TSTP Solution File: SYN044^4 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYN044^4 : TPTP v8.1.2. Released v4.0.0.
% 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 : Sun May 5 11:55:41 EDT 2024
% Result : Theorem 0.13s 0.39s
% Output : Refutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SYN044^4 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.12 % 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
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri May 3 17:22:08 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.13/0.33 This is a TH0_THM_EQU_NAR problem
% 0.13/0.33 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.KXv2WnKxyj/Vampire---4.8_7248
% 0.13/0.35 % (7360)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)
% 0.13/0.35 % (7358)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)
% 0.13/0.35 % (7359)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)
% 0.13/0.35 % (7364)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.13/0.35 % (7361)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.13/0.35 % (7365)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)
% 0.13/0.35 % (7362)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)
% 0.13/0.35 % (7363)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)
% 0.13/0.35 % (7361)Instruction limit reached!
% 0.13/0.35 % (7361)------------------------------
% 0.13/0.35 % (7361)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.35 % (7361)Termination reason: Unknown
% 0.13/0.35 % (7361)Termination phase: shuffling
% 0.13/0.35
% 0.13/0.35 % (7362)Instruction limit reached!
% 0.13/0.35 % (7362)------------------------------
% 0.13/0.35 % (7362)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.35 % (7362)Termination reason: Unknown
% 0.13/0.35 % (7362)Termination phase: shuffling
% 0.13/0.35
% 0.13/0.35 % (7362)Memory used [KB]: 1023
% 0.13/0.35 % (7362)Time elapsed: 0.002 s
% 0.13/0.35 % (7362)Instructions burned: 2 (million)
% 0.13/0.35 % (7362)------------------------------
% 0.13/0.35 % (7362)------------------------------
% 0.13/0.35 % (7361)Memory used [KB]: 1023
% 0.13/0.35 % (7361)Time elapsed: 0.002 s
% 0.13/0.35 % (7361)Instructions burned: 2 (million)
% 0.13/0.35 % (7361)------------------------------
% 0.13/0.35 % (7361)------------------------------
% 0.13/0.35 % (7365)Instruction limit reached!
% 0.13/0.35 % (7365)------------------------------
% 0.13/0.35 % (7365)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.35 % (7365)Termination reason: Unknown
% 0.13/0.35 % (7365)Termination phase: Property scanning
% 0.13/0.35
% 0.13/0.35 % (7365)Memory used [KB]: 1023
% 0.13/0.35 % (7365)Time elapsed: 0.003 s
% 0.13/0.35 % (7365)Instructions burned: 3 (million)
% 0.13/0.35 % (7365)------------------------------
% 0.13/0.35 % (7365)------------------------------
% 0.13/0.35 % (7359)Instruction limit reached!
% 0.13/0.35 % (7359)------------------------------
% 0.13/0.35 % (7359)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.35 % (7359)Termination reason: Unknown
% 0.13/0.35 % (7359)Termination phase: Property scanning
% 0.13/0.35
% 0.13/0.35 % (7359)Memory used [KB]: 1023
% 0.13/0.35 % (7359)Time elapsed: 0.004 s
% 0.13/0.35 % (7359)Instructions burned: 5 (million)
% 0.13/0.35 % (7359)------------------------------
% 0.13/0.35 % (7359)------------------------------
% 0.13/0.35 % (7363)Refutation not found, incomplete strategy
% 0.13/0.35 % (7363)------------------------------
% 0.13/0.35 % (7363)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.35 % (7363)Termination reason: Refutation not found, incomplete strategy
% 0.13/0.35
% 0.13/0.35
% 0.13/0.35 % (7363)Memory used [KB]: 5500
% 0.13/0.35 % (7363)Time elapsed: 0.003 s
% 0.13/0.35 % (7363)Instructions burned: 4 (million)
% 0.13/0.35 % (7363)------------------------------
% 0.13/0.35 % (7363)------------------------------
% 0.13/0.35 % (7364)Instruction limit reached!
% 0.13/0.35 % (7364)------------------------------
% 0.13/0.35 % (7364)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.35 % (7364)Termination reason: Unknown
% 0.13/0.35 % (7364)Termination phase: Saturation
% 0.13/0.35
% 0.13/0.35 % (7364)Memory used [KB]: 5628
% 0.13/0.35 % (7364)Time elapsed: 0.010 s
% 0.13/0.35 % (7364)Instructions burned: 19 (million)
% 0.13/0.35 % (7364)------------------------------
% 0.13/0.35 % (7364)------------------------------
% 0.13/0.36 % (7366)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)
% 0.13/0.36 % (7369)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)
% 0.13/0.36 % (7367)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)
% 0.13/0.36 % (7360)Instruction limit reached!
% 0.13/0.36 % (7360)------------------------------
% 0.13/0.36 % (7360)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.36 % (7360)Termination reason: Unknown
% 0.13/0.36 % (7360)Termination phase: Saturation
% 0.13/0.36
% 0.13/0.36 % (7360)Memory used [KB]: 5756
% 0.13/0.36 % (7360)Time elapsed: 0.016 s
% 0.13/0.36 % (7360)Instructions burned: 28 (million)
% 0.13/0.36 % (7360)------------------------------
% 0.13/0.36 % (7360)------------------------------
% 0.13/0.36 % (7368)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)
% 0.13/0.36 % (7368)Instruction limit reached!
% 0.13/0.36 % (7368)------------------------------
% 0.13/0.36 % (7368)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.36 % (7368)Termination reason: Unknown
% 0.13/0.36 % (7368)Termination phase: Function definition elimination
% 0.13/0.36
% 0.13/0.36 % (7368)Memory used [KB]: 1023
% 0.13/0.36 % (7368)Time elapsed: 0.003 s
% 0.13/0.36 % (7368)Instructions burned: 4 (million)
% 0.13/0.36 % (7368)------------------------------
% 0.13/0.36 % (7368)------------------------------
% 0.13/0.36 % (7370)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)
% 0.13/0.36 % (7370)Instruction limit reached!
% 0.13/0.36 % (7370)------------------------------
% 0.13/0.36 % (7370)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.36 % (7370)Termination reason: Unknown
% 0.13/0.36 % (7370)Termination phase: Saturation
% 0.13/0.36
% 0.13/0.36 % (7370)Memory used [KB]: 1023
% 0.13/0.36 % (7370)Time elapsed: 0.004 s
% 0.13/0.36 % (7370)Instructions burned: 7 (million)
% 0.13/0.36 % (7370)------------------------------
% 0.13/0.36 % (7370)------------------------------
% 0.13/0.37 % (7371)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)
% 0.13/0.37 % (7367)Instruction limit reached!
% 0.13/0.37 % (7367)------------------------------
% 0.13/0.37 % (7367)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (7367)Termination reason: Unknown
% 0.13/0.37 % (7367)Termination phase: Saturation
% 0.13/0.37
% 0.13/0.37 % (7367)Memory used [KB]: 5628
% 0.13/0.37 % (7367)Time elapsed: 0.010 s
% 0.13/0.37 % (7367)Instructions burned: 16 (million)
% 0.13/0.37 % (7367)------------------------------
% 0.13/0.37 % (7367)------------------------------
% 0.13/0.37 % (7372)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)
% 0.13/0.37 % (7371)Instruction limit reached!
% 0.13/0.37 % (7371)------------------------------
% 0.13/0.37 % (7371)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (7371)Termination reason: Unknown
% 0.13/0.37 % (7371)Termination phase: Saturation
% 0.13/0.37
% 0.13/0.37 % (7371)Memory used [KB]: 5628
% 0.13/0.37 % (7371)Time elapsed: 0.008 s
% 0.13/0.37 % (7371)Instructions burned: 16 (million)
% 0.13/0.37 % (7371)------------------------------
% 0.13/0.37 % (7371)------------------------------
% 0.13/0.37 % (7373)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)
% 0.13/0.37 % (7372)Instruction limit reached!
% 0.13/0.37 % (7372)------------------------------
% 0.13/0.37 % (7372)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (7372)Termination reason: Unknown
% 0.13/0.37 % (7372)Termination phase: Property scanning
% 0.13/0.37
% 0.13/0.37 % (7372)Memory used [KB]: 1023
% 0.13/0.37 % (7372)Time elapsed: 0.003 s
% 0.13/0.37 % (7372)Instructions burned: 4 (million)
% 0.13/0.37 % (7372)------------------------------
% 0.13/0.37 % (7372)------------------------------
% 0.13/0.38 % (7373)Instruction limit reached!
% 0.13/0.38 % (7373)------------------------------
% 0.13/0.38 % (7373)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (7373)Termination reason: Unknown
% 0.13/0.38 % (7373)Termination phase: Preprocessing 1
% 0.13/0.38
% 0.13/0.38 % (7373)Memory used [KB]: 1023
% 0.13/0.38 % (7373)Time elapsed: 0.003 s
% 0.13/0.38 % (7373)Instructions burned: 3 (million)
% 0.13/0.38 % (7373)------------------------------
% 0.13/0.38 % (7373)------------------------------
% 0.13/0.38 % (7374)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)
% 0.13/0.38 % (7366)Instruction limit reached!
% 0.13/0.38 % (7366)------------------------------
% 0.13/0.38 % (7366)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (7366)Termination reason: Unknown
% 0.13/0.38 % (7366)Termination phase: Saturation
% 0.13/0.38
% 0.13/0.38 % (7366)Memory used [KB]: 5756
% 0.13/0.38 % (7366)Time elapsed: 0.020 s
% 0.13/0.38 % (7366)Instructions burned: 37 (million)
% 0.13/0.38 % (7366)------------------------------
% 0.13/0.38 % (7366)------------------------------
% 0.13/0.38 % (7374)Instruction limit reached!
% 0.13/0.38 % (7374)------------------------------
% 0.13/0.38 % (7374)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (7374)Termination reason: Unknown
% 0.13/0.38 % (7374)Termination phase: Saturation
% 0.13/0.38
% 0.13/0.38 % (7374)Memory used [KB]: 5500
% 0.13/0.38 % (7374)Time elapsed: 0.004 s
% 0.13/0.38 % (7374)Instructions burned: 7 (million)
% 0.13/0.38 % (7374)------------------------------
% 0.13/0.38 % (7374)------------------------------
% 0.13/0.38 % (7375)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)
% 0.13/0.38 % (7369)First to succeed.
% 0.13/0.38 % (7375)Instruction limit reached!
% 0.13/0.38 % (7375)------------------------------
% 0.13/0.38 % (7375)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (7375)Termination reason: Unknown
% 0.13/0.38 % (7375)Termination phase: Function definition elimination
% 0.13/0.38
% 0.13/0.38 % (7375)Memory used [KB]: 1023
% 0.13/0.38 % (7375)Time elapsed: 0.003 s
% 0.13/0.38 % (7375)Instructions burned: 4 (million)
% 0.13/0.38 % (7375)------------------------------
% 0.13/0.38 % (7375)------------------------------
% 0.13/0.38 % (7376)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on Vampire---4 for (2999ds/4Mi)
% 0.13/0.39 % (7376)Instruction limit reached!
% 0.13/0.39 % (7376)------------------------------
% 0.13/0.39 % (7376)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (7376)Termination reason: Unknown
% 0.13/0.39 % (7376)Termination phase: Function definition elimination
% 0.13/0.39
% 0.13/0.39 % (7376)Memory used [KB]: 1023
% 0.13/0.39 % (7376)Time elapsed: 0.003 s
% 0.13/0.39 % (7377)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.13/0.39 % (7376)Instructions burned: 4 (million)
% 0.13/0.39 % (7376)------------------------------
% 0.13/0.39 % (7376)------------------------------
% 0.13/0.39 % (7369)Refutation found. Thanks to Tanya!
% 0.13/0.39 % SZS status Theorem for Vampire---4
% 0.13/0.39 % SZS output start Proof for Vampire---4
% 0.13/0.39 thf(func_def_0, type, irel: $i > $i > $o).
% 0.13/0.39 thf(func_def_2, type, mnot: ($i > $o) > $i > $o).
% 0.13/0.39 thf(func_def_3, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.39 thf(func_def_4, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.39 thf(func_def_5, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.39 thf(func_def_6, type, mbox_s4: ($i > $o) > $i > $o).
% 0.13/0.39 thf(func_def_7, type, iatom: ($i > $o) > $i > $o).
% 0.13/0.39 thf(func_def_8, type, inot: ($i > $o) > $i > $o).
% 0.13/0.39 thf(func_def_9, type, itrue: $i > $o).
% 0.13/0.39 thf(func_def_10, type, ifalse: $i > $o).
% 0.13/0.39 thf(func_def_11, type, iand: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.39 thf(func_def_12, type, ior: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.39 thf(func_def_13, type, iimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.39 thf(func_def_14, type, iimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.39 thf(func_def_15, type, iequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.39 thf(func_def_16, type, ixor: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.39 thf(func_def_17, type, ivalid: ($i > $o) > $o).
% 0.13/0.39 thf(func_def_18, type, isatisfiable: ($i > $o) > $o).
% 0.13/0.39 thf(func_def_19, type, icountersatisfiable: ($i > $o) > $o).
% 0.13/0.39 thf(func_def_20, type, iinvalid: ($i > $o) > $o).
% 0.13/0.39 thf(func_def_21, type, p: $i > $o).
% 0.13/0.39 thf(func_def_22, type, q: $i > $o).
% 0.13/0.39 thf(func_def_23, type, r: $i > $o).
% 0.13/0.39 thf(func_def_37, type, ph1: !>[X0: $tType]:(X0)).
% 0.13/0.39 thf(f371,plain,(
% 0.13/0.39 $false),
% 0.13/0.39 inference(avatar_sat_refutation,[],[f157,f245,f370])).
% 0.13/0.39 thf(f370,plain,(
% 0.13/0.39 ~spl0_1),
% 0.13/0.39 inference(avatar_contradiction_clause,[],[f369])).
% 0.13/0.39 thf(f369,plain,(
% 0.13/0.39 $false | ~spl0_1),
% 0.13/0.39 inference(trivial_inequality_removal,[],[f368])).
% 0.13/0.39 thf(f368,plain,(
% 0.13/0.39 ($false = $true) | ~spl0_1),
% 0.13/0.39 inference(forward_demodulation,[],[f367,f274])).
% 0.13/0.39 thf(f274,plain,(
% 0.13/0.39 ($false = (q @ sK4)) | ~spl0_1),
% 0.13/0.39 inference(binary_proxy_clausification,[],[f273])).
% 0.13/0.39 thf(f273,plain,(
% 0.13/0.39 ($false = ((irel @ sK2 @ sK4) => (q @ sK4))) | ~spl0_1),
% 0.13/0.39 inference(beta_eta_normalization,[],[f269])).
% 0.13/0.39 thf(f269,plain,(
% 0.13/0.39 ($false = ((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0))) @ sK4)) | ~spl0_1),
% 0.13/0.39 inference(sigma_clausification,[],[f250])).
% 0.13/0.39 thf(f250,plain,(
% 0.13/0.39 ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0))))) | ~spl0_1),
% 0.13/0.39 inference(binary_proxy_clausification,[],[f153])).
% 0.13/0.39 thf(f153,plain,(
% 0.13/0.39 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0)))))) | ~spl0_1),
% 0.13/0.39 inference(avatar_component_clause,[],[f152])).
% 0.13/0.39 thf(f152,plain,(
% 0.13/0.39 spl0_1 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0))))))),
% 0.13/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.13/0.39 thf(f367,plain,(
% 0.13/0.39 ((q @ sK4) = $true) | ~spl0_1),
% 0.13/0.39 inference(boolean_simplification,[],[f366])).
% 0.13/0.39 thf(f366,plain,(
% 0.13/0.39 (($true => (q @ sK4)) = $true) | ~spl0_1),
% 0.13/0.39 inference(forward_demodulation,[],[f348,f275])).
% 0.13/0.39 thf(f275,plain,(
% 0.13/0.39 ((irel @ sK2 @ sK4) = $true) | ~spl0_1),
% 0.13/0.39 inference(binary_proxy_clausification,[],[f273])).
% 0.13/0.39 thf(f348,plain,(
% 0.13/0.39 ($true = ((irel @ sK2 @ sK4) => (q @ sK4))) | ~spl0_1),
% 0.13/0.39 inference(boolean_simplification,[],[f344])).
% 0.13/0.39 thf(f344,plain,(
% 0.13/0.39 (((irel @ sK2 @ sK4) => ((q @ sK4) & $true)) = $true) | ~spl0_1),
% 0.13/0.39 inference(superposition,[],[f340,f299])).
% 0.13/0.39 thf(f299,plain,(
% 0.13/0.39 ((p @ sK4) = $true) | ~spl0_1),
% 0.13/0.39 inference(boolean_simplification,[],[f294])).
% 0.13/0.39 thf(f294,plain,(
% 0.13/0.39 (($true => (p @ sK4)) = $true) | ~spl0_1),
% 0.13/0.39 inference(superposition,[],[f263,f275])).
% 0.13/0.39 thf(f263,plain,(
% 0.13/0.39 ( ! [X1 : $i] : ((((irel @ sK2 @ X1) => (p @ X1)) = $true)) ) | ~spl0_1),
% 0.13/0.39 inference(beta_eta_normalization,[],[f259])).
% 0.13/0.39 thf(f259,plain,(
% 0.13/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0))) @ X1))) ) | ~spl0_1),
% 0.13/0.39 inference(pi_clausification,[],[f254])).
% 0.13/0.39 thf(f254,plain,(
% 0.13/0.39 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0)))) = $true) | ~spl0_1),
% 0.13/0.39 inference(not_proxy_clausification,[],[f253])).
% 0.13/0.39 thf(f253,plain,(
% 0.13/0.39 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0)))))) | ~spl0_1),
% 0.13/0.39 inference(boolean_simplification,[],[f252])).
% 0.13/0.39 thf(f252,plain,(
% 0.13/0.39 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0))))) | $false)) | ~spl0_1),
% 0.13/0.39 inference(backward_demodulation,[],[f153,f250])).
% 0.13/0.39 thf(f340,plain,(
% 0.13/0.39 ( ! [X1 : $i] : ((((irel @ sK2 @ X1) => ((q @ X1) & (p @ X1))) = $true)) ) | ~spl0_1),
% 0.13/0.39 inference(beta_eta_normalization,[],[f338])).
% 0.13/0.39 thf(f338,plain,(
% 0.13/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((q @ Y0) & (p @ Y0)))) @ X1) = $true)) ) | ~spl0_1),
% 0.13/0.39 inference(pi_clausification,[],[f308])).
% 0.13/0.39 thf(f308,plain,(
% 0.13/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((q @ Y0) & (p @ Y0)))))) | ~spl0_1),
% 0.13/0.39 inference(boolean_simplification,[],[f307])).
% 0.13/0.39 thf(f307,plain,(
% 0.13/0.39 (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((q @ Y0) & (p @ Y0)))))) = $true) | ~spl0_1),
% 0.13/0.39 inference(boolean_simplification,[],[f305])).
% 0.13/0.39 thf(f305,plain,(
% 0.13/0.39 ($true = ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((q @ Y0) & (p @ Y0))))))) | ~spl0_1),
% 0.13/0.39 inference(superposition,[],[f140,f290])).
% 0.13/0.39 thf(f290,plain,(
% 0.13/0.39 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (r @ Y0)))) = $true) | ~spl0_1),
% 0.13/0.39 inference(boolean_simplification,[],[f289])).
% 0.13/0.39 thf(f289,plain,(
% 0.13/0.39 ($true = ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (r @ Y0)))))) | ~spl0_1),
% 0.13/0.39 inference(forward_demodulation,[],[f288,f250])).
% 0.13/0.39 thf(f288,plain,(
% 0.13/0.39 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (r @ Y0))))) = $true) | ~spl0_1),
% 0.13/0.39 inference(boolean_simplification,[],[f286])).
% 0.13/0.39 thf(f286,plain,(
% 0.13/0.39 (($true => ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (r @ Y0)))))) = $true) | ~spl0_1),
% 0.13/0.39 inference(superposition,[],[f283,f120])).
% 0.13/0.39 thf(f120,plain,(
% 0.13/0.39 ( ! [X1 : $i] : (($true = (irel @ X1 @ X1))) )),
% 0.13/0.39 inference(beta_eta_normalization,[],[f119])).
% 0.13/0.39 thf(f119,plain,(
% 0.13/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: (irel @ Y0 @ Y0)) @ X1) = $true)) )),
% 0.13/0.39 inference(pi_clausification,[],[f89])).
% 0.13/0.39 thf(f89,plain,(
% 0.13/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: (irel @ Y0 @ Y0))))),
% 0.13/0.39 inference(cnf_transformation,[],[f64])).
% 0.13/0.39 thf(f64,plain,(
% 0.13/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: (irel @ Y0 @ Y0))))),
% 0.13/0.39 inference(fool_elimination,[],[f63])).
% 0.13/0.39 thf(f63,plain,(
% 0.13/0.39 ! [X0] : (irel @ X0 @ X0)),
% 0.13/0.39 inference(rectify,[],[f1])).
% 0.13/0.39 thf(f1,axiom,(
% 0.13/0.39 ! [X0] : (irel @ X0 @ X0)),
% 0.13/0.39 file('/export/starexec/sandbox/tmp/tmp.KXv2WnKxyj/Vampire---4.8_7248',refl_axiom)).
% 0.13/0.39 thf(f283,plain,(
% 0.13/0.39 ( ! [X1 : $i] : ((((irel @ sK2 @ X1) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (q @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (r @ Y0)))))) = $true)) ) | ~spl0_1),
% 0.13/0.39 inference(beta_eta_normalization,[],[f280])).
% 0.13/0.39 thf(f280,plain,(
% 0.13/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1))))))) @ X1) = $true)) ) | ~spl0_1),
% 0.13/0.39 inference(pi_clausification,[],[f256])).
% 0.13/0.39 thf(f256,plain,(
% 0.13/0.39 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1)))))))) = $true) | ~spl0_1),
% 0.13/0.39 inference(boolean_simplification,[],[f255])).
% 0.13/0.39 thf(f255,plain,(
% 0.13/0.39 (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1))))))))) = $true) | ~spl0_1),
% 0.13/0.39 inference(superposition,[],[f143,f253])).
% 0.13/0.39 thf(f143,plain,(
% 0.13/0.39 ( ! [X1 : $i] : ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1))))))))) = $true)) )),
% 0.13/0.39 inference(beta_eta_normalization,[],[f142])).
% 0.13/0.39 thf(f142,plain,(
% 0.13/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (q @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (r @ Y2)))))))))) @ X1))) )),
% 0.13/0.39 inference(pi_clausification,[],[f115])).
% 0.13/0.39 thf(f115,plain,(
% 0.13/0.39 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (q @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (r @ Y2))))))))))) = $true)),
% 0.13/0.39 inference(beta_eta_normalization,[],[f114])).
% 0.13/0.39 thf(f114,plain,(
% 0.13/0.39 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ q) @ ((^[Y0 : $i > $o]: (Y0)) @ r)))) = $true)),
% 0.13/0.39 inference(definition_unfolding,[],[f101,f91,f107,f77,f106,f77,f77])).
% 0.13/0.39 thf(f106,plain,(
% 0.13/0.39 (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))))),
% 0.13/0.39 inference(definition_unfolding,[],[f86,f93,f98,f98])).
% 0.13/0.39 thf(f98,plain,(
% 0.13/0.39 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.13/0.39 inference(cnf_transformation,[],[f74])).
% 0.13/0.39 thf(f74,plain,(
% 0.13/0.39 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.13/0.39 inference(fool_elimination,[],[f73])).
% 0.13/0.39 thf(f73,plain,(
% 0.13/0.39 (mbox_s4 = (^[X0 : $i > $o, X1 : $i] : (! [X2] : ((irel @ X1 @ X2) => (X0 @ X2)))))),
% 0.13/0.39 inference(rectify,[],[f7])).
% 0.13/0.39 thf(f7,axiom,(
% 0.13/0.39 (mbox_s4 = (^[X5 : $i > $o, X0 : $i] : (! [X1] : ((irel @ X0 @ X1) => (X5 @ X1)))))),
% 0.13/0.39 file('/export/starexec/sandbox/tmp/tmp.KXv2WnKxyj/Vampire---4.8_7248',mbox_s4)).
% 0.13/0.39 thf(f93,plain,(
% 0.13/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.13/0.39 inference(cnf_transformation,[],[f47])).
% 0.13/0.39 thf(f47,plain,(
% 0.13/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.13/0.39 inference(fool_elimination,[],[f46])).
% 0.13/0.39 thf(f46,plain,(
% 0.13/0.39 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 0.13/0.39 inference(rectify,[],[f4])).
% 0.13/0.39 thf(f4,axiom,(
% 0.13/0.39 ((^[X0 : $i > $o, X1 : $i > $o, X3 : $i] : ((X1 @ X3) | (X0 @ X3))) = mor)),
% 0.13/0.39 file('/export/starexec/sandbox/tmp/tmp.KXv2WnKxyj/Vampire---4.8_7248',mor)).
% 0.13/0.39 thf(f86,plain,(
% 0.13/0.39 (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.13/0.39 inference(cnf_transformation,[],[f45])).
% 0.13/0.39 thf(f45,plain,(
% 0.13/0.39 (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.13/0.39 inference(fool_elimination,[],[f44])).
% 0.13/0.39 thf(f44,plain,(
% 0.13/0.39 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mbox_s4 @ X0) @ (mbox_s4 @ X1))) = ior)),
% 0.13/0.39 inference(rectify,[],[f13])).
% 0.13/0.39 thf(f13,axiom,(
% 0.13/0.39 ((^[X5 : $i > $o, X7 : $i > $o] : (mor @ (mbox_s4 @ X5) @ (mbox_s4 @ X7))) = ior)),
% 0.13/0.39 file('/export/starexec/sandbox/tmp/tmp.KXv2WnKxyj/Vampire---4.8_7248',ior)).
% 0.13/0.39 thf(f77,plain,(
% 0.13/0.39 (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 0.13/0.39 inference(cnf_transformation,[],[f39])).
% 0.13/0.39 thf(f39,plain,(
% 0.13/0.39 (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 0.13/0.39 inference(fool_elimination,[],[f38])).
% 0.13/0.39 thf(f38,plain,(
% 0.13/0.39 ((^[X0 : $i > $o] : (X0)) = iatom)),
% 0.13/0.39 inference(rectify,[],[f8])).
% 0.13/0.39 thf(f8,axiom,(
% 0.13/0.39 ((^[X5 : $i > $o] : (X5)) = iatom)),
% 0.13/0.39 file('/export/starexec/sandbox/tmp/tmp.KXv2WnKxyj/Vampire---4.8_7248',iatom)).
% 0.13/0.39 thf(f107,plain,(
% 0.13/0.39 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))))),
% 0.13/0.39 inference(definition_unfolding,[],[f85,f102,f98,f98])).
% 0.13/0.39 thf(f102,plain,(
% 0.13/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.13/0.39 inference(definition_unfolding,[],[f99,f93,f97])).
% 0.13/0.39 thf(f97,plain,(
% 0.13/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.13/0.39 inference(cnf_transformation,[],[f31])).
% 0.13/0.39 thf(f31,plain,(
% 0.13/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.13/0.39 inference(fool_elimination,[],[f30])).
% 0.13/0.39 thf(f30,plain,(
% 0.13/0.39 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.13/0.39 inference(rectify,[],[f3])).
% 0.13/0.39 thf(f3,axiom,(
% 0.13/0.39 ((^[X0 : $i > $o, X3 : $i] : (~(X0 @ X3))) = mnot)),
% 0.13/0.39 file('/export/starexec/sandbox/tmp/tmp.KXv2WnKxyj/Vampire---4.8_7248',mnot)).
% 0.13/0.39 thf(f99,plain,(
% 0.13/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.13/0.39 inference(cnf_transformation,[],[f41])).
% 0.13/0.39 thf(f41,plain,(
% 0.13/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.13/0.39 inference(fool_elimination,[],[f40])).
% 0.13/0.39 thf(f40,plain,(
% 0.13/0.39 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.13/0.39 inference(rectify,[],[f6])).
% 0.13/0.39 thf(f6,axiom,(
% 0.13/0.39 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.13/0.39 file('/export/starexec/sandbox/tmp/tmp.KXv2WnKxyj/Vampire---4.8_7248',mimplies)).
% 0.13/0.39 thf(f85,plain,(
% 0.13/0.39 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.13/0.39 inference(cnf_transformation,[],[f62])).
% 0.13/0.39 thf(f62,plain,(
% 0.13/0.39 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.13/0.39 inference(fool_elimination,[],[f61])).
% 0.13/0.39 thf(f61,plain,(
% 0.13/0.39 (iimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mimplies @ (mbox_s4 @ X0) @ (mbox_s4 @ X1))))),
% 0.13/0.39 inference(rectify,[],[f14])).
% 0.13/0.39 thf(f14,axiom,(
% 0.13/0.39 (iimplies = (^[X5 : $i > $o, X7 : $i > $o] : (mimplies @ (mbox_s4 @ X5) @ (mbox_s4 @ X7))))),
% 0.13/0.39 file('/export/starexec/sandbox/tmp/tmp.KXv2WnKxyj/Vampire---4.8_7248',iimplies)).
% 0.13/0.39 thf(f91,plain,(
% 0.13/0.39 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.13/0.39 inference(cnf_transformation,[],[f51])).
% 0.13/0.39 thf(f51,plain,(
% 0.13/0.39 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.13/0.39 inference(fool_elimination,[],[f50])).
% 0.13/0.39 thf(f50,plain,(
% 0.13/0.39 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = ivalid)),
% 0.13/0.39 inference(rectify,[],[f18])).
% 0.13/0.39 thf(f18,axiom,(
% 0.13/0.39 ((^[X8 : $i > $o] : (! [X6] : (X8 @ X6))) = ivalid)),
% 0.13/0.39 file('/export/starexec/sandbox/tmp/tmp.KXv2WnKxyj/Vampire---4.8_7248',ivalid)).
% 0.13/0.39 thf(f101,plain,(
% 0.13/0.39 ((ivalid @ (iimplies @ (iatom @ p) @ (ior @ (iatom @ q) @ (iatom @ r)))) = $true)),
% 0.13/0.39 inference(cnf_transformation,[],[f72])).
% 0.13/0.39 thf(f72,plain,(
% 0.13/0.39 ((ivalid @ (iimplies @ (iatom @ p) @ (ior @ (iatom @ q) @ (iatom @ r)))) = $true)),
% 0.13/0.39 inference(fool_elimination,[],[f71])).
% 0.13/0.39 thf(f71,plain,(
% 0.13/0.39 (ivalid @ (iimplies @ (iatom @ p) @ (ior @ (iatom @ q) @ (iatom @ r))))),
% 0.13/0.39 inference(rectify,[],[f24])).
% 0.13/0.39 thf(f24,axiom,(
% 0.13/0.39 (ivalid @ (iimplies @ (iatom @ p) @ (ior @ (iatom @ q) @ (iatom @ r))))),
% 0.13/0.39 file('/export/starexec/sandbox/tmp/tmp.KXv2WnKxyj/Vampire---4.8_7248',pel10_3)).
% 0.13/0.39 thf(f140,plain,(
% 0.13/0.39 ( ! [X1 : $i] : ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (r @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((q @ Y0) & (p @ Y0)))))) = $true)) )),
% 0.13/0.39 inference(beta_eta_normalization,[],[f139])).
% 0.13/0.39 thf(f139,plain,(
% 0.13/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((q @ Y1) & (p @ Y1))))))) @ X1) = $true)) )),
% 0.13/0.39 inference(pi_clausification,[],[f118])).
% 0.13/0.39 thf(f118,plain,(
% 0.13/0.39 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((q @ Y1) & (p @ Y1)))))))) = $true)),
% 0.13/0.39 inference(beta_eta_normalization,[],[f112])).
% 0.13/0.39 thf(f112,plain,(
% 0.13/0.39 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ r) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ Y4))))))) @ Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: (Y0)) @ p) @ ((^[Y0 : $i > $o]: (Y0)) @ q)))) = $true)),
% 0.13/0.39 inference(definition_unfolding,[],[f96,f91,f107,f77,f105,f77,f77])).
% 0.13/0.39 thf(f105,plain,(
% 0.13/0.39 (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ Y4))))))) @ Y0 @ Y1)))))),
% 0.13/0.39 inference(definition_unfolding,[],[f88,f80])).
% 0.13/0.39 thf(f80,plain,(
% 0.13/0.39 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 0.13/0.39 inference(cnf_transformation,[],[f57])).
% 0.13/0.39 thf(f57,plain,(
% 0.13/0.39 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 0.13/0.39 inference(fool_elimination,[],[f56])).
% 0.13/0.39 thf(f56,plain,(
% 0.13/0.39 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) & (X1 @ X2))) = mand)),
% 0.13/0.39 inference(rectify,[],[f5])).
% 0.13/0.39 thf(f5,axiom,(
% 0.13/0.39 ((^[X0 : $i > $o, X1 : $i > $o, X3 : $i] : ((X0 @ X3) & (X1 @ X3))) = mand)),
% 0.13/0.39 file('/export/starexec/sandbox/tmp/tmp.KXv2WnKxyj/Vampire---4.8_7248',mand)).
% 0.13/0.39 thf(f88,plain,(
% 0.13/0.39 (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ Y0 @ Y1)))))),
% 0.13/0.39 inference(cnf_transformation,[],[f29])).
% 0.13/0.39 thf(f29,plain,(
% 0.13/0.39 (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ Y0 @ Y1)))))),
% 0.13/0.39 inference(fool_elimination,[],[f28])).
% 0.13/0.39 thf(f28,plain,(
% 0.13/0.39 (iand = (^[X0 : $i > $o, X1 : $i > $o] : (mand @ X0 @ X1)))),
% 0.13/0.39 inference(rectify,[],[f12])).
% 0.13/0.39 thf(f12,axiom,(
% 0.13/0.39 (iand = (^[X5 : $i > $o, X7 : $i > $o] : (mand @ X5 @ X7)))),
% 0.13/0.39 file('/export/starexec/sandbox/tmp/tmp.KXv2WnKxyj/Vampire---4.8_7248',iand)).
% 0.13/0.39 thf(f96,plain,(
% 0.13/0.39 ((ivalid @ (iimplies @ (iatom @ r) @ (iand @ (iatom @ p) @ (iatom @ q)))) = $true)),
% 0.13/0.39 inference(cnf_transformation,[],[f66])).
% 0.13/0.39 thf(f66,plain,(
% 0.13/0.39 ((ivalid @ (iimplies @ (iatom @ r) @ (iand @ (iatom @ p) @ (iatom @ q)))) = $true)),
% 0.13/0.39 inference(fool_elimination,[],[f65])).
% 0.13/0.39 thf(f65,plain,(
% 0.13/0.39 (ivalid @ (iimplies @ (iatom @ r) @ (iand @ (iatom @ p) @ (iatom @ q))))),
% 0.13/0.39 inference(rectify,[],[f23])).
% 0.13/0.39 thf(f23,axiom,(
% 0.13/0.39 (ivalid @ (iimplies @ (iatom @ r) @ (iand @ (iatom @ p) @ (iatom @ q))))),
% 0.13/0.39 file('/export/starexec/sandbox/tmp/tmp.KXv2WnKxyj/Vampire---4.8_7248',pel10_2)).
% 0.13/0.39 thf(f245,plain,(
% 0.13/0.39 ~spl0_2),
% 0.13/0.39 inference(avatar_contradiction_clause,[],[f244])).
% 0.13/0.39 thf(f244,plain,(
% 0.13/0.39 $false | ~spl0_2),
% 0.13/0.39 inference(trivial_inequality_removal,[],[f243])).
% 0.13/0.39 thf(f243,plain,(
% 0.13/0.39 ($false = $true) | ~spl0_2),
% 0.13/0.39 inference(forward_demodulation,[],[f242,f187])).
% 0.13/0.39 thf(f187,plain,(
% 0.13/0.39 ($false = (p @ sK3)) | ~spl0_2),
% 0.13/0.39 inference(boolean_simplification,[],[f186])).
% 0.13/0.39 thf(f186,plain,(
% 0.13/0.39 ($false = ($true => (p @ sK3))) | ~spl0_2),
% 0.13/0.39 inference(backward_demodulation,[],[f183,f185])).
% 0.13/0.39 thf(f185,plain,(
% 0.13/0.39 ((irel @ sK2 @ sK3) = $true) | ~spl0_2),
% 0.13/0.39 inference(binary_proxy_clausification,[],[f183])).
% 0.13/0.39 thf(f183,plain,(
% 0.13/0.39 (((irel @ sK2 @ sK3) => (p @ sK3)) = $false) | ~spl0_2),
% 0.13/0.39 inference(beta_eta_normalization,[],[f179])).
% 0.13/0.39 thf(f179,plain,(
% 0.13/0.39 ($false = ((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0))) @ sK3)) | ~spl0_2),
% 0.13/0.39 inference(sigma_clausification,[],[f160])).
% 0.13/0.39 thf(f160,plain,(
% 0.13/0.39 ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0))))) | ~spl0_2),
% 0.13/0.39 inference(binary_proxy_clausification,[],[f156])).
% 0.13/0.39 thf(f156,plain,(
% 0.13/0.39 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0)))))) | ~spl0_2),
% 0.13/0.39 inference(avatar_component_clause,[],[f155])).
% 0.13/0.39 thf(f155,plain,(
% 0.13/0.39 spl0_2 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0))))))),
% 0.13/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.13/0.39 thf(f242,plain,(
% 0.13/0.39 ((p @ sK3) = $true) | ~spl0_2),
% 0.13/0.39 inference(boolean_simplification,[],[f241])).
% 0.13/0.39 thf(f241,plain,(
% 0.13/0.39 ($true = ($true => (p @ sK3))) | ~spl0_2),
% 0.13/0.39 inference(forward_demodulation,[],[f225,f185])).
% 0.13/0.39 thf(f225,plain,(
% 0.13/0.39 (((irel @ sK2 @ sK3) => (p @ sK3)) = $true) | ~spl0_2),
% 0.13/0.39 inference(boolean_simplification,[],[f221])).
% 0.13/0.39 thf(f221,plain,(
% 0.13/0.39 ($true = ((irel @ sK2 @ sK3) => ($true & (p @ sK3)))) | ~spl0_2),
% 0.13/0.39 inference(superposition,[],[f215,f193])).
% 0.13/0.39 thf(f193,plain,(
% 0.13/0.39 ($true = (q @ sK3)) | ~spl0_2),
% 0.13/0.39 inference(boolean_simplification,[],[f188])).
% 0.13/0.39 thf(f188,plain,(
% 0.13/0.39 (($true => (q @ sK3)) = $true) | ~spl0_2),
% 0.13/0.39 inference(superposition,[],[f171,f185])).
% 0.13/0.39 thf(f171,plain,(
% 0.13/0.39 ( ! [X1 : $i] : (($true = ((irel @ sK2 @ X1) => (q @ X1)))) ) | ~spl0_2),
% 0.13/0.39 inference(beta_eta_normalization,[],[f169])).
% 0.13/0.39 thf(f169,plain,(
% 0.13/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0))) @ X1) = $true)) ) | ~spl0_2),
% 0.13/0.39 inference(pi_clausification,[],[f164])).
% 0.13/0.39 thf(f164,plain,(
% 0.13/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0))))) | ~spl0_2),
% 0.13/0.39 inference(not_proxy_clausification,[],[f163])).
% 0.13/0.39 thf(f163,plain,(
% 0.13/0.39 ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0))))) = $false) | ~spl0_2),
% 0.13/0.39 inference(boolean_simplification,[],[f162])).
% 0.13/0.39 thf(f162,plain,(
% 0.13/0.39 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0))))) | $false)) | ~spl0_2),
% 0.13/0.39 inference(backward_demodulation,[],[f156,f160])).
% 0.13/0.39 thf(f215,plain,(
% 0.13/0.39 ( ! [X1 : $i] : ((((irel @ sK2 @ X1) => ((q @ X1) & (p @ X1))) = $true)) ) | ~spl0_2),
% 0.13/0.39 inference(beta_eta_normalization,[],[f212])).
% 0.13/0.39 thf(f212,plain,(
% 0.13/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((q @ Y0) & (p @ Y0)))) @ X1) = $true)) ) | ~spl0_2),
% 0.13/0.39 inference(pi_clausification,[],[f201])).
% 0.13/0.39 thf(f201,plain,(
% 0.13/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((q @ Y0) & (p @ Y0)))))) | ~spl0_2),
% 0.13/0.39 inference(boolean_simplification,[],[f200])).
% 0.13/0.39 thf(f200,plain,(
% 0.13/0.39 (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((q @ Y0) & (p @ Y0)))))) = $true) | ~spl0_2),
% 0.13/0.39 inference(boolean_simplification,[],[f198])).
% 0.13/0.39 thf(f198,plain,(
% 0.13/0.39 ($true = ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((q @ Y0) & (p @ Y0))))))) | ~spl0_2),
% 0.13/0.39 inference(superposition,[],[f140,f166])).
% 0.13/0.39 thf(f166,plain,(
% 0.13/0.39 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (r @ Y0)))) = $true) | ~spl0_2),
% 0.13/0.39 inference(boolean_simplification,[],[f165])).
% 0.13/0.39 thf(f165,plain,(
% 0.13/0.39 ($true = ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (r @ Y0)))))) | ~spl0_2),
% 0.13/0.39 inference(superposition,[],[f137,f163])).
% 0.13/0.39 thf(f137,plain,(
% 0.13/0.39 ( ! [X1 : $i] : (($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (q @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (r @ Y0))))))) )),
% 0.13/0.39 inference(beta_eta_normalization,[],[f136])).
% 0.13/0.39 thf(f136,plain,(
% 0.13/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1)))))) @ X1))) )),
% 0.13/0.39 inference(pi_clausification,[],[f117])).
% 0.13/0.39 thf(f117,plain,(
% 0.13/0.39 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1))))))) = $true)),
% 0.13/0.39 inference(beta_eta_normalization,[],[f113])).
% 0.13/0.39 thf(f113,plain,(
% 0.13/0.39 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ q) @ ((^[Y0 : $i > $o]: (Y0)) @ r))) = $true)),
% 0.13/0.39 inference(definition_unfolding,[],[f100,f91,f107,f77,f77])).
% 0.13/0.39 thf(f100,plain,(
% 0.13/0.39 ((ivalid @ (iimplies @ (iatom @ q) @ (iatom @ r))) = $true)),
% 0.13/0.39 inference(cnf_transformation,[],[f68])).
% 0.13/0.39 thf(f68,plain,(
% 0.13/0.39 ((ivalid @ (iimplies @ (iatom @ q) @ (iatom @ r))) = $true)),
% 0.13/0.39 inference(fool_elimination,[],[f67])).
% 0.13/0.39 thf(f67,plain,(
% 0.13/0.39 (ivalid @ (iimplies @ (iatom @ q) @ (iatom @ r)))),
% 0.13/0.39 inference(rectify,[],[f22])).
% 0.13/0.39 thf(f22,axiom,(
% 0.13/0.39 (ivalid @ (iimplies @ (iatom @ q) @ (iatom @ r)))),
% 0.13/0.39 file('/export/starexec/sandbox/tmp/tmp.KXv2WnKxyj/Vampire---4.8_7248',pel10_1)).
% 0.13/0.39 thf(f157,plain,(
% 0.13/0.39 spl0_1 | spl0_2),
% 0.13/0.39 inference(avatar_split_clause,[],[f150,f155,f152])).
% 0.13/0.39 thf(f150,plain,(
% 0.13/0.39 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0)))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0))))))),
% 0.13/0.39 inference(binary_proxy_clausification,[],[f149])).
% 0.13/0.39 thf(f149,plain,(
% 0.13/0.39 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0)))))) = $false)),
% 0.13/0.39 inference(beta_eta_normalization,[],[f148])).
% 0.13/0.39 thf(f148,plain,(
% 0.13/0.39 ($false = ((^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))))) @ sK2))),
% 0.13/0.39 inference(sigma_clausification,[],[f145])).
% 0.13/0.39 thf(f145,plain,(
% 0.13/0.39 ($false = (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1)))))))))),
% 0.13/0.39 inference(not_proxy_clausification,[],[f116])).
% 0.13/0.39 thf(f116,plain,(
% 0.13/0.39 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))))))))),
% 0.13/0.39 inference(beta_eta_normalization,[],[f111])).
% 0.13/0.39 thf(f111,plain,(
% 0.13/0.39 ((~ ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ Y2 @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p) @ ((^[Y0 : $i > $o]: (Y0)) @ q)))) = $true)),
% 0.13/0.39 inference(definition_unfolding,[],[f84,f91,f109,f77,f77])).
% 0.13/0.39 thf(f109,plain,(
% 0.13/0.39 (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ Y2 @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y1 @ Y0))))))),
% 0.13/0.39 inference(definition_unfolding,[],[f95,f105,f107,f107])).
% 0.13/0.39 thf(f95,plain,(
% 0.13/0.39 (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (iand @ (iimplies @ Y0 @ Y1) @ (iimplies @ Y1 @ Y0))))))),
% 0.13/0.39 inference(cnf_transformation,[],[f55])).
% 0.13/0.39 thf(f55,plain,(
% 0.13/0.39 (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (iand @ (iimplies @ Y0 @ Y1) @ (iimplies @ Y1 @ Y0))))))),
% 0.13/0.39 inference(fool_elimination,[],[f54])).
% 0.13/0.39 thf(f54,plain,(
% 0.13/0.39 (iequiv = (^[X0 : $i > $o, X1 : $i > $o] : (iand @ (iimplies @ X0 @ X1) @ (iimplies @ X1 @ X0))))),
% 0.13/0.39 inference(rectify,[],[f16])).
% 0.13/0.39 thf(f16,axiom,(
% 0.13/0.39 (iequiv = (^[X5 : $i > $o, X7 : $i > $o] : (iand @ (iimplies @ X5 @ X7) @ (iimplies @ X7 @ X5))))),
% 0.13/0.39 file('/export/starexec/sandbox/tmp/tmp.KXv2WnKxyj/Vampire---4.8_7248',iequiv)).
% 0.13/0.39 thf(f84,plain,(
% 0.13/0.39 ((~ (ivalid @ (iequiv @ (iatom @ p) @ (iatom @ q)))) = $true)),
% 0.13/0.39 inference(cnf_transformation,[],[f33])).
% 0.13/0.39 thf(f33,plain,(
% 0.13/0.39 ((~ (ivalid @ (iequiv @ (iatom @ p) @ (iatom @ q)))) = $true)),
% 0.13/0.39 inference(fool_elimination,[],[f32])).
% 0.13/0.39 thf(f32,plain,(
% 0.13/0.39 ~(ivalid @ (iequiv @ (iatom @ p) @ (iatom @ q)))),
% 0.13/0.39 inference(rectify,[],[f26])).
% 0.13/0.39 thf(f26,negated_conjecture,(
% 0.13/0.39 ~(ivalid @ (iequiv @ (iatom @ p) @ (iatom @ q)))),
% 0.13/0.39 inference(negated_conjecture,[],[f25])).
% 0.13/0.39 thf(f25,conjecture,(
% 0.13/0.39 (ivalid @ (iequiv @ (iatom @ p) @ (iatom @ q)))),
% 0.13/0.39 file('/export/starexec/sandbox/tmp/tmp.KXv2WnKxyj/Vampire---4.8_7248',pel10)).
% 0.13/0.39 % SZS output end Proof for Vampire---4
% 0.13/0.39 % (7369)------------------------------
% 0.13/0.39 % (7369)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (7369)Termination reason: Refutation
% 0.13/0.39
% 0.13/0.39 % (7369)Memory used [KB]: 5884
% 0.13/0.39 % (7369)Time elapsed: 0.028 s
% 0.13/0.39 % (7369)Instructions burned: 47 (million)
% 0.13/0.39 % (7369)------------------------------
% 0.13/0.39 % (7369)------------------------------
% 0.13/0.39 % (7357)Success in time 0.035 s
% 0.13/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------