TSTP Solution File: SEU619^2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU619^2 : 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 : n022.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 03:50:02 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU619^2 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.14 % 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
% 0.15/0.35 % Computer : n022.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun May 19 16:23:23 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 This is a TH0_THM_EQU_NAR problem
% 0.15/0.36 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
% 0.15/0.38 % (28321)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)
% 0.15/0.38 % (28316)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.38 % (28317)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)
% 0.15/0.38 % (28320)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)
% 0.15/0.38 % (28320)Instruction limit reached!
% 0.15/0.38 % (28320)------------------------------
% 0.15/0.38 % (28320)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (28323)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)
% 0.15/0.38 % (28320)Termination reason: Unknown
% 0.15/0.38 % (28320)Termination phase: Function definition elimination
% 0.15/0.38 % (28322)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.38
% 0.15/0.38 % (28320)Memory used [KB]: 895
% 0.15/0.38 % (28320)Time elapsed: 0.003 s
% 0.15/0.38 % (28320)Instructions burned: 3 (million)
% 0.15/0.38 % (28320)------------------------------
% 0.15/0.38 % (28320)------------------------------
% 0.15/0.38 % (28317)Instruction limit reached!
% 0.15/0.38 % (28317)------------------------------
% 0.15/0.38 % (28317)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (28317)Termination reason: Unknown
% 0.15/0.38 % (28317)Termination phase: Saturation
% 0.15/0.38
% 0.15/0.38 % (28323)Instruction limit reached!
% 0.15/0.38 % (28323)------------------------------
% 0.15/0.38 % (28323)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (28317)Memory used [KB]: 5500
% 0.15/0.38 % (28317)Time elapsed: 0.005 s
% 0.15/0.38 % (28317)Instructions burned: 5 (million)
% 0.15/0.38 % (28317)------------------------------
% 0.15/0.38 % (28317)------------------------------
% 0.15/0.38 % (28323)Termination reason: Unknown
% 0.15/0.38 % (28323)Termination phase: Saturation
% 0.15/0.38
% 0.15/0.38 % (28323)Memory used [KB]: 5500
% 0.15/0.38 % (28323)Time elapsed: 0.004 s
% 0.15/0.38 % (28323)Instructions burned: 3 (million)
% 0.15/0.38 % (28323)------------------------------
% 0.15/0.38 % (28323)------------------------------
% 0.15/0.38 % (28321)Refutation not found, incomplete strategy
% 0.15/0.38 % (28321)------------------------------
% 0.15/0.38 % (28321)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (28321)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.38
% 0.15/0.38
% 0.15/0.38 % (28321)Memory used [KB]: 5500
% 0.15/0.38 % (28321)Time elapsed: 0.006 s
% 0.15/0.38 % (28321)Instructions burned: 4 (million)
% 0.15/0.38 % (28321)------------------------------
% 0.15/0.38 % (28321)------------------------------
% 0.15/0.38 % (28318)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)
% 0.15/0.38 % (28316)First to succeed.
% 0.15/0.38 % (28322)Also succeeded, but the first one will report.
% 0.15/0.39 % (28316)Refutation found. Thanks to Tanya!
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39 % SZS output start Proof for theBenchmark
% 0.15/0.39 thf(func_def_0, type, in: $i > $i > $o).
% 0.15/0.39 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 0.15/0.39 thf(func_def_3, type, setunion: $i > $i).
% 0.15/0.39 thf(func_def_4, type, iskpair: $i > $o).
% 0.15/0.39 thf(f66,plain,(
% 0.15/0.39 $false),
% 0.15/0.39 inference(avatar_sat_refutation,[],[f53,f59,f65])).
% 0.15/0.39 thf(f65,plain,(
% 0.15/0.39 ~spl2_1),
% 0.15/0.39 inference(avatar_contradiction_clause,[],[f64])).
% 0.15/0.39 thf(f64,plain,(
% 0.15/0.39 $false | ~spl2_1),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f60])).
% 0.15/0.39 thf(f60,plain,(
% 0.15/0.39 ($false = $true) | ~spl2_1),
% 0.15/0.39 inference(superposition,[],[f48,f43])).
% 0.15/0.39 thf(f43,plain,(
% 0.15/0.39 ( ! [X2 : $i,X1 : $i] : (((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) = $true)) )),
% 0.15/0.39 inference(beta_eta_normalization,[],[f42])).
% 0.15/0.39 thf(f42,plain,(
% 0.15/0.39 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))) @ X2) = $true)) )),
% 0.15/0.39 inference(pi_clausification,[],[f41])).
% 0.15/0.39 thf(f41,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))) = $true)) )),
% 0.15/0.39 inference(beta_eta_normalization,[],[f40])).
% 0.15/0.39 thf(f40,plain,(
% 0.15/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))) @ X1) = $true)) )),
% 0.15/0.39 inference(pi_clausification,[],[f26])).
% 0.15/0.39 thf(f26,plain,(
% 0.15/0.39 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) = $true)),
% 0.15/0.39 inference(definition_unfolding,[],[f22,f19])).
% 0.15/0.39 thf(f19,plain,(
% 0.15/0.39 (setukpairIR = $true)),
% 0.15/0.39 inference(cnf_transformation,[],[f18])).
% 0.15/0.39 thf(f18,plain,(
% 0.15/0.39 ((iskpair @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) != $true) & (setukpairIL = $true) & (setukpairIR = $true)),
% 0.15/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f17])).
% 0.15/0.39 thf(f17,plain,(
% 0.15/0.39 ? [X0,X1] : ((iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) != $true) => ((iskpair @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) != $true)),
% 0.15/0.39 introduced(choice_axiom,[])).
% 0.15/0.39 thf(f16,plain,(
% 0.15/0.39 ? [X0,X1] : ((iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) != $true) & (setukpairIL = $true) & (setukpairIR = $true)),
% 0.15/0.39 inference(flattening,[],[f15])).
% 0.15/0.39 thf(f15,plain,(
% 0.15/0.39 (? [X0,X1] : ((iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) != $true) & (setukpairIR = $true)) & (setukpairIL = $true)),
% 0.15/0.39 inference(ennf_transformation,[],[f14])).
% 0.15/0.39 thf(f14,plain,(
% 0.15/0.39 ~((setukpairIL = $true) => ((setukpairIR = $true) => ! [X0,X1] : ((iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) = $true)))),
% 0.15/0.39 inference(fool_elimination,[],[f13])).
% 0.15/0.39 thf(f13,plain,(
% 0.15/0.39 ~(setukpairIL => (setukpairIR => ! [X0,X1] : (iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))))),
% 0.15/0.39 inference(rectify,[],[f5])).
% 0.15/0.39 thf(f5,negated_conjecture,(
% 0.15/0.39 ~(setukpairIL => (setukpairIR => ! [X2,X1] : (iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))))),
% 0.15/0.39 inference(negated_conjecture,[],[f4])).
% 0.15/0.39 thf(f4,conjecture,(
% 0.15/0.39 setukpairIL => (setukpairIR => ! [X2,X1] : (iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))))),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair)).
% 0.15/0.39 thf(f22,plain,(
% 0.15/0.39 (setukpairIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))))),
% 0.15/0.39 inference(cnf_transformation,[],[f10])).
% 0.15/0.39 thf(f10,plain,(
% 0.15/0.39 (setukpairIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))))),
% 0.15/0.39 inference(fool_elimination,[],[f9])).
% 0.15/0.39 thf(f9,plain,(
% 0.15/0.39 (setukpairIR = ! [X0,X1] : (in @ X0 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))))),
% 0.15/0.39 inference(rectify,[],[f3])).
% 0.15/0.39 thf(f3,axiom,(
% 0.15/0.39 (setukpairIR = ! [X2,X1] : (in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))))),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR)).
% 0.15/0.39 thf(f48,plain,(
% 0.15/0.39 ((in @ sK0 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) = $false) | ~spl2_1),
% 0.15/0.39 inference(avatar_component_clause,[],[f46])).
% 0.15/0.39 thf(f46,plain,(
% 0.15/0.39 spl2_1 <=> ((in @ sK0 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) = $false)),
% 0.15/0.39 introduced(avatar_definition,[new_symbols(naming,[spl2_1])])).
% 0.15/0.39 thf(f59,plain,(
% 0.15/0.39 ~spl2_2),
% 0.15/0.39 inference(avatar_contradiction_clause,[],[f58])).
% 0.15/0.39 thf(f58,plain,(
% 0.15/0.39 $false | ~spl2_2),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f55])).
% 0.15/0.39 thf(f55,plain,(
% 0.15/0.39 ($false = $true) | ~spl2_2),
% 0.15/0.39 inference(superposition,[],[f31,f52])).
% 0.15/0.39 thf(f52,plain,(
% 0.15/0.39 ((in @ sK1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) = $false) | ~spl2_2),
% 0.15/0.39 inference(avatar_component_clause,[],[f50])).
% 0.15/0.39 thf(f50,plain,(
% 0.15/0.39 spl2_2 <=> ((in @ sK1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) = $false)),
% 0.15/0.39 introduced(avatar_definition,[new_symbols(naming,[spl2_2])])).
% 0.15/0.39 thf(f31,plain,(
% 0.15/0.39 ( ! [X2 : $i,X1 : $i] : (((in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) = $true)) )),
% 0.15/0.39 inference(beta_eta_normalization,[],[f30])).
% 0.15/0.39 thf(f30,plain,(
% 0.15/0.39 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))) @ X2) = $true)) )),
% 0.15/0.39 inference(pi_clausification,[],[f29])).
% 0.15/0.39 thf(f29,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) )),
% 0.15/0.39 inference(beta_eta_normalization,[],[f28])).
% 0.15/0.39 thf(f28,plain,(
% 0.15/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))) @ X1) = $true)) )),
% 0.15/0.39 inference(pi_clausification,[],[f27])).
% 0.15/0.39 thf(f27,plain,(
% 0.15/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))))),
% 0.15/0.39 inference(definition_unfolding,[],[f24,f20])).
% 0.15/0.39 thf(f20,plain,(
% 0.15/0.39 (setukpairIL = $true)),
% 0.15/0.39 inference(cnf_transformation,[],[f18])).
% 0.15/0.39 thf(f24,plain,(
% 0.15/0.39 (setukpairIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))))),
% 0.15/0.39 inference(cnf_transformation,[],[f12])).
% 0.15/0.39 thf(f12,plain,(
% 0.15/0.39 (setukpairIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))))),
% 0.15/0.39 inference(fool_elimination,[],[f11])).
% 0.15/0.39 thf(f11,plain,(
% 0.15/0.39 (setukpairIL = ! [X0,X1] : (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))))),
% 0.15/0.39 inference(rectify,[],[f2])).
% 0.15/0.39 thf(f2,axiom,(
% 0.15/0.39 (setukpairIL = ! [X2,X1] : (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))))),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIL)).
% 0.15/0.39 thf(f53,plain,(
% 0.15/0.39 spl2_1 | spl2_2),
% 0.15/0.39 inference(avatar_split_clause,[],[f44,f50,f46])).
% 0.15/0.39 thf(f44,plain,(
% 0.15/0.39 ((in @ sK1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) = $false) | ((in @ sK0 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) = $false)),
% 0.15/0.39 inference(equality_resolution,[],[f39])).
% 0.15/0.39 thf(f39,plain,(
% 0.15/0.39 ( ! [X2 : $i,X1 : $i] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) | ($false = (in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))) | ($false = (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))))) )),
% 0.15/0.39 inference(equality_proxy_clausification,[],[f38])).
% 0.15/0.39 thf(f38,plain,(
% 0.15/0.39 ( ! [X2 : $i,X1 : $i] : (($false = ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) | ($false = (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))) | ($false = (in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))))) )),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f37])).
% 0.15/0.39 thf(f37,plain,(
% 0.15/0.39 ( ! [X2 : $i,X1 : $i] : (($false = (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))) | ((((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) & (in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))) = $false)) )),
% 0.15/0.39 inference(beta_eta_normalization,[],[f36])).
% 0.15/0.39 thf(f36,plain,(
% 0.15/0.39 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) & (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))))) @ X2) = $false) | ($false = (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))))) )),
% 0.15/0.39 inference(pi_clausification,[],[f35])).
% 0.15/0.39 thf(f35,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (($false = (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))) | ($false = (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) & (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))))))) )),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f34])).
% 0.15/0.39 thf(f34,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (($false = ((?? @ $i @ (^[Y0 : $i]: (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) & (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))))) & (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))))) )),
% 0.15/0.39 inference(beta_eta_normalization,[],[f33])).
% 0.15/0.39 thf(f33,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) & (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))))) & (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))))) @ X1))) )),
% 0.15/0.39 inference(pi_clausification,[],[f32])).
% 0.15/0.39 thf(f32,plain,(
% 0.15/0.39 ((?? @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) & (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))))) & (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))))) != $true)),
% 0.15/0.39 inference(beta_eta_normalization,[],[f25])).
% 0.15/0.39 thf(f25,plain,(
% 0.15/0.39 (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ (setunion @ Y0))))) & (in @ Y1 @ (setunion @ Y0)))))) @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) != $true)),
% 0.15/0.39 inference(definition_unfolding,[],[f21,f23])).
% 0.15/0.39 thf(f23,plain,(
% 0.15/0.39 (iskpair = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ (setunion @ Y0))))) & (in @ Y1 @ (setunion @ Y0)))))))),
% 0.15/0.39 inference(cnf_transformation,[],[f8])).
% 0.15/0.39 thf(f8,plain,(
% 0.15/0.39 (iskpair = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ (setunion @ Y0))))) & (in @ Y1 @ (setunion @ Y0)))))))),
% 0.15/0.39 inference(fool_elimination,[],[f7])).
% 0.15/0.39 thf(f7,plain,(
% 0.15/0.39 (iskpair = (^[X0 : $i] : (? [X1] : ((in @ X1 @ (setunion @ X0)) & ? [X2] : ((in @ X2 @ (setunion @ X0)) & ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = X0))))))),
% 0.15/0.39 inference(rectify,[],[f1])).
% 0.15/0.39 thf(f1,axiom,(
% 0.15/0.39 (iskpair = (^[X0 : $i] : (? [X1] : ((in @ X1 @ (setunion @ X0)) & ? [X2] : ((in @ X2 @ (setunion @ X0)) & ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = X0))))))),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',iskpair)).
% 0.15/0.39 thf(f21,plain,(
% 0.15/0.39 ((iskpair @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) != $true)),
% 0.15/0.39 inference(cnf_transformation,[],[f18])).
% 0.15/0.39 % SZS output end Proof for theBenchmark
% 0.15/0.39 % (28316)------------------------------
% 0.15/0.39 % (28316)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (28316)Termination reason: Refutation
% 0.15/0.39
% 0.15/0.39 % (28316)Memory used [KB]: 5628
% 0.15/0.39 % (28316)Time elapsed: 0.010 s
% 0.15/0.39 % (28316)Instructions burned: 8 (million)
% 0.15/0.39 % (28316)------------------------------
% 0.15/0.39 % (28316)------------------------------
% 0.15/0.39 % (28315)Success in time 0.013 s
% 0.15/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------