TSTP Solution File: SYO460^3 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO460^3 : 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 : n004.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 09:04:49 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 : SYO460^3 : 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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon May 20 10:54:23 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.34 This is a TH0_THM_EQU_NAR problem
% 0.14/0.34 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
% 0.14/0.36 % (14790)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)
% 0.14/0.36 % (14791)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.36 % (14792)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)
% 0.14/0.36 % (14785)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.36 % (14792)Instruction limit reached!
% 0.14/0.36 % (14792)------------------------------
% 0.14/0.36 % (14792)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.36 % (14792)Termination reason: Unknown
% 0.14/0.36 % (14792)Termination phase: shuffling
% 0.14/0.36
% 0.14/0.36 % (14792)Memory used [KB]: 1023
% 0.14/0.36 % (14792)Time elapsed: 0.003 s
% 0.14/0.36 % (14792)Instructions burned: 3 (million)
% 0.14/0.36 % (14792)------------------------------
% 0.14/0.36 % (14792)------------------------------
% 0.14/0.37 % (14787)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)
% 0.14/0.37 % (14790)Refutation not found, incomplete strategy
% 0.14/0.37 % (14790)------------------------------
% 0.14/0.37 % (14790)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (14790)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.37
% 0.14/0.37
% 0.14/0.37 % (14790)Memory used [KB]: 5628
% 0.14/0.37 % (14790)Time elapsed: 0.006 s
% 0.14/0.37 % (14790)Instructions burned: 8 (million)
% 0.14/0.37 % (14790)------------------------------
% 0.14/0.37 % (14790)------------------------------
% 0.14/0.37 % (14786)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 % (14791)First to succeed.
% 0.14/0.37 % (14786)Instruction limit reached!
% 0.14/0.37 % (14786)------------------------------
% 0.14/0.37 % (14786)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (14786)Termination reason: Unknown
% 0.14/0.37 % (14786)Termination phase: Property scanning
% 0.14/0.37
% 0.14/0.37 % (14786)Memory used [KB]: 1023
% 0.14/0.37 % (14786)Time elapsed: 0.004 s
% 0.14/0.37 % (14786)Instructions burned: 5 (million)
% 0.14/0.37 % (14786)------------------------------
% 0.14/0.37 % (14786)------------------------------
% 0.14/0.37 % (14785)Also succeeded, but the first one will report.
% 0.14/0.38 % (14791)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_m: $i > $i > $o).
% 0.14/0.38 thf(func_def_34, type, mbox_m: ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_35, type, mdia_m: ($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(func_def_38, type, r: $i > $o).
% 0.14/0.38 thf(f277,plain,(
% 0.14/0.38 $false),
% 0.14/0.38 inference(avatar_sat_refutation,[],[f215,f225,f249,f251,f266,f269,f276])).
% 0.14/0.38 thf(f276,plain,(
% 0.14/0.38 ~spl0_1 | ~spl0_4),
% 0.14/0.38 inference(avatar_contradiction_clause,[],[f275])).
% 0.14/0.38 thf(f275,plain,(
% 0.14/0.38 $false | (~spl0_1 | ~spl0_4)),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f274])).
% 0.14/0.38 thf(f274,plain,(
% 0.14/0.38 ($true = $false) | (~spl0_1 | ~spl0_4)),
% 0.14/0.38 inference(backward_demodulation,[],[f224,f273])).
% 0.14/0.38 thf(f273,plain,(
% 0.14/0.38 ((p @ sK4) = $false) | ~spl0_1),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f270])).
% 0.14/0.38 thf(f270,plain,(
% 0.14/0.38 ($true = $false) | ((p @ sK4) = $false) | ~spl0_1),
% 0.14/0.38 inference(superposition,[],[f210,f203])).
% 0.14/0.38 thf(f203,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (((rel_m @ sK1 @ X1) = $false) | ((p @ X1) = $false)) )),
% 0.14/0.38 inference(not_proxy_clausification,[],[f202])).
% 0.14/0.38 thf(f202,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (($true = (~ (p @ X1))) | ((rel_m @ sK1 @ X1) = $false)) )),
% 0.14/0.38 inference(not_proxy_clausification,[],[f201])).
% 0.14/0.38 thf(f201,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (((~ (rel_m @ sK1 @ X1)) = $true) | ($true = (~ (p @ X1)))) )),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f200])).
% 0.14/0.38 thf(f200,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (($true = ((~ (p @ X1)) | (~ (rel_m @ sK1 @ X1))))) )),
% 0.14/0.38 inference(beta_eta_normalization,[],[f199])).
% 0.14/0.38 thf(f199,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_m @ sK1 @ Y0)))) @ X1))) )),
% 0.14/0.38 inference(pi_clausification,[],[f198])).
% 0.14/0.38 thf(f198,plain,(
% 0.14/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_m @ sK1 @ Y0))))))),
% 0.14/0.38 inference(not_proxy_clausification,[],[f157])).
% 0.14/0.38 thf(f157,plain,(
% 0.14/0.38 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_m @ sK1 @ Y0)))))))),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f156])).
% 0.14/0.38 thf(f156,plain,(
% 0.14/0.38 (((~ ((~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (q @ Y0))) | (~ (rel_m @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (r @ Y0))) | (~ (rel_m @ sK1 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_m @ sK1 @ Y0))))))) = $false)),
% 0.14/0.38 inference(beta_eta_normalization,[],[f155])).
% 0.14/0.38 thf(f155,plain,(
% 0.14/0.38 (((^[Y0 : $i]: ((~ ((~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (~ (q @ Y1))) | (~ (rel_m @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (~ (r @ Y1))) | (~ (rel_m @ Y0 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_m @ Y0 @ Y1)))))))) @ sK1) = $false)),
% 0.14/0.38 inference(sigma_clausification,[],[f154])).
% 0.14/0.38 thf(f154,plain,(
% 0.14/0.38 ((!! @ $i @ (^[Y0 : $i]: ((~ ((~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (~ (q @ Y1))) | (~ (rel_m @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (~ (r @ Y1))) | (~ (rel_m @ Y0 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_m @ Y0 @ Y1))))))))) != $true)),
% 0.14/0.38 inference(boolean_simplification,[],[f153])).
% 0.14/0.38 thf(f153,plain,(
% 0.14/0.38 ((!! @ $i @ (^[Y0 : $i]: ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (~ ((~ (p @ Y1)) | (~ (q @ Y1))))) | (~ (rel_m @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (~ (r @ Y1))) | (~ (rel_m @ Y0 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_m @ Y0 @ Y1))))))))) != $true)),
% 0.14/0.38 inference(boolean_simplification,[],[f152])).
% 0.14/0.38 thf(f152,plain,(
% 0.14/0.38 ((!! @ $i @ (^[Y0 : $i]: ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (~ ((~ (p @ Y1)) | (~ (q @ Y1))))) | (~ (rel_m @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (~ ((~ (p @ Y1)) | (~ (r @ Y1))))) | (~ (rel_m @ Y0 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_m @ Y0 @ Y1))))))))) != $true)),
% 0.14/0.38 inference(beta_eta_normalization,[],[f150])).
% 0.14/0.38 thf(f150,plain,(
% 0.14/0.38 ($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]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_m @ 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]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_m @ 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 @ r))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_m @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ p))))),
% 0.14/0.38 inference(definition_unfolding,[],[f107,f113,f141,f111,f149,f140,f149,f140,f149])).
% 0.14/0.38 thf(f140,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,[],[f131,f106,f111,f106,f106])).
% 0.14/0.38 thf(f106,plain,(
% 0.14/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f85])).
% 0.14/0.38 thf(f85,plain,(
% 0.14/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.38 inference(fool_elimination,[],[f84])).
% 0.14/0.38 thf(f84,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/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.14/0.38 thf(f131,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,[],[f42])).
% 0.14/0.38 thf(f42,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,[],[f41])).
% 0.14/0.38 thf(f41,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/sandbox2/benchmark/theBenchmark.p',mand)).
% 0.14/0.38 thf(f149,plain,(
% 0.14/0.38 (mdia_m = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_m @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.14/0.38 inference(definition_unfolding,[],[f121,f106,f130,f106])).
% 0.14/0.38 thf(f130,plain,(
% 0.14/0.38 (mbox_m = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_m @ Y1 @ Y2)))))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f50])).
% 0.14/0.38 thf(f50,plain,(
% 0.14/0.38 (mbox_m = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_m @ Y1 @ Y2)))))))))),
% 0.14/0.38 inference(fool_elimination,[],[f49])).
% 0.14/0.38 thf(f49,plain,(
% 0.14/0.38 (mbox_m = (^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_m @ X1 @ X2) | (X0 @ X2)))))),
% 0.14/0.38 inference(rectify,[],[f32])).
% 0.14/0.38 thf(f32,axiom,(
% 0.14/0.38 (mbox_m = (^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_m @ X2 @ X7) | (X3 @ X7)))))),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_m)).
% 0.14/0.38 thf(f121,plain,(
% 0.14/0.38 (mdia_m = (^[Y0 : $i > $o]: (mnot @ (mbox_m @ (mnot @ Y0)))))),
% 0.14/0.38 inference(cnf_transformation,[],[f80])).
% 0.14/0.38 thf(f80,plain,(
% 0.14/0.38 (mdia_m = (^[Y0 : $i > $o]: (mnot @ (mbox_m @ (mnot @ Y0)))))),
% 0.14/0.38 inference(fool_elimination,[],[f79])).
% 0.14/0.38 thf(f79,plain,(
% 0.14/0.38 ((^[X0 : $i > $o] : (mnot @ (mbox_m @ (mnot @ X0)))) = mdia_m)),
% 0.14/0.38 inference(rectify,[],[f33])).
% 0.14/0.38 thf(f33,axiom,(
% 0.14/0.38 ((^[X3 : $i > $o] : (mnot @ (mbox_m @ (mnot @ X3)))) = mdia_m)),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_m)).
% 0.14/0.38 thf(f111,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,[],[f89])).
% 0.14/0.38 thf(f89,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,[],[f88])).
% 0.14/0.38 thf(f88,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/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.14/0.38 thf(f141,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,[],[f109,f111,f106])).
% 0.14/0.38 thf(f109,plain,(
% 0.14/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.38 inference(cnf_transformation,[],[f66])).
% 0.14/0.38 thf(f66,plain,(
% 0.14/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.38 inference(fool_elimination,[],[f65])).
% 0.14/0.38 thf(f65,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/sandbox2/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,[],[f91])).
% 0.14/0.38 thf(f91,plain,(
% 0.14/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.38 inference(fool_elimination,[],[f90])).
% 0.14/0.38 thf(f90,plain,(
% 0.14/0.38 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.14/0.38 inference(rectify,[],[f28])).
% 0.14/0.38 thf(f28,axiom,(
% 0.14/0.38 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.14/0.38 thf(f107,plain,(
% 0.14/0.38 ((mvalid @ (mimplies @ (mor @ (mdia_m @ (mand @ p @ q)) @ (mdia_m @ (mand @ p @ r))) @ (mdia_m @ p))) != $true)),
% 0.14/0.38 inference(cnf_transformation,[],[f104])).
% 0.14/0.38 thf(f104,plain,(
% 0.14/0.38 ((mvalid @ (mimplies @ (mor @ (mdia_m @ (mand @ p @ q)) @ (mdia_m @ (mand @ p @ r))) @ (mdia_m @ p))) != $true)),
% 0.14/0.38 inference(flattening,[],[f93])).
% 0.14/0.38 thf(f93,plain,(
% 0.14/0.38 ~((mvalid @ (mimplies @ (mor @ (mdia_m @ (mand @ p @ q)) @ (mdia_m @ (mand @ p @ r))) @ (mdia_m @ p))) = $true)),
% 0.14/0.38 inference(fool_elimination,[],[f92])).
% 0.14/0.38 thf(f92,plain,(
% 0.14/0.38 ~(mvalid @ (mimplies @ (mor @ (mdia_m @ (mand @ p @ q)) @ (mdia_m @ (mand @ p @ r))) @ (mdia_m @ p)))),
% 0.14/0.38 inference(rectify,[],[f36])).
% 0.14/0.38 thf(f36,negated_conjecture,(
% 0.14/0.38 ~(mvalid @ (mimplies @ (mor @ (mdia_m @ (mand @ p @ q)) @ (mdia_m @ (mand @ p @ r))) @ (mdia_m @ p)))),
% 0.14/0.38 inference(negated_conjecture,[],[f35])).
% 0.14/0.38 thf(f35,conjecture,(
% 0.14/0.38 (mvalid @ (mimplies @ (mor @ (mdia_m @ (mand @ p @ q)) @ (mdia_m @ (mand @ p @ r))) @ (mdia_m @ p)))),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.14/0.38 thf(f210,plain,(
% 0.14/0.38 ((rel_m @ sK1 @ sK4) = $true) | ~spl0_1),
% 0.14/0.38 inference(avatar_component_clause,[],[f208])).
% 0.14/0.38 thf(f208,plain,(
% 0.14/0.38 spl0_1 <=> ((rel_m @ sK1 @ sK4) = $true)),
% 0.14/0.38 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.14/0.38 thf(f224,plain,(
% 0.14/0.38 ((p @ sK4) = $true) | ~spl0_4),
% 0.14/0.38 inference(avatar_component_clause,[],[f222])).
% 0.14/0.38 thf(f222,plain,(
% 0.14/0.38 spl0_4 <=> ((p @ sK4) = $true)),
% 0.14/0.38 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.14/0.38 thf(f269,plain,(
% 0.14/0.38 ~spl0_2 | ~spl0_9),
% 0.14/0.38 inference(avatar_contradiction_clause,[],[f268])).
% 0.14/0.38 thf(f268,plain,(
% 0.14/0.38 $false | (~spl0_2 | ~spl0_9)),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f267])).
% 0.14/0.38 thf(f267,plain,(
% 0.14/0.38 ($true = $false) | (~spl0_2 | ~spl0_9)),
% 0.14/0.38 inference(forward_demodulation,[],[f248,f261])).
% 0.14/0.38 thf(f261,plain,(
% 0.14/0.38 ((p @ sK2) = $false) | ~spl0_2),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f256])).
% 0.14/0.38 thf(f256,plain,(
% 0.14/0.38 ((p @ sK2) = $false) | ($true = $false) | ~spl0_2),
% 0.14/0.38 inference(superposition,[],[f214,f203])).
% 0.14/0.38 thf(f214,plain,(
% 0.14/0.38 ((rel_m @ sK1 @ sK2) = $true) | ~spl0_2),
% 0.14/0.38 inference(avatar_component_clause,[],[f212])).
% 0.14/0.38 thf(f212,plain,(
% 0.14/0.38 spl0_2 <=> ((rel_m @ sK1 @ sK2) = $true)),
% 0.14/0.38 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.14/0.38 thf(f248,plain,(
% 0.14/0.38 ((p @ sK2) = $true) | ~spl0_9),
% 0.14/0.38 inference(avatar_component_clause,[],[f246])).
% 0.14/0.38 thf(f246,plain,(
% 0.14/0.38 spl0_9 <=> ((p @ sK2) = $true)),
% 0.14/0.38 introduced(avatar_definition,[new_symbols(naming,[spl0_9])])).
% 0.14/0.38 thf(f266,plain,(
% 0.14/0.38 ~spl0_5 | ~spl0_8),
% 0.14/0.38 inference(avatar_contradiction_clause,[],[f265])).
% 0.14/0.38 thf(f265,plain,(
% 0.14/0.38 $false | (~spl0_5 | ~spl0_8)),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f264])).
% 0.14/0.38 thf(f264,plain,(
% 0.14/0.38 ($true = $false) | (~spl0_5 | ~spl0_8)),
% 0.14/0.38 inference(backward_demodulation,[],[f243,f262])).
% 0.14/0.38 thf(f262,plain,(
% 0.14/0.38 ($false = (p @ sK3)) | ~spl0_5),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f257])).
% 0.14/0.38 thf(f257,plain,(
% 0.14/0.38 ($false = (p @ sK3)) | ($true = $false) | ~spl0_5),
% 0.14/0.38 inference(superposition,[],[f229,f203])).
% 0.14/0.38 thf(f229,plain,(
% 0.14/0.38 ($true = (rel_m @ sK1 @ sK3)) | ~spl0_5),
% 0.14/0.38 inference(avatar_component_clause,[],[f227])).
% 0.14/0.38 thf(f227,plain,(
% 0.14/0.38 spl0_5 <=> ($true = (rel_m @ sK1 @ sK3))),
% 0.14/0.38 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])).
% 0.14/0.38 thf(f243,plain,(
% 0.14/0.38 ($true = (p @ sK3)) | ~spl0_8),
% 0.14/0.38 inference(avatar_component_clause,[],[f241])).
% 0.14/0.38 thf(f241,plain,(
% 0.14/0.38 spl0_8 <=> ($true = (p @ sK3))),
% 0.14/0.38 introduced(avatar_definition,[new_symbols(naming,[spl0_8])])).
% 0.14/0.38 thf(f251,plain,(
% 0.14/0.38 spl0_8 | spl0_9),
% 0.14/0.38 inference(avatar_split_clause,[],[f176,f246,f241])).
% 0.14/0.38 thf(f176,plain,(
% 0.14/0.38 ((p @ sK2) = $true) | ($true = (p @ sK3))),
% 0.14/0.38 inference(not_proxy_clausification,[],[f175])).
% 0.14/0.38 thf(f175,plain,(
% 0.14/0.38 ((p @ sK2) = $true) | ((~ (p @ sK3)) = $false)),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f173])).
% 0.14/0.38 thf(f173,plain,(
% 0.14/0.38 (((~ (p @ sK3)) | (~ (q @ sK3))) = $false) | ((p @ sK2) = $true)),
% 0.14/0.38 inference(not_proxy_clausification,[],[f172])).
% 0.14/0.38 thf(f172,plain,(
% 0.14/0.38 ($false = (~ (p @ sK2))) | (((~ (p @ sK3)) | (~ (q @ sK3))) = $false)),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f170])).
% 0.14/0.38 thf(f170,plain,(
% 0.14/0.38 ($false = (((~ (p @ sK3)) | (~ (q @ sK3))) | (~ (rel_m @ sK1 @ sK3)))) | ($false = (~ (p @ sK2)))),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f168])).
% 0.14/0.38 thf(f168,plain,(
% 0.14/0.38 (((~ (p @ sK2)) | (~ (r @ sK2))) = $false) | ($false = (((~ (p @ sK3)) | (~ (q @ sK3))) | (~ (rel_m @ sK1 @ sK3))))),
% 0.14/0.38 inference(beta_eta_normalization,[],[f167])).
% 0.14/0.38 thf(f167,plain,(
% 0.14/0.38 (((^[Y0 : $i]: (((~ (p @ Y0)) | (~ (q @ Y0))) | (~ (rel_m @ sK1 @ Y0)))) @ sK3) = $false) | (((~ (p @ sK2)) | (~ (r @ sK2))) = $false)),
% 0.14/0.38 inference(sigma_clausification,[],[f166])).
% 0.14/0.38 thf(f166,plain,(
% 0.14/0.38 ($false = (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (q @ Y0))) | (~ (rel_m @ sK1 @ Y0)))))) | (((~ (p @ sK2)) | (~ (r @ sK2))) = $false)),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f164])).
% 0.14/0.38 thf(f164,plain,(
% 0.14/0.38 ((((~ (p @ sK2)) | (~ (r @ sK2))) | (~ (rel_m @ sK1 @ sK2))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (q @ Y0))) | (~ (rel_m @ sK1 @ Y0))))))),
% 0.14/0.38 inference(beta_eta_normalization,[],[f163])).
% 0.14/0.38 thf(f163,plain,(
% 0.14/0.38 ($false = (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (q @ Y0))) | (~ (rel_m @ sK1 @ Y0)))))) | (((^[Y0 : $i]: (((~ (p @ Y0)) | (~ (r @ Y0))) | (~ (rel_m @ sK1 @ Y0)))) @ sK2) = $false)),
% 0.14/0.38 inference(sigma_clausification,[],[f162])).
% 0.14/0.38 thf(f162,plain,(
% 0.14/0.38 ((!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (r @ Y0))) | (~ (rel_m @ sK1 @ Y0))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (q @ Y0))) | (~ (rel_m @ sK1 @ Y0))))))),
% 0.14/0.38 inference(not_proxy_clausification,[],[f161])).
% 0.14/0.38 thf(f161,plain,(
% 0.14/0.38 ((~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (q @ Y0))) | (~ (rel_m @ sK1 @ Y0)))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (r @ Y0))) | (~ (rel_m @ sK1 @ Y0))))) = $false)),
% 0.14/0.38 inference(not_proxy_clausification,[],[f160])).
% 0.14/0.38 thf(f160,plain,(
% 0.14/0.38 ((~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (r @ Y0))) | (~ (rel_m @ sK1 @ Y0)))))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (q @ Y0))) | (~ (rel_m @ sK1 @ Y0)))))) = $true)),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f159])).
% 0.14/0.38 thf(f159,plain,(
% 0.14/0.38 ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (q @ Y0))) | (~ (rel_m @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (r @ Y0))) | (~ (rel_m @ sK1 @ Y0))))))))),
% 0.14/0.38 inference(not_proxy_clausification,[],[f158])).
% 0.14/0.38 thf(f158,plain,(
% 0.14/0.38 ((~ ((~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (q @ Y0))) | (~ (rel_m @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (r @ Y0))) | (~ (rel_m @ sK1 @ Y0)))))))) = $false)),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f156])).
% 0.14/0.38 thf(f249,plain,(
% 0.14/0.38 spl0_9 | spl0_5),
% 0.14/0.38 inference(avatar_split_clause,[],[f179,f227,f246])).
% 0.14/0.38 thf(f179,plain,(
% 0.14/0.38 ((p @ sK2) = $true) | ($true = (rel_m @ sK1 @ sK3))),
% 0.14/0.38 inference(not_proxy_clausification,[],[f178])).
% 0.14/0.38 thf(f178,plain,(
% 0.14/0.38 ($false = (~ (p @ sK2))) | ($true = (rel_m @ sK1 @ sK3))),
% 0.14/0.38 inference(not_proxy_clausification,[],[f171])).
% 0.14/0.38 thf(f171,plain,(
% 0.14/0.38 ($false = (~ (rel_m @ sK1 @ sK3))) | ($false = (~ (p @ sK2)))),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f170])).
% 0.14/0.38 thf(f225,plain,(
% 0.14/0.38 spl0_4 | spl0_2),
% 0.14/0.38 inference(avatar_split_clause,[],[f195,f212,f222])).
% 0.14/0.38 thf(f195,plain,(
% 0.14/0.38 ((rel_m @ sK1 @ sK2) = $true) | ((p @ sK4) = $true)),
% 0.14/0.38 inference(not_proxy_clausification,[],[f194])).
% 0.14/0.38 thf(f194,plain,(
% 0.14/0.38 ((rel_m @ sK1 @ sK2) = $true) | ((~ (p @ sK4)) = $false)),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f192])).
% 0.14/0.38 thf(f192,plain,(
% 0.14/0.38 ((rel_m @ sK1 @ sK2) = $true) | (((~ (p @ sK4)) | (~ (q @ sK4))) = $false)),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f190])).
% 0.14/0.38 thf(f190,plain,(
% 0.14/0.38 ((rel_m @ sK1 @ sK2) = $true) | ($false = (((~ (p @ sK4)) | (~ (q @ sK4))) | (~ (rel_m @ sK1 @ sK4))))),
% 0.14/0.38 inference(not_proxy_clausification,[],[f189])).
% 0.14/0.38 thf(f189,plain,(
% 0.14/0.38 ((~ (rel_m @ sK1 @ sK2)) = $false) | ($false = (((~ (p @ sK4)) | (~ (q @ sK4))) | (~ (rel_m @ sK1 @ sK4))))),
% 0.14/0.38 inference(beta_eta_normalization,[],[f188])).
% 0.14/0.38 thf(f188,plain,(
% 0.14/0.38 ((~ (rel_m @ sK1 @ sK2)) = $false) | (((^[Y0 : $i]: (((~ (p @ Y0)) | (~ (q @ Y0))) | (~ (rel_m @ sK1 @ Y0)))) @ sK4) = $false)),
% 0.14/0.38 inference(sigma_clausification,[],[f165])).
% 0.14/0.38 thf(f165,plain,(
% 0.14/0.38 ($false = (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (q @ Y0))) | (~ (rel_m @ sK1 @ Y0)))))) | ((~ (rel_m @ sK1 @ sK2)) = $false)),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f164])).
% 0.14/0.38 thf(f215,plain,(
% 0.14/0.38 spl0_1 | spl0_2),
% 0.14/0.38 inference(avatar_split_clause,[],[f197,f212,f208])).
% 0.14/0.38 thf(f197,plain,(
% 0.14/0.38 ((rel_m @ sK1 @ sK2) = $true) | ((rel_m @ sK1 @ sK4) = $true)),
% 0.14/0.38 inference(not_proxy_clausification,[],[f191])).
% 0.14/0.38 thf(f191,plain,(
% 0.14/0.38 ((~ (rel_m @ sK1 @ sK4)) = $false) | ((rel_m @ sK1 @ sK2) = $true)),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f190])).
% 0.14/0.38 % SZS output end Proof for theBenchmark
% 0.14/0.38 % (14791)------------------------------
% 0.14/0.38 % (14791)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (14791)Termination reason: Refutation
% 0.14/0.38
% 0.14/0.38 % (14791)Memory used [KB]: 5756
% 0.14/0.38 % (14791)Time elapsed: 0.013 s
% 0.14/0.38 % (14791)Instructions burned: 17 (million)
% 0.14/0.38 % (14791)------------------------------
% 0.14/0.38 % (14791)------------------------------
% 0.14/0.38 % (14784)Success in time 0.026 s
% 0.14/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------