = X12) => ($true = ((X0 @ X12))))) => ! [X14 : b,X15 : (b > $o)] : (($true = ((X15 @ X14))) => ! [X16 : (b > $o)] : ((! [X17 : b] : (($true = ((X15 @ X17))) => ($true = ((X16 @ X17)))) & ! [X18 : (b > $o)] : (((^[Y0 : b]: (~ (X16 @ Y0))) = X18) => ($true = ((X0 @ X18))))) => ($true = ((X16 @ X14))))))),
% 0.10/0.25 inference(fool_elimination,[],[f3])).
% 0.10/0.25 thf(f5,plain,(
% 0.10/0.25 ~ ! [X0 : ((b > $o) > $o)] : ((! [X1 : (b > $o)] : (((^[Y0 : b]: ($false)) = X1) => (((X0 @ X1)) = $true)) & ! [X5 : (b > $o),X6 : (b > $o),X7 : (b > $o)] : (((((X0 @ X5)) = $true) & ($true = ((X0 @ X7))) & ((^[Y0 : b]: ((X7 @ Y0) & (X5 @ Y0))) = X6)) => (((X0 @ X6)) = $true)) & ! [X8 : (b > $o)] : (((^[Y0 : b]: (~ $false)) = X8) => ($true = ((X0 @ X8)))) & ! [X2 : ((b > $o) > $o),X3 : (b > $o)] : ((! [X4 : (b > $o)] : ((((X2 @ X4)) = $true) => (((X0 @ X4)) = $true)) & ((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y1 @ Y0) & (X2 @ Y1))))) = X3)) => ($true = ((X0 @ X3))))) => ! [X10 : (b > $o),X9 : b] : (($true = ((X10 @ X9))) => ! [X11 : (b > $o)] : ((! [X12 : b] : (($true = ((X10 @ X12))) => ($true = ((X11 @ X12)))) & ! [X13 : (b > $o)] : (((^[Y0 : b]: (~ (X11 @ Y0))) = X13) => ($true = ((X0 @ X13))))) => ($true = ((X11 @ X9))))))),
% 0.10/0.25 inference(rectify,[],[f4])).
% 0.10/0.25 thf(f6,plain,(
% 0.10/0.25 ? [X0 : ((b > $o) > $o)] : (? [X10 : (b > $o),X9 : b] : (? [X11 : (b > $o)] : (($true != ((X11 @ X9))) & (! [X12 : b] : (($true = ((X11 @ X12))) | ($true != ((X10 @ X12)))) & ! [X13 : (b > $o)] : (((^[Y0 : b]: (~ (X11 @ Y0))) != X13) | ($true = ((X0 @ X13)))))) & ($true = ((X10 @ X9)))) & (! [X1 : (b > $o)] : ((((X0 @ X1)) = $true) | ((^[Y0 : b]: ($false)) != X1)) & ! [X5 : (b > $o),X6 : (b > $o),X7 : (b > $o)] : ((((X0 @ X6)) = $true) | ((((X0 @ X5)) != $true) | ($true != ((X0 @ X7))) | ((^[Y0 : b]: ((X7 @ Y0) & (X5 @ Y0))) != X6))) & ! [X8 : (b > $o)] : (($true = ((X0 @ X8))) | ((^[Y0 : b]: (~ $false)) != X8)) & ! [X2 : ((b > $o) > $o),X3 : (b > $o)] : (($true = ((X0 @ X3))) | (? [X4 : (b > $o)] : ((((X2 @ X4)) = $true) & (((X0 @ X4)) != $true)) | ((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y1 @ Y0) & (X2 @ Y1))))) != X3)))))),
% 0.10/0.25 inference(ennf_transformation,[],[f5])).
% 0.10/0.25 thf(f7,plain,(
% 0.10/0.25 ? [X0 : ((b > $o) > $o)] : (? [X9 : b,X10 : (b > $o)] : (? [X11 : (b > $o)] : (! [X12 : b] : (($true = ((X11 @ X12))) | ($true != ((X10 @ X12)))) & ! [X13 : (b > $o)] : (((^[Y0 : b]: (~ (X11 @ Y0))) != X13) | ($true = ((X0 @ X13)))) & ($true != ((X11 @ X9)))) & ($true = ((X10 @ X9)))) & ! [X8 : (b > $o)] : (($true = ((X0 @ X8))) | ((^[Y0 : b]: (~ $false)) != X8)) & ! [X6 : (b > $o),X7 : (b > $o),X5 : (b > $o)] : (($true != ((X0 @ X7))) | (((X0 @ X6)) = $true) | (((X0 @ X5)) != $true) | ((^[Y0 : b]: ((X7 @ Y0) & (X5 @ Y0))) != X6)) & ! [X1 : (b > $o)] : ((((X0 @ X1)) = $true) | ((^[Y0 : b]: ($false)) != X1)) & ! [X2 : ((b > $o) > $o),X3 : (b > $o)] : (? [X4 : (b > $o)] : ((((X2 @ X4)) = $true) & (((X0 @ X4)) != $true)) | ((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y1 @ Y0) & (X2 @ Y1))))) != X3) | ($true = ((X0 @ X3)))))),
% 0.10/0.25 inference(flattening,[],[f6])).
% 0.10/0.25 thf(f8,plain,(
% 0.10/0.25 ? [X0 : ((b > $o) > $o)] : (? [X1 : b,X2 : (b > $o)] : (? [X3 : (b > $o)] : (! [X4 : b] : (($true = ((X3 @ X4))) | ($true != ((X2 @ X4)))) & ! [X5 : (b > $o)] : (((^[Y0 : b]: (~ (X3 @ Y0))) != X5) | (((X0 @ X5)) = $true)) & ($true != ((X3 @ X1)))) & ($true = ((X2 @ X1)))) & ! [X6 : (b > $o)] : ((((X0 @ X6)) = $true) | ((^[Y0 : b]: (~ $false)) != X6)) & ! [X7 : (b > $o),X8 : (b > $o),X9 : (b > $o)] : (($true != ((X0 @ X8))) | ($true = ((X0 @ X7))) | ($true != ((X0 @ X9))) | ((^[Y0 : b]: ((X8 @ Y0) & (X9 @ Y0))) != X7)) & ! [X10 : (b > $o)] : (($true = ((X0 @ X10))) | ((^[Y0 : b]: ($false)) != X10)) & ! [X11 : ((b > $o) > $o),X12 : (b > $o)] : (? [X13 : (b > $o)] : (($true = ((X11 @ X13))) & ($true != ((X0 @ X13)))) | ((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y1 @ Y0) & (X11 @ Y1))))) != X12) | ($true = ((X0 @ X12)))))),
% 0.10/0.25 inference(rectify,[],[f7])).
% 0.10/0.25 thf(f9,plain,(
% 0.10/0.25 ((! [X4 : b] : (($true = ((sK3 @ X4))) | ($true != ((sK2 @ X4)))) & ! [X5 : (b > $o)] : (((^[Y0 : b]: (~ (sK3 @ Y0))) != X5) | ($true = ((sK0 @ X5)))) & ($true != ((sK3 @ sK1)))) & ($true = ((sK2 @ sK1)))) & ! [X6 : (b > $o)] : (($true = ((sK0 @ X6))) | ((^[Y0 : b]: (~ $false)) != X6)) & ! [X7 : (b > $o),X8 : (b > $o),X9 : (b > $o)] : (($true != ((sK0 @ X8))) | ($true = ((sK0 @ X7))) | ($true != ((sK0 @ X9))) | ((^[Y0 : b]: ((X8 @ Y0) & (X9 @ Y0))) != X7)) & ! [X10 : (b > $o)] : (($true = ((sK0 @ X10))) | ((^[Y0 : b]: ($false)) != X10)) & ! [X11 : ((b > $o) > $o),X12 : (b > $o)] : ((($true = ((X11 @ (sK4 @ X11)))) & ($true != ((sK0 @ (sK4 @ X11))))) | ((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y1 @ Y0) & (X11 @ Y1))))) != X12) | ($true = ((sK0 @ X12))))),
% 0.10/0.25 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X13,sK4 @ X11)],[f8])).
% 0.10/0.25 thf(f15,plain,(
% 0.10/0.25 ($true = ((sK2 @ sK1)))),
% 0.10/0.25 inference(cnf_transformation,[],[f9])).
% 0.10/0.25 thf(f16,plain,(
% 0.10/0.25 ($true != ((sK3 @ sK1)))),
% 0.10/0.25 inference(cnf_transformation,[],[f9])).
% 0.10/0.25 thf(f18,plain,(
% 0.10/0.25 ( ! [X4 : b] : (($true != ((sK2 @ X4))) | ($true = ((sK3 @ X4)))) )),
% 0.10/0.25 inference(cnf_transformation,[],[f9])).
% 0.10/0.25 thf(f27,plain,(
% 0.10/0.25 ($true = ((sK3 @ sK1))) | ($true != $true)),
% 0.10/0.25 inference(superposition,[],[f18,f15])).
% 0.10/0.25 thf(f28,plain,(
% 0.10/0.25 ($true = ((sK3 @ sK1)))),
% 0.10/0.25 inference(trivial_inequality_removal,[],[f27])).
% 0.10/0.25 thf(f29,plain,(
% 0.10/0.25 $false),
% 0.10/0.25 inference(forward_subsumption_resolution,[],[f28,f16])).
% 0.10/0.25 % SZS output end Proof for theBenchmark
% 0.10/0.25 % (3298402)------------------------------
% 0.10/0.25 % (3298402)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.25 % (3298402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.25 % (3298402)CaDiCaL version: 2.1.3
% 0.10/0.25 % (3298402)Termination reason: Refutation
% 0.10/0.25 % (3298402)Time elapsed: 0.001 s
% 0.10/0.25 % (3298402)Peak memory usage: 12 MB
% 0.10/0.25 % (3298402)Instructions burned: 4 (million)
% 0.10/0.25 % (3298393)Success in time 0.034 s
% 0.10/0.25 % Vampire exiting
%------------------------------------------------------------------------------