TSTP Solution File: SYO046^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO046^1 : 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 : n018.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 09:02:27 EDT 2024
% Result : Theorem 0.23s 0.39s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO046^1 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.15 % 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
% 0.15/0.36 % Computer : n018.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 20 10:13:53 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a TH0_THM_EQU_NAR problem
% 0.15/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.38 % (30353)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)
% 0.15/0.38 % (30355)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)
% 0.15/0.38 % (30351)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.38 % (30351)Instruction limit reached!
% 0.15/0.38 % (30351)------------------------------
% 0.15/0.38 % (30351)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (30351)Termination reason: Unknown
% 0.15/0.38 % (30351)Termination phase: shuffling
% 0.15/0.38
% 0.15/0.38 % (30351)Memory used [KB]: 1023
% 0.15/0.38 % (30351)Time elapsed: 0.002 s
% 0.15/0.38 % (30351)Instructions burned: 2 (million)
% 0.15/0.38 % (30351)------------------------------
% 0.15/0.38 % (30351)------------------------------
% 0.15/0.38 % (30348)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.38 % (30349)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)
% 0.15/0.38 % (30355)Instruction limit reached!
% 0.15/0.38 % (30355)------------------------------
% 0.15/0.38 % (30355)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (30355)Termination reason: Unknown
% 0.15/0.38 % (30355)Termination phase: Property scanning
% 0.15/0.38
% 0.15/0.38 % (30355)Memory used [KB]: 1023
% 0.15/0.38 % (30355)Time elapsed: 0.003 s
% 0.15/0.38 % (30355)Instructions burned: 5 (million)
% 0.15/0.38 % (30355)------------------------------
% 0.15/0.38 % (30355)------------------------------
% 0.15/0.38 % (30350)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)
% 0.15/0.38 % (30354)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 % (30349)Instruction limit reached!
% 0.15/0.39 % (30349)------------------------------
% 0.15/0.39 % (30349)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (30349)Termination reason: Unknown
% 0.15/0.39 % (30349)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (30349)Memory used [KB]: 1023
% 0.15/0.39 % (30349)Time elapsed: 0.004 s
% 0.15/0.39 % (30349)Instructions burned: 4 (million)
% 0.15/0.39 % (30349)------------------------------
% 0.15/0.39 % (30349)------------------------------
% 0.15/0.39 % (30353)First to succeed.
% 0.23/0.39 % (30353)Refutation found. Thanks to Tanya!
% 0.23/0.39 % SZS status Theorem for theBenchmark
% 0.23/0.39 % SZS output start Proof for theBenchmark
% 0.23/0.39 thf(type_def_5, type, mu: $tType).
% 0.23/0.39 thf(func_def_0, type, mu: $tType).
% 0.23/0.39 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.23/0.39 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.39 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.23/0.39 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.39 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.39 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.39 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.39 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.39 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.39 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.23/0.39 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.23/0.39 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.23/0.39 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.23/0.39 thf(func_def_15, type, mtrue: $i > $o).
% 0.23/0.39 thf(func_def_16, type, mfalse: $i > $o).
% 0.23/0.39 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.23/0.39 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.23/0.39 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.23/0.39 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.23/0.39 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.23/0.39 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.23/0.39 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.23/0.39 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.23/0.39 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.23/0.39 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.23/0.39 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.23/0.39 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.23/0.39 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.23/0.39 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.23/0.39 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.23/0.39 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.23/0.39 thf(func_def_48, type, sK0: $i > $i > $o).
% 0.23/0.39 thf(func_def_51, type, sK3: $i > $o).
% 0.23/0.39 thf(func_def_52, type, sK4: $i > $o).
% 0.23/0.39 thf(f170,plain,(
% 0.23/0.39 $false),
% 0.23/0.39 inference(avatar_sat_refutation,[],[f148,f162,f169])).
% 0.23/0.39 thf(f169,plain,(
% 0.23/0.39 ~spl1_1),
% 0.23/0.39 inference(avatar_contradiction_clause,[],[f168])).
% 0.23/0.39 thf(f168,plain,(
% 0.23/0.39 $false | ~spl1_1),
% 0.23/0.39 inference(trivial_inequality_removal,[],[f165])).
% 0.23/0.39 thf(f165,plain,(
% 0.23/0.39 ($true = $false) | ~spl1_1),
% 0.23/0.39 inference(superposition,[],[f143,f156])).
% 0.23/0.39 thf(f156,plain,(
% 0.23/0.39 ((sK3 @ sK5) = $true)),
% 0.23/0.39 inference(trivial_inequality_removal,[],[f154])).
% 0.23/0.39 thf(f154,plain,(
% 0.23/0.39 ((sK3 @ sK5) = $true) | ($true = $false)),
% 0.23/0.39 inference(superposition,[],[f139,f131])).
% 0.23/0.39 thf(f131,plain,(
% 0.23/0.39 ( ! [X1 : $i] : (((sK0 @ sK2 @ X1) = $false) | ($true = (sK3 @ X1))) )),
% 0.23/0.39 inference(not_proxy_clausification,[],[f130])).
% 0.23/0.39 thf(f130,plain,(
% 0.23/0.39 ( ! [X1 : $i] : (($true = (~ (sK0 @ sK2 @ X1))) | ($true = (sK3 @ X1))) )),
% 0.23/0.39 inference(binary_proxy_clausification,[],[f129])).
% 0.23/0.39 thf(f129,plain,(
% 0.23/0.39 ( ! [X1 : $i] : (($true = ((sK3 @ X1) | (~ (sK0 @ sK2 @ X1))))) )),
% 0.23/0.39 inference(beta_eta_normalization,[],[f128])).
% 0.23/0.39 thf(f128,plain,(
% 0.23/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0)))) @ X1))) )),
% 0.23/0.39 inference(pi_clausification,[],[f127])).
% 0.23/0.39 thf(f127,plain,(
% 0.23/0.39 ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0))))) = $true)),
% 0.23/0.39 inference(not_proxy_clausification,[],[f119])).
% 0.23/0.39 thf(f119,plain,(
% 0.23/0.39 ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) = $false)),
% 0.23/0.39 inference(binary_proxy_clausification,[],[f118])).
% 0.23/0.39 thf(f118,plain,(
% 0.23/0.39 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0))))))) = $false)),
% 0.23/0.39 inference(binary_proxy_clausification,[],[f116])).
% 0.23/0.39 thf(f116,plain,(
% 0.23/0.39 ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0)))))) = $false)),
% 0.23/0.39 inference(beta_eta_normalization,[],[f115])).
% 0.23/0.39 thf(f115,plain,(
% 0.23/0.39 (((^[Y0 : $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (Y0 @ Y1)) | (~ (sK0 @ sK2 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (sK0 @ sK2 @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ ((Y0 @ Y1) | (~ (sK3 @ Y1)))) | (~ (sK0 @ sK2 @ Y1))))))) @ sK4) = $false)),
% 0.23/0.39 inference(sigma_clausification,[],[f114])).
% 0.23/0.39 thf(f114,plain,(
% 0.23/0.39 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (Y0 @ Y1)) | (~ (sK0 @ sK2 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (sK0 @ sK2 @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ ((Y0 @ Y1) | (~ (sK3 @ Y1)))) | (~ (sK0 @ sK2 @ Y1)))))))) = $false)),
% 0.23/0.39 inference(beta_eta_normalization,[],[f113])).
% 0.23/0.39 thf(f113,plain,(
% 0.23/0.39 (((^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) | (~ (sK0 @ sK2 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (sK0 @ sK2 @ Y2))))))) | (!! @ $i @ (^[Y2 : $i]: ((~ ((Y1 @ Y2) | (~ (Y0 @ Y2)))) | (~ (sK0 @ sK2 @ Y2))))))))) @ sK3) = $false)),
% 0.23/0.39 inference(sigma_clausification,[],[f112])).
% 0.23/0.39 thf(f112,plain,(
% 0.23/0.39 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) | (~ (sK0 @ sK2 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (sK0 @ sK2 @ Y2))))))) | (!! @ $i @ (^[Y2 : $i]: ((~ ((Y1 @ Y2) | (~ (Y0 @ Y2)))) | (~ (sK0 @ sK2 @ Y2)))))))))) = $false)),
% 0.23/0.39 inference(beta_eta_normalization,[],[f111])).
% 0.23/0.39 thf(f111,plain,(
% 0.23/0.39 (((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (sK0 @ Y0 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (sK0 @ Y0 @ Y3))))))) | (!! @ $i @ (^[Y3 : $i]: ((~ ((Y2 @ Y3) | (~ (Y1 @ Y3)))) | (~ (sK0 @ Y0 @ Y3))))))))))) @ sK2) = $false)),
% 0.23/0.39 inference(sigma_clausification,[],[f110])).
% 0.23/0.39 thf(f110,plain,(
% 0.23/0.39 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (sK0 @ Y0 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (sK0 @ Y0 @ Y3))))))) | (!! @ $i @ (^[Y3 : $i]: ((~ ((Y2 @ Y3) | (~ (Y1 @ Y3)))) | (~ (sK0 @ Y0 @ Y3)))))))))))))),
% 0.23/0.39 inference(boolean_simplification,[],[f109])).
% 0.23/0.39 thf(f109,plain,(
% 0.23/0.39 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (sK0 @ Y0 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (sK0 @ Y0 @ Y3))))))) | (~ (~ (!! @ $i @ (^[Y3 : $i]: ((~ ((Y2 @ Y3) | (~ (Y1 @ Y3)))) | (~ (sK0 @ Y0 @ Y3)))))))))))))))),
% 0.23/0.39 inference(beta_eta_normalization,[],[f108])).
% 0.23/0.39 thf(f108,plain,(
% 0.23/0.39 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : ($i > $o) > $i > $o]: ((^[Y2 : $i]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7) | (~ (Y4 @ Y6 @ Y7)))))))))) @ Y2 @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ sK0 @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1)) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5) | (~ (Y2 @ Y4 @ Y5)))))))))) @ sK0 @ Y0) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7) | (~ (Y4 @ Y6 @ Y7)))))))))) @ Y2 @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ sK0 @ Y1)))))))))),
% 0.23/0.39 inference(definition_unfolding,[],[f100,f105,f104,f104,f106,f107,f106,f106,f102,f107])).
% 0.23/0.39 thf(f102,plain,(
% 0.23/0.39 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))))),
% 0.23/0.39 inference(cnf_transformation,[],[f82])).
% 0.23/0.39 thf(f82,plain,(
% 0.23/0.39 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))))),
% 0.23/0.39 inference(fool_elimination,[],[f81])).
% 0.23/0.39 thf(f81,plain,(
% 0.23/0.39 ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : (~(X0 @ X2 @ X3) | (X1 @ X3)))) = mbox)),
% 0.23/0.39 inference(rectify,[],[f16])).
% 0.23/0.39 thf(f16,axiom,(
% 0.23/0.39 ((^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7] : (~(X6 @ X2 @ X7) | (X3 @ X7)))) = mbox)),
% 0.23/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox)).
% 0.23/0.39 thf(f107,plain,(
% 0.23/0.39 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5) | (~ (Y2 @ Y4 @ Y5)))))))))) @ Y0 @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.23/0.39 inference(definition_unfolding,[],[f103,f98,f102,f98])).
% 0.23/0.39 thf(f98,plain,(
% 0.23/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.23/0.39 inference(cnf_transformation,[],[f78])).
% 0.23/0.39 thf(f78,plain,(
% 0.23/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.23/0.39 inference(fool_elimination,[],[f77])).
% 0.23/0.39 thf(f77,plain,(
% 0.23/0.39 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.23/0.39 inference(rectify,[],[f3])).
% 0.23/0.39 thf(f3,axiom,(
% 0.23/0.39 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.23/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.23/0.39 thf(f103,plain,(
% 0.23/0.39 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mbox @ Y0 @ (mnot @ Y1)))))))),
% 0.23/0.39 inference(cnf_transformation,[],[f51])).
% 0.23/0.39 thf(f51,plain,(
% 0.23/0.39 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mbox @ Y0 @ (mnot @ Y1)))))))),
% 0.23/0.39 inference(fool_elimination,[],[f50])).
% 0.23/0.39 thf(f50,plain,(
% 0.23/0.39 ((^[X0 : $i > $i > $o, X1 : $i > $o] : (mnot @ (mbox @ X0 @ (mnot @ X1)))) = mdia)),
% 0.23/0.39 inference(rectify,[],[f17])).
% 0.23/0.39 thf(f17,axiom,(
% 0.23/0.39 ((^[X6 : $i > $i > $o, X3 : $i > $o] : (mnot @ (mbox @ X6 @ (mnot @ X3)))) = mdia)),
% 0.23/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia)).
% 0.23/0.39 thf(f106,plain,(
% 0.23/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.23/0.39 inference(definition_unfolding,[],[f101,f99,f98])).
% 0.23/0.39 thf(f99,plain,(
% 0.23/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.23/0.39 inference(cnf_transformation,[],[f72])).
% 0.23/0.39 thf(f72,plain,(
% 0.23/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.23/0.39 inference(fool_elimination,[],[f71])).
% 0.23/0.39 thf(f71,plain,(
% 0.23/0.39 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.23/0.39 inference(rectify,[],[f4])).
% 0.23/0.39 thf(f4,axiom,(
% 0.23/0.39 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))),
% 0.23/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.23/0.39 thf(f101,plain,(
% 0.23/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.23/0.39 inference(cnf_transformation,[],[f68])).
% 0.23/0.39 thf(f68,plain,(
% 0.23/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.23/0.39 inference(fool_elimination,[],[f67])).
% 0.23/0.39 thf(f67,plain,(
% 0.23/0.39 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.23/0.39 inference(rectify,[],[f6])).
% 0.23/0.39 thf(f6,axiom,(
% 0.23/0.39 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.23/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.23/0.39 thf(f104,plain,(
% 0.23/0.39 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.23/0.39 inference(cnf_transformation,[],[f38])).
% 0.23/0.39 thf(f38,plain,(
% 0.23/0.39 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.23/0.39 inference(fool_elimination,[],[f37])).
% 0.23/0.39 thf(f37,plain,(
% 0.23/0.39 ((^[X0 : ($i > $o) > $i > $o, X1 : $i] : (! [X2 : $i > $o] : (X0 @ X2 @ X1))) = mforall_prop)),
% 0.23/0.39 inference(rectify,[],[f11])).
% 0.23/0.39 thf(f11,axiom,(
% 0.23/0.39 ((^[X3 : ($i > $o) > $i > $o, X2 : $i] : (! [X5 : $i > $o] : (X3 @ X5 @ X2))) = mforall_prop)),
% 0.23/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_prop)).
% 0.23/0.39 thf(f105,plain,(
% 0.23/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.23/0.39 inference(cnf_transformation,[],[f66])).
% 0.23/0.39 thf(f66,plain,(
% 0.23/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.23/0.39 inference(fool_elimination,[],[f65])).
% 0.23/0.39 thf(f65,plain,(
% 0.23/0.39 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.23/0.39 inference(rectify,[],[f28])).
% 0.23/0.39 thf(f28,axiom,(
% 0.23/0.39 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.23/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.23/0.39 thf(f100,plain,(
% 0.23/0.39 ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mimplies @ (mdia @ sK0 @ (mimplies @ Y0 @ Y1)) @ (mimplies @ (mbox @ sK0 @ Y0) @ (mdia @ sK0 @ Y1)))))))) != $true)),
% 0.23/0.39 inference(cnf_transformation,[],[f97])).
% 0.23/0.39 thf(f97,plain,(
% 0.23/0.39 ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mimplies @ (mdia @ sK0 @ (mimplies @ Y0 @ Y1)) @ (mimplies @ (mbox @ sK0 @ Y0) @ (mdia @ sK0 @ Y1)))))))) != $true)),
% 0.23/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f95,f96])).
% 0.23/0.39 thf(f96,plain,(
% 0.23/0.39 ? [X0 : $i > $i > $o] : ($true != (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mimplies @ (mdia @ X0 @ (mimplies @ Y0 @ Y1)) @ (mimplies @ (mbox @ X0 @ Y0) @ (mdia @ X0 @ Y1))))))))) => ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mimplies @ (mdia @ sK0 @ (mimplies @ Y0 @ Y1)) @ (mimplies @ (mbox @ sK0 @ Y0) @ (mdia @ sK0 @ Y1)))))))) != $true)),
% 0.23/0.39 introduced(choice_axiom,[])).
% 0.23/0.39 thf(f95,plain,(
% 0.23/0.39 ? [X0 : $i > $i > $o] : ($true != (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mimplies @ (mdia @ X0 @ (mimplies @ Y0 @ Y1)) @ (mimplies @ (mbox @ X0 @ Y0) @ (mdia @ X0 @ Y1)))))))))),
% 0.23/0.39 inference(ennf_transformation,[],[f59])).
% 0.23/0.39 thf(f59,plain,(
% 0.23/0.39 ~! [X0 : $i > $i > $o] : ($true = (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mimplies @ (mdia @ X0 @ (mimplies @ Y0 @ Y1)) @ (mimplies @ (mbox @ X0 @ Y0) @ (mdia @ X0 @ Y1)))))))))),
% 0.23/0.39 inference(fool_elimination,[],[f58])).
% 0.23/0.39 thf(f58,plain,(
% 0.23/0.39 ~! [X0 : $i > $i > $o] : (mvalid @ (mforall_prop @ (^[X1 : $i > $o] : (mforall_prop @ (^[X2 : $i > $o] : (mimplies @ (mdia @ X0 @ (mimplies @ X1 @ X2)) @ (mimplies @ (mbox @ X0 @ X1) @ (mdia @ X0 @ X2))))))))),
% 0.23/0.39 inference(rectify,[],[f33])).
% 0.23/0.39 thf(f33,negated_conjecture,(
% 0.23/0.39 ~! [X6 : $i > $i > $o] : (mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mforall_prop @ (^[X12 : $i > $o] : (mimplies @ (mdia @ X6 @ (mimplies @ X11 @ X12)) @ (mimplies @ (mbox @ X6 @ X11) @ (mdia @ X6 @ X12))))))))),
% 0.23/0.39 inference(negated_conjecture,[],[f32])).
% 0.23/0.39 thf(f32,conjecture,(
% 0.23/0.39 ! [X6 : $i > $i > $o] : (mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mforall_prop @ (^[X12 : $i > $o] : (mimplies @ (mdia @ X6 @ (mimplies @ X11 @ X12)) @ (mimplies @ (mbox @ X6 @ X11) @ (mdia @ X6 @ X12))))))))),
% 0.23/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 0.23/0.39 thf(f139,plain,(
% 0.23/0.39 ($true = (sK0 @ sK2 @ sK5))),
% 0.23/0.39 inference(not_proxy_clausification,[],[f134])).
% 0.23/0.39 thf(f134,plain,(
% 0.23/0.39 ((~ (sK0 @ sK2 @ sK5)) = $false)),
% 0.23/0.39 inference(binary_proxy_clausification,[],[f133])).
% 0.23/0.39 thf(f133,plain,(
% 0.23/0.39 (((~ ((sK4 @ sK5) | (~ (sK3 @ sK5)))) | (~ (sK0 @ sK2 @ sK5))) = $false)),
% 0.23/0.39 inference(beta_eta_normalization,[],[f132])).
% 0.23/0.39 thf(f132,plain,(
% 0.23/0.39 (((^[Y0 : $i]: ((~ ((sK4 @ Y0) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0)))) @ sK5) = $false)),
% 0.23/0.39 inference(sigma_clausification,[],[f117])).
% 0.23/0.39 thf(f117,plain,(
% 0.23/0.39 ((!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0))))) = $false)),
% 0.23/0.39 inference(binary_proxy_clausification,[],[f116])).
% 0.23/0.39 thf(f143,plain,(
% 0.23/0.39 ((sK3 @ sK5) = $false) | ~spl1_1),
% 0.23/0.39 inference(avatar_component_clause,[],[f141])).
% 0.23/0.39 thf(f141,plain,(
% 0.23/0.39 spl1_1 <=> ((sK3 @ sK5) = $false)),
% 0.23/0.39 introduced(avatar_definition,[new_symbols(naming,[spl1_1])])).
% 0.23/0.39 thf(f162,plain,(
% 0.23/0.39 ~spl1_2),
% 0.23/0.39 inference(avatar_contradiction_clause,[],[f161])).
% 0.23/0.39 thf(f161,plain,(
% 0.23/0.39 $false | ~spl1_2),
% 0.23/0.39 inference(trivial_inequality_removal,[],[f158])).
% 0.23/0.39 thf(f158,plain,(
% 0.23/0.39 ($true = $false) | ~spl1_2),
% 0.23/0.39 inference(superposition,[],[f147,f152])).
% 0.23/0.39 thf(f152,plain,(
% 0.23/0.39 ((sK4 @ sK5) = $false)),
% 0.23/0.39 inference(trivial_inequality_removal,[],[f149])).
% 0.23/0.39 thf(f149,plain,(
% 0.23/0.39 ($true = $false) | ((sK4 @ sK5) = $false)),
% 0.23/0.39 inference(superposition,[],[f126,f139])).
% 0.23/0.39 thf(f126,plain,(
% 0.23/0.39 ( ! [X1 : $i] : (((sK0 @ sK2 @ X1) = $false) | ((sK4 @ X1) = $false)) )),
% 0.23/0.39 inference(not_proxy_clausification,[],[f125])).
% 0.23/0.39 thf(f125,plain,(
% 0.23/0.39 ( ! [X1 : $i] : (((sK4 @ X1) = $false) | ($true = (~ (sK0 @ sK2 @ X1)))) )),
% 0.23/0.39 inference(not_proxy_clausification,[],[f124])).
% 0.23/0.39 thf(f124,plain,(
% 0.23/0.39 ( ! [X1 : $i] : (($true = (~ (sK4 @ X1))) | ($true = (~ (sK0 @ sK2 @ X1)))) )),
% 0.23/0.39 inference(binary_proxy_clausification,[],[f123])).
% 0.23/0.39 thf(f123,plain,(
% 0.23/0.39 ( ! [X1 : $i] : (($true = ((~ (sK4 @ X1)) | (~ (sK0 @ sK2 @ X1))))) )),
% 0.23/0.39 inference(beta_eta_normalization,[],[f122])).
% 0.23/0.39 thf(f122,plain,(
% 0.23/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))) @ X1))) )),
% 0.23/0.39 inference(pi_clausification,[],[f121])).
% 0.23/0.39 thf(f121,plain,(
% 0.23/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))),
% 0.23/0.39 inference(not_proxy_clausification,[],[f120])).
% 0.23/0.39 thf(f120,plain,(
% 0.23/0.39 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) = $false)),
% 0.23/0.39 inference(binary_proxy_clausification,[],[f118])).
% 0.23/0.39 thf(f147,plain,(
% 0.23/0.39 ($true = (sK4 @ sK5)) | ~spl1_2),
% 0.23/0.39 inference(avatar_component_clause,[],[f145])).
% 0.23/0.39 thf(f145,plain,(
% 0.23/0.39 spl1_2 <=> ($true = (sK4 @ sK5))),
% 0.23/0.39 introduced(avatar_definition,[new_symbols(naming,[spl1_2])])).
% 0.23/0.39 thf(f148,plain,(
% 0.23/0.39 spl1_1 | spl1_2),
% 0.23/0.39 inference(avatar_split_clause,[],[f138,f145,f141])).
% 0.23/0.39 thf(f138,plain,(
% 0.23/0.39 ((sK3 @ sK5) = $false) | ($true = (sK4 @ sK5))),
% 0.23/0.39 inference(not_proxy_clausification,[],[f137])).
% 0.23/0.39 thf(f137,plain,(
% 0.23/0.39 ($true = (~ (sK3 @ sK5))) | ($true = (sK4 @ sK5))),
% 0.23/0.39 inference(binary_proxy_clausification,[],[f136])).
% 0.23/0.39 thf(f136,plain,(
% 0.23/0.39 ($true = ((sK4 @ sK5) | (~ (sK3 @ sK5))))),
% 0.23/0.39 inference(not_proxy_clausification,[],[f135])).
% 0.23/0.39 thf(f135,plain,(
% 0.23/0.39 ((~ ((sK4 @ sK5) | (~ (sK3 @ sK5)))) = $false)),
% 0.23/0.39 inference(binary_proxy_clausification,[],[f133])).
% 0.23/0.39 % SZS output end Proof for theBenchmark
% 0.23/0.39 % (30353)------------------------------
% 0.23/0.39 % (30353)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.39 % (30353)Termination reason: Refutation
% 0.23/0.39
% 0.23/0.39 % (30353)Memory used [KB]: 5756
% 0.23/0.39 % (30353)Time elapsed: 0.010 s
% 0.23/0.39 % (30353)Instructions burned: 12 (million)
% 0.23/0.39 % (30353)------------------------------
% 0.23/0.39 % (30353)------------------------------
% 0.23/0.39 % (30347)Success in time 0.014 s
% 0.23/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------