TSTP Solution File: SEU527^2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU527^2 : 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 : n009.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 03:49:22 EDT 2024
% Result : Theorem 0.14s 0.40s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU527^2 : TPTP v8.2.0. Released v3.7.0.
% 0.14/0.14 % 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
% 0.14/0.37 % Computer : n009.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Sun May 19 16:58:53 EDT 2024
% 0.14/0.37 % CPUTime :
% 0.14/0.37 This is a TH0_THM_EQU_NAR problem
% 0.14/0.37 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
% 0.14/0.39 % (14264)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 (3000ds/27Mi)
% 0.14/0.39 % (14262)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.14/0.39 % (14266)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 (3000ds/2Mi)
% 0.14/0.39 % (14265)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.14/0.39 % (14263)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 (3000ds/4Mi)
% 0.14/0.39 % (14267)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 (3000ds/275Mi)
% 0.14/0.39 % (14268)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.14/0.39 % (14269)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (3000ds/3Mi)
% 0.14/0.39 % (14266)Instruction limit reached!
% 0.14/0.39 % (14266)------------------------------
% 0.14/0.39 % (14266)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (14266)Termination reason: Unknown
% 0.14/0.39 % (14266)Termination phase: Property scanning
% 0.14/0.39
% 0.14/0.39 % (14266)Memory used [KB]: 895
% 0.14/0.39 % (14266)Time elapsed: 0.003 s
% 0.14/0.39 % (14266)Instructions burned: 2 (million)
% 0.14/0.39 % (14266)------------------------------
% 0.14/0.39 % (14266)------------------------------
% 0.14/0.39 % (14265)Instruction limit reached!
% 0.14/0.39 % (14265)------------------------------
% 0.14/0.39 % (14265)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (14265)Termination reason: Unknown
% 0.14/0.39 % (14265)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (14265)Memory used [KB]: 5500
% 0.14/0.39 % (14265)Time elapsed: 0.004 s
% 0.14/0.39 % (14265)Instructions burned: 3 (million)
% 0.14/0.39 % (14265)------------------------------
% 0.14/0.39 % (14265)------------------------------
% 0.14/0.39 % (14269)Instruction limit reached!
% 0.14/0.39 % (14269)------------------------------
% 0.14/0.39 % (14269)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (14269)Termination reason: Unknown
% 0.14/0.39 % (14269)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (14269)Memory used [KB]: 5500
% 0.14/0.39 % (14269)Time elapsed: 0.004 s
% 0.14/0.39 % (14269)Instructions burned: 3 (million)
% 0.14/0.39 % (14269)------------------------------
% 0.14/0.39 % (14269)------------------------------
% 0.14/0.39 % (14267)Refutation not found, incomplete strategy
% 0.14/0.39 % (14267)------------------------------
% 0.14/0.39 % (14267)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (14263)Instruction limit reached!
% 0.14/0.39 % (14263)------------------------------
% 0.14/0.39 % (14263)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (14263)Termination reason: Unknown
% 0.14/0.39 % (14263)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (14263)Memory used [KB]: 5500
% 0.14/0.39 % (14263)Time elapsed: 0.004 s
% 0.14/0.39 % (14263)Instructions burned: 4 (million)
% 0.14/0.39 % (14263)------------------------------
% 0.14/0.39 % (14263)------------------------------
% 0.14/0.39 % (14267)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.39
% 0.14/0.39
% 0.14/0.39 % (14267)Memory used [KB]: 5500
% 0.14/0.39 % (14267)Time elapsed: 0.004 s
% 0.14/0.39 % (14267)Instructions burned: 3 (million)
% 0.14/0.39 % (14267)------------------------------
% 0.14/0.39 % (14267)------------------------------
% 0.14/0.40 % (14268)First to succeed.
% 0.14/0.40 % (14264)Also succeeded, but the first one will report.
% 0.14/0.40 % (14268)Refutation found. Thanks to Tanya!
% 0.14/0.40 % SZS status Theorem for theBenchmark
% 0.14/0.40 % SZS output start Proof for theBenchmark
% 0.14/0.40 thf(func_def_0, type, in: $i > $i > $o).
% 0.14/0.40 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 0.14/0.40 thf(f81,plain,(
% 0.14/0.40 $false),
% 0.14/0.40 inference(avatar_sat_refutation,[],[f68,f73,f80])).
% 0.14/0.40 thf(f80,plain,(
% 0.14/0.40 ~spl8_1),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f79])).
% 0.14/0.40 thf(f79,plain,(
% 0.14/0.40 $false | ~spl8_1),
% 0.14/0.40 inference(equality_resolution,[],[f76])).
% 0.14/0.40 thf(f76,plain,(
% 0.14/0.40 ( ! [X0 : $o] : (($false != X0)) ) | ~spl8_1),
% 0.14/0.40 inference(superposition,[],[f5,f64])).
% 0.14/0.40 thf(f64,plain,(
% 0.14/0.40 ( ! [X3 : $o] : (($true = X3)) ) | ~spl8_1),
% 0.14/0.40 inference(avatar_component_clause,[],[f63])).
% 0.14/0.40 thf(f63,plain,(
% 0.14/0.40 spl8_1 <=> ! [X3 : $o] : ($true = X3)),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl8_1])])).
% 0.14/0.40 thf(f5,plain,(
% 0.14/0.40 ($true != $false)),
% 0.14/0.40 introduced(fool_axiom,[])).
% 0.14/0.40 thf(f73,plain,(
% 0.14/0.40 ~spl8_2),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f72])).
% 0.14/0.40 thf(f72,plain,(
% 0.14/0.40 $false | ~spl8_2),
% 0.14/0.40 inference(subsumption_resolution,[],[f71,f41])).
% 0.14/0.40 thf(f41,plain,(
% 0.14/0.40 (sK7 != sK6)),
% 0.14/0.40 inference(cnf_transformation,[],[f28])).
% 0.14/0.40 thf(f28,plain,(
% 0.14/0.40 (setadjoinE = $true) & (emptysetE = $true) & ((sK7 != sK6) & ($true = (in @ sK6 @ (setadjoin @ sK7 @ emptyset))))),
% 0.14/0.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f13,f27])).
% 0.14/0.40 thf(f27,plain,(
% 0.14/0.40 ? [X0,X1] : ((X0 != X1) & ((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true)) => ((sK7 != sK6) & ($true = (in @ sK6 @ (setadjoin @ sK7 @ emptyset))))),
% 0.14/0.40 introduced(choice_axiom,[])).
% 0.14/0.40 thf(f13,plain,(
% 0.14/0.40 (setadjoinE = $true) & (emptysetE = $true) & ? [X0,X1] : ((X0 != X1) & ((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true))),
% 0.14/0.40 inference(flattening,[],[f12])).
% 0.14/0.40 thf(f12,plain,(
% 0.14/0.40 (? [X0,X1] : ((X0 != X1) & ((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true)) & (setadjoinE = $true)) & (emptysetE = $true)),
% 0.14/0.40 inference(ennf_transformation,[],[f11])).
% 0.14/0.40 thf(f11,plain,(
% 0.14/0.40 ~((emptysetE = $true) => ((setadjoinE = $true) => ! [X0,X1] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true) => (X0 = X1))))),
% 0.14/0.40 inference(fool_elimination,[],[f10])).
% 0.14/0.40 thf(f10,plain,(
% 0.14/0.40 ~(emptysetE => (setadjoinE => ! [X0,X1] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1))))),
% 0.14/0.40 inference(rectify,[],[f4])).
% 0.14/0.40 thf(f4,negated_conjecture,(
% 0.14/0.40 ~(emptysetE => (setadjoinE => ! [X0,X3] : ((in @ X0 @ (setadjoin @ X3 @ emptyset)) => (X0 = X3))))),
% 0.14/0.40 inference(negated_conjecture,[],[f3])).
% 0.14/0.40 thf(f3,conjecture,(
% 0.14/0.40 emptysetE => (setadjoinE => ! [X0,X3] : ((in @ X0 @ (setadjoin @ X3 @ emptyset)) => (X0 = X3)))),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit)).
% 0.14/0.40 thf(f71,plain,(
% 0.14/0.40 (sK7 = sK6) | ~spl8_2),
% 0.14/0.40 inference(subsumption_resolution,[],[f70,f67])).
% 0.14/0.40 thf(f67,plain,(
% 0.14/0.40 ( ! [X2 : $i] : (($true != (in @ X2 @ emptyset))) ) | ~spl8_2),
% 0.14/0.40 inference(avatar_component_clause,[],[f66])).
% 0.14/0.40 thf(f66,plain,(
% 0.14/0.40 spl8_2 <=> ! [X2] : ($true != (in @ X2 @ emptyset))),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl8_2])])).
% 0.14/0.40 thf(f70,plain,(
% 0.14/0.40 (sK7 = sK6) | ($true = (in @ sK6 @ emptyset))),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f69])).
% 0.14/0.40 thf(f69,plain,(
% 0.14/0.40 ($true != $true) | ($true = (in @ sK6 @ emptyset)) | (sK7 = sK6)),
% 0.14/0.40 inference(superposition,[],[f59,f40])).
% 0.14/0.40 thf(f40,plain,(
% 0.14/0.40 ($true = (in @ sK6 @ (setadjoin @ sK7 @ emptyset)))),
% 0.14/0.40 inference(cnf_transformation,[],[f28])).
% 0.14/0.40 thf(f59,plain,(
% 0.14/0.40 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (setadjoin @ X2 @ X1))) | ($true = (in @ X0 @ X1)) | (X0 = X2)) )),
% 0.14/0.40 inference(condensation,[],[f58])).
% 0.14/0.40 thf(f58,plain,(
% 0.14/0.40 ( ! [X6 : $i,X7 : $o,X4 : $i,X5 : $i] : ((X4 = X6) | ($true = X7) | ((in @ X6 @ (setadjoin @ X4 @ X5)) != $true) | ($true = (in @ X6 @ X5))) )),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f49])).
% 0.14/0.40 thf(f49,plain,(
% 0.14/0.40 ( ! [X6 : $i,X7 : $o,X4 : $i,X5 : $i] : (((in @ X6 @ (setadjoin @ X4 @ X5)) != $true) | ($true = (in @ X6 @ X5)) | ($true = X7) | ($true != $true) | (X4 = X6)) )),
% 0.14/0.40 inference(definition_unfolding,[],[f31,f43])).
% 0.14/0.40 thf(f43,plain,(
% 0.14/0.40 (setadjoinE = $true)),
% 0.14/0.40 inference(cnf_transformation,[],[f28])).
% 0.14/0.40 thf(f31,plain,(
% 0.14/0.40 ( ! [X6 : $i,X7 : $o,X4 : $i,X5 : $i] : (($true = X7) | ($true = (in @ X6 @ X5)) | (X4 = X6) | ((in @ X6 @ (setadjoin @ X4 @ X5)) != $true) | (setadjoinE != $true)) )),
% 0.14/0.40 inference(cnf_transformation,[],[f21])).
% 0.14/0.40 thf(f21,plain,(
% 0.14/0.40 ((setadjoinE = $true) | (((sK3 != $true) & (($true != (in @ sK2 @ sK1)) | (sK3 = $true)) & ((sK3 = $true) | (sK0 != sK2))) & ((in @ sK2 @ (setadjoin @ sK0 @ sK1)) = $true))) & (! [X4,X5,X6] : (! [X7 : $o] : (($true = X7) | (($true = (in @ X6 @ X5)) & ($true != X7)) | (($true != X7) & (X4 = X6))) | ((in @ X6 @ (setadjoin @ X4 @ X5)) != $true)) | (setadjoinE != $true))),
% 0.14/0.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f18,f20,f19])).
% 0.14/0.40 thf(f19,plain,(
% 0.14/0.40 ? [X0,X1,X2] : (? [X3 : $o] : (($true != X3) & (((in @ X2 @ X1) != $true) | ($true = X3)) & (($true = X3) | (X0 != X2))) & ($true = (in @ X2 @ (setadjoin @ X0 @ X1)))) => (? [X3 : $o] : (($true != X3) & (($true != (in @ sK2 @ sK1)) | ($true = X3)) & (($true = X3) | (sK0 != sK2))) & ((in @ sK2 @ (setadjoin @ sK0 @ sK1)) = $true))),
% 0.14/0.40 introduced(choice_axiom,[])).
% 0.14/0.40 thf(f20,plain,(
% 0.14/0.40 ? [X3 : $o] : (($true != X3) & (($true != (in @ sK2 @ sK1)) | ($true = X3)) & (($true = X3) | (sK0 != sK2))) => ((sK3 != $true) & (($true != (in @ sK2 @ sK1)) | (sK3 = $true)) & ((sK3 = $true) | (sK0 != sK2)))),
% 0.14/0.40 introduced(choice_axiom,[])).
% 0.14/0.40 thf(f18,plain,(
% 0.14/0.40 ((setadjoinE = $true) | ? [X0,X1,X2] : (? [X3 : $o] : (($true != X3) & (((in @ X2 @ X1) != $true) | ($true = X3)) & (($true = X3) | (X0 != X2))) & ($true = (in @ X2 @ (setadjoin @ X0 @ X1))))) & (! [X4,X5,X6] : (! [X7 : $o] : (($true = X7) | (($true = (in @ X6 @ X5)) & ($true != X7)) | (($true != X7) & (X4 = X6))) | ((in @ X6 @ (setadjoin @ X4 @ X5)) != $true)) | (setadjoinE != $true))),
% 0.14/0.40 inference(rectify,[],[f17])).
% 0.14/0.40 thf(f17,plain,(
% 0.14/0.40 ((setadjoinE = $true) | ? [X1,X0,X2] : (? [X3 : $o] : (($true != X3) & (($true != (in @ X2 @ X0)) | ($true = X3)) & (($true = X3) | (X1 != X2))) & ((in @ X2 @ (setadjoin @ X1 @ X0)) = $true))) & (! [X1,X0,X2] : (! [X3 : $o] : (($true = X3) | (($true = (in @ X2 @ X0)) & ($true != X3)) | (($true != X3) & (X1 = X2))) | ((in @ X2 @ (setadjoin @ X1 @ X0)) != $true)) | (setadjoinE != $true))),
% 0.14/0.40 inference(nnf_transformation,[],[f15])).
% 0.14/0.40 thf(f15,plain,(
% 0.14/0.40 (setadjoinE = $true) <=> ! [X1,X0,X2] : (! [X3 : $o] : (($true = X3) | (($true = (in @ X2 @ X0)) & ($true != X3)) | (($true != X3) & (X1 = X2))) | ((in @ X2 @ (setadjoin @ X1 @ X0)) != $true))),
% 0.14/0.40 inference(flattening,[],[f14])).
% 0.14/0.40 thf(f14,plain,(
% 0.14/0.40 ! [X0,X2,X1] : (! [X3 : $o] : ((($true = X3) | (($true = (in @ X2 @ X0)) & ($true != X3))) | (($true != X3) & (X1 = X2))) | ((in @ X2 @ (setadjoin @ X1 @ X0)) != $true)) <=> (setadjoinE = $true)),
% 0.14/0.40 inference(ennf_transformation,[],[f9])).
% 0.14/0.40 thf(f9,plain,(
% 0.14/0.40 ! [X0,X2,X1] : (((in @ X2 @ (setadjoin @ X1 @ X0)) = $true) => ! [X3 : $o] : (((X1 = X2) => ($true = X3)) => ((($true = (in @ X2 @ X0)) => ($true = X3)) => ($true = X3)))) <=> (setadjoinE = $true)),
% 0.14/0.40 inference(fool_elimination,[],[f8])).
% 0.14/0.40 thf(f8,plain,(
% 0.14/0.40 (! [X0,X1,X2] : ((in @ X2 @ (setadjoin @ X1 @ X0)) => ! [X3 : $o] : (((X1 = X2) => X3) => (((in @ X2 @ X0) => X3) => X3))) = setadjoinE)),
% 0.14/0.40 inference(rectify,[],[f2])).
% 0.14/0.40 thf(f2,axiom,(
% 0.14/0.40 (! [X2,X0,X3] : ((in @ X3 @ (setadjoin @ X0 @ X2)) => ! [X1 : $o] : (((X0 = X3) => X1) => (((in @ X3 @ X2) => X1) => X1))) = setadjoinE)),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE)).
% 0.14/0.40 thf(f68,plain,(
% 0.14/0.40 spl8_1 | spl8_2),
% 0.14/0.40 inference(avatar_split_clause,[],[f60,f66,f63])).
% 0.14/0.40 thf(f60,plain,(
% 0.14/0.40 ( ! [X2 : $i,X3 : $o] : (($true = X3) | ($true != (in @ X2 @ emptyset))) )),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f54])).
% 0.14/0.40 thf(f54,plain,(
% 0.14/0.40 ( ! [X2 : $i,X3 : $o] : (($true = X3) | ($true != (in @ X2 @ emptyset)) | ($true != $true)) )),
% 0.14/0.40 inference(definition_unfolding,[],[f37,f42])).
% 0.14/0.40 thf(f42,plain,(
% 0.14/0.40 (emptysetE = $true)),
% 0.14/0.40 inference(cnf_transformation,[],[f28])).
% 0.14/0.40 thf(f37,plain,(
% 0.14/0.40 ( ! [X2 : $i,X3 : $o] : (($true = X3) | ($true != (in @ X2 @ emptyset)) | (emptysetE != $true)) )),
% 0.14/0.40 inference(cnf_transformation,[],[f26])).
% 0.14/0.40 thf(f26,plain,(
% 0.14/0.40 ((emptysetE = $true) | ((sK5 != $true) & ($true = (in @ sK4 @ emptyset)))) & (! [X2] : (! [X3 : $o] : ($true = X3) | ($true != (in @ X2 @ emptyset))) | (emptysetE != $true))),
% 0.14/0.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f23,f25,f24])).
% 0.14/0.40 thf(f24,plain,(
% 0.14/0.40 ? [X0] : (? [X1 : $o] : ($true != X1) & ((in @ X0 @ emptyset) = $true)) => (? [X1 : $o] : ($true != X1) & ($true = (in @ sK4 @ emptyset)))),
% 0.14/0.40 introduced(choice_axiom,[])).
% 0.14/0.40 thf(f25,plain,(
% 0.14/0.40 ? [X1 : $o] : ($true != X1) => (sK5 != $true)),
% 0.14/0.40 introduced(choice_axiom,[])).
% 0.14/0.40 thf(f23,plain,(
% 0.14/0.40 ((emptysetE = $true) | ? [X0] : (? [X1 : $o] : ($true != X1) & ((in @ X0 @ emptyset) = $true))) & (! [X2] : (! [X3 : $o] : ($true = X3) | ($true != (in @ X2 @ emptyset))) | (emptysetE != $true))),
% 0.14/0.40 inference(rectify,[],[f22])).
% 0.14/0.40 thf(f22,plain,(
% 0.14/0.40 ((emptysetE = $true) | ? [X0] : (? [X1 : $o] : ($true != X1) & ((in @ X0 @ emptyset) = $true))) & (! [X0] : (! [X1 : $o] : ($true = X1) | ((in @ X0 @ emptyset) != $true)) | (emptysetE != $true))),
% 0.14/0.40 inference(nnf_transformation,[],[f16])).
% 0.14/0.40 thf(f16,plain,(
% 0.14/0.40 (emptysetE = $true) <=> ! [X0] : (! [X1 : $o] : ($true = X1) | ((in @ X0 @ emptyset) != $true))),
% 0.14/0.40 inference(ennf_transformation,[],[f7])).
% 0.14/0.40 thf(f7,plain,(
% 0.14/0.40 ! [X0] : (((in @ X0 @ emptyset) = $true) => ! [X1 : $o] : ($true = X1)) <=> (emptysetE = $true)),
% 0.14/0.40 inference(fool_elimination,[],[f6])).
% 0.14/0.40 thf(f6,plain,(
% 0.14/0.40 (emptysetE = ! [X0] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 0.14/0.40 inference(rectify,[],[f1])).
% 0.14/0.40 thf(f1,axiom,(
% 0.14/0.40 (emptysetE = ! [X0] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE)).
% 0.14/0.40 % SZS output end Proof for theBenchmark
% 0.14/0.40 % (14268)------------------------------
% 0.14/0.40 % (14268)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (14268)Termination reason: Refutation
% 0.14/0.40
% 0.14/0.40 % (14268)Memory used [KB]: 5500
% 0.14/0.40 % (14268)Time elapsed: 0.007 s
% 0.14/0.40 % (14268)Instructions burned: 4 (million)
% 0.14/0.40 % (14268)------------------------------
% 0.14/0.40 % (14268)------------------------------
% 0.14/0.40 % (14261)Success in time 0.006 s
% 0.14/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------