TSTP Solution File: SEU534^2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU534^2 : 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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n011.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 03:49:25 EDT 2024
% Result : Theorem 0.20s 0.38s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU534^2 : TPTP v8.2.0. Released v3.7.0.
% 0.04/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 15:46:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.35 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/sandbox2/benchmark/theBenchmark.p
% 0.20/0.37 % (13990)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)
% 0.20/0.37 % (13991)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.37 % (13993)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.20/0.37 % (13992)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.37 % (13989)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.20/0.37 % (13994)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.37 % (13995)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.38 % (13991)Instruction limit reached!
% 0.20/0.38 % (13991)------------------------------
% 0.20/0.38 % (13991)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (13992)Instruction limit reached!
% 0.20/0.38 % (13992)------------------------------
% 0.20/0.38 % (13992)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (13991)Termination reason: Unknown
% 0.20/0.38 % (13991)Termination phase: Saturation
% 0.20/0.38
% 0.20/0.38 % (13991)Memory used [KB]: 5500
% 0.20/0.38 % (13991)Time elapsed: 0.004 s
% 0.20/0.38 % (13991)Instructions burned: 2 (million)
% 0.20/0.38 % (13991)------------------------------
% 0.20/0.38 % (13991)------------------------------
% 0.20/0.38 % (13992)Termination reason: Unknown
% 0.20/0.38 % (13992)Termination phase: Saturation
% 0.20/0.38
% 0.20/0.38 % (13992)Memory used [KB]: 5500
% 0.20/0.38 % (13992)Time elapsed: 0.003 s
% 0.20/0.38 % (13992)Instructions burned: 3 (million)
% 0.20/0.38 % (13992)------------------------------
% 0.20/0.38 % (13992)------------------------------
% 0.20/0.38 % (13995)Instruction limit reached!
% 0.20/0.38 % (13995)------------------------------
% 0.20/0.38 % (13995)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (13995)Termination reason: Unknown
% 0.20/0.38 % (13995)Termination phase: Saturation
% 0.20/0.38
% 0.20/0.38 % (13995)Memory used [KB]: 5500
% 0.20/0.38 % (13995)Time elapsed: 0.004 s
% 0.20/0.38 % (13995)Instructions burned: 3 (million)
% 0.20/0.38 % (13995)------------------------------
% 0.20/0.38 % (13995)------------------------------
% 0.20/0.38 % (13989)Instruction limit reached!
% 0.20/0.38 % (13989)------------------------------
% 0.20/0.38 % (13989)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (13989)Termination reason: Unknown
% 0.20/0.38 % (13993)Refutation not found, incomplete strategy
% 0.20/0.38 % (13993)------------------------------
% 0.20/0.38 % (13993)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (13993)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.38
% 0.20/0.38
% 0.20/0.38 % (13993)Memory used [KB]: 5500
% 0.20/0.38 % (13993)Time elapsed: 0.005 s
% 0.20/0.38 % (13993)Instructions burned: 3 (million)
% 0.20/0.38 % (13993)------------------------------
% 0.20/0.38 % (13993)------------------------------
% 0.20/0.38 % (13989)Termination phase: Saturation
% 0.20/0.38
% 0.20/0.38 % (13989)Memory used [KB]: 5500
% 0.20/0.38 % (13989)Time elapsed: 0.005 s
% 0.20/0.38 % (13989)Instructions burned: 4 (million)
% 0.20/0.38 % (13989)------------------------------
% 0.20/0.38 % (13989)------------------------------
% 0.20/0.38 % (13990)First to succeed.
% 0.20/0.38 % (13994)Also succeeded, but the first one will report.
% 0.20/0.38 % (13988)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.20/0.38 % (13990)Refutation found. Thanks to Tanya!
% 0.20/0.38 % SZS status Theorem for theBenchmark
% 0.20/0.38 % SZS output start Proof for theBenchmark
% 0.20/0.38 thf(func_def_0, type, in: $i > $i > $o).
% 0.20/0.38 thf(func_def_2, type, dsetconstr: $i > ($i > $o) > $i).
% 0.20/0.38 thf(func_def_6, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.20/0.38 thf(func_def_16, type, sK1: $i > $o).
% 0.20/0.38 thf(func_def_19, type, ph4: !>[X0: $tType]:(X0)).
% 0.20/0.38 thf(f68,plain,(
% 0.20/0.38 $false),
% 0.20/0.38 inference(avatar_sat_refutation,[],[f50,f56,f67])).
% 0.20/0.38 thf(f67,plain,(
% 0.20/0.38 ~spl3_1),
% 0.20/0.38 inference(avatar_contradiction_clause,[],[f66])).
% 0.20/0.38 thf(f66,plain,(
% 0.20/0.38 $false | ~spl3_1),
% 0.20/0.38 inference(trivial_inequality_removal,[],[f65])).
% 0.20/0.38 thf(f65,plain,(
% 0.20/0.38 ($true = $false) | ~spl3_1),
% 0.20/0.38 inference(backward_demodulation,[],[f21,f63])).
% 0.20/0.38 thf(f63,plain,(
% 0.20/0.38 ($false = (sK1 @ sK2)) | ~spl3_1),
% 0.20/0.38 inference(trivial_inequality_removal,[],[f61])).
% 0.20/0.38 thf(f61,plain,(
% 0.20/0.38 ($false = (sK1 @ sK2)) | ($true = $false) | ~spl3_1),
% 0.20/0.38 inference(superposition,[],[f59,f20])).
% 0.20/0.38 thf(f20,plain,(
% 0.20/0.38 ($true = (in @ sK2 @ sK0))),
% 0.20/0.38 inference(cnf_transformation,[],[f18])).
% 0.20/0.38 thf(f18,plain,(
% 0.20/0.38 (dsetconstrI = $true) & (emptysetE = $true) & ((emptyset = (dsetconstr @ sK0 @ (^[Y0 : $i]: (sK1 @ Y0)))) & (($true = (sK1 @ sK2)) & ($true = (in @ sK2 @ sK0))))),
% 0.20/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f15,f17,f16])).
% 0.20/0.38 thf(f16,plain,(
% 0.20/0.38 ? [X0,X1 : $i > $o] : ((emptyset = (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) & ? [X2] : (((X1 @ X2) = $true) & ((in @ X2 @ X0) = $true))) => ((emptyset = (dsetconstr @ sK0 @ (^[Y0 : $i]: (sK1 @ Y0)))) & ? [X2] : (((sK1 @ X2) = $true) & ((in @ X2 @ sK0) = $true)))),
% 0.20/0.38 introduced(choice_axiom,[])).
% 0.20/0.38 thf(f17,plain,(
% 0.20/0.38 ? [X2] : (((sK1 @ X2) = $true) & ((in @ X2 @ sK0) = $true)) => (($true = (sK1 @ sK2)) & ($true = (in @ sK2 @ sK0)))),
% 0.20/0.38 introduced(choice_axiom,[])).
% 0.20/0.38 thf(f15,plain,(
% 0.20/0.38 (dsetconstrI = $true) & (emptysetE = $true) & ? [X0,X1 : $i > $o] : ((emptyset = (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) & ? [X2] : (((X1 @ X2) = $true) & ((in @ X2 @ X0) = $true)))),
% 0.20/0.38 inference(flattening,[],[f14])).
% 0.20/0.38 thf(f14,plain,(
% 0.20/0.38 (? [X0,X1 : $i > $o] : ((emptyset = (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) & ? [X2] : (((X1 @ X2) = $true) & ((in @ X2 @ X0) = $true))) & (emptysetE = $true)) & (dsetconstrI = $true)),
% 0.20/0.38 inference(ennf_transformation,[],[f13])).
% 0.20/0.38 thf(f13,plain,(
% 0.20/0.38 ~((dsetconstrI = $true) => ((emptysetE = $true) => ! [X0,X1 : $i > $o] : (? [X2] : (((X1 @ X2) = $true) & ((in @ X2 @ X0) = $true)) => (emptyset != (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))))),
% 0.20/0.38 inference(flattening,[],[f12])).
% 0.20/0.38 thf(f12,plain,(
% 0.20/0.38 ~((dsetconstrI = $true) => ((emptysetE = $true) => ! [X0,X1 : $i > $o] : (? [X2] : (((X1 @ X2) = $true) & ((in @ X2 @ X0) = $true)) => ~(emptyset = (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))))),
% 0.20/0.38 inference(true_and_false_elimination,[],[f9])).
% 0.20/0.38 thf(f9,plain,(
% 0.20/0.38 ~((dsetconstrI = $true) => ((emptysetE = $true) => ! [X0,X1 : $i > $o] : (? [X2] : (((X1 @ X2) = $true) & ((in @ X2 @ X0) = $true)) => ((emptyset = (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) => $false))))),
% 0.20/0.38 inference(fool_elimination,[],[f8])).
% 0.20/0.38 thf(f8,plain,(
% 0.20/0.38 ~(dsetconstrI => (emptysetE => ! [X0,X1 : $i > $o] : (? [X2] : ((in @ X2 @ X0) & (X1 @ X2)) => (((dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3))) = emptyset) => $false))))),
% 0.20/0.38 inference(rectify,[],[f4])).
% 0.20/0.38 thf(f4,negated_conjecture,(
% 0.20/0.38 ~(dsetconstrI => (emptysetE => ! [X0,X1 : $i > $o] : (? [X2] : ((in @ X2 @ X0) & (X1 @ X2)) => (((dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))) = emptyset) => $false))))),
% 0.20/0.38 inference(negated_conjecture,[],[f3])).
% 0.20/0.38 thf(f3,conjecture,(
% 0.20/0.38 dsetconstrI => (emptysetE => ! [X0,X1 : $i > $o] : (? [X2] : ((in @ X2 @ X0) & (X1 @ X2)) => (((dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))) = emptyset) => $false)))),
% 0.20/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyE1)).
% 0.20/0.38 thf(f59,plain,(
% 0.20/0.38 ( ! [X0 : $i] : (((in @ X0 @ sK0) = $false) | ($false = (sK1 @ X0))) ) | ~spl3_1),
% 0.20/0.38 inference(trivial_inequality_removal,[],[f57])).
% 0.20/0.38 thf(f57,plain,(
% 0.20/0.38 ( ! [X0 : $i] : (($false = (sK1 @ X0)) | ($true = $false) | ((in @ X0 @ sK0) = $false)) ) | ~spl3_1),
% 0.20/0.38 inference(superposition,[],[f43,f46])).
% 0.20/0.38 thf(f46,plain,(
% 0.20/0.38 ( ! [X1 : $i] : (((in @ X1 @ (dsetconstr @ sK0 @ sK1)) = $false)) ) | ~spl3_1),
% 0.20/0.38 inference(avatar_component_clause,[],[f45])).
% 0.20/0.38 thf(f45,plain,(
% 0.20/0.38 spl3_1 <=> ! [X1] : ((in @ X1 @ (dsetconstr @ sK0 @ sK1)) = $false)),
% 0.20/0.38 introduced(avatar_definition,[new_symbols(naming,[spl3_1])])).
% 0.20/0.38 thf(f43,plain,(
% 0.20/0.38 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (((in @ X2 @ (dsetconstr @ X1 @ X3)) = $true) | ($false = (X3 @ X2)) | ($false = (in @ X2 @ X1))) )),
% 0.20/0.38 inference(binary_proxy_clausification,[],[f42])).
% 0.20/0.38 thf(f42,plain,(
% 0.20/0.38 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($false = (in @ X2 @ X1)) | (((X3 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ X3))) = $true)) )),
% 0.20/0.38 inference(binary_proxy_clausification,[],[f41])).
% 0.20/0.38 thf(f41,plain,(
% 0.20/0.38 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((in @ X2 @ X1) => ((X3 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ X3)))) = $true)) )),
% 0.20/0.38 inference(beta_eta_normalization,[],[f40])).
% 0.20/0.38 thf(f40,plain,(
% 0.20/0.38 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: ((in @ X2 @ X1) => ((Y0 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ Y0))))) @ X3))) )),
% 0.20/0.38 inference(pi_clausification,[],[f39])).
% 0.20/0.38 thf(f39,plain,(
% 0.20/0.38 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X2 @ X1) => ((Y0 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ Y0)))))))) )),
% 0.20/0.38 inference(beta_eta_normalization,[],[f38])).
% 0.20/0.38 thf(f38,plain,(
% 0.20/0.38 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ X1) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ X1 @ Y1))))))) @ X2))) )),
% 0.20/0.38 inference(pi_clausification,[],[f37])).
% 0.20/0.38 thf(f37,plain,(
% 0.20/0.38 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ X1) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ X1 @ Y1)))))))) = $true)) )),
% 0.20/0.38 inference(beta_eta_normalization,[],[f36])).
% 0.20/0.38 thf(f36,plain,(
% 0.20/0.38 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2))))))))) @ X1) = $true)) )),
% 0.20/0.38 inference(pi_clausification,[],[f35])).
% 0.20/0.38 thf(f35,plain,(
% 0.20/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))))),
% 0.20/0.38 inference(beta_eta_normalization,[],[f28])).
% 0.20/0.38 thf(f28,plain,(
% 0.20/0.38 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))) = $true)),
% 0.20/0.38 inference(definition_unfolding,[],[f25,f24])).
% 0.20/0.38 thf(f24,plain,(
% 0.20/0.38 (dsetconstrI = $true)),
% 0.20/0.38 inference(cnf_transformation,[],[f18])).
% 0.20/0.38 thf(f25,plain,(
% 0.20/0.38 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 0.20/0.38 inference(cnf_transformation,[],[f11])).
% 0.20/0.38 thf(f11,plain,(
% 0.20/0.38 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 0.20/0.38 inference(fool_elimination,[],[f10])).
% 0.20/0.38 thf(f10,plain,(
% 0.20/0.38 (dsetconstrI = ! [X0 : $i > $o,X1,X2] : ((in @ X1 @ X2) => ((X0 @ X1) => (in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X0 @ X3)))))))),
% 0.20/0.38 inference(rectify,[],[f1])).
% 0.20/0.38 thf(f1,axiom,(
% 0.20/0.38 (dsetconstrI = ! [X1 : $i > $o,X2,X0] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))))),
% 0.20/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI)).
% 0.20/0.38 thf(f21,plain,(
% 0.20/0.38 ($true = (sK1 @ sK2))),
% 0.20/0.38 inference(cnf_transformation,[],[f18])).
% 0.20/0.38 thf(f56,plain,(
% 0.20/0.38 ~spl3_2),
% 0.20/0.38 inference(avatar_contradiction_clause,[],[f55])).
% 0.20/0.38 thf(f55,plain,(
% 0.20/0.38 $false | ~spl3_2),
% 0.20/0.38 inference(equality_resolution,[],[f52])).
% 0.20/0.38 thf(f52,plain,(
% 0.20/0.38 ( ! [X0 : $o] : (($false != X0)) ) | ~spl3_2),
% 0.20/0.38 inference(superposition,[],[f5,f49])).
% 0.20/0.38 thf(f49,plain,(
% 0.20/0.38 ( ! [X2 : $o] : (($true = X2)) ) | ~spl3_2),
% 0.20/0.38 inference(avatar_component_clause,[],[f48])).
% 0.20/0.38 thf(f48,plain,(
% 0.20/0.38 spl3_2 <=> ! [X2 : $o] : ($true = X2)),
% 0.20/0.38 introduced(avatar_definition,[new_symbols(naming,[spl3_2])])).
% 0.20/0.38 thf(f5,plain,(
% 0.20/0.38 ($true != $false)),
% 0.20/0.38 introduced(fool_axiom,[])).
% 0.20/0.38 thf(f50,plain,(
% 0.20/0.38 spl3_1 | spl3_2),
% 0.20/0.38 inference(avatar_split_clause,[],[f34,f48,f45])).
% 0.20/0.38 thf(f34,plain,(
% 0.20/0.38 ( ! [X2 : $o,X1 : $i] : (($true = X2) | ((in @ X1 @ (dsetconstr @ sK0 @ sK1)) = $false)) )),
% 0.20/0.38 inference(beta_eta_normalization,[],[f33])).
% 0.20/0.38 thf(f33,plain,(
% 0.20/0.38 ( ! [X2 : $o,X1 : $i] : (((in @ X1 @ (dsetconstr @ sK0 @ sK1)) = $false) | ($true = ((^[Y0 : $o]: (Y0)) @ X2))) )),
% 0.20/0.38 inference(pi_clausification,[],[f32])).
% 0.20/0.38 thf(f32,plain,(
% 0.20/0.38 ( ! [X1 : $i] : (((in @ X1 @ (dsetconstr @ sK0 @ sK1)) = $false) | ((!! @ $o @ (^[Y0 : $o]: (Y0))) = $true)) )),
% 0.20/0.38 inference(binary_proxy_clausification,[],[f31])).
% 0.20/0.38 thf(f31,plain,(
% 0.20/0.38 ( ! [X1 : $i] : ((((in @ X1 @ (dsetconstr @ sK0 @ sK1)) => (!! @ $o @ (^[Y0 : $o]: (Y0)))) = $true)) )),
% 0.20/0.38 inference(beta_eta_normalization,[],[f30])).
% 0.20/0.38 thf(f30,plain,(
% 0.20/0.38 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK0 @ sK1)) => (!! @ $o @ (^[Y1 : $o]: (Y1))))) @ X1) = $true)) )),
% 0.20/0.38 inference(pi_clausification,[],[f29])).
% 0.20/0.38 thf(f29,plain,(
% 0.20/0.38 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK0 @ sK1)) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) = $true)),
% 0.20/0.38 inference(beta_eta_normalization,[],[f27])).
% 0.20/0.38 thf(f27,plain,(
% 0.20/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK0 @ (^[Y1 : $i]: (sK1 @ Y1)))) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))))),
% 0.20/0.38 inference(definition_unfolding,[],[f23,f26])).
% 0.20/0.38 thf(f26,plain,(
% 0.20/0.38 (emptysetE = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK0 @ (^[Y1 : $i]: (sK1 @ Y1)))) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))))),
% 0.20/0.38 inference(definition_unfolding,[],[f19,f22])).
% 0.20/0.38 thf(f22,plain,(
% 0.20/0.38 (emptyset = (dsetconstr @ sK0 @ (^[Y0 : $i]: (sK1 @ Y0))))),
% 0.20/0.38 inference(cnf_transformation,[],[f18])).
% 0.20/0.38 thf(f19,plain,(
% 0.20/0.38 (emptysetE = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))))),
% 0.20/0.38 inference(cnf_transformation,[],[f7])).
% 0.20/0.38 thf(f7,plain,(
% 0.20/0.38 (emptysetE = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))))),
% 0.20/0.38 inference(fool_elimination,[],[f6])).
% 0.20/0.38 thf(f6,plain,(
% 0.20/0.38 (emptysetE = ! [X0] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 0.20/0.38 inference(rectify,[],[f2])).
% 0.20/0.38 thf(f2,axiom,(
% 0.20/0.38 (emptysetE = ! [X2] : ((in @ X2 @ emptyset) => ! [X1 : $o] : X1))),
% 0.20/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE)).
% 0.20/0.38 thf(f23,plain,(
% 0.20/0.38 (emptysetE = $true)),
% 0.20/0.38 inference(cnf_transformation,[],[f18])).
% 0.20/0.38 % SZS output end Proof for theBenchmark
% 0.20/0.38 % (13990)------------------------------
% 0.20/0.38 % (13990)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (13990)Termination reason: Refutation
% 0.20/0.38
% 0.20/0.38 % (13990)Memory used [KB]: 5500
% 0.20/0.38 % (13990)Time elapsed: 0.009 s
% 0.20/0.38 % (13990)Instructions burned: 4 (million)
% 0.20/0.38 % (13990)------------------------------
% 0.20/0.38 % (13990)------------------------------
% 0.20/0.38 % (13985)Success in time 0.009 s
% 0.20/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------