TSTP Solution File: SYO455^5 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO455^5 : 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 : n026.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 09:04:41 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO455^5 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.13 % 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 : n026.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 10:22:23 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
% 0.14/0.37 % (7318)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)
% 0.14/0.37 % (7319)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.14/0.37 % (7321)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.37 % (7318)Instruction limit reached!
% 0.14/0.37 % (7318)------------------------------
% 0.14/0.37 % (7318)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (7318)Termination reason: Unknown
% 0.14/0.37 % (7318)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (7318)Memory used [KB]: 1023
% 0.14/0.37 % (7318)Time elapsed: 0.003 s
% 0.14/0.37 % (7318)Instructions burned: 4 (million)
% 0.14/0.37 % (7318)------------------------------
% 0.14/0.37 % (7318)------------------------------
% 0.14/0.37 % (7321)Instruction limit reached!
% 0.14/0.37 % (7321)------------------------------
% 0.14/0.37 % (7321)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (7321)Termination reason: Unknown
% 0.14/0.37 % (7321)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (7321)Memory used [KB]: 1023
% 0.14/0.37 % (7321)Time elapsed: 0.003 s
% 0.14/0.37 % (7321)Instructions burned: 3 (million)
% 0.14/0.37 % (7321)------------------------------
% 0.14/0.37 % (7321)------------------------------
% 0.14/0.37 % (7314)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.37 % (7315)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.14/0.37 % (7320)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.37 % (7315)Instruction limit reached!
% 0.14/0.37 % (7315)------------------------------
% 0.14/0.37 % (7315)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (7315)Termination reason: Unknown
% 0.14/0.37 % (7315)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (7315)Memory used [KB]: 1023
% 0.14/0.37 % (7315)Time elapsed: 0.004 s
% 0.14/0.37 % (7315)Instructions burned: 4 (million)
% 0.14/0.37 % (7315)------------------------------
% 0.14/0.37 % (7315)------------------------------
% 0.14/0.37 % (7319)Refutation not found, incomplete strategy
% 0.14/0.37 % (7319)------------------------------
% 0.14/0.37 % (7319)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (7319)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.37
% 0.14/0.37
% 0.14/0.37 % (7319)Memory used [KB]: 5628
% 0.14/0.37 % (7319)Time elapsed: 0.006 s
% 0.14/0.37 % (7319)Instructions burned: 9 (million)
% 0.14/0.37 % (7319)------------------------------
% 0.14/0.37 % (7319)------------------------------
% 0.14/0.38 % (7314)First to succeed.
% 0.14/0.38 % (7316)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 % (7320)Also succeeded, but the first one will report.
% 0.14/0.38 % (7322)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.14/0.38 % (7314)Refutation found. Thanks to Tanya!
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38 % SZS output start Proof for theBenchmark
% 0.14/0.38 thf(type_def_5, type, mu: $tType).
% 0.14/0.38 thf(func_def_0, type, mu: $tType).
% 0.14/0.38 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.14/0.38 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_15, type, mtrue: $i > $o).
% 0.14/0.38 thf(func_def_16, type, mfalse: $i > $o).
% 0.14/0.38 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.14/0.38 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.14/0.38 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.14/0.38 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.14/0.38 thf(func_def_33, type, rel_s4: $i > $i > $o).
% 0.14/0.38 thf(func_def_34, type, mbox_s4: ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_35, type, mdia_s4: ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_36, type, p: $i > $o).
% 0.14/0.38 thf(func_def_37, type, q: $i > $o).
% 0.14/0.38 thf(f229,plain,(
% 0.14/0.38 $false),
% 0.14/0.38 inference(avatar_sat_refutation,[],[f216,f222,f228])).
% 0.14/0.38 thf(f228,plain,(
% 0.14/0.38 ~spl0_1),
% 0.14/0.38 inference(avatar_contradiction_clause,[],[f227])).
% 0.14/0.38 thf(f227,plain,(
% 0.14/0.38 $false | ~spl0_1),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f224])).
% 0.14/0.38 thf(f224,plain,(
% 0.14/0.38 ($true = $false) | ~spl0_1),
% 0.14/0.38 inference(superposition,[],[f202,f210])).
% 0.14/0.38 thf(f210,plain,(
% 0.14/0.38 ($false = (p @ sK1)) | ~spl0_1),
% 0.14/0.38 inference(avatar_component_clause,[],[f208])).
% 0.14/0.38 thf(f208,plain,(
% 0.14/0.38 spl0_1 <=> ($false = (p @ sK1))),
% 0.14/0.38 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.14/0.38 thf(f202,plain,(
% 0.14/0.38 ($true = (p @ sK1))),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f199])).
% 0.14/0.38 thf(f199,plain,(
% 0.14/0.38 ($true = (p @ sK1)) | ($true = $false)),
% 0.14/0.38 inference(superposition,[],[f169,f194])).
% 0.14/0.38 thf(f194,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (($true = (rel_s4 @ X1 @ X1))) )),
% 0.14/0.38 inference(beta_eta_normalization,[],[f193])).
% 0.14/0.38 thf(f193,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (rel_s4 @ Y0 @ Y0)) @ X1))) )),
% 0.14/0.38 inference(pi_clausification,[],[f192])).
% 0.14/0.38 thf(f192,plain,(
% 0.14/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))))),
% 0.14/0.38 inference(beta_eta_normalization,[],[f154])).
% 0.14/0.38 thf(f154,plain,(
% 0.14/0.38 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ rel_s4))),
% 0.14/0.38 inference(definition_unfolding,[],[f108,f143])).
% 0.14/0.38 thf(f143,plain,(
% 0.14/0.38 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.14/0.38 inference(cnf_transformation,[],[f100])).
% 0.14/0.38 thf(f100,plain,(
% 0.14/0.38 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.14/0.38 inference(fool_elimination,[],[f99])).
% 0.14/0.38 thf(f99,plain,(
% 0.14/0.38 ((^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))) = mreflexive)),
% 0.14/0.38 inference(rectify,[],[f18])).
% 0.14/0.38 thf(f18,axiom,(
% 0.14/0.38 ((^[X6 : $i > $i > $o] : (! [X8] : (X6 @ X8 @ X8))) = mreflexive)),
% 0.14/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mreflexive)).
% 0.14/0.38 thf(f108,plain,(
% 0.14/0.38 ((mreflexive @ rel_s4) = $true)),
% 0.14/0.38 inference(cnf_transformation,[],[f98])).
% 0.14/0.38 thf(f98,plain,(
% 0.14/0.38 ((mreflexive @ rel_s4) = $true)),
% 0.14/0.38 inference(fool_elimination,[],[f97])).
% 0.14/0.38 thf(f97,plain,(
% 0.14/0.38 (mreflexive @ rel_s4)),
% 0.14/0.38 inference(rectify,[],[f34])).
% 0.14/0.38 thf(f34,axiom,(
% 0.14/0.38 (mreflexive @ rel_s4)),
% 0.14/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1)).
% 0.14/0.38 thf(f169,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (((rel_s4 @ sK1 @ X1) = $false) | ($true = (p @ X1))) )),
% 0.14/0.38 inference(not_proxy_clausification,[],[f168])).
% 0.14/0.38 thf(f168,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (($true = (~ (rel_s4 @ sK1 @ X1))) | ($true = (p @ X1))) )),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f167])).
% 0.14/0.38 thf(f167,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (($true = ((p @ X1) | (~ (rel_s4 @ sK1 @ X1))))) )),
% 0.14/0.38 inference(beta_eta_normalization,[],[f166])).
% 0.14/0.38 thf(f166,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((p @ Y0) | (~ (rel_s4 @ sK1 @ Y0)))) @ X1))) )),
% 0.14/0.38 inference(pi_clausification,[],[f165])).
% 0.14/0.38 thf(f165,plain,(
% 0.14/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s4 @ sK1 @ Y0))))))),
% 0.14/0.38 inference(not_proxy_clausification,[],[f164])).
% 0.14/0.38 thf(f164,plain,(
% 0.14/0.38 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s4 @ sK1 @ Y0)))))))),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f162])).
% 0.14/0.38 thf(f162,plain,(
% 0.14/0.38 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s4 @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (q @ Y0)) | (~ (rel_s4 @ sK1 @ Y0))))))))),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f160])).
% 0.14/0.38 thf(f160,plain,(
% 0.14/0.38 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s4 @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (q @ Y0)) | (~ (rel_s4 @ sK1 @ Y0))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s4 @ sK1 @ Y0))))))))),
% 0.14/0.38 inference(beta_eta_normalization,[],[f159])).
% 0.14/0.38 thf(f159,plain,(
% 0.14/0.38 (((^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (q @ Y1)) | (~ (rel_s4 @ Y0 @ Y1))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s4 @ Y0 @ Y1)))))))) @ sK1) = $false)),
% 0.14/0.38 inference(sigma_clausification,[],[f158])).
% 0.14/0.38 thf(f158,plain,(
% 0.14/0.38 ((!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (q @ Y1)) | (~ (rel_s4 @ Y0 @ Y1))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s4 @ Y0 @ Y1))))))))) != $true)),
% 0.14/0.38 inference(boolean_simplification,[],[f157])).
% 0.14/0.38 thf(f157,plain,(
% 0.14/0.38 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (q @ Y1)) | (~ (rel_s4 @ Y0 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s4 @ Y0 @ Y1))))))))))),
% 0.14/0.38 inference(beta_eta_normalization,[],[f156])).
% 0.14/0.38 thf(f156,plain,(
% 0.14/0.38 (((^[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 > $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]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))) @ p) @ q))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ q))) != $true)),
% 0.14/0.38 inference(definition_unfolding,[],[f138,f113,f145,f144,f134,f134,f129,f115,f153])).
% 0.14/0.38 thf(f153,plain,(
% 0.14/0.38 (mdia_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.14/0.38 inference(definition_unfolding,[],[f139,f115,f134,f115])).
% 0.14/0.38 thf(f139,plain,(
% 0.14/0.38 (mdia_s4 = (^[Y0 : $i > $o]: (mnot @ (mbox_s4 @ (mnot @ Y0)))))),
% 0.14/0.38 inference(cnf_transformation,[],[f44])).
% 0.14/0.38 thf(f44,plain,(
% 0.14/0.38 (mdia_s4 = (^[Y0 : $i > $o]: (mnot @ (mbox_s4 @ (mnot @ Y0)))))),
% 0.14/0.38 inference(fool_elimination,[],[f43])).
% 0.14/0.38 thf(f43,plain,(
% 0.14/0.38 ((^[X0 : $i > $o] : (mnot @ (mbox_s4 @ (mnot @ X0)))) = mdia_s4)),
% 0.14/0.38 inference(rectify,[],[f33])).
% 0.14/0.38 thf(f33,axiom,(
% 0.14/0.38 ((^[X3 : $i > $o] : (mnot @ (mbox_s4 @ (mnot @ X3)))) = mdia_s4)),
% 0.14/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_s4)).
% 0.14/0.38 thf(f115,plain,(
% 0.14/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f104])).
% 0.14/0.38 thf(f104,plain,(
% 0.14/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.38 inference(fool_elimination,[],[f103])).
% 0.14/0.38 thf(f103,plain,(
% 0.14/0.38 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.14/0.38 inference(rectify,[],[f3])).
% 0.14/0.38 thf(f3,axiom,(
% 0.14/0.38 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.14/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.14/0.38 thf(f129,plain,(
% 0.14/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f68])).
% 0.14/0.38 thf(f68,plain,(
% 0.14/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.14/0.38 inference(fool_elimination,[],[f67])).
% 0.14/0.38 thf(f67,plain,(
% 0.14/0.38 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 0.14/0.38 inference(rectify,[],[f4])).
% 0.14/0.38 thf(f4,axiom,(
% 0.14/0.38 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))) = mor)),
% 0.14/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.14/0.38 thf(f134,plain,(
% 0.14/0.38 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f54])).
% 0.14/0.38 thf(f54,plain,(
% 0.14/0.38 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))))),
% 0.14/0.38 inference(fool_elimination,[],[f53])).
% 0.14/0.38 thf(f53,plain,(
% 0.14/0.38 (mbox_s4 = (^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_s4 @ X1 @ X2) | (X0 @ X2)))))),
% 0.14/0.38 inference(rectify,[],[f32])).
% 0.14/0.38 thf(f32,axiom,(
% 0.14/0.38 (mbox_s4 = (^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_s4 @ X2 @ X7) | (X3 @ X7)))))),
% 0.14/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s4)).
% 0.14/0.38 thf(f144,plain,(
% 0.14/0.38 (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)))))))),
% 0.14/0.38 inference(definition_unfolding,[],[f117,f115,f129,f115,f115])).
% 0.14/0.38 thf(f117,plain,(
% 0.14/0.38 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f73])).
% 0.14/0.38 thf(f73,plain,(
% 0.14/0.38 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.14/0.38 inference(fool_elimination,[],[f72])).
% 0.14/0.38 thf(f72,plain,(
% 0.14/0.38 ((^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))) = mand)),
% 0.14/0.38 inference(rectify,[],[f5])).
% 0.14/0.38 thf(f5,axiom,(
% 0.14/0.38 ((^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))) = mand)),
% 0.14/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.14/0.38 thf(f145,plain,(
% 0.14/0.38 (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)))))),
% 0.14/0.38 inference(definition_unfolding,[],[f124,f129,f115])).
% 0.14/0.38 thf(f124,plain,(
% 0.14/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.38 inference(cnf_transformation,[],[f94])).
% 0.14/0.38 thf(f94,plain,(
% 0.14/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.38 inference(fool_elimination,[],[f93])).
% 0.14/0.38 thf(f93,plain,(
% 0.14/0.38 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.14/0.38 inference(rectify,[],[f6])).
% 0.14/0.38 thf(f6,axiom,(
% 0.14/0.38 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.14/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.14/0.38 thf(f113,plain,(
% 0.14/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.38 inference(cnf_transformation,[],[f46])).
% 0.14/0.38 thf(f46,plain,(
% 0.14/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.38 inference(fool_elimination,[],[f45])).
% 0.14/0.38 thf(f45,plain,(
% 0.14/0.38 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.14/0.38 inference(rectify,[],[f28])).
% 0.14/0.38 thf(f28,axiom,(
% 0.14/0.38 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.14/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.14/0.38 thf(f138,plain,(
% 0.14/0.38 ((mvalid @ (mimplies @ (mand @ (mbox_s4 @ p) @ (mbox_s4 @ (mor @ (mnot @ p) @ q))) @ (mdia_s4 @ q))) != $true)),
% 0.14/0.38 inference(cnf_transformation,[],[f107])).
% 0.14/0.38 thf(f107,plain,(
% 0.14/0.38 ((mvalid @ (mimplies @ (mand @ (mbox_s4 @ p) @ (mbox_s4 @ (mor @ (mnot @ p) @ q))) @ (mdia_s4 @ q))) != $true)),
% 0.14/0.38 inference(flattening,[],[f42])).
% 0.14/0.38 thf(f42,plain,(
% 0.14/0.38 ~((mvalid @ (mimplies @ (mand @ (mbox_s4 @ p) @ (mbox_s4 @ (mor @ (mnot @ p) @ q))) @ (mdia_s4 @ q))) = $true)),
% 0.14/0.38 inference(fool_elimination,[],[f41])).
% 0.14/0.38 thf(f41,plain,(
% 0.14/0.38 ~(mvalid @ (mimplies @ (mand @ (mbox_s4 @ p) @ (mbox_s4 @ (mor @ (mnot @ p) @ q))) @ (mdia_s4 @ q)))),
% 0.14/0.38 inference(rectify,[],[f37])).
% 0.14/0.38 thf(f37,negated_conjecture,(
% 0.14/0.38 ~(mvalid @ (mimplies @ (mand @ (mbox_s4 @ p) @ (mbox_s4 @ (mor @ (mnot @ p) @ q))) @ (mdia_s4 @ q)))),
% 0.14/0.38 inference(negated_conjecture,[],[f36])).
% 0.14/0.38 thf(f36,conjecture,(
% 0.14/0.38 (mvalid @ (mimplies @ (mand @ (mbox_s4 @ p) @ (mbox_s4 @ (mor @ (mnot @ p) @ q))) @ (mdia_s4 @ q)))),
% 0.14/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.14/0.38 thf(f222,plain,(
% 0.14/0.38 ~spl0_2),
% 0.14/0.38 inference(avatar_contradiction_clause,[],[f221])).
% 0.14/0.38 thf(f221,plain,(
% 0.14/0.38 $false | ~spl0_2),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f217])).
% 0.14/0.38 thf(f217,plain,(
% 0.14/0.38 ($true = $false) | ~spl0_2),
% 0.14/0.38 inference(superposition,[],[f214,f198])).
% 0.14/0.38 thf(f198,plain,(
% 0.14/0.38 ($false = (q @ sK1))),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f195])).
% 0.14/0.38 thf(f195,plain,(
% 0.14/0.38 ($true = $false) | ($false = (q @ sK1))),
% 0.14/0.38 inference(superposition,[],[f182,f194])).
% 0.14/0.38 thf(f182,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (((rel_s4 @ sK1 @ X1) = $false) | ((q @ X1) = $false)) )),
% 0.14/0.38 inference(not_proxy_clausification,[],[f181])).
% 0.14/0.38 thf(f181,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (((q @ X1) = $false) | ($true = (~ (rel_s4 @ sK1 @ X1)))) )),
% 0.14/0.38 inference(not_proxy_clausification,[],[f180])).
% 0.14/0.38 thf(f180,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (($true = (~ (q @ X1))) | ($true = (~ (rel_s4 @ sK1 @ X1)))) )),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f179])).
% 0.14/0.38 thf(f179,plain,(
% 0.14/0.38 ( ! [X1 : $i] : ((((~ (q @ X1)) | (~ (rel_s4 @ sK1 @ X1))) = $true)) )),
% 0.14/0.38 inference(beta_eta_normalization,[],[f178])).
% 0.14/0.38 thf(f178,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s4 @ sK1 @ Y0)))) @ X1))) )),
% 0.14/0.38 inference(pi_clausification,[],[f177])).
% 0.14/0.38 thf(f177,plain,(
% 0.14/0.38 ((!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s4 @ sK1 @ Y0))))) = $true)),
% 0.14/0.38 inference(not_proxy_clausification,[],[f161])).
% 0.14/0.38 thf(f161,plain,(
% 0.14/0.38 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s4 @ sK1 @ Y0)))))))),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f160])).
% 0.14/0.38 thf(f214,plain,(
% 0.14/0.38 ($true = (q @ sK1)) | ~spl0_2),
% 0.14/0.38 inference(avatar_component_clause,[],[f212])).
% 0.14/0.38 thf(f212,plain,(
% 0.14/0.38 spl0_2 <=> ($true = (q @ sK1))),
% 0.14/0.38 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.14/0.38 thf(f216,plain,(
% 0.14/0.38 spl0_2 | spl0_1),
% 0.14/0.38 inference(avatar_split_clause,[],[f205,f208,f212])).
% 0.14/0.38 thf(f205,plain,(
% 0.14/0.38 ($true = (q @ sK1)) | ($false = (p @ sK1))),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f204])).
% 0.14/0.38 thf(f204,plain,(
% 0.14/0.38 ($true = (q @ sK1)) | ($true = $false) | ($false = (p @ sK1))),
% 0.14/0.38 inference(superposition,[],[f194,f176])).
% 0.14/0.38 thf(f176,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (((rel_s4 @ sK1 @ X1) = $false) | ($false = (p @ X1)) | ((q @ X1) = $true)) )),
% 0.14/0.38 inference(not_proxy_clausification,[],[f175])).
% 0.14/0.38 thf(f175,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (((rel_s4 @ sK1 @ X1) = $false) | ((q @ X1) = $true) | ($true = (~ (p @ X1)))) )),
% 0.14/0.38 inference(not_proxy_clausification,[],[f174])).
% 0.14/0.38 thf(f174,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (($true = (~ (rel_s4 @ sK1 @ X1))) | ((q @ X1) = $true) | ($true = (~ (p @ X1)))) )),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f173])).
% 0.14/0.38 thf(f173,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (($true = ((~ (p @ X1)) | (q @ X1))) | ($true = (~ (rel_s4 @ sK1 @ X1)))) )),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f172])).
% 0.14/0.38 thf(f172,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (($true = (((~ (p @ X1)) | (q @ X1)) | (~ (rel_s4 @ sK1 @ X1))))) )),
% 0.14/0.38 inference(beta_eta_normalization,[],[f171])).
% 0.14/0.38 thf(f171,plain,(
% 0.14/0.38 ( ! [X1 : $i] : ((((^[Y0 : $i]: (((~ (p @ Y0)) | (q @ Y0)) | (~ (rel_s4 @ sK1 @ Y0)))) @ X1) = $true)) )),
% 0.14/0.38 inference(pi_clausification,[],[f170])).
% 0.14/0.38 thf(f170,plain,(
% 0.14/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (q @ Y0)) | (~ (rel_s4 @ sK1 @ Y0))))))),
% 0.14/0.38 inference(not_proxy_clausification,[],[f163])).
% 0.14/0.38 thf(f163,plain,(
% 0.14/0.38 ($false = (~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (q @ Y0)) | (~ (rel_s4 @ sK1 @ Y0)))))))),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f162])).
% 0.14/0.38 % SZS output end Proof for theBenchmark
% 0.14/0.38 % (7314)------------------------------
% 0.14/0.38 % (7314)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (7314)Termination reason: Refutation
% 0.14/0.38
% 0.14/0.38 % (7314)Memory used [KB]: 5628
% 0.14/0.38 % (7314)Time elapsed: 0.013 s
% 0.14/0.38 % (7314)Instructions burned: 14 (million)
% 0.14/0.38 % (7314)------------------------------
% 0.14/0.38 % (7314)------------------------------
% 0.14/0.38 % (7313)Success in time 0.026 s
% 0.14/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------