TSTP Solution File: SYO572^7 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO572^7 : TPTP v8.2.0. Released v5.5.0.
% 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 : n021.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 09:06:16 EDT 2024
% Result : Theorem 0.22s 0.39s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO572^7 : TPTP v8.2.0. Released v5.5.0.
% 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
% 0.15/0.35 % Computer : n021.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 20 09:42:53 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 This is a TH0_THM_EQU_NAR problem
% 0.15/0.35 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
% 0.15/0.37 % (21403)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.37 % (21405)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)
% 0.15/0.37 % (21404)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)
% 0.15/0.37 % (21406)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.37 % (21407)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)
% 0.15/0.37 % (21408)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)
% 0.15/0.37 % (21409)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.38 % (21406)Instruction limit reached!
% 0.15/0.38 % (21406)------------------------------
% 0.15/0.38 % (21406)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (21406)Termination reason: Unknown
% 0.15/0.38 % (21406)Termination phase: shuffling
% 0.15/0.38
% 0.15/0.38 % (21406)Memory used [KB]: 1023
% 0.15/0.38 % (21406)Time elapsed: 0.003 s
% 0.15/0.38 % (21406)Instructions burned: 2 (million)
% 0.15/0.38 % (21406)------------------------------
% 0.15/0.38 % (21406)------------------------------
% 0.15/0.38 % (21407)Instruction limit reached!
% 0.15/0.38 % (21407)------------------------------
% 0.15/0.38 % (21407)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38 % (21407)Termination reason: Unknown
% 0.22/0.38 % (21407)Termination phase: shuffling
% 0.22/0.38
% 0.22/0.38 % (21407)Memory used [KB]: 1023
% 0.22/0.38 % (21407)Time elapsed: 0.004 s
% 0.22/0.38 % (21407)Instructions burned: 3 (million)
% 0.22/0.38 % (21407)------------------------------
% 0.22/0.38 % (21407)------------------------------
% 0.22/0.38 % (21404)Instruction limit reached!
% 0.22/0.38 % (21404)------------------------------
% 0.22/0.38 % (21404)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38 % (21404)Termination reason: Unknown
% 0.22/0.38 % (21410)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)
% 0.22/0.38 % (21404)Termination phase: Property scanning
% 0.22/0.38
% 0.22/0.38 % (21404)Memory used [KB]: 1023
% 0.22/0.38 % (21404)Time elapsed: 0.004 s
% 0.22/0.38 % (21404)Instructions burned: 5 (million)
% 0.22/0.38 % (21404)------------------------------
% 0.22/0.38 % (21404)------------------------------
% 0.22/0.38 % (21410)Instruction limit reached!
% 0.22/0.38 % (21410)------------------------------
% 0.22/0.38 % (21410)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38 % (21410)Termination reason: Unknown
% 0.22/0.38 % (21410)Termination phase: shuffling
% 0.22/0.38
% 0.22/0.38 % (21410)Memory used [KB]: 1023
% 0.22/0.38 % (21410)Time elapsed: 0.004 s
% 0.22/0.38 % (21410)Instructions burned: 3 (million)
% 0.22/0.38 % (21410)------------------------------
% 0.22/0.38 % (21410)------------------------------
% 0.22/0.38 % (21408)Refutation not found, incomplete strategy
% 0.22/0.38 % (21408)------------------------------
% 0.22/0.38 % (21408)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38 % (21408)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.38
% 0.22/0.38
% 0.22/0.38 % (21408)Memory used [KB]: 5628
% 0.22/0.38 % (21408)Time elapsed: 0.008 s
% 0.22/0.38 % (21408)Instructions burned: 9 (million)
% 0.22/0.38 % (21408)------------------------------
% 0.22/0.38 % (21408)------------------------------
% 0.22/0.39 % (21409)Instruction limit reached!
% 0.22/0.39 % (21409)------------------------------
% 0.22/0.39 % (21409)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39 % (21409)Termination reason: Unknown
% 0.22/0.39 % (21409)Termination phase: Saturation
% 0.22/0.39
% 0.22/0.39 % (21409)Memory used [KB]: 5756
% 0.22/0.39 % (21409)Time elapsed: 0.013 s
% 0.22/0.39 % (21409)Instructions burned: 18 (million)
% 0.22/0.39 % (21409)------------------------------
% 0.22/0.39 % (21409)------------------------------
% 0.22/0.39 % (21405)First to succeed.
% 0.22/0.39 % (21403)Also succeeded, but the first one will report.
% 0.22/0.39 % (21405)Refutation found. Thanks to Tanya!
% 0.22/0.39 % SZS status Theorem for theBenchmark
% 0.22/0.39 % SZS output start Proof for theBenchmark
% 0.22/0.39 thf(type_def_5, type, mu: $tType).
% 0.22/0.39 thf(func_def_0, type, mu: $tType).
% 0.22/0.39 thf(func_def_1, type, qmltpeq: mu > mu > $i > $o).
% 0.22/0.39 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_6, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_7, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_8, type, mtrue: $i > $o).
% 0.22/0.39 thf(func_def_9, type, mfalse: $i > $o).
% 0.22/0.39 thf(func_def_10, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_11, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_12, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_13, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_14, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_15, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_16, type, exists_in_world: mu > $i > $o).
% 0.22/0.39 thf(func_def_17, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_18, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_19, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_20, type, mreflexive: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_21, type, msymmetric: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_22, type, mserial: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_23, type, mtransitive: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_24, type, meuclidean: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_25, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_26, type, mfunctional: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_27, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_28, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_29, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_30, type, mvalid: ($i > $o) > $o).
% 0.22/0.39 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.22/0.39 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.22/0.39 thf(func_def_33, type, minvalid: ($i > $o) > $o).
% 0.22/0.39 thf(func_def_34, type, rel_s4: $i > $i > $o).
% 0.22/0.39 thf(func_def_35, type, mbox_s4: ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_36, type, mdia_s4: ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_37, type, f: mu > $i > $o).
% 0.22/0.39 thf(func_def_38, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.22/0.39 thf(func_def_54, type, sK0: $i > mu).
% 0.22/0.39 thf(f232,plain,(
% 0.22/0.39 $false),
% 0.22/0.39 inference(trivial_inequality_removal,[],[f230])).
% 0.22/0.39 thf(f230,plain,(
% 0.22/0.39 ($true = $false)),
% 0.22/0.39 inference(backward_demodulation,[],[f207,f222])).
% 0.22/0.39 thf(f222,plain,(
% 0.22/0.39 ((exists_in_world @ (sK0 @ sK2) @ sK3) = $false)),
% 0.22/0.39 inference(trivial_inequality_removal,[],[f221])).
% 0.22/0.39 thf(f221,plain,(
% 0.22/0.39 ((exists_in_world @ (sK0 @ sK2) @ sK3) = $false) | ($true = $false)),
% 0.22/0.39 inference(forward_demodulation,[],[f220,f181])).
% 0.22/0.39 thf(f181,plain,(
% 0.22/0.39 ($true = (rel_s4 @ sK2 @ sK3))),
% 0.22/0.39 inference(not_proxy_clausification,[],[f175])).
% 0.22/0.39 thf(f175,plain,(
% 0.22/0.39 ((~ (rel_s4 @ sK2 @ sK3)) = $false)),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f174])).
% 0.22/0.39 thf(f174,plain,(
% 0.22/0.39 (((~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK3) => (f @ Y0 @ sK3))))) | (~ (rel_s4 @ sK2 @ sK3))) = $false)),
% 0.22/0.39 inference(beta_eta_normalization,[],[f173])).
% 0.22/0.39 thf(f173,plain,(
% 0.22/0.39 ($false = ((^[Y0 : $i]: ((~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (f @ Y1 @ Y0))))) | (~ (rel_s4 @ sK2 @ Y0)))) @ sK3))),
% 0.22/0.39 inference(sigma_clausification,[],[f172])).
% 0.22/0.39 thf(f172,plain,(
% 0.22/0.39 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (f @ Y1 @ Y0))))) | (~ (rel_s4 @ sK2 @ Y0))))) = $false)),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f170])).
% 0.22/0.39 thf(f170,plain,(
% 0.22/0.39 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (f @ Y1 @ Y0))))) | (~ (rel_s4 @ sK2 @ Y0))))) | (~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((~ (f @ Y0 @ Y1)) | (~ (rel_s4 @ sK2 @ Y1)))))))))))),
% 0.22/0.39 inference(beta_eta_normalization,[],[f169])).
% 0.22/0.39 thf(f169,plain,(
% 0.22/0.39 ($false = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (f @ Y2 @ Y1))))) | (~ (rel_s4 @ Y0 @ Y1))))) | (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (f @ Y1 @ Y2)) | (~ (rel_s4 @ Y0 @ Y2))))))))))) @ sK2))),
% 0.22/0.39 inference(sigma_clausification,[],[f168])).
% 0.22/0.39 thf(f168,plain,(
% 0.22/0.39 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (f @ Y2 @ Y1))))) | (~ (rel_s4 @ Y0 @ Y1))))) | (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (f @ Y1 @ Y2)) | (~ (rel_s4 @ Y0 @ Y2)))))))))))) != $true)),
% 0.22/0.39 inference(boolean_simplification,[],[f167])).
% 0.22/0.39 thf(f167,plain,(
% 0.22/0.39 ((!! @ $i @ (^[Y0 : $i]: ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (f @ Y2 @ Y1))))) | (~ (rel_s4 @ Y0 @ Y1))))))) | (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (f @ Y1 @ Y2)) | (~ (rel_s4 @ Y0 @ Y2)))))))))))) != $true)),
% 0.22/0.39 inference(boolean_simplification,[],[f166])).
% 0.22/0.39 thf(f166,plain,(
% 0.22/0.39 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (f @ Y2 @ Y1))))) | (~ (rel_s4 @ Y0 @ Y1))))))) | (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (~ (!! @ $i @ (^[Y2 : $i]: ((~ (f @ Y1 @ Y2)) | (~ (rel_s4 @ Y0 @ Y2)))))))))))))))),
% 0.22/0.39 inference(beta_eta_normalization,[],[f165])).
% 0.22/0.39 thf(f165,plain,(
% 0.22/0.39 ($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]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : mu]: (f @ Y0)))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ (Y0 @ Y1)))))) @ (^[Y0 : mu]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))) @ (f @ Y0)))))))),
% 0.22/0.39 inference(definition_unfolding,[],[f152,f146,f155,f162,f143,f160,f162])).
% 0.22/0.39 thf(f160,plain,(
% 0.22/0.39 (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ (Y0 @ Y1)))))))),
% 0.22/0.39 inference(definition_unfolding,[],[f140,f131,f143,f131])).
% 0.22/0.39 thf(f131,plain,(
% 0.22/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.22/0.39 inference(cnf_transformation,[],[f67])).
% 0.22/0.39 thf(f67,plain,(
% 0.22/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.22/0.39 inference(fool_elimination,[],[f66])).
% 0.22/0.39 thf(f66,plain,(
% 0.22/0.39 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.22/0.39 inference(rectify,[],[f2])).
% 0.22/0.39 thf(f2,axiom,(
% 0.22/0.39 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.22/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.22/0.39 thf(f140,plain,(
% 0.22/0.39 (mexists_ind = (^[Y0 : mu > $i > $o]: (mnot @ (mforall_ind @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))))))),
% 0.22/0.39 inference(cnf_transformation,[],[f109])).
% 0.22/0.39 thf(f109,plain,(
% 0.22/0.39 (mexists_ind = (^[Y0 : mu > $i > $o]: (mnot @ (mforall_ind @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))))))),
% 0.22/0.39 inference(fool_elimination,[],[f108])).
% 0.22/0.39 thf(f108,plain,(
% 0.22/0.39 ((^[X0 : mu > $i > $o] : (mnot @ (mforall_ind @ (^[X1 : mu] : (mnot @ (X0 @ X1)))))) = mexists_ind)),
% 0.22/0.39 inference(rectify,[],[f16])).
% 0.22/0.39 thf(f16,axiom,(
% 0.22/0.39 ((^[X3 : mu > $i > $o] : (mnot @ (mforall_ind @ (^[X0 : mu] : (mnot @ (X3 @ X0)))))) = mexists_ind)),
% 0.22/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_ind)).
% 0.22/0.39 thf(f143,plain,(
% 0.22/0.39 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.22/0.39 inference(cnf_transformation,[],[f91])).
% 0.22/0.39 thf(f91,plain,(
% 0.22/0.39 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.22/0.39 inference(fool_elimination,[],[f90])).
% 0.22/0.39 thf(f90,plain,(
% 0.22/0.39 ((^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : ((exists_in_world @ X2 @ X1) => (X0 @ X2 @ X1)))) = mforall_ind)),
% 0.22/0.39 inference(rectify,[],[f15])).
% 0.22/0.39 thf(f15,axiom,(
% 0.22/0.39 ((^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : ((exists_in_world @ X0 @ X2) => (X3 @ X0 @ X2)))) = mforall_ind)),
% 0.22/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind)).
% 0.22/0.39 thf(f162,plain,(
% 0.22/0.39 (mdia_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.22/0.39 inference(definition_unfolding,[],[f124,f131,f119,f131])).
% 0.22/0.39 thf(f119,plain,(
% 0.22/0.39 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))))),
% 0.22/0.39 inference(cnf_transformation,[],[f49])).
% 0.22/0.39 thf(f49,plain,(
% 0.22/0.39 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))))),
% 0.22/0.39 inference(fool_elimination,[],[f48])).
% 0.22/0.39 thf(f48,plain,(
% 0.22/0.39 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_s4 @ X1 @ X2) | (X0 @ X2)))) = mbox_s4)),
% 0.22/0.39 inference(rectify,[],[f32])).
% 0.22/0.39 thf(f32,axiom,(
% 0.22/0.39 ((^[X3 : $i > $o, X2 : $i] : (! [X6] : (~(rel_s4 @ X2 @ X6) | (X3 @ X6)))) = mbox_s4)),
% 0.22/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s4)).
% 0.22/0.39 thf(f124,plain,(
% 0.22/0.39 (mdia_s4 = (^[Y0 : $i > $o]: (mnot @ (mbox_s4 @ (mnot @ Y0)))))),
% 0.22/0.39 inference(cnf_transformation,[],[f105])).
% 0.22/0.39 thf(f105,plain,(
% 0.22/0.39 (mdia_s4 = (^[Y0 : $i > $o]: (mnot @ (mbox_s4 @ (mnot @ Y0)))))),
% 0.22/0.39 inference(fool_elimination,[],[f104])).
% 0.22/0.39 thf(f104,plain,(
% 0.22/0.39 ((^[X0 : $i > $o] : (mnot @ (mbox_s4 @ (mnot @ X0)))) = mdia_s4)),
% 0.22/0.39 inference(rectify,[],[f33])).
% 0.22/0.39 thf(f33,axiom,(
% 0.22/0.39 ((^[X3 : $i > $o] : (mnot @ (mbox_s4 @ (mnot @ X3)))) = mdia_s4)),
% 0.22/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_s4)).
% 0.22/0.39 thf(f155,plain,(
% 0.22/0.39 (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)))))),
% 0.22/0.39 inference(definition_unfolding,[],[f129,f151,f131])).
% 0.22/0.39 thf(f151,plain,(
% 0.22/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.22/0.39 inference(cnf_transformation,[],[f43])).
% 0.22/0.39 thf(f43,plain,(
% 0.22/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.22/0.39 inference(fool_elimination,[],[f42])).
% 0.22/0.39 thf(f42,plain,(
% 0.22/0.39 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.22/0.39 inference(rectify,[],[f3])).
% 0.22/0.39 thf(f3,axiom,(
% 0.22/0.39 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))))),
% 0.22/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.22/0.39 thf(f129,plain,(
% 0.22/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.22/0.39 inference(cnf_transformation,[],[f69])).
% 0.22/0.39 thf(f69,plain,(
% 0.22/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.22/0.39 inference(fool_elimination,[],[f68])).
% 0.22/0.39 thf(f68,plain,(
% 0.22/0.39 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.22/0.39 inference(rectify,[],[f9])).
% 0.22/0.39 thf(f9,axiom,(
% 0.22/0.39 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.22/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.22/0.39 thf(f146,plain,(
% 0.22/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.22/0.39 inference(cnf_transformation,[],[f97])).
% 0.22/0.39 thf(f97,plain,(
% 0.22/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.22/0.39 inference(fool_elimination,[],[f96])).
% 0.22/0.39 thf(f96,plain,(
% 0.22/0.39 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.22/0.39 inference(rectify,[],[f28])).
% 0.22/0.39 thf(f28,axiom,(
% 0.22/0.39 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.22/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.22/0.39 thf(f152,plain,(
% 0.22/0.39 ($true != (mvalid @ (mimplies @ (mdia_s4 @ (mforall_ind @ (^[Y0 : mu]: (f @ Y0)))) @ (mexists_ind @ (^[Y0 : mu]: (mdia_s4 @ (f @ Y0)))))))),
% 0.22/0.39 inference(cnf_transformation,[],[f111])).
% 0.22/0.39 thf(f111,plain,(
% 0.22/0.39 ($true != (mvalid @ (mimplies @ (mdia_s4 @ (mforall_ind @ (^[Y0 : mu]: (f @ Y0)))) @ (mexists_ind @ (^[Y0 : mu]: (mdia_s4 @ (f @ Y0)))))))),
% 0.22/0.39 inference(flattening,[],[f87])).
% 0.22/0.39 thf(f87,plain,(
% 0.22/0.39 ~($true = (mvalid @ (mimplies @ (mdia_s4 @ (mforall_ind @ (^[Y0 : mu]: (f @ Y0)))) @ (mexists_ind @ (^[Y0 : mu]: (mdia_s4 @ (f @ Y0)))))))),
% 0.22/0.39 inference(fool_elimination,[],[f86])).
% 0.22/0.39 thf(f86,plain,(
% 0.22/0.39 ~(mvalid @ (mimplies @ (mdia_s4 @ (mforall_ind @ (^[X0 : mu] : (f @ X0)))) @ (mexists_ind @ (^[X1 : mu] : (mdia_s4 @ (f @ X1))))))),
% 0.22/0.39 inference(rectify,[],[f38])).
% 0.22/0.39 thf(f38,negated_conjecture,(
% 0.22/0.39 ~(mvalid @ (mimplies @ (mdia_s4 @ (mforall_ind @ (^[X0 : mu] : (f @ X0)))) @ (mexists_ind @ (^[X0 : mu] : (mdia_s4 @ (f @ X0))))))),
% 0.22/0.39 inference(negated_conjecture,[],[f37])).
% 0.22/0.39 thf(f37,conjecture,(
% 0.22/0.39 (mvalid @ (mimplies @ (mdia_s4 @ (mforall_ind @ (^[X0 : mu] : (f @ X0)))) @ (mexists_ind @ (^[X0 : mu] : (mdia_s4 @ (f @ X0))))))),
% 0.22/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)).
% 0.22/0.39 thf(f220,plain,(
% 0.22/0.39 ((exists_in_world @ (sK0 @ sK2) @ sK3) = $false) | ($false = (rel_s4 @ sK2 @ sK3))),
% 0.22/0.39 inference(trivial_inequality_removal,[],[f218])).
% 0.22/0.39 thf(f218,plain,(
% 0.22/0.39 ((exists_in_world @ (sK0 @ sK2) @ sK3) = $false) | ($false = (rel_s4 @ sK2 @ sK3)) | ($true = $false)),
% 0.22/0.39 inference(superposition,[],[f180,f215])).
% 0.22/0.39 thf(f215,plain,(
% 0.22/0.39 ( ! [X0 : $i] : (($false = (f @ (sK0 @ sK2) @ X0)) | ((rel_s4 @ sK2 @ X0) = $false)) )),
% 0.22/0.39 inference(trivial_inequality_removal,[],[f212])).
% 0.22/0.39 thf(f212,plain,(
% 0.22/0.39 ( ! [X0 : $i] : (($true = $false) | ($false = (f @ (sK0 @ sK2) @ X0)) | ((rel_s4 @ sK2 @ X0) = $false)) )),
% 0.22/0.39 inference(superposition,[],[f190,f150])).
% 0.22/0.39 thf(f150,plain,(
% 0.22/0.39 ( ! [X0 : $i] : (($true = (exists_in_world @ (sK0 @ X0) @ X0))) )),
% 0.22/0.39 inference(cnf_transformation,[],[f115])).
% 0.22/0.39 thf(f115,plain,(
% 0.22/0.39 ! [X0] : ($true = (exists_in_world @ (sK0 @ X0) @ X0))),
% 0.22/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f47,f114])).
% 0.22/0.39 thf(f114,plain,(
% 0.22/0.39 ! [X0] : (? [X1 : mu] : ((exists_in_world @ X1 @ X0) = $true) => ($true = (exists_in_world @ (sK0 @ X0) @ X0)))),
% 0.22/0.39 introduced(choice_axiom,[])).
% 0.22/0.39 thf(f47,plain,(
% 0.22/0.39 ! [X0] : ? [X1 : mu] : ((exists_in_world @ X1 @ X0) = $true)),
% 0.22/0.39 inference(fool_elimination,[],[f46])).
% 0.22/0.39 thf(f46,plain,(
% 0.22/0.39 ! [X0] : ? [X1 : mu] : (exists_in_world @ X1 @ X0)),
% 0.22/0.39 inference(rectify,[],[f14])).
% 0.22/0.39 thf(f14,axiom,(
% 0.22/0.39 ! [X6] : ? [X0 : mu] : (exists_in_world @ X0 @ X6)),
% 0.22/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty_ax)).
% 0.22/0.39 thf(f190,plain,(
% 0.22/0.39 ( ! [X2 : $i,X1 : mu] : (($false = (exists_in_world @ X1 @ sK2)) | ((f @ X1 @ X2) = $false) | ($false = (rel_s4 @ sK2 @ X2))) )),
% 0.22/0.39 inference(not_proxy_clausification,[],[f189])).
% 0.22/0.39 thf(f189,plain,(
% 0.22/0.39 ( ! [X2 : $i,X1 : mu] : (($true = (~ (f @ X1 @ X2))) | ($false = (rel_s4 @ sK2 @ X2)) | ($false = (exists_in_world @ X1 @ sK2))) )),
% 0.22/0.39 inference(not_proxy_clausification,[],[f188])).
% 0.22/0.39 thf(f188,plain,(
% 0.22/0.39 ( ! [X2 : $i,X1 : mu] : (($true = (~ (rel_s4 @ sK2 @ X2))) | ($true = (~ (f @ X1 @ X2))) | ($false = (exists_in_world @ X1 @ sK2))) )),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f187])).
% 0.22/0.39 thf(f187,plain,(
% 0.22/0.39 ( ! [X2 : $i,X1 : mu] : (($false = (exists_in_world @ X1 @ sK2)) | (((~ (f @ X1 @ X2)) | (~ (rel_s4 @ sK2 @ X2))) = $true)) )),
% 0.22/0.39 inference(beta_eta_normalization,[],[f186])).
% 0.22/0.39 thf(f186,plain,(
% 0.22/0.39 ( ! [X2 : $i,X1 : mu] : (($true = ((^[Y0 : $i]: ((~ (f @ X1 @ Y0)) | (~ (rel_s4 @ sK2 @ Y0)))) @ X2)) | ($false = (exists_in_world @ X1 @ sK2))) )),
% 0.22/0.39 inference(pi_clausification,[],[f185])).
% 0.22/0.39 thf(f185,plain,(
% 0.22/0.39 ( ! [X1 : mu] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (f @ X1 @ Y0)) | (~ (rel_s4 @ sK2 @ Y0)))))) | ($false = (exists_in_world @ X1 @ sK2))) )),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f184])).
% 0.22/0.39 thf(f184,plain,(
% 0.22/0.39 ( ! [X1 : mu] : ((((exists_in_world @ X1 @ sK2) => (!! @ $i @ (^[Y0 : $i]: ((~ (f @ X1 @ Y0)) | (~ (rel_s4 @ sK2 @ Y0)))))) = $true)) )),
% 0.22/0.39 inference(beta_eta_normalization,[],[f183])).
% 0.22/0.39 thf(f183,plain,(
% 0.22/0.39 ( ! [X1 : mu] : (($true = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((~ (f @ Y0 @ Y1)) | (~ (rel_s4 @ sK2 @ Y1))))))) @ X1))) )),
% 0.22/0.39 inference(pi_clausification,[],[f182])).
% 0.22/0.39 thf(f182,plain,(
% 0.22/0.39 ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((~ (f @ Y0 @ Y1)) | (~ (rel_s4 @ sK2 @ Y1)))))))) = $true)),
% 0.22/0.39 inference(not_proxy_clausification,[],[f171])).
% 0.22/0.39 thf(f171,plain,(
% 0.22/0.39 ((~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((~ (f @ Y0 @ Y1)) | (~ (rel_s4 @ sK2 @ Y1))))))))) = $false)),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f170])).
% 0.22/0.39 thf(f180,plain,(
% 0.22/0.39 ( ! [X1 : mu] : (($true = (f @ X1 @ sK3)) | ($false = (exists_in_world @ X1 @ sK3))) )),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f179])).
% 0.22/0.39 thf(f179,plain,(
% 0.22/0.39 ( ! [X1 : mu] : (($true = ((exists_in_world @ X1 @ sK3) => (f @ X1 @ sK3)))) )),
% 0.22/0.39 inference(beta_eta_normalization,[],[f178])).
% 0.22/0.39 thf(f178,plain,(
% 0.22/0.39 ( ! [X1 : mu] : ((((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK3) => (f @ Y0 @ sK3))) @ X1) = $true)) )),
% 0.22/0.39 inference(pi_clausification,[],[f177])).
% 0.22/0.39 thf(f177,plain,(
% 0.22/0.39 ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK3) => (f @ Y0 @ sK3)))) = $true)),
% 0.22/0.39 inference(not_proxy_clausification,[],[f176])).
% 0.22/0.39 thf(f176,plain,(
% 0.22/0.39 ((~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK3) => (f @ Y0 @ sK3))))) = $false)),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f174])).
% 0.22/0.39 thf(f207,plain,(
% 0.22/0.39 ((exists_in_world @ (sK0 @ sK2) @ sK3) = $true)),
% 0.22/0.39 inference(trivial_inequality_removal,[],[f206])).
% 0.22/0.39 thf(f206,plain,(
% 0.22/0.39 ((exists_in_world @ (sK0 @ sK2) @ sK3) = $true) | ($true != $true)),
% 0.22/0.39 inference(superposition,[],[f205,f150])).
% 0.22/0.39 thf(f205,plain,(
% 0.22/0.39 ( ! [X0 : mu] : (($true != (exists_in_world @ X0 @ sK2)) | ($true = (exists_in_world @ X0 @ sK3))) )),
% 0.22/0.39 inference(trivial_inequality_removal,[],[f204])).
% 0.22/0.39 thf(f204,plain,(
% 0.22/0.39 ( ! [X0 : mu] : (($true != $true) | ($true != (exists_in_world @ X0 @ sK2)) | ($true = (exists_in_world @ X0 @ sK3))) )),
% 0.22/0.39 inference(superposition,[],[f135,f181])).
% 0.22/0.39 thf(f135,plain,(
% 0.22/0.39 ( ! [X2 : mu,X0 : $i,X1 : $i] : (($true != (rel_s4 @ X1 @ X0)) | ((exists_in_world @ X2 @ X1) != $true) | ((exists_in_world @ X2 @ X0) = $true)) )),
% 0.22/0.39 inference(cnf_transformation,[],[f113])).
% 0.22/0.39 thf(f113,plain,(
% 0.22/0.39 ! [X0,X1,X2 : mu] : (($true != (rel_s4 @ X1 @ X0)) | ((exists_in_world @ X2 @ X1) != $true) | ((exists_in_world @ X2 @ X0) = $true))),
% 0.22/0.39 inference(flattening,[],[f112])).
% 0.22/0.39 thf(f112,plain,(
% 0.22/0.39 ! [X0,X1,X2 : mu] : (((exists_in_world @ X2 @ X0) = $true) | (((exists_in_world @ X2 @ X1) != $true) | ($true != (rel_s4 @ X1 @ X0))))),
% 0.22/0.39 inference(ennf_transformation,[],[f89])).
% 0.22/0.39 thf(f89,plain,(
% 0.22/0.39 ! [X0,X1,X2 : mu] : ((((exists_in_world @ X2 @ X1) = $true) & ($true = (rel_s4 @ X1 @ X0))) => ((exists_in_world @ X2 @ X0) = $true))),
% 0.22/0.39 inference(fool_elimination,[],[f88])).
% 0.22/0.39 thf(f88,plain,(
% 0.22/0.39 ! [X0,X1,X2 : mu] : (((rel_s4 @ X1 @ X0) & (exists_in_world @ X2 @ X1)) => (exists_in_world @ X2 @ X0))),
% 0.22/0.39 inference(rectify,[],[f36])).
% 0.22/0.39 thf(f36,axiom,(
% 0.22/0.39 ! [X2,X6,X0 : mu] : (((rel_s4 @ X6 @ X2) & (exists_in_world @ X0 @ X6)) => (exists_in_world @ X0 @ X2))),
% 0.22/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cumulative_ax)).
% 0.22/0.39 % SZS output end Proof for theBenchmark
% 0.22/0.39 % (21405)------------------------------
% 0.22/0.39 % (21405)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39 % (21405)Termination reason: Refutation
% 0.22/0.39
% 0.22/0.39 % (21405)Memory used [KB]: 5756
% 0.22/0.39 % (21405)Time elapsed: 0.017 s
% 0.22/0.39 % (21405)Instructions burned: 17 (million)
% 0.22/0.39 % (21405)------------------------------
% 0.22/0.39 % (21405)------------------------------
% 0.22/0.39 % (21402)Success in time 0.038 s
% 0.22/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------