TSTP Solution File: SEU626^2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU626^2 : 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 : n021.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 03:50:06 EDT 2024
% Result : Theorem 0.21s 0.38s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU626^2 : 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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun May 19 17:37:53 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 This is a TH0_THM_EQU_NAR problem
% 0.13/0.35 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
% 0.21/0.37 % (16649)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)
% 0.21/0.37 % (16646)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)
% 0.21/0.37 % (16645)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.21/0.37 % (16653)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)
% 0.21/0.38 % (16648)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.38 % (16649)Instruction limit reached!
% 0.21/0.38 % (16649)------------------------------
% 0.21/0.38 % (16649)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (16649)Termination reason: Unknown
% 0.21/0.38 % (16649)Termination phase: Saturation
% 0.21/0.38
% 0.21/0.38 % (16649)Memory used [KB]: 895
% 0.21/0.38 % (16649)Time elapsed: 0.004 s
% 0.21/0.38 % (16649)Instructions burned: 3 (million)
% 0.21/0.38 % (16649)------------------------------
% 0.21/0.38 % (16649)------------------------------
% 0.21/0.38 % (16653)Instruction limit reached!
% 0.21/0.38 % (16653)------------------------------
% 0.21/0.38 % (16653)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (16653)Termination reason: Unknown
% 0.21/0.38 % (16653)Termination phase: Saturation
% 0.21/0.38
% 0.21/0.38 % (16653)Memory used [KB]: 5500
% 0.21/0.38 % (16653)Time elapsed: 0.004 s
% 0.21/0.38 % (16653)Instructions burned: 3 (million)
% 0.21/0.38 % (16653)------------------------------
% 0.21/0.38 % (16653)------------------------------
% 0.21/0.38 % (16647)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)
% 0.21/0.38 % (16648)Instruction limit reached!
% 0.21/0.38 % (16648)------------------------------
% 0.21/0.38 % (16648)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (16648)Termination reason: Unknown
% 0.21/0.38 % (16648)Termination phase: Preprocessing 3
% 0.21/0.38
% 0.21/0.38 % (16648)Memory used [KB]: 895
% 0.21/0.38 % (16648)Time elapsed: 0.004 s
% 0.21/0.38 % (16648)Instructions burned: 2 (million)
% 0.21/0.38 % (16648)------------------------------
% 0.21/0.38 % (16648)------------------------------
% 0.21/0.38 % (16651)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)
% 0.21/0.38 % (16652)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.38 % (16646)Instruction limit reached!
% 0.21/0.38 % (16646)------------------------------
% 0.21/0.38 % (16646)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (16646)Termination reason: Unknown
% 0.21/0.38 % (16646)Termination phase: Saturation
% 0.21/0.38
% 0.21/0.38 % (16646)Memory used [KB]: 5500
% 0.21/0.38 % (16646)Time elapsed: 0.006 s
% 0.21/0.38 % (16646)Instructions burned: 5 (million)
% 0.21/0.38 % (16646)------------------------------
% 0.21/0.38 % (16646)------------------------------
% 0.21/0.38 % (16645)First to succeed.
% 0.21/0.38 % (16651)Also succeeded, but the first one will report.
% 0.21/0.38 % (16645)Refutation found. Thanks to Tanya!
% 0.21/0.38 % SZS status Theorem for theBenchmark
% 0.21/0.38 % SZS output start Proof for theBenchmark
% 0.21/0.38 thf(func_def_0, type, in: $i > $i > $o).
% 0.21/0.38 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 0.21/0.38 thf(func_def_3, type, powerset: $i > $i).
% 0.21/0.38 thf(func_def_4, type, subset: $i > $i > $o).
% 0.21/0.38 thf(func_def_7, type, binunion: $i > $i > $i).
% 0.21/0.38 thf(f69,plain,(
% 0.21/0.38 $false),
% 0.21/0.38 inference(avatar_sat_refutation,[],[f56,f62,f68])).
% 0.21/0.38 thf(f68,plain,(
% 0.21/0.38 ~spl4_1),
% 0.21/0.38 inference(avatar_contradiction_clause,[],[f67])).
% 0.21/0.38 thf(f67,plain,(
% 0.21/0.38 $false | ~spl4_1),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f63])).
% 0.21/0.38 thf(f63,plain,(
% 0.21/0.38 ($false = $true) | ~spl4_1),
% 0.21/0.38 inference(superposition,[],[f50,f17])).
% 0.21/0.38 thf(f17,plain,(
% 0.21/0.38 ((in @ sK3 @ sK2) = $true)),
% 0.21/0.38 inference(cnf_transformation,[],[f16])).
% 0.21/0.38 thf(f16,plain,(
% 0.21/0.38 (powersetI1 = $true) & (upairsubunion = $true) & (((in @ sK1 @ sK0) = $true) & (((in @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK2))) != $true) & ((in @ sK3 @ sK2) = $true)))),
% 0.21/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f13,f15,f14])).
% 0.21/0.38 thf(f14,plain,(
% 0.21/0.38 ? [X0,X1,X2] : (((in @ X1 @ X0) = $true) & ? [X3] : (((in @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X0 @ X2))) != $true) & ((in @ X3 @ X2) = $true))) => (((in @ sK1 @ sK0) = $true) & ? [X3] : (($true != (in @ (setadjoin @ sK1 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK2)))) & ((in @ X3 @ sK2) = $true)))),
% 0.21/0.38 introduced(choice_axiom,[])).
% 0.21/0.38 thf(f15,plain,(
% 0.21/0.38 ? [X3] : (($true != (in @ (setadjoin @ sK1 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK2)))) & ((in @ X3 @ sK2) = $true)) => (((in @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK2))) != $true) & ((in @ sK3 @ sK2) = $true))),
% 0.21/0.38 introduced(choice_axiom,[])).
% 0.21/0.38 thf(f13,plain,(
% 0.21/0.38 (powersetI1 = $true) & (upairsubunion = $true) & ? [X0,X1,X2] : (((in @ X1 @ X0) = $true) & ? [X3] : (((in @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X0 @ X2))) != $true) & ((in @ X3 @ X2) = $true)))),
% 0.21/0.38 inference(flattening,[],[f12])).
% 0.21/0.38 thf(f12,plain,(
% 0.21/0.38 (? [X0,X1,X2] : (((in @ X1 @ X0) = $true) & ? [X3] : (((in @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X0 @ X2))) != $true) & ((in @ X3 @ X2) = $true))) & (upairsubunion = $true)) & (powersetI1 = $true)),
% 0.21/0.38 inference(ennf_transformation,[],[f7])).
% 0.21/0.38 thf(f7,plain,(
% 0.21/0.38 ~((powersetI1 = $true) => ((upairsubunion = $true) => ! [X0,X1,X2] : (((in @ X1 @ X0) = $true) => ! [X3] : (((in @ X3 @ X2) = $true) => ((in @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X0 @ X2))) = $true)))))),
% 0.21/0.38 inference(fool_elimination,[],[f6])).
% 0.21/0.38 thf(f6,plain,(
% 0.21/0.38 ~(powersetI1 => (upairsubunion => ! [X0,X1,X2] : ((in @ X1 @ X0) => ! [X3] : ((in @ X3 @ X2) => (in @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X0 @ X2)))))))),
% 0.21/0.38 inference(rectify,[],[f4])).
% 0.21/0.38 thf(f4,negated_conjecture,(
% 0.21/0.38 ~(powersetI1 => (upairsubunion => ! [X0,X2,X1] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X1) => (in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X0 @ X1)))))))),
% 0.21/0.38 inference(negated_conjecture,[],[f3])).
% 0.21/0.38 thf(f3,conjecture,(
% 0.21/0.38 powersetI1 => (upairsubunion => ! [X0,X2,X1] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X1) => (in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X0 @ X1))))))),
% 0.21/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairinpowunion)).
% 0.21/0.38 thf(f50,plain,(
% 0.21/0.38 ($false = (in @ sK3 @ sK2)) | ~spl4_1),
% 0.21/0.38 inference(avatar_component_clause,[],[f48])).
% 0.21/0.38 thf(f48,plain,(
% 0.21/0.38 spl4_1 <=> ($false = (in @ sK3 @ sK2))),
% 0.21/0.38 introduced(avatar_definition,[new_symbols(naming,[spl4_1])])).
% 0.21/0.38 thf(f62,plain,(
% 0.21/0.38 ~spl4_2),
% 0.21/0.38 inference(avatar_contradiction_clause,[],[f61])).
% 0.21/0.38 thf(f61,plain,(
% 0.21/0.38 $false | ~spl4_2),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f58])).
% 0.21/0.38 thf(f58,plain,(
% 0.21/0.38 ($false = $true) | ~spl4_2),
% 0.21/0.38 inference(superposition,[],[f19,f54])).
% 0.21/0.38 thf(f54,plain,(
% 0.21/0.38 ((in @ sK1 @ sK0) = $false) | ~spl4_2),
% 0.21/0.38 inference(avatar_component_clause,[],[f52])).
% 0.21/0.38 thf(f52,plain,(
% 0.21/0.38 spl4_2 <=> ((in @ sK1 @ sK0) = $false)),
% 0.21/0.38 introduced(avatar_definition,[new_symbols(naming,[spl4_2])])).
% 0.21/0.38 thf(f19,plain,(
% 0.21/0.38 ((in @ sK1 @ sK0) = $true)),
% 0.21/0.38 inference(cnf_transformation,[],[f16])).
% 0.21/0.38 thf(f56,plain,(
% 0.21/0.38 spl4_2 | spl4_1),
% 0.21/0.38 inference(avatar_split_clause,[],[f45,f48,f52])).
% 0.21/0.38 thf(f45,plain,(
% 0.21/0.38 ((in @ sK1 @ sK0) = $false) | ($false = (in @ sK3 @ sK2))),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f43])).
% 0.21/0.38 thf(f43,plain,(
% 0.21/0.38 ($false = $true) | ($false = (in @ sK3 @ sK2)) | ((in @ sK1 @ sK0) = $false)),
% 0.21/0.38 inference(superposition,[],[f40,f42])).
% 0.21/0.38 thf(f42,plain,(
% 0.21/0.38 ((subset @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ (binunion @ sK0 @ sK2)) = $false)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f41])).
% 0.21/0.38 thf(f41,plain,(
% 0.21/0.38 ((subset @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ (binunion @ sK0 @ sK2)) = $false) | ($true != $true)),
% 0.21/0.38 inference(superposition,[],[f18,f30])).
% 0.21/0.38 thf(f30,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : (($true = (in @ X2 @ (powerset @ X1))) | ((subset @ X2 @ X1) = $false)) )),
% 0.21/0.38 inference(binary_proxy_clausification,[],[f29])).
% 0.21/0.38 thf(f29,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : ((((subset @ X2 @ X1) => (in @ X2 @ (powerset @ X1))) = $true)) )),
% 0.21/0.38 inference(beta_eta_normalization,[],[f28])).
% 0.21/0.38 thf(f28,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((subset @ Y0 @ X1) => (in @ Y0 @ (powerset @ X1)))) @ X2) = $true)) )),
% 0.21/0.38 inference(pi_clausification,[],[f27])).
% 0.21/0.38 thf(f27,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ X1) => (in @ Y0 @ (powerset @ X1))))) = $true)) )),
% 0.21/0.38 inference(beta_eta_normalization,[],[f26])).
% 0.21/0.38 thf(f26,plain,(
% 0.21/0.38 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0)))))) @ X1) = $true)) )),
% 0.21/0.38 inference(pi_clausification,[],[f24])).
% 0.21/0.38 thf(f24,plain,(
% 0.21/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))))),
% 0.21/0.38 inference(definition_unfolding,[],[f22,f21])).
% 0.21/0.38 thf(f21,plain,(
% 0.21/0.38 (powersetI1 = $true)),
% 0.21/0.38 inference(cnf_transformation,[],[f16])).
% 0.21/0.38 thf(f22,plain,(
% 0.21/0.38 (powersetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))))),
% 0.21/0.38 inference(cnf_transformation,[],[f9])).
% 0.21/0.38 thf(f9,plain,(
% 0.21/0.38 (powersetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))))),
% 0.21/0.38 inference(fool_elimination,[],[f8])).
% 0.21/0.38 thf(f8,plain,(
% 0.21/0.38 (! [X0,X1] : ((subset @ X0 @ X1) => (in @ X0 @ (powerset @ X1))) = powersetI1)),
% 0.21/0.38 inference(rectify,[],[f1])).
% 0.21/0.38 thf(f1,axiom,(
% 0.21/0.38 (! [X1,X0] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))) = powersetI1)),
% 0.21/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1)).
% 0.21/0.38 thf(f18,plain,(
% 0.21/0.38 ((in @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK2))) != $true)),
% 0.21/0.38 inference(cnf_transformation,[],[f16])).
% 0.21/0.38 thf(f40,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((subset @ (setadjoin @ X2 @ (setadjoin @ X4 @ emptyset)) @ (binunion @ X3 @ X1)) = $true) | ($false = (in @ X4 @ X1)) | ($false = (in @ X2 @ X3))) )),
% 0.21/0.38 inference(binary_proxy_clausification,[],[f39])).
% 0.21/0.38 thf(f39,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (in @ X2 @ X3)) | (((in @ X4 @ X1) => (subset @ (setadjoin @ X2 @ (setadjoin @ X4 @ emptyset)) @ (binunion @ X3 @ X1))) = $true)) )),
% 0.21/0.38 inference(beta_eta_normalization,[],[f38])).
% 0.21/0.38 thf(f38,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ X1) => (subset @ (setadjoin @ X2 @ (setadjoin @ Y0 @ emptyset)) @ (binunion @ X3 @ X1)))) @ X4)) | ($false = (in @ X2 @ X3))) )),
% 0.21/0.38 inference(pi_clausification,[],[f37])).
% 0.21/0.38 thf(f37,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (subset @ (setadjoin @ X2 @ (setadjoin @ Y0 @ emptyset)) @ (binunion @ X3 @ X1)))))) | ($false = (in @ X2 @ X3))) )),
% 0.21/0.38 inference(binary_proxy_clausification,[],[f36])).
% 0.21/0.38 thf(f36,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X2 @ X3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (subset @ (setadjoin @ X2 @ (setadjoin @ Y0 @ emptyset)) @ (binunion @ X3 @ X1)))))) = $true)) )),
% 0.21/0.38 inference(beta_eta_normalization,[],[f35])).
% 0.21/0.38 thf(f35,plain,(
% 0.21/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X2 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (subset @ (setadjoin @ X2 @ (setadjoin @ Y1 @ emptyset)) @ (binunion @ Y0 @ X1))))))) @ X3) = $true)) )),
% 0.21/0.38 inference(pi_clausification,[],[f34])).
% 0.21/0.38 thf(f34,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (subset @ (setadjoin @ X2 @ (setadjoin @ Y1 @ emptyset)) @ (binunion @ Y0 @ X1)))))))) = $true)) )),
% 0.21/0.38 inference(beta_eta_normalization,[],[f33])).
% 0.21/0.38 thf(f33,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ (binunion @ Y1 @ X1))))))))) @ X2) = $true)) )),
% 0.21/0.38 inference(pi_clausification,[],[f32])).
% 0.21/0.38 thf(f32,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ (binunion @ Y1 @ X1)))))))))) = $true)) )),
% 0.21/0.38 inference(beta_eta_normalization,[],[f31])).
% 0.21/0.38 thf(f31,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y2 @ Y0))))))))))) @ X1))) )),
% 0.21/0.38 inference(pi_clausification,[],[f25])).
% 0.21/0.38 thf(f25,plain,(
% 0.21/0.38 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y2 @ Y0)))))))))))) = $true)),
% 0.21/0.38 inference(definition_unfolding,[],[f23,f20])).
% 0.21/0.38 thf(f20,plain,(
% 0.21/0.38 (upairsubunion = $true)),
% 0.21/0.38 inference(cnf_transformation,[],[f16])).
% 0.21/0.38 thf(f23,plain,(
% 0.21/0.38 (upairsubunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y2 @ Y0)))))))))))))),
% 0.21/0.38 inference(cnf_transformation,[],[f11])).
% 0.21/0.38 thf(f11,plain,(
% 0.21/0.38 (upairsubunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y2 @ Y0)))))))))))))),
% 0.21/0.38 inference(fool_elimination,[],[f10])).
% 0.21/0.38 thf(f10,plain,(
% 0.21/0.38 (! [X0,X1,X2] : ((in @ X1 @ X0) => ! [X3] : ((in @ X3 @ X2) => (subset @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X0 @ X2)))) = upairsubunion)),
% 0.21/0.38 inference(rectify,[],[f2])).
% 0.21/0.38 thf(f2,axiom,(
% 0.21/0.38 (! [X0,X2,X1] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X1) => (subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X0 @ X1)))) = upairsubunion)),
% 0.21/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsubunion)).
% 0.21/0.38 % SZS output end Proof for theBenchmark
% 0.21/0.38 % (16645)------------------------------
% 0.21/0.38 % (16645)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (16645)Termination reason: Refutation
% 0.21/0.38
% 0.21/0.38 % (16645)Memory used [KB]: 5500
% 0.21/0.38 % (16645)Time elapsed: 0.009 s
% 0.21/0.38 % (16645)Instructions burned: 6 (million)
% 0.21/0.38 % (16645)------------------------------
% 0.21/0.38 % (16645)------------------------------
% 0.21/0.38 % (16642)Success in time 0.008 s
% 0.21/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------