%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV185^5 : 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 : n018.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 08:37:59 AM UTC 2026
% Result : Theorem 0.33s 0.46s
% Output : Refutation 0.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV185^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8046.5625MB
% 0.12/0.33 % OS : Linux 6.8.0-71-generic
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Sep 29 15:21:27 UTC 2026
% 0.26/0.33 % CPUTime :
% 0.26/0.33 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.39 Running higher-order theorem proving
% 0.33/0.41 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
% 0.33/0.46 % (213450)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.33/0.46 % (213457)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1825516117:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.33/0.46 % (213457) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-213450-213457"...
% 0.33/0.46 % (213457)...printing done.
% 0.33/0.46 % (213457)Refutation found. Thanks to Tanya!
% 0.33/0.46 % SZS status Theorem for theBenchmark
% 0.33/0.46 % SZS output start Proof for theBenchmark
% 0.33/0.46 thf(type_def_5, type, b: $tType).
% 0.33/0.46 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.33/0.46 thf(func_def_3, type, sK0: ((b > $o) > b > $o)).
% 0.33/0.46 thf(func_def_4, type, sK1: ((b > $o) > $o)).
% 0.33/0.46 thf(func_def_5, type, sK2: b).
% 0.33/0.46 thf(func_def_6, type, sK3: (b > $o)).
% 0.33/0.46 thf(func_def_7, type, sK4: (b > $o)).
% 0.33/0.46 thf(func_def_8, type, sK5: ((b > $o) > (b > $o) > b)).
% 0.33/0.46 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.33/0.46 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.33/0.46 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 0.33/0.46 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.33/0.46 thf(f1,conjecture,(
% 0.33/0.46 ! [X1 : ((b > $o) > $o),X0 : ((b > $o) > b > $o)] : (! [X2 : (b > $o)] : ((X1 @ X2) => ! [X3 : (b > $o),X4 : b] : (((X0 @ X3 @ X4) & ! [X5 : b] : ((X3 @ X5) => (X2 @ X5))) => (X2 @ X4))) => ! [X4 : b,X3 : (b > $o)] : ((! [X2 : b] : ((X3 @ X2) => ! [X6 : (b > $o)] : ((X1 @ X6) => (X6 @ X2))) & (X0 @ X3 @ X4)) => ! [X6 : (b > $o)] : ((X1 @ X6) => (X6 @ X4))))),
% 0.33/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM564_pme)).
% 0.33/0.46 thf(f2,negated_conjecture,(
% 0.33/0.46 ~ ! [X1 : ((b > $o) > $o),X0 : ((b > $o) > b > $o)] : (! [X2 : (b > $o)] : ((X1 @ X2) => ! [X3 : (b > $o),X4 : b] : (((X0 @ X3 @ X4) & ! [X5 : b] : ((X3 @ X5) => (X2 @ X5))) => (X2 @ X4))) => ! [X4 : b,X3 : (b > $o)] : ((! [X2 : b] : ((X3 @ X2) => ! [X6 : (b > $o)] : ((X1 @ X6) => (X6 @ X2))) & (X0 @ X3 @ X4)) => ! [X6 : (b > $o)] : ((X1 @ X6) => (X6 @ X4))))),
% 0.33/0.46 inference(negated_conjecture,[status(cth)],[f1])).
% 0.33/0.46 thf(f3,plain,(
% 0.33/0.46 ~ ! [X0 : ((b > $o) > $o),X1 : ((b > $o) > b > $o)] : (! [X2 : (b > $o)] : ((X0 @ X2) => ! [X3 : (b > $o),X4 : b] : (((X1 @ X3 @ X4) & ! [X5 : b] : ((X3 @ X5) => (X2 @ X5))) => (X2 @ X4))) => ! [X6 : b,X7 : (b > $o)] : ((! [X8 : b] : ((X7 @ X8) => ! [X9 : (b > $o)] : ((X0 @ X9) => (X9 @ X8))) & (X1 @ X7 @ X6)) => ! [X10 : (b > $o)] : ((X0 @ X10) => (X10 @ X6))))),
% 0.33/0.46 inference(rectify,[],[f2])).
% 0.33/0.46 thf(f4,plain,(
% 0.33/0.46 ~ ! [X1 : ((b > $o) > b > $o),X0 : ((b > $o) > $o)] : (! [X2 : (b > $o)] : (($true = ((X0 @ X2))) => ! [X3 : (b > $o),X4 : b] : ((! [X5 : b] : ((((X3 @ X5)) = $true) => (((X2 @ X5)) = $true)) & (((X1 @ X3 @ X4)) = $true)) => (((X2 @ X4)) = $true))) => ! [X7 : (b > $o),X6 : b] : ((! [X8 : b] : (($true = ((X7 @ X8))) => ! [X9 : (b > $o)] : (($true = ((X0 @ X9))) => (((X9 @ X8)) = $true))) & ($true = ((X1 @ X7 @ X6)))) => ! [X10 : (b > $o)] : (($true = ((X0 @ X10))) => ($true = ((X10 @ X6))))))),
% 0.33/0.46 inference(fool_elimination,[],[f3])).
% 0.33/0.46 thf(f5,plain,(
% 0.33/0.46 ? [X1 : ((b > $o) > b > $o),X0 : ((b > $o) > $o)] : (? [X7 : (b > $o),X6 : b] : (? [X10 : (b > $o)] : (($true = ((X0 @ X10))) & ($true != ((X10 @ X6)))) & (! [X8 : b] : (($true != ((X7 @ X8))) | ! [X9 : (b > $o)] : (($true != ((X0 @ X9))) | (((X9 @ X8)) = $true))) & ($true = ((X1 @ X7 @ X6))))) & ! [X2 : (b > $o)] : (! [X3 : (b > $o),X4 : b] : ((((X2 @ X4)) = $true) | (? [X5 : b] : ((((X2 @ X5)) != $true) & (((X3 @ X5)) = $true)) | (((X1 @ X3 @ X4)) != $true))) | ($true != ((X0 @ X2)))))),
% 0.33/0.46 inference(ennf_transformation,[],[f4])).
% 0.33/0.46 thf(f6,plain,(
% 0.33/0.46 ? [X1 : ((b > $o) > b > $o),X0 : ((b > $o) > $o)] : (? [X6 : b,X7 : (b > $o)] : (! [X8 : b] : (($true != ((X7 @ X8))) | ! [X9 : (b > $o)] : (($true != ((X0 @ X9))) | (((X9 @ X8)) = $true))) & ? [X10 : (b > $o)] : (($true = ((X0 @ X10))) & ($true != ((X10 @ X6)))) & ($true = ((X1 @ X7 @ X6)))) & ! [X2 : (b > $o)] : (($true != ((X0 @ X2))) | ! [X4 : b,X3 : (b > $o)] : ((((X1 @ X3 @ X4)) != $true) | ? [X5 : b] : ((((X2 @ X5)) != $true) & (((X3 @ X5)) = $true)) | (((X2 @ X4)) = $true))))),
% 0.33/0.46 inference(flattening,[],[f5])).
% 0.33/0.46 thf(f7,plain,(
% 0.33/0.46 ? [X0 : ((b > $o) > b > $o),X1 : ((b > $o) > $o)] : (? [X2 : b,X3 : (b > $o)] : (! [X4 : b] : (($true != ((X3 @ X4))) | ! [X5 : (b > $o)] : (($true != ((X1 @ X5))) | ($true = ((X5 @ X4))))) & ? [X6 : (b > $o)] : ((((X1 @ X6)) = $true) & (((X6 @ X2)) != $true)) & ($true = ((X0 @ X3 @ X2)))) & ! [X7 : (b > $o)] : (($true != ((X1 @ X7))) | ! [X8 : b,X9 : (b > $o)] : (($true != ((X0 @ X9 @ X8))) | ? [X10 : b] : (($true != ((X7 @ X10))) & ($true = ((X9 @ X10)))) | ($true = ((X7 @ X8))))))),
% 0.33/0.46 inference(rectify,[],[f6])).
% 0.33/0.46 thf(f8,plain,(
% 0.33/0.46 (! [X4 : b] : (($true != ((sK3 @ X4))) | ! [X5 : (b > $o)] : ((((sK1 @ X5)) != $true) | ($true = ((X5 @ X4))))) & (($true = ((sK1 @ sK4))) & ($true != ((sK4 @ sK2)))) & ($true = ((sK0 @ sK3 @ sK2)))) & ! [X7 : (b > $o)] : (($true != ((sK1 @ X7))) | ! [X8 : b,X9 : (b > $o)] : (($true != ((sK0 @ X9 @ X8))) | ((((X7 @ (sK5 @ X9 @ X7))) != $true) & ($true = ((X9 @ (sK5 @ X9 @ X7))))) | ($true = ((X7 @ X8)))))),
% 0.33/0.46 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X6,sK4),skolemize(X10,sK5 @ X9 @ X7)],[f7])).
% 0.33/0.46 thf(f9,plain,(
% 0.33/0.46 ( ! [X8 : b,X9 : (b > $o),X7 : (b > $o)] : (($true != ((sK0 @ X9 @ X8))) | ($true = ((X9 @ (sK5 @ X9 @ X7)))) | ($true = ((X7 @ X8))) | ($true != ((sK1 @ X7)))) )),
% 0.33/0.46 inference(cnf_transformation,[],[f8])).
% 0.33/0.46 thf(f10,plain,(
% 0.33/0.46 ( ! [X8 : b,X9 : (b > $o),X7 : (b > $o)] : ((((X7 @ (sK5 @ X9 @ X7))) != $true) | ($true != ((sK1 @ X7))) | ($true = ((X7 @ X8))) | ($true != ((sK0 @ X9 @ X8)))) )),
% 0.33/0.46 inference(cnf_transformation,[],[f8])).
% 0.33/0.46 thf(f11,plain,(
% 0.33/0.46 ($true = ((sK0 @ sK3 @ sK2)))),
% 0.33/0.46 inference(cnf_transformation,[],[f8])).
% 0.33/0.46 thf(f12,plain,(
% 0.33/0.46 ($true != ((sK4 @ sK2)))),
% 0.33/0.46 inference(cnf_transformation,[],[f8])).
% 0.33/0.46 thf(f13,plain,(
% 0.33/0.46 ($true = ((sK1 @ sK4)))),
% 0.33/0.46 inference(cnf_transformation,[],[f8])).
% 0.33/0.46 thf(f14,plain,(
% 0.33/0.46 ( ! [X4 : b,X5 : (b > $o)] : ((((sK1 @ X5)) != $true) | ($true = ((X5 @ X4))) | ($true != ((sK3 @ X4)))) )),
% 0.33/0.46 inference(cnf_transformation,[],[f8])).
% 0.33/0.46 thf(f17,plain,(
% 0.33/0.46 ( ! [X0 : b] : (($true != $true) | ($true = ((sK4 @ X0))) | (((sK3 @ X0)) != $true)) )),
% 0.33/0.46 inference(constrained_superposition,[],[f14,f13])).
% 0.33/0.46 thf(f18,plain,(
% 0.33/0.46 ( ! [X0 : b] : ((((sK3 @ X0)) != $true) | ($true = ((sK4 @ X0)))) )),
% 0.33/0.46 inference(trivial_inequality_removal,[],[f17])).
% 0.33/0.46 thf(f19,plain,(
% 0.33/0.46 ( ! [X0 : (b > $o)] : ((((X0 @ sK2)) = $true) | ($true = ((sK3 @ (sK5 @ sK3 @ X0)))) | ($true != ((sK1 @ X0))) | ($true != $true)) )),
% 0.33/0.46 inference(constrained_superposition,[],[f9,f11])).
% 0.33/0.46 thf(f20,plain,(
% 0.33/0.46 ( ! [X0 : (b > $o)] : (($true != ((sK1 @ X0))) | ($true = ((sK3 @ (sK5 @ sK3 @ X0)))) | (((X0 @ sK2)) = $true)) )),
% 0.33/0.46 inference(trivial_inequality_removal,[],[f19])).
% 0.33/0.46 thf(f21,plain,(
% 0.33/0.46 ($true = ((sK3 @ (sK5 @ sK3 @ sK4)))) | ($true = ((sK4 @ sK2))) | ($true != $true)),
% 0.33/0.46 inference(constrained_superposition,[],[f20,f13])).
% 0.33/0.46 thf(f22,plain,(
% 0.33/0.46 ($true = ((sK4 @ sK2))) | ($true = ((sK3 @ (sK5 @ sK3 @ sK4))))),
% 0.33/0.46 inference(trivial_inequality_removal,[],[f21])).
% 0.33/0.46 thf(f23,plain,(
% 0.33/0.46 ($true = ((sK3 @ (sK5 @ sK3 @ sK4))))),
% 0.33/0.46 inference(forward_subsumption_resolution,[],[f22,f12])).
% 0.33/0.46 thf(f33,plain,(
% 0.33/0.46 (((sK4 @ (sK5 @ sK3 @ sK4))) = $true) | ($true != $true)),
% 0.33/0.46 inference(constrained_superposition,[],[f18,f23])).
% 0.33/0.46 thf(f34,plain,(
% 0.33/0.46 (((sK4 @ (sK5 @ sK3 @ sK4))) = $true)),
% 0.33/0.46 inference(trivial_inequality_removal,[],[f33])).
% 0.33/0.46 thf(f35,plain,(
% 0.33/0.46 ( ! [X0 : b] : (($true = ((sK4 @ X0))) | ($true != ((sK0 @ sK3 @ X0))) | ($true != $true) | ($true != ((sK1 @ sK4)))) )),
% 0.33/0.46 inference(constrained_superposition,[],[f10,f34])).
% 0.33/0.46 thf(f36,plain,(
% 0.33/0.46 ( ! [X0 : b] : (($true != ((sK1 @ sK4))) | ($true != ((sK0 @ sK3 @ X0))) | ($true = ((sK4 @ X0)))) )),
% 0.33/0.46 inference(trivial_inequality_removal,[],[f35])).
% 0.33/0.46 thf(f37,plain,(
% 0.33/0.46 ( ! [X0 : b] : (($true != ((sK0 @ sK3 @ X0))) | ($true = ((sK4 @ X0)))) )),
% 0.33/0.46 inference(forward_subsumption_resolution,[],[f36,f13])).
% 0.33/0.46 thf(f38,plain,(
% 0.33/0.46 ($true != $true) | ($true = ((sK4 @ sK2)))),
% 0.33/0.46 inference(constrained_superposition,[],[f37,f11])).
% 0.33/0.46 thf(f39,plain,(
% 0.33/0.46 ($true = ((sK4 @ sK2)))),
% 0.33/0.46 inference(trivial_inequality_removal,[],[f38])).
% 0.33/0.46 thf(f40,plain,(
% 0.33/0.46 $false),
% 0.33/0.46 inference(forward_subsumption_resolution,[],[f39,f12])).
% 0.33/0.46 % SZS output end Proof for theBenchmark
% 0.33/0.46 % (213457)------------------------------
% 0.33/0.46 % (213457)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.46 % (213457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.46 % (213457)CaDiCaL version: 2.1.3
% 0.33/0.46 % (213457)Termination reason: Refutation
% 0.33/0.46 % (213457)Time elapsed: 0.004 s
% 0.33/0.46 % (213457)Peak memory usage: 12 MB
% 0.33/0.46 % (213457)Instructions burned: 5 (million)
% 0.33/0.46 % (213450)Success in time 0.037 s
% 0.33/0.46 % Vampire exiting
%------------------------------------------------------------------------------