TSTP Solution File: SYO459^6 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO459^6 : TPTP v8.2.0. 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 : n020.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 09:04:48 EDT 2024
% Result : Theorem 0.21s 0.42s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO459^6 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.14 % 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
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 09:38:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.38 % (7694)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)
% 0.21/0.38 % (7693)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)
% 0.21/0.38 % (7695)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.38 % (7696)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)
% 0.21/0.38 % (7692)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.21/0.38 % (7697)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)
% 0.21/0.38 % (7698)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.38 % (7699)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)
% 0.21/0.38 % (7696)Instruction limit reached!
% 0.21/0.38 % (7696)------------------------------
% 0.21/0.38 % (7696)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (7696)Termination reason: Unknown
% 0.21/0.38 % (7696)Termination phase: shuffling
% 0.21/0.38
% 0.21/0.38 % (7696)Memory used [KB]: 1023
% 0.21/0.38 % (7696)Time elapsed: 0.003 s
% 0.21/0.38 % (7696)Instructions burned: 2 (million)
% 0.21/0.38 % (7696)------------------------------
% 0.21/0.38 % (7696)------------------------------
% 0.21/0.38 % (7695)Instruction limit reached!
% 0.21/0.38 % (7695)------------------------------
% 0.21/0.38 % (7695)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (7695)Termination reason: Unknown
% 0.21/0.38 % (7695)Termination phase: shuffling
% 0.21/0.38
% 0.21/0.38 % (7695)Memory used [KB]: 1023
% 0.21/0.38 % (7695)Time elapsed: 0.004 s
% 0.21/0.38 % (7695)Instructions burned: 3 (million)
% 0.21/0.38 % (7695)------------------------------
% 0.21/0.38 % (7695)------------------------------
% 0.21/0.38 % (7699)Instruction limit reached!
% 0.21/0.38 % (7699)------------------------------
% 0.21/0.38 % (7699)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (7699)Termination reason: Unknown
% 0.21/0.38 % (7699)Termination phase: shuffling
% 0.21/0.38
% 0.21/0.38 % (7699)Memory used [KB]: 1023
% 0.21/0.38 % (7699)Time elapsed: 0.004 s
% 0.21/0.38 % (7699)Instructions burned: 3 (million)
% 0.21/0.38 % (7699)------------------------------
% 0.21/0.38 % (7699)------------------------------
% 0.21/0.38 % (7693)Instruction limit reached!
% 0.21/0.38 % (7693)------------------------------
% 0.21/0.38 % (7693)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (7693)Termination reason: Unknown
% 0.21/0.38 % (7693)Termination phase: Property scanning
% 0.21/0.38
% 0.21/0.38 % (7693)Memory used [KB]: 1023
% 0.21/0.38 % (7693)Time elapsed: 0.005 s
% 0.21/0.38 % (7693)Instructions burned: 5 (million)
% 0.21/0.38 % (7693)------------------------------
% 0.21/0.38 % (7693)------------------------------
% 0.21/0.39 % (7697)Refutation not found, incomplete strategy
% 0.21/0.39 % (7697)------------------------------
% 0.21/0.39 % (7697)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (7697)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.39
% 0.21/0.39
% 0.21/0.39 % (7697)Memory used [KB]: 5628
% 0.21/0.39 % (7697)Time elapsed: 0.012 s
% 0.21/0.39 % (7697)Instructions burned: 16 (million)
% 0.21/0.39 % (7697)------------------------------
% 0.21/0.39 % (7697)------------------------------
% 0.21/0.39 % (7698)Instruction limit reached!
% 0.21/0.39 % (7698)------------------------------
% 0.21/0.39 % (7698)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (7698)Termination reason: Unknown
% 0.21/0.39 % (7698)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (7698)Memory used [KB]: 5628
% 0.21/0.39 % (7698)Time elapsed: 0.013 s
% 0.21/0.39 % (7698)Instructions burned: 18 (million)
% 0.21/0.39 % (7698)------------------------------
% 0.21/0.39 % (7698)------------------------------
% 0.21/0.39 % (7700)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)
% 0.21/0.39 % (7701)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)
% 0.21/0.39 % (7694)Instruction limit reached!
% 0.21/0.39 % (7694)------------------------------
% 0.21/0.39 % (7694)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (7694)Termination reason: Unknown
% 0.21/0.39 % (7694)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (7694)Memory used [KB]: 5756
% 0.21/0.39 % (7694)Time elapsed: 0.019 s
% 0.21/0.39 % (7694)Instructions burned: 27 (million)
% 0.21/0.39 % (7694)------------------------------
% 0.21/0.39 % (7694)------------------------------
% 0.21/0.39 % (7702)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)
% 0.21/0.39 % (7703)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)
% 0.21/0.40 % (7702)Instruction limit reached!
% 0.21/0.40 % (7702)------------------------------
% 0.21/0.40 % (7702)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (7702)Termination reason: Unknown
% 0.21/0.40 % (7702)Termination phase: shuffling
% 0.21/0.40
% 0.21/0.40 % (7702)Memory used [KB]: 1023
% 0.21/0.40 % (7702)Time elapsed: 0.004 s
% 0.21/0.40 % (7702)Instructions burned: 4 (million)
% 0.21/0.40 % (7702)------------------------------
% 0.21/0.40 % (7702)------------------------------
% 0.21/0.40 % (7701)Instruction limit reached!
% 0.21/0.40 % (7701)------------------------------
% 0.21/0.40 % (7701)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (7701)Termination reason: Unknown
% 0.21/0.40 % (7701)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (7701)Memory used [KB]: 5756
% 0.21/0.40 % (7701)Time elapsed: 0.011 s
% 0.21/0.40 % (7701)Instructions burned: 15 (million)
% 0.21/0.40 % (7701)------------------------------
% 0.21/0.40 % (7701)------------------------------
% 0.21/0.40 % (7704)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.40 % (7705)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.21/0.41 % (7704)Instruction limit reached!
% 0.21/0.41 % (7704)------------------------------
% 0.21/0.41 % (7704)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (7704)Termination reason: Unknown
% 0.21/0.41 % (7704)Termination phase: Function definition elimination
% 0.21/0.41
% 0.21/0.41 % (7704)Memory used [KB]: 1023
% 0.21/0.41 % (7704)Time elapsed: 0.006 s
% 0.21/0.41 % (7704)Instructions burned: 8 (million)
% 0.21/0.41 % (7704)------------------------------
% 0.21/0.41 % (7704)------------------------------
% 0.21/0.41 % (7706)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)
% 0.21/0.41 % (7706)Instruction limit reached!
% 0.21/0.41 % (7706)------------------------------
% 0.21/0.41 % (7706)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (7706)Termination reason: Unknown
% 0.21/0.41 % (7706)Termination phase: shuffling
% 0.21/0.41
% 0.21/0.41 % (7706)Memory used [KB]: 1023
% 0.21/0.41 % (7706)Time elapsed: 0.004 s
% 0.21/0.41 % (7706)Instructions burned: 3 (million)
% 0.21/0.41 % (7706)------------------------------
% 0.21/0.41 % (7706)------------------------------
% 0.21/0.41 % (7707)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)
% 0.21/0.41 % (7707)Instruction limit reached!
% 0.21/0.41 % (7707)------------------------------
% 0.21/0.41 % (7707)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (7707)Termination reason: Unknown
% 0.21/0.41 % (7707)Termination phase: shuffling
% 0.21/0.41
% 0.21/0.41 % (7707)Memory used [KB]: 1023
% 0.21/0.41 % (7707)Time elapsed: 0.004 s
% 0.21/0.41 % (7707)Instructions burned: 3 (million)
% 0.21/0.41 % (7707)------------------------------
% 0.21/0.41 % (7707)------------------------------
% 0.21/0.41 % (7705)Instruction limit reached!
% 0.21/0.41 % (7705)------------------------------
% 0.21/0.41 % (7705)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (7705)Termination reason: Unknown
% 0.21/0.41 % (7705)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (7705)Memory used [KB]: 5756
% 0.21/0.41 % (7705)Time elapsed: 0.012 s
% 0.21/0.41 % (7705)Instructions burned: 16 (million)
% 0.21/0.41 % (7705)------------------------------
% 0.21/0.41 % (7705)------------------------------
% 0.21/0.41 % (7700)Instruction limit reached!
% 0.21/0.41 % (7700)------------------------------
% 0.21/0.41 % (7700)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (7700)Termination reason: Unknown
% 0.21/0.41 % (7700)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (7700)Memory used [KB]: 5756
% 0.21/0.41 % (7700)Time elapsed: 0.024 s
% 0.21/0.41 % (7700)Instructions burned: 37 (million)
% 0.21/0.41 % (7700)------------------------------
% 0.21/0.41 % (7700)------------------------------
% 0.21/0.42 % (7692)First to succeed.
% 0.21/0.42 % (7708)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)
% 0.21/0.42 % (7692)Refutation found. Thanks to Tanya!
% 0.21/0.42 % SZS status Theorem for theBenchmark
% 0.21/0.42 % SZS output start Proof for theBenchmark
% 0.21/0.42 thf(type_def_5, type, mu: $tType).
% 0.21/0.42 thf(func_def_0, type, mu: $tType).
% 0.21/0.42 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.21/0.42 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_15, type, mtrue: $i > $o).
% 0.21/0.42 thf(func_def_16, type, mfalse: $i > $o).
% 0.21/0.42 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.21/0.42 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.21/0.42 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.21/0.42 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.21/0.42 thf(func_def_33, type, rel_s5: $i > $i > $o).
% 0.21/0.42 thf(func_def_34, type, mbox_s5: ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_35, type, mdia_s5: ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_36, type, p: $i > $o).
% 0.21/0.42 thf(func_def_54, type, sK2: $i > $i).
% 0.21/0.42 thf(func_def_55, type, sK3: $i > $i).
% 0.21/0.42 thf(f703,plain,(
% 0.21/0.42 $false),
% 0.21/0.42 inference(avatar_sat_refutation,[],[f300,f563,f589,f702])).
% 0.21/0.42 thf(f702,plain,(
% 0.21/0.42 ~spl0_10),
% 0.21/0.42 inference(avatar_contradiction_clause,[],[f701])).
% 0.21/0.42 thf(f701,plain,(
% 0.21/0.42 $false | ~spl0_10),
% 0.21/0.42 inference(trivial_inequality_removal,[],[f698])).
% 0.21/0.42 thf(f698,plain,(
% 0.21/0.42 ($true = $false) | ~spl0_10),
% 0.21/0.42 inference(superposition,[],[f538,f687])).
% 0.21/0.42 thf(f687,plain,(
% 0.21/0.42 ($false = (p @ (sK3 @ sK4)))),
% 0.21/0.42 inference(trivial_inequality_removal,[],[f671])).
% 0.21/0.42 thf(f671,plain,(
% 0.21/0.42 ($false = (p @ (sK3 @ sK4))) | ($true = $false)),
% 0.21/0.42 inference(superposition,[],[f207,f659])).
% 0.21/0.42 thf(f659,plain,(
% 0.21/0.42 ( ! [X0 : $i] : (($false = (rel_s5 @ sK1 @ X0)) | ($false = (p @ (sK3 @ X0)))) )),
% 0.21/0.42 inference(trivial_inequality_removal,[],[f658])).
% 0.21/0.42 thf(f658,plain,(
% 0.21/0.42 ( ! [X0 : $i] : (($false = (p @ (sK3 @ X0))) | ($false = (rel_s5 @ sK1 @ X0)) | ($true = $false)) )),
% 0.21/0.42 inference(duplicate_literal_removal,[],[f649])).
% 0.21/0.42 thf(f649,plain,(
% 0.21/0.42 ( ! [X0 : $i] : (($false = (rel_s5 @ sK1 @ X0)) | ($false = (p @ (sK3 @ X0))) | ($true = $false) | ($false = (rel_s5 @ sK1 @ X0))) )),
% 0.21/0.42 inference(superposition,[],[f190,f395])).
% 0.21/0.42 thf(f395,plain,(
% 0.21/0.42 ( ! [X0 : $i,X1 : $i] : (($false = (rel_s5 @ X1 @ (sK2 @ X0))) | ($false = (p @ (sK3 @ X1))) | ($false = (rel_s5 @ sK1 @ X0))) )),
% 0.21/0.42 inference(trivial_inequality_removal,[],[f382])).
% 0.21/0.42 thf(f382,plain,(
% 0.21/0.42 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($false = (p @ (sK3 @ X1))) | ($false = (rel_s5 @ sK1 @ X0)) | ($false = (rel_s5 @ X1 @ (sK2 @ X0)))) )),
% 0.21/0.42 inference(superposition,[],[f200,f218])).
% 0.21/0.42 thf(f218,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (($true = (rel_s5 @ X1 @ X2)) | ($false = (rel_s5 @ X2 @ X1))) )),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f217])).
% 0.21/0.42 thf(f217,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (($true = ((rel_s5 @ X2 @ X1) => (rel_s5 @ X1 @ X2)))) )),
% 0.21/0.42 inference(beta_eta_normalization,[],[f216])).
% 0.21/0.42 thf(f216,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((rel_s5 @ Y0 @ X1) => (rel_s5 @ X1 @ Y0))) @ X2))) )),
% 0.21/0.42 inference(pi_clausification,[],[f215])).
% 0.21/0.42 thf(f215,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((rel_s5 @ Y0 @ X1) => (rel_s5 @ X1 @ Y0)))))) )),
% 0.21/0.42 inference(beta_eta_normalization,[],[f214])).
% 0.21/0.42 thf(f214,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y1 @ Y0) => (rel_s5 @ Y0 @ Y1))))) @ X1))) )),
% 0.21/0.42 inference(pi_clausification,[],[f213])).
% 0.21/0.42 thf(f213,plain,(
% 0.21/0.42 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y1 @ Y0) => (rel_s5 @ Y0 @ Y1)))))))),
% 0.21/0.42 inference(beta_eta_normalization,[],[f159])).
% 0.21/0.42 thf(f159,plain,(
% 0.21/0.42 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))) @ rel_s5))),
% 0.21/0.42 inference(definition_unfolding,[],[f138,f134])).
% 0.21/0.42 thf(f134,plain,(
% 0.21/0.42 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))))),
% 0.21/0.42 inference(cnf_transformation,[],[f78])).
% 0.21/0.42 thf(f78,plain,(
% 0.21/0.42 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))))),
% 0.21/0.42 inference(fool_elimination,[],[f77])).
% 0.21/0.42 thf(f77,plain,(
% 0.21/0.42 ((^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X1 @ X2) => (X0 @ X2 @ X1)))) = msymmetric)),
% 0.21/0.42 inference(rectify,[],[f19])).
% 0.21/0.42 thf(f19,axiom,(
% 0.21/0.42 ((^[X6 : $i > $i > $o] : (! [X8,X9] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))) = msymmetric)),
% 0.21/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',msymmetric)).
% 0.21/0.42 thf(f138,plain,(
% 0.21/0.42 ((msymmetric @ rel_s5) = $true)),
% 0.21/0.42 inference(cnf_transformation,[],[f86])).
% 0.21/0.42 thf(f86,plain,(
% 0.21/0.42 ((msymmetric @ rel_s5) = $true)),
% 0.21/0.42 inference(fool_elimination,[],[f85])).
% 0.21/0.42 thf(f85,plain,(
% 0.21/0.42 (msymmetric @ rel_s5)),
% 0.21/0.42 inference(rectify,[],[f36])).
% 0.21/0.42 thf(f36,axiom,(
% 0.21/0.42 (msymmetric @ rel_s5)),
% 0.21/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3)).
% 0.21/0.42 thf(f200,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (((rel_s5 @ (sK2 @ X1) @ X2) = $false) | ($false = (rel_s5 @ sK1 @ X1)) | ($false = (p @ (sK3 @ X2)))) )),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f199])).
% 0.21/0.42 thf(f199,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (((rel_s5 @ (sK2 @ X1) @ X2) = $false) | ($false = (rel_s5 @ sK1 @ X1)) | (((~ (rel_s5 @ X2 @ (sK3 @ X2))) | (p @ (sK3 @ X2))) = $false)) )),
% 0.21/0.42 inference(beta_eta_normalization,[],[f198])).
% 0.21/0.42 thf(f198,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (rel_s5 @ sK1 @ X1)) | ($false = ((^[Y0 : $i]: ((~ (rel_s5 @ X2 @ Y0)) | (p @ Y0))) @ (sK3 @ X2))) | ((rel_s5 @ (sK2 @ X1) @ X2) = $false)) )),
% 0.21/0.42 inference(sigma_clausification,[],[f197])).
% 0.21/0.42 thf(f197,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (rel_s5 @ sK1 @ X1)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ X2 @ Y0)) | (p @ Y0)))) = $false) | ((rel_s5 @ (sK2 @ X1) @ X2) = $false)) )),
% 0.21/0.42 inference(not_proxy_clausification,[],[f196])).
% 0.21/0.42 thf(f196,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (rel_s5 @ sK1 @ X1)) | ((rel_s5 @ (sK2 @ X1) @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ X2 @ Y0)) | (p @ Y0))))))) )),
% 0.21/0.42 inference(not_proxy_clausification,[],[f195])).
% 0.21/0.42 thf(f195,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (($true = (~ (rel_s5 @ (sK2 @ X1) @ X2))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ X2 @ Y0)) | (p @ Y0)))))) | ($false = (rel_s5 @ sK1 @ X1))) )),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f194])).
% 0.21/0.42 thf(f194,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (rel_s5 @ sK1 @ X1)) | ($true = ((~ (rel_s5 @ (sK2 @ X1) @ X2)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ X2 @ Y0)) | (p @ Y0)))))))) )),
% 0.21/0.42 inference(beta_eta_normalization,[],[f193])).
% 0.21/0.42 thf(f193,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (rel_s5 @ sK1 @ X1)) | ($true = ((^[Y0 : $i]: ((~ (rel_s5 @ (sK2 @ X1) @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))))) @ X2))) )),
% 0.21/0.42 inference(pi_clausification,[],[f192])).
% 0.21/0.42 thf(f192,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ (sK2 @ X1) @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))))))) | ($false = (rel_s5 @ sK1 @ X1))) )),
% 0.21/0.42 inference(not_proxy_clausification,[],[f191])).
% 0.21/0.42 thf(f191,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ (sK2 @ X1) @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))))))) | ($false = (rel_s5 @ sK1 @ X1))) )),
% 0.21/0.42 inference(not_proxy_clausification,[],[f187])).
% 0.21/0.42 thf(f187,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = (~ (rel_s5 @ sK1 @ X1))) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ (sK2 @ X1) @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))))))))) )),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f186])).
% 0.21/0.42 thf(f186,plain,(
% 0.21/0.42 ( ! [X1 : $i] : ((((~ (rel_s5 @ X1 @ (sK2 @ X1))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ (sK2 @ X1) @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))))))) = $false) | ($true = (~ (rel_s5 @ sK1 @ X1)))) )),
% 0.21/0.42 inference(beta_eta_normalization,[],[f185])).
% 0.21/0.42 thf(f185,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((~ (rel_s5 @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2))))))))))) @ (sK2 @ X1))) | ($true = (~ (rel_s5 @ sK1 @ X1)))) )),
% 0.21/0.42 inference(sigma_clausification,[],[f184])).
% 0.21/0.42 thf(f184,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2))))))))))))) | ($true = (~ (rel_s5 @ sK1 @ X1)))) )),
% 0.21/0.42 inference(not_proxy_clausification,[],[f183])).
% 0.21/0.42 thf(f183,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2)))))))))))))) | ($true = (~ (rel_s5 @ sK1 @ X1)))) )),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f182])).
% 0.21/0.42 thf(f182,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = ((~ (rel_s5 @ sK1 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2)))))))))))))))) )),
% 0.21/0.42 inference(beta_eta_normalization,[],[f181])).
% 0.21/0.42 thf(f181,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3))))))))))))))) @ X1))) )),
% 0.21/0.42 inference(pi_clausification,[],[f180])).
% 0.21/0.42 thf(f180,plain,(
% 0.21/0.42 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))))))))))))))))),
% 0.21/0.42 inference(not_proxy_clausification,[],[f179])).
% 0.21/0.42 thf(f179,plain,(
% 0.21/0.42 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3))))))))))))))))) = $false)),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f177])).
% 0.21/0.42 thf(f177,plain,(
% 0.21/0.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3))))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))))))))),
% 0.21/0.42 inference(beta_eta_normalization,[],[f176])).
% 0.21/0.42 thf(f176,plain,(
% 0.21/0.42 ($false = ((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s5 @ Y3 @ Y4)) | (p @ Y4))))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2)))))))))) @ sK1))),
% 0.21/0.42 inference(sigma_clausification,[],[f175])).
% 0.21/0.42 thf(f175,plain,(
% 0.21/0.42 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s5 @ Y3 @ Y4)) | (p @ Y4))))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2))))))))))))),
% 0.21/0.42 inference(boolean_simplification,[],[f174])).
% 0.21/0.42 thf(f174,plain,(
% 0.21/0.42 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s5 @ Y3 @ Y4)) | (p @ Y4))))))))))))))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2))))))))))))))),
% 0.21/0.42 inference(beta_eta_normalization,[],[f160])).
% 0.21/0.42 thf(f160,plain,(
% 0.21/0.42 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[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))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p)))))))),
% 0.21/0.42 inference(definition_unfolding,[],[f146,f113,f149,f157,f144,f157,f144,f157,f144])).
% 0.21/0.42 thf(f144,plain,(
% 0.21/0.42 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.21/0.42 inference(cnf_transformation,[],[f53])).
% 0.21/0.42 thf(f53,plain,(
% 0.21/0.42 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.21/0.42 inference(fool_elimination,[],[f52])).
% 0.21/0.42 thf(f52,plain,(
% 0.21/0.42 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_s5 @ X1 @ X2)))) = mbox_s5)),
% 0.21/0.42 inference(rectify,[],[f32])).
% 0.21/0.42 thf(f32,axiom,(
% 0.21/0.42 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_s5 @ X2 @ X7)))) = mbox_s5)),
% 0.21/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s5)).
% 0.21/0.42 thf(f157,plain,(
% 0.21/0.42 (mdia_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.21/0.42 inference(definition_unfolding,[],[f135,f111,f144,f111])).
% 0.21/0.42 thf(f111,plain,(
% 0.21/0.42 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.42 inference(cnf_transformation,[],[f105])).
% 0.21/0.42 thf(f105,plain,(
% 0.21/0.42 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.42 inference(fool_elimination,[],[f104])).
% 0.21/0.42 thf(f104,plain,(
% 0.21/0.42 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.21/0.42 inference(rectify,[],[f3])).
% 0.21/0.42 thf(f3,axiom,(
% 0.21/0.42 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.21/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.21/0.42 thf(f135,plain,(
% 0.21/0.42 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.21/0.42 inference(cnf_transformation,[],[f109])).
% 0.21/0.42 thf(f109,plain,(
% 0.21/0.42 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.21/0.42 inference(fool_elimination,[],[f108])).
% 0.21/0.42 thf(f108,plain,(
% 0.21/0.42 (mdia_s5 = (^[X0 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X0)))))),
% 0.21/0.42 inference(rectify,[],[f33])).
% 0.21/0.42 thf(f33,axiom,(
% 0.21/0.42 (mdia_s5 = (^[X3 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X3)))))),
% 0.21/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_s5)).
% 0.21/0.42 thf(f149,plain,(
% 0.21/0.42 (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)))))),
% 0.21/0.42 inference(definition_unfolding,[],[f145,f122,f111])).
% 0.21/0.42 thf(f122,plain,(
% 0.21/0.42 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.21/0.42 inference(cnf_transformation,[],[f61])).
% 0.21/0.42 thf(f61,plain,(
% 0.21/0.42 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.21/0.42 inference(fool_elimination,[],[f60])).
% 0.21/0.42 thf(f60,plain,(
% 0.21/0.42 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.21/0.42 inference(rectify,[],[f4])).
% 0.21/0.42 thf(f4,axiom,(
% 0.21/0.42 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))),
% 0.21/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.21/0.42 thf(f145,plain,(
% 0.21/0.42 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.42 inference(cnf_transformation,[],[f82])).
% 0.21/0.42 thf(f82,plain,(
% 0.21/0.42 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.42 inference(fool_elimination,[],[f81])).
% 0.21/0.42 thf(f81,plain,(
% 0.21/0.42 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.21/0.42 inference(rectify,[],[f6])).
% 0.21/0.42 thf(f6,axiom,(
% 0.21/0.42 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.21/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.21/0.42 thf(f113,plain,(
% 0.21/0.42 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.42 inference(cnf_transformation,[],[f71])).
% 0.21/0.42 thf(f71,plain,(
% 0.21/0.42 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.42 inference(fool_elimination,[],[f70])).
% 0.21/0.42 thf(f70,plain,(
% 0.21/0.42 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.21/0.42 inference(rectify,[],[f28])).
% 0.21/0.42 thf(f28,axiom,(
% 0.21/0.42 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.21/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.21/0.42 thf(f146,plain,(
% 0.21/0.42 ((mvalid @ (mimplies @ (mdia_s5 @ (mbox_s5 @ p)) @ (mdia_s5 @ (mbox_s5 @ (mdia_s5 @ (mbox_s5 @ p)))))) != $true)),
% 0.21/0.42 inference(cnf_transformation,[],[f110])).
% 0.21/0.42 thf(f110,plain,(
% 0.21/0.42 ((mvalid @ (mimplies @ (mdia_s5 @ (mbox_s5 @ p)) @ (mdia_s5 @ (mbox_s5 @ (mdia_s5 @ (mbox_s5 @ p)))))) != $true)),
% 0.21/0.42 inference(flattening,[],[f97])).
% 0.21/0.42 thf(f97,plain,(
% 0.21/0.42 ~((mvalid @ (mimplies @ (mdia_s5 @ (mbox_s5 @ p)) @ (mdia_s5 @ (mbox_s5 @ (mdia_s5 @ (mbox_s5 @ p)))))) = $true)),
% 0.21/0.42 inference(fool_elimination,[],[f96])).
% 0.21/0.42 thf(f96,plain,(
% 0.21/0.42 ~(mvalid @ (mimplies @ (mdia_s5 @ (mbox_s5 @ p)) @ (mdia_s5 @ (mbox_s5 @ (mdia_s5 @ (mbox_s5 @ p))))))),
% 0.21/0.42 inference(rectify,[],[f38])).
% 0.21/0.42 thf(f38,negated_conjecture,(
% 0.21/0.42 ~(mvalid @ (mimplies @ (mdia_s5 @ (mbox_s5 @ p)) @ (mdia_s5 @ (mbox_s5 @ (mdia_s5 @ (mbox_s5 @ p))))))),
% 0.21/0.42 inference(negated_conjecture,[],[f37])).
% 0.21/0.42 thf(f37,conjecture,(
% 0.21/0.42 (mvalid @ (mimplies @ (mdia_s5 @ (mbox_s5 @ p)) @ (mdia_s5 @ (mbox_s5 @ (mdia_s5 @ (mbox_s5 @ p))))))),
% 0.21/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.21/0.42 thf(f190,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = (rel_s5 @ X1 @ (sK2 @ X1))) | ($false = (rel_s5 @ sK1 @ X1))) )),
% 0.21/0.42 inference(not_proxy_clausification,[],[f189])).
% 0.21/0.42 thf(f189,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (((~ (rel_s5 @ X1 @ (sK2 @ X1))) = $false) | ($false = (rel_s5 @ sK1 @ X1))) )),
% 0.21/0.42 inference(not_proxy_clausification,[],[f188])).
% 0.21/0.42 thf(f188,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = (~ (rel_s5 @ sK1 @ X1))) | ((~ (rel_s5 @ X1 @ (sK2 @ X1))) = $false)) )),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f186])).
% 0.21/0.42 thf(f207,plain,(
% 0.21/0.42 ($true = (rel_s5 @ sK1 @ sK4))),
% 0.21/0.42 inference(not_proxy_clausification,[],[f206])).
% 0.21/0.42 thf(f206,plain,(
% 0.21/0.42 ((~ (rel_s5 @ sK1 @ sK4)) = $false)),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f204])).
% 0.21/0.42 thf(f204,plain,(
% 0.21/0.42 ($false = ((~ (rel_s5 @ sK1 @ sK4)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK4 @ Y0)) | (p @ Y0)))))))),
% 0.21/0.42 inference(beta_eta_normalization,[],[f203])).
% 0.21/0.42 thf(f203,plain,(
% 0.21/0.42 ($false = ((^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))))) @ sK4))),
% 0.21/0.42 inference(sigma_clausification,[],[f178])).
% 0.21/0.42 thf(f178,plain,(
% 0.21/0.42 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))))) = $false)),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f177])).
% 0.21/0.42 thf(f538,plain,(
% 0.21/0.42 ($true = (p @ (sK3 @ sK4))) | ~spl0_10),
% 0.21/0.42 inference(avatar_component_clause,[],[f536])).
% 0.21/0.42 thf(f536,plain,(
% 0.21/0.42 spl0_10 <=> ($true = (p @ (sK3 @ sK4)))),
% 0.21/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_10])])).
% 0.21/0.42 thf(f589,plain,(
% 0.21/0.42 spl0_1 | ~spl0_11),
% 0.21/0.42 inference(avatar_contradiction_clause,[],[f588])).
% 0.21/0.42 thf(f588,plain,(
% 0.21/0.42 $false | (spl0_1 | ~spl0_11)),
% 0.21/0.42 inference(subsumption_resolution,[],[f579,f246])).
% 0.21/0.42 thf(f246,plain,(
% 0.21/0.42 ($false != (rel_s5 @ sK1 @ sK4)) | spl0_1),
% 0.21/0.42 inference(avatar_component_clause,[],[f245])).
% 0.21/0.42 thf(f245,plain,(
% 0.21/0.42 spl0_1 <=> ($false = (rel_s5 @ sK1 @ sK4))),
% 0.21/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.21/0.42 thf(f579,plain,(
% 0.21/0.42 ($false = (rel_s5 @ sK1 @ sK4)) | ~spl0_11),
% 0.21/0.42 inference(trivial_inequality_removal,[],[f578])).
% 0.21/0.42 thf(f578,plain,(
% 0.21/0.42 ($false = (rel_s5 @ sK1 @ sK4)) | ($true = $false) | ~spl0_11),
% 0.21/0.42 inference(duplicate_literal_removal,[],[f572])).
% 0.21/0.42 thf(f572,plain,(
% 0.21/0.42 ($false = (rel_s5 @ sK1 @ sK4)) | ($true = $false) | ($false = (rel_s5 @ sK1 @ sK4)) | ~spl0_11),
% 0.21/0.42 inference(superposition,[],[f569,f190])).
% 0.21/0.42 thf(f569,plain,(
% 0.21/0.42 ( ! [X0 : $i] : (($false = (rel_s5 @ sK4 @ (sK2 @ X0))) | ($false = (rel_s5 @ sK1 @ X0))) ) | ~spl0_11),
% 0.21/0.42 inference(trivial_inequality_removal,[],[f567])).
% 0.21/0.42 thf(f567,plain,(
% 0.21/0.42 ( ! [X0 : $i] : (($false = (rel_s5 @ sK4 @ (sK2 @ X0))) | ($false = (rel_s5 @ sK1 @ X0)) | ($true = $false)) ) | ~spl0_11),
% 0.21/0.42 inference(superposition,[],[f218,f541])).
% 0.21/0.42 thf(f541,plain,(
% 0.21/0.42 ( ! [X0 : $i] : (($false = (rel_s5 @ (sK2 @ X0) @ sK4)) | ($false = (rel_s5 @ sK1 @ X0))) ) | ~spl0_11),
% 0.21/0.42 inference(avatar_component_clause,[],[f540])).
% 0.21/0.42 thf(f540,plain,(
% 0.21/0.42 spl0_11 <=> ! [X0] : (($false = (rel_s5 @ (sK2 @ X0) @ sK4)) | ($false = (rel_s5 @ sK1 @ X0)))),
% 0.21/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_11])])).
% 0.21/0.42 thf(f563,plain,(
% 0.21/0.42 spl0_11 | spl0_10),
% 0.21/0.42 inference(avatar_split_clause,[],[f515,f536,f540])).
% 0.21/0.42 thf(f515,plain,(
% 0.21/0.42 ( ! [X0 : $i] : (($false = (rel_s5 @ sK1 @ X0)) | ($true = (p @ (sK3 @ sK4))) | ($false = (rel_s5 @ (sK2 @ X0) @ sK4))) )),
% 0.21/0.42 inference(trivial_inequality_removal,[],[f507])).
% 0.21/0.42 thf(f507,plain,(
% 0.21/0.42 ( ! [X0 : $i] : (($false = (rel_s5 @ sK1 @ X0)) | ($false = (rel_s5 @ (sK2 @ X0) @ sK4)) | ($true = $false) | ($true = (p @ (sK3 @ sK4)))) )),
% 0.21/0.42 inference(superposition,[],[f202,f212])).
% 0.21/0.42 thf(f212,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($false = (rel_s5 @ sK4 @ X1)) | ($true = (p @ X1))) )),
% 0.21/0.42 inference(not_proxy_clausification,[],[f211])).
% 0.21/0.42 thf(f211,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = (p @ X1)) | ($true = (~ (rel_s5 @ sK4 @ X1)))) )),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f210])).
% 0.21/0.42 thf(f210,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = ((~ (rel_s5 @ sK4 @ X1)) | (p @ X1)))) )),
% 0.21/0.42 inference(beta_eta_normalization,[],[f209])).
% 0.21/0.42 thf(f209,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s5 @ sK4 @ Y0)) | (p @ Y0))) @ X1))) )),
% 0.21/0.42 inference(pi_clausification,[],[f208])).
% 0.21/0.42 thf(f208,plain,(
% 0.21/0.42 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK4 @ Y0)) | (p @ Y0)))))),
% 0.21/0.42 inference(not_proxy_clausification,[],[f205])).
% 0.21/0.42 thf(f205,plain,(
% 0.21/0.42 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK4 @ Y0)) | (p @ Y0))))))),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f204])).
% 0.21/0.42 thf(f202,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (($true = (rel_s5 @ X2 @ (sK3 @ X2))) | ((rel_s5 @ (sK2 @ X1) @ X2) = $false) | ($false = (rel_s5 @ sK1 @ X1))) )),
% 0.21/0.42 inference(not_proxy_clausification,[],[f201])).
% 0.21/0.42 thf(f201,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (~ (rel_s5 @ X2 @ (sK3 @ X2)))) | ((rel_s5 @ (sK2 @ X1) @ X2) = $false) | ($false = (rel_s5 @ sK1 @ X1))) )),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f199])).
% 0.21/0.42 thf(f300,plain,(
% 0.21/0.42 ~spl0_1),
% 0.21/0.42 inference(avatar_contradiction_clause,[],[f299])).
% 0.21/0.42 thf(f299,plain,(
% 0.21/0.42 $false | ~spl0_1),
% 0.21/0.42 inference(trivial_inequality_removal,[],[f290])).
% 0.21/0.42 thf(f290,plain,(
% 0.21/0.42 ($true = $false) | ~spl0_1),
% 0.21/0.42 inference(superposition,[],[f207,f247])).
% 0.21/0.42 thf(f247,plain,(
% 0.21/0.42 ($false = (rel_s5 @ sK1 @ sK4)) | ~spl0_1),
% 0.21/0.42 inference(avatar_component_clause,[],[f245])).
% 0.21/0.42 % SZS output end Proof for theBenchmark
% 0.21/0.42 % (7692)------------------------------
% 0.21/0.42 % (7692)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (7692)Termination reason: Refutation
% 0.21/0.42
% 0.21/0.42 % (7692)Memory used [KB]: 6012
% 0.21/0.42 % (7692)Time elapsed: 0.044 s
% 0.21/0.42 % (7692)Instructions burned: 61 (million)
% 0.21/0.42 % (7692)------------------------------
% 0.21/0.42 % (7692)------------------------------
% 0.21/0.42 % (7691)Success in time 0.043 s
% 0.21/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------