TSTP Solution File: SET047^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET047^1 : TPTP v8.2.0. 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 : n023.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 03:08:16 EDT 2024
% Result : Theorem 0.08s 0.35s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SET047^1 : TPTP v8.2.0. Released v8.1.0.
% 0.00/0.10 % 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
% 0.08/0.29 % Computer : n023.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Mon May 20 12:47:53 EDT 2024
% 0.08/0.30 % CPUTime :
% 0.08/0.30 This is a TH0_THM_EQU_NAR problem
% 0.08/0.30 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.31 % (26128)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.08/0.31 % (26128)Instruction limit reached!
% 0.08/0.31 % (26128)------------------------------
% 0.08/0.31 % (26128)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.08/0.31 % (26128)Termination reason: Unknown
% 0.08/0.31 % (26128)Termination phase: Saturation
% 0.08/0.31
% 0.08/0.31 % (26128)Memory used [KB]: 5500
% 0.08/0.31 % (26128)Time elapsed: 0.002 s
% 0.08/0.31 % (26128)Instructions burned: 4 (million)
% 0.08/0.31 % (26128)------------------------------
% 0.08/0.31 % (26128)------------------------------
% 0.08/0.31 % (26129)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)
% 0.08/0.31 % (26132)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)
% 0.08/0.31 % (26129)Instruction limit reached!
% 0.08/0.31 % (26129)------------------------------
% 0.08/0.31 % (26129)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.08/0.31 % (26129)Termination reason: Unknown
% 0.08/0.31 % (26129)Termination phase: Property scanning
% 0.08/0.31
% 0.08/0.31 % (26129)Memory used [KB]: 1023
% 0.08/0.31 % (26129)Time elapsed: 0.002 s
% 0.08/0.31 % (26129)Instructions burned: 2 (million)
% 0.08/0.31 % (26129)------------------------------
% 0.08/0.31 % (26129)------------------------------
% 0.08/0.32 % (26130)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)
% 0.08/0.32 % (26132)Instruction limit reached!
% 0.08/0.32 % (26132)------------------------------
% 0.08/0.32 % (26132)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.08/0.32 % (26132)Termination reason: Unknown
% 0.08/0.32 % (26132)Termination phase: Saturation
% 0.08/0.32
% 0.08/0.32 % (26132)Memory used [KB]: 5500
% 0.08/0.32 % (26132)Time elapsed: 0.003 s
% 0.08/0.32 % (26132)Instructions burned: 5 (million)
% 0.08/0.32 % (26132)------------------------------
% 0.08/0.32 % (26132)------------------------------
% 0.08/0.32 % (26130)Refutation not found, incomplete strategy
% 0.08/0.32 % (26130)------------------------------
% 0.08/0.32 % (26130)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.08/0.32 % (26130)Termination reason: Refutation not found, incomplete strategy
% 0.08/0.32
% 0.08/0.32
% 0.08/0.32 % (26130)Memory used [KB]: 5500
% 0.08/0.32 % (26130)Time elapsed: 0.003 s
% 0.08/0.32 % (26130)Instructions burned: 3 (million)
% 0.08/0.32 % (26130)------------------------------
% 0.08/0.32 % (26130)------------------------------
% 0.08/0.32 % (26126)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)
% 0.08/0.32 % (26125)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.08/0.32 % (26127)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)
% 0.08/0.32 % (26126)Instruction limit reached!
% 0.08/0.32 % (26126)------------------------------
% 0.08/0.32 % (26126)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.08/0.32 % (26126)Termination reason: Unknown
% 0.08/0.32 % (26126)Termination phase: Saturation
% 0.08/0.32
% 0.08/0.32 % (26126)Memory used [KB]: 5500
% 0.08/0.32 % (26126)Time elapsed: 0.004 s
% 0.08/0.32 % (26126)Instructions burned: 4 (million)
% 0.08/0.32 % (26126)------------------------------
% 0.08/0.32 % (26126)------------------------------
% 0.08/0.32 % (26133)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)
% 0.08/0.32 % (26134)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)
% 0.08/0.33 % (26134)Refutation not found, incomplete strategy
% 0.08/0.33 % (26134)------------------------------
% 0.08/0.33 % (26134)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.08/0.33 % (26134)Termination reason: Refutation not found, incomplete strategy
% 0.08/0.33
% 0.08/0.33
% 0.08/0.33 % (26134)Memory used [KB]: 5500
% 0.08/0.33 % (26134)Time elapsed: 0.004 s
% 0.08/0.33 % (26134)Instructions burned: 6 (million)
% 0.08/0.33 % (26134)------------------------------
% 0.08/0.33 % (26134)------------------------------
% 0.08/0.33 % (26127)Instruction limit reached!
% 0.08/0.33 % (26127)------------------------------
% 0.08/0.33 % (26127)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.08/0.33 % (26127)Termination reason: Unknown
% 0.08/0.33 % (26127)Termination phase: Saturation
% 0.08/0.33
% 0.08/0.33 % (26127)Memory used [KB]: 5628
% 0.08/0.33 % (26127)Time elapsed: 0.010 s
% 0.08/0.33 % (26127)Instructions burned: 28 (million)
% 0.08/0.33 % (26127)------------------------------
% 0.08/0.33 % (26127)------------------------------
% 0.08/0.33 % (26131)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.08/0.33 % (26137)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.08/0.33 % (26131)Instruction limit reached!
% 0.08/0.33 % (26131)------------------------------
% 0.08/0.33 % (26131)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.08/0.33 % (26131)Termination reason: Unknown
% 0.08/0.33 % (26131)Termination phase: Saturation
% 0.08/0.33
% 0.08/0.33 % (26131)Memory used [KB]: 5628
% 0.08/0.33 % (26131)Time elapsed: 0.008 s
% 0.08/0.33 % (26131)Instructions burned: 18 (million)
% 0.08/0.33 % (26131)------------------------------
% 0.08/0.33 % (26131)------------------------------
% 0.08/0.34 % (26133)Instruction limit reached!
% 0.08/0.34 % (26133)------------------------------
% 0.08/0.34 % (26133)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.08/0.34 % (26133)Termination reason: Unknown
% 0.08/0.34 % (26133)Termination phase: Saturation
% 0.08/0.34
% 0.08/0.34 % (26133)Memory used [KB]: 5756
% 0.08/0.34 % (26133)Time elapsed: 0.017 s
% 0.08/0.34 % (26133)Instructions burned: 39 (million)
% 0.08/0.34 % (26133)------------------------------
% 0.08/0.34 % (26133)------------------------------
% 0.08/0.34 % (26137)Instruction limit reached!
% 0.08/0.34 % (26137)------------------------------
% 0.08/0.34 % (26137)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.08/0.34 % (26137)Termination reason: Unknown
% 0.08/0.34 % (26137)Termination phase: Saturation
% 0.08/0.34
% 0.08/0.34 % (26137)Memory used [KB]: 1023
% 0.08/0.34 % (26137)Time elapsed: 0.005 s
% 0.08/0.34 % (26137)Instructions burned: 7 (million)
% 0.08/0.34 % (26137)------------------------------
% 0.08/0.34 % (26137)------------------------------
% 0.08/0.34 % (26135)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)
% 0.08/0.34 % (26135)Instruction limit reached!
% 0.08/0.34 % (26135)------------------------------
% 0.08/0.34 % (26135)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.08/0.34 % (26135)Termination reason: Unknown
% 0.08/0.34 % (26135)Termination phase: Preprocessing 1
% 0.08/0.34
% 0.08/0.34 % (26135)Memory used [KB]: 1023
% 0.08/0.34 % (26135)Time elapsed: 0.002 s
% 0.08/0.34 % (26135)Instructions burned: 3 (million)
% 0.08/0.34 % (26135)------------------------------
% 0.08/0.34 % (26135)------------------------------
% 0.08/0.34 % (26136)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 theBenchmark for (2999ds/1041Mi)
% 0.08/0.34 % (26138)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.08/0.35 % (26125)First to succeed.
% 0.08/0.35 % (26140)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 theBenchmark for (2999ds/3Mi)
% 0.08/0.35 % (26140)Instruction limit reached!
% 0.08/0.35 % (26140)------------------------------
% 0.08/0.35 % (26140)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.08/0.35 % (26140)Termination reason: Unknown
% 0.08/0.35 % (26140)Termination phase: Property scanning
% 0.08/0.35
% 0.08/0.35 % (26140)Memory used [KB]: 1023
% 0.08/0.35 % (26139)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 theBenchmark for (2999ds/3Mi)
% 0.08/0.35 % (26140)Time elapsed: 0.003 s
% 0.08/0.35 % (26140)Instructions burned: 4 (million)
% 0.08/0.35 % (26140)------------------------------
% 0.08/0.35 % (26140)------------------------------
% 0.08/0.35 % (26125)Refutation found. Thanks to Tanya!
% 0.08/0.35 % SZS status Theorem for theBenchmark
% 0.08/0.35 % SZS output start Proof for theBenchmark
% 0.08/0.35 thf(type_def_5, type, mworld: $tType).
% 0.08/0.35 thf(func_def_0, type, mworld: $tType).
% 0.08/0.35 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 0.08/0.35 thf(func_def_2, type, mactual: mworld).
% 0.08/0.35 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 0.08/0.35 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 0.08/0.35 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.08/0.35 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.08/0.35 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.08/0.35 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.08/0.35 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 0.08/0.35 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 0.08/0.35 thf(func_def_12, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 0.08/0.35 thf(func_def_13, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 0.08/0.35 thf(func_def_14, type, set_equal: $i > $i > mworld > $o).
% 0.08/0.35 thf(func_def_15, type, element: $i > $i > mworld > $o).
% 0.08/0.35 thf(func_def_32, type, sK1: $i > $i > $i).
% 0.08/0.35 thf(f482,plain,(
% 0.08/0.35 $false),
% 0.08/0.35 inference(avatar_sat_refutation,[],[f87,f96,f102,f462,f478,f481])).
% 0.08/0.35 thf(f481,plain,(
% 0.08/0.35 spl0_3 | ~spl0_4),
% 0.08/0.35 inference(avatar_contradiction_clause,[],[f480])).
% 0.08/0.35 thf(f480,plain,(
% 0.08/0.35 $false | (spl0_3 | ~spl0_4)),
% 0.08/0.35 inference(subsumption_resolution,[],[f471,f90])).
% 0.08/0.35 thf(f90,plain,(
% 0.08/0.35 ((set_equal @ sK3 @ sK2 @ mactual) != $false) | spl0_3),
% 0.08/0.35 inference(avatar_component_clause,[],[f89])).
% 0.08/0.35 thf(f89,plain,(
% 0.08/0.35 spl0_3 <=> ((set_equal @ sK3 @ sK2 @ mactual) = $false)),
% 0.08/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.08/0.35 thf(f471,plain,(
% 0.08/0.35 ((set_equal @ sK3 @ sK2 @ mactual) = $false) | ~spl0_4),
% 0.08/0.35 inference(trivial_inequality_removal,[],[f464])).
% 0.08/0.35 thf(f464,plain,(
% 0.08/0.35 ((set_equal @ sK3 @ sK2 @ mactual) = $false) | ($true = $false) | ~spl0_4),
% 0.08/0.35 inference(superposition,[],[f95,f450])).
% 0.08/0.35 thf(f450,plain,(
% 0.08/0.35 ( ! [X0 : $i,X1 : $i] : (($true = (set_equal @ X0 @ X1 @ mactual)) | ($false = (set_equal @ X1 @ X0 @ mactual))) )),
% 0.08/0.35 inference(trivial_inequality_removal,[],[f449])).
% 0.08/0.35 thf(f449,plain,(
% 0.08/0.35 ( ! [X0 : $i,X1 : $i] : (($false = (set_equal @ X1 @ X0 @ mactual)) | ($true = $false) | ($true = (set_equal @ X0 @ X1 @ mactual))) )),
% 0.08/0.35 inference(duplicate_literal_removal,[],[f400])).
% 0.08/0.35 thf(f400,plain,(
% 0.08/0.35 ( ! [X0 : $i,X1 : $i] : (($false = (set_equal @ X1 @ X0 @ mactual)) | ($true = (set_equal @ X0 @ X1 @ mactual)) | ($true = (set_equal @ X0 @ X1 @ mactual)) | ($true = $false) | ($false = (set_equal @ X1 @ X0 @ mactual))) )),
% 0.08/0.35 inference(superposition,[],[f390,f298])).
% 0.08/0.35 thf(f298,plain,(
% 0.08/0.35 ( ! [X0 : $i,X1 : $i] : (($false = (element @ (sK1 @ X0 @ X1) @ X0 @ mactual)) | ($false = (set_equal @ X1 @ X0 @ mactual)) | ($true = (set_equal @ X0 @ X1 @ mactual))) )),
% 0.08/0.35 inference(trivial_inequality_removal,[],[f289])).
% 0.08/0.35 thf(f289,plain,(
% 0.08/0.35 ( ! [X0 : $i,X1 : $i] : (($false != $false) | ($false = (element @ (sK1 @ X0 @ X1) @ X0 @ mactual)) | ($false = (set_equal @ X1 @ X0 @ mactual)) | ($true = (set_equal @ X0 @ X1 @ mactual))) )),
% 0.08/0.35 inference(equality_factoring,[],[f129])).
% 0.08/0.35 thf(f129,plain,(
% 0.08/0.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (element @ (sK1 @ X0 @ X1) @ X2 @ mactual)) | ($false = (set_equal @ X1 @ X2 @ mactual)) | ($false = (element @ (sK1 @ X0 @ X1) @ X0 @ mactual)) | ($true = (set_equal @ X0 @ X1 @ mactual))) )),
% 0.08/0.35 inference(trivial_inequality_removal,[],[f109])).
% 0.08/0.35 thf(f109,plain,(
% 0.08/0.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (set_equal @ X1 @ X2 @ mactual)) | ($true = $false) | ($true = (set_equal @ X0 @ X1 @ mactual)) | ($false = (element @ (sK1 @ X0 @ X1) @ X0 @ mactual)) | ($false = (element @ (sK1 @ X0 @ X1) @ X2 @ mactual))) )),
% 0.08/0.35 inference(superposition,[],[f65,f70])).
% 0.08/0.35 thf(f70,plain,(
% 0.08/0.35 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (element @ X3 @ X1 @ mactual)) | ($false = (element @ X3 @ X2 @ mactual)) | ($false = (set_equal @ X1 @ X2 @ mactual))) )),
% 0.08/0.35 inference(binary_proxy_clausification,[],[f68])).
% 0.08/0.35 thf(f68,plain,(
% 0.08/0.35 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (set_equal @ X1 @ X2 @ mactual)) | ((element @ X3 @ X2 @ mactual) = (element @ X3 @ X1 @ mactual))) )),
% 0.08/0.35 inference(binary_proxy_clausification,[],[f67])).
% 0.08/0.35 thf(f67,plain,(
% 0.08/0.35 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (set_equal @ X1 @ X2 @ mactual)) | (((element @ X3 @ X1 @ mactual) = (element @ X3 @ X2 @ mactual)) = $true)) )),
% 0.08/0.35 inference(beta_eta_normalization,[],[f66])).
% 0.08/0.35 thf(f66,plain,(
% 0.08/0.35 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((element @ Y0 @ X1 @ mactual) = (element @ Y0 @ X2 @ mactual))) @ X3)) | ($false = (set_equal @ X1 @ X2 @ mactual))) )),
% 0.08/0.35 inference(pi_clausification,[],[f59])).
% 0.08/0.35 thf(f59,plain,(
% 0.08/0.35 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((element @ Y0 @ X1 @ mactual) = (element @ Y0 @ X2 @ mactual)))) = $true) | ($false = (set_equal @ X1 @ X2 @ mactual))) )),
% 0.08/0.35 inference(binary_proxy_clausification,[],[f58])).
% 0.08/0.35 thf(f58,plain,(
% 0.08/0.35 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((element @ Y0 @ X1 @ mactual) = (element @ Y0 @ X2 @ mactual)))) = (set_equal @ X1 @ X2 @ mactual))) )),
% 0.08/0.35 inference(binary_proxy_clausification,[],[f57])).
% 0.08/0.35 thf(f57,plain,(
% 0.08/0.35 ( ! [X2 : $i,X1 : $i] : (($true = ((set_equal @ X1 @ X2 @ mactual) = (!! @ $i @ (^[Y0 : $i]: ((element @ Y0 @ X1 @ mactual) = (element @ Y0 @ X2 @ mactual))))))) )),
% 0.08/0.35 inference(beta_eta_normalization,[],[f56])).
% 0.08/0.35 thf(f56,plain,(
% 0.08/0.35 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((set_equal @ X1 @ Y0 @ mactual) = (!! @ $i @ (^[Y1 : $i]: ((element @ Y1 @ X1 @ mactual) = (element @ Y1 @ Y0 @ mactual)))))) @ X2))) )),
% 0.08/0.35 inference(pi_clausification,[],[f55])).
% 0.08/0.35 thf(f55,plain,(
% 0.08/0.35 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((set_equal @ X1 @ Y0 @ mactual) = (!! @ $i @ (^[Y1 : $i]: ((element @ Y1 @ X1 @ mactual) = (element @ Y1 @ Y0 @ mactual))))))))) )),
% 0.08/0.35 inference(beta_eta_normalization,[],[f54])).
% 0.08/0.35 thf(f54,plain,(
% 0.08/0.35 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((set_equal @ Y0 @ Y1 @ mactual) = (!! @ $i @ (^[Y2 : $i]: ((element @ Y2 @ Y0 @ mactual) = (element @ Y2 @ Y1 @ mactual)))))))) @ X1) = $true)) )),
% 0.08/0.35 inference(pi_clausification,[],[f53])).
% 0.08/0.35 thf(f53,plain,(
% 0.08/0.35 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((set_equal @ Y0 @ Y1 @ mactual) = (!! @ $i @ (^[Y2 : $i]: ((element @ Y2 @ Y0 @ mactual) = (element @ Y2 @ Y1 @ mactual))))))))))),
% 0.08/0.35 inference(beta_eta_normalization,[],[f52])).
% 0.08/0.35 thf(f52,plain,(
% 0.08/0.35 (((^[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]: ((Y2 @ Y4) = (Y3 @ 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]: ((Y3 @ Y5) = (Y4 @ Y5))))))) @ (element @ Y2 @ Y0) @ (element @ Y2 @ Y1)))))))))) = $true)),
% 0.08/0.35 inference(definition_unfolding,[],[f49,f41,f39,f39,f50,f39,f50])).
% 0.08/0.35 thf(f50,plain,(
% 0.08/0.35 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 0.08/0.35 inference(cnf_transformation,[],[f20])).
% 0.08/0.35 thf(f20,plain,(
% 0.08/0.35 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 0.08/0.35 inference(fool_elimination,[],[f19])).
% 0.08/0.35 thf(f19,plain,(
% 0.08/0.35 (mequiv = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) <=> (X1 @ X2))))),
% 0.08/0.35 inference(rectify,[],[f6])).
% 0.08/0.35 thf(f6,axiom,(
% 0.08/0.35 (mequiv = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) <=> (X3 @ X2))))),
% 0.08/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv_def)).
% 0.08/0.35 thf(f39,plain,(
% 0.08/0.35 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.08/0.35 inference(cnf_transformation,[],[f16])).
% 0.08/0.35 thf(f16,plain,(
% 0.08/0.35 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.08/0.35 inference(fool_elimination,[],[f15])).
% 0.08/0.35 thf(f15,plain,(
% 0.08/0.35 ((^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2] : (X0 @ X2 @ X1))) = mforall_di)),
% 0.08/0.35 inference(rectify,[],[f9])).
% 0.08/0.35 thf(f9,axiom,(
% 0.08/0.35 ((^[X1 : $i > mworld > $o, X2 : mworld] : (! [X5] : (X1 @ X5 @ X2))) = mforall_di)),
% 0.08/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_di_def)).
% 0.08/0.35 thf(f41,plain,(
% 0.08/0.35 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.08/0.35 inference(cnf_transformation,[],[f27])).
% 0.08/0.35 thf(f27,plain,(
% 0.08/0.35 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.08/0.35 inference(fool_elimination,[],[f1])).
% 0.08/0.35 thf(f1,axiom,(
% 0.08/0.35 (mlocal = (^[X0 : mworld > $o] : (X0 @ mactual)))),
% 0.08/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def)).
% 0.08/0.35 thf(f49,plain,(
% 0.08/0.35 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (set_equal @ Y0 @ Y1) @ (mforall_di @ (^[Y2 : $i]: (mequiv @ (element @ Y2 @ Y0) @ (element @ Y2 @ Y1)))))))))))),
% 0.08/0.35 inference(cnf_transformation,[],[f37])).
% 0.08/0.35 thf(f37,plain,(
% 0.08/0.35 ($true = (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)))))))))))),
% 0.08/0.35 inference(fool_elimination,[],[f36])).
% 0.08/0.35 thf(f36,plain,(
% 0.08/0.35 (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))))))))))),
% 0.08/0.35 inference(rectify,[],[f11])).
% 0.08/0.35 thf(f11,axiom,(
% 0.08/0.35 (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))))))))))),
% 0.08/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel43_1)).
% 0.08/0.35 thf(f65,plain,(
% 0.08/0.35 ( ! [X2 : $i,X1 : $i] : (($false = (element @ (sK1 @ X1 @ X2) @ X2 @ mactual)) | ($true = (set_equal @ X1 @ X2 @ mactual)) | ($false = (element @ (sK1 @ X1 @ X2) @ X1 @ mactual))) )),
% 0.08/0.35 inference(binary_proxy_clausification,[],[f63])).
% 0.08/0.35 thf(f63,plain,(
% 0.08/0.35 ( ! [X2 : $i,X1 : $i] : (($true = (set_equal @ X1 @ X2 @ mactual)) | ((element @ (sK1 @ X1 @ X2) @ X1 @ mactual) != (element @ (sK1 @ X1 @ X2) @ X2 @ mactual))) )),
% 0.08/0.35 inference(binary_proxy_clausification,[],[f62])).
% 0.08/0.35 thf(f62,plain,(
% 0.08/0.35 ( ! [X2 : $i,X1 : $i] : (($true = (set_equal @ X1 @ X2 @ mactual)) | ($false = ((element @ (sK1 @ X1 @ X2) @ X1 @ mactual) = (element @ (sK1 @ X1 @ X2) @ X2 @ mactual)))) )),
% 0.08/0.35 inference(beta_eta_normalization,[],[f61])).
% 0.08/0.35 thf(f61,plain,(
% 0.08/0.35 ( ! [X2 : $i,X1 : $i] : (($false = ((^[Y0 : $i]: ((element @ Y0 @ X1 @ mactual) = (element @ Y0 @ X2 @ mactual))) @ (sK1 @ X1 @ X2))) | ($true = (set_equal @ X1 @ X2 @ mactual))) )),
% 0.08/0.35 inference(sigma_clausification,[],[f60])).
% 0.08/0.35 thf(f60,plain,(
% 0.08/0.35 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((element @ Y0 @ X1 @ mactual) = (element @ Y0 @ X2 @ mactual)))) = $false) | ($true = (set_equal @ X1 @ X2 @ mactual))) )),
% 0.08/0.35 inference(binary_proxy_clausification,[],[f58])).
% 0.08/0.35 thf(f390,plain,(
% 0.08/0.35 ( ! [X0 : $i,X1 : $i] : (($true = (element @ (sK1 @ X0 @ X1) @ X0 @ mactual)) | ($false = (set_equal @ X1 @ X0 @ mactual)) | ($true = (set_equal @ X0 @ X1 @ mactual))) )),
% 0.08/0.35 inference(trivial_inequality_removal,[],[f389])).
% 0.08/0.35 thf(f389,plain,(
% 0.08/0.35 ( ! [X0 : $i,X1 : $i] : (($false = (set_equal @ X1 @ X0 @ mactual)) | ($true = (element @ (sK1 @ X0 @ X1) @ X0 @ mactual)) | ($true = (set_equal @ X0 @ X1 @ mactual)) | ($true = $false)) )),
% 0.08/0.35 inference(duplicate_literal_removal,[],[f375])).
% 0.08/0.35 thf(f375,plain,(
% 0.08/0.35 ( ! [X0 : $i,X1 : $i] : (($true = (element @ (sK1 @ X0 @ X1) @ X0 @ mactual)) | ($false = (set_equal @ X1 @ X0 @ mactual)) | ($true = (set_equal @ X0 @ X1 @ mactual)) | ($false = (set_equal @ X1 @ X0 @ mactual)) | ($true = $false) | ($true = (set_equal @ X0 @ X1 @ mactual))) )),
% 0.08/0.35 inference(superposition,[],[f64,f334])).
% 0.08/0.35 thf(f334,plain,(
% 0.08/0.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (element @ (sK1 @ X0 @ X1) @ X2 @ mactual)) | ($false = (set_equal @ X2 @ X0 @ mactual)) | ($true = (set_equal @ X0 @ X1 @ mactual)) | ($false = (set_equal @ X1 @ X0 @ mactual))) )),
% 0.08/0.35 inference(trivial_inequality_removal,[],[f317])).
% 0.08/0.35 thf(f317,plain,(
% 0.08/0.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = $false) | ($false = (element @ (sK1 @ X0 @ X1) @ X2 @ mactual)) | ($true = (set_equal @ X0 @ X1 @ mactual)) | ($false = (set_equal @ X1 @ X0 @ mactual)) | ($false = (set_equal @ X2 @ X0 @ mactual))) )),
% 0.08/0.35 inference(superposition,[],[f69,f298])).
% 0.08/0.35 thf(f69,plain,(
% 0.08/0.35 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (element @ X3 @ X2 @ mactual)) | ($false = (set_equal @ X1 @ X2 @ mactual)) | ($false = (element @ X3 @ X1 @ mactual))) )),
% 0.08/0.35 inference(binary_proxy_clausification,[],[f68])).
% 0.08/0.35 thf(f64,plain,(
% 0.08/0.35 ( ! [X2 : $i,X1 : $i] : (($true = (element @ (sK1 @ X1 @ X2) @ X2 @ mactual)) | ($true = (set_equal @ X1 @ X2 @ mactual)) | ($true = (element @ (sK1 @ X1 @ X2) @ X1 @ mactual))) )),
% 0.08/0.35 inference(binary_proxy_clausification,[],[f63])).
% 0.08/0.35 thf(f95,plain,(
% 0.08/0.35 ($false = (set_equal @ sK2 @ sK3 @ mactual)) | ~spl0_4),
% 0.08/0.35 inference(avatar_component_clause,[],[f93])).
% 0.08/0.35 thf(f93,plain,(
% 0.08/0.35 spl0_4 <=> ($false = (set_equal @ sK2 @ sK3 @ mactual))),
% 0.08/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.08/0.35 thf(f478,plain,(
% 0.08/0.35 ~spl0_1 | ~spl0_4),
% 0.08/0.35 inference(avatar_contradiction_clause,[],[f477])).
% 0.08/0.35 thf(f477,plain,(
% 0.08/0.35 $false | (~spl0_1 | ~spl0_4)),
% 0.08/0.35 inference(trivial_inequality_removal,[],[f463])).
% 0.08/0.35 thf(f463,plain,(
% 0.08/0.35 ($true = $false) | (~spl0_1 | ~spl0_4)),
% 0.08/0.35 inference(superposition,[],[f95,f82])).
% 0.08/0.35 thf(f82,plain,(
% 0.08/0.35 ($true = (set_equal @ sK2 @ sK3 @ mactual)) | ~spl0_1),
% 0.08/0.35 inference(avatar_component_clause,[],[f80])).
% 0.08/0.35 thf(f80,plain,(
% 0.08/0.35 spl0_1 <=> ($true = (set_equal @ sK2 @ sK3 @ mactual))),
% 0.08/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.08/0.35 thf(f462,plain,(
% 0.08/0.35 spl0_4 | ~spl0_3),
% 0.08/0.35 inference(avatar_split_clause,[],[f457,f89,f93])).
% 0.08/0.35 thf(f457,plain,(
% 0.08/0.35 ($false = (set_equal @ sK2 @ sK3 @ mactual)) | ~spl0_3),
% 0.08/0.35 inference(trivial_inequality_removal,[],[f455])).
% 0.08/0.35 thf(f455,plain,(
% 0.08/0.35 ($false = (set_equal @ sK2 @ sK3 @ mactual)) | ($true = $false) | ~spl0_3),
% 0.08/0.35 inference(superposition,[],[f91,f450])).
% 0.08/0.35 thf(f91,plain,(
% 0.08/0.35 ((set_equal @ sK3 @ sK2 @ mactual) = $false) | ~spl0_3),
% 0.08/0.35 inference(avatar_component_clause,[],[f89])).
% 0.08/0.35 thf(f102,plain,(
% 0.08/0.35 ~spl0_2 | ~spl0_3),
% 0.08/0.35 inference(avatar_contradiction_clause,[],[f101])).
% 0.08/0.35 thf(f101,plain,(
% 0.08/0.35 $false | (~spl0_2 | ~spl0_3)),
% 0.08/0.35 inference(trivial_inequality_removal,[],[f97])).
% 0.08/0.35 thf(f97,plain,(
% 0.08/0.35 ($true = $false) | (~spl0_2 | ~spl0_3)),
% 0.08/0.35 inference(superposition,[],[f91,f86])).
% 0.08/0.35 thf(f86,plain,(
% 0.08/0.35 ((set_equal @ sK3 @ sK2 @ mactual) = $true) | ~spl0_2),
% 0.08/0.35 inference(avatar_component_clause,[],[f84])).
% 0.08/0.35 thf(f84,plain,(
% 0.08/0.35 spl0_2 <=> ((set_equal @ sK3 @ sK2 @ mactual) = $true)),
% 0.08/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.08/0.35 thf(f96,plain,(
% 0.08/0.35 spl0_3 | spl0_4),
% 0.08/0.35 inference(avatar_split_clause,[],[f78,f93,f89])).
% 0.08/0.35 thf(f78,plain,(
% 0.08/0.35 ((set_equal @ sK3 @ sK2 @ mactual) = $false) | ($false = (set_equal @ sK2 @ sK3 @ mactual))),
% 0.08/0.35 inference(binary_proxy_clausification,[],[f76])).
% 0.08/0.35 thf(f76,plain,(
% 0.08/0.35 ((set_equal @ sK3 @ sK2 @ mactual) != (set_equal @ sK2 @ sK3 @ mactual))),
% 0.08/0.35 inference(binary_proxy_clausification,[],[f75])).
% 0.08/0.35 thf(f75,plain,(
% 0.08/0.35 ($false = ((set_equal @ sK2 @ sK3 @ mactual) = (set_equal @ sK3 @ sK2 @ mactual)))),
% 0.08/0.35 inference(beta_eta_normalization,[],[f74])).
% 0.08/0.35 thf(f74,plain,(
% 0.08/0.35 ($false = ((^[Y0 : $i]: ((set_equal @ sK2 @ Y0 @ mactual) = (set_equal @ Y0 @ sK2 @ mactual))) @ sK3))),
% 0.08/0.35 inference(sigma_clausification,[],[f73])).
% 0.08/0.35 thf(f73,plain,(
% 0.08/0.35 ((!! @ $i @ (^[Y0 : $i]: ((set_equal @ sK2 @ Y0 @ mactual) = (set_equal @ Y0 @ sK2 @ mactual)))) = $false)),
% 0.08/0.35 inference(beta_eta_normalization,[],[f72])).
% 0.08/0.35 thf(f72,plain,(
% 0.08/0.35 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((set_equal @ Y0 @ Y1 @ mactual) = (set_equal @ Y1 @ Y0 @ mactual))))) @ sK2))),
% 0.08/0.35 inference(sigma_clausification,[],[f71])).
% 0.08/0.35 thf(f71,plain,(
% 0.08/0.35 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((set_equal @ Y0 @ Y1 @ mactual) = (set_equal @ Y1 @ Y0 @ mactual)))))))),
% 0.08/0.35 inference(beta_eta_normalization,[],[f51])).
% 0.08/0.35 thf(f51,plain,(
% 0.08/0.35 ($true != ((^[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 > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) = (Y3 @ Y4))))))) @ (set_equal @ Y0 @ Y1) @ (set_equal @ Y1 @ Y0))))))))),
% 0.08/0.35 inference(definition_unfolding,[],[f45,f41,f39,f39,f50])).
% 0.08/0.35 thf(f45,plain,(
% 0.08/0.35 ($true != (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (set_equal @ Y0 @ Y1) @ (set_equal @ Y1 @ Y0))))))))),
% 0.08/0.35 inference(cnf_transformation,[],[f38])).
% 0.08/0.35 thf(f38,plain,(
% 0.08/0.35 ($true != (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (set_equal @ Y0 @ Y1) @ (set_equal @ Y1 @ Y0))))))))),
% 0.08/0.35 inference(flattening,[],[f26])).
% 0.08/0.35 thf(f26,plain,(
% 0.08/0.35 ~($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (set_equal @ Y0 @ Y1) @ (set_equal @ Y1 @ Y0))))))))),
% 0.08/0.35 inference(fool_elimination,[],[f25])).
% 0.08/0.35 thf(f25,plain,(
% 0.08/0.35 ~(mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mequiv @ (set_equal @ X0 @ X1) @ (set_equal @ X1 @ X0)))))))),
% 0.08/0.35 inference(rectify,[],[f13])).
% 0.08/0.35 thf(f13,negated_conjecture,(
% 0.08/0.35 ~(mlocal @ (mforall_di @ (^[X5 : $i] : (mforall_di @ (^[X6 : $i] : (mequiv @ (set_equal @ X5 @ X6) @ (set_equal @ X6 @ X5)))))))),
% 0.08/0.35 inference(negated_conjecture,[],[f12])).
% 0.08/0.35 thf(f12,conjecture,(
% 0.08/0.35 (mlocal @ (mforall_di @ (^[X5 : $i] : (mforall_di @ (^[X6 : $i] : (mequiv @ (set_equal @ X5 @ X6) @ (set_equal @ X6 @ X5)))))))),
% 0.08/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel43)).
% 0.08/0.35 thf(f87,plain,(
% 0.08/0.35 spl0_1 | spl0_2),
% 0.08/0.35 inference(avatar_split_clause,[],[f77,f84,f80])).
% 0.08/0.35 thf(f77,plain,(
% 0.08/0.35 ((set_equal @ sK3 @ sK2 @ mactual) = $true) | ($true = (set_equal @ sK2 @ sK3 @ mactual))),
% 0.08/0.35 inference(binary_proxy_clausification,[],[f76])).
% 0.08/0.35 % SZS output end Proof for theBenchmark
% 0.08/0.35 % (26125)------------------------------
% 0.08/0.35 % (26125)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.08/0.35 % (26125)Termination reason: Refutation
% 0.08/0.35
% 0.08/0.35 % (26125)Memory used [KB]: 5884
% 0.08/0.35 % (26125)Time elapsed: 0.034 s
% 0.08/0.35 % (26125)Instructions burned: 63 (million)
% 0.08/0.35 % (26125)------------------------------
% 0.08/0.35 % (26125)------------------------------
% 0.08/0.35 % (26124)Success in time 0.044 s
% 0.08/0.35 % Vampire---4.8 exiting
%------------------------------------------------------------------------------