%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n010.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 08:50:34 AM UTC 2026
% Result : Theorem 0.26s 0.26s
% Output : Refutation 0.26s
% 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 SAT
% 0.09/0.18 % Computer : n010.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 17:26:33 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.26/0.26 % (3172477)Will run a generic schedule for satisfiability detection.
% 0.26/0.26 % (3172484)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3063840903:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.26/0.26 % (3172484) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3172477-3172484"...
% 0.26/0.26 % (3172483)% WARNING: option uhcvi not known.
% 0.26/0.26 % (3172484)...printing done.
% 0.26/0.26 % (3172484)Refutation found. Thanks to Tanya!
% 0.26/0.26 % SZS status Theorem for theBenchmark
% 0.26/0.26 % SZS output start Proof for theBenchmark
% 0.26/0.26 thf(type_def_5, type, mworld: $tType).
% 0.26/0.26 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.26/0.26 thf(func_def_0, type, mrel: (mworld > mworld > $o)).
% 0.26/0.26 thf(func_def_1, type, mactual: mworld).
% 0.26/0.26 thf(func_def_2, type, mlocal: ((mworld > $o) > $o)).
% 0.26/0.26 thf(func_def_4, type, mnot: ((mworld > $o) > mworld > $o)).
% 0.26/0.26 thf(func_def_5, type, mand: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.26/0.26 thf(func_def_6, type, mor: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.26/0.26 thf(func_def_7, type, mimplies: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.26/0.26 thf(func_def_8, type, mequiv: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.26/0.26 thf(func_def_9, type, mbox: ((mworld > $o) > mworld > $o)).
% 0.26/0.26 thf(func_def_10, type, mdia: ((mworld > $o) > mworld > $o)).
% 0.26/0.26 thf(func_def_11, type, p: (mworld > $o)).
% 0.26/0.26 thf(func_def_12, type, q: (mworld > $o)).
% 0.26/0.26 thf(func_def_13, type, db0: !>[X0: $tType]:(X0)).
% 0.26/0.26 thf(func_def_14, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.26/0.26 thf(func_def_15, type, vNOT: ($o > $o)).
% 0.26/0.26 thf(func_def_16, type, db1: !>[X0: $tType]:(X0)).
% 0.26/0.26 thf(func_def_17, type, vAND: ($o > $o > $o)).
% 0.26/0.26 thf(func_def_18, type, db2: !>[X0: $tType]:(X0)).
% 0.26/0.26 thf(func_def_19, type, vOR: ($o > $o > $o)).
% 0.26/0.26 thf(func_def_20, type, vIMP: ($o > $o > $o)).
% 0.26/0.26 thf(func_def_21, type, vIFF: ($o > $o > $o)).
% 0.26/0.26 thf(func_def_22, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.26/0.26 thf(func_def_23, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.26/0.26 thf(func_def_26, type, sK0: (mworld > mworld)).
% 0.26/0.26 thf(f1,axiom,(
% 0.26/0.26 (mlocal = (^[X0 : (mworld > $o)] : ((X0 @ mactual))))),
% 0.26/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def)).
% 0.26/0.26 thf(f5,axiom,(
% 0.26/0.26 (mimplies = (^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 0.26/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def)).
% 0.26/0.26 thf(f7,axiom,(
% 0.26/0.26 (mbox = (^[X0 : (mworld > $o), X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 0.26/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def)).
% 0.26/0.26 thf(f8,axiom,(
% 0.26/0.26 (mdia = (^[X0 : (mworld > $o), X1 : mworld] : (? [X2 : mworld] : ((X0 @ X2) & (mrel @ X1 @ X2)))))),
% 0.26/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_def)).
% 0.26/0.26 thf(f9,axiom,(
% 0.26/0.26 ! [X0 : mworld] : ? [X1 : mworld] : (mrel @ X0 @ X1)),
% 0.26/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_serial)).
% 0.26/0.26 thf(f10,conjecture,(
% 0.26/0.26 (mlocal @ (mimplies @ (mbox @ p) @ (mdia @ (mimplies @ q @ p))))),
% 0.26/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)).
% 0.26/0.26 thf(f11,negated_conjecture,(
% 0.26/0.26 ~(mlocal @ (mimplies @ (mbox @ p) @ (mdia @ (mimplies @ q @ p))))),
% 0.26/0.26 inference(negated_conjecture,[status(cth)],[f10])).
% 0.26/0.26 thf(f12,plain,(
% 0.26/0.26 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.26/0.26 inference(fool_elimination,[],[f1])).
% 0.26/0.26 thf(f19,plain,(
% 0.26/0.26 (mimplies = (^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 0.26/0.26 inference(rectify,[],[f5])).
% 0.26/0.26 thf(f20,plain,(
% 0.26/0.26 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.26/0.26 inference(fool_elimination,[],[f19])).
% 0.26/0.26 thf(f23,plain,(
% 0.26/0.26 (mbox = (^[X0 : (mworld > $o), X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 0.26/0.26 inference(rectify,[],[f7])).
% 0.26/0.26 thf(f24,plain,(
% 0.26/0.26 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.26/0.26 inference(fool_elimination,[],[f23])).
% 0.26/0.26 thf(f25,plain,(
% 0.26/0.26 (mdia = (^[X0 : (mworld > $o), X1 : mworld] : (? [X2 : mworld] : ((X0 @ X2) & (mrel @ X1 @ X2)))))),
% 0.26/0.26 inference(rectify,[],[f8])).
% 0.26/0.26 thf(f26,plain,(
% 0.26/0.26 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) & (Y0 @ Y2))))))))),
% 0.26/0.26 inference(fool_elimination,[],[f25])).
% 0.26/0.26 thf(f27,plain,(
% 0.26/0.26 ! [X0 : mworld] : ? [X1 : mworld] : (mrel @ X0 @ X1)),
% 0.26/0.26 inference(rectify,[],[f9])).
% 0.26/0.26 thf(f28,plain,(
% 0.26/0.26 ! [X0 : mworld] : ? [X1 : mworld] : (((mrel @ X0 @ X1)) = $true)),
% 0.26/0.26 inference(fool_elimination,[],[f27])).
% 0.26/0.26 thf(f29,plain,(
% 0.26/0.26 ~(mlocal @ (mimplies @ (mbox @ p) @ (mdia @ (mimplies @ q @ p))))),
% 0.26/0.26 inference(rectify,[],[f11])).
% 0.26/0.26 thf(f30,plain,(
% 0.26/0.26 ~ (((mlocal @ (mimplies @ (mbox @ p) @ (mdia @ (mimplies @ q @ p))))) = $true)),
% 0.26/0.26 inference(fool_elimination,[],[f29])).
% 0.26/0.26 thf(f31,plain,(
% 0.26/0.26 (((mlocal @ (mimplies @ (mbox @ p) @ (mdia @ (mimplies @ q @ p))))) != $true)),
% 0.26/0.26 inference(flattening,[],[f30])).
% 0.26/0.26 thf(f32,plain,(
% 0.26/0.26 ! [X0 : mworld] : ($true = ((mrel @ X0 @ (sK0 @ X0))))),
% 0.26/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK0 @ X0)],[f28])).
% 0.26/0.26 thf(f33,plain,(
% 0.26/0.26 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.26/0.26 inference(cnf_transformation,[],[f12])).
% 0.26/0.26 thf(f37,plain,(
% 0.26/0.26 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.26/0.26 inference(cnf_transformation,[],[f20])).
% 0.26/0.26 thf(f39,plain,(
% 0.26/0.26 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.26/0.26 inference(cnf_transformation,[],[f24])).
% 0.26/0.26 thf(f40,plain,(
% 0.26/0.26 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) & (Y0 @ Y2))))))))),
% 0.26/0.26 inference(cnf_transformation,[],[f26])).
% 0.26/0.26 thf(f41,plain,(
% 0.26/0.26 ( ! [X0 : mworld] : (($true = ((mrel @ X0 @ (sK0 @ X0))))) )),
% 0.26/0.26 inference(cnf_transformation,[],[f32])).
% 0.26/0.26 thf(f42,plain,(
% 0.26/0.26 (((mlocal @ (mimplies @ (mbox @ p) @ (mdia @ (mimplies @ q @ p))))) != $true)),
% 0.26/0.26 inference(cnf_transformation,[],[f31])).
% 0.26/0.26 thf(f45,plain,(
% 0.26/0.26 ($true != (((^[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]: ((mrel @ Y1 @ Y2) & (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ q @ p))))))),
% 0.26/0.26 inference(definition_unfolding,[],[f42,f33,f37,f39,f40,f37])).
% 0.26/0.26 thf(f46,plain,(
% 0.26/0.26 ($true != (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (p @ Y0)))) => (?? @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) & ((q @ Y0) => (p @ Y0))))))))),
% 0.26/0.26 inference(beta-eta_normalization,[],[f45])).
% 0.26/0.26 thf(f47,plain,(
% 0.26/0.26 ($false = ((?? @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) & ((q @ Y0) => (p @ Y0)))))))),
% 0.26/0.26 inference(imp_proxy_clausification,[],[f46])).
% 0.26/0.26 thf(f48,plain,(
% 0.26/0.26 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (p @ Y0))))))),
% 0.26/0.26 inference(imp_proxy_clausification,[],[f46])).
% 0.26/0.26 thf(f49,plain,(
% 0.26/0.26 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (p @ Y0))) @ X1)))) )),
% 0.26/0.26 inference(pi_proxy_clausification,[],[f48])).
% 0.26/0.26 thf(f50,plain,(
% 0.26/0.26 ( ! [X1 : mworld] : (($true = (((mrel @ mactual @ X1) => (p @ X1))))) )),
% 0.26/0.26 inference(beta-eta_normalization,[],[f49])).
% 0.26/0.26 thf(f51,plain,(
% 0.26/0.26 ( ! [X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((p @ X1)))) )),
% 0.26/0.26 inference(imp_proxy_clausification,[],[f50])).
% 0.26/0.26 thf(f52,plain,(
% 0.26/0.26 ( ! [X1 : mworld] : (($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) & ((q @ Y0) => (p @ Y0)))) @ X1)))) )),
% 0.26/0.26 inference(pi_proxy_clausification,[],[f47])).
% 0.26/0.26 thf(f53,plain,(
% 0.26/0.26 ( ! [X1 : mworld] : (($false = (((mrel @ mactual @ X1) & ((q @ X1) => (p @ X1)))))) )),
% 0.26/0.26 inference(beta-eta_normalization,[],[f52])).
% 0.26/0.26 thf(f54,plain,(
% 0.26/0.26 ( ! [X1 : mworld] : (($false = (((q @ X1) => (p @ X1)))) | ($false = ((mrel @ mactual @ X1)))) )),
% 0.26/0.26 inference(and_proxy_clausification,[],[f53])).
% 0.26/0.26 thf(f55,plain,(
% 0.26/0.26 ( ! [X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((p @ X1)))) )),
% 0.26/0.26 inference(imp_proxy_clausification,[],[f54])).
% 0.26/0.26 thf(f111,plain,(
% 0.26/0.26 ($true = $false) | ($true = ((p @ (sK0 @ mactual))))),
% 0.26/0.26 inference(constrained_superposition,[],[f51,f41])).
% 0.26/0.26 thf(f112,plain,(
% 0.26/0.26 ($true = ((p @ (sK0 @ mactual))))),
% 0.26/0.26 inference(trivial_inequality_removal,[],[f111])).
% 0.26/0.26 thf(f126,plain,(
% 0.26/0.26 ($true = $false) | ($false = ((p @ (sK0 @ mactual))))),
% 0.26/0.26 inference(constrained_superposition,[],[f41,f55])).
% 0.26/0.26 thf(f127,plain,(
% 0.26/0.26 ($false = ((p @ (sK0 @ mactual))))),
% 0.26/0.26 inference(trivial_inequality_removal,[],[f126])).
% 0.26/0.26 thf(f140,plain,(
% 0.26/0.26 ($true = $false)),
% 0.26/0.26 inference(constrained_superposition,[],[f112,f127])).
% 0.26/0.26 thf(f141,plain,(
% 0.26/0.26 $false),
% 0.26/0.26 inference(trivial_inequality_removal,[],[f140])).
% 0.26/0.26 % SZS output end Proof for theBenchmark
% 0.26/0.26 % (3172484)------------------------------
% 0.26/0.26 % (3172484)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.26 % (3172484)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.26 % (3172484)CaDiCaL version: 2.1.3
% 0.26/0.26 % (3172484)Termination reason: Refutation
% 0.26/0.26 % (3172484)Time elapsed: 0.003 s
% 0.26/0.26 % (3172484)Peak memory usage: 12 MB
% 0.26/0.26 % (3172484)Instructions burned: 7 (million)
% 0.26/0.26 % (3172477)Success in time 0.033 s
% 0.26/0.26 % Vampire exiting
%------------------------------------------------------------------------------