%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV200^5 : 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 : n017.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 08:38:01 AM UTC 2026
% Result : Theorem 0.24s 0.31s
% Output : Refutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV200^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n017.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 15:16:12 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.10/0.25 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
% 0.24/0.31 % (454297)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.31 % (454302)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2185441699:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.31 % (454303)lrs+10_16_si=on:nwc=1.5:random_seed=3197092084:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.31 % (454305)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=3491918634: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)
% 0.24/0.31 % (454303) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-454297-454303"...
% 0.24/0.31 % (454302) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-454297-454302"...
% 0.24/0.31 % (454304)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2380567156:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.31 % (454305) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-454297-454305"...
% 0.24/0.31 % (454302)...printing done.
% 0.24/0.31 % (454303)...printing done.
% 0.24/0.31 % (454304) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-454297-454304"...
% 0.24/0.31 % (454302)Refutation found. Thanks to Tanya!
% 0.24/0.31 % SZS status Theorem for theBenchmark
% 0.24/0.31 % SZS output start Proof for theBenchmark
% 0.24/0.31 thf(type_def_5, type, a: $tType).
% 0.24/0.31 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.24/0.31 thf(func_def_0, type, x: a).
% 0.24/0.31 thf(func_def_1, type, cZ: a).
% 0.24/0.31 thf(func_def_2, type, cP: (a > a > a)).
% 0.24/0.31 thf(func_def_6, type, sK0: (a > a > a > $o)).
% 0.24/0.31 thf(func_def_7, type, sK1: ((a > $o) > a)).
% 0.24/0.31 thf(func_def_8, type, sK2: ((a > $o) > a)).
% 0.24/0.31 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.24/0.31 thf(f1,conjecture,(
% 0.24/0.31 (! [X4 : (a > $o)] : (((X4 @ cZ) & ! [X0 : a,X1 : a] : (((X4 @ X0) & (X4 @ X1)) => (X4 @ (cP @ X0 @ X1)))) => ! [X0 : a] : (X4 @ X0)) & ! [X1 : a,X0 : a] : (((cP @ X0 @ X1)) != cZ) & ! [X1 : a,X2 : a,X0 : a,X3 : a] : ((((cP @ X0 @ X2)) = ((cP @ X1 @ X3))) => ((X0 = X1) & (X2 = X3)))) => ! [X5 : (a > a > a > $o)] : ((! [X7 : a,X8 : a,X6 : a] : ((((X6 = X8) & (X7 = cZ)) | ((X6 = cZ) & (X7 = X8)) | ? [X14 : a,X10 : a,X9 : a,X13 : a,X11 : a,X12 : a] : ((X5 @ X9 @ X11 @ X13) & (X8 = ((cP @ X13 @ X14))) & (X6 = ((cP @ X9 @ X10))) & (X7 = ((cP @ X11 @ X12))) & (X5 @ X10 @ X12 @ X14))) => (X5 @ X6 @ X7 @ X8)) & $true) => (X5 @ cZ @ x @ x))),
% 0.24/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cS_LEM1C_pme)).
% 0.24/0.31 thf(f2,negated_conjecture,(
% 0.24/0.31 ~((! [X4 : (a > $o)] : (((X4 @ cZ) & ! [X0 : a,X1 : a] : (((X4 @ X0) & (X4 @ X1)) => (X4 @ (cP @ X0 @ X1)))) => ! [X0 : a] : (X4 @ X0)) & ! [X1 : a,X0 : a] : (((cP @ X0 @ X1)) != cZ) & ! [X1 : a,X2 : a,X0 : a,X3 : a] : ((((cP @ X0 @ X2)) = ((cP @ X1 @ X3))) => ((X0 = X1) & (X2 = X3)))) => ! [X5 : (a > a > a > $o)] : ((! [X7 : a,X8 : a,X6 : a] : ((((X6 = X8) & (X7 = cZ)) | ((X6 = cZ) & (X7 = X8)) | ? [X14 : a,X10 : a,X9 : a,X13 : a,X11 : a,X12 : a] : ((X5 @ X9 @ X11 @ X13) & (X8 = ((cP @ X13 @ X14))) & (X6 = ((cP @ X9 @ X10))) & (X7 = ((cP @ X11 @ X12))) & (X5 @ X10 @ X12 @ X14))) => (X5 @ X6 @ X7 @ X8)) & $true) => (X5 @ cZ @ x @ x)))),
% 0.24/0.31 inference(negated_conjecture,[status(cth)],[f1])).
% 0.24/0.31 thf(f3,plain,(
% 0.24/0.31 ~((! [X0 : (a > $o)] : (((X0 @ cZ) & ! [X1 : a,X2 : a] : (((X0 @ X1) & (X0 @ X2)) => (X0 @ (cP @ X1 @ X2)))) => ! [X3 : a] : (X0 @ X3)) & ! [X4 : a,X5 : a] : (cZ != ((cP @ X5 @ X4))) & ! [X6 : a,X7 : a,X8 : a,X9 : a] : ((((cP @ X8 @ X7)) = ((cP @ X6 @ X9))) => ((X6 = X8) & (X7 = X9)))) => ! [X10 : (a > a > a > $o)] : ((! [X11 : a,X12 : a,X13 : a] : ((((X12 = X13) & (cZ = X11)) | ((cZ = X13) & (X11 = X12)) | ? [X14 : a,X15 : a,X16 : a,X17 : a,X18 : a,X19 : a] : ((X10 @ X16 @ X18 @ X17) & (((cP @ X17 @ X14)) = X12) & (((cP @ X16 @ X15)) = X13) & (((cP @ X18 @ X19)) = X11) & (X10 @ X15 @ X19 @ X14))) => (X10 @ X13 @ X11 @ X12)) & $true) => (X10 @ cZ @ x @ x)))),
% 0.24/0.31 inference(rectify,[],[f2])).
% 0.24/0.31 thf(f4,plain,(
% 0.24/0.31 ~((! [X5 : a,X4 : a] : (cZ != ((cP @ X5 @ X4))) & ! [X0 : (a > $o)] : ((($true = ((X0 @ cZ))) & ! [X2 : a,X1 : a] : ((($true = ((X0 @ X1))) & ($true = ((X0 @ X2)))) => ($true = ((X0 @ (cP @ X1 @ X2)))))) => ! [X3 : a] : ($true = ((X0 @ X3)))) & ! [X6 : a,X9 : a,X7 : a,X8 : a] : ((((cP @ X8 @ X7)) = ((cP @ X6 @ X9))) => ((X6 = X8) & (X7 = X9)))) => ! [X10 : (a > a > a > $o)] : ((! [X13 : a,X11 : a,X12 : a] : ((((X12 = X13) & (cZ = X11)) | ((X11 = X12) & (cZ = X13)) | ? [X16 : a,X15 : a,X17 : a,X18 : a,X19 : a,X14 : a] : ((((X10 @ X16 @ X18 @ X17)) = $true) & (((X10 @ X15 @ X19 @ X14)) = $true) & (((cP @ X17 @ X14)) = X12) & (((cP @ X18 @ X19)) = X11) & (((cP @ X16 @ X15)) = X13))) => ($true = ((X10 @ X13 @ X11 @ X12)))) & $true) => (((X10 @ cZ @ x @ x)) = $true)))),
% 0.24/0.31 inference(fool_elimination,[],[f3])).
% 0.24/0.31 thf(f5,plain,(
% 0.24/0.31 ~((! [X5 : a,X4 : a] : (cZ != ((cP @ X5 @ X4))) & ! [X0 : (a > $o)] : ((($true = ((X0 @ cZ))) & ! [X2 : a,X1 : a] : ((($true = ((X0 @ X1))) & ($true = ((X0 @ X2)))) => ($true = ((X0 @ (cP @ X1 @ X2)))))) => ! [X3 : a] : ($true = ((X0 @ X3)))) & ! [X6 : a,X9 : a,X7 : a,X8 : a] : ((((cP @ X8 @ X7)) = ((cP @ X6 @ X9))) => ((X6 = X8) & (X7 = X9)))) => ! [X10 : (a > a > a > $o)] : (! [X13 : a,X11 : a,X12 : a] : ((((X12 = X13) & (cZ = X11)) | ((X11 = X12) & (cZ = X13)) | ? [X16 : a,X15 : a,X17 : a,X18 : a,X19 : a,X14 : a] : ((((X10 @ X16 @ X18 @ X17)) = $true) & (((X10 @ X15 @ X19 @ X14)) = $true) & (((cP @ X17 @ X14)) = X12) & (((cP @ X18 @ X19)) = X11) & (((cP @ X16 @ X15)) = X13))) => ($true = ((X10 @ X13 @ X11 @ X12)))) => (((X10 @ cZ @ x @ x)) = $true)))),
% 0.24/0.31 inference(true_and_false_elimination,[],[f4])).
% 0.24/0.31 thf(f6,plain,(
% 0.24/0.31 ? [X10 : (a > a > a > $o)] : ((((X10 @ cZ @ x @ x)) != $true) & ! [X11 : a,X13 : a,X12 : a] : (($true = ((X10 @ X13 @ X11 @ X12))) | (! [X19 : a,X16 : a,X14 : a,X15 : a,X17 : a,X18 : a] : ((((cP @ X16 @ X15)) != X13) | (((X10 @ X15 @ X19 @ X14)) != $true) | (((cP @ X18 @ X19)) != X11) | (((cP @ X17 @ X14)) != X12) | (((X10 @ X16 @ X18 @ X17)) != $true)) & ((X12 != X13) | (cZ != X11)) & ((X11 != X12) | (cZ != X13))))) & (! [X5 : a,X4 : a] : (cZ != ((cP @ X5 @ X4))) & ! [X0 : (a > $o)] : (! [X3 : a] : ($true = ((X0 @ X3))) | (($true != ((X0 @ cZ))) | ? [X2 : a,X1 : a] : (($true != ((X0 @ (cP @ X1 @ X2)))) & (($true = ((X0 @ X1))) & ($true = ((X0 @ X2))))))) & ! [X7 : a,X8 : a,X6 : a,X9 : a] : ((((cP @ X8 @ X7)) != ((cP @ X6 @ X9))) | ((X6 = X8) & (X7 = X9))))),
% 0.24/0.31 inference(ennf_transformation,[],[f5])).
% 0.24/0.31 thf(f7,plain,(
% 0.24/0.31 ? [X10 : (a > a > a > $o)] : ((((X10 @ cZ @ x @ x)) != $true) & ! [X11 : a,X13 : a,X12 : a] : (($true = ((X10 @ X13 @ X11 @ X12))) | (! [X19 : a,X16 : a,X14 : a,X15 : a,X17 : a,X18 : a] : ((((cP @ X16 @ X15)) != X13) | (((X10 @ X15 @ X19 @ X14)) != $true) | (((cP @ X18 @ X19)) != X11) | (((cP @ X17 @ X14)) != X12) | (((X10 @ X16 @ X18 @ X17)) != $true)) & ((X12 != X13) | (cZ != X11)) & ((X11 != X12) | (cZ != X13))))) & ! [X5 : a,X4 : a] : (cZ != ((cP @ X5 @ X4))) & ! [X0 : (a > $o)] : (? [X2 : a,X1 : a] : (($true = ((X0 @ X2))) & ($true = ((X0 @ X1))) & ($true != ((X0 @ (cP @ X1 @ X2))))) | ($true != ((X0 @ cZ))) | ! [X3 : a] : ($true = ((X0 @ X3)))) & ! [X7 : a,X8 : a,X6 : a,X9 : a] : ((((cP @ X8 @ X7)) != ((cP @ X6 @ X9))) | ((X6 = X8) & (X7 = X9)))),
% 0.24/0.31 inference(flattening,[],[f6])).
% 0.24/0.31 thf(f8,plain,(
% 0.24/0.31 ? [X0 : (a > a > a > $o)] : (($true != ((X0 @ cZ @ x @ x))) & ! [X1 : a,X2 : a,X3 : a] : (($true = ((X0 @ X2 @ X1 @ X3))) | (! [X4 : a,X5 : a,X6 : a,X7 : a,X8 : a,X9 : a] : ((((cP @ X5 @ X7)) != X2) | ($true != ((X0 @ X7 @ X4 @ X6))) | (((cP @ X9 @ X4)) != X1) | (((cP @ X8 @ X6)) != X3) | (((X0 @ X5 @ X9 @ X8)) != $true)) & ((X2 != X3) | (cZ != X1)) & ((X1 != X3) | (cZ != X2))))) & ! [X10 : a,X11 : a] : (cZ != ((cP @ X10 @ X11))) & ! [X12 : (a > $o)] : (? [X13 : a,X14 : a] : ((((X12 @ X13)) = $true) & ($true = ((X12 @ X14))) & (((X12 @ (cP @ X14 @ X13))) != $true)) | (((X12 @ cZ)) != $true) | ! [X15 : a] : ($true = ((X12 @ X15)))) & ! [X16 : a,X17 : a,X18 : a,X19 : a] : ((((cP @ X18 @ X19)) != ((cP @ X17 @ X16))) | ((X17 = X18) & (X16 = X19)))),
% 0.24/0.31 inference(rectify,[],[f7])).
% 0.24/0.31 thf(f9,plain,(
% 0.24/0.31 ((((sK0 @ cZ @ x @ x)) != $true) & ! [X1 : a,X2 : a,X3 : a] : ((((sK0 @ X2 @ X1 @ X3)) = $true) | (! [X4 : a,X5 : a,X6 : a,X7 : a,X8 : a,X9 : a] : ((((cP @ X5 @ X7)) != X2) | ($true != ((sK0 @ X7 @ X4 @ X6))) | (((cP @ X9 @ X4)) != X1) | (((cP @ X8 @ X6)) != X3) | ($true != ((sK0 @ X5 @ X9 @ X8)))) & ((X2 != X3) | (cZ != X1)) & ((X1 != X3) | (cZ != X2))))) & ! [X10 : a,X11 : a] : (cZ != ((cP @ X10 @ X11))) & ! [X12 : (a > $o)] : (((((X12 @ (sK1 @ X12))) = $true) & ($true = ((X12 @ (sK2 @ X12)))) & (((X12 @ (cP @ (sK2 @ X12) @ (sK1 @ X12)))) != $true)) | (((X12 @ cZ)) != $true) | ! [X15 : a] : ($true = ((X12 @ X15)))) & ! [X16 : a,X17 : a,X18 : a,X19 : a] : ((((cP @ X18 @ X19)) != ((cP @ X17 @ X16))) | ((X17 = X18) & (X16 = X19)))),
% 0.24/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X14,sK2 @ X12),skolemize(X14,sK2 @ X12)],[f8])).
% 0.24/0.31 thf(f16,plain,(
% 0.24/0.31 ( ! [X2 : a,X3 : a,X1 : a] : ((((sK0 @ X2 @ X1 @ X3)) = $true) | (X1 != X3) | (cZ != X2)) )),
% 0.24/0.31 inference(cnf_transformation,[],[f9])).
% 0.24/0.31 thf(f19,plain,(
% 0.24/0.31 (((sK0 @ cZ @ x @ x)) != $true)),
% 0.24/0.31 inference(cnf_transformation,[],[f9])).
% 0.24/0.31 thf(f27,plain,(
% 0.24/0.31 ( ! [X2 : a,X3 : a] : (($true = ((sK0 @ X2 @ X3 @ X3))) | (cZ != X2)) )),
% 0.24/0.31 inference(equality_resolution,[],[f16])).
% 0.24/0.31 thf(f28,plain,(
% 0.24/0.31 ( ! [X3 : a] : (($true = ((sK0 @ cZ @ X3 @ X3)))) )),
% 0.24/0.31 inference(equality_resolution,[],[f27])).
% 0.24/0.31 thf(f29,plain,(
% 0.24/0.31 ($true != $true)),
% 0.24/0.31 inference(constrained_superposition,[],[f19,f28])).
% 0.24/0.31 thf(f30,plain,(
% 0.24/0.31 $false),
% 0.24/0.31 inference(trivial_inequality_removal,[],[f29])).
% 0.24/0.31 % SZS output end Proof for theBenchmark
% 0.24/0.31 % (454302)------------------------------
% 0.24/0.31 % (454302)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.31 % (454302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.31 % (454302)CaDiCaL version: 2.1.3
% 0.24/0.31 % (454302)Termination reason: Refutation
% 0.24/0.31 % (454302)Time elapsed: 0.004 s
% 0.24/0.31 % (454302)Peak memory usage: 12 MB
% 0.24/0.31 % (454302)Instructions burned: 5 (million)
% 0.24/0.31 % (454297)Success in time 0.044 s
% 0.24/0.31 % Vampire exiting
%------------------------------------------------------------------------------