TSTP Solution File: SYO396^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO396^1 : 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 : n006.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 09:04:17 EDT 2024
% Result : Theorem 0.13s 0.38s
% Output : Refutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO396^1 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.14 % 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
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon May 20 09:39:38 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 This is a TH0_THM_EQU_NAR problem
% 0.13/0.35 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/sandbox2/benchmark/theBenchmark.p
% 0.13/0.37 % (23184)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.37 % (23178)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.37 % (23179)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)
% 0.13/0.37 % (23180)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)
% 0.13/0.37 % (23185)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)
% 0.13/0.37 % (23179)Instruction limit reached!
% 0.13/0.37 % (23179)------------------------------
% 0.13/0.37 % (23179)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (23179)Termination reason: Unknown
% 0.13/0.37 % (23179)Termination phase: Property scanning
% 0.13/0.37
% 0.13/0.37 % (23179)Memory used [KB]: 1023
% 0.13/0.37 % (23179)Time elapsed: 0.004 s
% 0.13/0.37 % (23179)Instructions burned: 4 (million)
% 0.13/0.37 % (23179)------------------------------
% 0.13/0.37 % (23179)------------------------------
% 0.13/0.37 % (23185)Instruction limit reached!
% 0.13/0.37 % (23185)------------------------------
% 0.13/0.37 % (23185)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (23185)Termination reason: Unknown
% 0.13/0.37 % (23185)Termination phase: shuffling
% 0.13/0.37
% 0.13/0.37 % (23185)Memory used [KB]: 1023
% 0.13/0.37 % (23185)Time elapsed: 0.003 s
% 0.13/0.37 % (23182)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)
% 0.13/0.37 % (23185)Instructions burned: 3 (million)
% 0.13/0.37 % (23185)------------------------------
% 0.13/0.37 % (23185)------------------------------
% 0.13/0.37 % (23182)Instruction limit reached!
% 0.13/0.37 % (23182)------------------------------
% 0.13/0.37 % (23182)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (23182)Termination reason: Unknown
% 0.13/0.37 % (23182)Termination phase: shuffling
% 0.13/0.37
% 0.13/0.37 % (23182)Memory used [KB]: 1023
% 0.13/0.37 % (23182)Time elapsed: 0.003 s
% 0.13/0.37 % (23182)Instructions burned: 3 (million)
% 0.13/0.37 % (23182)------------------------------
% 0.13/0.37 % (23182)------------------------------
% 0.13/0.37 % (23184)First to succeed.
% 0.13/0.38 % (23181)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.38 % (23181)Instruction limit reached!
% 0.13/0.38 % (23181)------------------------------
% 0.13/0.38 % (23181)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (23181)Termination reason: Unknown
% 0.13/0.38 % (23181)Termination phase: shuffling
% 0.13/0.38
% 0.13/0.38 % (23181)Memory used [KB]: 1023
% 0.13/0.38 % (23181)Time elapsed: 0.002 s
% 0.13/0.38 % (23181)Instructions burned: 2 (million)
% 0.13/0.38 % (23181)------------------------------
% 0.13/0.38 % (23181)------------------------------
% 0.13/0.38 % (23180)Also succeeded, but the first one will report.
% 0.13/0.38 % (23184)Refutation found. Thanks to Tanya!
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38 % SZS output start Proof for theBenchmark
% 0.13/0.38 thf(type_def_5, type, mu: $tType).
% 0.13/0.38 thf(func_def_0, type, mu: $tType).
% 0.13/0.38 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.13/0.38 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_15, type, mtrue: $i > $o).
% 0.13/0.38 thf(func_def_16, type, mfalse: $i > $o).
% 0.13/0.38 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.13/0.38 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.13/0.38 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.13/0.38 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.13/0.38 thf(func_def_33, type, rel_k: $i > $i > $o).
% 0.13/0.38 thf(func_def_34, type, mbox_k: ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_35, type, mdia_k: ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_36, type, p: $i > $o).
% 0.13/0.38 thf(f157,plain,(
% 0.13/0.38 $false),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f156])).
% 0.13/0.38 thf(f156,plain,(
% 0.13/0.38 ($false = $true)),
% 0.13/0.38 inference(beta_eta_normalization,[],[f155])).
% 0.13/0.38 thf(f155,plain,(
% 0.13/0.38 ($false = ((^[Y0 : $i]: ($true)) @ sK1))),
% 0.13/0.38 inference(sigma_clausification,[],[f154])).
% 0.13/0.38 thf(f154,plain,(
% 0.13/0.38 ((!! @ $i @ (^[Y0 : $i]: ($true))) != $true)),
% 0.13/0.38 inference(boolean_simplification,[],[f153])).
% 0.13/0.38 thf(f153,plain,(
% 0.13/0.38 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1))))))))) != $true)),
% 0.13/0.38 inference(boolean_simplification,[],[f152])).
% 0.13/0.38 thf(f152,plain,(
% 0.13/0.38 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1))))) | (~ (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1))))))))))) != $true)),
% 0.13/0.38 inference(boolean_simplification,[],[f151])).
% 0.13/0.38 thf(f151,plain,(
% 0.13/0.38 ((!! @ $i @ (^[Y0 : $i]: (~ (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1))))) | (~ (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1))))))))))))) != $true)),
% 0.13/0.38 inference(boolean_simplification,[],[f150])).
% 0.13/0.38 thf(f150,plain,(
% 0.13/0.38 ($true != (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1))))) | (~ (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))))))) | $false)))))),
% 0.13/0.38 inference(boolean_simplification,[],[f149])).
% 0.13/0.38 thf(f149,plain,(
% 0.13/0.38 ((!! @ $i @ (^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1))))) | (~ (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))))))) | (~ $true))))) != $true)),
% 0.13/0.38 inference(boolean_simplification,[],[f148])).
% 0.13/0.38 thf(f148,plain,(
% 0.13/0.38 ($true != (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1))))) | (~ (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))))))) | (~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))))))))))),
% 0.13/0.38 inference(boolean_simplification,[],[f147])).
% 0.13/0.38 thf(f147,plain,(
% 0.13/0.38 ($true != (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (~ (p @ Y1))) | (~ (rel_k @ Y0 @ Y1))))) | (~ (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))))))) | (~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (~ (p @ Y1))) | (~ (rel_k @ Y0 @ Y1)))))))))))))),
% 0.13/0.38 inference(beta_eta_normalization,[],[f146])).
% 0.13/0.38 thf(f146,plain,(
% 0.13/0.38 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[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)))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_k @ Y1 @ Y2)))))))) @ ((^[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)))) @ p @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))) @ p))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_k @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ p)))) != $true)),
% 0.13/0.38 inference(definition_unfolding,[],[f120,f107,f139,f119,f137,f133,f133,f145])).
% 0.13/0.38 thf(f145,plain,(
% 0.13/0.38 (mdia_k = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_k @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.13/0.38 inference(definition_unfolding,[],[f109,f133,f119,f133])).
% 0.13/0.38 thf(f109,plain,(
% 0.13/0.38 (mdia_k = (^[Y0 : $i > $o]: (mnot @ (mbox_k @ (mnot @ Y0)))))),
% 0.13/0.38 inference(cnf_transformation,[],[f38])).
% 0.13/0.38 thf(f38,plain,(
% 0.13/0.38 (mdia_k = (^[Y0 : $i > $o]: (mnot @ (mbox_k @ (mnot @ Y0)))))),
% 0.13/0.38 inference(fool_elimination,[],[f37])).
% 0.13/0.38 thf(f37,plain,(
% 0.13/0.38 ((^[X0 : $i > $o] : (mnot @ (mbox_k @ (mnot @ X0)))) = mdia_k)),
% 0.13/0.38 inference(rectify,[],[f33])).
% 0.13/0.38 thf(f33,axiom,(
% 0.13/0.38 ((^[X3 : $i > $o] : (mnot @ (mbox_k @ (mnot @ X3)))) = mdia_k)),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_k)).
% 0.13/0.38 thf(f133,plain,(
% 0.13/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.13/0.38 inference(cnf_transformation,[],[f94])).
% 0.13/0.38 thf(f94,plain,(
% 0.13/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.13/0.38 inference(fool_elimination,[],[f93])).
% 0.13/0.38 thf(f93,plain,(
% 0.13/0.38 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.13/0.38 inference(rectify,[],[f3])).
% 0.13/0.38 thf(f3,axiom,(
% 0.13/0.38 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.13/0.38 thf(f137,plain,(
% 0.13/0.38 (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)))))),
% 0.13/0.38 inference(definition_unfolding,[],[f129,f127,f133])).
% 0.13/0.38 thf(f127,plain,(
% 0.13/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.13/0.38 inference(cnf_transformation,[],[f82])).
% 0.13/0.38 thf(f82,plain,(
% 0.13/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.13/0.38 inference(fool_elimination,[],[f81])).
% 0.13/0.38 thf(f81,plain,(
% 0.13/0.38 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor)),
% 0.13/0.38 inference(rectify,[],[f4])).
% 0.13/0.38 thf(f4,axiom,(
% 0.13/0.38 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))) = mor)),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.13/0.38 thf(f129,plain,(
% 0.13/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.13/0.38 inference(cnf_transformation,[],[f54])).
% 0.13/0.38 thf(f54,plain,(
% 0.13/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.13/0.38 inference(fool_elimination,[],[f53])).
% 0.13/0.38 thf(f53,plain,(
% 0.13/0.38 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.13/0.38 inference(rectify,[],[f6])).
% 0.13/0.38 thf(f6,axiom,(
% 0.13/0.38 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.13/0.38 thf(f119,plain,(
% 0.13/0.38 (mbox_k = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_k @ Y1 @ Y2)))))))))),
% 0.13/0.38 inference(cnf_transformation,[],[f90])).
% 0.13/0.38 thf(f90,plain,(
% 0.13/0.38 (mbox_k = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_k @ Y1 @ Y2)))))))))),
% 0.13/0.38 inference(fool_elimination,[],[f89])).
% 0.13/0.38 thf(f89,plain,(
% 0.13/0.38 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_k @ X1 @ X2) | (X0 @ X2)))) = mbox_k)),
% 0.13/0.38 inference(rectify,[],[f32])).
% 0.13/0.38 thf(f32,axiom,(
% 0.13/0.38 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_k @ X2 @ X7) | (X3 @ X7)))) = mbox_k)),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_k)).
% 0.13/0.38 thf(f139,plain,(
% 0.13/0.38 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[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)))) @ Y1 @ Y0))))))),
% 0.13/0.38 inference(definition_unfolding,[],[f108,f136,f137,f137])).
% 0.13/0.38 thf(f136,plain,(
% 0.13/0.38 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.13/0.38 inference(definition_unfolding,[],[f103,f133,f127,f133,f133])).
% 0.13/0.38 thf(f103,plain,(
% 0.13/0.38 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.13/0.38 inference(cnf_transformation,[],[f98])).
% 0.13/0.38 thf(f98,plain,(
% 0.13/0.38 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.13/0.38 inference(fool_elimination,[],[f97])).
% 0.13/0.38 thf(f97,plain,(
% 0.13/0.38 ((^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))) = mand)),
% 0.13/0.38 inference(rectify,[],[f5])).
% 0.13/0.38 thf(f5,axiom,(
% 0.13/0.38 ((^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))) = mand)),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)).
% 0.13/0.38 thf(f108,plain,(
% 0.13/0.38 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.13/0.38 inference(cnf_transformation,[],[f86])).
% 0.13/0.38 thf(f86,plain,(
% 0.13/0.38 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.13/0.38 inference(fool_elimination,[],[f85])).
% 0.13/0.38 thf(f85,plain,(
% 0.13/0.38 (mequiv = (^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))))),
% 0.13/0.38 inference(rectify,[],[f8])).
% 0.13/0.38 thf(f8,axiom,(
% 0.13/0.38 (mequiv = (^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))))),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv)).
% 0.13/0.38 thf(f107,plain,(
% 0.13/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.13/0.38 inference(cnf_transformation,[],[f70])).
% 0.13/0.38 thf(f70,plain,(
% 0.13/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.13/0.38 inference(fool_elimination,[],[f69])).
% 0.13/0.38 thf(f69,plain,(
% 0.13/0.38 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.13/0.38 inference(rectify,[],[f28])).
% 0.13/0.38 thf(f28,axiom,(
% 0.13/0.38 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.13/0.38 thf(f120,plain,(
% 0.13/0.38 ((mvalid @ (mequiv @ (mbox_k @ (mimplies @ p @ (mnot @ p))) @ (mnot @ (mdia_k @ p)))) != $true)),
% 0.13/0.38 inference(cnf_transformation,[],[f101])).
% 0.13/0.38 thf(f101,plain,(
% 0.13/0.38 ((mvalid @ (mequiv @ (mbox_k @ (mimplies @ p @ (mnot @ p))) @ (mnot @ (mdia_k @ p)))) != $true)),
% 0.13/0.38 inference(flattening,[],[f88])).
% 0.13/0.38 thf(f88,plain,(
% 0.13/0.38 ~((mvalid @ (mequiv @ (mbox_k @ (mimplies @ p @ (mnot @ p))) @ (mnot @ (mdia_k @ p)))) = $true)),
% 0.13/0.38 inference(fool_elimination,[],[f87])).
% 0.13/0.38 thf(f87,plain,(
% 0.13/0.38 ~(mvalid @ (mequiv @ (mbox_k @ (mimplies @ p @ (mnot @ p))) @ (mnot @ (mdia_k @ p))))),
% 0.13/0.38 inference(rectify,[],[f35])).
% 0.13/0.38 thf(f35,negated_conjecture,(
% 0.13/0.38 ~(mvalid @ (mequiv @ (mbox_k @ (mimplies @ p @ (mnot @ p))) @ (mnot @ (mdia_k @ p))))),
% 0.13/0.38 inference(negated_conjecture,[],[f34])).
% 0.13/0.38 thf(f34,conjecture,(
% 0.13/0.38 (mvalid @ (mequiv @ (mbox_k @ (mimplies @ p @ (mnot @ p))) @ (mnot @ (mdia_k @ p))))),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.13/0.38 % SZS output end Proof for theBenchmark
% 0.13/0.38 % (23184)------------------------------
% 0.13/0.38 % (23184)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (23184)Termination reason: Refutation
% 0.13/0.38
% 0.13/0.38 % (23184)Memory used [KB]: 5628
% 0.13/0.38 % (23184)Time elapsed: 0.009 s
% 0.13/0.38 % (23184)Instructions burned: 9 (million)
% 0.13/0.38 % (23184)------------------------------
% 0.13/0.38 % (23184)------------------------------
% 0.13/0.38 % (23177)Success in time 0.022 s
% 0.13/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------