TSTP Solution File: SYO394^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO394^1 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n019.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 09:04:16 EDT 2024
% Result : Theorem 0.21s 0.38s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO394^1 : 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 : n019.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 10:44:38 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/sandbox/benchmark/theBenchmark.p
% 0.21/0.37 % (17141)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)
% 0.21/0.37 % (17144)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)
% 0.21/0.37 % (17143)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.37 % (17140)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.21/0.37 % (17146)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.37 % (17147)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)
% 0.21/0.37 % (17145)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)
% 0.21/0.37 % (17143)Instruction limit reached!
% 0.21/0.37 % (17143)------------------------------
% 0.21/0.37 % (17143)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (17143)Termination reason: Unknown
% 0.21/0.37 % (17143)Termination phase: shuffling
% 0.21/0.37
% 0.21/0.37 % (17143)Memory used [KB]: 1023
% 0.21/0.37 % (17144)Instruction limit reached!
% 0.21/0.37 % (17144)------------------------------
% 0.21/0.37 % (17144)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (17143)Time elapsed: 0.003 s
% 0.21/0.37 % (17144)Termination reason: Unknown
% 0.21/0.37 % (17144)Termination phase: shuffling
% 0.21/0.37
% 0.21/0.37 % (17144)Memory used [KB]: 1023
% 0.21/0.37 % (17144)Time elapsed: 0.003 s
% 0.21/0.37 % (17144)Instructions burned: 3 (million)
% 0.21/0.37 % (17144)------------------------------
% 0.21/0.37 % (17144)------------------------------
% 0.21/0.37 % (17143)Instructions burned: 3 (million)
% 0.21/0.37 % (17143)------------------------------
% 0.21/0.37 % (17143)------------------------------
% 0.21/0.37 % (17142)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)
% 0.21/0.37 % (17147)Instruction limit reached!
% 0.21/0.37 % (17147)------------------------------
% 0.21/0.37 % (17147)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (17147)Termination reason: Unknown
% 0.21/0.37 % (17147)Termination phase: shuffling
% 0.21/0.37
% 0.21/0.37 % (17147)Memory used [KB]: 1023
% 0.21/0.37 % (17147)Time elapsed: 0.003 s
% 0.21/0.37 % (17147)Instructions burned: 3 (million)
% 0.21/0.37 % (17147)------------------------------
% 0.21/0.37 % (17147)------------------------------
% 0.21/0.37 % (17141)Instruction limit reached!
% 0.21/0.37 % (17141)------------------------------
% 0.21/0.37 % (17141)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (17141)Termination reason: Unknown
% 0.21/0.37 % (17141)Termination phase: Property scanning
% 0.21/0.37
% 0.21/0.37 % (17141)Memory used [KB]: 1023
% 0.21/0.37 % (17141)Time elapsed: 0.004 s
% 0.21/0.37 % (17141)Instructions burned: 5 (million)
% 0.21/0.37 % (17141)------------------------------
% 0.21/0.37 % (17141)------------------------------
% 0.21/0.38 % (17145)Refutation not found, incomplete strategy
% 0.21/0.38 % (17145)------------------------------
% 0.21/0.38 % (17145)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (17145)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.38
% 0.21/0.38
% 0.21/0.38 % (17145)Memory used [KB]: 5628
% 0.21/0.38 % (17145)Time elapsed: 0.006 s
% 0.21/0.38 % (17145)Instructions burned: 7 (million)
% 0.21/0.38 % (17145)------------------------------
% 0.21/0.38 % (17145)------------------------------
% 0.21/0.38 % (17140)First to succeed.
% 0.21/0.38 % (17146)Also succeeded, but the first one will report.
% 0.21/0.38 % (17142)Also succeeded, but the first one will report.
% 0.21/0.38 % (17140)Refutation found. Thanks to Tanya!
% 0.21/0.38 % SZS status Theorem for theBenchmark
% 0.21/0.38 % SZS output start Proof for theBenchmark
% 0.21/0.38 thf(type_def_5, type, mu: $tType).
% 0.21/0.38 thf(func_def_0, type, mu: $tType).
% 0.21/0.38 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.21/0.38 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_15, type, mtrue: $i > $o).
% 0.21/0.38 thf(func_def_16, type, mfalse: $i > $o).
% 0.21/0.38 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.21/0.38 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.21/0.38 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.21/0.38 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.21/0.38 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.21/0.38 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.21/0.38 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.21/0.38 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.21/0.38 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.21/0.38 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.21/0.38 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.21/0.38 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.21/0.38 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.21/0.38 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.21/0.38 thf(func_def_33, type, rel_k: $i > $i > $o).
% 0.21/0.38 thf(func_def_34, type, mbox_k: ($i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_35, type, mdia_k: ($i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_36, type, p: $i > $o).
% 0.21/0.38 thf(func_def_37, type, q: $i > $o).
% 0.21/0.38 thf(f204,plain,(
% 0.21/0.38 $false),
% 0.21/0.38 inference(avatar_sat_refutation,[],[f183,f193,f203])).
% 0.21/0.38 thf(f203,plain,(
% 0.21/0.38 ~spl0_1),
% 0.21/0.38 inference(avatar_contradiction_clause,[],[f202])).
% 0.21/0.38 thf(f202,plain,(
% 0.21/0.38 $false | ~spl0_1),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f199])).
% 0.21/0.38 thf(f199,plain,(
% 0.21/0.38 ($true = $false) | ~spl0_1),
% 0.21/0.38 inference(superposition,[],[f162,f197])).
% 0.21/0.38 thf(f197,plain,(
% 0.21/0.38 ($false = (p @ sK2)) | ~spl0_1),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f194])).
% 0.21/0.38 thf(f194,plain,(
% 0.21/0.38 ($false = (p @ sK2)) | ($true = $false) | ~spl0_1),
% 0.21/0.38 inference(superposition,[],[f179,f164])).
% 0.21/0.38 thf(f164,plain,(
% 0.21/0.38 ($true = (rel_k @ sK1 @ sK2))),
% 0.21/0.38 inference(not_proxy_clausification,[],[f158])).
% 0.21/0.38 thf(f158,plain,(
% 0.21/0.38 ($false = (~ (rel_k @ sK1 @ sK2)))),
% 0.21/0.38 inference(binary_proxy_clausification,[],[f157])).
% 0.21/0.38 thf(f157,plain,(
% 0.21/0.38 ((((~ (p @ sK2)) | (~ (q @ sK2))) | (~ (rel_k @ sK1 @ sK2))) = $false)),
% 0.21/0.38 inference(beta_eta_normalization,[],[f156])).
% 0.21/0.38 thf(f156,plain,(
% 0.21/0.38 ($false = ((^[Y0 : $i]: (((~ (p @ Y0)) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))) @ sK2))),
% 0.21/0.38 inference(sigma_clausification,[],[f155])).
% 0.21/0.38 thf(f155,plain,(
% 0.21/0.38 ($false = (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0))))))),
% 0.21/0.38 inference(binary_proxy_clausification,[],[f153])).
% 0.21/0.38 thf(f153,plain,(
% 0.21/0.38 (((!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))))) = $false)),
% 0.21/0.38 inference(beta_eta_normalization,[],[f152])).
% 0.21/0.38 thf(f152,plain,(
% 0.21/0.38 ($false = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (~ (q @ Y1))) | (~ (rel_k @ Y0 @ Y1))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_k @ Y0 @ Y1))))))))) @ sK1))),
% 0.21/0.38 inference(sigma_clausification,[],[f151])).
% 0.21/0.38 thf(f151,plain,(
% 0.21/0.38 ($true != (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (~ (q @ Y1))) | (~ (rel_k @ Y0 @ Y1))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))))))))),
% 0.21/0.38 inference(boolean_simplification,[],[f150])).
% 0.21/0.38 thf(f150,plain,(
% 0.21/0.38 ($true != (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (~ ((~ (p @ Y1)) | (~ (q @ Y1))))) | (~ (rel_k @ Y0 @ Y1))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))))))))),
% 0.21/0.38 inference(boolean_simplification,[],[f149])).
% 0.21/0.38 thf(f149,plain,(
% 0.21/0.38 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (~ ((~ (p @ Y1)) | (~ (q @ Y1))))) | (~ (rel_k @ Y0 @ Y1))))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))))))))),
% 0.21/0.38 inference(boolean_simplification,[],[f148])).
% 0.21/0.38 thf(f148,plain,(
% 0.21/0.38 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (~ ((~ (p @ Y1)) | (~ (q @ Y1))))) | (~ (rel_k @ Y0 @ Y1))))))) | (~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))))))))),
% 0.21/0.38 inference(boolean_simplification,[],[f147])).
% 0.21/0.38 thf(f147,plain,(
% 0.21/0.38 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (~ ((~ (p @ Y1)) | (~ (q @ Y1))))) | (~ (rel_k @ Y0 @ Y1))))))) | (~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1))))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))))))))))),
% 0.21/0.38 inference(beta_eta_normalization,[],[f146])).
% 0.21/0.38 thf(f146,plain,(
% 0.21/0.38 (((^[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 > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_k @ Y2 @ 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)))))) @ p @ q)) @ ((^[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]: ((Y1 @ Y3) | (~ (rel_k @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_k @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ q)))) != $true)),
% 0.21/0.38 inference(definition_unfolding,[],[f132,f119,f137,f145,f136,f136,f145,f145])).
% 0.21/0.38 thf(f136,plain,(
% 0.21/0.38 (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)))))))),
% 0.21/0.38 inference(definition_unfolding,[],[f123,f120,f112,f120,f120])).
% 0.21/0.38 thf(f112,plain,(
% 0.21/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.21/0.38 inference(cnf_transformation,[],[f44])).
% 0.21/0.38 thf(f44,plain,(
% 0.21/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.21/0.38 inference(fool_elimination,[],[f43])).
% 0.21/0.38 thf(f43,plain,(
% 0.21/0.38 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 0.21/0.38 inference(rectify,[],[f4])).
% 0.21/0.38 thf(f4,axiom,(
% 0.21/0.38 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))) = mor)),
% 0.21/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.21/0.38 thf(f120,plain,(
% 0.21/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.38 inference(cnf_transformation,[],[f38])).
% 0.21/0.38 thf(f38,plain,(
% 0.21/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.38 inference(fool_elimination,[],[f37])).
% 0.21/0.38 thf(f37,plain,(
% 0.21/0.38 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.21/0.38 inference(rectify,[],[f3])).
% 0.21/0.38 thf(f3,axiom,(
% 0.21/0.38 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.21/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.21/0.38 thf(f123,plain,(
% 0.21/0.38 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.21/0.38 inference(cnf_transformation,[],[f82])).
% 0.21/0.38 thf(f82,plain,(
% 0.21/0.38 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.21/0.38 inference(fool_elimination,[],[f81])).
% 0.21/0.38 thf(f81,plain,(
% 0.21/0.38 ((^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))) = mand)),
% 0.21/0.38 inference(rectify,[],[f5])).
% 0.21/0.38 thf(f5,axiom,(
% 0.21/0.38 ((^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))) = mand)),
% 0.21/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.21/0.38 thf(f145,plain,(
% 0.21/0.38 (mdia_k = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_k @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.21/0.38 inference(definition_unfolding,[],[f125,f120,f106,f120])).
% 0.21/0.38 thf(f106,plain,(
% 0.21/0.38 (mbox_k = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_k @ Y1 @ Y2)))))))))),
% 0.21/0.38 inference(cnf_transformation,[],[f100])).
% 0.21/0.38 thf(f100,plain,(
% 0.21/0.38 (mbox_k = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_k @ Y1 @ Y2)))))))))),
% 0.21/0.38 inference(fool_elimination,[],[f99])).
% 0.21/0.38 thf(f99,plain,(
% 0.21/0.38 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_k @ X1 @ X2) | (X0 @ X2)))) = mbox_k)),
% 0.21/0.38 inference(rectify,[],[f32])).
% 0.21/0.38 thf(f32,axiom,(
% 0.21/0.38 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_k @ X2 @ X7) | (X3 @ X7)))) = mbox_k)),
% 0.21/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_k)).
% 0.21/0.38 thf(f125,plain,(
% 0.21/0.38 (mdia_k = (^[Y0 : $i > $o]: (mnot @ (mbox_k @ (mnot @ Y0)))))),
% 0.21/0.38 inference(cnf_transformation,[],[f46])).
% 0.21/0.38 thf(f46,plain,(
% 0.21/0.38 (mdia_k = (^[Y0 : $i > $o]: (mnot @ (mbox_k @ (mnot @ Y0)))))),
% 0.21/0.38 inference(fool_elimination,[],[f45])).
% 0.21/0.38 thf(f45,plain,(
% 0.21/0.38 ((^[X0 : $i > $o] : (mnot @ (mbox_k @ (mnot @ X0)))) = mdia_k)),
% 0.21/0.38 inference(rectify,[],[f33])).
% 0.21/0.38 thf(f33,axiom,(
% 0.21/0.38 ((^[X3 : $i > $o] : (mnot @ (mbox_k @ (mnot @ X3)))) = mdia_k)),
% 0.21/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_k)).
% 0.21/0.38 thf(f137,plain,(
% 0.21/0.38 (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)))))),
% 0.21/0.38 inference(definition_unfolding,[],[f122,f112,f120])).
% 0.21/0.38 thf(f122,plain,(
% 0.21/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.38 inference(cnf_transformation,[],[f70])).
% 0.21/0.38 thf(f70,plain,(
% 0.21/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.38 inference(fool_elimination,[],[f69])).
% 0.21/0.38 thf(f69,plain,(
% 0.21/0.38 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.21/0.38 inference(rectify,[],[f6])).
% 0.21/0.38 thf(f6,axiom,(
% 0.21/0.38 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.21/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.21/0.38 thf(f119,plain,(
% 0.21/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.38 inference(cnf_transformation,[],[f57])).
% 0.21/0.38 thf(f57,plain,(
% 0.21/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.38 inference(fool_elimination,[],[f56])).
% 0.21/0.38 thf(f56,plain,(
% 0.21/0.38 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.21/0.38 inference(rectify,[],[f28])).
% 0.21/0.38 thf(f28,axiom,(
% 0.21/0.38 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.21/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.21/0.38 thf(f132,plain,(
% 0.21/0.38 ((mvalid @ (mimplies @ (mdia_k @ (mand @ p @ q)) @ (mand @ (mdia_k @ p) @ (mdia_k @ q)))) != $true)),
% 0.21/0.38 inference(cnf_transformation,[],[f101])).
% 0.21/0.38 thf(f101,plain,(
% 0.21/0.38 ((mvalid @ (mimplies @ (mdia_k @ (mand @ p @ q)) @ (mand @ (mdia_k @ p) @ (mdia_k @ q)))) != $true)),
% 0.21/0.38 inference(flattening,[],[f88])).
% 0.21/0.38 thf(f88,plain,(
% 0.21/0.38 ~((mvalid @ (mimplies @ (mdia_k @ (mand @ p @ q)) @ (mand @ (mdia_k @ p) @ (mdia_k @ q)))) = $true)),
% 0.21/0.38 inference(fool_elimination,[],[f87])).
% 0.21/0.38 thf(f87,plain,(
% 0.21/0.38 ~(mvalid @ (mimplies @ (mdia_k @ (mand @ p @ q)) @ (mand @ (mdia_k @ p) @ (mdia_k @ q))))),
% 0.21/0.38 inference(rectify,[],[f35])).
% 0.21/0.38 thf(f35,negated_conjecture,(
% 0.21/0.38 ~(mvalid @ (mimplies @ (mdia_k @ (mand @ p @ q)) @ (mand @ (mdia_k @ p) @ (mdia_k @ q))))),
% 0.21/0.38 inference(negated_conjecture,[],[f34])).
% 0.21/0.38 thf(f34,conjecture,(
% 0.21/0.38 (mvalid @ (mimplies @ (mdia_k @ (mand @ p @ q)) @ (mand @ (mdia_k @ p) @ (mdia_k @ q))))),
% 0.21/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.21/0.38 thf(f179,plain,(
% 0.21/0.38 ( ! [X2 : $i] : (($false = (rel_k @ sK1 @ X2)) | ($false = (p @ X2))) ) | ~spl0_1),
% 0.21/0.38 inference(avatar_component_clause,[],[f178])).
% 0.21/0.38 thf(f178,plain,(
% 0.21/0.38 spl0_1 <=> ! [X2] : (($false = (p @ X2)) | ($false = (rel_k @ sK1 @ X2)))),
% 0.21/0.38 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.21/0.38 thf(f162,plain,(
% 0.21/0.38 ($true = (p @ sK2))),
% 0.21/0.38 inference(not_proxy_clausification,[],[f161])).
% 0.21/0.38 thf(f161,plain,(
% 0.21/0.38 ((~ (p @ sK2)) = $false)),
% 0.21/0.38 inference(binary_proxy_clausification,[],[f159])).
% 0.21/0.38 thf(f159,plain,(
% 0.21/0.38 ($false = ((~ (p @ sK2)) | (~ (q @ sK2))))),
% 0.21/0.38 inference(binary_proxy_clausification,[],[f157])).
% 0.21/0.38 thf(f193,plain,(
% 0.21/0.38 ~spl0_2),
% 0.21/0.38 inference(avatar_contradiction_clause,[],[f192])).
% 0.21/0.38 thf(f192,plain,(
% 0.21/0.38 $false | ~spl0_2),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f188])).
% 0.21/0.38 thf(f188,plain,(
% 0.21/0.38 ($true = $false) | ~spl0_2),
% 0.21/0.38 inference(superposition,[],[f187,f163])).
% 0.21/0.38 thf(f163,plain,(
% 0.21/0.38 ($true = (q @ sK2))),
% 0.21/0.38 inference(not_proxy_clausification,[],[f160])).
% 0.21/0.38 thf(f160,plain,(
% 0.21/0.38 ((~ (q @ sK2)) = $false)),
% 0.21/0.38 inference(binary_proxy_clausification,[],[f159])).
% 0.21/0.38 thf(f187,plain,(
% 0.21/0.38 ($false = (q @ sK2)) | ~spl0_2),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f184])).
% 0.21/0.38 thf(f184,plain,(
% 0.21/0.38 ($false = (q @ sK2)) | ($true = $false) | ~spl0_2),
% 0.21/0.38 inference(superposition,[],[f164,f182])).
% 0.21/0.38 thf(f182,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ((q @ X1) = $false)) ) | ~spl0_2),
% 0.21/0.38 inference(avatar_component_clause,[],[f181])).
% 0.21/0.38 thf(f181,plain,(
% 0.21/0.38 spl0_2 <=> ! [X1] : (((rel_k @ sK1 @ X1) = $false) | ((q @ X1) = $false))),
% 0.21/0.38 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.21/0.38 thf(f183,plain,(
% 0.21/0.38 spl0_1 | spl0_2),
% 0.21/0.38 inference(avatar_split_clause,[],[f176,f181,f178])).
% 0.21/0.38 thf(f176,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ((q @ X1) = $false) | ($false = (p @ X2)) | ($false = (rel_k @ sK1 @ X2))) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f175])).
% 0.21/0.38 thf(f175,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : (((q @ X1) = $false) | ((~ (rel_k @ sK1 @ X2)) = $true) | ((rel_k @ sK1 @ X1) = $false) | ($false = (p @ X2))) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f174])).
% 0.21/0.38 thf(f174,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ((~ (p @ X2)) = $true) | ((q @ X1) = $false) | ((~ (rel_k @ sK1 @ X2)) = $true)) )),
% 0.21/0.38 inference(binary_proxy_clausification,[],[f173])).
% 0.21/0.38 thf(f173,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : (((q @ X1) = $false) | ((rel_k @ sK1 @ X1) = $false) | ($true = ((~ (p @ X2)) | (~ (rel_k @ sK1 @ X2))))) )),
% 0.21/0.38 inference(beta_eta_normalization,[],[f172])).
% 0.21/0.38 thf(f172,plain,(
% 0.21/0.38 ( ! [X2 : $i,X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ($true = ((^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0)))) @ X2)) | ((q @ X1) = $false)) )),
% 0.21/0.38 inference(pi_clausification,[],[f171])).
% 0.21/0.38 thf(f171,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | ((rel_k @ sK1 @ X1) = $false) | ((q @ X1) = $false)) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f170])).
% 0.21/0.38 thf(f170,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (($true = (~ (q @ X1))) | ((rel_k @ sK1 @ X1) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f169])).
% 0.21/0.38 thf(f169,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (((~ (rel_k @ sK1 @ X1)) = $true) | ($true = (~ (q @ X1))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))) )),
% 0.21/0.38 inference(binary_proxy_clausification,[],[f168])).
% 0.21/0.38 thf(f168,plain,(
% 0.21/0.38 ( ! [X1 : $i] : ((((~ (q @ X1)) | (~ (rel_k @ sK1 @ X1))) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))) )),
% 0.21/0.38 inference(beta_eta_normalization,[],[f167])).
% 0.21/0.38 thf(f167,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | ($true = ((^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))) @ X1))) )),
% 0.21/0.38 inference(pi_clausification,[],[f166])).
% 0.21/0.38 thf(f166,plain,(
% 0.21/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))),
% 0.21/0.38 inference(binary_proxy_clausification,[],[f165])).
% 0.21/0.38 thf(f165,plain,(
% 0.21/0.38 (((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) = $true)),
% 0.21/0.38 inference(not_proxy_clausification,[],[f154])).
% 0.21/0.38 thf(f154,plain,(
% 0.21/0.38 ($false = (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))))),
% 0.21/0.38 inference(binary_proxy_clausification,[],[f153])).
% 0.21/0.38 % SZS output end Proof for theBenchmark
% 0.21/0.38 % (17140)------------------------------
% 0.21/0.38 % (17140)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (17140)Termination reason: Refutation
% 0.21/0.38
% 0.21/0.38 % (17140)Memory used [KB]: 5628
% 0.21/0.38 % (17140)Time elapsed: 0.010 s
% 0.21/0.38 % (17140)Instructions burned: 12 (million)
% 0.21/0.38 % (17140)------------------------------
% 0.21/0.38 % (17140)------------------------------
% 0.21/0.38 % (17139)Success in time 0.012 s
% 0.21/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------