TSTP Solution File: SYO485^6 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO485^6 : 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 : 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 09:05:23 EDT 2024
% Result : Theorem 0.19s 0.38s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYO485^6 : TPTP v8.2.0. Released v4.0.0.
% 0.13/0.14 % 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 10:27:53 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 This is a TH0_THM_EQU_NAR problem
% 0.19/0.35 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
% 0.19/0.37 % (5010)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)
% 0.19/0.37 % (5012)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.19/0.37 % (5011)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)
% 0.19/0.37 % (5013)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)
% 0.19/0.37 % (5008)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)
% 0.19/0.37 % (5010)Instruction limit reached!
% 0.19/0.37 % (5010)------------------------------
% 0.19/0.37 % (5010)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.37 % (5010)Termination reason: Unknown
% 0.19/0.37 % (5010)Termination phase: shuffling
% 0.19/0.37
% 0.19/0.37 % (5010)Memory used [KB]: 1023
% 0.19/0.37 % (5010)Time elapsed: 0.003 s
% 0.19/0.37 % (5010)Instructions burned: 3 (million)
% 0.19/0.37 % (5010)------------------------------
% 0.19/0.37 % (5010)------------------------------
% 0.19/0.37 % (5013)Instruction limit reached!
% 0.19/0.37 % (5013)------------------------------
% 0.19/0.37 % (5013)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.37 % (5013)Termination reason: Unknown
% 0.19/0.37 % (5013)Termination phase: shuffling
% 0.19/0.37
% 0.19/0.37 % (5013)Memory used [KB]: 1023
% 0.19/0.37 % (5013)Time elapsed: 0.003 s
% 0.19/0.37 % (5013)Instructions burned: 3 (million)
% 0.19/0.37 % (5013)------------------------------
% 0.19/0.37 % (5013)------------------------------
% 0.19/0.37 % (5006)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.19/0.38 % (5011)Refutation not found, incomplete strategy
% 0.19/0.38 % (5011)------------------------------
% 0.19/0.38 % (5011)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.38 % (5011)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.38
% 0.19/0.38
% 0.19/0.38 % (5011)Memory used [KB]: 5628
% 0.19/0.38 % (5011)Time elapsed: 0.006 s
% 0.19/0.38 % (5011)Instructions burned: 7 (million)
% 0.19/0.38 % (5011)------------------------------
% 0.19/0.38 % (5011)------------------------------
% 0.19/0.38 % (5012)First to succeed.
% 0.19/0.38 % (5006)Also succeeded, but the first one will report.
% 0.19/0.38 % (5009)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.38 % (5008)Also succeeded, but the first one will report.
% 0.19/0.38 % (5012)Refutation found. Thanks to Tanya!
% 0.19/0.38 % SZS status Theorem for theBenchmark
% 0.19/0.38 % SZS output start Proof for theBenchmark
% 0.19/0.38 thf(type_def_5, type, mu: $tType).
% 0.19/0.38 thf(func_def_0, type, mu: $tType).
% 0.19/0.38 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.19/0.38 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_15, type, mtrue: $i > $o).
% 0.19/0.38 thf(func_def_16, type, mfalse: $i > $o).
% 0.19/0.38 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.19/0.38 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.19/0.38 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.19/0.38 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.19/0.38 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.19/0.38 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.19/0.38 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.19/0.38 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.19/0.38 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.19/0.38 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.19/0.38 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.19/0.38 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.19/0.38 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.19/0.38 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.19/0.38 thf(func_def_33, type, rel_s5: $i > $i > $o).
% 0.19/0.38 thf(func_def_34, type, mbox_s5: ($i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_35, type, mdia_s5: ($i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_54, type, sK2: mu).
% 0.19/0.38 thf(f210,plain,(
% 0.19/0.38 $false),
% 0.19/0.38 inference(avatar_sat_refutation,[],[f201,f203,f209])).
% 0.19/0.38 thf(f209,plain,(
% 0.19/0.38 ~spl0_1),
% 0.19/0.38 inference(avatar_contradiction_clause,[],[f208])).
% 0.19/0.38 thf(f208,plain,(
% 0.19/0.38 $false | ~spl0_1),
% 0.19/0.38 inference(trivial_inequality_removal,[],[f205])).
% 0.19/0.38 thf(f205,plain,(
% 0.19/0.38 ($true = $false) | ~spl0_1),
% 0.19/0.38 inference(superposition,[],[f197,f188])).
% 0.19/0.38 thf(f188,plain,(
% 0.19/0.38 ( ! [X1 : $i] : (($true = (rel_s5 @ X1 @ X1))) )),
% 0.19/0.38 inference(beta_eta_normalization,[],[f187])).
% 0.19/0.38 thf(f187,plain,(
% 0.19/0.38 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (rel_s5 @ Y0 @ Y0)) @ X1))) )),
% 0.19/0.38 inference(pi_clausification,[],[f186])).
% 0.19/0.38 thf(f186,plain,(
% 0.19/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: (rel_s5 @ Y0 @ Y0))))),
% 0.19/0.38 inference(beta_eta_normalization,[],[f159])).
% 0.19/0.38 thf(f159,plain,(
% 0.19/0.38 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ rel_s5))),
% 0.19/0.38 inference(definition_unfolding,[],[f134,f137])).
% 0.19/0.38 thf(f137,plain,(
% 0.19/0.38 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.19/0.38 inference(cnf_transformation,[],[f71])).
% 0.19/0.38 thf(f71,plain,(
% 0.19/0.38 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.19/0.38 inference(fool_elimination,[],[f70])).
% 0.19/0.38 thf(f70,plain,(
% 0.19/0.38 (mreflexive = (^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))))),
% 0.19/0.38 inference(rectify,[],[f18])).
% 0.19/0.38 thf(f18,axiom,(
% 0.19/0.38 (mreflexive = (^[X6 : $i > $i > $o] : (! [X8] : (X6 @ X8 @ X8))))),
% 0.19/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive)).
% 0.19/0.38 thf(f134,plain,(
% 0.19/0.38 ((mreflexive @ rel_s5) = $true)),
% 0.19/0.38 inference(cnf_transformation,[],[f55])).
% 0.19/0.38 thf(f55,plain,(
% 0.19/0.38 ((mreflexive @ rel_s5) = $true)),
% 0.19/0.38 inference(fool_elimination,[],[f54])).
% 0.19/0.38 thf(f54,plain,(
% 0.19/0.38 (mreflexive @ rel_s5)),
% 0.19/0.38 inference(rectify,[],[f34])).
% 0.19/0.38 thf(f34,axiom,(
% 0.19/0.38 (mreflexive @ rel_s5)),
% 0.19/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
% 0.19/0.38 thf(f197,plain,(
% 0.19/0.38 ( ! [X1 : $i] : (($false = (rel_s5 @ sK1 @ X1))) ) | ~spl0_1),
% 0.19/0.38 inference(avatar_component_clause,[],[f196])).
% 0.19/0.38 thf(f196,plain,(
% 0.19/0.38 spl0_1 <=> ! [X1] : ($false = (rel_s5 @ sK1 @ X1))),
% 0.19/0.38 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.19/0.38 thf(f203,plain,(
% 0.19/0.38 ~spl0_2),
% 0.19/0.38 inference(avatar_contradiction_clause,[],[f202])).
% 0.19/0.38 thf(f202,plain,(
% 0.19/0.38 $false | ~spl0_2),
% 0.19/0.38 inference(equality_resolution,[],[f200])).
% 0.19/0.38 thf(f200,plain,(
% 0.19/0.38 ( ! [X2 : mu] : ((sK2 != X2)) ) | ~spl0_2),
% 0.19/0.38 inference(avatar_component_clause,[],[f199])).
% 0.19/0.38 thf(f199,plain,(
% 0.19/0.38 spl0_2 <=> ! [X2 : mu] : (sK2 != X2)),
% 0.19/0.38 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.19/0.38 thf(f201,plain,(
% 0.19/0.38 spl0_1 | spl0_2),
% 0.19/0.38 inference(avatar_split_clause,[],[f185,f199,f196])).
% 0.19/0.38 thf(f185,plain,(
% 0.19/0.38 ( ! [X2 : mu,X1 : $i] : (($false = (rel_s5 @ sK1 @ X1)) | (sK2 != X2)) )),
% 0.19/0.38 inference(equality_proxy_clausification,[],[f184])).
% 0.19/0.38 thf(f184,plain,(
% 0.19/0.38 ( ! [X2 : mu,X1 : $i] : (((sK2 = X2) = $false) | ($false = (rel_s5 @ sK1 @ X1))) )),
% 0.19/0.38 inference(not_proxy_clausification,[],[f183])).
% 0.19/0.38 thf(f183,plain,(
% 0.19/0.38 ( ! [X2 : mu,X1 : $i] : (($true = (~ (sK2 = X2))) | ($false = (rel_s5 @ sK1 @ X1))) )),
% 0.19/0.38 inference(beta_eta_normalization,[],[f182])).
% 0.19/0.38 thf(f182,plain,(
% 0.19/0.38 ( ! [X2 : mu,X1 : $i] : (($true = ((^[Y0 : mu]: (~ (sK2 = Y0))) @ X2)) | ($false = (rel_s5 @ sK1 @ X1))) )),
% 0.19/0.38 inference(pi_clausification,[],[f181])).
% 0.19/0.38 thf(f181,plain,(
% 0.19/0.38 ( ! [X1 : $i] : (($true = (!! @ mu @ (^[Y0 : mu]: (~ (sK2 = Y0))))) | ($false = (rel_s5 @ sK1 @ X1))) )),
% 0.19/0.38 inference(not_proxy_clausification,[],[f180])).
% 0.19/0.38 thf(f180,plain,(
% 0.19/0.38 ( ! [X1 : $i] : (($true = (~ (rel_s5 @ sK1 @ X1))) | ($true = (!! @ mu @ (^[Y0 : mu]: (~ (sK2 = Y0)))))) )),
% 0.19/0.38 inference(binary_proxy_clausification,[],[f179])).
% 0.19/0.38 thf(f179,plain,(
% 0.19/0.38 ( ! [X1 : $i] : (($true = ((~ (rel_s5 @ sK1 @ X1)) | (!! @ mu @ (^[Y0 : mu]: (~ (sK2 = Y0))))))) )),
% 0.19/0.38 inference(beta_eta_normalization,[],[f178])).
% 0.19/0.38 thf(f178,plain,(
% 0.19/0.38 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: (~ (sK2 = Y1)))))) @ X1))) )),
% 0.19/0.38 inference(pi_clausification,[],[f177])).
% 0.19/0.38 thf(f177,plain,(
% 0.19/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: (~ (sK2 = Y1))))))))),
% 0.19/0.38 inference(not_proxy_clausification,[],[f176])).
% 0.19/0.38 thf(f176,plain,(
% 0.19/0.38 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: (~ (sK2 = Y1)))))))))),
% 0.19/0.38 inference(beta_eta_normalization,[],[f175])).
% 0.19/0.38 thf(f175,plain,(
% 0.19/0.38 (((^[Y0 : mu]: (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ sK1 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: (~ (Y0 = Y2))))))))) @ sK2) = $false)),
% 0.19/0.38 inference(sigma_clausification,[],[f174])).
% 0.19/0.38 thf(f174,plain,(
% 0.19/0.38 ((!! @ mu @ (^[Y0 : mu]: (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ sK1 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: (~ (Y0 = Y2)))))))))) = $false)),
% 0.19/0.38 inference(beta_eta_normalization,[],[f173])).
% 0.19/0.38 thf(f173,plain,(
% 0.19/0.38 ($false = ((^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y0 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: (~ (Y1 = Y3))))))))))) @ sK1))),
% 0.19/0.38 inference(sigma_clausification,[],[f172])).
% 0.19/0.38 thf(f172,plain,(
% 0.19/0.38 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y0 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: (~ (Y1 = Y3)))))))))))))),
% 0.19/0.38 inference(boolean_simplification,[],[f171])).
% 0.19/0.38 thf(f171,plain,(
% 0.19/0.38 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y0 @ Y2)) | (~ (~ (!! @ mu @ (^[Y3 : mu]: (~ (Y1 = Y3)))))))))))))))),
% 0.19/0.38 inference(beta_eta_normalization,[],[f158])).
% 0.19/0.38 thf(f158,plain,(
% 0.19/0.38 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[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]: ((~ (rel_s5 @ Y3 @ Y4)) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))) @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : mu > $i > $o]: ((^[Y3 : $i]: (!! @ mu @ (^[Y4 : mu]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : mu]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ (Y1 @ Y2)))))) @ (^[Y1 : mu]: ((^[Y2 : mu]: ((^[Y3 : mu]: ((^[Y4 : $i]: (Y2 = Y3)))))) @ Y0 @ Y1))))))))),
% 0.19/0.38 inference(definition_unfolding,[],[f129,f123,f128,f157,f153,f121])).
% 0.19/0.38 thf(f121,plain,(
% 0.19/0.38 (meq_ind = (^[Y0 : mu]: ((^[Y1 : mu]: ((^[Y2 : $i]: (Y0 = Y1)))))))),
% 0.19/0.38 inference(cnf_transformation,[],[f90])).
% 0.19/0.38 thf(f90,plain,(
% 0.19/0.38 (meq_ind = (^[Y0 : mu]: ((^[Y1 : mu]: ((^[Y2 : $i]: (Y0 = Y1)))))))),
% 0.19/0.38 inference(fool_elimination,[],[f1])).
% 0.19/0.38 thf(f1,axiom,(
% 0.19/0.38 (meq_ind = (^[X0 : mu, X1 : mu, X2 : $i] : ((X0 = X1))))),
% 0.19/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meq_ind)).
% 0.19/0.38 thf(f153,plain,(
% 0.19/0.38 (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ (Y0 @ Y1)))))))),
% 0.19/0.38 inference(definition_unfolding,[],[f115,f143,f128,f143])).
% 0.19/0.38 thf(f143,plain,(
% 0.19/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.19/0.38 inference(cnf_transformation,[],[f85])).
% 0.19/0.38 thf(f85,plain,(
% 0.19/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.19/0.38 inference(fool_elimination,[],[f84])).
% 0.19/0.38 thf(f84,plain,(
% 0.19/0.38 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.19/0.38 inference(rectify,[],[f3])).
% 0.19/0.38 thf(f3,axiom,(
% 0.19/0.38 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.19/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.19/0.38 thf(f115,plain,(
% 0.19/0.38 (mexists_ind = (^[Y0 : mu > $i > $o]: (mnot @ (mforall_ind @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))))))),
% 0.19/0.38 inference(cnf_transformation,[],[f57])).
% 0.19/0.38 thf(f57,plain,(
% 0.19/0.38 (mexists_ind = (^[Y0 : mu > $i > $o]: (mnot @ (mforall_ind @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))))))),
% 0.19/0.38 inference(fool_elimination,[],[f56])).
% 0.19/0.38 thf(f56,plain,(
% 0.19/0.38 (mexists_ind = (^[X0 : mu > $i > $o] : (mnot @ (mforall_ind @ (^[X1 : mu] : (mnot @ (X0 @ X1)))))))),
% 0.19/0.38 inference(rectify,[],[f12])).
% 0.19/0.38 thf(f12,axiom,(
% 0.19/0.38 (mexists_ind = (^[X3 : mu > $i > $o] : (mnot @ (mforall_ind @ (^[X0 : mu] : (mnot @ (X3 @ X0)))))))),
% 0.19/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_ind)).
% 0.19/0.38 thf(f157,plain,(
% 0.19/0.38 (mdia_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.19/0.38 inference(definition_unfolding,[],[f114,f143,f139,f143])).
% 0.19/0.38 thf(f139,plain,(
% 0.19/0.38 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.19/0.38 inference(cnf_transformation,[],[f109])).
% 0.19/0.38 thf(f109,plain,(
% 0.19/0.38 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.19/0.38 inference(fool_elimination,[],[f108])).
% 0.19/0.38 thf(f108,plain,(
% 0.19/0.38 (mbox_s5 = (^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_s5 @ X1 @ X2)))))),
% 0.19/0.38 inference(rectify,[],[f32])).
% 0.19/0.38 thf(f32,axiom,(
% 0.19/0.38 (mbox_s5 = (^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_s5 @ X2 @ X7)))))),
% 0.19/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s5)).
% 0.19/0.38 thf(f114,plain,(
% 0.19/0.38 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.19/0.38 inference(cnf_transformation,[],[f81])).
% 0.19/0.38 thf(f81,plain,(
% 0.19/0.38 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.19/0.38 inference(fool_elimination,[],[f80])).
% 0.19/0.38 thf(f80,plain,(
% 0.19/0.38 ((^[X0 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X0)))) = mdia_s5)),
% 0.19/0.38 inference(rectify,[],[f33])).
% 0.19/0.38 thf(f33,axiom,(
% 0.19/0.38 ((^[X3 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X3)))) = mdia_s5)),
% 0.19/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_s5)).
% 0.19/0.38 thf(f128,plain,(
% 0.19/0.38 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.19/0.38 inference(cnf_transformation,[],[f63])).
% 0.19/0.38 thf(f63,plain,(
% 0.19/0.38 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.19/0.38 inference(fool_elimination,[],[f62])).
% 0.19/0.38 thf(f62,plain,(
% 0.19/0.38 ((^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : (X0 @ X2 @ X1))) = mforall_ind)),
% 0.19/0.38 inference(rectify,[],[f10])).
% 0.19/0.38 thf(f10,axiom,(
% 0.19/0.38 ((^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : (X3 @ X0 @ X2))) = mforall_ind)),
% 0.19/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind)).
% 0.19/0.38 thf(f123,plain,(
% 0.19/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.19/0.38 inference(cnf_transformation,[],[f77])).
% 0.19/0.38 thf(f77,plain,(
% 0.19/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.19/0.38 inference(fool_elimination,[],[f76])).
% 0.19/0.38 thf(f76,plain,(
% 0.19/0.38 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.19/0.38 inference(rectify,[],[f28])).
% 0.19/0.38 thf(f28,axiom,(
% 0.19/0.38 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.19/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.19/0.38 thf(f129,plain,(
% 0.19/0.38 ($true != (mvalid @ (mforall_ind @ (^[Y0 : mu]: (mdia_s5 @ (mexists_ind @ (^[Y1 : mu]: (meq_ind @ Y0 @ Y1))))))))),
% 0.19/0.38 inference(cnf_transformation,[],[f110])).
% 0.19/0.38 thf(f110,plain,(
% 0.19/0.38 ($true != (mvalid @ (mforall_ind @ (^[Y0 : mu]: (mdia_s5 @ (mexists_ind @ (^[Y1 : mu]: (meq_ind @ Y0 @ Y1))))))))),
% 0.19/0.38 inference(flattening,[],[f92])).
% 0.19/0.38 thf(f92,plain,(
% 0.19/0.38 ~($true = (mvalid @ (mforall_ind @ (^[Y0 : mu]: (mdia_s5 @ (mexists_ind @ (^[Y1 : mu]: (meq_ind @ Y0 @ Y1))))))))),
% 0.19/0.38 inference(fool_elimination,[],[f91])).
% 0.19/0.38 thf(f91,plain,(
% 0.19/0.38 ~(mvalid @ (mforall_ind @ (^[X0 : mu] : (mdia_s5 @ (mexists_ind @ (^[X1 : mu] : (meq_ind @ X0 @ X1)))))))),
% 0.19/0.38 inference(rectify,[],[f38])).
% 0.19/0.38 thf(f38,negated_conjecture,(
% 0.19/0.38 ~(mvalid @ (mforall_ind @ (^[X0 : mu] : (mdia_s5 @ (mexists_ind @ (^[X1 : mu] : (meq_ind @ X0 @ X1)))))))),
% 0.19/0.38 inference(negated_conjecture,[],[f37])).
% 0.19/0.38 thf(f37,conjecture,(
% 0.19/0.38 (mvalid @ (mforall_ind @ (^[X0 : mu] : (mdia_s5 @ (mexists_ind @ (^[X1 : mu] : (meq_ind @ X0 @ X1)))))))),
% 0.19/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.19/0.38 % SZS output end Proof for theBenchmark
% 0.19/0.38 % (5012)------------------------------
% 0.19/0.38 % (5012)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.38 % (5012)Termination reason: Refutation
% 0.19/0.38
% 0.19/0.38 % (5012)Memory used [KB]: 5628
% 0.19/0.38 % (5012)Time elapsed: 0.009 s
% 0.19/0.38 % (5012)Instructions burned: 11 (million)
% 0.19/0.38 % (5012)------------------------------
% 0.19/0.38 % (5012)------------------------------
% 0.19/0.38 % (5005)Success in time 0.022 s
% 0.19/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------