TSTP Solution File: SET027^7 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET027^7 : TPTP v8.2.0. Released v5.5.0.
% 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 : n015.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 03:07:58 EDT 2024
% Result : Theorem 0.14s 0.39s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET027^7 : TPTP v8.2.0. Released v5.5.0.
% 0.11/0.13 % 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
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon May 20 12:34:38 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.34 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
% 0.14/0.36 % (11143)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.36 % (11137)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.37 % (11143)Instruction limit reached!
% 0.14/0.37 % (11143)------------------------------
% 0.14/0.37 % (11143)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (11143)Termination reason: Unknown
% 0.14/0.37 % (11143)Termination phase: Saturation
% 0.14/0.37
% 0.14/0.37 % (11143)Memory used [KB]: 5628
% 0.14/0.37 % (11143)Time elapsed: 0.009 s
% 0.14/0.37 % (11143)Instructions burned: 20 (million)
% 0.14/0.37 % (11143)------------------------------
% 0.14/0.37 % (11143)------------------------------
% 0.14/0.37 % (11139)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)
% 0.14/0.37 % (11138)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)
% 0.14/0.37 % (11142)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)
% 0.14/0.37 % (11144)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)
% 0.14/0.37 % (11141)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)
% 0.14/0.37 % (11138)Instruction limit reached!
% 0.14/0.37 % (11138)------------------------------
% 0.14/0.37 % (11138)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (11140)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37 % (11138)Termination reason: Unknown
% 0.14/0.37 % (11138)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (11138)Memory used [KB]: 1023
% 0.14/0.37 % (11138)Time elapsed: 0.005 s
% 0.14/0.37 % (11138)Instructions burned: 4 (million)
% 0.14/0.37 % (11138)------------------------------
% 0.14/0.37 % (11138)------------------------------
% 0.14/0.37 % (11141)Instruction limit reached!
% 0.14/0.37 % (11141)------------------------------
% 0.14/0.37 % (11141)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (11141)Termination reason: Unknown
% 0.14/0.37 % (11141)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (11141)Memory used [KB]: 1023
% 0.14/0.37 % (11144)Instruction limit reached!
% 0.14/0.37 % (11144)------------------------------
% 0.14/0.37 % (11144)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (11144)Termination reason: Unknown
% 0.14/0.37 % (11144)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (11144)Memory used [KB]: 1023
% 0.14/0.37 % (11144)Time elapsed: 0.004 s
% 0.14/0.37 % (11144)Instructions burned: 3 (million)
% 0.14/0.37 % (11144)------------------------------
% 0.14/0.37 % (11144)------------------------------
% 0.14/0.37 % (11141)Time elapsed: 0.003 s
% 0.14/0.37 % (11141)Instructions burned: 2 (million)
% 0.14/0.37 % (11141)------------------------------
% 0.14/0.37 % (11141)------------------------------
% 0.14/0.37 % (11140)Instruction limit reached!
% 0.14/0.37 % (11140)------------------------------
% 0.14/0.37 % (11140)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (11140)Termination reason: Unknown
% 0.14/0.37 % (11140)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (11140)Memory used [KB]: 1023
% 0.14/0.37 % (11140)Time elapsed: 0.003 s
% 0.14/0.37 % (11140)Instructions burned: 3 (million)
% 0.14/0.37 % (11140)------------------------------
% 0.14/0.37 % (11140)------------------------------
% 0.14/0.37 % (11142)Refutation not found, incomplete strategy
% 0.14/0.37 % (11142)------------------------------
% 0.14/0.37 % (11142)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (11142)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.37
% 0.14/0.37
% 0.14/0.37 % (11142)Memory used [KB]: 5628
% 0.14/0.37 % (11142)Time elapsed: 0.007 s
% 0.14/0.37 % (11142)Instructions burned: 9 (million)
% 0.14/0.37 % (11142)------------------------------
% 0.14/0.37 % (11142)------------------------------
% 0.14/0.38 % (11161)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.14/0.38 % (11137)First to succeed.
% 0.14/0.38 % (11139)Instruction limit reached!
% 0.14/0.38 % (11139)------------------------------
% 0.14/0.38 % (11139)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (11139)Termination reason: Unknown
% 0.14/0.38 % (11139)Termination phase: Saturation
% 0.14/0.38
% 0.14/0.38 % (11139)Memory used [KB]: 5756
% 0.14/0.38 % (11139)Time elapsed: 0.018 s
% 0.14/0.38 % (11139)Instructions burned: 27 (million)
% 0.14/0.38 % (11139)------------------------------
% 0.14/0.38 % (11139)------------------------------
% 0.14/0.38 % (11164)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.39 % (11137)Refutation found. Thanks to Tanya!
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39 % SZS output start Proof for theBenchmark
% 0.14/0.39 thf(type_def_5, type, mu: $tType).
% 0.14/0.39 thf(func_def_0, type, mu: $tType).
% 0.14/0.39 thf(func_def_1, type, qmltpeq: mu > mu > $i > $o).
% 0.14/0.39 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_6, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_7, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_8, type, mtrue: $i > $o).
% 0.14/0.39 thf(func_def_9, type, mfalse: $i > $o).
% 0.14/0.39 thf(func_def_10, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_11, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_12, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_13, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_14, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_15, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_16, type, exists_in_world: mu > $i > $o).
% 0.14/0.39 thf(func_def_17, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_18, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_19, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_20, type, mreflexive: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_21, type, msymmetric: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_22, type, mserial: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_23, type, mtransitive: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_24, type, meuclidean: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_25, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_26, type, mfunctional: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_27, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_28, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_29, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_30, type, mvalid: ($i > $o) > $o).
% 0.14/0.39 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.14/0.39 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.14/0.39 thf(func_def_33, type, minvalid: ($i > $o) > $o).
% 0.14/0.39 thf(func_def_34, type, rel_s4: $i > $i > $o).
% 0.14/0.39 thf(func_def_35, type, mbox_s4: ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_36, type, mdia_s4: ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_37, type, member: mu > mu > $i > $o).
% 0.14/0.39 thf(func_def_38, type, subset: mu > mu > $i > $o).
% 0.14/0.39 thf(func_def_54, type, sK0: $i > mu).
% 0.14/0.39 thf(func_def_56, type, sK2: mu > $i > mu > mu).
% 0.14/0.39 thf(func_def_58, type, sK4: mu).
% 0.14/0.39 thf(func_def_59, type, sK5: mu).
% 0.14/0.39 thf(func_def_60, type, sK6: mu).
% 0.14/0.39 thf(f449,plain,(
% 0.14/0.39 $false),
% 0.14/0.39 inference(avatar_sat_refutation,[],[f365,f375,f385,f436,f447])).
% 0.14/0.39 thf(f447,plain,(
% 0.14/0.39 ~spl1_1),
% 0.14/0.39 inference(avatar_contradiction_clause,[],[f446])).
% 0.14/0.39 thf(f446,plain,(
% 0.14/0.39 $false | ~spl1_1),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f439])).
% 0.14/0.39 thf(f439,plain,(
% 0.14/0.39 ($false = $true) | ~spl1_1),
% 0.14/0.39 inference(superposition,[],[f347,f235])).
% 0.14/0.39 thf(f235,plain,(
% 0.14/0.39 ($true = (exists_in_world @ sK5 @ sK3))),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f233])).
% 0.14/0.39 thf(f233,plain,(
% 0.14/0.39 (((exists_in_world @ sK5 @ sK3) => (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK3) => ((subset @ sK4 @ Y0 @ sK3) | ((~ (subset @ sK5 @ Y0 @ sK3)) | (~ (subset @ sK4 @ sK5 @ sK3)))))))) = $false)),
% 0.14/0.39 inference(beta_eta_normalization,[],[f232])).
% 0.14/0.39 thf(f232,plain,(
% 0.14/0.39 ($false = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK3) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK3) => ((subset @ sK4 @ Y1 @ sK3) | ((~ (subset @ Y0 @ Y1 @ sK3)) | (~ (subset @ sK4 @ Y0 @ sK3))))))))) @ sK5))),
% 0.14/0.39 inference(sigma_clausification,[],[f230])).
% 0.14/0.39 thf(f230,plain,(
% 0.14/0.39 ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK3) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK3) => ((subset @ sK4 @ Y1 @ sK3) | ((~ (subset @ Y0 @ Y1 @ sK3)) | (~ (subset @ sK4 @ Y0 @ sK3)))))))))))),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f229])).
% 0.14/0.39 thf(f229,plain,(
% 0.14/0.39 ($false = ((exists_in_world @ sK4 @ sK3) => (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK3) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK3) => ((subset @ sK4 @ Y1 @ sK3) | ((~ (subset @ Y0 @ Y1 @ sK3)) | (~ (subset @ sK4 @ Y0 @ sK3))))))))))))),
% 0.14/0.39 inference(beta_eta_normalization,[],[f228])).
% 0.14/0.39 thf(f228,plain,(
% 0.14/0.39 (((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK3) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK3) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ sK3) => ((subset @ Y0 @ Y2 @ sK3) | ((~ (subset @ Y1 @ Y2 @ sK3)) | (~ (subset @ Y0 @ Y1 @ sK3)))))))))))) @ sK4) = $false)),
% 0.14/0.39 inference(sigma_clausification,[],[f227])).
% 0.14/0.39 thf(f227,plain,(
% 0.14/0.39 ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK3) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK3) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ sK3) => ((subset @ Y0 @ Y2 @ sK3) | ((~ (subset @ Y1 @ Y2 @ sK3)) | (~ (subset @ Y0 @ Y1 @ sK3))))))))))))) = $false)),
% 0.14/0.39 inference(beta_eta_normalization,[],[f226])).
% 0.14/0.39 thf(f226,plain,(
% 0.14/0.39 ($false = ((^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y0) => ((subset @ Y1 @ Y3 @ Y0) | ((~ (subset @ Y2 @ Y3 @ Y0)) | (~ (subset @ Y1 @ Y2 @ Y0)))))))))))))) @ sK3))),
% 0.14/0.39 inference(sigma_clausification,[],[f225])).
% 0.14/0.39 thf(f225,plain,(
% 0.14/0.39 ((!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y0) => ((subset @ Y1 @ Y3 @ Y0) | ((~ (subset @ Y2 @ Y3 @ Y0)) | (~ (subset @ Y1 @ Y2 @ Y0))))))))))))))) != $true)),
% 0.14/0.39 inference(boolean_simplification,[],[f224])).
% 0.14/0.39 thf(f224,plain,(
% 0.14/0.39 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y0) => ((subset @ Y1 @ Y3 @ Y0) | (~ (~ ((~ (subset @ Y2 @ Y3 @ Y0)) | (~ (subset @ Y1 @ Y2 @ Y0))))))))))))))))))),
% 0.14/0.39 inference(beta_eta_normalization,[],[f173])).
% 0.14/0.39 thf(f173,plain,(
% 0.14/0.39 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : mu]: ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : mu]: ((^[Y2 : mu > $i > $o]: ((^[Y3 : $i]: (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) @ (^[Y2 : mu]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: ((Y6 @ Y7) | (Y5 @ Y7))))))) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ Y3) @ Y4)))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: ((Y6 @ Y7) | (Y5 @ Y7))))))) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ Y3) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ Y4)))))) @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y2)) @ (subset @ Y0 @ Y2))))))))) != $true)),
% 0.14/0.39 inference(definition_unfolding,[],[f142,f125,f156,f156,f156,f163,f162])).
% 0.14/0.39 thf(f162,plain,(
% 0.14/0.39 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.14/0.39 inference(definition_unfolding,[],[f138,f145,f128,f145,f145])).
% 0.14/0.39 thf(f128,plain,(
% 0.14/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.14/0.39 inference(cnf_transformation,[],[f76])).
% 0.14/0.39 thf(f76,plain,(
% 0.14/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.14/0.39 inference(fool_elimination,[],[f75])).
% 0.14/0.39 thf(f75,plain,(
% 0.14/0.39 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.14/0.39 inference(rectify,[],[f3])).
% 0.14/0.39 thf(f3,axiom,(
% 0.14/0.39 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.14/0.39 thf(f145,plain,(
% 0.14/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.39 inference(cnf_transformation,[],[f104])).
% 0.14/0.39 thf(f104,plain,(
% 0.14/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.39 inference(fool_elimination,[],[f103])).
% 0.14/0.39 thf(f103,plain,(
% 0.14/0.39 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.14/0.39 inference(rectify,[],[f2])).
% 0.14/0.39 thf(f2,axiom,(
% 0.14/0.39 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.14/0.39 thf(f138,plain,(
% 0.14/0.39 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.14/0.39 inference(cnf_transformation,[],[f110])).
% 0.14/0.39 thf(f110,plain,(
% 0.14/0.39 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.14/0.39 inference(fool_elimination,[],[f109])).
% 0.14/0.39 thf(f109,plain,(
% 0.14/0.39 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.14/0.39 inference(rectify,[],[f8])).
% 0.14/0.39 thf(f8,axiom,(
% 0.14/0.39 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)).
% 0.14/0.39 thf(f163,plain,(
% 0.14/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.14/0.39 inference(definition_unfolding,[],[f132,f128,f145])).
% 0.14/0.39 thf(f132,plain,(
% 0.14/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.39 inference(cnf_transformation,[],[f114])).
% 0.14/0.39 thf(f114,plain,(
% 0.14/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.39 inference(fool_elimination,[],[f113])).
% 0.14/0.39 thf(f113,plain,(
% 0.14/0.39 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.14/0.39 inference(rectify,[],[f9])).
% 0.14/0.39 thf(f9,axiom,(
% 0.14/0.39 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.14/0.39 thf(f156,plain,(
% 0.14/0.39 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.14/0.39 inference(cnf_transformation,[],[f55])).
% 0.14/0.39 thf(f55,plain,(
% 0.14/0.39 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.14/0.39 inference(fool_elimination,[],[f54])).
% 0.14/0.39 thf(f54,plain,(
% 0.14/0.39 (mforall_ind = (^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : ((exists_in_world @ X2 @ X1) => (X0 @ X2 @ X1)))))),
% 0.14/0.39 inference(rectify,[],[f15])).
% 0.14/0.39 thf(f15,axiom,(
% 0.14/0.39 (mforall_ind = (^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : ((exists_in_world @ X0 @ X2) => (X3 @ X0 @ X2)))))),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind)).
% 0.14/0.39 thf(f125,plain,(
% 0.14/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.39 inference(cnf_transformation,[],[f51])).
% 0.14/0.39 thf(f51,plain,(
% 0.14/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.39 inference(fool_elimination,[],[f50])).
% 0.14/0.39 thf(f50,plain,(
% 0.14/0.39 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.14/0.39 inference(rectify,[],[f28])).
% 0.14/0.39 thf(f28,axiom,(
% 0.14/0.39 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.14/0.39 thf(f142,plain,(
% 0.14/0.39 ($true != (mvalid @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mforall_ind @ (^[Y2 : mu]: (mimplies @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y2)) @ (subset @ Y0 @ Y2))))))))))),
% 0.14/0.39 inference(cnf_transformation,[],[f117])).
% 0.14/0.39 thf(f117,plain,(
% 0.14/0.39 ($true != (mvalid @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mforall_ind @ (^[Y2 : mu]: (mimplies @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y2)) @ (subset @ Y0 @ Y2))))))))))),
% 0.14/0.39 inference(flattening,[],[f84])).
% 0.14/0.39 thf(f84,plain,(
% 0.14/0.39 ~($true = (mvalid @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mforall_ind @ (^[Y2 : mu]: (mimplies @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y2)) @ (subset @ Y0 @ Y2))))))))))),
% 0.14/0.39 inference(fool_elimination,[],[f83])).
% 0.14/0.39 thf(f83,plain,(
% 0.14/0.39 ~(mvalid @ (mforall_ind @ (^[X0 : mu] : (mforall_ind @ (^[X1 : mu] : (mforall_ind @ (^[X2 : mu] : (mimplies @ (mand @ (subset @ X0 @ X1) @ (subset @ X1 @ X2)) @ (subset @ X0 @ X2)))))))))),
% 0.14/0.39 inference(rectify,[],[f40])).
% 0.14/0.39 thf(f40,negated_conjecture,(
% 0.14/0.39 ~(mvalid @ (mforall_ind @ (^[X11 : mu] : (mforall_ind @ (^[X12 : mu] : (mforall_ind @ (^[X13 : mu] : (mimplies @ (mand @ (subset @ X11 @ X12) @ (subset @ X12 @ X13)) @ (subset @ X11 @ X13)))))))))),
% 0.14/0.39 inference(negated_conjecture,[],[f39])).
% 0.14/0.39 thf(f39,conjecture,(
% 0.14/0.39 (mvalid @ (mforall_ind @ (^[X11 : mu] : (mforall_ind @ (^[X12 : mu] : (mforall_ind @ (^[X13 : mu] : (mimplies @ (mand @ (subset @ X11 @ X12) @ (subset @ X12 @ X13)) @ (subset @ X11 @ X13)))))))))),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_transitivity_of_subset)).
% 0.14/0.39 thf(f347,plain,(
% 0.14/0.39 ($false = (exists_in_world @ sK5 @ sK3)) | ~spl1_1),
% 0.14/0.39 inference(avatar_component_clause,[],[f345])).
% 0.14/0.39 thf(f345,plain,(
% 0.14/0.39 spl1_1 <=> ($false = (exists_in_world @ sK5 @ sK3))),
% 0.14/0.39 introduced(avatar_definition,[new_symbols(naming,[spl1_1])])).
% 0.14/0.39 thf(f436,plain,(
% 0.14/0.39 spl1_2 | ~spl1_5),
% 0.14/0.39 inference(avatar_contradiction_clause,[],[f435])).
% 0.14/0.39 thf(f435,plain,(
% 0.14/0.39 $false | (spl1_2 | ~spl1_5)),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f427])).
% 0.14/0.39 thf(f427,plain,(
% 0.14/0.39 ($false = $true) | (spl1_2 | ~spl1_5)),
% 0.14/0.39 inference(superposition,[],[f426,f241])).
% 0.14/0.39 thf(f241,plain,(
% 0.14/0.39 ($false = (subset @ sK4 @ sK6 @ sK3))),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f238])).
% 0.14/0.39 thf(f238,plain,(
% 0.14/0.39 ($false = ((subset @ sK4 @ sK6 @ sK3) | ((~ (subset @ sK5 @ sK6 @ sK3)) | (~ (subset @ sK4 @ sK5 @ sK3)))))),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f237])).
% 0.14/0.39 thf(f237,plain,(
% 0.14/0.39 ($false = ((exists_in_world @ sK6 @ sK3) => ((subset @ sK4 @ sK6 @ sK3) | ((~ (subset @ sK5 @ sK6 @ sK3)) | (~ (subset @ sK4 @ sK5 @ sK3))))))),
% 0.14/0.39 inference(beta_eta_normalization,[],[f236])).
% 0.14/0.39 thf(f236,plain,(
% 0.14/0.39 (((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK3) => ((subset @ sK4 @ Y0 @ sK3) | ((~ (subset @ sK5 @ Y0 @ sK3)) | (~ (subset @ sK4 @ sK5 @ sK3)))))) @ sK6) = $false)),
% 0.14/0.39 inference(sigma_clausification,[],[f234])).
% 0.14/0.39 thf(f234,plain,(
% 0.14/0.39 ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK3) => ((subset @ sK4 @ Y0 @ sK3) | ((~ (subset @ sK5 @ Y0 @ sK3)) | (~ (subset @ sK4 @ sK5 @ sK3))))))) = $false)),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f233])).
% 0.14/0.39 thf(f426,plain,(
% 0.14/0.39 ($true = (subset @ sK4 @ sK6 @ sK3)) | (spl1_2 | ~spl1_5)),
% 0.14/0.39 inference(subsumption_resolution,[],[f425,f350])).
% 0.14/0.39 thf(f350,plain,(
% 0.14/0.39 ($false != (exists_in_world @ sK4 @ sK3)) | spl1_2),
% 0.14/0.39 inference(avatar_component_clause,[],[f349])).
% 0.14/0.39 thf(f349,plain,(
% 0.14/0.39 spl1_2 <=> ($false = (exists_in_world @ sK4 @ sK3))),
% 0.14/0.39 introduced(avatar_definition,[new_symbols(naming,[spl1_2])])).
% 0.14/0.39 thf(f425,plain,(
% 0.14/0.39 ($false = (exists_in_world @ sK4 @ sK3)) | ($true = (subset @ sK4 @ sK6 @ sK3)) | ~spl1_5),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f412])).
% 0.14/0.39 thf(f412,plain,(
% 0.14/0.39 ($true = (subset @ sK4 @ sK6 @ sK3)) | ($false = $true) | ($false = (exists_in_world @ sK4 @ sK3)) | ~spl1_5),
% 0.14/0.39 inference(superposition,[],[f363,f245])).
% 0.14/0.39 thf(f245,plain,(
% 0.14/0.39 ((subset @ sK4 @ sK5 @ sK3) = $true)),
% 0.14/0.39 inference(not_proxy_clausification,[],[f242])).
% 0.14/0.39 thf(f242,plain,(
% 0.14/0.39 ($false = (~ (subset @ sK4 @ sK5 @ sK3)))),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f240])).
% 0.14/0.39 thf(f240,plain,(
% 0.14/0.39 ($false = ((~ (subset @ sK5 @ sK6 @ sK3)) | (~ (subset @ sK4 @ sK5 @ sK3))))),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f238])).
% 0.14/0.39 thf(f363,plain,(
% 0.14/0.39 ( ! [X0 : mu] : (($false = (subset @ X0 @ sK5 @ sK3)) | ($false = (exists_in_world @ X0 @ sK3)) | ((subset @ X0 @ sK6 @ sK3) = $true)) ) | ~spl1_5),
% 0.14/0.39 inference(avatar_component_clause,[],[f362])).
% 0.14/0.39 thf(f362,plain,(
% 0.14/0.39 spl1_5 <=> ! [X0 : mu] : (($false = (subset @ X0 @ sK5 @ sK3)) | ($false = (exists_in_world @ X0 @ sK3)) | ((subset @ X0 @ sK6 @ sK3) = $true))),
% 0.14/0.39 introduced(avatar_definition,[new_symbols(naming,[spl1_5])])).
% 0.14/0.39 thf(f385,plain,(
% 0.14/0.39 ~spl1_4),
% 0.14/0.39 inference(avatar_contradiction_clause,[],[f384])).
% 0.14/0.39 thf(f384,plain,(
% 0.14/0.39 $false | ~spl1_4),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f378])).
% 0.14/0.39 thf(f378,plain,(
% 0.14/0.39 ($false = $true) | ~spl1_4),
% 0.14/0.39 inference(superposition,[],[f360,f239])).
% 0.14/0.39 thf(f239,plain,(
% 0.14/0.39 ((exists_in_world @ sK6 @ sK3) = $true)),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f237])).
% 0.14/0.39 thf(f360,plain,(
% 0.14/0.39 ((exists_in_world @ sK6 @ sK3) = $false) | ~spl1_4),
% 0.14/0.39 inference(avatar_component_clause,[],[f358])).
% 0.14/0.39 thf(f358,plain,(
% 0.14/0.39 spl1_4 <=> ((exists_in_world @ sK6 @ sK3) = $false)),
% 0.14/0.39 introduced(avatar_definition,[new_symbols(naming,[spl1_4])])).
% 0.14/0.39 thf(f375,plain,(
% 0.14/0.39 ~spl1_2),
% 0.14/0.39 inference(avatar_contradiction_clause,[],[f374])).
% 0.14/0.39 thf(f374,plain,(
% 0.14/0.39 $false | ~spl1_2),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f368])).
% 0.14/0.39 thf(f368,plain,(
% 0.14/0.39 ($false = $true) | ~spl1_2),
% 0.14/0.39 inference(superposition,[],[f231,f351])).
% 0.14/0.39 thf(f351,plain,(
% 0.14/0.39 ($false = (exists_in_world @ sK4 @ sK3)) | ~spl1_2),
% 0.14/0.39 inference(avatar_component_clause,[],[f349])).
% 0.14/0.39 thf(f231,plain,(
% 0.14/0.39 ($true = (exists_in_world @ sK4 @ sK3))),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f229])).
% 0.14/0.39 thf(f365,plain,(
% 0.14/0.39 spl1_4 | spl1_1 | spl1_5),
% 0.14/0.39 inference(avatar_split_clause,[],[f335,f362,f345,f358])).
% 0.14/0.39 thf(f335,plain,(
% 0.14/0.39 ( ! [X0 : mu] : (($false = (exists_in_world @ X0 @ sK3)) | ($false = (subset @ X0 @ sK5 @ sK3)) | ((exists_in_world @ sK6 @ sK3) = $false) | ($false = (exists_in_world @ sK5 @ sK3)) | ((subset @ X0 @ sK6 @ sK3) = $true)) )),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f321])).
% 0.14/0.39 thf(f321,plain,(
% 0.14/0.39 ( ! [X0 : mu] : (($false = (subset @ X0 @ sK5 @ sK3)) | ($false = (exists_in_world @ sK5 @ sK3)) | ($false = $true) | ((exists_in_world @ sK6 @ sK3) = $false) | ($false = (exists_in_world @ X0 @ sK3)) | ((subset @ X0 @ sK6 @ sK3) = $true)) )),
% 0.14/0.39 inference(superposition,[],[f319,f244])).
% 0.14/0.39 thf(f244,plain,(
% 0.14/0.39 ($true = (subset @ sK5 @ sK6 @ sK3))),
% 0.14/0.39 inference(not_proxy_clausification,[],[f243])).
% 0.14/0.39 thf(f243,plain,(
% 0.14/0.39 ($false = (~ (subset @ sK5 @ sK6 @ sK3)))),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f240])).
% 0.14/0.39 thf(f319,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X0 : mu,X1 : $i] : (($false = (subset @ X3 @ X0 @ X1)) | ($false = (exists_in_world @ X0 @ X1)) | ((exists_in_world @ X2 @ X1) = $false) | ((subset @ X2 @ X0 @ X1) = $true) | ($false = (exists_in_world @ X3 @ X1)) | ((subset @ X2 @ X3 @ X1) = $false)) )),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f318])).
% 0.14/0.39 thf(f318,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X0 : mu,X1 : $i] : (($false = $true) | ($false = (subset @ X3 @ X0 @ X1)) | ($false = (exists_in_world @ X3 @ X1)) | ($false = (exists_in_world @ X0 @ X1)) | ((exists_in_world @ X2 @ X1) = $false) | ((subset @ X2 @ X0 @ X1) = $true) | ((subset @ X2 @ X3 @ X1) = $false)) )),
% 0.14/0.39 inference(duplicate_literal_removal,[],[f309])).
% 0.14/0.39 thf(f309,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X0 : mu,X1 : $i] : (($false = $true) | ((subset @ X2 @ X0 @ X1) = $true) | ($false = (exists_in_world @ X0 @ X1)) | ($false = (exists_in_world @ X0 @ X1)) | ((exists_in_world @ X2 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ((subset @ X2 @ X3 @ X1) = $false) | ($false = (exists_in_world @ X3 @ X1)) | ((subset @ X2 @ X0 @ X1) = $true) | ($false = (subset @ X3 @ X0 @ X1))) )),
% 0.14/0.39 inference(superposition,[],[f194,f299])).
% 0.14/0.39 thf(f299,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X0 : mu,X1 : $i] : (($false = (exists_in_world @ (sK2 @ X0 @ X1 @ X2) @ X1)) | ((subset @ X2 @ X0 @ X1) = $true) | ((exists_in_world @ X2 @ X1) = $false) | ((subset @ X2 @ X3 @ X1) = $false) | ($false = (exists_in_world @ X3 @ X1)) | ($false = (subset @ X3 @ X0 @ X1)) | ($false = (exists_in_world @ X0 @ X1))) )),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f298])).
% 0.14/0.39 thf(f298,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X0 : mu,X1 : $i] : (($false = (exists_in_world @ (sK2 @ X0 @ X1 @ X2) @ X1)) | ((subset @ X2 @ X3 @ X1) = $false) | ((subset @ X2 @ X0 @ X1) = $true) | ($false = $true) | ($false = (exists_in_world @ X0 @ X1)) | ($false = (exists_in_world @ X3 @ X1)) | ($false = (subset @ X3 @ X0 @ X1)) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.14/0.39 inference(duplicate_literal_removal,[],[f288])).
% 0.14/0.39 thf(f288,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X0 : mu,X1 : $i] : (((exists_in_world @ X2 @ X1) = $false) | ($false = (exists_in_world @ (sK2 @ X0 @ X1 @ X2) @ X1)) | ($false = (exists_in_world @ X3 @ X1)) | ($false = (exists_in_world @ X0 @ X1)) | ($false = (exists_in_world @ X0 @ X1)) | ($false = (exists_in_world @ X0 @ X1)) | ((subset @ X2 @ X0 @ X1) = $true) | ((subset @ X2 @ X0 @ X1) = $true) | ((exists_in_world @ X2 @ X1) = $false) | ((subset @ X2 @ X3 @ X1) = $false) | ($false = (subset @ X3 @ X0 @ X1)) | ($false = $true)) )),
% 0.14/0.39 inference(superposition,[],[f273,f196])).
% 0.14/0.39 thf(f196,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($false = (member @ (sK2 @ X3 @ X1 @ X2) @ X3 @ X1)) | ((subset @ X2 @ X3 @ X1) = $true) | ($false = (exists_in_world @ X3 @ X1)) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f193])).
% 0.14/0.39 thf(f193,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (((exists_in_world @ X2 @ X1) = $false) | ((subset @ X2 @ X3 @ X1) = $true) | ($false = (exists_in_world @ X3 @ X1)) | (((member @ (sK2 @ X3 @ X1 @ X2) @ X3 @ X1) | (~ (member @ (sK2 @ X3 @ X1 @ X2) @ X2 @ X1))) = $false)) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f192])).
% 0.14/0.39 thf(f192,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (((subset @ X2 @ X3 @ X1) = $true) | ((exists_in_world @ X2 @ X1) = $false) | ($false = (exists_in_world @ X3 @ X1)) | ($false = ((exists_in_world @ (sK2 @ X3 @ X1 @ X2) @ X1) => ((member @ (sK2 @ X3 @ X1 @ X2) @ X3 @ X1) | (~ (member @ (sK2 @ X3 @ X1 @ X2) @ X2 @ X1)))))) )),
% 0.14/0.39 inference(beta_eta_normalization,[],[f191])).
% 0.14/0.39 thf(f191,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (((exists_in_world @ X2 @ X1) = $false) | ($false = (exists_in_world @ X3 @ X1)) | ((subset @ X2 @ X3 @ X1) = $true) | ($false = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => ((member @ Y0 @ X3 @ X1) | (~ (member @ Y0 @ X2 @ X1))))) @ (sK2 @ X3 @ X1 @ X2)))) )),
% 0.14/0.39 inference(sigma_clausification,[],[f190])).
% 0.14/0.39 thf(f190,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (((exists_in_world @ X2 @ X1) = $false) | ($false = (exists_in_world @ X3 @ X1)) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => ((member @ Y0 @ X3 @ X1) | (~ (member @ Y0 @ X2 @ X1)))))) = $false) | ((subset @ X2 @ X3 @ X1) = $true)) )),
% 0.14/0.39 inference(not_proxy_clausification,[],[f189])).
% 0.14/0.39 thf(f189,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (((subset @ X2 @ X3 @ X1) = $true) | ($false = (exists_in_world @ X3 @ X1)) | ((exists_in_world @ X2 @ X1) = $false) | ($true = (~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => ((member @ Y0 @ X3 @ X1) | (~ (member @ Y0 @ X2 @ X1))))))))) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f188])).
% 0.14/0.39 thf(f188,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (((exists_in_world @ X2 @ X1) = $false) | (((subset @ X2 @ X3 @ X1) | (~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => ((member @ Y0 @ X3 @ X1) | (~ (member @ Y0 @ X2 @ X1)))))))) = $true) | ($false = (exists_in_world @ X3 @ X1))) )),
% 0.14/0.39 inference(not_proxy_clausification,[],[f187])).
% 0.14/0.39 thf(f187,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (((exists_in_world @ X2 @ X1) = $false) | ((~ ((subset @ X2 @ X3 @ X1) | (~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => ((member @ Y0 @ X3 @ X1) | (~ (member @ Y0 @ X2 @ X1))))))))) = $false) | ($false = (exists_in_world @ X3 @ X1))) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f185])).
% 0.14/0.39 thf(f185,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (((exists_in_world @ X2 @ X1) = $false) | (((~ ((subset @ X2 @ X3 @ X1) | (~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => ((member @ Y0 @ X3 @ X1) | (~ (member @ Y0 @ X2 @ X1))))))))) | (~ ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => ((member @ Y0 @ X3 @ X1) | (~ (member @ Y0 @ X2 @ X1)))))) | (~ (subset @ X2 @ X3 @ X1))))) = $false) | ($false = (exists_in_world @ X3 @ X1))) )),
% 0.14/0.39 inference(not_proxy_clausification,[],[f184])).
% 0.14/0.39 thf(f184,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (((~ ((~ ((subset @ X2 @ X3 @ X1) | (~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => ((member @ Y0 @ X3 @ X1) | (~ (member @ Y0 @ X2 @ X1))))))))) | (~ ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => ((member @ Y0 @ X3 @ X1) | (~ (member @ Y0 @ X2 @ X1)))))) | (~ (subset @ X2 @ X3 @ X1)))))) = $true) | ((exists_in_world @ X2 @ X1) = $false) | ($false = (exists_in_world @ X3 @ X1))) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f183])).
% 0.14/0.39 thf(f183,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : ((((exists_in_world @ X3 @ X1) => (~ ((~ ((subset @ X2 @ X3 @ X1) | (~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => ((member @ Y0 @ X3 @ X1) | (~ (member @ Y0 @ X2 @ X1))))))))) | (~ ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => ((member @ Y0 @ X3 @ X1) | (~ (member @ Y0 @ X2 @ X1)))))) | (~ (subset @ X2 @ X3 @ X1))))))) = $true) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.14/0.39 inference(beta_eta_normalization,[],[f182])).
% 0.14/0.39 thf(f182,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (((exists_in_world @ X2 @ X1) = $false) | (((^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ ((~ ((subset @ X2 @ Y0 @ X1) | (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X1) => ((member @ Y1 @ Y0 @ X1) | (~ (member @ Y1 @ X2 @ X1))))))))) | (~ ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X1) => ((member @ Y1 @ Y0 @ X1) | (~ (member @ Y1 @ X2 @ X1)))))) | (~ (subset @ X2 @ Y0 @ X1)))))))) @ X3) = $true)) )),
% 0.14/0.39 inference(pi_clausification,[],[f181])).
% 0.14/0.39 thf(f181,plain,(
% 0.14/0.39 ( ! [X2 : mu,X1 : $i] : (((exists_in_world @ X2 @ X1) = $false) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ ((~ ((subset @ X2 @ Y0 @ X1) | (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X1) => ((member @ Y1 @ Y0 @ X1) | (~ (member @ Y1 @ X2 @ X1))))))))) | (~ ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X1) => ((member @ Y1 @ Y0 @ X1) | (~ (member @ Y1 @ X2 @ X1)))))) | (~ (subset @ X2 @ Y0 @ X1))))))))) = $true)) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f180])).
% 0.14/0.39 thf(f180,plain,(
% 0.14/0.39 ( ! [X2 : mu,X1 : $i] : ((((exists_in_world @ X2 @ X1) => (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ ((~ ((subset @ X2 @ Y0 @ X1) | (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X1) => ((member @ Y1 @ Y0 @ X1) | (~ (member @ Y1 @ X2 @ X1))))))))) | (~ ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X1) => ((member @ Y1 @ Y0 @ X1) | (~ (member @ Y1 @ X2 @ X1)))))) | (~ (subset @ X2 @ Y0 @ X1)))))))))) = $true)) )),
% 0.14/0.39 inference(beta_eta_normalization,[],[f179])).
% 0.14/0.39 thf(f179,plain,(
% 0.14/0.39 ( ! [X2 : mu,X1 : $i] : ((((^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X1) => (~ ((~ ((subset @ Y0 @ Y1 @ X1) | (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ X1) => ((member @ Y2 @ Y1 @ X1) | (~ (member @ Y2 @ Y0 @ X1))))))))) | (~ ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ X1) => ((member @ Y2 @ Y1 @ X1) | (~ (member @ Y2 @ Y0 @ X1)))))) | (~ (subset @ Y0 @ Y1 @ X1))))))))))) @ X2) = $true)) )),
% 0.14/0.39 inference(pi_clausification,[],[f178])).
% 0.14/0.39 thf(f178,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X1) => (~ ((~ ((subset @ Y0 @ Y1 @ X1) | (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ X1) => ((member @ Y2 @ Y1 @ X1) | (~ (member @ Y2 @ Y0 @ X1))))))))) | (~ ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ X1) => ((member @ Y2 @ Y1 @ X1) | (~ (member @ Y2 @ Y0 @ X1)))))) | (~ (subset @ Y0 @ Y1 @ X1)))))))))))) = $true)) )),
% 0.14/0.39 inference(beta_eta_normalization,[],[f177])).
% 0.14/0.39 thf(f177,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => (~ ((~ ((subset @ Y1 @ Y2 @ Y0) | (~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y0) => ((member @ Y3 @ Y2 @ Y0) | (~ (member @ Y3 @ Y1 @ Y0))))))))) | (~ ((!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y0) => ((member @ Y3 @ Y2 @ Y0) | (~ (member @ Y3 @ Y1 @ Y0)))))) | (~ (subset @ Y1 @ Y2 @ Y0))))))))))))) @ X1))) )),
% 0.14/0.39 inference(pi_clausification,[],[f176])).
% 0.14/0.39 thf(f176,plain,(
% 0.14/0.39 ((!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => (~ ((~ ((subset @ Y1 @ Y2 @ Y0) | (~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y0) => ((member @ Y3 @ Y2 @ Y0) | (~ (member @ Y3 @ Y1 @ Y0))))))))) | (~ ((!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y0) => ((member @ Y3 @ Y2 @ Y0) | (~ (member @ Y3 @ Y1 @ Y0)))))) | (~ (subset @ Y1 @ Y2 @ Y0)))))))))))))) = $true)),
% 0.14/0.39 inference(beta_eta_normalization,[],[f174])).
% 0.14/0.39 thf(f174,plain,(
% 0.14/0.39 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : mu]: ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y7 @ Y8) | (Y6 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y5)))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y7 @ Y8) | (Y6 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ Y2 @ Y3) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y7 @ Y8) | (Y6 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ Y3 @ Y2))))) @ (subset @ Y0 @ Y1) @ ((^[Y2 : mu > $i > $o]: ((^[Y3 : $i]: (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) @ (^[Y2 : mu]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: ((Y6 @ Y7) | (Y5 @ Y7))))))) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ Y3) @ Y4)))) @ (member @ Y2 @ Y0) @ (member @ Y2 @ Y1)))))))))) = $true)),
% 0.14/0.39 inference(definition_unfolding,[],[f147,f125,f156,f156,f165,f156,f163])).
% 0.14/0.39 thf(f165,plain,(
% 0.14/0.39 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))))),
% 0.14/0.39 inference(definition_unfolding,[],[f122,f162,f163,f163])).
% 0.14/0.39 thf(f122,plain,(
% 0.14/0.39 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.14/0.39 inference(cnf_transformation,[],[f63])).
% 0.14/0.39 thf(f63,plain,(
% 0.14/0.39 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.14/0.39 inference(fool_elimination,[],[f62])).
% 0.14/0.39 thf(f62,plain,(
% 0.14/0.39 (mequiv = (^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))))),
% 0.14/0.39 inference(rectify,[],[f11])).
% 0.14/0.39 thf(f11,axiom,(
% 0.14/0.39 (mequiv = (^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))))),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv)).
% 0.14/0.39 thf(f147,plain,(
% 0.14/0.39 ((mvalid @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mequiv @ (subset @ Y0 @ Y1) @ (mforall_ind @ (^[Y2 : mu]: (mimplies @ (member @ Y2 @ Y0) @ (member @ Y2 @ Y1)))))))))) = $true)),
% 0.14/0.39 inference(cnf_transformation,[],[f100])).
% 0.14/0.39 thf(f100,plain,(
% 0.14/0.39 ((mvalid @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mequiv @ (subset @ Y0 @ Y1) @ (mforall_ind @ (^[Y2 : mu]: (mimplies @ (member @ Y2 @ Y0) @ (member @ Y2 @ Y1)))))))))) = $true)),
% 0.14/0.39 inference(fool_elimination,[],[f99])).
% 0.14/0.39 thf(f99,plain,(
% 0.14/0.39 (mvalid @ (mforall_ind @ (^[X0 : mu] : (mforall_ind @ (^[X1 : mu] : (mequiv @ (subset @ X0 @ X1) @ (mforall_ind @ (^[X2 : mu] : (mimplies @ (member @ X2 @ X0) @ (member @ X2 @ X1))))))))))),
% 0.14/0.39 inference(rectify,[],[f37])).
% 0.14/0.39 thf(f37,axiom,(
% 0.14/0.39 (mvalid @ (mforall_ind @ (^[X11 : mu] : (mforall_ind @ (^[X12 : mu] : (mequiv @ (subset @ X11 @ X12) @ (mforall_ind @ (^[X13 : mu] : (mimplies @ (member @ X13 @ X11) @ (member @ X13 @ X12))))))))))),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn)).
% 0.14/0.39 thf(f273,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X0 : mu,X1 : $i,X4 : mu] : (($true = (member @ (sK2 @ X0 @ X1 @ X2) @ X4 @ X1)) | ((exists_in_world @ X2 @ X1) = $false) | ((exists_in_world @ X4 @ X1) = $false) | ($false = (subset @ X3 @ X4 @ X1)) | ($false = (exists_in_world @ X3 @ X1)) | ($false = (exists_in_world @ (sK2 @ X0 @ X1 @ X2) @ X1)) | ($false = (exists_in_world @ X0 @ X1)) | ((subset @ X2 @ X3 @ X1) = $false) | ((subset @ X2 @ X0 @ X1) = $true)) )),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f272])).
% 0.14/0.39 thf(f272,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X0 : mu,X1 : $i,X4 : mu] : (($false = (exists_in_world @ X0 @ X1)) | ($false = (subset @ X3 @ X4 @ X1)) | ($false = $true) | ((exists_in_world @ X4 @ X1) = $false) | ($false = (exists_in_world @ (sK2 @ X0 @ X1 @ X2) @ X1)) | ((subset @ X2 @ X0 @ X1) = $true) | ($true = (member @ (sK2 @ X0 @ X1 @ X2) @ X4 @ X1)) | ((exists_in_world @ X2 @ X1) = $false) | ((subset @ X2 @ X3 @ X1) = $false) | ($false = (exists_in_world @ X3 @ X1))) )),
% 0.14/0.39 inference(duplicate_literal_removal,[],[f265])).
% 0.14/0.39 thf(f265,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X0 : mu,X1 : $i,X4 : mu] : (($false = (exists_in_world @ X3 @ X1)) | ((exists_in_world @ X4 @ X1) = $false) | ($false = $true) | ((exists_in_world @ X2 @ X1) = $false) | ($false = (exists_in_world @ (sK2 @ X0 @ X1 @ X2) @ X1)) | ($true = (member @ (sK2 @ X0 @ X1 @ X2) @ X4 @ X1)) | ((subset @ X2 @ X0 @ X1) = $true) | ($false = (subset @ X3 @ X4 @ X1)) | ($false = (exists_in_world @ X0 @ X1)) | ($false = (exists_in_world @ (sK2 @ X0 @ X1 @ X2) @ X1)) | ((subset @ X2 @ X3 @ X1) = $false) | ($false = (exists_in_world @ X3 @ X1))) )),
% 0.14/0.39 inference(superposition,[],[f205,f261])).
% 0.14/0.39 thf(f261,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X0 : mu,X1 : $i] : (((member @ (sK2 @ X0 @ X1 @ X2) @ X3 @ X1) = $true) | ($false = (exists_in_world @ (sK2 @ X0 @ X1 @ X2) @ X1)) | ($false = (exists_in_world @ X0 @ X1)) | ((subset @ X2 @ X0 @ X1) = $true) | ($false = (exists_in_world @ X3 @ X1)) | ((subset @ X2 @ X3 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f260])).
% 0.14/0.39 thf(f260,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X0 : mu,X1 : $i] : (($false = $true) | ((subset @ X2 @ X3 @ X1) = $false) | ((member @ (sK2 @ X0 @ X1 @ X2) @ X3 @ X1) = $true) | ($false = (exists_in_world @ X3 @ X1)) | ($false = (exists_in_world @ X0 @ X1)) | ($false = (exists_in_world @ (sK2 @ X0 @ X1 @ X2) @ X1)) | ((exists_in_world @ X2 @ X1) = $false) | ((subset @ X2 @ X0 @ X1) = $true)) )),
% 0.14/0.39 inference(duplicate_literal_removal,[],[f254])).
% 0.14/0.39 thf(f254,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X0 : mu,X1 : $i] : (((exists_in_world @ X2 @ X1) = $false) | ($false = (exists_in_world @ (sK2 @ X0 @ X1 @ X2) @ X1)) | ((subset @ X2 @ X0 @ X1) = $true) | ((subset @ X2 @ X3 @ X1) = $false) | ((member @ (sK2 @ X0 @ X1 @ X2) @ X3 @ X1) = $true) | ($false = $true) | ($false = (exists_in_world @ X0 @ X1)) | ($false = (exists_in_world @ X3 @ X1)) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.14/0.39 inference(superposition,[],[f205,f197])).
% 0.14/0.39 thf(f197,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($true = (member @ (sK2 @ X3 @ X1 @ X2) @ X2 @ X1)) | ((subset @ X2 @ X3 @ X1) = $true) | ((exists_in_world @ X2 @ X1) = $false) | ($false = (exists_in_world @ X3 @ X1))) )),
% 0.14/0.39 inference(not_proxy_clausification,[],[f195])).
% 0.14/0.39 thf(f195,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (((~ (member @ (sK2 @ X3 @ X1 @ X2) @ X2 @ X1)) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ((subset @ X2 @ X3 @ X1) = $true) | ($false = (exists_in_world @ X3 @ X1))) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f193])).
% 0.14/0.39 thf(f205,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i,X4 : mu] : (($false = (member @ X4 @ X2 @ X1)) | ((exists_in_world @ X4 @ X1) = $false) | ((subset @ X2 @ X3 @ X1) = $false) | ((member @ X4 @ X3 @ X1) = $true) | ($false = (exists_in_world @ X3 @ X1)) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.14/0.39 inference(not_proxy_clausification,[],[f204])).
% 0.14/0.39 thf(f204,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i,X4 : mu] : (((subset @ X2 @ X3 @ X1) = $false) | ((~ (member @ X4 @ X2 @ X1)) = $true) | ((exists_in_world @ X2 @ X1) = $false) | ((member @ X4 @ X3 @ X1) = $true) | ((exists_in_world @ X4 @ X1) = $false) | ($false = (exists_in_world @ X3 @ X1))) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f203])).
% 0.14/0.39 thf(f203,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i,X4 : mu] : (((exists_in_world @ X2 @ X1) = $false) | ((exists_in_world @ X4 @ X1) = $false) | ((subset @ X2 @ X3 @ X1) = $false) | ($false = (exists_in_world @ X3 @ X1)) | ($true = ((member @ X4 @ X3 @ X1) | (~ (member @ X4 @ X2 @ X1))))) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f202])).
% 0.14/0.39 thf(f202,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i,X4 : mu] : (((subset @ X2 @ X3 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ($true = ((exists_in_world @ X4 @ X1) => ((member @ X4 @ X3 @ X1) | (~ (member @ X4 @ X2 @ X1))))) | ($false = (exists_in_world @ X3 @ X1))) )),
% 0.14/0.39 inference(not_proxy_clausification,[],[f201])).
% 0.14/0.39 thf(f201,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i,X4 : mu] : (((~ (subset @ X2 @ X3 @ X1)) = $true) | ((exists_in_world @ X2 @ X1) = $false) | ($false = (exists_in_world @ X3 @ X1)) | ($true = ((exists_in_world @ X4 @ X1) => ((member @ X4 @ X3 @ X1) | (~ (member @ X4 @ X2 @ X1)))))) )),
% 0.14/0.39 inference(beta_eta_normalization,[],[f200])).
% 0.14/0.39 thf(f200,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i,X4 : mu] : (($true = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => ((member @ Y0 @ X3 @ X1) | (~ (member @ Y0 @ X2 @ X1))))) @ X4)) | ((~ (subset @ X2 @ X3 @ X1)) = $true) | ($false = (exists_in_world @ X3 @ X1)) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.14/0.39 inference(pi_clausification,[],[f199])).
% 0.14/0.39 thf(f199,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($false = (exists_in_world @ X3 @ X1)) | ((exists_in_world @ X2 @ X1) = $false) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => ((member @ Y0 @ X3 @ X1) | (~ (member @ Y0 @ X2 @ X1)))))) = $true) | ((~ (subset @ X2 @ X3 @ X1)) = $true)) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f198])).
% 0.14/0.39 thf(f198,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (((exists_in_world @ X2 @ X1) = $false) | ($true = ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => ((member @ Y0 @ X3 @ X1) | (~ (member @ Y0 @ X2 @ X1)))))) | (~ (subset @ X2 @ X3 @ X1)))) | ($false = (exists_in_world @ X3 @ X1))) )),
% 0.14/0.39 inference(not_proxy_clausification,[],[f186])).
% 0.14/0.39 thf(f186,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($false = (~ ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => ((member @ Y0 @ X3 @ X1) | (~ (member @ Y0 @ X2 @ X1)))))) | (~ (subset @ X2 @ X3 @ X1))))) | ($false = (exists_in_world @ X3 @ X1)) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f185])).
% 0.14/0.39 thf(f194,plain,(
% 0.14/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (((exists_in_world @ (sK2 @ X3 @ X1 @ X2) @ X1) = $true) | ($false = (exists_in_world @ X3 @ X1)) | ((exists_in_world @ X2 @ X1) = $false) | ((subset @ X2 @ X3 @ X1) = $true)) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f192])).
% 0.14/0.39 % SZS output end Proof for theBenchmark
% 0.14/0.39 % (11137)------------------------------
% 0.14/0.39 % (11137)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (11137)Termination reason: Refutation
% 0.14/0.39
% 0.14/0.39 % (11137)Memory used [KB]: 6012
% 0.14/0.39 % (11137)Time elapsed: 0.026 s
% 0.14/0.39 % (11137)Instructions burned: 60 (million)
% 0.14/0.39 % (11137)------------------------------
% 0.14/0.39 % (11137)------------------------------
% 0.14/0.39 % (11134)Success in time 0.032 s
% 0.14/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------