TSTP Solution File: SET027^7 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SET027^7 : TPTP v8.2.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n001.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 : Mon Jun 24 14:49:35 EDT 2024
% Result : Theorem 0.22s 0.43s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET027^7 : TPTP v8.2.0. Released v5.5.0.
% 0.03/0.13 % Command : run_vampire %s %d THM
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Jun 23 15:11:54 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.36 This is a TH0_THM_EQU_NAR problem
% 0.13/0.36 Running higher-order theorem proving
% 0.13/0.36 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/benchmark/theBenchmark.p -m 16384 -t 300
% 0.22/0.39 % (1003)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.40 % (1000)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.22/0.40 % (1006)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.40 % (1001)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)
% 0.22/0.40 % (1001)Instruction limit reached!
% 0.22/0.40 % (1001)------------------------------
% 0.22/0.40 % (1001)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.40 % (1001)Termination reason: Unknown
% 0.22/0.40 % (1001)Termination phase: Property scanning
% 0.22/0.40
% 0.22/0.40 % (1001)Memory used [KB]: 1023
% 0.22/0.40 % (1001)Time elapsed: 0.004 s
% 0.22/0.40 % (1001)Instructions burned: 4 (million)
% 0.22/0.40 % (1001)------------------------------
% 0.22/0.40 % (1001)------------------------------
% 0.22/0.40 % (1002)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)
% 0.22/0.40 % (1005)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)
% 0.22/0.41 % (1005)Refutation not found, incomplete strategy
% 0.22/0.41 % (1005)------------------------------
% 0.22/0.41 % (1005)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.41 % (1005)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.41
% 0.22/0.41
% 0.22/0.41 % (1005)Memory used [KB]: 5628
% 0.22/0.41 % (1005)Time elapsed: 0.007 s
% 0.22/0.41 % (1005)Instructions burned: 8 (million)
% 0.22/0.41 % (1005)------------------------------
% 0.22/0.41 % (1005)------------------------------
% 0.22/0.41 % (1003)Instruction limit reached!
% 0.22/0.41 % (1003)------------------------------
% 0.22/0.41 % (1003)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.41 % (1003)Termination reason: Unknown
% 0.22/0.41 % (1003)Termination phase: shuffling
% 0.22/0.41
% 0.22/0.41 % (1003)Memory used [KB]: 1023
% 0.22/0.41 % (1003)Time elapsed: 0.005 s
% 0.22/0.41 % (1003)Instructions burned: 3 (million)
% 0.22/0.41 % (1003)------------------------------
% 0.22/0.41 % (1003)------------------------------
% 0.22/0.41 % (1004)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)
% 0.22/0.41 % (1004)Instruction limit reached!
% 0.22/0.41 % (1004)------------------------------
% 0.22/0.41 % (1004)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.41 % (1004)Termination reason: Unknown
% 0.22/0.41 % (1004)Termination phase: shuffling
% 0.22/0.41
% 0.22/0.41 % (1004)Memory used [KB]: 1023
% 0.22/0.41 % (1004)Time elapsed: 0.004 s
% 0.22/0.41 % (1004)Instructions burned: 3 (million)
% 0.22/0.41 % (1004)------------------------------
% 0.22/0.41 % (1004)------------------------------
% 0.22/0.42 % (1007)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)
% 0.22/0.42 % (1007)Instruction limit reached!
% 0.22/0.42 % (1007)------------------------------
% 0.22/0.42 % (1007)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.42 % (1007)Termination reason: Unknown
% 0.22/0.42 % (1007)Termination phase: shuffling
% 0.22/0.42
% 0.22/0.42 % (1007)Memory used [KB]: 1023
% 0.22/0.42 % (1007)Time elapsed: 0.003 s
% 0.22/0.42 % (1007)Instructions burned: 3 (million)
% 0.22/0.42 % (1007)------------------------------
% 0.22/0.42 % (1007)------------------------------
% 0.22/0.42 % (1006)Instruction limit reached!
% 0.22/0.42 % (1006)------------------------------
% 0.22/0.42 % (1006)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.42 % (1006)Termination reason: Unknown
% 0.22/0.42 % (1006)Termination phase: Saturation
% 0.22/0.42
% 0.22/0.42 % (1006)Memory used [KB]: 5628
% 0.22/0.42 % (1006)Time elapsed: 0.015 s
% 0.22/0.42 % (1006)Instructions burned: 18 (million)
% 0.22/0.42 % (1006)------------------------------
% 0.22/0.42 % (1006)------------------------------
% 0.22/0.42 % (1000)First to succeed.
% 0.22/0.42 % (1002)Instruction limit reached!
% 0.22/0.42 % (1002)------------------------------
% 0.22/0.42 % (1002)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.42 % (1002)Termination reason: Unknown
% 0.22/0.42 % (1002)Termination phase: Saturation
% 0.22/0.42
% 0.22/0.42 % (1002)Memory used [KB]: 5756
% 0.22/0.42 % (1002)Time elapsed: 0.046 s
% 0.22/0.42 % (1002)Instructions burned: 27 (million)
% 0.22/0.42 % (1002)------------------------------
% 0.22/0.42 % (1002)------------------------------
% 0.22/0.42 % (1008)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)
% 0.22/0.42 % (1009)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.22/0.43 % (1000)Refutation found. Thanks to Tanya!
% 0.22/0.43 % SZS status Theorem for theBenchmark
% 0.22/0.43 % SZS output start Proof for theBenchmark
% 0.22/0.43 thf(type_def_5, type, mu: $tType).
% 0.22/0.43 thf(func_def_0, type, mu: $tType).
% 0.22/0.43 thf(func_def_1, type, qmltpeq: mu > mu > $i > $o).
% 0.22/0.43 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_6, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_7, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_8, type, mtrue: $i > $o).
% 0.22/0.43 thf(func_def_9, type, mfalse: $i > $o).
% 0.22/0.43 thf(func_def_10, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_11, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_12, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_13, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_14, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_15, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_16, type, exists_in_world: mu > $i > $o).
% 0.22/0.43 thf(func_def_17, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_18, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_19, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_20, type, mreflexive: ($i > $i > $o) > $o).
% 0.22/0.43 thf(func_def_21, type, msymmetric: ($i > $i > $o) > $o).
% 0.22/0.43 thf(func_def_22, type, mserial: ($i > $i > $o) > $o).
% 0.22/0.43 thf(func_def_23, type, mtransitive: ($i > $i > $o) > $o).
% 0.22/0.43 thf(func_def_24, type, meuclidean: ($i > $i > $o) > $o).
% 0.22/0.43 thf(func_def_25, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.22/0.43 thf(func_def_26, type, mfunctional: ($i > $i > $o) > $o).
% 0.22/0.43 thf(func_def_27, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.22/0.43 thf(func_def_28, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.22/0.43 thf(func_def_29, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.22/0.43 thf(func_def_30, type, mvalid: ($i > $o) > $o).
% 0.22/0.43 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.22/0.43 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.22/0.43 thf(func_def_33, type, minvalid: ($i > $o) > $o).
% 0.22/0.43 thf(func_def_34, type, rel_s4: $i > $i > $o).
% 0.22/0.43 thf(func_def_35, type, mbox_s4: ($i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_36, type, mdia_s4: ($i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_37, type, member: mu > mu > $i > $o).
% 0.22/0.43 thf(func_def_38, type, subset: mu > mu > $i > $o).
% 0.22/0.43 thf(func_def_54, type, sK0: $i > mu).
% 0.22/0.43 thf(func_def_57, type, sK3: mu).
% 0.22/0.43 thf(func_def_58, type, sK4: mu).
% 0.22/0.43 thf(func_def_59, type, sK5: mu).
% 0.22/0.43 thf(func_def_60, type, sK6: mu > $i > mu > mu).
% 0.22/0.43 thf(f433,plain,(
% 0.22/0.43 $false),
% 0.22/0.43 inference(avatar_sat_refutation,[],[f297,f298,f308,f323,f385,f395,f411,f432])).
% 0.22/0.43 thf(f432,plain,(
% 0.22/0.43 spl1_2 | spl1_4 | spl1_6 | ~spl1_7),
% 0.22/0.43 inference(avatar_contradiction_clause,[],[f431])).
% 0.22/0.43 thf(f431,plain,(
% 0.22/0.43 $false | (spl1_2 | spl1_4 | spl1_6 | ~spl1_7)),
% 0.22/0.43 inference(subsumption_resolution,[],[f430,f282])).
% 0.22/0.43 thf(f282,plain,(
% 0.22/0.43 ($false != (exists_in_world @ sK3 @ sK2)) | spl1_2),
% 0.22/0.43 inference(avatar_component_clause,[],[f281])).
% 0.22/0.43 thf(f281,plain,(
% 0.22/0.43 spl1_2 <=> ($false = (exists_in_world @ sK3 @ sK2))),
% 0.22/0.43 introduced(avatar_definition,[new_symbols(naming,[spl1_2])])).
% 0.22/0.43 thf(f430,plain,(
% 0.22/0.43 ($false = (exists_in_world @ sK3 @ sK2)) | (spl1_4 | spl1_6 | ~spl1_7)),
% 0.22/0.43 inference(subsumption_resolution,[],[f429,f377])).
% 0.22/0.43 thf(f377,plain,(
% 0.22/0.43 ((subset @ sK3 @ sK5 @ sK2) != $true) | spl1_6),
% 0.22/0.43 inference(avatar_component_clause,[],[f376])).
% 0.22/0.43 thf(f376,plain,(
% 0.22/0.43 spl1_6 <=> ((subset @ sK3 @ sK5 @ sK2) = $true)),
% 0.22/0.43 introduced(avatar_definition,[new_symbols(naming,[spl1_6])])).
% 0.22/0.43 thf(f429,plain,(
% 0.22/0.43 ((subset @ sK3 @ sK5 @ sK2) = $true) | ($false = (exists_in_world @ sK3 @ sK2)) | (spl1_4 | ~spl1_7)),
% 0.22/0.43 inference(subsumption_resolution,[],[f421,f291])).
% 0.22/0.43 thf(f291,plain,(
% 0.22/0.43 ((exists_in_world @ sK5 @ sK2) != $false) | spl1_4),
% 0.22/0.43 inference(avatar_component_clause,[],[f290])).
% 0.22/0.43 thf(f290,plain,(
% 0.22/0.43 spl1_4 <=> ((exists_in_world @ sK5 @ sK2) = $false)),
% 0.22/0.43 introduced(avatar_definition,[new_symbols(naming,[spl1_4])])).
% 0.22/0.43 thf(f421,plain,(
% 0.22/0.43 ((exists_in_world @ sK5 @ sK2) = $false) | ((subset @ sK3 @ sK5 @ sK2) = $true) | ($false = (exists_in_world @ sK3 @ sK2)) | ~spl1_7),
% 0.22/0.43 inference(trivial_inequality_removal,[],[f417])).
% 0.22/0.43 thf(f417,plain,(
% 0.22/0.43 ($false = (exists_in_world @ sK3 @ sK2)) | ($true = $false) | ((subset @ sK3 @ sK5 @ sK2) = $true) | ((exists_in_world @ sK5 @ sK2) = $false) | ~spl1_7),
% 0.22/0.43 inference(superposition,[],[f382,f234])).
% 0.22/0.43 thf(f234,plain,(
% 0.22/0.43 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($true = (exists_in_world @ (sK6 @ X3 @ X1 @ X2) @ X1)) | ($false = (exists_in_world @ X2 @ X1)) | ($true = (subset @ X2 @ X3 @ X1)) | ((exists_in_world @ X3 @ X1) = $false)) )),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f232])).
% 0.22/0.43 thf(f232,plain,(
% 0.22/0.43 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($false = (exists_in_world @ X2 @ X1)) | ($true = (subset @ X2 @ X3 @ X1)) | ((exists_in_world @ X3 @ X1) = $false) | (((exists_in_world @ (sK6 @ X3 @ X1 @ X2) @ X1) => ((member @ (sK6 @ X3 @ X1 @ X2) @ X3 @ X1) | (~ (member @ (sK6 @ X3 @ X1 @ X2) @ X2 @ X1)))) = $false)) )),
% 0.22/0.43 inference(beta_eta_normalization,[],[f231])).
% 0.22/0.43 thf(f231,plain,(
% 0.22/0.43 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($false = (exists_in_world @ X2 @ X1)) | ((exists_in_world @ X3 @ X1) = $false) | (((^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => ((member @ Y0 @ X3 @ X1) | (~ (member @ Y0 @ X2 @ X1))))) @ (sK6 @ X3 @ X1 @ X2)) = $false) | ($true = (subset @ X2 @ X3 @ X1))) )),
% 0.22/0.43 inference(sigma_clausification,[],[f230])).
% 0.22/0.43 thf(f230,plain,(
% 0.22/0.43 ( ! [X2 : mu,X3 : mu,X1 : $i] : (((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => ((member @ Y0 @ X3 @ X1) | (~ (member @ Y0 @ X2 @ X1)))))) = $false) | ((exists_in_world @ X3 @ X1) = $false) | ($false = (exists_in_world @ X2 @ X1)) | ($true = (subset @ X2 @ X3 @ X1))) )),
% 0.22/0.43 inference(not_proxy_clausification,[],[f229])).
% 0.22/0.43 thf(f229,plain,(
% 0.22/0.43 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($true = (subset @ X2 @ X3 @ X1)) | ($false = (exists_in_world @ X2 @ X1)) | ($true = (~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => ((member @ Y0 @ X3 @ X1) | (~ (member @ Y0 @ X2 @ X1)))))))) | ((exists_in_world @ X3 @ X1) = $false)) )),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f228])).
% 0.22/0.43 thf(f228,plain,(
% 0.22/0.43 ( ! [X2 : mu,X3 : mu,X1 : $i] : (((exists_in_world @ X3 @ X1) = $false) | ($false = (exists_in_world @ X2 @ X1)) | ($true = ((subset @ X2 @ X3 @ X1) | (~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => ((member @ Y0 @ X3 @ X1) | (~ (member @ Y0 @ X2 @ X1)))))))))) )),
% 0.22/0.43 inference(not_proxy_clausification,[],[f227])).
% 0.22/0.43 thf(f227,plain,(
% 0.22/0.43 ( ! [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))))))))) = $false) | ((exists_in_world @ X3 @ X1) = $false) | ($false = (exists_in_world @ X2 @ X1))) )),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f225])).
% 0.22/0.43 thf(f225,plain,(
% 0.22/0.43 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($false = (exists_in_world @ X2 @ 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))))) = $false) | ((exists_in_world @ X3 @ X1) = $false)) )),
% 0.22/0.43 inference(not_proxy_clausification,[],[f224])).
% 0.22/0.43 thf(f224,plain,(
% 0.22/0.43 ( ! [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)))))) = $true) | ($false = (exists_in_world @ X2 @ X1)) | ((exists_in_world @ X3 @ X1) = $false)) )),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f223])).
% 0.22/0.43 thf(f223,plain,(
% 0.22/0.43 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($false = (exists_in_world @ X2 @ X1)) | (((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)) )),
% 0.22/0.43 inference(beta_eta_normalization,[],[f222])).
% 0.22/0.43 thf(f222,plain,(
% 0.22/0.43 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($false = (exists_in_world @ X2 @ X1)) | (((^[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)) )),
% 0.22/0.43 inference(pi_clausification,[],[f221])).
% 0.22/0.43 thf(f221,plain,(
% 0.22/0.43 ( ! [X2 : mu,X1 : $i] : (($false = (exists_in_world @ X2 @ X1)) | ($true = (!! @ 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))))))))))) )),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f220])).
% 0.22/0.43 thf(f220,plain,(
% 0.22/0.43 ( ! [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)) )),
% 0.22/0.43 inference(beta_eta_normalization,[],[f219])).
% 0.22/0.43 thf(f219,plain,(
% 0.22/0.43 ( ! [X2 : mu,X1 : $i] : (($true = ((^[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))) )),
% 0.22/0.43 inference(pi_clausification,[],[f218])).
% 0.22/0.43 thf(f218,plain,(
% 0.22/0.43 ( ! [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)) )),
% 0.22/0.43 inference(beta_eta_normalization,[],[f217])).
% 0.22/0.43 thf(f217,plain,(
% 0.22/0.43 ( ! [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))) )),
% 0.22/0.43 inference(pi_clausification,[],[f216])).
% 0.22/0.43 thf(f216,plain,(
% 0.22/0.43 ((!! @ $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)))))))))))))) = $true)),
% 0.22/0.43 inference(beta_eta_normalization,[],[f171])).
% 0.22/0.43 thf(f171,plain,(
% 0.22/0.43 ($true = ((^[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)))))))))))),
% 0.22/0.43 inference(definition_unfolding,[],[f122,f152,f149,f149,f165,f149,f163])).
% 0.22/0.43 thf(f163,plain,(
% 0.22/0.43 (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)))))),
% 0.22/0.43 inference(definition_unfolding,[],[f127,f139,f129])).
% 0.22/0.43 thf(f129,plain,(
% 0.22/0.43 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.22/0.43 inference(cnf_transformation,[],[f102])).
% 0.22/0.43 thf(f102,plain,(
% 0.22/0.43 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.22/0.43 inference(fool_elimination,[],[f101])).
% 0.22/0.43 thf(f101,plain,(
% 0.22/0.43 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.22/0.43 inference(rectify,[],[f2])).
% 0.22/0.43 thf(f2,axiom,(
% 0.22/0.43 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.22/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.22/0.43 thf(f139,plain,(
% 0.22/0.43 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.22/0.43 inference(cnf_transformation,[],[f86])).
% 0.22/0.43 thf(f86,plain,(
% 0.22/0.43 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.22/0.43 inference(fool_elimination,[],[f85])).
% 0.22/0.43 thf(f85,plain,(
% 0.22/0.43 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.22/0.43 inference(rectify,[],[f3])).
% 0.22/0.43 thf(f3,axiom,(
% 0.22/0.43 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))),
% 0.22/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.22/0.43 thf(f127,plain,(
% 0.22/0.43 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.22/0.43 inference(cnf_transformation,[],[f78])).
% 0.22/0.43 thf(f78,plain,(
% 0.22/0.43 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.22/0.43 inference(fool_elimination,[],[f77])).
% 0.22/0.43 thf(f77,plain,(
% 0.22/0.43 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.22/0.43 inference(rectify,[],[f9])).
% 0.22/0.43 thf(f9,axiom,(
% 0.22/0.43 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.22/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.22/0.43 thf(f165,plain,(
% 0.22/0.43 (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))))))),
% 0.22/0.43 inference(definition_unfolding,[],[f134,f162,f163,f163])).
% 0.22/0.43 thf(f162,plain,(
% 0.22/0.43 (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)))))))),
% 0.22/0.43 inference(definition_unfolding,[],[f140,f129,f139,f129,f129])).
% 0.22/0.43 thf(f140,plain,(
% 0.22/0.43 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.22/0.43 inference(cnf_transformation,[],[f116])).
% 0.22/0.43 thf(f116,plain,(
% 0.22/0.43 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.22/0.43 inference(fool_elimination,[],[f115])).
% 0.22/0.43 thf(f115,plain,(
% 0.22/0.43 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.22/0.43 inference(rectify,[],[f8])).
% 0.22/0.43 thf(f8,axiom,(
% 0.22/0.43 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.22/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.22/0.43 thf(f134,plain,(
% 0.22/0.43 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.22/0.43 inference(cnf_transformation,[],[f50])).
% 0.22/0.43 thf(f50,plain,(
% 0.22/0.43 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.22/0.43 inference(fool_elimination,[],[f49])).
% 0.22/0.43 thf(f49,plain,(
% 0.22/0.43 ((^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))) = mequiv)),
% 0.22/0.43 inference(rectify,[],[f11])).
% 0.22/0.43 thf(f11,axiom,(
% 0.22/0.43 ((^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))) = mequiv)),
% 0.22/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv)).
% 0.22/0.43 thf(f149,plain,(
% 0.22/0.43 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.22/0.43 inference(cnf_transformation,[],[f76])).
% 0.22/0.43 thf(f76,plain,(
% 0.22/0.43 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.22/0.43 inference(fool_elimination,[],[f75])).
% 0.22/0.43 thf(f75,plain,(
% 0.22/0.43 (mforall_ind = (^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : ((exists_in_world @ X2 @ X1) => (X0 @ X2 @ X1)))))),
% 0.22/0.43 inference(rectify,[],[f15])).
% 0.22/0.43 thf(f15,axiom,(
% 0.22/0.43 (mforall_ind = (^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : ((exists_in_world @ X0 @ X2) => (X3 @ X0 @ X2)))))),
% 0.22/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_ind)).
% 0.22/0.43 thf(f152,plain,(
% 0.22/0.43 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.22/0.43 inference(cnf_transformation,[],[f56])).
% 0.22/0.43 thf(f56,plain,(
% 0.22/0.43 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.22/0.43 inference(fool_elimination,[],[f55])).
% 0.22/0.43 thf(f55,plain,(
% 0.22/0.43 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.22/0.43 inference(rectify,[],[f28])).
% 0.22/0.43 thf(f28,axiom,(
% 0.22/0.43 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.22/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.22/0.43 thf(f122,plain,(
% 0.22/0.43 ($true = (mvalid @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mequiv @ (subset @ Y0 @ Y1) @ (mforall_ind @ (^[Y2 : mu]: (mimplies @ (member @ Y2 @ Y0) @ (member @ Y2 @ Y1)))))))))))),
% 0.22/0.43 inference(cnf_transformation,[],[f114])).
% 0.22/0.43 thf(f114,plain,(
% 0.22/0.43 ($true = (mvalid @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mequiv @ (subset @ Y0 @ Y1) @ (mforall_ind @ (^[Y2 : mu]: (mimplies @ (member @ Y2 @ Y0) @ (member @ Y2 @ Y1)))))))))))),
% 0.22/0.43 inference(fool_elimination,[],[f113])).
% 0.22/0.43 thf(f113,plain,(
% 0.22/0.43 (mvalid @ (mforall_ind @ (^[X0 : mu] : (mforall_ind @ (^[X1 : mu] : (mequiv @ (subset @ X0 @ X1) @ (mforall_ind @ (^[X2 : mu] : (mimplies @ (member @ X2 @ X0) @ (member @ X2 @ X1))))))))))),
% 0.22/0.43 inference(rectify,[],[f37])).
% 0.22/0.43 thf(f37,axiom,(
% 0.22/0.43 (mvalid @ (mforall_ind @ (^[X11 : mu] : (mforall_ind @ (^[X12 : mu] : (mequiv @ (subset @ X11 @ X12) @ (mforall_ind @ (^[X13 : mu] : (mimplies @ (member @ X13 @ X11) @ (member @ X13 @ X12))))))))))),
% 0.22/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn)).
% 0.22/0.43 thf(f382,plain,(
% 0.22/0.43 ((exists_in_world @ (sK6 @ sK5 @ sK2 @ sK3) @ sK2) = $false) | ~spl1_7),
% 0.22/0.43 inference(avatar_component_clause,[],[f380])).
% 0.22/0.43 thf(f380,plain,(
% 0.22/0.43 spl1_7 <=> ((exists_in_world @ (sK6 @ sK5 @ sK2 @ sK3) @ sK2) = $false)),
% 0.22/0.43 introduced(avatar_definition,[new_symbols(naming,[spl1_7])])).
% 0.22/0.43 thf(f411,plain,(
% 0.22/0.43 ~spl1_2),
% 0.22/0.43 inference(avatar_contradiction_clause,[],[f410])).
% 0.22/0.43 thf(f410,plain,(
% 0.22/0.43 $false | ~spl1_2),
% 0.22/0.43 inference(trivial_inequality_removal,[],[f405])).
% 0.22/0.43 thf(f405,plain,(
% 0.22/0.43 ($true = $false) | ~spl1_2),
% 0.22/0.43 inference(superposition,[],[f183,f283])).
% 0.22/0.43 thf(f283,plain,(
% 0.22/0.43 ($false = (exists_in_world @ sK3 @ sK2)) | ~spl1_2),
% 0.22/0.43 inference(avatar_component_clause,[],[f281])).
% 0.22/0.43 thf(f183,plain,(
% 0.22/0.43 ($true = (exists_in_world @ sK3 @ sK2))),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f181])).
% 0.22/0.43 thf(f181,plain,(
% 0.22/0.43 (((exists_in_world @ sK3 @ sK2) => (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK2) => ((subset @ sK3 @ Y1 @ sK2) | ((~ (subset @ Y0 @ Y1 @ sK2)) | (~ (subset @ sK3 @ Y0 @ sK2))))))))))) = $false)),
% 0.22/0.43 inference(beta_eta_normalization,[],[f180])).
% 0.22/0.43 thf(f180,plain,(
% 0.22/0.43 (((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK2) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ sK2) => ((subset @ Y0 @ Y2 @ sK2) | ((~ (subset @ Y1 @ Y2 @ sK2)) | (~ (subset @ Y0 @ Y1 @ sK2)))))))))))) @ sK3) = $false)),
% 0.22/0.43 inference(sigma_clausification,[],[f179])).
% 0.22/0.43 thf(f179,plain,(
% 0.22/0.43 ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK2) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ sK2) => ((subset @ Y0 @ Y2 @ sK2) | ((~ (subset @ Y1 @ Y2 @ sK2)) | (~ (subset @ Y0 @ Y1 @ sK2))))))))))))) = $false)),
% 0.22/0.43 inference(beta_eta_normalization,[],[f178])).
% 0.22/0.43 thf(f178,plain,(
% 0.22/0.43 (((^[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)))))))))))))) @ sK2) = $false)),
% 0.22/0.43 inference(sigma_clausification,[],[f177])).
% 0.22/0.43 thf(f177,plain,(
% 0.22/0.43 ((!! @ $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))))))))))))))) != $true)),
% 0.22/0.43 inference(boolean_simplification,[],[f176])).
% 0.22/0.43 thf(f176,plain,(
% 0.22/0.43 ($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))))))))))))))))))),
% 0.22/0.43 inference(beta_eta_normalization,[],[f174])).
% 0.22/0.43 thf(f174,plain,(
% 0.22/0.43 (((^[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)),
% 0.22/0.43 inference(definition_unfolding,[],[f141,f152,f149,f149,f149,f163,f162])).
% 0.22/0.43 thf(f141,plain,(
% 0.22/0.43 ((mvalid @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mforall_ind @ (^[Y2 : mu]: (mimplies @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y2)) @ (subset @ Y0 @ Y2))))))))) != $true)),
% 0.22/0.43 inference(cnf_transformation,[],[f117])).
% 0.22/0.43 thf(f117,plain,(
% 0.22/0.43 ((mvalid @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mforall_ind @ (^[Y2 : mu]: (mimplies @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y2)) @ (subset @ Y0 @ Y2))))))))) != $true)),
% 0.22/0.43 inference(flattening,[],[f82])).
% 0.22/0.43 thf(f82,plain,(
% 0.22/0.43 ~((mvalid @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mforall_ind @ (^[Y2 : mu]: (mimplies @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y2)) @ (subset @ Y0 @ Y2))))))))) = $true)),
% 0.22/0.43 inference(fool_elimination,[],[f81])).
% 0.22/0.43 thf(f81,plain,(
% 0.22/0.43 ~(mvalid @ (mforall_ind @ (^[X0 : mu] : (mforall_ind @ (^[X1 : mu] : (mforall_ind @ (^[X2 : mu] : (mimplies @ (mand @ (subset @ X0 @ X1) @ (subset @ X1 @ X2)) @ (subset @ X0 @ X2)))))))))),
% 0.22/0.43 inference(rectify,[],[f40])).
% 0.22/0.43 thf(f40,negated_conjecture,(
% 0.22/0.43 ~(mvalid @ (mforall_ind @ (^[X11 : mu] : (mforall_ind @ (^[X12 : mu] : (mforall_ind @ (^[X13 : mu] : (mimplies @ (mand @ (subset @ X11 @ X12) @ (subset @ X12 @ X13)) @ (subset @ X11 @ X13)))))))))),
% 0.22/0.43 inference(negated_conjecture,[],[f39])).
% 0.22/0.43 thf(f39,conjecture,(
% 0.22/0.43 (mvalid @ (mforall_ind @ (^[X11 : mu] : (mforall_ind @ (^[X12 : mu] : (mforall_ind @ (^[X13 : mu] : (mimplies @ (mand @ (subset @ X11 @ X12) @ (subset @ X12 @ X13)) @ (subset @ X11 @ X13)))))))))),
% 0.22/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_transitivity_of_subset)).
% 0.22/0.43 thf(f395,plain,(
% 0.22/0.43 ~spl1_6),
% 0.22/0.43 inference(avatar_contradiction_clause,[],[f394])).
% 0.22/0.43 thf(f394,plain,(
% 0.22/0.43 $false | ~spl1_6),
% 0.22/0.43 inference(trivial_inequality_removal,[],[f386])).
% 0.22/0.43 thf(f386,plain,(
% 0.22/0.43 ($true = $false) | ~spl1_6),
% 0.22/0.43 inference(superposition,[],[f378,f193])).
% 0.22/0.43 thf(f193,plain,(
% 0.22/0.43 ((subset @ sK3 @ sK5 @ sK2) = $false)),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f190])).
% 0.22/0.43 thf(f190,plain,(
% 0.22/0.43 (((subset @ sK3 @ sK5 @ sK2) | ((~ (subset @ sK4 @ sK5 @ sK2)) | (~ (subset @ sK3 @ sK4 @ sK2)))) = $false)),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f189])).
% 0.22/0.43 thf(f189,plain,(
% 0.22/0.43 (((exists_in_world @ sK5 @ sK2) => ((subset @ sK3 @ sK5 @ sK2) | ((~ (subset @ sK4 @ sK5 @ sK2)) | (~ (subset @ sK3 @ sK4 @ sK2))))) = $false)),
% 0.22/0.43 inference(beta_eta_normalization,[],[f188])).
% 0.22/0.43 thf(f188,plain,(
% 0.22/0.43 (((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => ((subset @ sK3 @ Y0 @ sK2) | ((~ (subset @ sK4 @ Y0 @ sK2)) | (~ (subset @ sK3 @ sK4 @ sK2)))))) @ sK5) = $false)),
% 0.22/0.43 inference(sigma_clausification,[],[f186])).
% 0.22/0.43 thf(f186,plain,(
% 0.22/0.43 ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => ((subset @ sK3 @ Y0 @ sK2) | ((~ (subset @ sK4 @ Y0 @ sK2)) | (~ (subset @ sK3 @ sK4 @ sK2))))))))),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f185])).
% 0.22/0.43 thf(f185,plain,(
% 0.22/0.43 (((exists_in_world @ sK4 @ sK2) => (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => ((subset @ sK3 @ Y0 @ sK2) | ((~ (subset @ sK4 @ Y0 @ sK2)) | (~ (subset @ sK3 @ sK4 @ sK2)))))))) = $false)),
% 0.22/0.43 inference(beta_eta_normalization,[],[f184])).
% 0.22/0.43 thf(f184,plain,(
% 0.22/0.43 (((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK2) => ((subset @ sK3 @ Y1 @ sK2) | ((~ (subset @ Y0 @ Y1 @ sK2)) | (~ (subset @ sK3 @ Y0 @ sK2))))))))) @ sK4) = $false)),
% 0.22/0.43 inference(sigma_clausification,[],[f182])).
% 0.22/0.43 thf(f182,plain,(
% 0.22/0.43 ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK2) => ((subset @ sK3 @ Y1 @ sK2) | ((~ (subset @ Y0 @ Y1 @ sK2)) | (~ (subset @ sK3 @ Y0 @ sK2)))))))))) = $false)),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f181])).
% 0.22/0.43 thf(f378,plain,(
% 0.22/0.43 ((subset @ sK3 @ sK5 @ sK2) = $true) | ~spl1_6),
% 0.22/0.43 inference(avatar_component_clause,[],[f376])).
% 0.22/0.43 thf(f385,plain,(
% 0.22/0.43 spl1_6 | spl1_7 | spl1_2 | ~spl1_1 | spl1_4 | ~spl1_5),
% 0.22/0.43 inference(avatar_split_clause,[],[f384,f294,f290,f278,f281,f380,f376])).
% 0.22/0.43 thf(f278,plain,(
% 0.22/0.43 spl1_1 <=> ! [X0 : mu] : (((member @ X0 @ sK3 @ sK2) = $false) | ((exists_in_world @ X0 @ sK2) = $false) | ((member @ X0 @ sK4 @ sK2) = $true))),
% 0.22/0.43 introduced(avatar_definition,[new_symbols(naming,[spl1_1])])).
% 0.22/0.43 thf(f294,plain,(
% 0.22/0.43 spl1_5 <=> ! [X0 : mu] : (((member @ X0 @ sK4 @ sK2) = $false) | ((member @ X0 @ sK5 @ sK2) = $true) | ((exists_in_world @ X0 @ sK2) = $false))),
% 0.22/0.43 introduced(avatar_definition,[new_symbols(naming,[spl1_5])])).
% 0.22/0.43 thf(f384,plain,(
% 0.22/0.43 ((exists_in_world @ (sK6 @ sK5 @ sK2 @ sK3) @ sK2) = $false) | ($false = (exists_in_world @ sK3 @ sK2)) | ((subset @ sK3 @ sK5 @ sK2) = $true) | (~spl1_1 | spl1_4 | ~spl1_5)),
% 0.22/0.43 inference(subsumption_resolution,[],[f369,f291])).
% 0.22/0.43 thf(f369,plain,(
% 0.22/0.43 ((subset @ sK3 @ sK5 @ sK2) = $true) | ((exists_in_world @ sK5 @ sK2) = $false) | ((exists_in_world @ (sK6 @ sK5 @ sK2 @ sK3) @ sK2) = $false) | ($false = (exists_in_world @ sK3 @ sK2)) | (~spl1_1 | spl1_4 | ~spl1_5)),
% 0.22/0.43 inference(trivial_inequality_removal,[],[f368])).
% 0.22/0.43 thf(f368,plain,(
% 0.22/0.43 ($true = $false) | ((exists_in_world @ sK5 @ sK2) = $false) | ((exists_in_world @ (sK6 @ sK5 @ sK2 @ sK3) @ sK2) = $false) | ((subset @ sK3 @ sK5 @ sK2) = $true) | ($false = (exists_in_world @ sK3 @ sK2)) | (~spl1_1 | spl1_4 | ~spl1_5)),
% 0.22/0.43 inference(duplicate_literal_removal,[],[f364])).
% 0.22/0.43 thf(f364,plain,(
% 0.22/0.43 ($true = $false) | ((subset @ sK3 @ sK5 @ sK2) = $true) | ($false = (exists_in_world @ sK3 @ sK2)) | ((subset @ sK3 @ sK5 @ sK2) = $true) | ((exists_in_world @ sK5 @ sK2) = $false) | ($false = (exists_in_world @ sK3 @ sK2)) | ((exists_in_world @ (sK6 @ sK5 @ sK2 @ sK3) @ sK2) = $false) | (~spl1_1 | spl1_4 | ~spl1_5)),
% 0.22/0.43 inference(superposition,[],[f361,f237])).
% 0.22/0.43 thf(f237,plain,(
% 0.22/0.43 ( ! [X2 : mu,X3 : mu,X1 : $i] : (((member @ (sK6 @ X3 @ X1 @ X2) @ X2 @ X1) = $true) | ((exists_in_world @ X3 @ X1) = $false) | ($true = (subset @ X2 @ X3 @ X1)) | ($false = (exists_in_world @ X2 @ X1))) )),
% 0.22/0.43 inference(not_proxy_clausification,[],[f235])).
% 0.22/0.43 thf(f235,plain,(
% 0.22/0.43 ( ! [X2 : mu,X3 : mu,X1 : $i] : (((~ (member @ (sK6 @ X3 @ X1 @ X2) @ X2 @ X1)) = $false) | ($true = (subset @ X2 @ X3 @ X1)) | ((exists_in_world @ X3 @ X1) = $false) | ($false = (exists_in_world @ X2 @ X1))) )),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f233])).
% 0.22/0.43 thf(f233,plain,(
% 0.22/0.43 ( ! [X2 : mu,X3 : mu,X1 : $i] : (((exists_in_world @ X3 @ X1) = $false) | ($false = ((member @ (sK6 @ X3 @ X1 @ X2) @ X3 @ X1) | (~ (member @ (sK6 @ X3 @ X1 @ X2) @ X2 @ X1)))) | ($true = (subset @ X2 @ X3 @ X1)) | ($false = (exists_in_world @ X2 @ X1))) )),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f232])).
% 0.22/0.43 thf(f361,plain,(
% 0.22/0.43 ( ! [X0 : mu] : (((member @ (sK6 @ sK5 @ sK2 @ X0) @ sK3 @ sK2) = $false) | ($false = (exists_in_world @ (sK6 @ sK5 @ sK2 @ X0) @ sK2)) | ((subset @ X0 @ sK5 @ sK2) = $true) | ((exists_in_world @ X0 @ sK2) = $false)) ) | (~spl1_1 | spl1_4 | ~spl1_5)),
% 0.22/0.43 inference(trivial_inequality_removal,[],[f360])).
% 0.22/0.43 thf(f360,plain,(
% 0.22/0.43 ( ! [X0 : mu] : (($true = $false) | ((member @ (sK6 @ sK5 @ sK2 @ X0) @ sK3 @ sK2) = $false) | ((subset @ X0 @ sK5 @ sK2) = $true) | ((exists_in_world @ X0 @ sK2) = $false) | ($false = (exists_in_world @ (sK6 @ sK5 @ sK2 @ X0) @ sK2))) ) | (~spl1_1 | spl1_4 | ~spl1_5)),
% 0.22/0.43 inference(duplicate_literal_removal,[],[f348])).
% 0.22/0.43 thf(f348,plain,(
% 0.22/0.43 ( ! [X0 : mu] : (((subset @ X0 @ sK5 @ sK2) = $true) | ($false = (exists_in_world @ (sK6 @ sK5 @ sK2 @ X0) @ sK2)) | ($false = (exists_in_world @ (sK6 @ sK5 @ sK2 @ X0) @ sK2)) | ($true = $false) | ((exists_in_world @ X0 @ sK2) = $false) | ((member @ (sK6 @ sK5 @ sK2 @ X0) @ sK3 @ sK2) = $false)) ) | (~spl1_1 | spl1_4 | ~spl1_5)),
% 0.22/0.43 inference(superposition,[],[f337,f279])).
% 0.22/0.43 thf(f279,plain,(
% 0.22/0.43 ( ! [X0 : mu] : (((member @ X0 @ sK4 @ sK2) = $true) | ((exists_in_world @ X0 @ sK2) = $false) | ((member @ X0 @ sK3 @ sK2) = $false)) ) | ~spl1_1),
% 0.22/0.43 inference(avatar_component_clause,[],[f278])).
% 0.22/0.43 thf(f337,plain,(
% 0.22/0.43 ( ! [X0 : mu] : (($false = (member @ (sK6 @ sK5 @ sK2 @ X0) @ sK4 @ sK2)) | ($false = (exists_in_world @ (sK6 @ sK5 @ sK2 @ X0) @ sK2)) | ((subset @ X0 @ sK5 @ sK2) = $true) | ((exists_in_world @ X0 @ sK2) = $false)) ) | (spl1_4 | ~spl1_5)),
% 0.22/0.43 inference(subsumption_resolution,[],[f336,f291])).
% 0.22/0.43 thf(f336,plain,(
% 0.22/0.43 ( ! [X0 : mu] : (($false = (member @ (sK6 @ sK5 @ sK2 @ X0) @ sK4 @ sK2)) | ((exists_in_world @ sK5 @ sK2) = $false) | ((exists_in_world @ X0 @ sK2) = $false) | ((subset @ X0 @ sK5 @ sK2) = $true) | ($false = (exists_in_world @ (sK6 @ sK5 @ sK2 @ X0) @ sK2))) ) | ~spl1_5),
% 0.22/0.43 inference(trivial_inequality_removal,[],[f333])).
% 0.22/0.43 thf(f333,plain,(
% 0.22/0.43 ( ! [X0 : mu] : (($true = $false) | ($false = (member @ (sK6 @ sK5 @ sK2 @ X0) @ sK4 @ sK2)) | ((exists_in_world @ sK5 @ sK2) = $false) | ($false = (exists_in_world @ (sK6 @ sK5 @ sK2 @ X0) @ sK2)) | ((subset @ X0 @ sK5 @ sK2) = $true) | ((exists_in_world @ X0 @ sK2) = $false)) ) | ~spl1_5),
% 0.22/0.43 inference(superposition,[],[f295,f236])).
% 0.22/0.43 thf(f236,plain,(
% 0.22/0.43 ( ! [X2 : mu,X3 : mu,X1 : $i] : (((member @ (sK6 @ X3 @ X1 @ X2) @ X3 @ X1) = $false) | ((exists_in_world @ X3 @ X1) = $false) | ($false = (exists_in_world @ X2 @ X1)) | ($true = (subset @ X2 @ X3 @ X1))) )),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f233])).
% 0.22/0.43 thf(f295,plain,(
% 0.22/0.43 ( ! [X0 : mu] : (((member @ X0 @ sK5 @ sK2) = $true) | ((member @ X0 @ sK4 @ sK2) = $false) | ((exists_in_world @ X0 @ sK2) = $false)) ) | ~spl1_5),
% 0.22/0.43 inference(avatar_component_clause,[],[f294])).
% 0.22/0.43 thf(f323,plain,(
% 0.22/0.43 ~spl1_4),
% 0.22/0.43 inference(avatar_contradiction_clause,[],[f322])).
% 0.22/0.43 thf(f322,plain,(
% 0.22/0.43 $false | ~spl1_4),
% 0.22/0.43 inference(trivial_inequality_removal,[],[f318])).
% 0.22/0.43 thf(f318,plain,(
% 0.22/0.43 ($true = $false) | ~spl1_4),
% 0.22/0.43 inference(superposition,[],[f191,f292])).
% 0.22/0.43 thf(f292,plain,(
% 0.22/0.43 ((exists_in_world @ sK5 @ sK2) = $false) | ~spl1_4),
% 0.22/0.43 inference(avatar_component_clause,[],[f290])).
% 0.22/0.43 thf(f191,plain,(
% 0.22/0.43 ($true = (exists_in_world @ sK5 @ sK2))),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f189])).
% 0.22/0.43 thf(f308,plain,(
% 0.22/0.43 ~spl1_3),
% 0.22/0.43 inference(avatar_contradiction_clause,[],[f307])).
% 0.22/0.43 thf(f307,plain,(
% 0.22/0.43 $false | ~spl1_3),
% 0.22/0.43 inference(trivial_inequality_removal,[],[f299])).
% 0.22/0.43 thf(f299,plain,(
% 0.22/0.43 ($true = $false) | ~spl1_3),
% 0.22/0.43 inference(superposition,[],[f287,f187])).
% 0.22/0.43 thf(f187,plain,(
% 0.22/0.43 ((exists_in_world @ sK4 @ sK2) = $true)),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f185])).
% 0.22/0.43 thf(f287,plain,(
% 0.22/0.43 ((exists_in_world @ sK4 @ sK2) = $false) | ~spl1_3),
% 0.22/0.43 inference(avatar_component_clause,[],[f285])).
% 0.22/0.43 thf(f285,plain,(
% 0.22/0.43 spl1_3 <=> ((exists_in_world @ sK4 @ sK2) = $false)),
% 0.22/0.43 introduced(avatar_definition,[new_symbols(naming,[spl1_3])])).
% 0.22/0.43 thf(f298,plain,(
% 0.22/0.43 spl1_3 | spl1_5 | spl1_4),
% 0.22/0.43 inference(avatar_split_clause,[],[f269,f290,f294,f285])).
% 0.22/0.43 thf(f269,plain,(
% 0.22/0.43 ( ! [X0 : mu] : (((exists_in_world @ X0 @ sK2) = $false) | ((member @ X0 @ sK4 @ sK2) = $false) | ((exists_in_world @ sK4 @ sK2) = $false) | ((member @ X0 @ sK5 @ sK2) = $true) | ((exists_in_world @ sK5 @ sK2) = $false)) )),
% 0.22/0.43 inference(trivial_inequality_removal,[],[f266])).
% 0.22/0.43 thf(f266,plain,(
% 0.22/0.43 ( ! [X0 : mu] : (((member @ X0 @ sK5 @ sK2) = $true) | ((exists_in_world @ sK4 @ sK2) = $false) | ((member @ X0 @ sK4 @ sK2) = $false) | ((exists_in_world @ X0 @ sK2) = $false) | ((exists_in_world @ sK5 @ sK2) = $false) | ($true = $false)) )),
% 0.22/0.43 inference(superposition,[],[f196,f245])).
% 0.22/0.43 thf(f245,plain,(
% 0.22/0.43 ( ! [X2 : mu,X3 : mu,X1 : $i,X4 : mu] : (((subset @ X2 @ X3 @ X1) = $false) | ((exists_in_world @ X3 @ X1) = $false) | ((member @ X4 @ X3 @ X1) = $true) | ((member @ X4 @ X2 @ X1) = $false) | ($false = (exists_in_world @ X2 @ X1)) | ((exists_in_world @ X4 @ X1) = $false)) )),
% 0.22/0.43 inference(not_proxy_clausification,[],[f244])).
% 0.22/0.43 thf(f244,plain,(
% 0.22/0.43 ( ! [X2 : mu,X3 : mu,X1 : $i,X4 : mu] : (($false = (exists_in_world @ X2 @ X1)) | ((subset @ X2 @ X3 @ X1) = $false) | ((exists_in_world @ X3 @ X1) = $false) | ((exists_in_world @ X4 @ X1) = $false) | ((~ (member @ X4 @ X2 @ X1)) = $true) | ((member @ X4 @ X3 @ X1) = $true)) )),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f243])).
% 0.22/0.43 thf(f243,plain,(
% 0.22/0.43 ( ! [X2 : mu,X3 : mu,X1 : $i,X4 : mu] : (((subset @ X2 @ X3 @ X1) = $false) | ((exists_in_world @ X3 @ X1) = $false) | ((exists_in_world @ X4 @ X1) = $false) | ($false = (exists_in_world @ X2 @ X1)) | (((member @ X4 @ X3 @ X1) | (~ (member @ X4 @ X2 @ X1))) = $true)) )),
% 0.22/0.43 inference(not_proxy_clausification,[],[f242])).
% 0.22/0.43 thf(f242,plain,(
% 0.22/0.43 ( ! [X2 : mu,X3 : mu,X1 : $i,X4 : mu] : (((~ (subset @ X2 @ X3 @ X1)) = $true) | (((member @ X4 @ X3 @ X1) | (~ (member @ X4 @ X2 @ X1))) = $true) | ((exists_in_world @ X3 @ X1) = $false) | ($false = (exists_in_world @ X2 @ X1)) | ((exists_in_world @ X4 @ X1) = $false)) )),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f241])).
% 0.22/0.43 thf(f241,plain,(
% 0.22/0.43 ( ! [X2 : mu,X3 : mu,X1 : $i,X4 : mu] : ((((exists_in_world @ X4 @ X1) => ((member @ X4 @ X3 @ X1) | (~ (member @ X4 @ X2 @ X1)))) = $true) | ((exists_in_world @ X3 @ X1) = $false) | ((~ (subset @ X2 @ X3 @ X1)) = $true) | ($false = (exists_in_world @ X2 @ X1))) )),
% 0.22/0.43 inference(beta_eta_normalization,[],[f240])).
% 0.22/0.43 thf(f240,plain,(
% 0.22/0.43 ( ! [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)) | ((exists_in_world @ X3 @ X1) = $false) | ($false = (exists_in_world @ X2 @ X1)) | ((~ (subset @ X2 @ X3 @ X1)) = $true)) )),
% 0.22/0.43 inference(pi_clausification,[],[f239])).
% 0.22/0.43 thf(f239,plain,(
% 0.22/0.43 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($false = (exists_in_world @ X2 @ X1)) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => ((member @ Y0 @ X3 @ X1) | (~ (member @ Y0 @ X2 @ X1)))))) = $true) | ((~ (subset @ X2 @ X3 @ X1)) = $true) | ((exists_in_world @ X3 @ X1) = $false)) )),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f238])).
% 0.22/0.43 thf(f238,plain,(
% 0.22/0.43 ( ! [X2 : mu,X3 : mu,X1 : $i] : ((((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => ((member @ Y0 @ X3 @ X1) | (~ (member @ Y0 @ X2 @ X1)))))) | (~ (subset @ X2 @ X3 @ X1))) = $true) | ((exists_in_world @ X3 @ X1) = $false) | ($false = (exists_in_world @ X2 @ X1))) )),
% 0.22/0.43 inference(not_proxy_clausification,[],[f226])).
% 0.22/0.43 thf(f226,plain,(
% 0.22/0.43 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($false = (exists_in_world @ X2 @ X1)) | ((~ ((!! @ 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) = $false)) )),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f225])).
% 0.22/0.43 thf(f196,plain,(
% 0.22/0.43 ((subset @ sK4 @ sK5 @ sK2) = $true)),
% 0.22/0.43 inference(not_proxy_clausification,[],[f195])).
% 0.22/0.43 thf(f195,plain,(
% 0.22/0.43 ((~ (subset @ sK4 @ sK5 @ sK2)) = $false)),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f192])).
% 0.22/0.43 thf(f192,plain,(
% 0.22/0.43 ($false = ((~ (subset @ sK4 @ sK5 @ sK2)) | (~ (subset @ sK3 @ sK4 @ sK2))))),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f190])).
% 0.22/0.43 thf(f297,plain,(
% 0.22/0.43 spl1_1 | spl1_2 | spl1_3),
% 0.22/0.43 inference(avatar_split_clause,[],[f270,f285,f281,f278])).
% 0.22/0.43 thf(f270,plain,(
% 0.22/0.43 ( ! [X0 : mu] : (($false = (exists_in_world @ sK3 @ sK2)) | ((member @ X0 @ sK4 @ sK2) = $true) | ((exists_in_world @ sK4 @ sK2) = $false) | ((member @ X0 @ sK3 @ sK2) = $false) | ((exists_in_world @ X0 @ sK2) = $false)) )),
% 0.22/0.43 inference(trivial_inequality_removal,[],[f264])).
% 0.22/0.43 thf(f264,plain,(
% 0.22/0.43 ( ! [X0 : mu] : (((exists_in_world @ sK4 @ sK2) = $false) | ($true = $false) | ((member @ X0 @ sK3 @ sK2) = $false) | ($false = (exists_in_world @ sK3 @ sK2)) | ((exists_in_world @ X0 @ sK2) = $false) | ((member @ X0 @ sK4 @ sK2) = $true)) )),
% 0.22/0.43 inference(superposition,[],[f245,f197])).
% 0.22/0.43 thf(f197,plain,(
% 0.22/0.43 ((subset @ sK3 @ sK4 @ sK2) = $true)),
% 0.22/0.43 inference(not_proxy_clausification,[],[f194])).
% 0.22/0.43 thf(f194,plain,(
% 0.22/0.43 ((~ (subset @ sK3 @ sK4 @ sK2)) = $false)),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f192])).
% 0.22/0.43 % SZS output end Proof for theBenchmark
% 0.22/0.43 % (1000)------------------------------
% 0.22/0.43 % (1000)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.43 % (1000)Termination reason: Refutation
% 0.22/0.43
% 0.22/0.43 % (1000)Memory used [KB]: 6012
% 0.22/0.43 % (1000)Time elapsed: 0.030 s
% 0.22/0.43 % (1000)Instructions burned: 41 (million)
% 0.22/0.43 % (1000)------------------------------
% 0.22/0.43 % (1000)------------------------------
% 0.22/0.43 % (999)Success in time 0.055 s
%------------------------------------------------------------------------------