TSTP Solution File: SYO574^7 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO574^7 : TPTP v8.2.0. Released v5.5.0.
% 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 09:06:17 EDT 2024
% Result : Theorem 0.14s 0.39s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO574^7 : TPTP v8.2.0. Released v5.5.0.
% 0.11/0.14 % 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
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon May 20 10:45:08 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a TH0_THM_EQU_NAR problem
% 0.14/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.38 % (18615)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.38 % (18616)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.14/0.38 % (18617)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.14/0.38 % (18618)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.38 % (18621)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.38 % (18620)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.14/0.38 % (18619)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.38 % (18622)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.38 % (18618)Instruction limit reached!
% 0.14/0.38 % (18618)------------------------------
% 0.14/0.38 % (18618)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (18618)Termination reason: Unknown
% 0.14/0.38 % (18619)Instruction limit reached!
% 0.14/0.38 % (18619)------------------------------
% 0.14/0.38 % (18619)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (18618)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (18618)Memory used [KB]: 1023
% 0.14/0.38 % (18618)Time elapsed: 0.004 s
% 0.14/0.38 % (18618)Instructions burned: 3 (million)
% 0.14/0.38 % (18618)------------------------------
% 0.14/0.38 % (18618)------------------------------
% 0.14/0.38 % (18619)Termination reason: Unknown
% 0.14/0.38 % (18619)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (18619)Memory used [KB]: 1023
% 0.14/0.38 % (18619)Time elapsed: 0.003 s
% 0.14/0.38 % (18619)Instructions burned: 3 (million)
% 0.14/0.38 % (18619)------------------------------
% 0.14/0.38 % (18619)------------------------------
% 0.14/0.38 % (18622)Instruction limit reached!
% 0.14/0.38 % (18622)------------------------------
% 0.14/0.38 % (18622)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (18622)Termination reason: Unknown
% 0.14/0.38 % (18622)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (18622)Memory used [KB]: 1023
% 0.14/0.38 % (18622)Time elapsed: 0.004 s
% 0.14/0.38 % (18622)Instructions burned: 3 (million)
% 0.14/0.38 % (18622)------------------------------
% 0.14/0.38 % (18622)------------------------------
% 0.14/0.38 % (18616)Instruction limit reached!
% 0.14/0.38 % (18616)------------------------------
% 0.14/0.38 % (18616)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (18616)Termination reason: Unknown
% 0.14/0.38 % (18616)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (18616)Memory used [KB]: 1023
% 0.14/0.38 % (18616)Time elapsed: 0.005 s
% 0.14/0.38 % (18616)Instructions burned: 5 (million)
% 0.14/0.38 % (18616)------------------------------
% 0.14/0.38 % (18616)------------------------------
% 0.14/0.39 % (18620)Refutation not found, incomplete strategy
% 0.14/0.39 % (18620)------------------------------
% 0.14/0.39 % (18620)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (18620)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.39
% 0.14/0.39
% 0.14/0.39 % (18620)Memory used [KB]: 5628
% 0.14/0.39 % (18620)Time elapsed: 0.008 s
% 0.14/0.39 % (18620)Instructions burned: 11 (million)
% 0.14/0.39 % (18620)------------------------------
% 0.14/0.39 % (18620)------------------------------
% 0.14/0.39 % (18615)First to succeed.
% 0.14/0.39 % (18621)Also succeeded, but the first one will report.
% 0.14/0.39 % (18615)Refutation found. Thanks to Tanya!
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39 % SZS output start Proof for theBenchmark
% 0.14/0.39 thf(type_def_5, type, mu: $tType).
% 0.14/0.39 thf(func_def_0, type, mu: $tType).
% 0.14/0.39 thf(func_def_1, type, qmltpeq: mu > mu > $i > $o).
% 0.14/0.39 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_6, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_7, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_8, type, mtrue: $i > $o).
% 0.14/0.39 thf(func_def_9, type, mfalse: $i > $o).
% 0.14/0.39 thf(func_def_10, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_11, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_12, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_13, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_14, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_15, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_16, type, exists_in_world: mu > $i > $o).
% 0.14/0.39 thf(func_def_17, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_18, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_19, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_20, type, mreflexive: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_21, type, msymmetric: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_22, type, mserial: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_23, type, mtransitive: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_24, type, meuclidean: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_25, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_26, type, mfunctional: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_27, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_28, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_29, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_30, type, mvalid: ($i > $o) > $o).
% 0.14/0.39 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.14/0.39 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.14/0.39 thf(func_def_33, type, minvalid: ($i > $o) > $o).
% 0.14/0.39 thf(func_def_34, type, rel_s4: $i > $i > $o).
% 0.14/0.39 thf(func_def_35, type, mbox_s4: ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_36, type, mdia_s4: ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_37, type, q: $i > $o).
% 0.14/0.39 thf(func_def_38, type, p: $i > $o).
% 0.14/0.39 thf(func_def_54, type, sK0: $i > mu).
% 0.14/0.39 thf(f250,plain,(
% 0.14/0.39 $false),
% 0.14/0.39 inference(avatar_sat_refutation,[],[f216,f230,f249])).
% 0.14/0.39 thf(f249,plain,(
% 0.14/0.39 ~spl1_1),
% 0.14/0.39 inference(avatar_contradiction_clause,[],[f248])).
% 0.14/0.39 thf(f248,plain,(
% 0.14/0.39 $false | ~spl1_1),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f245])).
% 0.14/0.39 thf(f245,plain,(
% 0.14/0.39 ($true = $false) | ~spl1_1),
% 0.14/0.39 inference(superposition,[],[f237,f243])).
% 0.14/0.39 thf(f243,plain,(
% 0.14/0.39 ($true = (q @ sK3)) | ~spl1_1),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f240])).
% 0.14/0.39 thf(f240,plain,(
% 0.14/0.39 ($true = (q @ sK3)) | ($true = $false) | ~spl1_1),
% 0.14/0.39 inference(superposition,[],[f211,f208])).
% 0.14/0.39 thf(f208,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($true = (rel_s4 @ X1 @ X1))) )),
% 0.14/0.39 inference(beta_eta_normalization,[],[f207])).
% 0.14/0.39 thf(f207,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (rel_s4 @ Y0 @ Y0)) @ X1))) )),
% 0.14/0.39 inference(pi_clausification,[],[f206])).
% 0.14/0.39 thf(f206,plain,(
% 0.14/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))))),
% 0.14/0.39 inference(beta_eta_normalization,[],[f165])).
% 0.14/0.39 thf(f165,plain,(
% 0.14/0.39 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ rel_s4))),
% 0.14/0.39 inference(definition_unfolding,[],[f141,f124])).
% 0.14/0.39 thf(f124,plain,(
% 0.14/0.39 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.14/0.39 inference(cnf_transformation,[],[f81])).
% 0.14/0.39 thf(f81,plain,(
% 0.14/0.39 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.14/0.39 inference(fool_elimination,[],[f80])).
% 0.14/0.39 thf(f80,plain,(
% 0.14/0.39 (mreflexive = (^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))))),
% 0.14/0.39 inference(rectify,[],[f18])).
% 0.14/0.39 thf(f18,axiom,(
% 0.14/0.39 (mreflexive = (^[X5 : $i > $i > $o] : (! [X8] : (X5 @ X8 @ X8))))),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mreflexive)).
% 0.14/0.39 thf(f141,plain,(
% 0.14/0.39 ((mreflexive @ rel_s4) = $true)),
% 0.14/0.39 inference(cnf_transformation,[],[f59])).
% 0.14/0.39 thf(f59,plain,(
% 0.14/0.39 ((mreflexive @ rel_s4) = $true)),
% 0.14/0.39 inference(fool_elimination,[],[f58])).
% 0.14/0.39 thf(f58,plain,(
% 0.14/0.39 (mreflexive @ rel_s4)),
% 0.14/0.39 inference(rectify,[],[f34])).
% 0.14/0.39 thf(f34,axiom,(
% 0.14/0.39 (mreflexive @ rel_s4)),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1)).
% 0.14/0.39 thf(f211,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (((rel_s4 @ sK3 @ X1) = $false) | ($true = (q @ X1))) ) | ~spl1_1),
% 0.14/0.39 inference(avatar_component_clause,[],[f210])).
% 0.14/0.39 thf(f210,plain,(
% 0.14/0.39 spl1_1 <=> ! [X1] : (($true = (q @ X1)) | ((rel_s4 @ sK3 @ X1) = $false))),
% 0.14/0.39 introduced(avatar_definition,[new_symbols(naming,[spl1_1])])).
% 0.14/0.39 thf(f237,plain,(
% 0.14/0.39 ((q @ sK3) = $false)),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f233])).
% 0.14/0.39 thf(f233,plain,(
% 0.14/0.39 ($true = $false) | ((q @ sK3) = $false)),
% 0.14/0.39 inference(superposition,[],[f196,f176])).
% 0.14/0.39 thf(f176,plain,(
% 0.14/0.39 ($true = (rel_s4 @ sK2 @ sK3))),
% 0.14/0.39 inference(not_proxy_clausification,[],[f175])).
% 0.14/0.39 thf(f175,plain,(
% 0.14/0.39 ($false = (~ (rel_s4 @ sK2 @ sK3)))),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f173])).
% 0.14/0.39 thf(f173,plain,(
% 0.14/0.39 (((~ (rel_s4 @ sK2 @ sK3)) | (~ ((~ (p @ sK3)) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (q @ Y0))))))) = $false)),
% 0.14/0.39 inference(beta_eta_normalization,[],[f172])).
% 0.14/0.39 thf(f172,plain,(
% 0.14/0.39 ($false = ((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ ((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1)))))))) @ sK3))),
% 0.14/0.39 inference(sigma_clausification,[],[f171])).
% 0.14/0.39 thf(f171,plain,(
% 0.14/0.39 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ ((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1))))))))) = $false)),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f169])).
% 0.14/0.39 thf(f169,plain,(
% 0.14/0.39 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ ((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (q @ Y1))))))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ (q @ Y0)))))))))),
% 0.14/0.39 inference(beta_eta_normalization,[],[f168])).
% 0.14/0.39 thf(f168,plain,(
% 0.14/0.39 ($false = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ ((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (q @ Y2))))))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (q @ Y1))))))))) @ sK2))),
% 0.14/0.39 inference(sigma_clausification,[],[f167])).
% 0.14/0.39 thf(f167,plain,(
% 0.14/0.39 ($true != (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ ((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (q @ Y2))))))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (q @ Y1)))))))))))),
% 0.14/0.39 inference(boolean_simplification,[],[f166])).
% 0.14/0.39 thf(f166,plain,(
% 0.14/0.39 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ ((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (q @ Y2))))))))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (q @ Y1)))))))))))),
% 0.14/0.39 inference(beta_eta_normalization,[],[f164])).
% 0.14/0.39 thf(f164,plain,(
% 0.14/0.39 ($true != ((^[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]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[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_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ q))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ q)))))),
% 0.14/0.39 inference(definition_unfolding,[],[f140,f121,f155,f162,f155,f150,f155,f150,f162])).
% 0.14/0.39 thf(f150,plain,(
% 0.14/0.39 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.14/0.39 inference(cnf_transformation,[],[f102])).
% 0.14/0.39 thf(f102,plain,(
% 0.14/0.39 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.14/0.39 inference(fool_elimination,[],[f101])).
% 0.14/0.39 thf(f101,plain,(
% 0.14/0.39 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_s4 @ X1 @ X2)))) = mbox_s4)),
% 0.14/0.39 inference(rectify,[],[f32])).
% 0.14/0.39 thf(f32,axiom,(
% 0.14/0.39 ((^[X3 : $i > $o, X2 : $i] : (! [X6] : ((X3 @ X6) | ~(rel_s4 @ X2 @ X6)))) = mbox_s4)),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s4)).
% 0.14/0.39 thf(f162,plain,(
% 0.14/0.39 (mdia_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.14/0.39 inference(definition_unfolding,[],[f142,f146,f150,f146])).
% 0.14/0.39 thf(f146,plain,(
% 0.14/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.39 inference(cnf_transformation,[],[f53])).
% 0.14/0.39 thf(f53,plain,(
% 0.14/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.39 inference(fool_elimination,[],[f52])).
% 0.14/0.39 thf(f52,plain,(
% 0.14/0.39 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.14/0.39 inference(rectify,[],[f2])).
% 0.14/0.39 thf(f2,axiom,(
% 0.14/0.39 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.14/0.39 thf(f142,plain,(
% 0.14/0.39 (mdia_s4 = (^[Y0 : $i > $o]: (mnot @ (mbox_s4 @ (mnot @ Y0)))))),
% 0.14/0.39 inference(cnf_transformation,[],[f65])).
% 0.14/0.39 thf(f65,plain,(
% 0.14/0.39 (mdia_s4 = (^[Y0 : $i > $o]: (mnot @ (mbox_s4 @ (mnot @ Y0)))))),
% 0.14/0.39 inference(fool_elimination,[],[f64])).
% 0.14/0.39 thf(f64,plain,(
% 0.14/0.39 ((^[X0 : $i > $o] : (mnot @ (mbox_s4 @ (mnot @ X0)))) = mdia_s4)),
% 0.14/0.39 inference(rectify,[],[f33])).
% 0.14/0.39 thf(f33,axiom,(
% 0.14/0.39 ((^[X3 : $i > $o] : (mnot @ (mbox_s4 @ (mnot @ X3)))) = mdia_s4)),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_s4)).
% 0.14/0.39 thf(f155,plain,(
% 0.14/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.14/0.39 inference(definition_unfolding,[],[f118,f125,f146])).
% 0.14/0.39 thf(f125,plain,(
% 0.14/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.14/0.39 inference(cnf_transformation,[],[f75])).
% 0.14/0.39 thf(f75,plain,(
% 0.14/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.14/0.39 inference(fool_elimination,[],[f74])).
% 0.14/0.39 thf(f74,plain,(
% 0.14/0.39 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 0.14/0.39 inference(rectify,[],[f3])).
% 0.14/0.39 thf(f3,axiom,(
% 0.14/0.39 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))) = mor)),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.14/0.39 thf(f118,plain,(
% 0.14/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.39 inference(cnf_transformation,[],[f89])).
% 0.14/0.39 thf(f89,plain,(
% 0.14/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.39 inference(fool_elimination,[],[f88])).
% 0.14/0.39 thf(f88,plain,(
% 0.14/0.39 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.14/0.39 inference(rectify,[],[f9])).
% 0.14/0.39 thf(f9,axiom,(
% 0.14/0.39 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.14/0.39 thf(f121,plain,(
% 0.14/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.39 inference(cnf_transformation,[],[f87])).
% 0.14/0.39 thf(f87,plain,(
% 0.14/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.39 inference(fool_elimination,[],[f86])).
% 0.14/0.39 thf(f86,plain,(
% 0.14/0.39 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.14/0.39 inference(rectify,[],[f28])).
% 0.14/0.39 thf(f28,axiom,(
% 0.14/0.39 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.14/0.39 thf(f140,plain,(
% 0.14/0.39 ((mvalid @ (mimplies @ (mdia_s4 @ (mimplies @ p @ (mbox_s4 @ q))) @ (mimplies @ (mbox_s4 @ p) @ (mdia_s4 @ q)))) != $true)),
% 0.14/0.39 inference(cnf_transformation,[],[f111])).
% 0.14/0.39 thf(f111,plain,(
% 0.14/0.39 ((mvalid @ (mimplies @ (mdia_s4 @ (mimplies @ p @ (mbox_s4 @ q))) @ (mimplies @ (mbox_s4 @ p) @ (mdia_s4 @ q)))) != $true)),
% 0.14/0.39 inference(flattening,[],[f94])).
% 0.14/0.39 thf(f94,plain,(
% 0.14/0.39 ~((mvalid @ (mimplies @ (mdia_s4 @ (mimplies @ p @ (mbox_s4 @ q))) @ (mimplies @ (mbox_s4 @ p) @ (mdia_s4 @ q)))) = $true)),
% 0.14/0.39 inference(fool_elimination,[],[f93])).
% 0.14/0.39 thf(f93,plain,(
% 0.14/0.39 ~(mvalid @ (mimplies @ (mdia_s4 @ (mimplies @ p @ (mbox_s4 @ q))) @ (mimplies @ (mbox_s4 @ p) @ (mdia_s4 @ q))))),
% 0.14/0.39 inference(rectify,[],[f38])).
% 0.14/0.39 thf(f38,negated_conjecture,(
% 0.14/0.39 ~(mvalid @ (mimplies @ (mdia_s4 @ (mimplies @ p @ (mbox_s4 @ q))) @ (mimplies @ (mbox_s4 @ p) @ (mdia_s4 @ q))))),
% 0.14/0.39 inference(negated_conjecture,[],[f37])).
% 0.14/0.39 thf(f37,conjecture,(
% 0.14/0.39 (mvalid @ (mimplies @ (mdia_s4 @ (mimplies @ p @ (mbox_s4 @ q))) @ (mimplies @ (mbox_s4 @ p) @ (mdia_s4 @ q))))),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',con)).
% 0.14/0.39 thf(f196,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (((rel_s4 @ sK2 @ X1) = $false) | ($false = (q @ X1))) )),
% 0.14/0.39 inference(not_proxy_clausification,[],[f195])).
% 0.14/0.39 thf(f195,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($false = (q @ X1)) | ($true = (~ (rel_s4 @ sK2 @ X1)))) )),
% 0.14/0.39 inference(not_proxy_clausification,[],[f194])).
% 0.14/0.39 thf(f194,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($true = (~ (q @ X1))) | ($true = (~ (rel_s4 @ sK2 @ X1)))) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f193])).
% 0.14/0.39 thf(f193,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($true = ((~ (rel_s4 @ sK2 @ X1)) | (~ (q @ X1))))) )),
% 0.14/0.39 inference(beta_eta_normalization,[],[f192])).
% 0.14/0.39 thf(f192,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ (q @ Y0)))) @ X1))) )),
% 0.14/0.39 inference(pi_clausification,[],[f191])).
% 0.14/0.39 thf(f191,plain,(
% 0.14/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ (q @ Y0))))))),
% 0.14/0.39 inference(not_proxy_clausification,[],[f184])).
% 0.14/0.39 thf(f184,plain,(
% 0.14/0.39 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ (q @ Y0)))))) = $false)),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f170])).
% 0.14/0.39 thf(f170,plain,(
% 0.14/0.39 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ (q @ Y0))))))) = $false)),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f169])).
% 0.14/0.39 thf(f230,plain,(
% 0.14/0.39 ~spl1_2),
% 0.14/0.39 inference(avatar_contradiction_clause,[],[f229])).
% 0.14/0.39 thf(f229,plain,(
% 0.14/0.39 $false | ~spl1_2),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f226])).
% 0.14/0.39 thf(f226,plain,(
% 0.14/0.39 ($true = $false) | ~spl1_2),
% 0.14/0.39 inference(superposition,[],[f215,f223])).
% 0.14/0.39 thf(f223,plain,(
% 0.14/0.39 ($true = (p @ sK3))),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f218])).
% 0.14/0.39 thf(f218,plain,(
% 0.14/0.39 ($true = $false) | ($true = (p @ sK3))),
% 0.14/0.39 inference(superposition,[],[f190,f176])).
% 0.14/0.39 thf(f190,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (((rel_s4 @ sK2 @ X1) = $false) | ($true = (p @ X1))) )),
% 0.14/0.39 inference(not_proxy_clausification,[],[f189])).
% 0.14/0.39 thf(f189,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($true = (p @ X1)) | ($true = (~ (rel_s4 @ sK2 @ X1)))) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f188])).
% 0.14/0.39 thf(f188,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($true = ((~ (rel_s4 @ sK2 @ X1)) | (p @ X1)))) )),
% 0.14/0.39 inference(beta_eta_normalization,[],[f187])).
% 0.14/0.39 thf(f187,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (p @ Y0))) @ X1))) )),
% 0.14/0.39 inference(pi_clausification,[],[f186])).
% 0.14/0.39 thf(f186,plain,(
% 0.14/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (p @ Y0)))))),
% 0.14/0.39 inference(not_proxy_clausification,[],[f185])).
% 0.14/0.39 thf(f185,plain,(
% 0.14/0.39 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (p @ Y0))))) = $false)),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f170])).
% 0.14/0.39 thf(f215,plain,(
% 0.14/0.39 ($false = (p @ sK3)) | ~spl1_2),
% 0.14/0.39 inference(avatar_component_clause,[],[f213])).
% 0.14/0.39 thf(f213,plain,(
% 0.14/0.39 spl1_2 <=> ($false = (p @ sK3))),
% 0.14/0.39 introduced(avatar_definition,[new_symbols(naming,[spl1_2])])).
% 0.14/0.39 thf(f216,plain,(
% 0.14/0.39 spl1_1 | spl1_2),
% 0.14/0.39 inference(avatar_split_clause,[],[f183,f213,f210])).
% 0.14/0.39 thf(f183,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($true = (q @ X1)) | ($false = (p @ sK3)) | ((rel_s4 @ sK3 @ X1) = $false)) )),
% 0.14/0.39 inference(not_proxy_clausification,[],[f182])).
% 0.14/0.39 thf(f182,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($true = (~ (rel_s4 @ sK3 @ X1))) | ($true = (q @ X1)) | ($false = (p @ sK3))) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f181])).
% 0.14/0.39 thf(f181,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($false = (p @ sK3)) | ($true = ((~ (rel_s4 @ sK3 @ X1)) | (q @ X1)))) )),
% 0.14/0.39 inference(beta_eta_normalization,[],[f180])).
% 0.14/0.39 thf(f180,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (q @ Y0))) @ X1)) | ($false = (p @ sK3))) )),
% 0.14/0.39 inference(pi_clausification,[],[f179])).
% 0.14/0.39 thf(f179,plain,(
% 0.14/0.39 ($false = (p @ sK3)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (q @ Y0)))))),
% 0.14/0.39 inference(not_proxy_clausification,[],[f178])).
% 0.14/0.39 thf(f178,plain,(
% 0.14/0.39 ($true = (~ (p @ sK3))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (q @ Y0)))))),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f177])).
% 0.14/0.39 thf(f177,plain,(
% 0.14/0.39 ($true = ((~ (p @ sK3)) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (q @ Y0))))))),
% 0.14/0.39 inference(not_proxy_clausification,[],[f174])).
% 0.14/0.39 thf(f174,plain,(
% 0.14/0.39 ((~ ((~ (p @ sK3)) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (q @ Y0)))))) = $false)),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f173])).
% 0.14/0.39 % SZS output end Proof for theBenchmark
% 0.14/0.39 % (18615)------------------------------
% 0.14/0.39 % (18615)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (18615)Termination reason: Refutation
% 0.14/0.39
% 0.14/0.39 % (18615)Memory used [KB]: 5756
% 0.14/0.39 % (18615)Time elapsed: 0.013 s
% 0.14/0.39 % (18615)Instructions burned: 15 (million)
% 0.14/0.39 % (18615)------------------------------
% 0.14/0.39 % (18615)------------------------------
% 0.14/0.39 % (18614)Success in time 0.04 s
% 0.14/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------