%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU894^5 : 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 : n007.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 08:31:53 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU894^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n007.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:42:26 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
% 0.21/0.28 % (3456785)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (3456792)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1518867566:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.28 % (3456792) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3456785-3456792"...
% 0.21/0.28 % (3456792)...printing done.
% 0.21/0.28 % (3456792)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% 0.21/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.28 thf(func_def_3, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.28 thf(func_def_4, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.28 thf(func_def_5, type, sK0: ($i > $i)).
% 0.21/0.28 thf(func_def_6, type, sK1: (($i > $i) > $i)).
% 0.21/0.28 thf(func_def_7, type, sK2: ((($i > $i) > $o) > $i > $i)).
% 0.21/0.28 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.21/0.28 thf(f1,conjecture,(
% 0.21/0.28 ! [X0 : ($i > $i)] : ? [X1 : ($i > $i)] : ((! [X2 : (($i > $i) > $o)] : (((X2 @ X0) & ! [X3 : ($i > $i)] : ((X2 @ X3) => (X2 @ (^[X4 : $i] : ((X0 @ (X3 @ X4))))))) => (X2 @ X1)) & ? [X5 : $i] : ((((X1 @ X5)) = X5) & ! [X6 : $i] : ((((X1 @ X6)) = X6) => (X5 = X6)))) => ? [X6 : $i] : (((X0 @ X6)) = X6))),
% 0.21/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM15_0_pme)).
% 0.21/0.28 thf(f2,negated_conjecture,(
% 0.21/0.28 ~ ! [X0 : ($i > $i)] : ? [X1 : ($i > $i)] : ((! [X2 : (($i > $i) > $o)] : (((X2 @ X0) & ! [X3 : ($i > $i)] : ((X2 @ X3) => (X2 @ (^[X4 : $i] : ((X0 @ (X3 @ X4))))))) => (X2 @ X1)) & ? [X5 : $i] : ((((X1 @ X5)) = X5) & ! [X6 : $i] : ((((X1 @ X6)) = X6) => (X5 = X6)))) => ? [X6 : $i] : (((X0 @ X6)) = X6))),
% 0.21/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.28 thf(f3,plain,(
% 0.21/0.28 ~ ! [X0 : ($i > $i)] : ? [X1 : ($i > $i)] : ((! [X2 : (($i > $i) > $o)] : (((X2 @ X0) & ! [X3 : ($i > $i)] : ((X2 @ X3) => (X2 @ (^[X4 : $i] : ((X0 @ (X3 @ X4))))))) => (X2 @ X1)) & ? [X5 : $i] : ((((X1 @ X5)) = X5) & ! [X6 : $i] : ((((X1 @ X6)) = X6) => (X5 = X6)))) => ? [X7 : $i] : (((X0 @ X7)) = X7))),
% 0.21/0.28 inference(rectify,[],[f2])).
% 0.21/0.28 thf(f4,plain,(
% 0.21/0.28 ~ ! [X0 : ($i > $i)] : ? [X1 : ($i > $i)] : ((! [X2 : (($i > $i) > $o)] : (((((X2 @ X0)) = $true) & ! [X3 : ($i > $i)] : ((((X2 @ X3)) = $true) => ($true = ((X2 @ (^[Y0 : $i]: (X0 @ (X3 @ Y0)))))))) => (((X2 @ X1)) = $true)) & ? [X5 : $i] : ((((X1 @ X5)) = X5) & ! [X6 : $i] : ((((X1 @ X6)) = X6) => (X5 = X6)))) => ? [X7 : $i] : (((X0 @ X7)) = X7))),
% 0.21/0.28 inference(fool_elimination,[],[f3])).
% 0.21/0.28 thf(f5,plain,(
% 0.21/0.28 ~ ! [X0 : ($i > $i)] : ? [X1 : ($i > $i)] : ((? [X4 : $i] : (! [X5 : $i] : ((((X1 @ X5)) = X5) => (X4 = X5)) & (((X1 @ X4)) = X4)) & ! [X2 : (($i > $i) > $o)] : (((((X2 @ X0)) = $true) & ! [X3 : ($i > $i)] : ((((X2 @ X3)) = $true) => ($true = ((X2 @ (^[Y0 : $i]: (X0 @ (X3 @ Y0)))))))) => (((X2 @ X1)) = $true))) => ? [X6 : $i] : (((X0 @ X6)) = X6))),
% 0.21/0.28 inference(rectify,[],[f4])).
% 0.21/0.28 thf(f6,plain,(
% 0.21/0.28 ? [X0 : ($i > $i)] : ! [X1 : ($i > $i)] : (! [X6 : $i] : (((X0 @ X6)) != X6) & (? [X4 : $i] : (! [X5 : $i] : ((X4 = X5) | (((X1 @ X5)) != X5)) & (((X1 @ X4)) = X4)) & ! [X2 : (($i > $i) > $o)] : ((((X2 @ X1)) = $true) | ((((X2 @ X0)) != $true) | ? [X3 : ($i > $i)] : (($true != ((X2 @ (^[Y0 : $i]: (X0 @ (X3 @ Y0)))))) & (((X2 @ X3)) = $true))))))),
% 0.21/0.28 inference(ennf_transformation,[],[f5])).
% 0.21/0.28 thf(f7,plain,(
% 0.21/0.28 ? [X0 : ($i > $i)] : ! [X1 : ($i > $i)] : (! [X6 : $i] : (((X0 @ X6)) != X6) & ? [X4 : $i] : (! [X5 : $i] : ((X4 = X5) | (((X1 @ X5)) != X5)) & (((X1 @ X4)) = X4)) & ! [X2 : (($i > $i) > $o)] : ((((X2 @ X0)) != $true) | (((X2 @ X1)) = $true) | ? [X3 : ($i > $i)] : (($true != ((X2 @ (^[Y0 : $i]: (X0 @ (X3 @ Y0)))))) & (((X2 @ X3)) = $true))))),
% 0.21/0.28 inference(flattening,[],[f6])).
% 0.21/0.28 thf(f8,plain,(
% 0.21/0.28 ? [X0 : ($i > $i)] : ! [X1 : ($i > $i)] : (! [X2 : $i] : (((X0 @ X2)) != X2) & ? [X3 : $i] : (! [X4 : $i] : ((X3 = X4) | (((X1 @ X4)) != X4)) & (((X1 @ X3)) = X3)) & ! [X5 : (($i > $i) > $o)] : (($true != ((X5 @ X0))) | ($true = ((X5 @ X1))) | ? [X6 : ($i > $i)] : (($true != ((X5 @ (^[Y0 : $i]: (X0 @ (X6 @ Y0)))))) & ($true = ((X5 @ X6))))))),
% 0.21/0.28 inference(rectify,[],[f7])).
% 0.21/0.28 thf(f9,plain,(
% 0.21/0.28 ! [X1 : ($i > $i)] : (! [X2 : $i] : (((sK0 @ X2)) != X2) & (! [X4 : $i] : ((((sK1 @ X1)) = X4) | (((X1 @ X4)) != X4)) & (((X1 @ (sK1 @ X1))) = ((sK1 @ X1)))) & ! [X5 : (($i > $i) > $o)] : ((((X5 @ sK0)) != $true) | ($true = ((X5 @ X1))) | ((((X5 @ (^[Y0 : $i]: (sK0 @ (sK2 @ X5 @ Y0))))) != $true) & (((X5 @ (sK2 @ X5))) = $true))))),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X6,sK2 @ X5),skolemize(X6,sK2 @ X5)],[f8])).
% 0.21/0.28 thf(f12,plain,(
% 0.21/0.28 ( ! [X1 : ($i > $i)] : ((((X1 @ (sK1 @ X1))) = ((sK1 @ X1)))) )),
% 0.21/0.28 inference(cnf_transformation,[],[f9])).
% 0.21/0.28 thf(f14,plain,(
% 0.21/0.28 ( ! [X2 : $i] : ((((sK0 @ X2)) != X2)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f9])).
% 0.21/0.28 thf(f20,plain,(
% 0.21/0.28 (((sK1 @ sK0)) != ((sK1 @ sK0)))),
% 0.21/0.28 inference(constrained_superposition,[],[f14,f12])).
% 0.21/0.28 thf(f21,plain,(
% 0.21/0.28 $false),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f20])).
% 0.21/0.28 % SZS output end Proof for theBenchmark
% 0.21/0.28 % (3456792)------------------------------
% 0.21/0.28 % (3456792)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (3456792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (3456792)CaDiCaL version: 2.1.3
% 0.21/0.28 % (3456792)Termination reason: Refutation
% 0.21/0.28 % (3456792)Time elapsed: 0.001 s
% 0.21/0.28 % (3456792)Peak memory usage: 12 MB
% 0.21/0.28 % (3456792)Instructions burned: 2 (million)
% 0.21/0.28 % (3456785)Success in time 0.032 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------