%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV070^5 : 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 : n019.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 08:37:35 AM UTC 2026
% Result : Theorem 0.09s 0.27s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV070^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n019.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 15:06:18 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.09/0.27 % (897984)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.27 % (897993)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3312232289:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.09/0.27 % (897993) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-897984-897993"...
% 0.09/0.27 % (897993)...printing done.
% 0.09/0.27 % (897993)Refutation found. Thanks to Tanya!
% 0.09/0.27 % SZS status Theorem for theBenchmark
% 0.09/0.27 % SZS output start Proof for theBenchmark
% 0.09/0.27 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.27 thf(func_def_0, type, cS: ($i > $i)).
% 0.09/0.27 thf(func_def_7, type, sK3: (($i > $o) > $i)).
% 0.09/0.27 thf(func_def_8, type, sK4: (($i > $o) > $i)).
% 0.09/0.27 thf(func_def_9, type, sK5: ($i > $o)).
% 0.09/0.27 thf(func_def_10, type, vNOT: ($o > $o)).
% 0.09/0.27 thf(func_def_11, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.09/0.27 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.09/0.27 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.09/0.27 thf(f1,conjecture,(
% 0.09/0.27 ! [X0 : $i,X2 : $i,X1 : $i] : ((! [X3 : ($i > $o)] : ((! [X4 : $i] : ((X3 @ X4) => (X3 @ (cS @ X4))) & (X3 @ X1)) => (X3 @ X2)) & ! [X3 : ($i > $o)] : (((X3 @ X0) & ! [X4 : $i] : ((X3 @ X4) => (X3 @ (cS @ X4)))) => (X3 @ X1))) => ! [X3 : ($i > $o)] : ((! [X4 : $i] : ((X3 @ X4) => (X3 @ (cS @ X4))) & (X3 @ X0)) => (X3 @ X2)))),
% 0.09/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM577_pme)).
% 0.09/0.27 thf(f2,negated_conjecture,(
% 0.09/0.27 ~ ! [X0 : $i,X2 : $i,X1 : $i] : ((! [X3 : ($i > $o)] : ((! [X4 : $i] : ((X3 @ X4) => (X3 @ (cS @ X4))) & (X3 @ X1)) => (X3 @ X2)) & ! [X3 : ($i > $o)] : (((X3 @ X0) & ! [X4 : $i] : ((X3 @ X4) => (X3 @ (cS @ X4)))) => (X3 @ X1))) => ! [X3 : ($i > $o)] : ((! [X4 : $i] : ((X3 @ X4) => (X3 @ (cS @ X4))) & (X3 @ X0)) => (X3 @ X2)))),
% 0.09/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.09/0.27 thf(f3,plain,(
% 0.09/0.27 ~ ! [X0 : $i,X1 : $i,X2 : $i] : ((! [X3 : ($i > $o)] : ((! [X4 : $i] : ((X3 @ X4) => (X3 @ (cS @ X4))) & (X3 @ X2)) => (X3 @ X1)) & ! [X5 : ($i > $o)] : (((X5 @ X0) & ! [X6 : $i] : ((X5 @ X6) => (X5 @ (cS @ X6)))) => (X5 @ X2))) => ! [X7 : ($i > $o)] : ((! [X8 : $i] : ((X7 @ X8) => (X7 @ (cS @ X8))) & (X7 @ X0)) => (X7 @ X1)))),
% 0.09/0.27 inference(rectify,[],[f2])).
% 0.09/0.27 thf(f4,plain,(
% 0.09/0.27 ~ ! [X0 : $i,X2 : $i,X1 : $i] : ((! [X3 : ($i > $o)] : ((! [X4 : $i] : ((((X3 @ X4)) = $true) => (((X3 @ (cS @ X4))) = $true)) & (((X3 @ X2)) = $true)) => (((X3 @ X1)) = $true)) & ! [X5 : ($i > $o)] : ((! [X6 : $i] : ((((X5 @ X6)) = $true) => (((X5 @ (cS @ X6))) = $true)) & (((X5 @ X0)) = $true)) => (((X5 @ X2)) = $true))) => ! [X7 : ($i > $o)] : ((! [X8 : $i] : ((((X7 @ X8)) = $true) => ($true = ((X7 @ (cS @ X8))))) & (((X7 @ X0)) = $true)) => (((X7 @ X1)) = $true)))),
% 0.09/0.27 inference(fool_elimination,[],[f3])).
% 0.09/0.27 thf(f5,plain,(
% 0.09/0.27 ? [X0 : $i,X2 : $i,X1 : $i] : (? [X7 : ($i > $o)] : ((((X7 @ X1)) != $true) & (! [X8 : $i] : (($true = ((X7 @ (cS @ X8)))) | (((X7 @ X8)) != $true)) & (((X7 @ X0)) = $true))) & (! [X3 : ($i > $o)] : ((((X3 @ X1)) = $true) | (? [X4 : $i] : ((((X3 @ (cS @ X4))) != $true) & (((X3 @ X4)) = $true)) | (((X3 @ X2)) != $true))) & ! [X5 : ($i > $o)] : ((((X5 @ X2)) = $true) | (? [X6 : $i] : ((((X5 @ (cS @ X6))) != $true) & (((X5 @ X6)) = $true)) | (((X5 @ X0)) != $true)))))),
% 0.09/0.27 inference(ennf_transformation,[],[f4])).
% 0.09/0.27 thf(f6,plain,(
% 0.09/0.27 ? [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : ($i > $o)] : ((((X3 @ X2)) != $true) | ? [X4 : $i] : ((((X3 @ (cS @ X4))) != $true) & (((X3 @ X4)) = $true)) | (((X3 @ X1)) = $true)) & ! [X5 : ($i > $o)] : (? [X6 : $i] : ((((X5 @ (cS @ X6))) != $true) & (((X5 @ X6)) = $true)) | (((X5 @ X2)) = $true) | (((X5 @ X0)) != $true)) & ? [X7 : ($i > $o)] : ((((X7 @ X0)) = $true) & (((X7 @ X1)) != $true) & ! [X8 : $i] : (($true = ((X7 @ (cS @ X8)))) | (((X7 @ X8)) != $true))))),
% 0.09/0.27 inference(flattening,[],[f5])).
% 0.09/0.27 thf(f7,plain,(
% 0.09/0.27 ! [X3 : ($i > $o)] : ((((X3 @ sK2)) != $true) | (($true != ((X3 @ (cS @ (sK3 @ X3))))) & (((X3 @ (sK3 @ X3))) = $true)) | (((X3 @ sK1)) = $true)) & ! [X5 : ($i > $o)] : ((($true != ((X5 @ (cS @ (sK4 @ X5))))) & (((X5 @ (sK4 @ X5))) = $true)) | ($true = ((X5 @ sK2))) | (((X5 @ sK0)) != $true)) & ((((sK5 @ sK0)) = $true) & ($true != ((sK5 @ sK1))) & ! [X8 : $i] : ((((sK5 @ (cS @ X8))) = $true) | (((sK5 @ X8)) != $true)))),
% 0.09/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,vAPP,vAPP,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X6,sK4 @ X5),skolemize(X6,sK4 @ X5),skolemize(X7,sK5)],[f6])).
% 0.09/0.27 thf(f8,plain,(
% 0.09/0.27 ( ! [X8 : $i] : ((((sK5 @ (cS @ X8))) = $true) | (((sK5 @ X8)) != $true)) )),
% 0.09/0.27 inference(cnf_transformation,[],[f7])).
% 0.09/0.27 thf(f9,plain,(
% 0.09/0.27 ($true != ((sK5 @ sK1)))),
% 0.09/0.27 inference(cnf_transformation,[],[f7])).
% 0.09/0.27 thf(f10,plain,(
% 0.09/0.27 (((sK5 @ sK0)) = $true)),
% 0.09/0.27 inference(cnf_transformation,[],[f7])).
% 0.09/0.27 thf(f11,plain,(
% 0.09/0.27 ( ! [X5 : ($i > $o)] : ((((X5 @ (sK4 @ X5))) = $true) | ($true = ((X5 @ sK2))) | (((X5 @ sK0)) != $true)) )),
% 0.09/0.27 inference(cnf_transformation,[],[f7])).
% 0.09/0.27 thf(f12,plain,(
% 0.09/0.27 ( ! [X5 : ($i > $o)] : (($true != ((X5 @ (cS @ (sK4 @ X5))))) | (((X5 @ sK0)) != $true) | ($true = ((X5 @ sK2)))) )),
% 0.09/0.27 inference(cnf_transformation,[],[f7])).
% 0.09/0.27 thf(f13,plain,(
% 0.09/0.27 ( ! [X3 : ($i > $o)] : ((((X3 @ (sK3 @ X3))) = $true) | (((X3 @ sK1)) = $true) | (((X3 @ sK2)) != $true)) )),
% 0.09/0.27 inference(cnf_transformation,[],[f7])).
% 0.09/0.27 thf(f14,plain,(
% 0.09/0.27 ( ! [X3 : ($i > $o)] : (($true != ((X3 @ (cS @ (sK3 @ X3))))) | (((X3 @ sK1)) = $true) | (((X3 @ sK2)) != $true)) )),
% 0.09/0.27 inference(cnf_transformation,[],[f7])).
% 0.09/0.27 thf(f58,plain,(
% 0.09/0.27 (((sK5 @ (sK4 @ sK5))) != $true) | ($true != $true) | (((sK5 @ sK0)) != $true) | (((sK5 @ sK2)) = $true)),
% 0.09/0.27 inference(superposition,[],[f12,f8])).
% 0.09/0.27 thf(f70,plain,(
% 0.09/0.27 (((sK5 @ sK0)) != $true) | (((sK5 @ (sK4 @ sK5))) != $true) | (((sK5 @ sK2)) = $true)),
% 0.09/0.27 inference(trivial_inequality_removal,[],[f58])).
% 0.09/0.27 thf(f78,plain,(
% 0.09/0.27 (((sK5 @ (sK4 @ sK5))) != $true) | (((sK5 @ sK2)) = $true)),
% 0.09/0.27 inference(forward_subsumption_resolution,[],[f70,f10])).
% 0.09/0.27 thf(f79,plain,(
% 0.09/0.27 (((sK5 @ sK2)) = $true) | ($true != $true) | (((sK5 @ sK2)) = $true) | (((sK5 @ sK0)) != $true)),
% 0.09/0.27 inference(superposition,[],[f78,f11])).
% 0.09/0.27 thf(f80,plain,(
% 0.09/0.27 (((sK5 @ sK2)) = $true) | (((sK5 @ sK0)) != $true) | ($true != $true)),
% 0.09/0.27 inference(duplicate_literal_removal,[],[f79])).
% 0.09/0.27 thf(f81,plain,(
% 0.09/0.27 (((sK5 @ sK2)) = $true) | (((sK5 @ sK0)) != $true)),
% 0.09/0.27 inference(trivial_inequality_removal,[],[f80])).
% 0.09/0.27 thf(f82,plain,(
% 0.09/0.27 (((sK5 @ sK2)) = $true)),
% 0.09/0.27 inference(forward_subsumption_resolution,[],[f81,f10])).
% 0.09/0.27 thf(f89,plain,(
% 0.09/0.27 ($true = ((sK5 @ sK1))) | (((sK5 @ (sK3 @ sK5))) != $true) | ($true != $true) | (((sK5 @ sK2)) != $true)),
% 0.09/0.27 inference(superposition,[],[f14,f8])).
% 0.09/0.27 thf(f97,plain,(
% 0.09/0.27 ($true = ((sK5 @ sK1))) | (((sK5 @ sK2)) != $true) | (((sK5 @ (sK3 @ sK5))) != $true)),
% 0.09/0.27 inference(trivial_inequality_removal,[],[f89])).
% 0.09/0.27 thf(f109,plain,(
% 0.09/0.27 (((sK5 @ sK2)) != $true) | (((sK5 @ (sK3 @ sK5))) != $true)),
% 0.09/0.27 inference(forward_subsumption_resolution,[],[f97,f9])).
% 0.09/0.27 thf(f110,plain,(
% 0.09/0.27 (((sK5 @ (sK3 @ sK5))) != $true)),
% 0.09/0.27 inference(forward_subsumption_resolution,[],[f109,f82])).
% 0.09/0.27 thf(f111,plain,(
% 0.09/0.27 ($true = ((sK5 @ sK1))) | ($true != $true) | (((sK5 @ sK2)) != $true)),
% 0.09/0.27 inference(superposition,[],[f110,f13])).
% 0.09/0.27 thf(f112,plain,(
% 0.09/0.27 (((sK5 @ sK2)) != $true) | ($true = ((sK5 @ sK1)))),
% 0.09/0.27 inference(trivial_inequality_removal,[],[f111])).
% 0.09/0.27 thf(f113,plain,(
% 0.09/0.27 ($true = ((sK5 @ sK1)))),
% 0.09/0.27 inference(forward_subsumption_resolution,[],[f112,f82])).
% 0.09/0.27 thf(f114,plain,(
% 0.09/0.27 $false),
% 0.09/0.27 inference(forward_subsumption_resolution,[],[f113,f9])).
% 0.09/0.27 % SZS output end Proof for theBenchmark
% 0.09/0.27 % (897993)------------------------------
% 0.09/0.27 % (897993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.27 % (897993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.27 % (897993)CaDiCaL version: 2.1.3
% 0.09/0.27 % (897993)Termination reason: Refutation
% 0.09/0.27 % (897993)Time elapsed: 0.003 s
% 0.09/0.27 % (897993)Peak memory usage: 12 MB
% 0.09/0.27 % (897993)Instructions burned: 6 (million)
% 0.09/0.27 % (897984)Success in time 0.027 s
% 0.09/0.27 % Vampire exiting
%------------------------------------------------------------------------------