TSTP Solution File: SET047^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET047^1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n016.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 : Sun May 5 09:03:24 EDT 2024
% Result : Theorem 0.15s 0.42s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET047^1 : TPTP v8.1.2. Released v8.1.0.
% 0.12/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36 % Computer : n016.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 16:51:23 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a TH0_THM_EQU_NAR problem
% 0.15/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.2NbixMKwtH/Vampire---4.8_19389
% 0.15/0.38 % (19658)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 Vampire---4 for (2999ds/27Mi)
% 0.15/0.38 % (19659)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.38 % (19656)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (2999ds/183Mi)
% 0.15/0.38 % (19660)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.38 % (19661)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (2999ds/275Mi)
% 0.15/0.38 % (19662)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.15/0.38 % (19657)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 Vampire---4 for (2999ds/4Mi)
% 0.15/0.38 % (19659)Instruction limit reached!
% 0.15/0.38 % (19659)------------------------------
% 0.15/0.38 % (19659)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (19663)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.15/0.38 % (19659)Termination reason: Unknown
% 0.15/0.38 % (19659)Termination phase: shuffling
% 0.15/0.38
% 0.15/0.38 % (19659)Memory used [KB]: 895
% 0.15/0.38 % (19659)Time elapsed: 0.003 s
% 0.15/0.38 % (19659)Instructions burned: 2 (million)
% 0.15/0.38 % (19659)------------------------------
% 0.15/0.38 % (19659)------------------------------
% 0.15/0.38 % (19660)Instruction limit reached!
% 0.15/0.38 % (19660)------------------------------
% 0.15/0.38 % (19660)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (19660)Termination reason: Unknown
% 0.15/0.38 % (19660)Termination phase: Property scanning
% 0.15/0.38
% 0.15/0.38 % (19660)Memory used [KB]: 1023
% 0.15/0.38 % (19660)Time elapsed: 0.004 s
% 0.15/0.38 % (19660)Instructions burned: 3 (million)
% 0.15/0.38 % (19660)------------------------------
% 0.15/0.38 % (19660)------------------------------
% 0.15/0.38 % (19663)Instruction limit reached!
% 0.15/0.38 % (19663)------------------------------
% 0.15/0.38 % (19663)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (19663)Termination reason: Unknown
% 0.15/0.38 % (19663)Termination phase: Function definition elimination
% 0.15/0.38
% 0.15/0.38 % (19663)Memory used [KB]: 1023
% 0.15/0.38 % (19661)Refutation not found, incomplete strategy
% 0.15/0.38 % (19661)------------------------------
% 0.15/0.38 % (19661)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (19663)Time elapsed: 0.003 s
% 0.15/0.38 % (19663)Instructions burned: 3 (million)
% 0.15/0.38 % (19663)------------------------------
% 0.15/0.38 % (19663)------------------------------
% 0.15/0.38 % (19661)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.38
% 0.15/0.38
% 0.15/0.38 % (19661)Memory used [KB]: 5500
% 0.15/0.38 % (19661)Time elapsed: 0.004 s
% 0.15/0.38 % (19661)Instructions burned: 3 (million)
% 0.15/0.38 % (19661)------------------------------
% 0.15/0.38 % (19661)------------------------------
% 0.15/0.38 % (19657)Instruction limit reached!
% 0.15/0.38 % (19657)------------------------------
% 0.15/0.38 % (19657)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (19657)Termination reason: Unknown
% 0.15/0.38 % (19657)Termination phase: Saturation
% 0.15/0.38
% 0.15/0.38 % (19657)Memory used [KB]: 5500
% 0.15/0.38 % (19657)Time elapsed: 0.004 s
% 0.15/0.38 % (19657)Instructions burned: 4 (million)
% 0.15/0.38 % (19657)------------------------------
% 0.15/0.38 % (19657)------------------------------
% 0.15/0.39 % (19662)Instruction limit reached!
% 0.15/0.39 % (19662)------------------------------
% 0.15/0.39 % (19662)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (19662)Termination reason: Unknown
% 0.15/0.39 % (19662)Termination phase: Saturation
% 0.15/0.39
% 0.15/0.39 % (19662)Memory used [KB]: 5628
% 0.15/0.39 % (19662)Time elapsed: 0.014 s
% 0.15/0.39 % (19662)Instructions burned: 18 (million)
% 0.15/0.39 % (19662)------------------------------
% 0.15/0.39 % (19662)------------------------------
% 0.15/0.40 % (19664)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 Vampire---4 for (2999ds/37Mi)
% 0.15/0.40 % (19658)Instruction limit reached!
% 0.15/0.40 % (19658)------------------------------
% 0.15/0.40 % (19658)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (19658)Termination reason: Unknown
% 0.15/0.40 % (19665)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 Vampire---4 for (2999ds/15Mi)
% 0.15/0.40 % (19658)Termination phase: Saturation
% 0.15/0.40
% 0.15/0.40 % (19658)Memory used [KB]: 5628
% 0.15/0.40 % (19658)Time elapsed: 0.019 s
% 0.15/0.40 % (19658)Instructions burned: 27 (million)
% 0.15/0.40 % (19658)------------------------------
% 0.15/0.40 % (19658)------------------------------
% 0.15/0.40 % (19666)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.15/0.40 % (19667)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on Vampire---4 for (2999ds/1041Mi)
% 0.15/0.40 % (19668)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.15/0.40 % (19666)Instruction limit reached!
% 0.15/0.40 % (19666)------------------------------
% 0.15/0.40 % (19666)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (19666)Termination reason: Unknown
% 0.15/0.40 % (19666)Termination phase: Saturation
% 0.15/0.40
% 0.15/0.40 % (19666)Memory used [KB]: 5500
% 0.15/0.40 % (19666)Time elapsed: 0.004 s
% 0.15/0.40 % (19666)Instructions burned: 4 (million)
% 0.15/0.40 % (19666)------------------------------
% 0.15/0.40 % (19666)------------------------------
% 0.15/0.40 % (19665)Refutation not found, incomplete strategy
% 0.15/0.40 % (19665)------------------------------
% 0.15/0.40 % (19665)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (19665)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.40
% 0.15/0.40
% 0.15/0.40 % (19665)Memory used [KB]: 5628
% 0.15/0.40 % (19665)Time elapsed: 0.006 s
% 0.15/0.40 % (19665)Instructions burned: 6 (million)
% 0.15/0.40 % (19665)------------------------------
% 0.15/0.40 % (19665)------------------------------
% 0.15/0.40 % (19668)Instruction limit reached!
% 0.15/0.40 % (19668)------------------------------
% 0.15/0.40 % (19668)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (19668)Termination reason: Unknown
% 0.15/0.40 % (19668)Termination phase: Saturation
% 0.15/0.40
% 0.15/0.40 % (19668)Memory used [KB]: 1023
% 0.15/0.40 % (19668)Time elapsed: 0.006 s
% 0.15/0.40 % (19668)Instructions burned: 7 (million)
% 0.15/0.40 % (19668)------------------------------
% 0.15/0.40 % (19668)------------------------------
% 0.15/0.41 % (19669)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on Vampire---4 for (2999ds/16Mi)
% 0.15/0.41 % (19670)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.15/0.41 % (19670)Instruction limit reached!
% 0.15/0.41 % (19670)------------------------------
% 0.15/0.41 % (19670)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.41 % (19656)First to succeed.
% 0.15/0.41 % (19670)Termination reason: Unknown
% 0.15/0.41 % (19670)Termination phase: Property scanning
% 0.15/0.41
% 0.15/0.41 % (19670)Memory used [KB]: 1023
% 0.15/0.41 % (19670)Time elapsed: 0.004 s
% 0.15/0.41 % (19670)Instructions burned: 4 (million)
% 0.15/0.41 % (19670)------------------------------
% 0.15/0.41 % (19670)------------------------------
% 0.15/0.42 % (19671)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.15/0.42 % (19671)Instruction limit reached!
% 0.15/0.42 % (19671)------------------------------
% 0.15/0.42 % (19671)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.42 % (19671)Termination reason: Unknown
% 0.15/0.42 % (19671)Termination phase: Equality resolution with deletion
% 0.15/0.42
% 0.15/0.42 % (19671)Memory used [KB]: 1023
% 0.15/0.42 % (19671)Time elapsed: 0.004 s
% 0.15/0.42 % (19671)Instructions burned: 4 (million)
% 0.15/0.42 % (19671)------------------------------
% 0.15/0.42 % (19671)------------------------------
% 0.15/0.42 % (19672)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.15/0.42 % (19673)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.15/0.42 % (19656)Refutation found. Thanks to Tanya!
% 0.15/0.42 % SZS status Theorem for Vampire---4
% 0.15/0.42 % SZS output start Proof for Vampire---4
% 0.15/0.42 thf(type_def_5, type, mworld: $tType).
% 0.15/0.42 thf(func_def_0, type, mworld: $tType).
% 0.15/0.42 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 0.15/0.42 thf(func_def_2, type, mactual: mworld).
% 0.15/0.42 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 0.15/0.42 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 0.15/0.42 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.15/0.42 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.15/0.42 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.15/0.42 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.15/0.42 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 0.15/0.42 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 0.15/0.42 thf(func_def_12, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 0.15/0.42 thf(func_def_13, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 0.15/0.42 thf(func_def_14, type, set_equal: $i > $i > mworld > $o).
% 0.15/0.42 thf(func_def_15, type, element: $i > $i > mworld > $o).
% 0.15/0.42 thf(func_def_34, type, sK3: $i > $i > $i).
% 0.15/0.42 thf(f418,plain,(
% 0.15/0.42 $false),
% 0.15/0.42 inference(avatar_sat_refutation,[],[f87,f96,f392,f402,f411,f417])).
% 0.15/0.42 thf(f417,plain,(
% 0.15/0.42 ~spl0_1 | spl0_2),
% 0.15/0.42 inference(avatar_contradiction_clause,[],[f416])).
% 0.15/0.42 thf(f416,plain,(
% 0.15/0.42 $false | (~spl0_1 | spl0_2)),
% 0.15/0.42 inference(subsumption_resolution,[],[f399,f85])).
% 0.15/0.42 thf(f85,plain,(
% 0.15/0.42 ((set_equal @ sK2 @ sK1 @ mactual) != $true) | spl0_2),
% 0.15/0.42 inference(avatar_component_clause,[],[f84])).
% 0.15/0.42 thf(f84,plain,(
% 0.15/0.42 spl0_2 <=> ((set_equal @ sK2 @ sK1 @ mactual) = $true)),
% 0.15/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.15/0.42 thf(f399,plain,(
% 0.15/0.42 ((set_equal @ sK2 @ sK1 @ mactual) = $true) | ~spl0_1),
% 0.15/0.42 inference(trivial_inequality_removal,[],[f394])).
% 0.15/0.42 thf(f394,plain,(
% 0.15/0.42 ((set_equal @ sK2 @ sK1 @ mactual) = $true) | ($true = $false) | ~spl0_1),
% 0.15/0.42 inference(superposition,[],[f82,f379])).
% 0.15/0.42 thf(f379,plain,(
% 0.15/0.42 ( ! [X0 : $i,X1 : $i] : (((set_equal @ X1 @ X0 @ mactual) = $false) | ((set_equal @ X0 @ X1 @ mactual) = $true)) )),
% 0.15/0.42 inference(trivial_inequality_removal,[],[f378])).
% 0.15/0.42 thf(f378,plain,(
% 0.15/0.42 ( ! [X0 : $i,X1 : $i] : (((set_equal @ X1 @ X0 @ mactual) = $false) | ($true = $false) | ((set_equal @ X0 @ X1 @ mactual) = $true)) )),
% 0.15/0.42 inference(duplicate_literal_removal,[],[f334])).
% 0.15/0.42 thf(f334,plain,(
% 0.15/0.42 ( ! [X0 : $i,X1 : $i] : (((set_equal @ X0 @ X1 @ mactual) = $true) | ((set_equal @ X0 @ X1 @ mactual) = $true) | ($true = $false) | ((set_equal @ X1 @ X0 @ mactual) = $false) | ($true = $false) | ((set_equal @ X1 @ X0 @ mactual) = $false)) )),
% 0.15/0.42 inference(superposition,[],[f140,f234])).
% 0.15/0.42 thf(f234,plain,(
% 0.15/0.42 ( ! [X0 : $i,X1 : $i] : (((element @ (sK3 @ X0 @ X1) @ X0 @ mactual) = $true) | ((set_equal @ X0 @ X1 @ mactual) = $true) | ((set_equal @ X1 @ X0 @ mactual) = $false)) )),
% 0.15/0.42 inference(trivial_inequality_removal,[],[f225])).
% 0.15/0.42 thf(f225,plain,(
% 0.15/0.42 ( ! [X0 : $i,X1 : $i] : (((set_equal @ X0 @ X1 @ mactual) = $true) | ($true != $true) | ((set_equal @ X1 @ X0 @ mactual) = $false) | ((element @ (sK3 @ X0 @ X1) @ X0 @ mactual) = $true)) )),
% 0.15/0.42 inference(equality_factoring,[],[f108])).
% 0.15/0.42 thf(f108,plain,(
% 0.15/0.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((element @ (sK3 @ X0 @ X1) @ X2 @ mactual) = $true) | ((set_equal @ X1 @ X2 @ mactual) = $false) | ((element @ (sK3 @ X0 @ X1) @ X0 @ mactual) = $true) | ((set_equal @ X0 @ X1 @ mactual) = $true)) )),
% 0.15/0.42 inference(trivial_inequality_removal,[],[f103])).
% 0.15/0.42 thf(f103,plain,(
% 0.15/0.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((set_equal @ X1 @ X2 @ mactual) = $false) | ((element @ (sK3 @ X0 @ X1) @ X0 @ mactual) = $true) | ($true = $false) | ((element @ (sK3 @ X0 @ X1) @ X2 @ mactual) = $true) | ((set_equal @ X0 @ X1 @ mactual) = $true)) )),
% 0.15/0.42 inference(superposition,[],[f72,f77])).
% 0.15/0.42 thf(f77,plain,(
% 0.15/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (element @ X3 @ X1 @ mactual)) | ((set_equal @ X1 @ X2 @ mactual) = $false) | ((element @ X3 @ X2 @ mactual) = $true)) )),
% 0.15/0.42 inference(binary_proxy_clausification,[],[f76])).
% 0.15/0.42 thf(f76,plain,(
% 0.15/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((element @ X3 @ X2 @ mactual) = (element @ X3 @ X1 @ mactual)) | ((set_equal @ X1 @ X2 @ mactual) = $false)) )),
% 0.15/0.42 inference(binary_proxy_clausification,[],[f75])).
% 0.15/0.42 thf(f75,plain,(
% 0.15/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((set_equal @ X1 @ X2 @ mactual) = $false) | (((element @ X3 @ X2 @ mactual) = (element @ X3 @ X1 @ mactual)) = $true)) )),
% 0.15/0.42 inference(beta_eta_normalization,[],[f74])).
% 0.15/0.42 thf(f74,plain,(
% 0.15/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((set_equal @ X1 @ X2 @ mactual) = $false) | (((^[Y0 : $i]: ((element @ Y0 @ X2 @ mactual) = (element @ Y0 @ X1 @ mactual))) @ X3) = $true)) )),
% 0.15/0.42 inference(pi_clausification,[],[f67])).
% 0.15/0.42 thf(f67,plain,(
% 0.15/0.42 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((element @ Y0 @ X2 @ mactual) = (element @ Y0 @ X1 @ mactual)))) = $true) | ((set_equal @ X1 @ X2 @ mactual) = $false)) )),
% 0.15/0.42 inference(binary_proxy_clausification,[],[f66])).
% 0.15/0.42 thf(f66,plain,(
% 0.15/0.42 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((element @ Y0 @ X2 @ mactual) = (element @ Y0 @ X1 @ mactual)))) = (set_equal @ X1 @ X2 @ mactual))) )),
% 0.15/0.42 inference(binary_proxy_clausification,[],[f65])).
% 0.15/0.42 thf(f65,plain,(
% 0.15/0.42 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((element @ Y0 @ X2 @ mactual) = (element @ Y0 @ X1 @ mactual)))) = (set_equal @ X1 @ X2 @ mactual)))) )),
% 0.15/0.42 inference(beta_eta_normalization,[],[f64])).
% 0.15/0.42 thf(f64,plain,(
% 0.15/0.42 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((element @ Y1 @ Y0 @ mactual) = (element @ Y1 @ X1 @ mactual)))) = (set_equal @ X1 @ Y0 @ mactual))) @ X2))) )),
% 0.15/0.42 inference(pi_clausification,[],[f63])).
% 0.15/0.42 thf(f63,plain,(
% 0.15/0.42 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((element @ Y1 @ Y0 @ mactual) = (element @ Y1 @ X1 @ mactual)))) = (set_equal @ X1 @ Y0 @ mactual)))) = $true)) )),
% 0.15/0.42 inference(beta_eta_normalization,[],[f62])).
% 0.15/0.42 thf(f62,plain,(
% 0.15/0.42 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((element @ Y2 @ Y1 @ mactual) = (element @ Y2 @ Y0 @ mactual)))) = (set_equal @ Y0 @ Y1 @ mactual))))) @ X1) = $true)) )),
% 0.15/0.42 inference(pi_clausification,[],[f61])).
% 0.15/0.42 thf(f61,plain,(
% 0.15/0.42 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((element @ Y2 @ Y1 @ mactual) = (element @ Y2 @ Y0 @ mactual)))) = (set_equal @ Y0 @ Y1 @ mactual)))))) = $true)),
% 0.15/0.42 inference(beta_eta_normalization,[],[f52])).
% 0.15/0.42 thf(f52,plain,(
% 0.15/0.42 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y3 @ Y4) = (Y2 @ Y4))))))) @ (set_equal @ Y0 @ Y1) @ ((^[Y2 : $i > mworld > $o]: ((^[Y3 : mworld]: (!! @ $i @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : $i]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y4 @ Y5) = (Y3 @ Y5))))))) @ (element @ Y2 @ Y0) @ (element @ Y2 @ Y1)))))))))) = $true)),
% 0.15/0.42 inference(definition_unfolding,[],[f49,f46,f44,f44,f39,f44,f39])).
% 0.15/0.42 thf(f39,plain,(
% 0.15/0.42 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) = (Y0 @ Y2))))))))),
% 0.15/0.42 inference(cnf_transformation,[],[f35])).
% 0.15/0.42 thf(f35,plain,(
% 0.15/0.42 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) = (Y0 @ Y2))))))))),
% 0.15/0.42 inference(fool_elimination,[],[f34])).
% 0.15/0.42 thf(f34,plain,(
% 0.15/0.42 (mequiv = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) <=> (X0 @ X2))))),
% 0.15/0.42 inference(rectify,[],[f6])).
% 0.15/0.42 thf(f6,axiom,(
% 0.15/0.42 (mequiv = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) <=> (X1 @ X2))))),
% 0.15/0.42 file('/export/starexec/sandbox/tmp/tmp.2NbixMKwtH/Vampire---4.8_19389',mequiv_def)).
% 0.15/0.42 thf(f44,plain,(
% 0.15/0.42 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.15/0.42 inference(cnf_transformation,[],[f33])).
% 0.15/0.42 thf(f33,plain,(
% 0.15/0.42 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.15/0.42 inference(fool_elimination,[],[f32])).
% 0.15/0.42 thf(f32,plain,(
% 0.15/0.42 ((^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2] : (X0 @ X2 @ X1))) = mforall_di)),
% 0.15/0.42 inference(rectify,[],[f9])).
% 0.15/0.42 thf(f9,axiom,(
% 0.15/0.42 ((^[X1 : $i > mworld > $o, X2 : mworld] : (! [X5] : (X1 @ X5 @ X2))) = mforall_di)),
% 0.15/0.42 file('/export/starexec/sandbox/tmp/tmp.2NbixMKwtH/Vampire---4.8_19389',mforall_di_def)).
% 0.15/0.42 thf(f46,plain,(
% 0.15/0.42 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.15/0.42 inference(cnf_transformation,[],[f15])).
% 0.15/0.42 thf(f15,plain,(
% 0.15/0.42 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.15/0.42 inference(fool_elimination,[],[f1])).
% 0.15/0.42 thf(f1,axiom,(
% 0.15/0.42 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 0.15/0.42 file('/export/starexec/sandbox/tmp/tmp.2NbixMKwtH/Vampire---4.8_19389',mlocal_def)).
% 0.15/0.42 thf(f49,plain,(
% 0.15/0.42 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (set_equal @ Y0 @ Y1) @ (mforall_di @ (^[Y2 : $i]: (mequiv @ (element @ Y2 @ Y0) @ (element @ Y2 @ Y1)))))))))) = $true)),
% 0.15/0.42 inference(cnf_transformation,[],[f21])).
% 0.15/0.42 thf(f21,plain,(
% 0.15/0.42 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (set_equal @ Y0 @ Y1) @ (mforall_di @ (^[Y2 : $i]: (mequiv @ (element @ Y2 @ Y0) @ (element @ Y2 @ Y1)))))))))) = $true)),
% 0.15/0.42 inference(fool_elimination,[],[f20])).
% 0.15/0.42 thf(f20,plain,(
% 0.15/0.42 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mequiv @ (set_equal @ X0 @ X1) @ (mforall_di @ (^[X2 : $i] : (mequiv @ (element @ X2 @ X0) @ (element @ X2 @ X1))))))))))),
% 0.15/0.42 inference(rectify,[],[f11])).
% 0.15/0.42 thf(f11,axiom,(
% 0.15/0.42 (mlocal @ (mforall_di @ (^[X5 : $i] : (mforall_di @ (^[X6 : $i] : (mequiv @ (set_equal @ X5 @ X6) @ (mforall_di @ (^[X7 : $i] : (mequiv @ (element @ X7 @ X5) @ (element @ X7 @ X6))))))))))),
% 0.15/0.42 file('/export/starexec/sandbox/tmp/tmp.2NbixMKwtH/Vampire---4.8_19389',pel43_1)).
% 0.15/0.42 thf(f72,plain,(
% 0.15/0.42 ( ! [X2 : $i,X1 : $i] : (((element @ (sK3 @ X1 @ X2) @ X2 @ mactual) = $true) | ((element @ (sK3 @ X1 @ X2) @ X1 @ mactual) = $true) | ((set_equal @ X1 @ X2 @ mactual) = $true)) )),
% 0.15/0.42 inference(binary_proxy_clausification,[],[f71])).
% 0.15/0.42 thf(f71,plain,(
% 0.15/0.42 ( ! [X2 : $i,X1 : $i] : (((element @ (sK3 @ X1 @ X2) @ X2 @ mactual) != (element @ (sK3 @ X1 @ X2) @ X1 @ mactual)) | ((set_equal @ X1 @ X2 @ mactual) = $true)) )),
% 0.15/0.42 inference(binary_proxy_clausification,[],[f70])).
% 0.15/0.42 thf(f70,plain,(
% 0.15/0.42 ( ! [X2 : $i,X1 : $i] : (((set_equal @ X1 @ X2 @ mactual) = $true) | (((element @ (sK3 @ X1 @ X2) @ X2 @ mactual) = (element @ (sK3 @ X1 @ X2) @ X1 @ mactual)) = $false)) )),
% 0.15/0.42 inference(beta_eta_normalization,[],[f69])).
% 0.15/0.42 thf(f69,plain,(
% 0.15/0.42 ( ! [X2 : $i,X1 : $i] : (((set_equal @ X1 @ X2 @ mactual) = $true) | ($false = ((^[Y0 : $i]: ((element @ Y0 @ X2 @ mactual) = (element @ Y0 @ X1 @ mactual))) @ (sK3 @ X1 @ X2)))) )),
% 0.15/0.42 inference(sigma_clausification,[],[f68])).
% 0.15/0.42 thf(f68,plain,(
% 0.15/0.42 ( ! [X2 : $i,X1 : $i] : (((set_equal @ X1 @ X2 @ mactual) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((element @ Y0 @ X2 @ mactual) = (element @ Y0 @ X1 @ mactual)))) = $false)) )),
% 0.15/0.42 inference(binary_proxy_clausification,[],[f66])).
% 0.15/0.42 thf(f140,plain,(
% 0.15/0.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((element @ (sK3 @ X0 @ X1) @ X2 @ mactual) = $false) | ((set_equal @ X0 @ X1 @ mactual) = $true) | ((set_equal @ X1 @ X2 @ mactual) = $false) | ((element @ (sK3 @ X0 @ X1) @ X0 @ mactual) = $false)) )),
% 0.15/0.42 inference(trivial_inequality_removal,[],[f123])).
% 0.15/0.42 thf(f123,plain,(
% 0.15/0.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((element @ (sK3 @ X0 @ X1) @ X2 @ mactual) = $false) | ((element @ (sK3 @ X0 @ X1) @ X0 @ mactual) = $false) | ($true = $false) | ((set_equal @ X0 @ X1 @ mactual) = $true) | ((set_equal @ X1 @ X2 @ mactual) = $false)) )),
% 0.15/0.42 inference(superposition,[],[f78,f73])).
% 0.15/0.42 thf(f73,plain,(
% 0.15/0.42 ( ! [X2 : $i,X1 : $i] : (((element @ (sK3 @ X1 @ X2) @ X2 @ mactual) = $false) | ((element @ (sK3 @ X1 @ X2) @ X1 @ mactual) = $false) | ((set_equal @ X1 @ X2 @ mactual) = $true)) )),
% 0.15/0.42 inference(binary_proxy_clausification,[],[f71])).
% 0.15/0.42 thf(f78,plain,(
% 0.15/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (element @ X3 @ X1 @ mactual)) | ((set_equal @ X1 @ X2 @ mactual) = $false) | ((element @ X3 @ X2 @ mactual) = $false)) )),
% 0.15/0.42 inference(binary_proxy_clausification,[],[f76])).
% 0.15/0.42 thf(f82,plain,(
% 0.15/0.42 ((set_equal @ sK1 @ sK2 @ mactual) = $true) | ~spl0_1),
% 0.15/0.42 inference(avatar_component_clause,[],[f80])).
% 0.15/0.42 thf(f80,plain,(
% 0.15/0.42 spl0_1 <=> ((set_equal @ sK1 @ sK2 @ mactual) = $true)),
% 0.15/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.15/0.42 thf(f411,plain,(
% 0.15/0.42 ~spl0_2 | ~spl0_4),
% 0.15/0.42 inference(avatar_contradiction_clause,[],[f410])).
% 0.15/0.42 thf(f410,plain,(
% 0.15/0.42 $false | (~spl0_2 | ~spl0_4)),
% 0.15/0.42 inference(trivial_inequality_removal,[],[f407])).
% 0.15/0.42 thf(f407,plain,(
% 0.15/0.42 ($true = $false) | (~spl0_2 | ~spl0_4)),
% 0.15/0.42 inference(superposition,[],[f86,f95])).
% 0.15/0.42 thf(f95,plain,(
% 0.15/0.42 ((set_equal @ sK2 @ sK1 @ mactual) = $false) | ~spl0_4),
% 0.15/0.42 inference(avatar_component_clause,[],[f93])).
% 0.15/0.42 thf(f93,plain,(
% 0.15/0.42 spl0_4 <=> ((set_equal @ sK2 @ sK1 @ mactual) = $false)),
% 0.15/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.15/0.42 thf(f86,plain,(
% 0.15/0.42 ((set_equal @ sK2 @ sK1 @ mactual) = $true) | ~spl0_2),
% 0.15/0.42 inference(avatar_component_clause,[],[f84])).
% 0.15/0.42 thf(f402,plain,(
% 0.15/0.42 ~spl0_1 | ~spl0_3),
% 0.15/0.42 inference(avatar_contradiction_clause,[],[f401])).
% 0.15/0.42 thf(f401,plain,(
% 0.15/0.42 $false | (~spl0_1 | ~spl0_3)),
% 0.15/0.42 inference(trivial_inequality_removal,[],[f393])).
% 0.15/0.42 thf(f393,plain,(
% 0.15/0.42 ($true = $false) | (~spl0_1 | ~spl0_3)),
% 0.15/0.42 inference(superposition,[],[f82,f91])).
% 0.15/0.42 thf(f91,plain,(
% 0.15/0.42 ((set_equal @ sK1 @ sK2 @ mactual) = $false) | ~spl0_3),
% 0.15/0.42 inference(avatar_component_clause,[],[f89])).
% 0.15/0.42 thf(f89,plain,(
% 0.15/0.42 spl0_3 <=> ((set_equal @ sK1 @ sK2 @ mactual) = $false)),
% 0.15/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.15/0.42 thf(f392,plain,(
% 0.15/0.42 spl0_1 | ~spl0_2),
% 0.15/0.42 inference(avatar_split_clause,[],[f388,f84,f80])).
% 0.15/0.42 thf(f388,plain,(
% 0.15/0.42 ((set_equal @ sK1 @ sK2 @ mactual) = $true) | ~spl0_2),
% 0.15/0.42 inference(trivial_inequality_removal,[],[f384])).
% 0.15/0.42 thf(f384,plain,(
% 0.15/0.42 ($true = $false) | ((set_equal @ sK1 @ sK2 @ mactual) = $true) | ~spl0_2),
% 0.15/0.42 inference(superposition,[],[f86,f379])).
% 0.15/0.42 thf(f96,plain,(
% 0.15/0.42 spl0_3 | spl0_4),
% 0.15/0.42 inference(avatar_split_clause,[],[f60,f93,f89])).
% 0.15/0.42 thf(f60,plain,(
% 0.15/0.42 ((set_equal @ sK2 @ sK1 @ mactual) = $false) | ((set_equal @ sK1 @ sK2 @ mactual) = $false)),
% 0.15/0.42 inference(binary_proxy_clausification,[],[f58])).
% 0.15/0.42 thf(f58,plain,(
% 0.15/0.42 ((set_equal @ sK2 @ sK1 @ mactual) != (set_equal @ sK1 @ sK2 @ mactual))),
% 0.15/0.42 inference(binary_proxy_clausification,[],[f57])).
% 0.15/0.42 thf(f57,plain,(
% 0.15/0.42 (((set_equal @ sK2 @ sK1 @ mactual) = (set_equal @ sK1 @ sK2 @ mactual)) = $false)),
% 0.15/0.42 inference(beta_eta_normalization,[],[f56])).
% 0.15/0.42 thf(f56,plain,(
% 0.15/0.42 (((^[Y0 : $i]: ((set_equal @ Y0 @ sK1 @ mactual) = (set_equal @ sK1 @ Y0 @ mactual))) @ sK2) = $false)),
% 0.15/0.42 inference(sigma_clausification,[],[f55])).
% 0.15/0.42 thf(f55,plain,(
% 0.15/0.42 ((!! @ $i @ (^[Y0 : $i]: ((set_equal @ Y0 @ sK1 @ mactual) = (set_equal @ sK1 @ Y0 @ mactual)))) = $false)),
% 0.15/0.42 inference(beta_eta_normalization,[],[f54])).
% 0.15/0.42 thf(f54,plain,(
% 0.15/0.42 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((set_equal @ Y1 @ Y0 @ mactual) = (set_equal @ Y0 @ Y1 @ mactual))))) @ sK1) = $false)),
% 0.15/0.42 inference(sigma_clausification,[],[f53])).
% 0.15/0.42 thf(f53,plain,(
% 0.15/0.42 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((set_equal @ Y1 @ Y0 @ mactual) = (set_equal @ Y0 @ Y1 @ mactual)))))) != $true)),
% 0.15/0.42 inference(beta_eta_normalization,[],[f51])).
% 0.15/0.42 thf(f51,plain,(
% 0.15/0.42 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y3 @ Y4) = (Y2 @ Y4))))))) @ (set_equal @ Y0 @ Y1) @ (set_equal @ Y1 @ Y0))))))) != $true)),
% 0.15/0.42 inference(definition_unfolding,[],[f45,f46,f44,f44,f39])).
% 0.15/0.42 thf(f45,plain,(
% 0.15/0.42 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (set_equal @ Y0 @ Y1) @ (set_equal @ Y1 @ Y0))))))) != $true)),
% 0.15/0.42 inference(cnf_transformation,[],[f38])).
% 0.15/0.42 thf(f38,plain,(
% 0.15/0.42 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (set_equal @ Y0 @ Y1) @ (set_equal @ Y1 @ Y0))))))) != $true)),
% 0.15/0.42 inference(flattening,[],[f31])).
% 0.15/0.42 thf(f31,plain,(
% 0.15/0.42 ~((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (set_equal @ Y0 @ Y1) @ (set_equal @ Y1 @ Y0))))))) = $true)),
% 0.15/0.42 inference(fool_elimination,[],[f30])).
% 0.15/0.42 thf(f30,plain,(
% 0.15/0.42 ~(mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mequiv @ (set_equal @ X0 @ X1) @ (set_equal @ X1 @ X0)))))))),
% 0.15/0.42 inference(rectify,[],[f13])).
% 0.15/0.42 thf(f13,negated_conjecture,(
% 0.15/0.42 ~(mlocal @ (mforall_di @ (^[X5 : $i] : (mforall_di @ (^[X6 : $i] : (mequiv @ (set_equal @ X5 @ X6) @ (set_equal @ X6 @ X5)))))))),
% 0.15/0.42 inference(negated_conjecture,[],[f12])).
% 0.15/0.42 thf(f12,conjecture,(
% 0.15/0.42 (mlocal @ (mforall_di @ (^[X5 : $i] : (mforall_di @ (^[X6 : $i] : (mequiv @ (set_equal @ X5 @ X6) @ (set_equal @ X6 @ X5)))))))),
% 0.15/0.42 file('/export/starexec/sandbox/tmp/tmp.2NbixMKwtH/Vampire---4.8_19389',pel43)).
% 0.15/0.42 thf(f87,plain,(
% 0.15/0.42 spl0_1 | spl0_2),
% 0.15/0.42 inference(avatar_split_clause,[],[f59,f84,f80])).
% 0.15/0.42 thf(f59,plain,(
% 0.15/0.42 ((set_equal @ sK2 @ sK1 @ mactual) = $true) | ((set_equal @ sK1 @ sK2 @ mactual) = $true)),
% 0.15/0.42 inference(binary_proxy_clausification,[],[f58])).
% 0.15/0.42 % SZS output end Proof for Vampire---4
% 0.15/0.42 % (19656)------------------------------
% 0.15/0.42 % (19656)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.42 % (19656)Termination reason: Refutation
% 0.15/0.42
% 0.15/0.42 % (19656)Memory used [KB]: 5756
% 0.15/0.42 % (19656)Time elapsed: 0.037 s
% 0.15/0.42 % (19656)Instructions burned: 54 (million)
% 0.15/0.42 % (19656)------------------------------
% 0.15/0.42 % (19656)------------------------------
% 0.15/0.42 % (19655)Success in time 0.045 s
% 0.15/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------