%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU967^5 : 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 : n006.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 08:32:03 AM UTC 2026
% Result : Theorem 0.20s 0.26s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU967^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n006.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:54:22 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.23 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
% 0.20/0.26 % (829458)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.26 % (829463)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2518036928:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.26 % (829463) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-829458-829463"...
% 0.20/0.26 % (829463)...printing done.
% 0.20/0.26 % (829463)Refutation found. Thanks to Tanya!
% 0.20/0.26 % SZS status Theorem for theBenchmark
% 0.20/0.26 % SZS output start Proof for theBenchmark
% 0.20/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.26 thf(func_def_0, type, cY_0: ((($i > $i) > $o) > $i)).
% 0.20/0.26 thf(func_def_1, type, cG_0: ((($i > $i) > $o) > $i > $i)).
% 0.20/0.26 thf(func_def_2, type, cP_0: ($i > $o)).
% 0.20/0.26 thf(func_def_3, type, cH_0: ((($i > $i) > $o) > $i > $i)).
% 0.20/0.26 thf(func_def_5, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.26 thf(func_def_6, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.26 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.26 thf(func_def_8, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.26 thf(func_def_11, type, sK0: ((($i > $i) > $i > $o) > $i)).
% 0.20/0.27 thf(func_def_12, type, sK1: ((($i > $i) > $i > $o) > $i)).
% 0.20/0.27 thf(func_def_13, type, vNOT: ($o > $o)).
% 0.20/0.27 thf(f1,conjecture,(
% 0.20/0.27 ~ ! [X0 : (($i > $i) > $i > $o)] : (? [X1 : $i] : (X0 @ (cH_0 @ (^[X2 : ($i > $i)] : (? [X3 : $i] : (X0 @ X2 @ X3)))) @ X1) & ? [X1 : $i] : (X0 @ (cG_0 @ (^[X2 : ($i > $i)] : (? [X3 : $i] : (X0 @ X2 @ X3)))) @ X1) & (~ ? [X1 : $i] : (X0 @ (^[X4 : $i] : ((cG_0 @ (^[X2 : ($i > $i)] : (? [X3 : $i] : (X0 @ X2 @ X3))) @ (cH_0 @ (^[X2 : ($i > $i)] : (? [X3 : $i] : (X0 @ X2 @ X3))) @ X4)))) @ X1) | (~(cP_0 @ (cG_0 @ (^[X2 : ($i > $i)] : (? [X1 : $i] : (X0 @ X2 @ X1))) @ (cY_0 @ (^[X2 : ($i > $i)] : (? [X1 : $i] : (X0 @ X2 @ X1)))))) & (cP_0 @ (cY_0 @ (^[X2 : ($i > $i)] : (? [X1 : $i] : (X0 @ X2 @ X1))))))))),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBUGWFFA_pme)).
% 0.20/0.27 thf(f2,negated_conjecture,(
% 0.20/0.27 ~ ~ ! [X0 : (($i > $i) > $i > $o)] : (? [X1 : $i] : (X0 @ (cH_0 @ (^[X2 : ($i > $i)] : (? [X3 : $i] : (X0 @ X2 @ X3)))) @ X1) & ? [X1 : $i] : (X0 @ (cG_0 @ (^[X2 : ($i > $i)] : (? [X3 : $i] : (X0 @ X2 @ X3)))) @ X1) & (~ ? [X1 : $i] : (X0 @ (^[X4 : $i] : ((cG_0 @ (^[X2 : ($i > $i)] : (? [X3 : $i] : (X0 @ X2 @ X3))) @ (cH_0 @ (^[X2 : ($i > $i)] : (? [X3 : $i] : (X0 @ X2 @ X3))) @ X4)))) @ X1) | (~(cP_0 @ (cG_0 @ (^[X2 : ($i > $i)] : (? [X1 : $i] : (X0 @ X2 @ X1))) @ (cY_0 @ (^[X2 : ($i > $i)] : (? [X1 : $i] : (X0 @ X2 @ X1)))))) & (cP_0 @ (cY_0 @ (^[X2 : ($i > $i)] : (? [X1 : $i] : (X0 @ X2 @ X1))))))))),
% 0.20/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.27 thf(f3,plain,(
% 0.20/0.27 ~ ~ ! [X0 : (($i > $i) > $i > $o)] : (? [X1 : $i] : (X0 @ (cH_0 @ (^[X2 : ($i > $i)] : (? [X3 : $i] : (X0 @ X2 @ X3)))) @ X1) & ? [X4 : $i] : (X0 @ (cG_0 @ (^[X5 : ($i > $i)] : (? [X6 : $i] : (X0 @ X5 @ X6)))) @ X4) & (~ ? [X7 : $i] : (X0 @ (^[X8 : $i] : ((cG_0 @ (^[X9 : ($i > $i)] : (? [X10 : $i] : (X0 @ X9 @ X10))) @ (cH_0 @ (^[X11 : ($i > $i)] : (? [X12 : $i] : (X0 @ X11 @ X12))) @ X8)))) @ X7) | (~(cP_0 @ (cG_0 @ (^[X13 : ($i > $i)] : (? [X14 : $i] : (X0 @ X13 @ X14))) @ (cY_0 @ (^[X15 : ($i > $i)] : (? [X16 : $i] : (X0 @ X15 @ X16)))))) & (cP_0 @ (cY_0 @ (^[X17 : ($i > $i)] : (? [X18 : $i] : (X0 @ X17 @ X18))))))))),
% 0.20/0.27 inference(rectify,[],[f2])).
% 0.20/0.27 thf(f4,plain,(
% 0.20/0.27 ~ ~ ! [X0 : (($i > $i) > $i > $o)] : (? [X1 : $i] : (((X0 @ (cH_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1))))) @ X1)) = $true) & ? [X4 : $i] : (((X0 @ (cG_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1))))) @ X4)) = $true) & (~ ? [X7 : $i] : (((X0 @ (^[Y0 : $i]: (cG_0 @ (^[Y1 : $i > $i]: (?? @ $i @ (^[Y2 : $i]: (X0 @ Y1 @ Y2)))) @ (cH_0 @ (^[Y1 : $i > $i]: (?? @ $i @ (^[Y2 : $i]: (X0 @ Y1 @ Y2)))) @ Y0))) @ X7)) = $true) | (~ (((cP_0 @ (cG_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1)))) @ (cY_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1)))))))) = $true) & (((cP_0 @ (cY_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1))))))) = $true))))),
% 0.20/0.27 inference(fool_elimination,[],[f3])).
% 0.20/0.27 thf(f5,plain,(
% 0.20/0.27 ~ ~ ! [X0 : (($i > $i) > $i > $o)] : (? [X1 : $i] : (((X0 @ (cH_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1))))) @ X1)) = $true) & ? [X2 : $i] : (((X0 @ (cG_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1))))) @ X2)) = $true) & (~ ? [X3 : $i] : (((X0 @ (^[Y0 : $i]: (cG_0 @ (^[Y1 : $i > $i]: (?? @ $i @ (^[Y2 : $i]: (X0 @ Y1 @ Y2)))) @ (cH_0 @ (^[Y1 : $i > $i]: (?? @ $i @ (^[Y2 : $i]: (X0 @ Y1 @ Y2)))) @ Y0))) @ X3)) = $true) | (~ (((cP_0 @ (cG_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1)))) @ (cY_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1)))))))) = $true) & (((cP_0 @ (cY_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1))))))) = $true))))),
% 0.20/0.27 inference(rectify,[],[f4])).
% 0.20/0.27 thf(f6,plain,(
% 0.20/0.27 ! [X0 : (($i > $i) > $i > $o)] : ((~ ? [X3 : $i] : (((X0 @ (^[Y0 : $i]: (cG_0 @ (^[Y1 : $i > $i]: (?? @ $i @ (^[Y2 : $i]: (X0 @ Y1 @ Y2)))) @ (cH_0 @ (^[Y1 : $i > $i]: (?? @ $i @ (^[Y2 : $i]: (X0 @ Y1 @ Y2)))) @ Y0))) @ X3)) = $true) | ((((cP_0 @ (cY_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1))))))) = $true) & (((cP_0 @ (cG_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1)))) @ (cY_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1)))))))) != $true))) & ? [X1 : $i] : (((X0 @ (cH_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1))))) @ X1)) = $true) & ? [X2 : $i] : (((X0 @ (cG_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1))))) @ X2)) = $true))),
% 0.20/0.27 inference(flattening,[],[f5])).
% 0.20/0.27 thf(f7,plain,(
% 0.20/0.27 ! [X0 : (($i > $i) > $i > $o)] : ((! [X3 : $i] : (((X0 @ (^[Y0 : $i]: (cG_0 @ (^[Y1 : $i > $i]: (?? @ $i @ (^[Y2 : $i]: (X0 @ Y1 @ Y2)))) @ (cH_0 @ (^[Y1 : $i > $i]: (?? @ $i @ (^[Y2 : $i]: (X0 @ Y1 @ Y2)))) @ Y0))) @ X3)) != $true) | ((((cP_0 @ (cY_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1))))))) = $true) & (((cP_0 @ (cG_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1)))) @ (cY_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1)))))))) != $true))) & ? [X2 : $i] : (((X0 @ (cG_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1))))) @ X2)) = $true) & ? [X1 : $i] : (((X0 @ (cH_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1))))) @ X1)) = $true))),
% 0.20/0.27 inference(ennf_transformation,[],[f6])).
% 0.20/0.27 thf(f8,plain,(
% 0.20/0.27 ! [X0 : (($i > $i) > $i > $o)] : ((! [X1 : $i] : (((X0 @ (^[Y0 : $i]: (cG_0 @ (^[Y1 : $i > $i]: (?? @ $i @ (^[Y2 : $i]: (X0 @ Y1 @ Y2)))) @ (cH_0 @ (^[Y1 : $i > $i]: (?? @ $i @ (^[Y2 : $i]: (X0 @ Y1 @ Y2)))) @ Y0))) @ X1)) != $true) | ((((cP_0 @ (cY_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1))))))) = $true) & (((cP_0 @ (cG_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1)))) @ (cY_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1)))))))) != $true))) & ? [X2 : $i] : (((X0 @ (cG_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1))))) @ X2)) = $true) & ? [X3 : $i] : (((X0 @ (cH_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1))))) @ X3)) = $true))),
% 0.20/0.27 inference(rectify,[],[f7])).
% 0.20/0.27 thf(f9,plain,(
% 0.20/0.27 ! [X0 : (($i > $i) > $i > $o)] : ((! [X1 : $i] : (((X0 @ (^[Y0 : $i]: (cG_0 @ (^[Y1 : $i > $i]: (?? @ $i @ (^[Y2 : $i]: (X0 @ Y1 @ Y2)))) @ (cH_0 @ (^[Y1 : $i > $i]: (?? @ $i @ (^[Y2 : $i]: (X0 @ Y1 @ Y2)))) @ Y0))) @ X1)) != $true) | ((((cP_0 @ (cY_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1))))))) = $true) & (((cP_0 @ (cG_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1)))) @ (cY_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1)))))))) != $true))) & (((X0 @ (cG_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1))))) @ (sK0 @ X0))) = $true) & (((X0 @ (cH_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1))))) @ (sK1 @ X0))) = $true))),
% 0.20/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X3,sK1 @ X0),skolemize(X3,sK1 @ X0)],[f8])).
% 0.20/0.27 thf(f11,plain,(
% 0.20/0.27 ( ! [X0 : (($i > $i) > $i > $o)] : ((((X0 @ (cG_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1))))) @ (sK0 @ X0))) = $true)) )),
% 0.20/0.27 inference(cnf_transformation,[],[f9])).
% 0.20/0.27 thf(f18,plain,(
% 0.20/0.27 ( ! [X0 : (($i > $i) > $i > $o)] : ((((X0 @ (cG_0 @ (^[Y0 : $i > $i]: (?? @ $i @ (X0 @ Y0)))) @ (sK0 @ X0))) = $true)) )),
% 0.20/0.27 inference(beta-eta_normalization,[],[f11])).
% 0.20/0.27 thf(f21,plain,(
% 0.20/0.27 ((((^[Y0 : $i > $i]: ((^[Y1 : $i]: ($false)))) @ (cG_0 @ (^[Y0 : $i > $i]: (?? @ $i @ ((^[Y1 : $i > $i]: ((^[Y2 : $i]: ($false)))) @ Y0)))) @ (sK0 @ (^[Y0 : $i > $i]: ((^[Y1 : $i]: ($false))))))) = $true)),
% 0.20/0.27 inference(primitive_instantiation,[],[f18])).
% 0.20/0.27 thf(f26,plain,(
% 0.20/0.27 ($false = $true)),
% 0.20/0.27 inference(beta-eta_normalization,[],[f21])).
% 0.20/0.27 thf(f27,plain,(
% 0.20/0.27 $false),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f26])).
% 0.20/0.27 % SZS output end Proof for theBenchmark
% 0.20/0.27 % (829463)------------------------------
% 0.20/0.27 % (829463)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (829463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (829463)CaDiCaL version: 2.1.3
% 0.20/0.27 % (829463)Termination reason: Refutation
% 0.20/0.27 % (829463)Time elapsed: 0.002 s
% 0.20/0.27 % (829463)Peak memory usage: 12 MB
% 0.20/0.27 % (829463)Instructions burned: 5 (million)
% 0.20/0.27 % (829458)Success in time 0.028 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------