TSTP Solution File: SYO480^6 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO480^6 : 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 : n023.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 09:05:22 EDT 2024
% Result : Theorem 0.12s 0.36s
% Output : Refutation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYO480^6 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.13 % 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
% 0.12/0.32 % Computer : n023.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon May 20 08:36:38 EDT 2024
% 0.12/0.32 % CPUTime :
% 0.12/0.32 This is a TH0_THM_EQU_NAR problem
% 0.12/0.33 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
% 0.12/0.35 % (22411)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)
% 0.12/0.35 % (22406)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.12/0.35 % (22408)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)
% 0.12/0.35 % (22409)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.35 % (22410)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)
% 0.12/0.35 % (22407)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)
% 0.12/0.35 % (22413)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.12/0.35 % (22411)Refutation not found, incomplete strategy
% 0.12/0.35 % (22411)------------------------------
% 0.12/0.35 % (22411)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.35 % (22411)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.35
% 0.12/0.35
% 0.12/0.35 % (22411)Memory used [KB]: 5628
% 0.12/0.35 % (22411)Time elapsed: 0.005 s
% 0.12/0.35 % (22411)Instructions burned: 8 (million)
% 0.12/0.35 % (22411)------------------------------
% 0.12/0.35 % (22411)------------------------------
% 0.12/0.35 % (22409)Instruction limit reached!
% 0.12/0.35 % (22409)------------------------------
% 0.12/0.35 % (22409)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.35 % (22409)Termination reason: Unknown
% 0.12/0.35 % (22410)Instruction limit reached!
% 0.12/0.35 % (22410)------------------------------
% 0.12/0.35 % (22410)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.35 % (22410)Termination reason: Unknown
% 0.12/0.35 % (22410)Termination phase: shuffling
% 0.12/0.35
% 0.12/0.35 % (22410)Memory used [KB]: 1023
% 0.12/0.35 % (22410)Time elapsed: 0.004 s
% 0.12/0.35 % (22410)Instructions burned: 3 (million)
% 0.12/0.35 % (22410)------------------------------
% 0.12/0.35 % (22410)------------------------------
% 0.12/0.35 % (22409)Termination phase: shuffling
% 0.12/0.35
% 0.12/0.35 % (22409)Memory used [KB]: 1023
% 0.12/0.35 % (22409)Time elapsed: 0.004 s
% 0.12/0.35 % (22409)Instructions burned: 3 (million)
% 0.12/0.35 % (22409)------------------------------
% 0.12/0.35 % (22409)------------------------------
% 0.12/0.35 % (22407)Instruction limit reached!
% 0.12/0.35 % (22407)------------------------------
% 0.12/0.35 % (22407)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.35 % (22407)Termination reason: Unknown
% 0.12/0.35 % (22407)Termination phase: Property scanning
% 0.12/0.35
% 0.12/0.35 % (22407)Memory used [KB]: 1023
% 0.12/0.35 % (22407)Time elapsed: 0.004 s
% 0.12/0.35 % (22407)Instructions burned: 4 (million)
% 0.12/0.35 % (22407)------------------------------
% 0.12/0.35 % (22407)------------------------------
% 0.12/0.35 % (22414)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)
% 0.12/0.35 % (22414)Instruction limit reached!
% 0.12/0.35 % (22414)------------------------------
% 0.12/0.35 % (22414)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.35 % (22414)Termination reason: Unknown
% 0.12/0.35 % (22414)Termination phase: shuffling
% 0.12/0.35
% 0.12/0.35 % (22414)Memory used [KB]: 1023
% 0.12/0.35 % (22414)Time elapsed: 0.003 s
% 0.12/0.35 % (22414)Instructions burned: 3 (million)
% 0.12/0.35 % (22414)------------------------------
% 0.12/0.35 % (22414)------------------------------
% 0.12/0.36 % (22406)First to succeed.
% 0.12/0.36 % (22413)Also succeeded, but the first one will report.
% 0.12/0.36 % (22406)Refutation found. Thanks to Tanya!
% 0.12/0.36 % SZS status Theorem for theBenchmark
% 0.12/0.36 % SZS output start Proof for theBenchmark
% 0.12/0.36 thf(type_def_5, type, mu: $tType).
% 0.12/0.36 thf(func_def_0, type, mu: $tType).
% 0.12/0.36 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.12/0.36 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.36 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.12/0.36 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.36 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.36 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.36 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.36 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.36 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.36 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.12/0.36 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.12/0.36 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.12/0.36 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.12/0.36 thf(func_def_15, type, mtrue: $i > $o).
% 0.12/0.36 thf(func_def_16, type, mfalse: $i > $o).
% 0.12/0.36 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.12/0.36 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.12/0.36 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.12/0.36 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.12/0.36 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.12/0.36 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.12/0.36 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.12/0.36 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.12/0.36 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.12/0.36 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.12/0.36 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.12/0.36 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.12/0.36 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.12/0.36 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.12/0.36 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.12/0.36 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.12/0.36 thf(func_def_33, type, rel_s5: $i > $i > $o).
% 0.12/0.36 thf(func_def_34, type, mbox_s5: ($i > $o) > $i > $o).
% 0.12/0.36 thf(func_def_35, type, mdia_s5: ($i > $o) > $i > $o).
% 0.12/0.36 thf(func_def_36, type, f: mu > $i > $o).
% 0.12/0.36 thf(func_def_55, type, sK3: mu).
% 0.12/0.36 thf(f212,plain,(
% 0.12/0.36 $false),
% 0.12/0.36 inference(trivial_inequality_removal,[],[f209])).
% 0.12/0.36 thf(f209,plain,(
% 0.12/0.36 ($false = $true)),
% 0.12/0.36 inference(superposition,[],[f193,f206])).
% 0.12/0.36 thf(f206,plain,(
% 0.12/0.36 ((rel_s5 @ sK1 @ sK2) = $false)),
% 0.12/0.36 inference(trivial_inequality_removal,[],[f204])).
% 0.12/0.36 thf(f204,plain,(
% 0.12/0.36 ((rel_s5 @ sK1 @ sK2) = $false) | ($false = $true)),
% 0.12/0.36 inference(superposition,[],[f192,f201])).
% 0.12/0.36 thf(f201,plain,(
% 0.12/0.36 ( ! [X1 : $i] : (($false = (f @ sK3 @ X1)) | ($false = (rel_s5 @ sK1 @ X1))) )),
% 0.12/0.36 inference(not_proxy_clausification,[],[f200])).
% 0.12/0.36 thf(f200,plain,(
% 0.12/0.36 ( ! [X1 : $i] : (((~ (rel_s5 @ sK1 @ X1)) = $true) | ($false = (f @ sK3 @ X1))) )),
% 0.12/0.36 inference(not_proxy_clausification,[],[f199])).
% 0.12/0.36 thf(f199,plain,(
% 0.12/0.36 ( ! [X1 : $i] : (((~ (f @ sK3 @ X1)) = $true) | ((~ (rel_s5 @ sK1 @ X1)) = $true)) )),
% 0.12/0.36 inference(binary_proxy_clausification,[],[f198])).
% 0.12/0.36 thf(f198,plain,(
% 0.12/0.36 ( ! [X1 : $i] : ((((~ (f @ sK3 @ X1)) | (~ (rel_s5 @ sK1 @ X1))) = $true)) )),
% 0.12/0.36 inference(beta_eta_normalization,[],[f197])).
% 0.12/0.36 thf(f197,plain,(
% 0.12/0.36 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (f @ sK3 @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))) @ X1) = $true)) )),
% 0.12/0.36 inference(pi_clausification,[],[f196])).
% 0.12/0.36 thf(f196,plain,(
% 0.12/0.36 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (f @ sK3 @ Y0)) | (~ (rel_s5 @ sK1 @ Y0))))))),
% 0.12/0.36 inference(not_proxy_clausification,[],[f195])).
% 0.12/0.36 thf(f195,plain,(
% 0.12/0.36 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (f @ sK3 @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) = $false)),
% 0.12/0.36 inference(beta_eta_normalization,[],[f194])).
% 0.12/0.36 thf(f194,plain,(
% 0.12/0.36 (((^[Y0 : mu]: (~ (!! @ $i @ (^[Y1 : $i]: ((~ (f @ Y0 @ Y1)) | (~ (rel_s5 @ sK1 @ Y1))))))) @ sK3) = $false)),
% 0.12/0.36 inference(sigma_clausification,[],[f184])).
% 0.12/0.36 thf(f184,plain,(
% 0.12/0.36 ((!! @ mu @ (^[Y0 : mu]: (~ (!! @ $i @ (^[Y1 : $i]: ((~ (f @ Y0 @ Y1)) | (~ (rel_s5 @ sK1 @ Y1)))))))) = $false)),
% 0.12/0.36 inference(binary_proxy_clausification,[],[f183])).
% 0.12/0.36 thf(f183,plain,(
% 0.12/0.36 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ mu @ (^[Y1 : mu]: (f @ Y1 @ Y0)))) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ mu @ (^[Y0 : mu]: (~ (!! @ $i @ (^[Y1 : $i]: ((~ (f @ Y0 @ Y1)) | (~ (rel_s5 @ sK1 @ Y1))))))))))),
% 0.12/0.36 inference(beta_eta_normalization,[],[f182])).
% 0.12/0.36 thf(f182,plain,(
% 0.12/0.36 ($false = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ mu @ (^[Y2 : mu]: (f @ Y2 @ Y1)))) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ mu @ (^[Y1 : mu]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (f @ Y1 @ Y2)) | (~ (rel_s5 @ Y0 @ Y2)))))))))) @ sK1))),
% 0.12/0.36 inference(sigma_clausification,[],[f181])).
% 0.12/0.36 thf(f181,plain,(
% 0.12/0.36 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ mu @ (^[Y2 : mu]: (f @ Y2 @ Y1)))) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ mu @ (^[Y1 : mu]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (f @ Y1 @ Y2)) | (~ (rel_s5 @ Y0 @ Y2))))))))))) != $true)),
% 0.12/0.36 inference(boolean_simplification,[],[f180])).
% 0.12/0.36 thf(f180,plain,(
% 0.12/0.36 ((!! @ $i @ (^[Y0 : $i]: ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ mu @ (^[Y2 : mu]: (f @ Y2 @ Y1)))) | (~ (rel_s5 @ Y0 @ Y1))))))) | (!! @ mu @ (^[Y1 : mu]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (f @ Y1 @ Y2)) | (~ (rel_s5 @ Y0 @ Y2))))))))))) != $true)),
% 0.12/0.36 inference(beta_eta_normalization,[],[f161])).
% 0.12/0.36 thf(f161,plain,(
% 0.12/0.36 (((^[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]: ((Y1 @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : mu]: (f @ Y0)))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : mu]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (rel_s5 @ Y3 @ Y4)))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))) @ (f @ Y0)))))) != $true)),
% 0.12/0.36 inference(definition_unfolding,[],[f146,f135,f149,f157,f114,f114,f157])).
% 0.12/0.36 thf(f114,plain,(
% 0.12/0.36 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.12/0.36 inference(cnf_transformation,[],[f73])).
% 0.12/0.36 thf(f73,plain,(
% 0.12/0.36 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.12/0.36 inference(fool_elimination,[],[f72])).
% 0.12/0.36 thf(f72,plain,(
% 0.12/0.36 ((^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : (X0 @ X2 @ X1))) = mforall_ind)),
% 0.12/0.36 inference(rectify,[],[f10])).
% 0.12/0.36 thf(f10,axiom,(
% 0.12/0.36 ((^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : (X3 @ X0 @ X2))) = mforall_ind)),
% 0.12/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind)).
% 0.12/0.36 thf(f157,plain,(
% 0.12/0.36 (mdia_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.12/0.36 inference(definition_unfolding,[],[f143,f125,f113,f125])).
% 0.12/0.36 thf(f113,plain,(
% 0.12/0.36 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))))),
% 0.12/0.36 inference(cnf_transformation,[],[f53])).
% 0.12/0.36 thf(f53,plain,(
% 0.12/0.36 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))))),
% 0.12/0.36 inference(fool_elimination,[],[f52])).
% 0.12/0.36 thf(f52,plain,(
% 0.12/0.36 (mbox_s5 = (^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_s5 @ X1 @ X2) | (X0 @ X2)))))),
% 0.12/0.36 inference(rectify,[],[f32])).
% 0.12/0.36 thf(f32,axiom,(
% 0.12/0.36 (mbox_s5 = (^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_s5 @ X2 @ X7) | (X3 @ X7)))))),
% 0.12/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s5)).
% 0.12/0.36 thf(f125,plain,(
% 0.12/0.36 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.12/0.36 inference(cnf_transformation,[],[f47])).
% 0.12/0.36 thf(f47,plain,(
% 0.12/0.36 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.12/0.36 inference(fool_elimination,[],[f46])).
% 0.12/0.36 thf(f46,plain,(
% 0.12/0.36 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.12/0.36 inference(rectify,[],[f3])).
% 0.12/0.36 thf(f3,axiom,(
% 0.12/0.36 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.12/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.12/0.36 thf(f143,plain,(
% 0.12/0.36 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.12/0.36 inference(cnf_transformation,[],[f103])).
% 0.12/0.36 thf(f103,plain,(
% 0.12/0.36 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.12/0.36 inference(fool_elimination,[],[f102])).
% 0.12/0.36 thf(f102,plain,(
% 0.12/0.36 ((^[X0 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X0)))) = mdia_s5)),
% 0.12/0.36 inference(rectify,[],[f33])).
% 0.12/0.36 thf(f33,axiom,(
% 0.12/0.36 ((^[X3 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X3)))) = mdia_s5)),
% 0.12/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_s5)).
% 0.12/0.36 thf(f149,plain,(
% 0.12/0.36 (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)))))),
% 0.12/0.36 inference(definition_unfolding,[],[f131,f121,f125])).
% 0.12/0.36 thf(f121,plain,(
% 0.12/0.36 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.12/0.36 inference(cnf_transformation,[],[f79])).
% 0.12/0.36 thf(f79,plain,(
% 0.12/0.36 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.12/0.36 inference(fool_elimination,[],[f78])).
% 0.12/0.36 thf(f78,plain,(
% 0.12/0.36 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.12/0.36 inference(rectify,[],[f4])).
% 0.12/0.36 thf(f4,axiom,(
% 0.12/0.36 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))))),
% 0.12/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.12/0.36 thf(f131,plain,(
% 0.12/0.36 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.12/0.36 inference(cnf_transformation,[],[f97])).
% 0.12/0.36 thf(f97,plain,(
% 0.12/0.36 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.12/0.36 inference(fool_elimination,[],[f96])).
% 0.12/0.36 thf(f96,plain,(
% 0.12/0.36 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.12/0.36 inference(rectify,[],[f6])).
% 0.12/0.36 thf(f6,axiom,(
% 0.12/0.36 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.12/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.12/0.36 thf(f135,plain,(
% 0.12/0.36 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.12/0.36 inference(cnf_transformation,[],[f59])).
% 0.12/0.36 thf(f59,plain,(
% 0.12/0.36 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.12/0.36 inference(fool_elimination,[],[f58])).
% 0.12/0.36 thf(f58,plain,(
% 0.12/0.36 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.12/0.36 inference(rectify,[],[f28])).
% 0.12/0.36 thf(f28,axiom,(
% 0.12/0.36 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.12/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.12/0.36 thf(f146,plain,(
% 0.12/0.36 ((mvalid @ (mimplies @ (mdia_s5 @ (mforall_ind @ (^[Y0 : mu]: (f @ Y0)))) @ (mforall_ind @ (^[Y0 : mu]: (mdia_s5 @ (f @ Y0)))))) != $true)),
% 0.12/0.36 inference(cnf_transformation,[],[f110])).
% 0.12/0.36 thf(f110,plain,(
% 0.12/0.36 ((mvalid @ (mimplies @ (mdia_s5 @ (mforall_ind @ (^[Y0 : mu]: (f @ Y0)))) @ (mforall_ind @ (^[Y0 : mu]: (mdia_s5 @ (f @ Y0)))))) != $true)),
% 0.12/0.36 inference(flattening,[],[f99])).
% 0.12/0.36 thf(f99,plain,(
% 0.12/0.36 ~((mvalid @ (mimplies @ (mdia_s5 @ (mforall_ind @ (^[Y0 : mu]: (f @ Y0)))) @ (mforall_ind @ (^[Y0 : mu]: (mdia_s5 @ (f @ Y0)))))) = $true)),
% 0.12/0.36 inference(fool_elimination,[],[f98])).
% 0.12/0.36 thf(f98,plain,(
% 0.12/0.36 ~(mvalid @ (mimplies @ (mdia_s5 @ (mforall_ind @ (^[X0 : mu] : (f @ X0)))) @ (mforall_ind @ (^[X1 : mu] : (mdia_s5 @ (f @ X1))))))),
% 0.12/0.36 inference(rectify,[],[f38])).
% 0.12/0.36 thf(f38,negated_conjecture,(
% 0.12/0.36 ~(mvalid @ (mimplies @ (mdia_s5 @ (mforall_ind @ (^[X0 : mu] : (f @ X0)))) @ (mforall_ind @ (^[X0 : mu] : (mdia_s5 @ (f @ X0))))))),
% 0.12/0.36 inference(negated_conjecture,[],[f37])).
% 0.12/0.36 thf(f37,conjecture,(
% 0.12/0.36 (mvalid @ (mimplies @ (mdia_s5 @ (mforall_ind @ (^[X0 : mu] : (f @ X0)))) @ (mforall_ind @ (^[X0 : mu] : (mdia_s5 @ (f @ X0))))))),
% 0.12/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.12/0.36 thf(f192,plain,(
% 0.12/0.36 ( ! [X1 : mu] : (((f @ X1 @ sK2) = $true)) )),
% 0.12/0.36 inference(beta_eta_normalization,[],[f191])).
% 0.12/0.36 thf(f191,plain,(
% 0.12/0.36 ( ! [X1 : mu] : ((((^[Y0 : mu]: (f @ Y0 @ sK2)) @ X1) = $true)) )),
% 0.12/0.36 inference(pi_clausification,[],[f190])).
% 0.12/0.36 thf(f190,plain,(
% 0.12/0.36 ((!! @ mu @ (^[Y0 : mu]: (f @ Y0 @ sK2))) = $true)),
% 0.12/0.36 inference(not_proxy_clausification,[],[f189])).
% 0.12/0.36 thf(f189,plain,(
% 0.12/0.36 ((~ (!! @ mu @ (^[Y0 : mu]: (f @ Y0 @ sK2)))) = $false)),
% 0.12/0.36 inference(binary_proxy_clausification,[],[f187])).
% 0.12/0.36 thf(f187,plain,(
% 0.12/0.36 ($false = ((~ (!! @ mu @ (^[Y0 : mu]: (f @ Y0 @ sK2)))) | (~ (rel_s5 @ sK1 @ sK2))))),
% 0.12/0.36 inference(beta_eta_normalization,[],[f186])).
% 0.12/0.36 thf(f186,plain,(
% 0.12/0.36 ($false = ((^[Y0 : $i]: ((~ (!! @ mu @ (^[Y1 : mu]: (f @ Y1 @ Y0)))) | (~ (rel_s5 @ sK1 @ Y0)))) @ sK2))),
% 0.12/0.36 inference(sigma_clausification,[],[f185])).
% 0.12/0.36 thf(f185,plain,(
% 0.12/0.36 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ mu @ (^[Y1 : mu]: (f @ Y1 @ Y0)))) | (~ (rel_s5 @ sK1 @ Y0))))) = $false)),
% 0.12/0.36 inference(binary_proxy_clausification,[],[f183])).
% 0.12/0.36 thf(f193,plain,(
% 0.12/0.36 ((rel_s5 @ sK1 @ sK2) = $true)),
% 0.12/0.36 inference(not_proxy_clausification,[],[f188])).
% 0.12/0.36 thf(f188,plain,(
% 0.12/0.36 ($false = (~ (rel_s5 @ sK1 @ sK2)))),
% 0.12/0.36 inference(binary_proxy_clausification,[],[f187])).
% 0.12/0.36 % SZS output end Proof for theBenchmark
% 0.12/0.36 % (22406)------------------------------
% 0.12/0.36 % (22406)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.36 % (22406)Termination reason: Refutation
% 0.12/0.36
% 0.12/0.36 % (22406)Memory used [KB]: 5628
% 0.12/0.36 % (22406)Time elapsed: 0.011 s
% 0.12/0.36 % (22406)Instructions burned: 12 (million)
% 0.12/0.36 % (22406)------------------------------
% 0.12/0.36 % (22406)------------------------------
% 0.12/0.36 % (22401)Success in time 0.014 s
% 0.12/0.36 % Vampire---4.8 exiting
%------------------------------------------------------------------------------