TSTP Solution File: SYO454^6 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO454^6 : 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 : n007.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 09:04:40 EDT 2024
% Result : Theorem 0.22s 0.42s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SYO454^6 : TPTP v8.2.0. Released v4.0.0.
% 0.08/0.15 % 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
% 0.15/0.37 % Computer : n007.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon May 20 08:32:53 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.15/0.37 This is a TH0_THM_EQU_NAR problem
% 0.15/0.37 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
% 0.15/0.39 % (14883)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)
% 0.15/0.39 % (14879)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.39 % (14880)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)
% 0.15/0.39 % (14879)Instruction limit reached!
% 0.15/0.39 % (14879)------------------------------
% 0.15/0.39 % (14879)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (14879)Termination reason: Unknown
% 0.15/0.39 % (14879)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (14879)Memory used [KB]: 1023
% 0.15/0.39 % (14880)Instruction limit reached!
% 0.15/0.39 % (14880)------------------------------
% 0.15/0.39 % (14880)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (14880)Termination reason: Unknown
% 0.15/0.39 % (14880)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (14880)Memory used [KB]: 1023
% 0.15/0.39 % (14880)Time elapsed: 0.002 s
% 0.15/0.39 % (14880)Instructions burned: 2 (million)
% 0.15/0.39 % (14880)------------------------------
% 0.15/0.39 % (14880)------------------------------
% 0.15/0.39 % (14879)Time elapsed: 0.002 s
% 0.15/0.39 % (14879)Instructions burned: 2 (million)
% 0.15/0.39 % (14879)------------------------------
% 0.15/0.39 % (14879)------------------------------
% 0.15/0.39 % (14883)Instruction limit reached!
% 0.15/0.39 % (14883)------------------------------
% 0.15/0.39 % (14883)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (14883)Termination reason: Unknown
% 0.15/0.39 % (14883)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (14883)Memory used [KB]: 1023
% 0.15/0.39 % (14883)Time elapsed: 0.003 s
% 0.15/0.39 % (14883)Instructions burned: 4 (million)
% 0.15/0.39 % (14883)------------------------------
% 0.15/0.39 % (14883)------------------------------
% 0.15/0.39 % (14877)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)
% 0.15/0.39 % (14876)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.39 % (14882)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.39 % (14881)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)
% 0.15/0.40 % (14877)Instruction limit reached!
% 0.15/0.40 % (14877)------------------------------
% 0.15/0.40 % (14877)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (14877)Termination reason: Unknown
% 0.15/0.40 % (14877)Termination phase: shuffling
% 0.15/0.40
% 0.15/0.40 % (14877)Memory used [KB]: 1023
% 0.15/0.40 % (14877)Time elapsed: 0.004 s
% 0.15/0.40 % (14877)Instructions burned: 4 (million)
% 0.15/0.40 % (14877)------------------------------
% 0.15/0.40 % (14877)------------------------------
% 0.15/0.40 % (14881)Refutation not found, incomplete strategy
% 0.15/0.40 % (14881)------------------------------
% 0.15/0.40 % (14881)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (14881)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.40
% 0.15/0.40
% 0.15/0.40 % (14881)Memory used [KB]: 5628
% 0.15/0.40 % (14881)Time elapsed: 0.007 s
% 0.15/0.40 % (14881)Instructions burned: 11 (million)
% 0.15/0.40 % (14881)------------------------------
% 0.15/0.40 % (14881)------------------------------
% 0.15/0.40 % (14886)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)
% 0.15/0.40 % (14886)Instruction limit reached!
% 0.15/0.40 % (14886)------------------------------
% 0.15/0.40 % (14886)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (14886)Termination reason: Unknown
% 0.15/0.40 % (14886)Termination phase: shuffling
% 0.15/0.40
% 0.15/0.40 % (14886)Memory used [KB]: 1023
% 0.15/0.40 % (14886)Time elapsed: 0.003 s
% 0.15/0.40 % (14886)Instructions burned: 4 (million)
% 0.15/0.40 % (14886)------------------------------
% 0.15/0.40 % (14886)------------------------------
% 0.15/0.40 % (14878)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)
% 0.15/0.40 % (14884)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)
% 0.15/0.40 % (14885)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)
% 0.15/0.40 % (14882)Instruction limit reached!
% 0.15/0.40 % (14882)------------------------------
% 0.15/0.40 % (14882)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (14882)Termination reason: Unknown
% 0.15/0.40 % (14882)Termination phase: Saturation
% 0.15/0.40
% 0.15/0.40 % (14882)Memory used [KB]: 5628
% 0.15/0.40 % (14882)Time elapsed: 0.013 s
% 0.15/0.40 % (14882)Instructions burned: 19 (million)
% 0.15/0.40 % (14882)------------------------------
% 0.15/0.40 % (14882)------------------------------
% 0.15/0.41 % (14887)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)
% 0.15/0.41 % (14885)Instruction limit reached!
% 0.15/0.41 % (14885)------------------------------
% 0.15/0.41 % (14885)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.41 % (14885)Termination reason: Unknown
% 0.15/0.41 % (14885)Termination phase: Saturation
% 0.15/0.41
% 0.15/0.41 % (14885)Memory used [KB]: 5628
% 0.15/0.41 % (14885)Time elapsed: 0.008 s
% 0.15/0.41 % (14885)Instructions burned: 16 (million)
% 0.15/0.41 % (14885)------------------------------
% 0.15/0.41 % (14885)------------------------------
% 0.22/0.41 % (14888)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.41 % (14876)First to succeed.
% 0.22/0.42 % (14878)Instruction limit reached!
% 0.22/0.42 % (14878)------------------------------
% 0.22/0.42 % (14878)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (14878)Termination reason: Unknown
% 0.22/0.42 % (14878)Termination phase: Saturation
% 0.22/0.42
% 0.22/0.42 % (14878)Memory used [KB]: 5756
% 0.22/0.42 % (14878)Time elapsed: 0.014 s
% 0.22/0.42 % (14878)Instructions burned: 28 (million)
% 0.22/0.42 % (14878)------------------------------
% 0.22/0.42 % (14878)------------------------------
% 0.22/0.42 % (14889)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.22/0.42 % (14888)Instruction limit reached!
% 0.22/0.42 % (14888)------------------------------
% 0.22/0.42 % (14888)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (14888)Termination reason: Unknown
% 0.22/0.42 % (14888)Termination phase: Property scanning
% 0.22/0.42
% 0.22/0.42 % (14888)Memory used [KB]: 1023
% 0.22/0.42 % (14888)Time elapsed: 0.004 s
% 0.22/0.42 % (14888)Instructions burned: 7 (million)
% 0.22/0.42 % (14888)------------------------------
% 0.22/0.42 % (14888)------------------------------
% 0.22/0.42 % (14890)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)
% 0.22/0.42 % (14876)Refutation found. Thanks to Tanya!
% 0.22/0.42 % SZS status Theorem for theBenchmark
% 0.22/0.42 % SZS output start Proof for theBenchmark
% 0.22/0.42 thf(type_def_5, type, mu: $tType).
% 0.22/0.42 thf(func_def_0, type, mu: $tType).
% 0.22/0.42 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.22/0.42 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.42 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.22/0.42 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.42 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.42 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.42 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.42 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.42 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.42 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.22/0.42 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.22/0.42 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.22/0.42 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.22/0.42 thf(func_def_15, type, mtrue: $i > $o).
% 0.22/0.42 thf(func_def_16, type, mfalse: $i > $o).
% 0.22/0.42 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.22/0.42 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.22/0.42 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.22/0.42 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.22/0.42 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.22/0.42 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.22/0.42 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.22/0.42 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.22/0.42 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.22/0.42 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.22/0.42 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.22/0.42 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.22/0.42 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.22/0.42 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.22/0.42 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.22/0.42 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.22/0.42 thf(func_def_33, type, rel_s5: $i > $i > $o).
% 0.22/0.42 thf(func_def_34, type, mbox_s5: ($i > $o) > $i > $o).
% 0.22/0.42 thf(func_def_35, type, mdia_s5: ($i > $o) > $i > $o).
% 0.22/0.42 thf(func_def_36, type, p: $i > $o).
% 0.22/0.42 thf(func_def_37, type, q: $i > $o).
% 0.22/0.42 thf(f459,plain,(
% 0.22/0.42 $false),
% 0.22/0.42 inference(avatar_sat_refutation,[],[f404,f438,f450,f458])).
% 0.22/0.42 thf(f458,plain,(
% 0.22/0.42 ~spl0_10),
% 0.22/0.42 inference(avatar_contradiction_clause,[],[f457])).
% 0.22/0.42 thf(f457,plain,(
% 0.22/0.42 $false | ~spl0_10),
% 0.22/0.42 inference(trivial_inequality_removal,[],[f453])).
% 0.22/0.42 thf(f453,plain,(
% 0.22/0.42 ($false = $true) | ~spl0_10),
% 0.22/0.42 inference(superposition,[],[f402,f209])).
% 0.22/0.42 thf(f209,plain,(
% 0.22/0.42 ($false = (q @ sK3))),
% 0.22/0.42 inference(binary_proxy_clausification,[],[f208])).
% 0.22/0.42 thf(f208,plain,(
% 0.22/0.42 ($false = ((~ (rel_s5 @ sK2 @ sK3)) | (q @ sK3)))),
% 0.22/0.42 inference(beta_eta_normalization,[],[f207])).
% 0.22/0.42 thf(f207,plain,(
% 0.22/0.42 (((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0))) @ sK3) = $false)),
% 0.22/0.42 inference(sigma_clausification,[],[f204])).
% 0.22/0.42 thf(f204,plain,(
% 0.22/0.42 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0)))) = $false)),
% 0.22/0.42 inference(binary_proxy_clausification,[],[f201])).
% 0.22/0.42 thf(f201,plain,(
% 0.22/0.42 ($false = ((~ (p @ sK2)) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0))))))),
% 0.22/0.42 inference(binary_proxy_clausification,[],[f200])).
% 0.22/0.42 thf(f200,plain,(
% 0.22/0.42 (((~ (rel_s5 @ sK1 @ sK2)) | ((~ (p @ sK2)) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0)))))) = $false)),
% 0.22/0.42 inference(beta_eta_normalization,[],[f199])).
% 0.22/0.42 thf(f199,plain,(
% 0.22/0.42 ($false = ((^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | ((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))))) @ sK2))),
% 0.22/0.42 inference(sigma_clausification,[],[f186])).
% 0.22/0.42 thf(f186,plain,(
% 0.22/0.42 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | ((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1)))))))))),
% 0.22/0.42 inference(binary_proxy_clausification,[],[f185])).
% 0.22/0.42 thf(f185,plain,(
% 0.22/0.42 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (p @ Y1))))) | (q @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | ((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))))))) = $false)),
% 0.22/0.42 inference(beta_eta_normalization,[],[f184])).
% 0.22/0.42 thf(f184,plain,(
% 0.22/0.42 (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (p @ Y2))))) | (q @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (q @ Y2)))))))))) @ sK1) = $false)),
% 0.22/0.42 inference(sigma_clausification,[],[f183])).
% 0.22/0.42 thf(f183,plain,(
% 0.22/0.42 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (p @ Y2))))) | (q @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (q @ Y2))))))))))) != $true)),
% 0.22/0.42 inference(boolean_simplification,[],[f182])).
% 0.22/0.42 thf(f182,plain,(
% 0.22/0.42 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((~ (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (p @ Y2))))))) | (q @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (q @ Y2))))))))))))),
% 0.22/0.42 inference(boolean_simplification,[],[f181])).
% 0.22/0.42 thf(f181,plain,(
% 0.22/0.42 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((~ (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (p @ Y2))))))) | (~ (~ (q @ Y1)))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (q @ Y2))))))))))))),
% 0.22/0.42 inference(boolean_simplification,[],[f180])).
% 0.22/0.42 thf(f180,plain,(
% 0.22/0.42 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (~ ((~ (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (p @ Y2))))))) | (~ (~ (q @ Y1)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (q @ Y2))))))))))))),
% 0.22/0.42 inference(beta_eta_normalization,[],[f159])).
% 0.22/0.42 thf(f159,plain,(
% 0.22/0.42 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ 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 > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ 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))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))) @ q))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[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)))) @ p @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ q))))))),
% 0.22/0.42 inference(definition_unfolding,[],[f114,f132,f143,f157,f148,f157,f138,f139,f149,f139])).
% 0.22/0.42 thf(f149,plain,(
% 0.22/0.42 (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)))))),
% 0.22/0.42 inference(definition_unfolding,[],[f120,f143,f138])).
% 0.22/0.42 thf(f120,plain,(
% 0.22/0.42 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.22/0.42 inference(cnf_transformation,[],[f69])).
% 0.22/0.42 thf(f69,plain,(
% 0.22/0.42 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.22/0.42 inference(fool_elimination,[],[f68])).
% 0.22/0.42 thf(f68,plain,(
% 0.22/0.42 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.22/0.42 inference(rectify,[],[f6])).
% 0.22/0.42 thf(f6,axiom,(
% 0.22/0.42 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.22/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.22/0.42 thf(f139,plain,(
% 0.22/0.42 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.22/0.42 inference(cnf_transformation,[],[f79])).
% 0.22/0.42 thf(f79,plain,(
% 0.22/0.42 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.22/0.42 inference(fool_elimination,[],[f78])).
% 0.22/0.42 thf(f78,plain,(
% 0.22/0.42 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_s5 @ X1 @ X2)))) = mbox_s5)),
% 0.22/0.42 inference(rectify,[],[f32])).
% 0.22/0.42 thf(f32,axiom,(
% 0.22/0.42 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_s5 @ X2 @ X7)))) = mbox_s5)),
% 0.22/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s5)).
% 0.22/0.42 thf(f138,plain,(
% 0.22/0.42 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.22/0.42 inference(cnf_transformation,[],[f109])).
% 0.22/0.42 thf(f109,plain,(
% 0.22/0.42 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.22/0.42 inference(fool_elimination,[],[f108])).
% 0.22/0.42 thf(f108,plain,(
% 0.22/0.42 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.22/0.42 inference(rectify,[],[f3])).
% 0.22/0.42 thf(f3,axiom,(
% 0.22/0.42 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.22/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.22/0.42 thf(f148,plain,(
% 0.22/0.42 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.22/0.42 inference(definition_unfolding,[],[f122,f138,f143,f138,f138])).
% 0.22/0.42 thf(f122,plain,(
% 0.22/0.42 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.22/0.42 inference(cnf_transformation,[],[f63])).
% 0.22/0.42 thf(f63,plain,(
% 0.22/0.42 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.22/0.42 inference(fool_elimination,[],[f62])).
% 0.22/0.42 thf(f62,plain,(
% 0.22/0.42 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.22/0.42 inference(rectify,[],[f5])).
% 0.22/0.42 thf(f5,axiom,(
% 0.22/0.42 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.22/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.22/0.42 thf(f157,plain,(
% 0.22/0.42 (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)))))),
% 0.22/0.42 inference(definition_unfolding,[],[f137,f138,f139,f138])).
% 0.22/0.42 thf(f137,plain,(
% 0.22/0.42 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.22/0.42 inference(cnf_transformation,[],[f106])).
% 0.22/0.42 thf(f106,plain,(
% 0.22/0.42 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.22/0.42 inference(fool_elimination,[],[f105])).
% 0.22/0.42 thf(f105,plain,(
% 0.22/0.42 (mdia_s5 = (^[X0 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X0)))))),
% 0.22/0.42 inference(rectify,[],[f33])).
% 0.22/0.42 thf(f33,axiom,(
% 0.22/0.42 (mdia_s5 = (^[X3 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X3)))))),
% 0.22/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_s5)).
% 0.22/0.42 thf(f143,plain,(
% 0.22/0.42 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.22/0.42 inference(cnf_transformation,[],[f83])).
% 0.22/0.42 thf(f83,plain,(
% 0.22/0.42 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.22/0.42 inference(fool_elimination,[],[f82])).
% 0.22/0.42 thf(f82,plain,(
% 0.22/0.42 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 0.22/0.42 inference(rectify,[],[f4])).
% 0.22/0.42 thf(f4,axiom,(
% 0.22/0.42 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))) = mor)),
% 0.22/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.22/0.42 thf(f132,plain,(
% 0.22/0.42 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.22/0.42 inference(cnf_transformation,[],[f95])).
% 0.22/0.42 thf(f95,plain,(
% 0.22/0.42 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.22/0.42 inference(fool_elimination,[],[f94])).
% 0.22/0.42 thf(f94,plain,(
% 0.22/0.42 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.22/0.42 inference(rectify,[],[f28])).
% 0.22/0.42 thf(f28,axiom,(
% 0.22/0.42 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.22/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.22/0.42 thf(f114,plain,(
% 0.22/0.42 ((mvalid @ (mor @ (mdia_s5 @ (mand @ (mdia_s5 @ p) @ (mnot @ q))) @ (mbox_s5 @ (mimplies @ p @ (mbox_s5 @ q))))) != $true)),
% 0.22/0.42 inference(cnf_transformation,[],[f110])).
% 0.22/0.42 thf(f110,plain,(
% 0.22/0.42 ((mvalid @ (mor @ (mdia_s5 @ (mand @ (mdia_s5 @ p) @ (mnot @ q))) @ (mbox_s5 @ (mimplies @ p @ (mbox_s5 @ q))))) != $true)),
% 0.22/0.42 inference(flattening,[],[f77])).
% 0.22/0.42 thf(f77,plain,(
% 0.22/0.42 ~((mvalid @ (mor @ (mdia_s5 @ (mand @ (mdia_s5 @ p) @ (mnot @ q))) @ (mbox_s5 @ (mimplies @ p @ (mbox_s5 @ q))))) = $true)),
% 0.22/0.42 inference(fool_elimination,[],[f76])).
% 0.22/0.42 thf(f76,plain,(
% 0.22/0.42 ~(mvalid @ (mor @ (mdia_s5 @ (mand @ (mdia_s5 @ p) @ (mnot @ q))) @ (mbox_s5 @ (mimplies @ p @ (mbox_s5 @ q)))))),
% 0.22/0.42 inference(rectify,[],[f38])).
% 0.22/0.42 thf(f38,negated_conjecture,(
% 0.22/0.42 ~(mvalid @ (mor @ (mdia_s5 @ (mand @ (mdia_s5 @ p) @ (mnot @ q))) @ (mbox_s5 @ (mimplies @ p @ (mbox_s5 @ q)))))),
% 0.22/0.42 inference(negated_conjecture,[],[f37])).
% 0.22/0.42 thf(f37,conjecture,(
% 0.22/0.42 (mvalid @ (mor @ (mdia_s5 @ (mand @ (mdia_s5 @ p) @ (mnot @ q))) @ (mbox_s5 @ (mimplies @ p @ (mbox_s5 @ q)))))),
% 0.22/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.22/0.42 thf(f402,plain,(
% 0.22/0.42 ($true = (q @ sK3)) | ~spl0_10),
% 0.22/0.42 inference(avatar_component_clause,[],[f400])).
% 0.22/0.42 thf(f400,plain,(
% 0.22/0.42 spl0_10 <=> ($true = (q @ sK3))),
% 0.22/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_10])])).
% 0.22/0.42 thf(f450,plain,(
% 0.22/0.42 ~spl0_9),
% 0.22/0.42 inference(avatar_contradiction_clause,[],[f449])).
% 0.22/0.42 thf(f449,plain,(
% 0.22/0.42 $false | ~spl0_9),
% 0.22/0.42 inference(trivial_inequality_removal,[],[f439])).
% 0.22/0.42 thf(f439,plain,(
% 0.22/0.42 ($false = $true) | ~spl0_9),
% 0.22/0.42 inference(superposition,[],[f398,f203])).
% 0.22/0.42 thf(f203,plain,(
% 0.22/0.42 ($true = (rel_s5 @ sK1 @ sK2))),
% 0.22/0.42 inference(not_proxy_clausification,[],[f202])).
% 0.22/0.42 thf(f202,plain,(
% 0.22/0.42 ($false = (~ (rel_s5 @ sK1 @ sK2)))),
% 0.22/0.42 inference(binary_proxy_clausification,[],[f200])).
% 0.22/0.42 thf(f398,plain,(
% 0.22/0.42 ($false = (rel_s5 @ sK1 @ sK2)) | ~spl0_9),
% 0.22/0.42 inference(avatar_component_clause,[],[f396])).
% 0.22/0.42 thf(f396,plain,(
% 0.22/0.42 spl0_9 <=> ($false = (rel_s5 @ sK1 @ sK2))),
% 0.22/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_9])])).
% 0.22/0.42 thf(f438,plain,(
% 0.22/0.42 ~spl0_8),
% 0.22/0.42 inference(avatar_contradiction_clause,[],[f437])).
% 0.22/0.42 thf(f437,plain,(
% 0.22/0.42 $false | ~spl0_8),
% 0.22/0.42 inference(trivial_inequality_removal,[],[f434])).
% 0.22/0.42 thf(f434,plain,(
% 0.22/0.42 ($false = $true) | ~spl0_8),
% 0.22/0.42 inference(superposition,[],[f206,f428])).
% 0.22/0.42 thf(f428,plain,(
% 0.22/0.42 ($false = (p @ sK2)) | ~spl0_8),
% 0.22/0.42 inference(trivial_inequality_removal,[],[f421])).
% 0.22/0.42 thf(f421,plain,(
% 0.22/0.42 ($false = $true) | ($false = (p @ sK2)) | ~spl0_8),
% 0.22/0.42 inference(superposition,[],[f211,f416])).
% 0.22/0.42 thf(f416,plain,(
% 0.22/0.42 ( ! [X0 : $i] : (($false = (rel_s5 @ X0 @ sK3)) | ((p @ X0) = $false)) ) | ~spl0_8),
% 0.22/0.42 inference(trivial_inequality_removal,[],[f407])).
% 0.22/0.42 thf(f407,plain,(
% 0.22/0.42 ( ! [X0 : $i] : (($false = $true) | ((p @ X0) = $false) | ($false = (rel_s5 @ X0 @ sK3))) ) | ~spl0_8),
% 0.22/0.42 inference(superposition,[],[f394,f179])).
% 0.22/0.42 thf(f179,plain,(
% 0.22/0.42 ( ! [X2 : $i,X1 : $i] : (($true = (rel_s5 @ X2 @ X1)) | ((rel_s5 @ X1 @ X2) = $false)) )),
% 0.22/0.42 inference(binary_proxy_clausification,[],[f178])).
% 0.22/0.42 thf(f178,plain,(
% 0.22/0.42 ( ! [X2 : $i,X1 : $i] : ((((rel_s5 @ X1 @ X2) => (rel_s5 @ X2 @ X1)) = $true)) )),
% 0.22/0.42 inference(beta_eta_normalization,[],[f177])).
% 0.22/0.42 thf(f177,plain,(
% 0.22/0.42 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((rel_s5 @ X1 @ Y0) => (rel_s5 @ Y0 @ X1))) @ X2) = $true)) )),
% 0.22/0.42 inference(pi_clausification,[],[f176])).
% 0.22/0.42 thf(f176,plain,(
% 0.22/0.42 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((rel_s5 @ X1 @ Y0) => (rel_s5 @ Y0 @ X1)))) = $true)) )),
% 0.22/0.42 inference(beta_eta_normalization,[],[f175])).
% 0.22/0.42 thf(f175,plain,(
% 0.22/0.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y0 @ Y1) => (rel_s5 @ Y1 @ Y0))))) @ X1))) )),
% 0.22/0.42 inference(pi_clausification,[],[f174])).
% 0.22/0.42 thf(f174,plain,(
% 0.22/0.42 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y0 @ Y1) => (rel_s5 @ Y1 @ Y0)))))))),
% 0.22/0.42 inference(beta_eta_normalization,[],[f161])).
% 0.22/0.42 thf(f161,plain,(
% 0.22/0.42 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) @ rel_s5))),
% 0.22/0.42 inference(definition_unfolding,[],[f124,f119])).
% 0.22/0.42 thf(f119,plain,(
% 0.22/0.42 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.22/0.42 inference(cnf_transformation,[],[f93])).
% 0.22/0.42 thf(f93,plain,(
% 0.22/0.42 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.22/0.42 inference(fool_elimination,[],[f92])).
% 0.22/0.42 thf(f92,plain,(
% 0.22/0.42 (msymmetric = (^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X2 @ X1) => (X0 @ X1 @ X2)))))),
% 0.22/0.42 inference(rectify,[],[f19])).
% 0.22/0.42 thf(f19,axiom,(
% 0.22/0.42 (msymmetric = (^[X6 : $i > $i > $o] : (! [X9,X8] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))))),
% 0.22/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',msymmetric)).
% 0.22/0.42 thf(f124,plain,(
% 0.22/0.42 ((msymmetric @ rel_s5) = $true)),
% 0.22/0.42 inference(cnf_transformation,[],[f71])).
% 0.22/0.42 thf(f71,plain,(
% 0.22/0.42 ((msymmetric @ rel_s5) = $true)),
% 0.22/0.42 inference(fool_elimination,[],[f70])).
% 0.22/0.42 thf(f70,plain,(
% 0.22/0.42 (msymmetric @ rel_s5)),
% 0.22/0.42 inference(rectify,[],[f36])).
% 0.22/0.42 thf(f36,axiom,(
% 0.22/0.42 (msymmetric @ rel_s5)),
% 0.22/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3)).
% 0.22/0.42 thf(f394,plain,(
% 0.22/0.42 ( ! [X0 : $i] : (($false = (rel_s5 @ sK3 @ X0)) | ((p @ X0) = $false)) ) | ~spl0_8),
% 0.22/0.42 inference(avatar_component_clause,[],[f393])).
% 0.22/0.42 thf(f393,plain,(
% 0.22/0.42 spl0_8 <=> ! [X0] : (($false = (rel_s5 @ sK3 @ X0)) | ((p @ X0) = $false))),
% 0.22/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_8])])).
% 0.22/0.42 thf(f211,plain,(
% 0.22/0.42 ($true = (rel_s5 @ sK2 @ sK3))),
% 0.22/0.42 inference(not_proxy_clausification,[],[f210])).
% 0.22/0.42 thf(f210,plain,(
% 0.22/0.42 ((~ (rel_s5 @ sK2 @ sK3)) = $false)),
% 0.22/0.42 inference(binary_proxy_clausification,[],[f208])).
% 0.22/0.42 thf(f206,plain,(
% 0.22/0.42 ($true = (p @ sK2))),
% 0.22/0.42 inference(not_proxy_clausification,[],[f205])).
% 0.22/0.42 thf(f205,plain,(
% 0.22/0.42 ($false = (~ (p @ sK2)))),
% 0.22/0.42 inference(binary_proxy_clausification,[],[f201])).
% 0.22/0.42 thf(f404,plain,(
% 0.22/0.42 spl0_8 | spl0_9 | spl0_10),
% 0.22/0.42 inference(avatar_split_clause,[],[f389,f400,f396,f393])).
% 0.22/0.42 thf(f389,plain,(
% 0.22/0.42 ( ! [X0 : $i] : (($false = (rel_s5 @ sK3 @ X0)) | ((p @ X0) = $false) | ($false = (rel_s5 @ sK1 @ sK2)) | ($true = (q @ sK3))) )),
% 0.22/0.42 inference(trivial_inequality_removal,[],[f377])).
% 0.22/0.42 thf(f377,plain,(
% 0.22/0.42 ( ! [X0 : $i] : (($false = (rel_s5 @ sK1 @ sK2)) | ($true = (q @ sK3)) | ($false = $true) | ($false = (rel_s5 @ sK3 @ X0)) | ((p @ X0) = $false)) )),
% 0.22/0.42 inference(superposition,[],[f211,f231])).
% 0.22/0.42 thf(f231,plain,(
% 0.22/0.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (rel_s5 @ X2 @ X0)) | ((rel_s5 @ sK1 @ X2) = $false) | ((q @ X0) = $true) | ($false = (rel_s5 @ X0 @ X1)) | ((p @ X1) = $false)) )),
% 0.22/0.42 inference(trivial_inequality_removal,[],[f216])).
% 0.22/0.42 thf(f216,plain,(
% 0.22/0.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (rel_s5 @ X2 @ X0)) | ($false = $true) | ((p @ X1) = $false) | ((rel_s5 @ sK1 @ X2) = $false) | ((q @ X0) = $true) | ($false = (rel_s5 @ X0 @ X1))) )),
% 0.22/0.42 inference(superposition,[],[f198,f170])).
% 0.22/0.42 thf(f170,plain,(
% 0.22/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (rel_s5 @ X2 @ X1)) | ($false = (rel_s5 @ X2 @ X3)) | ($false = (rel_s5 @ X3 @ X1))) )),
% 0.22/0.42 inference(binary_proxy_clausification,[],[f169])).
% 0.22/0.42 thf(f169,plain,(
% 0.22/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (rel_s5 @ X2 @ X1)) | ($false = ((rel_s5 @ X2 @ X3) & (rel_s5 @ X3 @ X1)))) )),
% 0.22/0.42 inference(binary_proxy_clausification,[],[f168])).
% 0.22/0.42 thf(f168,plain,(
% 0.22/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((rel_s5 @ X2 @ X3) & (rel_s5 @ X3 @ X1)) => (rel_s5 @ X2 @ X1)) = $true)) )),
% 0.22/0.42 inference(beta_eta_normalization,[],[f167])).
% 0.22/0.42 thf(f167,plain,(
% 0.22/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((rel_s5 @ X2 @ Y0) & (rel_s5 @ Y0 @ X1)) => (rel_s5 @ X2 @ X1))) @ X3) = $true)) )),
% 0.22/0.42 inference(pi_clausification,[],[f166])).
% 0.22/0.42 thf(f166,plain,(
% 0.22/0.42 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((rel_s5 @ X2 @ Y0) & (rel_s5 @ Y0 @ X1)) => (rel_s5 @ X2 @ X1)))))) )),
% 0.22/0.42 inference(beta_eta_normalization,[],[f165])).
% 0.22/0.42 thf(f165,plain,(
% 0.22/0.42 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ Y0 @ Y1) & (rel_s5 @ Y1 @ X1)) => (rel_s5 @ Y0 @ X1))))) @ X2))) )),
% 0.22/0.42 inference(pi_clausification,[],[f164])).
% 0.22/0.42 thf(f164,plain,(
% 0.22/0.42 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ Y0 @ Y1) & (rel_s5 @ Y1 @ X1)) => (rel_s5 @ Y0 @ X1)))))))) )),
% 0.22/0.42 inference(beta_eta_normalization,[],[f163])).
% 0.22/0.42 thf(f163,plain,(
% 0.22/0.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y1 @ Y2) & (rel_s5 @ Y2 @ Y0)) => (rel_s5 @ Y1 @ Y0))))))) @ X1))) )),
% 0.22/0.42 inference(pi_clausification,[],[f162])).
% 0.22/0.42 thf(f162,plain,(
% 0.22/0.42 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y1 @ Y2) & (rel_s5 @ Y2 @ Y0)) => (rel_s5 @ Y1 @ Y0)))))))) = $true)),
% 0.22/0.42 inference(beta_eta_normalization,[],[f158])).
% 0.22/0.42 thf(f158,plain,(
% 0.22/0.42 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) @ rel_s5))),
% 0.22/0.42 inference(definition_unfolding,[],[f112,f140])).
% 0.22/0.42 thf(f140,plain,(
% 0.22/0.42 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))))),
% 0.22/0.42 inference(cnf_transformation,[],[f100])).
% 0.22/0.42 thf(f100,plain,(
% 0.22/0.42 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))))),
% 0.22/0.42 inference(fool_elimination,[],[f99])).
% 0.22/0.42 thf(f99,plain,(
% 0.22/0.42 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X1 @ X3) & (X0 @ X2 @ X1)) => (X0 @ X2 @ X3)))) = mtransitive)),
% 0.22/0.42 inference(rectify,[],[f21])).
% 0.22/0.42 thf(f21,axiom,(
% 0.22/0.42 ((^[X6 : $i > $i > $o] : (! [X9,X8,X10] : (((X6 @ X9 @ X10) & (X6 @ X8 @ X9)) => (X6 @ X8 @ X10)))) = mtransitive)),
% 0.22/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtransitive)).
% 0.22/0.42 thf(f112,plain,(
% 0.22/0.42 ((mtransitive @ rel_s5) = $true)),
% 0.22/0.42 inference(cnf_transformation,[],[f85])).
% 0.22/0.42 thf(f85,plain,(
% 0.22/0.42 ((mtransitive @ rel_s5) = $true)),
% 0.22/0.42 inference(fool_elimination,[],[f84])).
% 0.22/0.42 thf(f84,plain,(
% 0.22/0.42 (mtransitive @ rel_s5)),
% 0.22/0.42 inference(rectify,[],[f35])).
% 0.22/0.42 thf(f35,axiom,(
% 0.22/0.42 (mtransitive @ rel_s5)),
% 0.22/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2)).
% 0.22/0.42 thf(f198,plain,(
% 0.22/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (rel_s5 @ sK1 @ X1)) | ((rel_s5 @ X1 @ X2) = $false) | ($false = (p @ X2)) | ($true = (q @ X1))) )),
% 0.22/0.42 inference(not_proxy_clausification,[],[f197])).
% 0.22/0.42 thf(f197,plain,(
% 0.22/0.42 ( ! [X2 : $i,X1 : $i] : (((~ (rel_s5 @ X1 @ X2)) = $true) | ($true = (q @ X1)) | ($false = (rel_s5 @ sK1 @ X1)) | ($false = (p @ X2))) )),
% 0.22/0.42 inference(not_proxy_clausification,[],[f196])).
% 0.22/0.42 thf(f196,plain,(
% 0.22/0.42 ( ! [X2 : $i,X1 : $i] : (($true = (~ (p @ X2))) | ((~ (rel_s5 @ X1 @ X2)) = $true) | ($false = (rel_s5 @ sK1 @ X1)) | ($true = (q @ X1))) )),
% 0.22/0.42 inference(binary_proxy_clausification,[],[f195])).
% 0.22/0.42 thf(f195,plain,(
% 0.22/0.42 ( ! [X2 : $i,X1 : $i] : ((((~ (rel_s5 @ X1 @ X2)) | (~ (p @ X2))) = $true) | ($false = (rel_s5 @ sK1 @ X1)) | ($true = (q @ X1))) )),
% 0.22/0.42 inference(beta_eta_normalization,[],[f194])).
% 0.22/0.42 thf(f194,plain,(
% 0.22/0.42 ( ! [X2 : $i,X1 : $i] : (($true = (q @ X1)) | (((^[Y0 : $i]: ((~ (rel_s5 @ X1 @ Y0)) | (~ (p @ Y0)))) @ X2) = $true) | ($false = (rel_s5 @ sK1 @ X1))) )),
% 0.22/0.42 inference(pi_clausification,[],[f193])).
% 0.22/0.42 thf(f193,plain,(
% 0.22/0.42 ( ! [X1 : $i] : (($true = (q @ X1)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ X1 @ Y0)) | (~ (p @ Y0))))) = $true) | ($false = (rel_s5 @ sK1 @ X1))) )),
% 0.22/0.42 inference(binary_proxy_clausification,[],[f192])).
% 0.22/0.42 thf(f192,plain,(
% 0.22/0.42 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ X1 @ Y0)) | (~ (p @ Y0))))) | (q @ X1))) | ($false = (rel_s5 @ sK1 @ X1))) )),
% 0.22/0.42 inference(not_proxy_clausification,[],[f191])).
% 0.22/0.42 thf(f191,plain,(
% 0.22/0.42 ( ! [X1 : $i] : (($true = (~ (rel_s5 @ sK1 @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ X1 @ Y0)) | (~ (p @ Y0))))) | (q @ X1)))) )),
% 0.22/0.42 inference(binary_proxy_clausification,[],[f190])).
% 0.22/0.42 thf(f190,plain,(
% 0.22/0.42 ( ! [X1 : $i] : ((((~ (rel_s5 @ sK1 @ X1)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ X1 @ Y0)) | (~ (p @ Y0))))) | (q @ X1))) = $true)) )),
% 0.22/0.42 inference(beta_eta_normalization,[],[f189])).
% 0.22/0.42 thf(f189,plain,(
% 0.22/0.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (p @ Y1))))) | (q @ Y0)))) @ X1))) )),
% 0.22/0.42 inference(pi_clausification,[],[f188])).
% 0.22/0.42 thf(f188,plain,(
% 0.22/0.42 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (p @ Y1))))) | (q @ Y0))))))),
% 0.22/0.42 inference(not_proxy_clausification,[],[f187])).
% 0.22/0.42 thf(f187,plain,(
% 0.22/0.42 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (p @ Y1))))) | (q @ Y0)))))) = $false)),
% 0.22/0.42 inference(binary_proxy_clausification,[],[f185])).
% 0.22/0.42 % SZS output end Proof for theBenchmark
% 0.22/0.42 % (14876)------------------------------
% 0.22/0.42 % (14876)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (14876)Termination reason: Refutation
% 0.22/0.42
% 0.22/0.42 % (14876)Memory used [KB]: 5884
% 0.22/0.42 % (14876)Time elapsed: 0.027 s
% 0.22/0.42 % (14876)Instructions burned: 34 (million)
% 0.22/0.42 % (14876)------------------------------
% 0.22/0.42 % (14876)------------------------------
% 0.22/0.42 % (14875)Success in time 0.038 s
% 0.22/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------