TSTP Solution File: SYN045^7 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYN045^7 : TPTP v8.2.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : 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 : Tue May 21 08:20:32 EDT 2024
% Result : Theorem 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYN045^7 : TPTP v8.2.0. Released v5.5.0.
% 0.10/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 14:07:08 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.34 This is a TH0_THM_EQU_NAR problem
% 0.13/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.37 % (3375)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.37 % (3376)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)
% 0.13/0.37 % (3378)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.37 % (3379)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)
% 0.13/0.37 % (3380)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)
% 0.13/0.37 % (3382)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)
% 0.13/0.37 % (3378)Instruction limit reached!
% 0.13/0.37 % (3378)------------------------------
% 0.13/0.37 % (3378)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (3378)Termination reason: Unknown
% 0.13/0.37 % (3378)Termination phase: shuffling
% 0.13/0.37
% 0.13/0.37 % (3378)Memory used [KB]: 1023
% 0.13/0.37 % (3378)Time elapsed: 0.003 s
% 0.13/0.37 % (3378)Instructions burned: 2 (million)
% 0.13/0.37 % (3378)------------------------------
% 0.13/0.37 % (3378)------------------------------
% 0.13/0.37 % (3379)Instruction limit reached!
% 0.13/0.37 % (3379)------------------------------
% 0.13/0.37 % (3379)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (3379)Termination reason: Unknown
% 0.13/0.37 % (3379)Termination phase: shuffling
% 0.13/0.37
% 0.13/0.37 % (3379)Memory used [KB]: 1023
% 0.13/0.37 % (3379)Time elapsed: 0.003 s
% 0.13/0.37 % (3379)Instructions burned: 2 (million)
% 0.13/0.37 % (3379)------------------------------
% 0.13/0.37 % (3379)------------------------------
% 0.13/0.37 % (3376)Instruction limit reached!
% 0.13/0.37 % (3376)------------------------------
% 0.13/0.37 % (3376)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (3376)Termination reason: Unknown
% 0.13/0.37 % (3376)Termination phase: shuffling
% 0.13/0.37
% 0.13/0.37 % (3376)Memory used [KB]: 1023
% 0.13/0.37 % (3376)Time elapsed: 0.004 s
% 0.13/0.37 % (3376)Instructions burned: 4 (million)
% 0.13/0.37 % (3376)------------------------------
% 0.13/0.37 % (3376)------------------------------
% 0.13/0.37 % (3377)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)
% 0.13/0.38 % (3381)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.38 % (3382)Instruction limit reached!
% 0.13/0.38 % (3382)------------------------------
% 0.13/0.38 % (3382)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (3382)Termination reason: Unknown
% 0.13/0.38 % (3382)Termination phase: shuffling
% 0.13/0.38
% 0.13/0.38 % (3382)Memory used [KB]: 1023
% 0.13/0.38 % (3382)Time elapsed: 0.005 s
% 0.13/0.38 % (3382)Instructions burned: 4 (million)
% 0.13/0.38 % (3382)------------------------------
% 0.13/0.38 % (3382)------------------------------
% 0.13/0.38 % (3384)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)
% 0.13/0.38 % (3383)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)
% 0.13/0.38 % (3385)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)
% 0.13/0.38 % (3377)Instruction limit reached!
% 0.13/0.38 % (3377)------------------------------
% 0.13/0.38 % (3377)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (3377)Termination reason: Unknown
% 0.13/0.38 % (3377)Termination phase: Saturation
% 0.13/0.38
% 0.13/0.38 % (3377)Memory used [KB]: 5628
% 0.13/0.38 % (3377)Time elapsed: 0.015 s
% 0.13/0.38 % (3377)Instructions burned: 27 (million)
% 0.13/0.39 % (3377)------------------------------
% 0.13/0.39 % (3377)------------------------------
% 0.13/0.39 % (3385)Instruction limit reached!
% 0.13/0.39 % (3385)------------------------------
% 0.13/0.39 % (3385)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (3385)Termination reason: Unknown
% 0.13/0.39 % (3385)Termination phase: shuffling
% 0.13/0.39
% 0.13/0.39 % (3385)Memory used [KB]: 1023
% 0.13/0.39 % (3385)Time elapsed: 0.004 s
% 0.13/0.39 % (3385)Instructions burned: 3 (million)
% 0.13/0.39 % (3385)------------------------------
% 0.13/0.39 % (3385)------------------------------
% 0.13/0.39 % (3381)Instruction limit reached!
% 0.13/0.39 % (3381)------------------------------
% 0.13/0.39 % (3381)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (3381)Termination reason: Unknown
% 0.13/0.39 % (3381)Termination phase: Saturation
% 0.13/0.39
% 0.13/0.39 % (3381)Memory used [KB]: 5628
% 0.13/0.39 % (3381)Time elapsed: 0.011 s
% 0.13/0.39 % (3381)Instructions burned: 19 (million)
% 0.13/0.39 % (3381)------------------------------
% 0.13/0.39 % (3381)------------------------------
% 0.13/0.39 % (3384)Instruction limit reached!
% 0.13/0.39 % (3384)------------------------------
% 0.13/0.39 % (3384)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (3384)Termination reason: Unknown
% 0.13/0.39 % (3384)Termination phase: Saturation
% 0.13/0.39
% 0.13/0.39 % (3384)Memory used [KB]: 5628
% 0.13/0.39 % (3384)Time elapsed: 0.009 s
% 0.13/0.39 % (3384)Instructions burned: 15 (million)
% 0.13/0.39 % (3384)------------------------------
% 0.13/0.39 % (3384)------------------------------
% 0.13/0.39 % (3386)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)
% 0.13/0.40 % (3387)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.13/0.40 % (3388)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.13/0.40 % (3383)Instruction limit reached!
% 0.13/0.40 % (3383)------------------------------
% 0.13/0.40 % (3383)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.40 % (3383)Termination reason: Unknown
% 0.13/0.40 % (3383)Termination phase: Saturation
% 0.13/0.40
% 0.13/0.40 % (3383)Memory used [KB]: 5756
% 0.13/0.40 % (3383)Time elapsed: 0.043 s
% 0.20/0.40 % (3383)Instructions burned: 37 (million)
% 0.20/0.40 % (3383)------------------------------
% 0.20/0.40 % (3383)------------------------------
% 0.20/0.40 % (3387)Instruction limit reached!
% 0.20/0.40 % (3387)------------------------------
% 0.20/0.40 % (3387)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (3387)Termination reason: Unknown
% 0.20/0.40 % (3387)Termination phase: Property scanning
% 0.20/0.40
% 0.20/0.40 % (3387)Memory used [KB]: 1023
% 0.20/0.40 % (3387)Time elapsed: 0.006 s
% 0.20/0.40 % (3387)Instructions burned: 8 (million)
% 0.20/0.40 % (3387)------------------------------
% 0.20/0.40 % (3387)------------------------------
% 0.20/0.40 % (3389)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)
% 0.20/0.41 % (3389)Instruction limit reached!
% 0.20/0.41 % (3389)------------------------------
% 0.20/0.41 % (3389)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (3389)Termination reason: Unknown
% 0.20/0.41 % (3389)Termination phase: shuffling
% 0.20/0.41
% 0.20/0.41 % (3389)Memory used [KB]: 1023
% 0.20/0.41 % (3389)Time elapsed: 0.004 s
% 0.20/0.41 % (3389)Instructions burned: 4 (million)
% 0.20/0.41 % (3389)------------------------------
% 0.20/0.41 % (3389)------------------------------
% 0.20/0.41 % (3388)Instruction limit reached!
% 0.20/0.41 % (3388)------------------------------
% 0.20/0.41 % (3388)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (3388)Termination reason: Unknown
% 0.20/0.41 % (3388)Termination phase: Saturation
% 0.20/0.41
% 0.20/0.41 % (3388)Memory used [KB]: 5756
% 0.20/0.41 % (3388)Time elapsed: 0.011 s
% 0.20/0.41 % (3388)Instructions burned: 16 (million)
% 0.20/0.41 % (3388)------------------------------
% 0.20/0.41 % (3388)------------------------------
% 0.20/0.41 % (3390)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)
% 0.20/0.41 % (3390)Instruction limit reached!
% 0.20/0.41 % (3390)------------------------------
% 0.20/0.41 % (3390)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (3390)Termination reason: Unknown
% 0.20/0.41 % (3390)Termination phase: shuffling
% 0.20/0.41
% 0.20/0.41 % (3390)Memory used [KB]: 1023
% 0.20/0.41 % (3390)Time elapsed: 0.004 s
% 0.20/0.41 % (3390)Instructions burned: 3 (million)
% 0.20/0.41 % (3390)------------------------------
% 0.20/0.41 % (3390)------------------------------
% 0.20/0.42 % (3391)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.42 % (3392)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.42 % (3392)Instruction limit reached!
% 0.20/0.42 % (3392)------------------------------
% 0.20/0.42 % (3392)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (3392)Termination reason: Unknown
% 0.20/0.42 % (3392)Termination phase: shuffling
% 0.20/0.42
% 0.20/0.42 % (3392)Memory used [KB]: 1023
% 0.20/0.42 % (3392)Time elapsed: 0.004 s
% 0.20/0.42 % (3392)Instructions burned: 4 (million)
% 0.20/0.42 % (3392)------------------------------
% 0.20/0.42 % (3392)------------------------------
% 0.20/0.42 % (3393)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.20/0.42 % (3391)Instruction limit reached!
% 0.20/0.42 % (3391)------------------------------
% 0.20/0.42 % (3391)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (3391)Termination reason: Unknown
% 0.20/0.42 % (3391)Termination phase: Property scanning
% 0.20/0.42
% 0.20/0.42 % (3391)Memory used [KB]: 1023
% 0.20/0.42 % (3391)Time elapsed: 0.006 s
% 0.20/0.42 % (3391)Instructions burned: 8 (million)
% 0.20/0.42 % (3391)------------------------------
% 0.20/0.42 % (3391)------------------------------
% 0.20/0.42 % (3393)Instruction limit reached!
% 0.20/0.42 % (3393)------------------------------
% 0.20/0.42 % (3393)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (3393)Termination reason: Unknown
% 0.20/0.42 % (3393)Termination phase: shuffling
% 0.20/0.42
% 0.20/0.42 % (3393)Memory used [KB]: 1023
% 0.20/0.42 % (3393)Time elapsed: 0.004 s
% 0.20/0.42 % (3393)Instructions burned: 4 (million)
% 0.20/0.42 % (3393)------------------------------
% 0.20/0.42 % (3393)------------------------------
% 0.20/0.42 % (3386)First to succeed.
% 0.20/0.42 % (3394)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.43 % (3386)Refutation found. Thanks to Tanya!
% 0.20/0.43 % SZS status Theorem for theBenchmark
% 0.20/0.43 % SZS output start Proof for theBenchmark
% 0.20/0.43 thf(type_def_5, type, mu: $tType).
% 0.20/0.43 thf(func_def_0, type, mu: $tType).
% 0.20/0.43 thf(func_def_1, type, qmltpeq: mu > mu > $i > $o).
% 0.20/0.43 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_6, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_7, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_8, type, mtrue: $i > $o).
% 0.20/0.43 thf(func_def_9, type, mfalse: $i > $o).
% 0.20/0.43 thf(func_def_10, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_11, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_12, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_13, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_14, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_15, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_16, type, exists_in_world: mu > $i > $o).
% 0.20/0.43 thf(func_def_17, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_18, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_19, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_20, type, mreflexive: ($i > $i > $o) > $o).
% 0.20/0.43 thf(func_def_21, type, msymmetric: ($i > $i > $o) > $o).
% 0.20/0.43 thf(func_def_22, type, mserial: ($i > $i > $o) > $o).
% 0.20/0.43 thf(func_def_23, type, mtransitive: ($i > $i > $o) > $o).
% 0.20/0.43 thf(func_def_24, type, meuclidean: ($i > $i > $o) > $o).
% 0.20/0.43 thf(func_def_25, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.20/0.43 thf(func_def_26, type, mfunctional: ($i > $i > $o) > $o).
% 0.20/0.43 thf(func_def_27, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.20/0.43 thf(func_def_28, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.20/0.43 thf(func_def_29, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.20/0.43 thf(func_def_30, type, mvalid: ($i > $o) > $o).
% 0.20/0.43 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.20/0.43 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.20/0.43 thf(func_def_33, type, minvalid: ($i > $o) > $o).
% 0.20/0.43 thf(func_def_34, type, rel_s4: $i > $i > $o).
% 0.20/0.43 thf(func_def_35, type, mbox_s4: ($i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_36, type, mdia_s4: ($i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_37, type, r: $i > $o).
% 0.20/0.43 thf(func_def_38, type, q: $i > $o).
% 0.20/0.43 thf(func_def_39, type, p: $i > $o).
% 0.20/0.43 thf(func_def_56, type, ph1: !>[X0: $tType]:(X0)).
% 0.20/0.43 thf(func_def_57, type, sK2: $i > mu).
% 0.20/0.43 thf(f413,plain,(
% 0.20/0.43 $false),
% 0.20/0.43 inference(avatar_sat_refutation,[],[f221,f294,f303,f336,f393,f403,f412])).
% 0.20/0.43 thf(f412,plain,(
% 0.20/0.43 ~spl0_1 | ~spl0_5),
% 0.20/0.43 inference(avatar_contradiction_clause,[],[f411])).
% 0.20/0.43 thf(f411,plain,(
% 0.20/0.43 $false | (~spl0_1 | ~spl0_5)),
% 0.20/0.43 inference(trivial_inequality_removal,[],[f410])).
% 0.20/0.43 thf(f410,plain,(
% 0.20/0.43 ($false = $true) | (~spl0_1 | ~spl0_5)),
% 0.20/0.43 inference(boolean_simplification,[],[f405])).
% 0.20/0.43 thf(f405,plain,(
% 0.20/0.43 ($false = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (r @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (q @ Y0))))))) | $true)) | (~spl0_1 | ~spl0_5)),
% 0.20/0.43 inference(backward_demodulation,[],[f357,f389])).
% 0.20/0.43 thf(f389,plain,(
% 0.20/0.43 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0)))) = $true) | ~spl0_5),
% 0.20/0.43 inference(avatar_component_clause,[],[f388])).
% 0.20/0.43 thf(f388,plain,(
% 0.20/0.43 spl0_5 <=> ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0)))) = $true)),
% 0.20/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])).
% 0.20/0.43 thf(f357,plain,(
% 0.20/0.43 ($false = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (r @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (q @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0)))))) | ~spl0_1),
% 0.20/0.43 inference(binary_proxy_clausification,[],[f353])).
% 0.20/0.43 thf(f353,plain,(
% 0.20/0.43 ($false = (((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (r @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (q @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0))))) | ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (r @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0)))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (q @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0))))))))) | ~spl0_1),
% 0.20/0.43 inference(boolean_simplification,[],[f352])).
% 0.20/0.43 thf(f352,plain,(
% 0.20/0.43 ($false = ($false | (((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (r @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (q @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0))))) | ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (r @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0)))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (q @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0)))))))))) | ~spl0_1),
% 0.20/0.43 inference(backward_demodulation,[],[f345,f351])).
% 0.20/0.43 thf(f351,plain,(
% 0.20/0.43 ($false = (~ (rel_s4 @ sK3 @ sK5))) | ~spl0_1),
% 0.20/0.43 inference(binary_proxy_clausification,[],[f345])).
% 0.20/0.43 thf(f345,plain,(
% 0.20/0.43 ($false = ((~ (rel_s4 @ sK3 @ sK5)) | (((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (r @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (q @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0))))) | ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (r @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0)))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (q @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0)))))))))) | ~spl0_1),
% 0.20/0.43 inference(beta_eta_normalization,[],[f344])).
% 0.20/0.43 thf(f344,plain,(
% 0.20/0.43 ($false = ((^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))) @ sK5)) | ~spl0_1),
% 0.20/0.43 inference(sigma_clausification,[],[f339])).
% 0.20/0.43 thf(f339,plain,(
% 0.20/0.43 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))))) | ~spl0_1),
% 0.20/0.43 inference(not_proxy_clausification,[],[f217])).
% 0.20/0.43 thf(f217,plain,(
% 0.20/0.43 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))))) | ~spl0_1),
% 0.20/0.43 inference(avatar_component_clause,[],[f216])).
% 0.20/0.43 thf(f216,plain,(
% 0.20/0.43 spl0_1 <=> ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))))))),
% 0.20/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.20/0.43 thf(f403,plain,(
% 0.20/0.43 ~spl0_1 | ~spl0_6),
% 0.20/0.43 inference(avatar_contradiction_clause,[],[f402])).
% 0.20/0.43 thf(f402,plain,(
% 0.20/0.43 $false | (~spl0_1 | ~spl0_6)),
% 0.20/0.43 inference(trivial_inequality_removal,[],[f401])).
% 0.20/0.43 thf(f401,plain,(
% 0.20/0.43 ($false = $true) | (~spl0_1 | ~spl0_6)),
% 0.20/0.43 inference(boolean_simplification,[],[f400])).
% 0.20/0.43 thf(f400,plain,(
% 0.20/0.43 ($false = (~ $false)) | (~spl0_1 | ~spl0_6)),
% 0.20/0.43 inference(backward_demodulation,[],[f363,f399])).
% 0.20/0.43 thf(f399,plain,(
% 0.20/0.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (q @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0)))))) | (~spl0_1 | ~spl0_6)),
% 0.20/0.43 inference(boolean_simplification,[],[f398])).
% 0.20/0.43 thf(f398,plain,(
% 0.20/0.43 ($false = ((~ (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (q @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0)))))) | (~spl0_1 | ~spl0_6)),
% 0.20/0.43 inference(boolean_simplification,[],[f397])).
% 0.20/0.43 thf(f397,plain,(
% 0.20/0.43 ($false = ((~ ($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (q @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0)))))) | (~spl0_1 | ~spl0_6)),
% 0.20/0.43 inference(boolean_simplification,[],[f395])).
% 0.20/0.43 thf(f395,plain,(
% 0.20/0.43 ($false = ((~ ((~ $true) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (q @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0)))))) | (~spl0_1 | ~spl0_6)),
% 0.20/0.43 inference(backward_demodulation,[],[f357,f392])).
% 0.20/0.43 thf(f392,plain,(
% 0.20/0.43 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (r @ Y0)))) = $true) | ~spl0_6),
% 0.20/0.43 inference(avatar_component_clause,[],[f391])).
% 0.20/0.43 thf(f391,plain,(
% 0.20/0.43 spl0_6 <=> ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (r @ Y0)))) = $true)),
% 0.20/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])).
% 0.20/0.43 thf(f363,plain,(
% 0.20/0.43 ($false = (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (q @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0))))))) | ~spl0_1),
% 0.20/0.43 inference(binary_proxy_clausification,[],[f359])).
% 0.20/0.43 thf(f359,plain,(
% 0.20/0.43 ($false = ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (r @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0)))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (q @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0)))))))) | ~spl0_1),
% 0.20/0.43 inference(boolean_simplification,[],[f358])).
% 0.20/0.43 thf(f358,plain,(
% 0.20/0.43 ($false = ($false | ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (r @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0)))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (q @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0))))))))) | ~spl0_1),
% 0.20/0.43 inference(backward_demodulation,[],[f353,f357])).
% 0.20/0.43 thf(f393,plain,(
% 0.20/0.43 spl0_5 | spl0_6 | ~spl0_1),
% 0.20/0.43 inference(avatar_split_clause,[],[f386,f216,f391,f388])).
% 0.20/0.43 thf(f386,plain,(
% 0.20/0.43 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (r @ Y0)))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0)))) = $true) | ~spl0_1),
% 0.20/0.43 inference(binary_proxy_clausification,[],[f377])).
% 0.20/0.43 thf(f377,plain,(
% 0.20/0.43 (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (r @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0))))) = $true) | ~spl0_1),
% 0.20/0.43 inference(not_proxy_clausification,[],[f366])).
% 0.20/0.43 thf(f366,plain,(
% 0.20/0.43 ($false = (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (r @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0))))))) | ~spl0_1),
% 0.20/0.43 inference(boolean_simplification,[],[f365])).
% 0.20/0.43 thf(f365,plain,(
% 0.20/0.43 ($false = ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (r @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0)))))) | $false)) | ~spl0_1),
% 0.20/0.43 inference(backward_demodulation,[],[f359,f363])).
% 0.20/0.43 thf(f336,plain,(
% 0.20/0.43 ~spl0_2 | ~spl0_4),
% 0.20/0.43 inference(avatar_contradiction_clause,[],[f335])).
% 0.20/0.43 thf(f335,plain,(
% 0.20/0.43 $false | (~spl0_2 | ~spl0_4)),
% 0.20/0.43 inference(trivial_inequality_removal,[],[f334])).
% 0.20/0.43 thf(f334,plain,(
% 0.20/0.43 ($false = $true) | (~spl0_2 | ~spl0_4)),
% 0.20/0.43 inference(boolean_simplification,[],[f331])).
% 0.20/0.43 thf(f331,plain,(
% 0.20/0.43 ($false = ($true | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0)))))) | (~spl0_2 | ~spl0_4)),
% 0.20/0.43 inference(backward_demodulation,[],[f320,f330])).
% 0.20/0.43 thf(f330,plain,(
% 0.20/0.43 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (q @ Y0)))) = $true) | ~spl0_4),
% 0.20/0.43 inference(not_proxy_clausification,[],[f310])).
% 0.20/0.43 thf(f310,plain,(
% 0.20/0.43 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (q @ Y0)))))) | ~spl0_4),
% 0.20/0.43 inference(binary_proxy_clausification,[],[f307])).
% 0.20/0.43 thf(f307,plain,(
% 0.20/0.43 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (r @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (q @ Y0))))))) | ~spl0_4),
% 0.20/0.43 inference(not_proxy_clausification,[],[f293])).
% 0.20/0.43 thf(f293,plain,(
% 0.20/0.43 ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (r @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (q @ Y0))))))) = $true) | ~spl0_4),
% 0.20/0.43 inference(avatar_component_clause,[],[f292])).
% 0.20/0.43 thf(f292,plain,(
% 0.20/0.43 spl0_4 <=> ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (r @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (q @ Y0))))))) = $true)),
% 0.20/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.20/0.43 thf(f320,plain,(
% 0.20/0.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (q @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0)))))) | (~spl0_2 | ~spl0_4)),
% 0.20/0.43 inference(boolean_simplification,[],[f319])).
% 0.20/0.43 thf(f319,plain,(
% 0.20/0.43 ($false = (~ (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (q @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0)))))))) | (~spl0_2 | ~spl0_4)),
% 0.20/0.43 inference(boolean_simplification,[],[f318])).
% 0.20/0.43 thf(f318,plain,(
% 0.20/0.43 ($false = (~ ($false | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (q @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0))))))))) | (~spl0_2 | ~spl0_4)),
% 0.20/0.43 inference(boolean_simplification,[],[f317])).
% 0.20/0.43 thf(f317,plain,(
% 0.20/0.43 ($false = (~ ((~ $true) | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (q @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0))))))))) | (~spl0_2 | ~spl0_4)),
% 0.20/0.43 inference(boolean_simplification,[],[f316])).
% 0.20/0.43 thf(f316,plain,(
% 0.20/0.43 ($false = (~ ((~ ($true | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0)))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (q @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0))))))))) | (~spl0_2 | ~spl0_4)),
% 0.20/0.43 inference(backward_demodulation,[],[f281,f314])).
% 0.20/0.43 thf(f314,plain,(
% 0.20/0.43 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (r @ Y0))))) | ~spl0_4),
% 0.20/0.43 inference(not_proxy_clausification,[],[f313])).
% 0.20/0.43 thf(f313,plain,(
% 0.20/0.43 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (r @ Y0)))))) | ~spl0_4),
% 0.20/0.43 inference(boolean_simplification,[],[f312])).
% 0.20/0.43 thf(f312,plain,(
% 0.20/0.43 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (r @ Y0))))) | $false)) | ~spl0_4),
% 0.20/0.43 inference(backward_demodulation,[],[f307,f310])).
% 0.20/0.43 thf(f281,plain,(
% 0.20/0.43 ($false = (~ ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (r @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0)))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (q @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0))))))))) | ~spl0_2),
% 0.20/0.43 inference(binary_proxy_clausification,[],[f229])).
% 0.20/0.43 thf(f229,plain,(
% 0.20/0.43 ($false = ((~ ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (r @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0)))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (q @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0)))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (r @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (q @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0)))))))) | ~spl0_2),
% 0.20/0.43 inference(binary_proxy_clausification,[],[f228])).
% 0.20/0.43 thf(f228,plain,(
% 0.20/0.43 ($false = ((~ (rel_s4 @ sK3 @ sK4)) | ((~ ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (r @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0)))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (q @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0)))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (r @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (q @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0))))))))) | ~spl0_2),
% 0.20/0.43 inference(beta_eta_normalization,[],[f227])).
% 0.20/0.43 thf(f227,plain,(
% 0.20/0.43 ($false = ((^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | ((~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))) @ sK4)) | ~spl0_2),
% 0.20/0.43 inference(sigma_clausification,[],[f224])).
% 0.20/0.43 thf(f224,plain,(
% 0.20/0.43 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | ((~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) | ~spl0_2),
% 0.20/0.43 inference(not_proxy_clausification,[],[f220])).
% 0.20/0.43 thf(f220,plain,(
% 0.20/0.43 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | ((~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) = $true) | ~spl0_2),
% 0.20/0.43 inference(avatar_component_clause,[],[f219])).
% 0.20/0.43 thf(f219,plain,(
% 0.20/0.43 spl0_2 <=> ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | ((~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) = $true)),
% 0.20/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.20/0.43 thf(f303,plain,(
% 0.20/0.43 ~spl0_2 | ~spl0_3),
% 0.20/0.43 inference(avatar_contradiction_clause,[],[f302])).
% 0.20/0.43 thf(f302,plain,(
% 0.20/0.43 $false | (~spl0_2 | ~spl0_3)),
% 0.20/0.43 inference(trivial_inequality_removal,[],[f301])).
% 0.20/0.43 thf(f301,plain,(
% 0.20/0.43 ($false = $true) | (~spl0_2 | ~spl0_3)),
% 0.20/0.43 inference(boolean_simplification,[],[f300])).
% 0.20/0.43 thf(f300,plain,(
% 0.20/0.43 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (r @ Y0)))) | $true)) | (~spl0_2 | ~spl0_3)),
% 0.20/0.43 inference(boolean_simplification,[],[f299])).
% 0.20/0.43 thf(f299,plain,(
% 0.20/0.43 ($false = (~ (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (r @ Y0)))) | $true)))) | (~spl0_2 | ~spl0_3)),
% 0.20/0.43 inference(boolean_simplification,[],[f298])).
% 0.20/0.43 thf(f298,plain,(
% 0.20/0.43 ($false = (~ ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (r @ Y0)))) | $true)) | $false))) | (~spl0_2 | ~spl0_3)),
% 0.20/0.43 inference(boolean_simplification,[],[f297])).
% 0.20/0.43 thf(f297,plain,(
% 0.20/0.43 ($false = (~ ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (r @ Y0)))) | $true)) | (~ $true)))) | (~spl0_2 | ~spl0_3)),
% 0.20/0.43 inference(boolean_simplification,[],[f296])).
% 0.20/0.43 thf(f296,plain,(
% 0.20/0.43 ((~ ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (r @ Y0)))) | $true)) | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (q @ Y0)))) | $true)))) = $false) | (~spl0_2 | ~spl0_3)),
% 0.20/0.43 inference(backward_demodulation,[],[f281,f290])).
% 0.20/0.43 thf(f290,plain,(
% 0.20/0.43 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0)))) = $true) | ~spl0_3),
% 0.20/0.43 inference(avatar_component_clause,[],[f289])).
% 0.20/0.43 thf(f289,plain,(
% 0.20/0.43 spl0_3 <=> ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0)))) = $true)),
% 0.20/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.20/0.43 thf(f294,plain,(
% 0.20/0.43 spl0_3 | spl0_4 | ~spl0_2),
% 0.20/0.43 inference(avatar_split_clause,[],[f287,f219,f292,f289])).
% 0.20/0.43 thf(f287,plain,(
% 0.20/0.43 ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (r @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (q @ Y0))))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0)))) = $true) | ~spl0_2),
% 0.20/0.43 inference(binary_proxy_clausification,[],[f284])).
% 0.20/0.43 thf(f284,plain,(
% 0.20/0.43 ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (r @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (q @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0)))))) | ~spl0_2),
% 0.20/0.43 inference(not_proxy_clausification,[],[f283])).
% 0.20/0.43 thf(f283,plain,(
% 0.20/0.43 ($false = (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (r @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (q @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0))))))) | ~spl0_2),
% 0.20/0.43 inference(boolean_simplification,[],[f282])).
% 0.20/0.43 thf(f282,plain,(
% 0.20/0.43 ($false = ($false | (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (r @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (q @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0)))))))) | ~spl0_2),
% 0.20/0.43 inference(backward_demodulation,[],[f229,f281])).
% 0.20/0.43 thf(f221,plain,(
% 0.20/0.43 spl0_1 | spl0_2),
% 0.20/0.43 inference(avatar_split_clause,[],[f214,f219,f216])).
% 0.20/0.43 thf(f214,plain,(
% 0.20/0.43 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | ((~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))))))),
% 0.20/0.43 inference(binary_proxy_clausification,[],[f211])).
% 0.20/0.43 thf(f211,plain,(
% 0.20/0.43 ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | ((~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))))))),
% 0.20/0.43 inference(not_proxy_clausification,[],[f210])).
% 0.20/0.43 thf(f210,plain,(
% 0.20/0.43 ($false = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | ((~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (r @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))))))),
% 0.20/0.43 inference(beta_eta_normalization,[],[f209])).
% 0.20/0.43 thf(f209,plain,(
% 0.20/0.43 ($false = ((^[Y0 : $i]: (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (r @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (q @ Y2))))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))) | ((~ ((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (r @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))) | (~ ((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (q @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | ((~ ((~ ((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (r @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))) | (~ ((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (q @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (r @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (q @ Y2))))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))))))))))) @ sK3))),
% 0.20/0.43 inference(sigma_clausification,[],[f206])).
% 0.20/0.43 thf(f206,plain,(
% 0.20/0.43 ($false = (!! @ $i @ (^[Y0 : $i]: (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (r @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (q @ Y2))))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))) | ((~ ((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (r @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))) | (~ ((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (q @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | ((~ ((~ ((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (r @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))) | (~ ((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (q @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (r @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (q @ Y2))))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))))))))),
% 0.20/0.43 inference(not_proxy_clausification,[],[f164])).
% 0.20/0.43 thf(f164,plain,(
% 0.20/0.43 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (r @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (q @ Y2))))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))) | ((~ ((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (r @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))) | (~ ((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (q @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | ((~ ((~ ((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (r @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))) | (~ ((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (q @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (r @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (q @ Y2))))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))))))))))))))),
% 0.20/0.43 inference(boolean_simplification,[],[f163])).
% 0.20/0.43 thf(f163,plain,(
% 0.20/0.43 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (r @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (q @ Y2))))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))) | (~ (~ ((~ ((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (r @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))) | (~ ((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (q @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | ((~ ((~ ((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (r @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))) | (~ ((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (q @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (r @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (q @ Y2))))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))))))))))))))),
% 0.20/0.43 inference(beta_eta_normalization,[],[f161])).
% 0.20/0.43 thf(f161,plain,(
% 0.20/0.43 ((~ ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ q) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ r))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ q)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ r))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ q)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ r))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ q) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ r)))))))) = $true)),
% 0.20/0.43 inference(definition_unfolding,[],[f131,f116,f150,f135,f151,f127,f135,f150,f135,f135,f150,f127,f135,f135,f127,f135,f135,f135,f151,f150,f127,f135,f135,f127,f135,f135,f127,f135,f150,f135,f135])).
% 0.20/0.43 thf(f127,plain,(
% 0.20/0.43 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.20/0.43 inference(cnf_transformation,[],[f51])).
% 0.20/0.43 thf(f51,plain,(
% 0.20/0.43 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.20/0.43 inference(fool_elimination,[],[f50])).
% 0.20/0.43 thf(f50,plain,(
% 0.20/0.43 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.20/0.43 inference(rectify,[],[f3])).
% 0.20/0.43 thf(f3,axiom,(
% 0.20/0.43 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))),
% 0.20/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.20/0.43 thf(f151,plain,(
% 0.20/0.43 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.20/0.43 inference(definition_unfolding,[],[f138,f127,f129])).
% 0.20/0.43 thf(f129,plain,(
% 0.20/0.43 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.43 inference(cnf_transformation,[],[f92])).
% 0.20/0.43 thf(f92,plain,(
% 0.20/0.43 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.43 inference(fool_elimination,[],[f91])).
% 0.20/0.43 thf(f91,plain,(
% 0.20/0.43 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.20/0.43 inference(rectify,[],[f2])).
% 0.20/0.43 thf(f2,axiom,(
% 0.20/0.43 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.20/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.20/0.43 thf(f138,plain,(
% 0.20/0.43 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.43 inference(cnf_transformation,[],[f68])).
% 0.20/0.43 thf(f68,plain,(
% 0.20/0.43 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.43 inference(fool_elimination,[],[f67])).
% 0.20/0.43 thf(f67,plain,(
% 0.20/0.43 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.20/0.43 inference(rectify,[],[f9])).
% 0.20/0.43 thf(f9,axiom,(
% 0.20/0.43 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.20/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.20/0.43 thf(f135,plain,(
% 0.20/0.43 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.20/0.43 inference(cnf_transformation,[],[f88])).
% 0.20/0.43 thf(f88,plain,(
% 0.20/0.43 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.20/0.43 inference(fool_elimination,[],[f87])).
% 0.20/0.43 thf(f87,plain,(
% 0.20/0.43 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_s4 @ X1 @ X2)))) = mbox_s4)),
% 0.20/0.43 inference(rectify,[],[f32])).
% 0.20/0.43 thf(f32,axiom,(
% 0.20/0.43 ((^[X3 : $i > $o, X2 : $i] : (! [X6] : ((X3 @ X6) | ~(rel_s4 @ X2 @ X6)))) = mbox_s4)),
% 0.20/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s4)).
% 0.20/0.43 thf(f150,plain,(
% 0.20/0.43 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.20/0.43 inference(definition_unfolding,[],[f122,f129,f127,f129,f129])).
% 0.20/0.43 thf(f122,plain,(
% 0.20/0.43 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.20/0.43 inference(cnf_transformation,[],[f72])).
% 0.20/0.43 thf(f72,plain,(
% 0.20/0.43 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.20/0.43 inference(fool_elimination,[],[f71])).
% 0.20/0.43 thf(f71,plain,(
% 0.20/0.43 ((^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))) = mand)),
% 0.20/0.43 inference(rectify,[],[f8])).
% 0.20/0.43 thf(f8,axiom,(
% 0.20/0.43 ((^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))) = mand)),
% 0.20/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)).
% 0.20/0.43 thf(f116,plain,(
% 0.20/0.43 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.43 inference(cnf_transformation,[],[f74])).
% 0.20/0.43 thf(f74,plain,(
% 0.20/0.43 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.43 inference(fool_elimination,[],[f73])).
% 0.20/0.43 thf(f73,plain,(
% 0.20/0.43 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.20/0.43 inference(rectify,[],[f28])).
% 0.20/0.43 thf(f28,axiom,(
% 0.20/0.43 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.20/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.20/0.43 thf(f131,plain,(
% 0.20/0.43 ((~ (mvalid @ (mand @ (mbox_s4 @ (mimplies @ (mor @ (mbox_s4 @ p) @ (mand @ (mbox_s4 @ q) @ (mbox_s4 @ r))) @ (mand @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ q)) @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ r))))) @ (mbox_s4 @ (mimplies @ (mand @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ q)) @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ r))) @ (mor @ (mbox_s4 @ p) @ (mand @ (mbox_s4 @ q) @ (mbox_s4 @ r)))))))) = $true)),
% 0.20/0.43 inference(cnf_transformation,[],[f109])).
% 0.20/0.43 thf(f109,plain,(
% 0.20/0.43 ((~ (mvalid @ (mand @ (mbox_s4 @ (mimplies @ (mor @ (mbox_s4 @ p) @ (mand @ (mbox_s4 @ q) @ (mbox_s4 @ r))) @ (mand @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ q)) @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ r))))) @ (mbox_s4 @ (mimplies @ (mand @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ q)) @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ r))) @ (mor @ (mbox_s4 @ p) @ (mand @ (mbox_s4 @ q) @ (mbox_s4 @ r)))))))) = $true)),
% 0.20/0.43 inference(fool_elimination,[],[f108])).
% 0.20/0.43 thf(f108,plain,(
% 0.20/0.43 ~(mvalid @ (mand @ (mbox_s4 @ (mimplies @ (mor @ (mbox_s4 @ p) @ (mand @ (mbox_s4 @ q) @ (mbox_s4 @ r))) @ (mand @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ q)) @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ r))))) @ (mbox_s4 @ (mimplies @ (mand @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ q)) @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ r))) @ (mor @ (mbox_s4 @ p) @ (mand @ (mbox_s4 @ q) @ (mbox_s4 @ r)))))))),
% 0.20/0.43 inference(rectify,[],[f38])).
% 0.20/0.43 thf(f38,negated_conjecture,(
% 0.20/0.43 ~(mvalid @ (mand @ (mbox_s4 @ (mimplies @ (mor @ (mbox_s4 @ p) @ (mand @ (mbox_s4 @ q) @ (mbox_s4 @ r))) @ (mand @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ q)) @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ r))))) @ (mbox_s4 @ (mimplies @ (mand @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ q)) @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ r))) @ (mor @ (mbox_s4 @ p) @ (mand @ (mbox_s4 @ q) @ (mbox_s4 @ r)))))))),
% 0.20/0.43 inference(negated_conjecture,[],[f37])).
% 0.20/0.43 thf(f37,conjecture,(
% 0.20/0.43 (mvalid @ (mand @ (mbox_s4 @ (mimplies @ (mor @ (mbox_s4 @ p) @ (mand @ (mbox_s4 @ q) @ (mbox_s4 @ r))) @ (mand @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ q)) @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ r))))) @ (mbox_s4 @ (mimplies @ (mand @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ q)) @ (mor @ (mbox_s4 @ p) @ (mbox_s4 @ r))) @ (mor @ (mbox_s4 @ p) @ (mand @ (mbox_s4 @ q) @ (mbox_s4 @ r)))))))),
% 0.20/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel13)).
% 0.20/0.43 % SZS output end Proof for theBenchmark
% 0.20/0.43 % (3386)------------------------------
% 0.20/0.43 % (3386)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (3386)Termination reason: Refutation
% 0.20/0.43
% 0.20/0.43 % (3386)Memory used [KB]: 6012
% 0.20/0.43 % (3386)Time elapsed: 0.059 s
% 0.20/0.43 % (3386)Instructions burned: 78 (million)
% 0.20/0.43 % (3386)------------------------------
% 0.20/0.43 % (3386)------------------------------
% 0.20/0.43 % (3374)Success in time 0.082 s
% 0.20/0.43 % Vampire---4.8 exiting
%------------------------------------------------------------------------------