TSTP Solution File: SYO435^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO435^1 : 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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 09:04:25 EDT 2024
% Result : Theorem 0.14s 0.40s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO435^1 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.13 % 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
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon May 20 10:06:53 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.35 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
% 0.14/0.37 % (10696)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)
% 0.14/0.37 % (10694)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)
% 0.14/0.37 % (10695)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.37 % (10696)Instruction limit reached!
% 0.14/0.37 % (10696)------------------------------
% 0.14/0.37 % (10696)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (10696)Termination reason: Unknown
% 0.14/0.37 % (10696)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (10696)Memory used [KB]: 1023
% 0.14/0.37 % (10696)Time elapsed: 0.003 s
% 0.14/0.37 % (10696)Instructions burned: 4 (million)
% 0.14/0.37 % (10696)------------------------------
% 0.14/0.37 % (10696)------------------------------
% 0.14/0.37 % (10690)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)
% 0.14/0.37 % (10690)Instruction limit reached!
% 0.14/0.37 % (10690)------------------------------
% 0.14/0.37 % (10690)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (10690)Termination reason: Unknown
% 0.14/0.37 % (10690)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (10690)Memory used [KB]: 1023
% 0.14/0.37 % (10690)Time elapsed: 0.003 s
% 0.14/0.37 % (10690)Instructions burned: 4 (million)
% 0.14/0.37 % (10690)------------------------------
% 0.14/0.37 % (10690)------------------------------
% 0.14/0.37 % (10694)Refutation not found, incomplete strategy
% 0.14/0.37 % (10694)------------------------------
% 0.14/0.37 % (10694)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (10694)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.37
% 0.14/0.37
% 0.14/0.37 % (10694)Memory used [KB]: 5628
% 0.14/0.37 % (10694)Time elapsed: 0.008 s
% 0.14/0.37 % (10694)Instructions burned: 14 (million)
% 0.14/0.37 % (10694)------------------------------
% 0.14/0.37 % (10694)------------------------------
% 0.14/0.37 % (10695)Instruction limit reached!
% 0.14/0.37 % (10695)------------------------------
% 0.14/0.37 % (10695)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (10695)Termination reason: Unknown
% 0.14/0.37 % (10695)Termination phase: Saturation
% 0.14/0.37
% 0.14/0.37 % (10695)Memory used [KB]: 5628
% 0.14/0.37 % (10695)Time elapsed: 0.010 s
% 0.14/0.37 % (10695)Instructions burned: 19 (million)
% 0.14/0.37 % (10695)------------------------------
% 0.14/0.37 % (10695)------------------------------
% 0.14/0.38 % (10692)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.38 % (10689)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.38 % (10692)Instruction limit reached!
% 0.14/0.38 % (10692)------------------------------
% 0.14/0.38 % (10692)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (10692)Termination reason: Unknown
% 0.14/0.38 % (10692)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (10692)Memory used [KB]: 1023
% 0.14/0.38 % (10692)Time elapsed: 0.003 s
% 0.14/0.38 % (10692)Instructions burned: 2 (million)
% 0.14/0.38 % (10692)------------------------------
% 0.14/0.38 % (10692)------------------------------
% 0.14/0.38 % (10693)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)
% 0.14/0.38 % (10693)Instruction limit reached!
% 0.14/0.38 % (10693)------------------------------
% 0.14/0.38 % (10693)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (10693)Termination reason: Unknown
% 0.14/0.38 % (10693)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (10693)Memory used [KB]: 1023
% 0.14/0.38 % (10693)Time elapsed: 0.003 s
% 0.14/0.38 % (10693)Instructions burned: 2 (million)
% 0.14/0.38 % (10693)------------------------------
% 0.14/0.38 % (10693)------------------------------
% 0.14/0.38 % (10697)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)
% 0.14/0.38 % (10691)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)
% 0.14/0.38 % (10698)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)
% 0.14/0.39 % (10699)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)
% 0.14/0.39 % (10698)Instruction limit reached!
% 0.14/0.39 % (10698)------------------------------
% 0.14/0.39 % (10698)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (10698)Termination reason: Unknown
% 0.14/0.39 % (10698)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (10698)Memory used [KB]: 5628
% 0.14/0.39 % (10698)Time elapsed: 0.008 s
% 0.14/0.39 % (10698)Instructions burned: 15 (million)
% 0.14/0.39 % (10698)------------------------------
% 0.14/0.39 % (10698)------------------------------
% 0.14/0.39 % (10702)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.14/0.39 % (10699)Instruction limit reached!
% 0.14/0.39 % (10699)------------------------------
% 0.14/0.39 % (10699)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (10699)Termination reason: Unknown
% 0.14/0.39 % (10699)Termination phase: Property scanning
% 0.14/0.39
% 0.14/0.39 % (10699)Memory used [KB]: 1023
% 0.14/0.39 % (10699)Time elapsed: 0.003 s
% 0.14/0.39 % (10699)Instructions burned: 5 (million)
% 0.14/0.39 % (10699)------------------------------
% 0.14/0.39 % (10699)------------------------------
% 0.14/0.39 % (10700)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)
% 0.14/0.39 % (10701)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.40 % (10689)First to succeed.
% 0.14/0.40 % (10697)Instruction limit reached!
% 0.14/0.40 % (10697)------------------------------
% 0.14/0.40 % (10697)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (10697)Termination reason: Unknown
% 0.14/0.40 % (10697)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (10697)Memory used [KB]: 5756
% 0.14/0.40 % (10697)Time elapsed: 0.019 s
% 0.14/0.40 % (10697)Instructions burned: 38 (million)
% 0.14/0.40 % (10697)------------------------------
% 0.14/0.40 % (10697)------------------------------
% 0.14/0.40 % (10691)Instruction limit reached!
% 0.14/0.40 % (10691)------------------------------
% 0.14/0.40 % (10691)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (10701)Instruction limit reached!
% 0.14/0.40 % (10701)------------------------------
% 0.14/0.40 % (10701)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (10701)Termination reason: Unknown
% 0.14/0.40 % (10701)Termination phase: Property scanning
% 0.14/0.40
% 0.14/0.40 % (10701)Memory used [KB]: 1023
% 0.14/0.40 % (10701)Time elapsed: 0.006 s
% 0.14/0.40 % (10701)Instructions burned: 8 (million)
% 0.14/0.40 % (10701)------------------------------
% 0.14/0.40 % (10701)------------------------------
% 0.14/0.40 % (10691)Termination reason: Unknown
% 0.14/0.40 % (10691)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (10691)Memory used [KB]: 5756
% 0.14/0.40 % (10691)Time elapsed: 0.040 s
% 0.14/0.40 % (10691)Instructions burned: 28 (million)
% 0.14/0.40 % (10691)------------------------------
% 0.14/0.40 % (10691)------------------------------
% 0.14/0.40 % (10702)Instruction limit reached!
% 0.14/0.40 % (10702)------------------------------
% 0.14/0.40 % (10702)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (10702)Termination reason: Unknown
% 0.14/0.40 % (10702)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (10702)Memory used [KB]: 5756
% 0.14/0.40 % (10702)Time elapsed: 0.009 s
% 0.14/0.40 % (10702)Instructions burned: 17 (million)
% 0.14/0.40 % (10702)------------------------------
% 0.14/0.40 % (10702)------------------------------
% 0.14/0.40 % (10689)Refutation found. Thanks to Tanya!
% 0.14/0.40 % SZS status Theorem for theBenchmark
% 0.14/0.40 % SZS output start Proof for theBenchmark
% 0.14/0.40 thf(type_def_5, type, mu: $tType).
% 0.14/0.40 thf(func_def_0, type, mu: $tType).
% 0.14/0.40 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.14/0.40 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_15, type, mtrue: $i > $o).
% 0.14/0.40 thf(func_def_16, type, mfalse: $i > $o).
% 0.14/0.40 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_33, type, rel_s4: $i > $i > $o).
% 0.14/0.40 thf(func_def_34, type, mbox_s4: ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_35, type, mdia_s4: ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_36, type, p: $i > $o).
% 0.14/0.40 thf(func_def_54, type, sK2: $i > $i).
% 0.14/0.40 thf(func_def_56, type, sK4: $i > $i).
% 0.14/0.40 thf(f519,plain,(
% 0.14/0.40 $false),
% 0.14/0.40 inference(avatar_sat_refutation,[],[f382,f518])).
% 0.14/0.40 thf(f518,plain,(
% 0.14/0.40 spl0_9),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f517])).
% 0.14/0.40 thf(f517,plain,(
% 0.14/0.40 $false | spl0_9),
% 0.14/0.40 inference(subsumption_resolution,[],[f499,f339])).
% 0.14/0.40 thf(f339,plain,(
% 0.14/0.40 ((rel_s4 @ sK3 @ sK3) != $false) | spl0_9),
% 0.14/0.40 inference(avatar_component_clause,[],[f338])).
% 0.14/0.40 thf(f338,plain,(
% 0.14/0.40 spl0_9 <=> ((rel_s4 @ sK3 @ sK3) = $false)),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_9])])).
% 0.14/0.40 thf(f499,plain,(
% 0.14/0.40 ((rel_s4 @ sK3 @ sK3) = $false)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f474])).
% 0.14/0.40 thf(f474,plain,(
% 0.14/0.40 ($false = $true) | ((rel_s4 @ sK3 @ sK3) = $false)),
% 0.14/0.40 inference(superposition,[],[f473,f181])).
% 0.14/0.40 thf(f181,plain,(
% 0.14/0.40 ((rel_s4 @ sK1 @ sK3) = $true)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f180])).
% 0.14/0.40 thf(f180,plain,(
% 0.14/0.40 ((~ (rel_s4 @ sK1 @ sK3)) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f178])).
% 0.14/0.40 thf(f178,plain,(
% 0.14/0.40 ($false = ((~ (rel_s4 @ sK1 @ sK3)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (~ (p @ Y2))))))))))))))))),
% 0.14/0.40 inference(beta_eta_normalization,[],[f177])).
% 0.14/0.40 thf(f177,plain,(
% 0.14/0.40 ($false = ((^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (~ (p @ Y3)))))))))))))))) @ sK3))),
% 0.14/0.40 inference(sigma_clausification,[],[f163])).
% 0.14/0.40 thf(f163,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (~ (p @ Y3))))))))))))))))) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f162])).
% 0.14/0.40 thf(f162,plain,(
% 0.14/0.40 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (p @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (~ (p @ Y3)))))))))))))))))) = $false)),
% 0.14/0.40 inference(beta_eta_normalization,[],[f161])).
% 0.14/0.40 thf(f161,plain,(
% 0.14/0.40 (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (~ (p @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y3 @ Y4)) | (~ (p @ Y4))))))))))))))))))) @ sK1) = $false)),
% 0.14/0.40 inference(sigma_clausification,[],[f160])).
% 0.14/0.40 thf(f160,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (~ (p @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y3 @ Y4)) | (~ (p @ Y4)))))))))))))))))))) != $true)),
% 0.14/0.40 inference(beta_eta_normalization,[],[f154])).
% 0.14/0.40 thf(f154,plain,(
% 0.14/0.40 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ p)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ p)))))) != $true)),
% 0.14/0.40 inference(definition_unfolding,[],[f119,f127,f145,f118,f153,f118,f153,f118,f153])).
% 0.14/0.40 thf(f153,plain,(
% 0.14/0.40 (mdia_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.14/0.40 inference(definition_unfolding,[],[f120,f129,f118,f129])).
% 0.14/0.40 thf(f129,plain,(
% 0.14/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f57])).
% 0.14/0.40 thf(f57,plain,(
% 0.14/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.40 inference(fool_elimination,[],[f56])).
% 0.14/0.40 thf(f56,plain,(
% 0.14/0.40 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.14/0.40 inference(rectify,[],[f3])).
% 0.14/0.40 thf(f3,axiom,(
% 0.14/0.40 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.14/0.40 thf(f120,plain,(
% 0.14/0.40 (mdia_s4 = (^[Y0 : $i > $o]: (mnot @ (mbox_s4 @ (mnot @ Y0)))))),
% 0.14/0.40 inference(cnf_transformation,[],[f42])).
% 0.14/0.40 thf(f42,plain,(
% 0.14/0.40 (mdia_s4 = (^[Y0 : $i > $o]: (mnot @ (mbox_s4 @ (mnot @ Y0)))))),
% 0.14/0.40 inference(fool_elimination,[],[f41])).
% 0.14/0.40 thf(f41,plain,(
% 0.14/0.40 ((^[X0 : $i > $o] : (mnot @ (mbox_s4 @ (mnot @ X0)))) = mdia_s4)),
% 0.14/0.40 inference(rectify,[],[f33])).
% 0.14/0.40 thf(f33,axiom,(
% 0.14/0.40 ((^[X3 : $i > $o] : (mnot @ (mbox_s4 @ (mnot @ X3)))) = mdia_s4)),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_s4)).
% 0.14/0.40 thf(f118,plain,(
% 0.14/0.40 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f59])).
% 0.14/0.40 thf(f59,plain,(
% 0.14/0.40 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.14/0.40 inference(fool_elimination,[],[f58])).
% 0.14/0.40 thf(f58,plain,(
% 0.14/0.40 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_s4 @ X1 @ X2)))) = mbox_s4)),
% 0.14/0.40 inference(rectify,[],[f32])).
% 0.14/0.40 thf(f32,axiom,(
% 0.14/0.40 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_s4 @ X2 @ X7)))) = mbox_s4)),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s4)).
% 0.14/0.40 thf(f145,plain,(
% 0.14/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.14/0.40 inference(definition_unfolding,[],[f135,f110,f129])).
% 0.14/0.40 thf(f110,plain,(
% 0.14/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f104])).
% 0.14/0.40 thf(f104,plain,(
% 0.14/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.14/0.40 inference(fool_elimination,[],[f103])).
% 0.14/0.40 thf(f103,plain,(
% 0.14/0.40 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.14/0.40 inference(rectify,[],[f4])).
% 0.14/0.40 thf(f4,axiom,(
% 0.14/0.40 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))))),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.14/0.40 thf(f135,plain,(
% 0.14/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.40 inference(cnf_transformation,[],[f44])).
% 0.14/0.40 thf(f44,plain,(
% 0.14/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.40 inference(fool_elimination,[],[f43])).
% 0.14/0.40 thf(f43,plain,(
% 0.14/0.40 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.14/0.40 inference(rectify,[],[f6])).
% 0.14/0.40 thf(f6,axiom,(
% 0.14/0.40 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.14/0.40 thf(f127,plain,(
% 0.14/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.40 inference(cnf_transformation,[],[f53])).
% 0.14/0.40 thf(f53,plain,(
% 0.14/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.40 inference(fool_elimination,[],[f52])).
% 0.14/0.40 thf(f52,plain,(
% 0.14/0.40 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.14/0.40 inference(rectify,[],[f28])).
% 0.14/0.40 thf(f28,axiom,(
% 0.14/0.40 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.14/0.40 thf(f119,plain,(
% 0.14/0.40 ((mvalid @ (mimplies @ (mbox_s4 @ (mdia_s4 @ p)) @ (mbox_s4 @ (mdia_s4 @ (mbox_s4 @ (mdia_s4 @ p)))))) != $true)),
% 0.14/0.40 inference(cnf_transformation,[],[f107])).
% 0.14/0.40 thf(f107,plain,(
% 0.14/0.40 ((mvalid @ (mimplies @ (mbox_s4 @ (mdia_s4 @ p)) @ (mbox_s4 @ (mdia_s4 @ (mbox_s4 @ (mdia_s4 @ p)))))) != $true)),
% 0.14/0.40 inference(flattening,[],[f61])).
% 0.14/0.40 thf(f61,plain,(
% 0.14/0.40 ~((mvalid @ (mimplies @ (mbox_s4 @ (mdia_s4 @ p)) @ (mbox_s4 @ (mdia_s4 @ (mbox_s4 @ (mdia_s4 @ p)))))) = $true)),
% 0.14/0.40 inference(fool_elimination,[],[f60])).
% 0.14/0.40 thf(f60,plain,(
% 0.14/0.40 ~(mvalid @ (mimplies @ (mbox_s4 @ (mdia_s4 @ p)) @ (mbox_s4 @ (mdia_s4 @ (mbox_s4 @ (mdia_s4 @ p))))))),
% 0.14/0.40 inference(rectify,[],[f37])).
% 0.14/0.40 thf(f37,negated_conjecture,(
% 0.14/0.40 ~(mvalid @ (mimplies @ (mbox_s4 @ (mdia_s4 @ p)) @ (mbox_s4 @ (mdia_s4 @ (mbox_s4 @ (mdia_s4 @ p))))))),
% 0.14/0.40 inference(negated_conjecture,[],[f36])).
% 0.14/0.40 thf(f36,conjecture,(
% 0.14/0.40 (mvalid @ (mimplies @ (mbox_s4 @ (mdia_s4 @ p)) @ (mbox_s4 @ (mdia_s4 @ (mbox_s4 @ (mdia_s4 @ p))))))),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.14/0.40 thf(f473,plain,(
% 0.14/0.40 ( ! [X0 : $i] : (($false = (rel_s4 @ sK1 @ X0)) | ((rel_s4 @ sK3 @ X0) = $false)) )),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f472])).
% 0.14/0.40 thf(f472,plain,(
% 0.14/0.40 ( ! [X0 : $i] : (($false = $true) | ($false = (rel_s4 @ sK1 @ X0)) | ((rel_s4 @ sK3 @ X0) = $false)) )),
% 0.14/0.40 inference(duplicate_literal_removal,[],[f468])).
% 0.14/0.40 thf(f468,plain,(
% 0.14/0.40 ( ! [X0 : $i] : (($false = $true) | ((rel_s4 @ sK3 @ X0) = $false) | ((rel_s4 @ sK3 @ X0) = $false) | ($false = (rel_s4 @ sK1 @ X0)) | ($false = (rel_s4 @ sK1 @ X0))) )),
% 0.14/0.40 inference(superposition,[],[f465,f437])).
% 0.14/0.40 thf(f437,plain,(
% 0.14/0.40 ( ! [X0 : $i] : (((p @ (sK2 @ (sK4 @ X0))) = $true) | ((rel_s4 @ sK3 @ X0) = $false) | ($false = (rel_s4 @ sK1 @ X0))) )),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f426])).
% 0.14/0.40 thf(f426,plain,(
% 0.14/0.40 ( ! [X0 : $i] : (((p @ (sK2 @ (sK4 @ X0))) = $true) | ((rel_s4 @ sK3 @ X0) = $false) | ($false = $true) | ($false = (rel_s4 @ sK1 @ X0))) )),
% 0.14/0.40 inference(superposition,[],[f176,f261])).
% 0.14/0.40 thf(f261,plain,(
% 0.14/0.40 ( ! [X0 : $i,X1 : $i] : (((rel_s4 @ X1 @ (sK4 @ X0)) = $true) | ((rel_s4 @ X1 @ X0) = $false) | ((rel_s4 @ sK3 @ X0) = $false)) )),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f246])).
% 0.14/0.40 thf(f246,plain,(
% 0.14/0.40 ( ! [X0 : $i,X1 : $i] : (((rel_s4 @ sK3 @ X0) = $false) | ($false = $true) | ((rel_s4 @ X1 @ X0) = $false) | ((rel_s4 @ X1 @ (sK4 @ X0)) = $true)) )),
% 0.14/0.40 inference(superposition,[],[f207,f192])).
% 0.14/0.40 thf(f192,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = (rel_s4 @ X1 @ (sK4 @ X1))) | ($false = (rel_s4 @ sK3 @ X1))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f191])).
% 0.14/0.40 thf(f191,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = (~ (rel_s4 @ X1 @ (sK4 @ X1)))) | ($false = (rel_s4 @ sK3 @ X1))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f189])).
% 0.14/0.40 thf(f189,plain,(
% 0.14/0.40 ( ! [X1 : $i] : ((((~ (rel_s4 @ X1 @ (sK4 @ X1))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ (sK4 @ X1) @ Y0)) | (~ (p @ Y0))))))) = $false) | ($false = (rel_s4 @ sK3 @ X1))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f188])).
% 0.14/0.40 thf(f188,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (p @ Y1)))))))) @ (sK4 @ X1))) | ($false = (rel_s4 @ sK3 @ X1))) )),
% 0.14/0.40 inference(sigma_clausification,[],[f187])).
% 0.14/0.40 thf(f187,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (p @ Y1))))))))) = $false) | ($false = (rel_s4 @ sK3 @ X1))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f186])).
% 0.14/0.40 thf(f186,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((~ (rel_s4 @ sK3 @ X1)) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (p @ Y1))))))))) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f185])).
% 0.14/0.40 thf(f185,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (p @ Y1)))))))))) = $true) | ((~ (rel_s4 @ sK3 @ X1)) = $true)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f184])).
% 0.14/0.40 thf(f184,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = ((~ (rel_s4 @ sK3 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (p @ Y1))))))))))))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f183])).
% 0.14/0.40 thf(f183,plain,(
% 0.14/0.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (~ (p @ Y2)))))))))))) @ X1) = $true)) )),
% 0.14/0.40 inference(pi_clausification,[],[f182])).
% 0.14/0.40 thf(f182,plain,(
% 0.14/0.40 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (~ (p @ Y2))))))))))))))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f179])).
% 0.14/0.40 thf(f179,plain,(
% 0.14/0.40 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (~ (p @ Y2)))))))))))))))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f178])).
% 0.14/0.40 thf(f207,plain,(
% 0.14/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((rel_s4 @ X3 @ X1) = $false) | ((rel_s4 @ X2 @ X1) = $true) | ((rel_s4 @ X2 @ X3) = $false)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f206])).
% 0.14/0.40 thf(f206,plain,(
% 0.14/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((rel_s4 @ X3 @ X1) & (rel_s4 @ X2 @ X3)) = $false) | ((rel_s4 @ X2 @ X1) = $true)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f205])).
% 0.14/0.40 thf(f205,plain,(
% 0.14/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((rel_s4 @ X3 @ X1) & (rel_s4 @ X2 @ X3)) => (rel_s4 @ X2 @ X1)) = $true)) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f204])).
% 0.14/0.40 thf(f204,plain,(
% 0.14/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((rel_s4 @ Y0 @ X1) & (rel_s4 @ X2 @ Y0)) => (rel_s4 @ X2 @ X1))) @ X3))) )),
% 0.14/0.40 inference(pi_clausification,[],[f203])).
% 0.14/0.40 thf(f203,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (((rel_s4 @ Y0 @ X1) & (rel_s4 @ X2 @ Y0)) => (rel_s4 @ X2 @ X1)))) = $true)) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f202])).
% 0.14/0.40 thf(f202,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s4 @ Y1 @ X1) & (rel_s4 @ Y0 @ Y1)) => (rel_s4 @ Y0 @ X1))))) @ X2) = $true)) )),
% 0.14/0.40 inference(pi_clausification,[],[f201])).
% 0.14/0.40 thf(f201,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s4 @ Y1 @ X1) & (rel_s4 @ Y0 @ Y1)) => (rel_s4 @ Y0 @ X1)))))) = $true)) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f200])).
% 0.14/0.40 thf(f200,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s4 @ Y2 @ Y0) & (rel_s4 @ Y1 @ Y2)) => (rel_s4 @ Y1 @ Y0))))))) @ X1))) )),
% 0.14/0.40 inference(pi_clausification,[],[f199])).
% 0.14/0.40 thf(f199,plain,(
% 0.14/0.40 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s4 @ Y2 @ Y0) & (rel_s4 @ Y1 @ Y2)) => (rel_s4 @ Y1 @ Y0)))))))))),
% 0.14/0.40 inference(beta_eta_normalization,[],[f156])).
% 0.14/0.40 thf(f156,plain,(
% 0.14/0.40 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) @ rel_s4) = $true)),
% 0.14/0.40 inference(definition_unfolding,[],[f134,f141])).
% 0.14/0.40 thf(f141,plain,(
% 0.14/0.40 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f69])).
% 0.14/0.40 thf(f69,plain,(
% 0.14/0.40 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))))),
% 0.14/0.40 inference(fool_elimination,[],[f68])).
% 0.14/0.40 thf(f68,plain,(
% 0.14/0.40 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X2 @ X1) & (X0 @ X1 @ X3)) => (X0 @ X2 @ X3)))) = mtransitive)),
% 0.14/0.40 inference(rectify,[],[f21])).
% 0.14/0.40 thf(f21,axiom,(
% 0.14/0.40 ((^[X6 : $i > $i > $o] : (! [X9,X8,X10] : (((X6 @ X8 @ X9) & (X6 @ X9 @ X10)) => (X6 @ X8 @ X10)))) = mtransitive)),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtransitive)).
% 0.14/0.40 thf(f134,plain,(
% 0.14/0.40 ((mtransitive @ rel_s4) = $true)),
% 0.14/0.40 inference(cnf_transformation,[],[f51])).
% 0.14/0.40 thf(f51,plain,(
% 0.14/0.40 ((mtransitive @ rel_s4) = $true)),
% 0.14/0.40 inference(fool_elimination,[],[f50])).
% 0.14/0.40 thf(f50,plain,(
% 0.14/0.40 (mtransitive @ rel_s4)),
% 0.14/0.40 inference(rectify,[],[f35])).
% 0.14/0.40 thf(f35,axiom,(
% 0.14/0.40 (mtransitive @ rel_s4)),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2)).
% 0.14/0.40 thf(f176,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((rel_s4 @ sK1 @ X1) = $false) | ((p @ (sK2 @ X1)) = $true)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f173])).
% 0.14/0.40 thf(f173,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((~ (p @ (sK2 @ X1))) = $false) | ((rel_s4 @ sK1 @ X1) = $false)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f172])).
% 0.14/0.40 thf(f172,plain,(
% 0.14/0.40 ( ! [X1 : $i] : ((((~ (rel_s4 @ X1 @ (sK2 @ X1))) | (~ (p @ (sK2 @ X1)))) = $false) | ((rel_s4 @ sK1 @ X1) = $false)) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f171])).
% 0.14/0.40 thf(f171,plain,(
% 0.14/0.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (~ (p @ Y0)))) @ (sK2 @ X1)) = $false) | ((rel_s4 @ sK1 @ X1) = $false)) )),
% 0.14/0.40 inference(sigma_clausification,[],[f170])).
% 0.14/0.40 thf(f170,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (~ (p @ Y0))))) = $false) | ((rel_s4 @ sK1 @ X1) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f169])).
% 0.14/0.40 thf(f169,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (~ (p @ Y0))))))) | ((rel_s4 @ sK1 @ X1) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f168])).
% 0.14/0.40 thf(f168,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = (~ (rel_s4 @ sK1 @ X1))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (~ (p @ Y0)))))))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f167])).
% 0.14/0.40 thf(f167,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = ((~ (rel_s4 @ sK1 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (~ (p @ Y0))))))))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f166])).
% 0.14/0.40 thf(f166,plain,(
% 0.14/0.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (p @ Y1)))))))) @ X1) = $true)) )),
% 0.14/0.40 inference(pi_clausification,[],[f165])).
% 0.14/0.40 thf(f165,plain,(
% 0.14/0.40 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (p @ Y1))))))))))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f164])).
% 0.14/0.40 thf(f164,plain,(
% 0.14/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (p @ Y1)))))))))) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f162])).
% 0.14/0.40 thf(f465,plain,(
% 0.14/0.40 ( ! [X0 : $i] : (((p @ (sK2 @ (sK4 @ X0))) = $false) | ($false = (rel_s4 @ sK1 @ X0)) | ((rel_s4 @ sK3 @ X0) = $false)) )),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f464])).
% 0.14/0.40 thf(f464,plain,(
% 0.14/0.40 ( ! [X0 : $i] : (((rel_s4 @ sK3 @ X0) = $false) | ((p @ (sK2 @ (sK4 @ X0))) = $false) | ($false = $true) | ($false = (rel_s4 @ sK1 @ X0))) )),
% 0.14/0.40 inference(duplicate_literal_removal,[],[f454])).
% 0.14/0.40 thf(f454,plain,(
% 0.14/0.40 ( ! [X0 : $i] : (((rel_s4 @ sK3 @ X0) = $false) | ($false = $true) | ($false = (rel_s4 @ sK1 @ X0)) | ((p @ (sK2 @ (sK4 @ X0))) = $false) | ((rel_s4 @ sK3 @ X0) = $false)) )),
% 0.14/0.40 inference(superposition,[],[f298,f261])).
% 0.14/0.40 thf(f298,plain,(
% 0.14/0.40 ( ! [X0 : $i] : (((rel_s4 @ sK1 @ (sK4 @ X0)) = $false) | ((p @ (sK2 @ (sK4 @ X0))) = $false) | ((rel_s4 @ sK3 @ X0) = $false)) )),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f288])).
% 0.14/0.40 thf(f288,plain,(
% 0.14/0.40 ( ! [X0 : $i] : (((rel_s4 @ sK1 @ (sK4 @ X0)) = $false) | ((rel_s4 @ sK3 @ X0) = $false) | ($false = $true) | ((p @ (sK2 @ (sK4 @ X0))) = $false)) )),
% 0.14/0.40 inference(superposition,[],[f175,f198])).
% 0.14/0.40 thf(f198,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (((rel_s4 @ (sK4 @ X1) @ X2) = $false) | ($false = (rel_s4 @ sK3 @ X1)) | ($false = (p @ X2))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f197])).
% 0.14/0.40 thf(f197,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (((rel_s4 @ (sK4 @ X1) @ X2) = $false) | ($false = (rel_s4 @ sK3 @ X1)) | ($true = (~ (p @ X2)))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f196])).
% 0.14/0.40 thf(f196,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (($true = (~ (rel_s4 @ (sK4 @ X1) @ X2))) | ($true = (~ (p @ X2))) | ($false = (rel_s4 @ sK3 @ X1))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f195])).
% 0.14/0.40 thf(f195,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : ((((~ (rel_s4 @ (sK4 @ X1) @ X2)) | (~ (p @ X2))) = $true) | ($false = (rel_s4 @ sK3 @ X1))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f194])).
% 0.14/0.40 thf(f194,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (rel_s4 @ sK3 @ X1)) | (((^[Y0 : $i]: ((~ (rel_s4 @ (sK4 @ X1) @ Y0)) | (~ (p @ Y0)))) @ X2) = $true)) )),
% 0.14/0.40 inference(pi_clausification,[],[f193])).
% 0.14/0.40 thf(f193,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = (rel_s4 @ sK3 @ X1)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ (sK4 @ X1) @ Y0)) | (~ (p @ Y0))))) = $true)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f190])).
% 0.14/0.40 thf(f190,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ (sK4 @ X1) @ Y0)) | (~ (p @ Y0)))))) = $false) | ($false = (rel_s4 @ sK3 @ X1))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f189])).
% 0.14/0.40 thf(f175,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((rel_s4 @ X1 @ (sK2 @ X1)) = $true) | ((rel_s4 @ sK1 @ X1) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f174])).
% 0.14/0.40 thf(f174,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = (~ (rel_s4 @ X1 @ (sK2 @ X1)))) | ((rel_s4 @ sK1 @ X1) = $false)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f172])).
% 0.14/0.40 thf(f382,plain,(
% 0.14/0.40 ~spl0_9),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f381])).
% 0.14/0.40 thf(f381,plain,(
% 0.14/0.40 $false | ~spl0_9),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f371])).
% 0.14/0.40 thf(f371,plain,(
% 0.14/0.40 ($false = $true) | ~spl0_9),
% 0.14/0.40 inference(superposition,[],[f340,f159])).
% 0.14/0.40 thf(f159,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((rel_s4 @ X1 @ X1) = $true)) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f158])).
% 0.14/0.40 thf(f158,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (rel_s4 @ Y0 @ Y0)) @ X1))) )),
% 0.14/0.40 inference(pi_clausification,[],[f157])).
% 0.14/0.40 thf(f157,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))) = $true)),
% 0.14/0.40 inference(beta_eta_normalization,[],[f155])).
% 0.14/0.40 thf(f155,plain,(
% 0.14/0.40 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ rel_s4) = $true)),
% 0.14/0.40 inference(definition_unfolding,[],[f121,f132])).
% 0.14/0.40 thf(f132,plain,(
% 0.14/0.40 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.14/0.40 inference(cnf_transformation,[],[f94])).
% 0.14/0.40 thf(f94,plain,(
% 0.14/0.40 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.14/0.40 inference(fool_elimination,[],[f93])).
% 0.14/0.40 thf(f93,plain,(
% 0.14/0.40 (mreflexive = (^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))))),
% 0.14/0.40 inference(rectify,[],[f18])).
% 0.14/0.40 thf(f18,axiom,(
% 0.14/0.40 (mreflexive = (^[X6 : $i > $i > $o] : (! [X8] : (X6 @ X8 @ X8))))),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive)).
% 0.14/0.40 thf(f121,plain,(
% 0.14/0.40 ((mreflexive @ rel_s4) = $true)),
% 0.14/0.40 inference(cnf_transformation,[],[f90])).
% 0.14/0.40 thf(f90,plain,(
% 0.14/0.40 ((mreflexive @ rel_s4) = $true)),
% 0.14/0.40 inference(fool_elimination,[],[f89])).
% 0.14/0.40 thf(f89,plain,(
% 0.14/0.40 (mreflexive @ rel_s4)),
% 0.14/0.40 inference(rectify,[],[f34])).
% 0.14/0.40 thf(f34,axiom,(
% 0.14/0.40 (mreflexive @ rel_s4)),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
% 0.14/0.40 thf(f340,plain,(
% 0.14/0.40 ((rel_s4 @ sK3 @ sK3) = $false) | ~spl0_9),
% 0.14/0.40 inference(avatar_component_clause,[],[f338])).
% 0.14/0.40 % SZS output end Proof for theBenchmark
% 0.14/0.40 % (10689)------------------------------
% 0.14/0.40 % (10689)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (10689)Termination reason: Refutation
% 0.14/0.40
% 0.14/0.40 % (10689)Memory used [KB]: 5884
% 0.14/0.40 % (10689)Time elapsed: 0.023 s
% 0.14/0.40 % (10689)Instructions burned: 41 (million)
% 0.14/0.40 % (10689)------------------------------
% 0.14/0.40 % (10689)------------------------------
% 0.14/0.40 % (10688)Success in time 0.04 s
% 0.14/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------