TSTP Solution File: SEU621^2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU621^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:50:04 EDT 2024
% Result : Theorem 0.22s 0.39s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU621^2 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun May 19 17:44:08 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a TH0_THM_EQU_NAR problem
% 0.14/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.38 % (31879)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.22/0.39 % (31879)First to succeed.
% 0.22/0.39 % (31879)Refutation found. Thanks to Tanya!
% 0.22/0.39 % SZS status Theorem for theBenchmark
% 0.22/0.39 % SZS output start Proof for theBenchmark
% 0.22/0.39 thf(func_def_0, type, in: $i > $i > $o).
% 0.22/0.39 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 0.22/0.39 thf(func_def_5, type, subset: $i > $i > $o).
% 0.22/0.39 thf(func_def_7, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.22/0.39 thf(func_def_20, type, sK3: $i > $i > $i).
% 0.22/0.39 thf(f68,plain,(
% 0.22/0.39 $false),
% 0.22/0.39 inference(avatar_sat_refutation,[],[f64,f67])).
% 0.22/0.39 thf(f67,plain,(
% 0.22/0.39 ~spl2_2),
% 0.22/0.39 inference(avatar_contradiction_clause,[],[f66])).
% 0.22/0.39 thf(f66,plain,(
% 0.22/0.39 $false | ~spl2_2),
% 0.22/0.39 inference(trivial_inequality_removal,[],[f65])).
% 0.22/0.39 thf(f65,plain,(
% 0.22/0.39 ($true != $true) | ~spl2_2),
% 0.22/0.39 inference(superposition,[],[f18,f60])).
% 0.22/0.39 thf(f60,plain,(
% 0.22/0.39 ($true = (subset @ (setadjoin @ sK0 @ emptyset) @ sK1)) | ~spl2_2),
% 0.22/0.39 inference(avatar_component_clause,[],[f58])).
% 0.22/0.39 thf(f58,plain,(
% 0.22/0.39 spl2_2 <=> ($true = (subset @ (setadjoin @ sK0 @ emptyset) @ sK1))),
% 0.22/0.39 introduced(avatar_definition,[new_symbols(naming,[spl2_2])])).
% 0.22/0.39 thf(f18,plain,(
% 0.22/0.39 ($true != (subset @ (setadjoin @ sK0 @ emptyset) @ sK1))),
% 0.22/0.39 inference(cnf_transformation,[],[f15])).
% 0.22/0.39 thf(f15,plain,(
% 0.22/0.39 (subsetI2 = $true) & (($true != (subset @ (setadjoin @ sK0 @ emptyset) @ sK1)) & ((in @ sK0 @ sK1) = $true)) & (uniqinunit = $true)),
% 0.22/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f14])).
% 0.22/0.39 thf(f14,plain,(
% 0.22/0.39 ? [X0,X1] : (((subset @ (setadjoin @ X0 @ emptyset) @ X1) != $true) & ($true = (in @ X0 @ X1))) => (($true != (subset @ (setadjoin @ sK0 @ emptyset) @ sK1)) & ((in @ sK0 @ sK1) = $true))),
% 0.22/0.39 introduced(choice_axiom,[])).
% 0.22/0.39 thf(f13,plain,(
% 0.22/0.39 (subsetI2 = $true) & ? [X0,X1] : (((subset @ (setadjoin @ X0 @ emptyset) @ X1) != $true) & ($true = (in @ X0 @ X1))) & (uniqinunit = $true)),
% 0.22/0.39 inference(flattening,[],[f12])).
% 0.22/0.39 thf(f12,plain,(
% 0.22/0.39 (? [X0,X1] : (((subset @ (setadjoin @ X0 @ emptyset) @ X1) != $true) & ($true = (in @ X0 @ X1))) & (subsetI2 = $true)) & (uniqinunit = $true)),
% 0.22/0.39 inference(ennf_transformation,[],[f9])).
% 0.22/0.39 thf(f9,plain,(
% 0.22/0.39 ~((uniqinunit = $true) => ((subsetI2 = $true) => ! [X0,X1] : (($true = (in @ X0 @ X1)) => ((subset @ (setadjoin @ X0 @ emptyset) @ X1) = $true))))),
% 0.22/0.39 inference(fool_elimination,[],[f8])).
% 0.22/0.39 thf(f8,plain,(
% 0.22/0.39 ~(uniqinunit => (subsetI2 => ! [X0,X1] : ((in @ X0 @ X1) => (subset @ (setadjoin @ X0 @ emptyset) @ X1))))),
% 0.22/0.39 inference(rectify,[],[f4])).
% 0.22/0.39 thf(f4,negated_conjecture,(
% 0.22/0.39 ~(uniqinunit => (subsetI2 => ! [X0,X2] : ((in @ X0 @ X2) => (subset @ (setadjoin @ X0 @ emptyset) @ X2))))),
% 0.22/0.39 inference(negated_conjecture,[],[f3])).
% 0.22/0.39 thf(f3,conjecture,(
% 0.22/0.39 uniqinunit => (subsetI2 => ! [X0,X2] : ((in @ X0 @ X2) => (subset @ (setadjoin @ X0 @ emptyset) @ X2)))),
% 0.22/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset)).
% 0.22/0.39 thf(f64,plain,(
% 0.22/0.39 spl2_2),
% 0.22/0.39 inference(avatar_split_clause,[],[f63,f58])).
% 0.22/0.39 thf(f63,plain,(
% 0.22/0.39 ($true = (subset @ (setadjoin @ sK0 @ emptyset) @ sK1))),
% 0.22/0.39 inference(trivial_inequality_removal,[],[f62])).
% 0.22/0.39 thf(f62,plain,(
% 0.22/0.39 ($true = (subset @ (setadjoin @ sK0 @ emptyset) @ sK1)) | ($false = $true)),
% 0.22/0.39 inference(forward_demodulation,[],[f52,f17])).
% 0.22/0.39 thf(f17,plain,(
% 0.22/0.39 ((in @ sK0 @ sK1) = $true)),
% 0.22/0.39 inference(cnf_transformation,[],[f15])).
% 0.22/0.39 thf(f52,plain,(
% 0.22/0.39 ($false = (in @ sK0 @ sK1)) | ($true = (subset @ (setadjoin @ sK0 @ emptyset) @ sK1))),
% 0.22/0.39 inference(superposition,[],[f31,f50])).
% 0.22/0.39 thf(f50,plain,(
% 0.22/0.39 (sK0 = (sK3 @ (setadjoin @ sK0 @ emptyset) @ sK1))),
% 0.22/0.39 inference(trivial_inequality_removal,[],[f49])).
% 0.22/0.39 thf(f49,plain,(
% 0.22/0.39 ($true != $true) | (sK0 = (sK3 @ (setadjoin @ sK0 @ emptyset) @ sK1))),
% 0.22/0.39 inference(superposition,[],[f18,f43])).
% 0.22/0.39 thf(f43,plain,(
% 0.22/0.39 ( ! [X0 : $i,X1 : $i] : (((subset @ (setadjoin @ X0 @ emptyset) @ X1) = $true) | ((sK3 @ (setadjoin @ X0 @ emptyset) @ X1) = X0)) )),
% 0.22/0.39 inference(trivial_inequality_removal,[],[f40])).
% 0.22/0.39 thf(f40,plain,(
% 0.22/0.39 ( ! [X0 : $i,X1 : $i] : (($false = $true) | ((sK3 @ (setadjoin @ X0 @ emptyset) @ X1) = X0) | ((subset @ (setadjoin @ X0 @ emptyset) @ X1) = $true)) )),
% 0.22/0.39 inference(superposition,[],[f32,f38])).
% 0.22/0.39 thf(f38,plain,(
% 0.22/0.39 ( ! [X2 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X2 @ emptyset)) = $false) | (X1 = X2)) )),
% 0.22/0.39 inference(equality_proxy_clausification,[],[f37])).
% 0.22/0.39 thf(f37,plain,(
% 0.22/0.39 ( ! [X2 : $i,X1 : $i] : (((X2 = X1) = $true) | ((in @ X1 @ (setadjoin @ X2 @ emptyset)) = $false)) )),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f36])).
% 0.22/0.39 thf(f36,plain,(
% 0.22/0.39 ( ! [X2 : $i,X1 : $i] : ((((in @ X1 @ (setadjoin @ X2 @ emptyset)) => (X2 = X1)) = $true)) )),
% 0.22/0.39 inference(beta_eta_normalization,[],[f35])).
% 0.22/0.39 thf(f35,plain,(
% 0.22/0.39 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X1 @ (setadjoin @ Y0 @ emptyset)) => (Y0 = X1))) @ X2) = $true)) )),
% 0.22/0.39 inference(pi_clausification,[],[f34])).
% 0.22/0.39 thf(f34,plain,(
% 0.22/0.39 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (setadjoin @ Y0 @ emptyset)) => (Y0 = X1)))))) )),
% 0.22/0.39 inference(beta_eta_normalization,[],[f33])).
% 0.22/0.39 thf(f33,plain,(
% 0.22/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0))))) @ X1) = $true)) )),
% 0.22/0.39 inference(pi_clausification,[],[f23])).
% 0.22/0.39 thf(f23,plain,(
% 0.22/0.39 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) = $true)),
% 0.22/0.39 inference(definition_unfolding,[],[f21,f16])).
% 0.22/0.39 thf(f16,plain,(
% 0.22/0.39 (uniqinunit = $true)),
% 0.22/0.39 inference(cnf_transformation,[],[f15])).
% 0.22/0.39 thf(f21,plain,(
% 0.22/0.39 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))))),
% 0.22/0.39 inference(cnf_transformation,[],[f11])).
% 0.22/0.39 thf(f11,plain,(
% 0.22/0.39 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))))),
% 0.22/0.39 inference(fool_elimination,[],[f10])).
% 0.22/0.39 thf(f10,plain,(
% 0.22/0.39 (! [X0,X1] : ((in @ X1 @ (setadjoin @ X0 @ emptyset)) => (X0 = X1)) = uniqinunit)),
% 0.22/0.39 inference(rectify,[],[f1])).
% 0.22/0.39 thf(f1,axiom,(
% 0.22/0.39 (! [X1,X0] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)) = uniqinunit)),
% 0.22/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit)).
% 0.22/0.39 thf(f32,plain,(
% 0.22/0.39 ( ! [X2 : $i,X1 : $i] : (((in @ (sK3 @ X1 @ X2) @ X1) = $true) | ($true = (subset @ X1 @ X2))) )),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f30])).
% 0.22/0.39 thf(f30,plain,(
% 0.22/0.39 ( ! [X2 : $i,X1 : $i] : (($true = (subset @ X1 @ X2)) | ($false = ((in @ (sK3 @ X1 @ X2) @ X1) => (in @ (sK3 @ X1 @ X2) @ X2)))) )),
% 0.22/0.39 inference(beta_eta_normalization,[],[f29])).
% 0.22/0.39 thf(f29,plain,(
% 0.22/0.39 ( ! [X2 : $i,X1 : $i] : (($false = ((^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2))) @ (sK3 @ X1 @ X2))) | ($true = (subset @ X1 @ X2))) )),
% 0.22/0.39 inference(sigma_clausification,[],[f28])).
% 0.22/0.39 thf(f28,plain,(
% 0.22/0.39 ( ! [X2 : $i,X1 : $i] : (($true = (subset @ X1 @ X2)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))))) )),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f27])).
% 0.22/0.39 thf(f27,plain,(
% 0.22/0.39 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => (subset @ X1 @ X2)) = $true)) )),
% 0.22/0.39 inference(beta_eta_normalization,[],[f26])).
% 0.22/0.39 thf(f26,plain,(
% 0.22/0.39 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (subset @ X1 @ Y0))) @ X2) = $true)) )),
% 0.22/0.39 inference(pi_clausification,[],[f25])).
% 0.22/0.39 thf(f25,plain,(
% 0.22/0.39 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (subset @ X1 @ Y0)))) = $true)) )),
% 0.22/0.39 inference(beta_eta_normalization,[],[f24])).
% 0.22/0.39 thf(f24,plain,(
% 0.22/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1))))) @ X1))) )),
% 0.22/0.39 inference(pi_clausification,[],[f22])).
% 0.22/0.39 thf(f22,plain,(
% 0.22/0.39 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) = $true)),
% 0.22/0.39 inference(definition_unfolding,[],[f20,f19])).
% 0.22/0.39 thf(f19,plain,(
% 0.22/0.39 (subsetI2 = $true)),
% 0.22/0.39 inference(cnf_transformation,[],[f15])).
% 0.22/0.39 thf(f20,plain,(
% 0.22/0.39 (subsetI2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))),
% 0.22/0.39 inference(cnf_transformation,[],[f7])).
% 0.22/0.39 thf(f7,plain,(
% 0.22/0.39 (subsetI2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))),
% 0.22/0.39 inference(fool_elimination,[],[f6])).
% 0.22/0.39 thf(f6,plain,(
% 0.22/0.39 (! [X0,X1] : (! [X2] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)) = subsetI2)),
% 0.22/0.39 inference(rectify,[],[f2])).
% 0.22/0.39 thf(f2,axiom,(
% 0.22/0.39 (! [X3,X2] : (! [X0] : ((in @ X0 @ X2) => (in @ X0 @ X3)) => (subset @ X2 @ X3)) = subsetI2)),
% 0.22/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2)).
% 0.22/0.39 thf(f31,plain,(
% 0.22/0.39 ( ! [X2 : $i,X1 : $i] : (($false = (in @ (sK3 @ X1 @ X2) @ X2)) | ($true = (subset @ X1 @ X2))) )),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f30])).
% 0.22/0.39 % SZS output end Proof for theBenchmark
% 0.22/0.39 % (31879)------------------------------
% 0.22/0.39 % (31879)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39 % (31879)Termination reason: Refutation
% 0.22/0.39
% 0.22/0.39 % (31879)Memory used [KB]: 5500
% 0.22/0.39 % (31879)Time elapsed: 0.008 s
% 0.22/0.39 % (31879)Instructions burned: 6 (million)
% 0.22/0.39 % (31879)------------------------------
% 0.22/0.39 % (31879)------------------------------
% 0.22/0.39 % (31876)Success in time 0.02 s
% 0.22/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------