%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU961^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:32:02 AM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU961^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n004.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 14:51:07 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.26 % (1391809)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.26 % (1391815)lrs+10_16_si=on:nwc=1.5:random_seed=862584968:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.09/0.26 % (1391815) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1391809-1391815"...
% 0.09/0.26 % (1391815)...printing done.
% 0.09/0.26 % (1391815)Refutation found. Thanks to Tanya!
% 0.09/0.26 % SZS status Theorem for theBenchmark
% 0.09/0.26 % SZS output start Proof for theBenchmark
% 0.09/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.26 thf(func_def_3, type, db0: !>[X0: $tType]:(X0)).
% 0.09/0.26 thf(func_def_4, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.09/0.26 thf(func_def_5, type, sK0: ($i > $i)).
% 0.09/0.26 thf(func_def_6, type, sK1: ($i > $i)).
% 0.09/0.26 thf(func_def_7, type, sK2: ((($i > $i) > $o) > $i > $i)).
% 0.09/0.26 thf(func_def_8, type, sK3: (($i > $i) > $o)).
% 0.09/0.26 thf(func_def_9, type, sK4: (($i > $i) > ($i > $i) > $i)).
% 0.09/0.26 thf(func_def_10, type, vNOT: ($o > $o)).
% 0.09/0.26 thf(f1,conjecture,(
% 0.09/0.26 (! [X2 : ($i > $i),X3 : ($i > $i)] : (! [X4 : $i] : (((X2 @ X4)) = ((X3 @ X4))) => (X2 = X3)) & ! [X0 : $i,X1 : $i] : (X0 = X1)) => ! [X6 : ($i > $i),X5 : ($i > $i)] : (! [X7 : (($i > $i) > $o)] : ((! [X8 : ($i > $i)] : ((X7 @ X8) => (X7 @ (^[X4 : $i] : ((X5 @ (X8 @ X4)))))) & (X7 @ X5)) => (X7 @ (^[X4 : $i] : ((X6 @ (X5 @ X4)))))) => ! [X7 : (($i > $i) > $o)] : (((X7 @ X5) & ! [X9 : ($i > $i)] : ((X7 @ X9) => (X7 @ (^[X4 : $i] : ((X5 @ (X9 @ X4))))))) => (X7 @ X6)))),
% 0.09/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM196C_pme)).
% 0.09/0.26 thf(f2,negated_conjecture,(
% 0.09/0.26 ~((! [X2 : ($i > $i),X3 : ($i > $i)] : (! [X4 : $i] : (((X2 @ X4)) = ((X3 @ X4))) => (X2 = X3)) & ! [X0 : $i,X1 : $i] : (X0 = X1)) => ! [X6 : ($i > $i),X5 : ($i > $i)] : (! [X7 : (($i > $i) > $o)] : ((! [X8 : ($i > $i)] : ((X7 @ X8) => (X7 @ (^[X4 : $i] : ((X5 @ (X8 @ X4)))))) & (X7 @ X5)) => (X7 @ (^[X4 : $i] : ((X6 @ (X5 @ X4)))))) => ! [X7 : (($i > $i) > $o)] : (((X7 @ X5) & ! [X9 : ($i > $i)] : ((X7 @ X9) => (X7 @ (^[X4 : $i] : ((X5 @ (X9 @ X4))))))) => (X7 @ X6))))),
% 0.09/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.09/0.26 thf(f3,plain,(
% 0.09/0.26 ~((! [X0 : ($i > $i),X1 : ($i > $i)] : (! [X2 : $i] : (((X0 @ X2)) = ((X1 @ X2))) => (X0 = X1)) & ! [X3 : $i,X4 : $i] : (X3 = X4)) => ! [X5 : ($i > $i),X6 : ($i > $i)] : (! [X7 : (($i > $i) > $o)] : ((! [X8 : ($i > $i)] : ((X7 @ X8) => (X7 @ (^[X9 : $i] : ((X6 @ (X8 @ X9)))))) & (X7 @ X6)) => (X7 @ (^[X10 : $i] : ((X5 @ (X6 @ X10)))))) => ! [X11 : (($i > $i) > $o)] : (((X11 @ X6) & ! [X12 : ($i > $i)] : ((X11 @ X12) => (X11 @ (^[X13 : $i] : ((X6 @ (X12 @ X13))))))) => (X11 @ X5))))),
% 0.09/0.26 inference(rectify,[],[f2])).
% 0.09/0.26 thf(f4,plain,(
% 0.09/0.26 ~((! [X3 : $i,X4 : $i] : (X3 = X4) & ! [X1 : ($i > $i),X0 : ($i > $i)] : (! [X2 : $i] : (((X0 @ X2)) = ((X1 @ X2))) => (X0 = X1))) => ! [X5 : ($i > $i),X6 : ($i > $i)] : (! [X7 : (($i > $i) > $o)] : (((((X7 @ X6)) = $true) & ! [X8 : ($i > $i)] : ((((X7 @ X8)) = $true) => ($true = ((X7 @ (^[Y0 : $i]: (X6 @ (X8 @ Y0)))))))) => (((X7 @ (^[Y0 : $i]: (X5 @ (X6 @ Y0))))) = $true)) => ! [X11 : (($i > $i) > $o)] : (((((X11 @ X6)) = $true) & ! [X12 : ($i > $i)] : ((((X11 @ X12)) = $true) => ($true = ((X11 @ (^[Y0 : $i]: (X6 @ (X12 @ Y0)))))))) => ($true = ((X11 @ X5))))))),
% 0.09/0.26 inference(fool_elimination,[],[f3])).
% 0.09/0.26 thf(f5,plain,(
% 0.09/0.26 ~((! [X3 : $i,X4 : $i] : (X3 = X4) & ! [X1 : ($i > $i),X0 : ($i > $i)] : (! [X2 : $i] : (((X0 @ X2)) = ((X1 @ X2))) => (X0 = X1))) => ! [X6 : ($i > $i),X5 : ($i > $i)] : (! [X7 : (($i > $i) > $o)] : (((((X7 @ X6)) = $true) & ! [X8 : ($i > $i)] : ((((X7 @ X8)) = $true) => ($true = ((X7 @ (^[Y0 : $i]: (X6 @ (X8 @ Y0)))))))) => (((X7 @ (^[Y0 : $i]: (X5 @ (X6 @ Y0))))) = $true)) => ! [X9 : (($i > $i) > $o)] : ((($true = ((X9 @ X6))) & ! [X10 : ($i > $i)] : ((((X9 @ X10)) = $true) => ($true = ((X9 @ (^[Y0 : $i]: (X6 @ (X10 @ Y0)))))))) => ($true = ((X9 @ X5))))))),
% 0.09/0.26 inference(rectify,[],[f4])).
% 0.09/0.26 thf(f6,plain,(
% 0.09/0.26 ? [X6 : ($i > $i),X5 : ($i > $i)] : (? [X9 : (($i > $i) > $o)] : (($true != ((X9 @ X5))) & (($true = ((X9 @ X6))) & ! [X10 : ($i > $i)] : (($true = ((X9 @ (^[Y0 : $i]: (X6 @ (X10 @ Y0)))))) | (((X9 @ X10)) != $true)))) & ! [X7 : (($i > $i) > $o)] : ((((X7 @ (^[Y0 : $i]: (X5 @ (X6 @ Y0))))) = $true) | ((((X7 @ X6)) != $true) | ? [X8 : ($i > $i)] : (($true != ((X7 @ (^[Y0 : $i]: (X6 @ (X8 @ Y0)))))) & (((X7 @ X8)) = $true))))) & (! [X3 : $i,X4 : $i] : (X3 = X4) & ! [X1 : ($i > $i),X0 : ($i > $i)] : ((X0 = X1) | ? [X2 : $i] : (((X0 @ X2)) != ((X1 @ X2)))))),
% 0.09/0.26 inference(ennf_transformation,[],[f5])).
% 0.09/0.26 thf(f7,plain,(
% 0.09/0.26 ? [X5 : ($i > $i),X6 : ($i > $i)] : (! [X7 : (($i > $i) > $o)] : (? [X8 : ($i > $i)] : (($true != ((X7 @ (^[Y0 : $i]: (X6 @ (X8 @ Y0)))))) & (((X7 @ X8)) = $true)) | (((X7 @ (^[Y0 : $i]: (X5 @ (X6 @ Y0))))) = $true) | (((X7 @ X6)) != $true)) & ? [X9 : (($i > $i) > $o)] : (! [X10 : ($i > $i)] : (($true = ((X9 @ (^[Y0 : $i]: (X6 @ (X10 @ Y0)))))) | (((X9 @ X10)) != $true)) & ($true = ((X9 @ X6))) & ($true != ((X9 @ X5))))) & ! [X3 : $i,X4 : $i] : (X3 = X4) & ! [X1 : ($i > $i),X0 : ($i > $i)] : ((X0 = X1) | ? [X2 : $i] : (((X0 @ X2)) != ((X1 @ X2))))),
% 0.09/0.26 inference(flattening,[],[f6])).
% 0.09/0.26 thf(f8,plain,(
% 0.09/0.26 ? [X0 : ($i > $i),X1 : ($i > $i)] : (! [X2 : (($i > $i) > $o)] : (? [X3 : ($i > $i)] : ((((X2 @ (^[Y0 : $i]: (X1 @ (X3 @ Y0))))) != $true) & (((X2 @ X3)) = $true)) | (((X2 @ (^[Y0 : $i]: (X0 @ (X1 @ Y0))))) = $true) | ($true != ((X2 @ X1)))) & ? [X4 : (($i > $i) > $o)] : (! [X5 : ($i > $i)] : ((((X4 @ (^[Y0 : $i]: (X1 @ (X5 @ Y0))))) = $true) | (((X4 @ X5)) != $true)) & ($true = ((X4 @ X1))) & ($true != ((X4 @ X0))))) & ! [X6 : $i,X7 : $i] : (X6 = X7) & ! [X8 : ($i > $i),X9 : ($i > $i)] : ((X8 = X9) | ? [X10 : $i] : (((X8 @ X10)) != ((X9 @ X10))))),
% 0.09/0.26 inference(rectify,[],[f7])).
% 0.09/0.26 thf(f9,plain,(
% 0.09/0.26 (! [X2 : (($i > $i) > $o)] : ((($true != ((X2 @ (^[Y0 : $i]: (sK1 @ (sK2 @ X2 @ Y0)))))) & (((X2 @ (sK2 @ X2))) = $true)) | ($true = ((X2 @ (^[Y0 : $i]: (sK0 @ (sK1 @ Y0)))))) | (((X2 @ sK1)) != $true)) & (! [X5 : ($i > $i)] : (($true = ((sK3 @ (^[Y0 : $i]: (sK1 @ (X5 @ Y0)))))) | ($true != ((sK3 @ X5)))) & (((sK3 @ sK1)) = $true) & ($true != ((sK3 @ sK0))))) & ! [X6 : $i,X7 : $i] : (X6 = X7) & ! [X8 : ($i > $i),X9 : ($i > $i)] : ((X8 = X9) | (((X8 @ (sK4 @ X9 @ X8))) != ((X9 @ (sK4 @ X9 @ X8)))))),
% 0.09/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP,sK3,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X10,sK4 @ X9 @ X8),skolemize(X4,sK3),skolemize(X10,sK4 @ X9 @ X8)],[f8])).
% 0.09/0.26 thf(f11,plain,(
% 0.09/0.26 ( ! [X6 : $i,X7 : $i] : ((X6 = X7)) )),
% 0.09/0.26 inference(cnf_transformation,[],[f9])).
% 0.09/0.26 thf(f12,plain,(
% 0.09/0.26 ($true != ((sK3 @ sK0)))),
% 0.09/0.26 inference(cnf_transformation,[],[f9])).
% 0.09/0.26 thf(f13,plain,(
% 0.09/0.26 (((sK3 @ sK1)) = $true)),
% 0.09/0.26 inference(cnf_transformation,[],[f9])).
% 0.09/0.26 thf(f19,plain,(
% 0.09/0.26 ($true != $true) | (sK0 != sK1)),
% 0.09/0.26 inference(constrained_superposition,[],[f12,f13])).
% 0.09/0.26 thf(f20,plain,(
% 0.09/0.26 (sK0 != sK1)),
% 0.09/0.26 inference(trivial_inequality_removal,[],[f19])).
% 0.09/0.26 thf(f21,plain,(
% 0.09/0.26 (((sK0 @ sK5)) != ((sK1 @ sK5)))),
% 0.09/0.26 inference(negative_extensionality,[],[f20])).
% 0.09/0.26 thf(f22,plain,(
% 0.09/0.26 $false),
% 0.09/0.26 inference(forward_subsumption_resolution,[],[f21,f11])).
% 0.09/0.26 % SZS output end Proof for theBenchmark
% 0.09/0.26 % (1391815)------------------------------
% 0.09/0.26 % (1391815)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (1391815)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (1391815)CaDiCaL version: 2.1.3
% 0.09/0.26 % (1391815)Termination reason: Refutation
% 0.09/0.26 % (1391815)Time elapsed: 0.002 s
% 0.09/0.26 % (1391815)Peak memory usage: 12 MB
% 0.09/0.26 % (1391815)Instructions burned: 3 (million)
% 0.09/0.26 % (1391809)Success in time 0.039 s
% 0.09/0.26 % Vampire exiting
%------------------------------------------------------------------------------