%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO898^9 : TPTP v9.3.1. Released v8.1.0.
% 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 08:48:36 AM UTC 2026
% Result : Theorem 0.11s 0.24s
% Output : Refutation 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO898^9 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.16 % Computer : n019.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Tue Sep 29 17:26:18 UTC 2026
% 0.11/0.16 % CPUTime :
% 0.11/0.16 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.19 Running higher-order theorem proving
% 0.11/0.20 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
% 0.11/0.24 % (1113070)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.11/0.24 % (1113076)lrs+10_16_si=on:nwc=1.5:random_seed=3387127575:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.11/0.24 % (1113076) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1113070-1113076"...
% 0.11/0.24 % (1113076)...printing done.
% 0.11/0.24 % (1113076)Refutation found. Thanks to Tanya!
% 0.11/0.24 % SZS status Theorem for theBenchmark
% 0.11/0.24 % SZS output start Proof for theBenchmark
% 0.11/0.24 thf(type_def_5, type, mworld: $tType).
% 0.11/0.24 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.11/0.24 thf(func_def_0, type, mrel: (mworld > mworld > $o)).
% 0.11/0.24 thf(func_def_1, type, mactual: mworld).
% 0.11/0.24 thf(func_def_2, type, mlocal: ((mworld > $o) > $o)).
% 0.11/0.24 thf(func_def_4, type, mnot: ((mworld > $o) > mworld > $o)).
% 0.11/0.24 thf(func_def_5, type, mand: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.11/0.24 thf(func_def_6, type, mor: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.11/0.24 thf(func_def_7, type, mimplies: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.11/0.24 thf(func_def_8, type, mequiv: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.11/0.24 thf(func_def_9, type, mbox: ((mworld > $o) > mworld > $o)).
% 0.11/0.24 thf(func_def_10, type, mdia: ((mworld > $o) > mworld > $o)).
% 0.11/0.24 thf(func_def_11, type, p: (mworld > $o)).
% 0.11/0.24 thf(func_def_12, type, q: (mworld > $o)).
% 0.11/0.24 thf(func_def_13, type, vOR: ($o > $o > $o)).
% 0.11/0.24 thf(func_def_14, type, db2: !>[X0: $tType]:(X0)).
% 0.11/0.24 thf(func_def_15, type, db0: !>[X0: $tType]:(X0)).
% 0.11/0.24 thf(func_def_16, type, db1: !>[X0: $tType]:(X0)).
% 0.11/0.24 thf(func_def_17, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.11/0.24 thf(func_def_20, type, vIFF: ($o > $o > $o)).
% 0.11/0.24 thf(func_def_21, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.11/0.24 thf(func_def_22, type, vAND: ($o > $o > $o)).
% 0.11/0.24 thf(func_def_23, type, vNOT: ($o > $o)).
% 0.11/0.24 thf(func_def_24, type, vIMP: ($o > $o > $o)).
% 0.11/0.24 thf(func_def_25, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.11/0.24 thf(func_def_26, type, sK0: (mworld > mworld)).
% 0.11/0.24 thf(f1,axiom,(
% 0.11/0.24 ((^[X0 : (mworld > $o)] : ((X0 @ mactual))) = mlocal)),
% 0.11/0.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def)).
% 0.11/0.24 thf(f5,axiom,(
% 0.11/0.24 ((^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X0 @ X2) => (X1 @ X2))) = mimplies)),
% 0.11/0.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def)).
% 0.11/0.24 thf(f7,axiom,(
% 0.11/0.24 ((^[X0 : (mworld > $o), X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))) = mbox)),
% 0.11/0.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def)).
% 0.11/0.24 thf(f8,axiom,(
% 0.11/0.24 ((^[X0 : (mworld > $o), X1 : mworld] : (? [X2 : mworld] : ((mrel @ X1 @ X2) & (X0 @ X2)))) = mdia)),
% 0.11/0.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_def)).
% 0.11/0.24 thf(f9,axiom,(
% 0.11/0.24 ! [X0 : mworld] : ? [X1 : mworld] : (mrel @ X0 @ X1)),
% 0.11/0.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_serial)).
% 0.11/0.24 thf(f10,conjecture,(
% 0.11/0.24 (mlocal @ (mimplies @ (mbox @ p) @ (mdia @ (mimplies @ q @ p))))),
% 0.11/0.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)).
% 0.11/0.24 thf(f11,negated_conjecture,(
% 0.11/0.24 ~(mlocal @ (mimplies @ (mbox @ p) @ (mdia @ (mimplies @ q @ p))))),
% 0.11/0.24 inference(negated_conjecture,[status(cth)],[f10])).
% 0.11/0.24 thf(f14,plain,(
% 0.11/0.24 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.11/0.24 inference(fool_elimination,[],[f1])).
% 0.11/0.24 thf(f15,plain,(
% 0.11/0.24 ~(mlocal @ (mimplies @ (mbox @ p) @ (mdia @ (mimplies @ q @ p))))),
% 0.11/0.24 inference(rectify,[],[f11])).
% 0.11/0.24 thf(f16,plain,(
% 0.11/0.24 ~ (((mlocal @ (mimplies @ (mbox @ p) @ (mdia @ (mimplies @ q @ p))))) = $true)),
% 0.11/0.24 inference(fool_elimination,[],[f15])).
% 0.11/0.24 thf(f17,plain,(
% 0.11/0.24 ! [X0 : mworld] : ? [X1 : mworld] : (mrel @ X0 @ X1)),
% 0.11/0.24 inference(rectify,[],[f9])).
% 0.11/0.24 thf(f18,plain,(
% 0.11/0.24 ! [X0 : mworld] : ? [X1 : mworld] : (((mrel @ X0 @ X1)) = $true)),
% 0.11/0.24 inference(fool_elimination,[],[f17])).
% 0.11/0.24 thf(f21,plain,(
% 0.11/0.24 ((^[X0 : (mworld > $o), X1 : mworld] : (? [X2 : mworld] : ((mrel @ X1 @ X2) & (X0 @ X2)))) = mdia)),
% 0.11/0.24 inference(rectify,[],[f8])).
% 0.11/0.24 thf(f22,plain,(
% 0.11/0.24 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))))),
% 0.11/0.24 inference(fool_elimination,[],[f21])).
% 0.11/0.24 thf(f27,plain,(
% 0.11/0.24 ((^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X0 @ X2) => (X1 @ X2))) = mimplies)),
% 0.11/0.24 inference(rectify,[],[f5])).
% 0.11/0.24 thf(f28,plain,(
% 0.11/0.24 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.11/0.24 inference(fool_elimination,[],[f27])).
% 0.11/0.24 thf(f29,plain,(
% 0.11/0.24 ((^[X0 : (mworld > $o), X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))) = mbox)),
% 0.11/0.24 inference(rectify,[],[f7])).
% 0.11/0.24 thf(f30,plain,(
% 0.11/0.24 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.11/0.24 inference(fool_elimination,[],[f29])).
% 0.11/0.24 thf(f31,plain,(
% 0.11/0.24 (((mlocal @ (mimplies @ (mbox @ p) @ (mdia @ (mimplies @ q @ p))))) != $true)),
% 0.11/0.24 inference(flattening,[],[f16])).
% 0.11/0.24 thf(f32,plain,(
% 0.11/0.24 ! [X0 : mworld] : (((mrel @ X0 @ (sK0 @ X0))) = $true)),
% 0.11/0.24 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK0 @ X0)],[f18])).
% 0.11/0.24 thf(f33,plain,(
% 0.11/0.24 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.11/0.24 inference(cnf_transformation,[],[f28])).
% 0.11/0.25 thf(f34,plain,(
% 0.11/0.25 ( ! [X0 : mworld] : ((((mrel @ X0 @ (sK0 @ X0))) = $true)) )),
% 0.11/0.25 inference(cnf_transformation,[],[f32])).
% 0.11/0.25 thf(f36,plain,(
% 0.11/0.25 (((mlocal @ (mimplies @ (mbox @ p) @ (mdia @ (mimplies @ q @ p))))) != $true)),
% 0.11/0.25 inference(cnf_transformation,[],[f31])).
% 0.11/0.25 thf(f37,plain,(
% 0.11/0.25 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.11/0.25 inference(cnf_transformation,[],[f30])).
% 0.11/0.25 thf(f39,plain,(
% 0.11/0.25 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))))),
% 0.11/0.25 inference(cnf_transformation,[],[f22])).
% 0.11/0.25 thf(f40,plain,(
% 0.11/0.25 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.11/0.25 inference(cnf_transformation,[],[f14])).
% 0.11/0.25 thf(f45,plain,(
% 0.11/0.25 ((((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ p) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ q @ p))))) != $true)),
% 0.11/0.25 inference(definition_unfolding,[],[f36,f40,f33,f37,f39,f33])).
% 0.11/0.25 thf(f46,plain,(
% 0.11/0.25 ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (p @ Y0)))) => (?? @ mworld @ (^[Y0 : mworld]: (((q @ Y0) => (p @ Y0)) & (mrel @ mactual @ Y0)))))) != $true)),
% 0.11/0.25 inference(beta-eta_normalization,[],[f45])).
% 0.11/0.25 thf(f47,plain,(
% 0.11/0.25 (((?? @ mworld @ (^[Y0 : mworld]: (((q @ Y0) => (p @ Y0)) & (mrel @ mactual @ Y0))))) = $false)),
% 0.11/0.25 inference(imp_proxy_clausification,[],[f46])).
% 0.11/0.25 thf(f48,plain,(
% 0.11/0.25 (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (p @ Y0))))) = $true)),
% 0.11/0.25 inference(imp_proxy_clausification,[],[f46])).
% 0.11/0.25 thf(f49,plain,(
% 0.11/0.25 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (p @ Y0))) @ X1)))) )),
% 0.11/0.25 inference(pi_proxy_clausification,[],[f48])).
% 0.11/0.25 thf(f50,plain,(
% 0.11/0.25 ( ! [X1 : mworld] : (((((mrel @ mactual @ X1) => (p @ X1))) = $true)) )),
% 0.11/0.25 inference(beta-eta_normalization,[],[f49])).
% 0.11/0.25 thf(f51,plain,(
% 0.11/0.25 ( ! [X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | (((p @ X1)) = $true)) )),
% 0.11/0.25 inference(imp_proxy_clausification,[],[f50])).
% 0.11/0.25 thf(f52,plain,(
% 0.11/0.25 ( ! [X1 : mworld] : (($false = (((^[Y0 : mworld]: (((q @ Y0) => (p @ Y0)) & (mrel @ mactual @ Y0))) @ X1)))) )),
% 0.11/0.25 inference(pi_proxy_clausification,[],[f47])).
% 0.11/0.25 thf(f53,plain,(
% 0.11/0.25 ( ! [X1 : mworld] : (($false = ((((q @ X1) => (p @ X1)) & (mrel @ mactual @ X1))))) )),
% 0.11/0.25 inference(beta-eta_normalization,[],[f52])).
% 0.11/0.25 thf(f54,plain,(
% 0.11/0.25 ( ! [X1 : mworld] : (($false = (((q @ X1) => (p @ X1)))) | ($false = ((mrel @ mactual @ X1)))) )),
% 0.11/0.25 inference(and_proxy_clausification,[],[f53])).
% 0.11/0.25 thf(f55,plain,(
% 0.11/0.25 ( ! [X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | (((p @ X1)) = $false)) )),
% 0.11/0.25 inference(imp_proxy_clausification,[],[f54])).
% 0.11/0.25 thf(f58,plain,(
% 0.11/0.25 ($false = $true) | (((p @ (sK0 @ mactual))) = $true)),
% 0.11/0.25 inference(constrained_superposition,[],[f51,f34])).
% 0.11/0.25 thf(f59,plain,(
% 0.11/0.25 (((p @ (sK0 @ mactual))) = $true)),
% 0.11/0.25 inference(trivial_inequality_removal,[],[f58])).
% 0.11/0.25 thf(f62,plain,(
% 0.11/0.25 ($false = ((p @ (sK0 @ mactual)))) | ($false = $true)),
% 0.11/0.25 inference(constrained_superposition,[],[f34,f55])).
% 0.11/0.25 thf(f63,plain,(
% 0.11/0.25 ($false = ((p @ (sK0 @ mactual))))),
% 0.11/0.25 inference(trivial_inequality_removal,[],[f62])).
% 0.11/0.25 thf(f65,plain,(
% 0.11/0.25 ($false = $true)),
% 0.11/0.25 inference(constrained_superposition,[],[f63,f59])).
% 0.11/0.25 thf(f67,plain,(
% 0.11/0.25 $false),
% 0.11/0.25 inference(trivial_inequality_removal,[],[f65])).
% 0.11/0.25 % SZS output end Proof for theBenchmark
% 0.11/0.25 % (1113076)------------------------------
% 0.11/0.25 % (1113076)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.25 % (1113076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.25 % (1113076)CaDiCaL version: 2.1.3
% 0.11/0.25 % (1113076)Termination reason: Refutation
% 0.11/0.25 % (1113076)Time elapsed: 0.002 s
% 0.11/0.25 % (1113076)Peak memory usage: 12 MB
% 0.11/0.25 % (1113076)Instructions burned: 5 (million)
% 0.11/0.25 % (1113070)Success in time 0.028 s
% 0.11/0.25 % Vampire exiting
%------------------------------------------------------------------------------