TSTP Solution File: SYO413^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO413^1 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n025.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 09:04:20 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO413^1 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.35 % Computer : n025.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 08:51:23 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 This is a TH0_THM_EQU_NAR problem
% 0.15/0.36 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/sandbox/benchmark/theBenchmark.p
% 0.15/0.38 % (26227)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)
% 0.15/0.38 % (26225)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.38 % (26228)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.38 % (26226)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)
% 0.15/0.38 % (26229)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)
% 0.15/0.38 % (26231)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 % (26230)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)
% 0.15/0.38 % (26232)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)
% 0.15/0.38 % (26229)Instruction limit reached!
% 0.15/0.38 % (26229)------------------------------
% 0.15/0.38 % (26229)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (26229)Termination reason: Unknown
% 0.15/0.38 % (26229)Termination phase: shuffling
% 0.15/0.38
% 0.15/0.38 % (26229)Memory used [KB]: 1023
% 0.15/0.38 % (26229)Time elapsed: 0.003 s
% 0.15/0.38 % (26229)Instructions burned: 2 (million)
% 0.15/0.38 % (26229)------------------------------
% 0.15/0.38 % (26229)------------------------------
% 0.15/0.38 % (26228)Instruction limit reached!
% 0.15/0.38 % (26228)------------------------------
% 0.15/0.38 % (26228)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (26228)Termination reason: Unknown
% 0.15/0.38 % (26228)Termination phase: shuffling
% 0.15/0.38
% 0.15/0.38 % (26228)Memory used [KB]: 1023
% 0.15/0.38 % (26228)Time elapsed: 0.004 s
% 0.15/0.38 % (26228)Instructions burned: 3 (million)
% 0.15/0.38 % (26228)------------------------------
% 0.15/0.38 % (26228)------------------------------
% 0.15/0.38 % (26232)Instruction limit reached!
% 0.15/0.38 % (26232)------------------------------
% 0.15/0.38 % (26232)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (26232)Termination reason: Unknown
% 0.15/0.38 % (26232)Termination phase: shuffling
% 0.15/0.38
% 0.15/0.38 % (26232)Memory used [KB]: 1023
% 0.15/0.38 % (26232)Time elapsed: 0.004 s
% 0.15/0.38 % (26232)Instructions burned: 3 (million)
% 0.15/0.38 % (26232)------------------------------
% 0.15/0.38 % (26232)------------------------------
% 0.15/0.38 % (26226)Instruction limit reached!
% 0.15/0.38 % (26226)------------------------------
% 0.15/0.38 % (26226)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (26226)Termination reason: Unknown
% 0.15/0.38 % (26226)Termination phase: Property scanning
% 0.15/0.38
% 0.15/0.38 % (26226)Memory used [KB]: 1023
% 0.15/0.38 % (26226)Time elapsed: 0.005 s
% 0.15/0.38 % (26226)Instructions burned: 5 (million)
% 0.15/0.38 % (26226)------------------------------
% 0.15/0.38 % (26226)------------------------------
% 0.15/0.38 % (26230)Refutation not found, incomplete strategy
% 0.15/0.38 % (26230)------------------------------
% 0.15/0.38 % (26230)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (26230)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.38
% 0.15/0.38
% 0.15/0.38 % (26230)Memory used [KB]: 5628
% 0.15/0.38 % (26230)Time elapsed: 0.007 s
% 0.15/0.38 % (26230)Instructions burned: 8 (million)
% 0.15/0.38 % (26230)------------------------------
% 0.15/0.38 % (26230)------------------------------
% 0.15/0.38 % (26225)First to succeed.
% 0.15/0.38 % (26227)Also succeeded, but the first one will report.
% 0.15/0.39 % (26225)Refutation found. Thanks to Tanya!
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39 % SZS output start Proof for theBenchmark
% 0.15/0.39 thf(type_def_5, type, mu: $tType).
% 0.15/0.39 thf(func_def_0, type, mu: $tType).
% 0.15/0.39 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.15/0.39 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_15, type, mtrue: $i > $o).
% 0.15/0.39 thf(func_def_16, type, mfalse: $i > $o).
% 0.15/0.39 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.15/0.39 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.15/0.39 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.15/0.39 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.15/0.39 thf(func_def_33, type, rel_k: $i > $i > $o).
% 0.15/0.39 thf(func_def_34, type, mbox_k: ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_35, type, mdia_k: ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_36, type, p: $i > $o).
% 0.15/0.39 thf(func_def_37, type, q: $i > $o).
% 0.15/0.39 thf(f182,plain,(
% 0.15/0.39 $false),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f180])).
% 0.15/0.39 thf(f180,plain,(
% 0.15/0.39 ($true = $false)),
% 0.15/0.39 inference(superposition,[],[f179,f175])).
% 0.15/0.39 thf(f175,plain,(
% 0.15/0.39 ((q @ sK2) = $false)),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f172])).
% 0.15/0.39 thf(f172,plain,(
% 0.15/0.39 ((q @ sK2) = $false) | ($true = $false)),
% 0.15/0.39 inference(superposition,[],[f160,f171])).
% 0.15/0.39 thf(f171,plain,(
% 0.15/0.39 ((rel_k @ sK1 @ sK2) = $true)),
% 0.15/0.39 inference(not_proxy_clausification,[],[f168])).
% 0.15/0.39 thf(f168,plain,(
% 0.15/0.39 ($false = (~ (rel_k @ sK1 @ sK2)))),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f167])).
% 0.15/0.39 thf(f167,plain,(
% 0.15/0.39 (((~ (p @ sK2)) | (~ (rel_k @ sK1 @ sK2))) = $false)),
% 0.15/0.39 inference(beta_eta_normalization,[],[f166])).
% 0.15/0.39 thf(f166,plain,(
% 0.15/0.39 (((^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0)))) @ sK2) = $false)),
% 0.15/0.39 inference(sigma_clausification,[],[f151])).
% 0.15/0.39 thf(f151,plain,(
% 0.15/0.39 ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))) = $false)),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f150])).
% 0.15/0.39 thf(f150,plain,(
% 0.15/0.39 ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_k @ sK1 @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) = $false)),
% 0.15/0.39 inference(beta_eta_normalization,[],[f149])).
% 0.15/0.39 thf(f149,plain,(
% 0.15/0.39 (((^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_k @ Y0 @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1))))))) @ sK1) = $false)),
% 0.15/0.39 inference(sigma_clausification,[],[f148])).
% 0.15/0.39 thf(f148,plain,(
% 0.15/0.39 ($true != (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_k @ Y0 @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))))))),
% 0.15/0.39 inference(boolean_simplification,[],[f147])).
% 0.15/0.39 thf(f147,plain,(
% 0.15/0.39 ((!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_k @ Y0 @ Y1))))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))))))) != $true)),
% 0.15/0.39 inference(beta_eta_normalization,[],[f146])).
% 0.15/0.39 thf(f146,plain,(
% 0.15/0.39 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[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)))) @ ((^[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) @ ((^[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)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_k @ Y1 @ Y2)))))))) @ q) @ ((^[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)))) @ q)))) != $true)),
% 0.15/0.39 inference(definition_unfolding,[],[f104,f107,f137,f145,f137,f117,f145])).
% 0.15/0.39 thf(f117,plain,(
% 0.15/0.39 (mbox_k = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_k @ Y1 @ Y2)))))))))),
% 0.15/0.39 inference(cnf_transformation,[],[f77])).
% 0.15/0.39 thf(f77,plain,(
% 0.15/0.39 (mbox_k = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_k @ Y1 @ Y2)))))))))),
% 0.15/0.39 inference(fool_elimination,[],[f76])).
% 0.15/0.39 thf(f76,plain,(
% 0.15/0.39 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_k @ X1 @ X2) | (X0 @ X2)))) = mbox_k)),
% 0.15/0.39 inference(rectify,[],[f32])).
% 0.15/0.39 thf(f32,axiom,(
% 0.15/0.39 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_k @ X2 @ X7) | (X3 @ X7)))) = mbox_k)),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_k)).
% 0.15/0.39 thf(f145,plain,(
% 0.15/0.39 (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)))))),
% 0.15/0.39 inference(definition_unfolding,[],[f103,f129,f117,f129])).
% 0.15/0.39 thf(f129,plain,(
% 0.15/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.15/0.39 inference(cnf_transformation,[],[f62])).
% 0.15/0.39 thf(f62,plain,(
% 0.15/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.15/0.39 inference(fool_elimination,[],[f61])).
% 0.15/0.39 thf(f61,plain,(
% 0.15/0.39 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.15/0.39 inference(rectify,[],[f3])).
% 0.15/0.39 thf(f3,axiom,(
% 0.15/0.39 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.15/0.39 thf(f103,plain,(
% 0.15/0.39 (mdia_k = (^[Y0 : $i > $o]: (mnot @ (mbox_k @ (mnot @ Y0)))))),
% 0.15/0.39 inference(cnf_transformation,[],[f79])).
% 0.15/0.39 thf(f79,plain,(
% 0.15/0.39 (mdia_k = (^[Y0 : $i > $o]: (mnot @ (mbox_k @ (mnot @ Y0)))))),
% 0.15/0.39 inference(fool_elimination,[],[f78])).
% 0.15/0.39 thf(f78,plain,(
% 0.15/0.39 ((^[X0 : $i > $o] : (mnot @ (mbox_k @ (mnot @ X0)))) = mdia_k)),
% 0.15/0.39 inference(rectify,[],[f33])).
% 0.15/0.39 thf(f33,axiom,(
% 0.15/0.39 ((^[X3 : $i > $o] : (mnot @ (mbox_k @ (mnot @ X3)))) = mdia_k)),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_k)).
% 0.15/0.39 thf(f137,plain,(
% 0.15/0.39 (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)))))),
% 0.15/0.39 inference(definition_unfolding,[],[f109,f121,f129])).
% 0.15/0.39 thf(f121,plain,(
% 0.15/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.15/0.39 inference(cnf_transformation,[],[f58])).
% 0.15/0.39 thf(f58,plain,(
% 0.15/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.15/0.39 inference(fool_elimination,[],[f57])).
% 0.15/0.39 thf(f57,plain,(
% 0.15/0.39 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor)),
% 0.15/0.39 inference(rectify,[],[f4])).
% 0.15/0.39 thf(f4,axiom,(
% 0.15/0.39 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))) = mor)),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.15/0.39 thf(f109,plain,(
% 0.15/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.15/0.39 inference(cnf_transformation,[],[f42])).
% 0.15/0.39 thf(f42,plain,(
% 0.15/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.15/0.39 inference(fool_elimination,[],[f41])).
% 0.15/0.39 thf(f41,plain,(
% 0.15/0.39 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.15/0.39 inference(rectify,[],[f6])).
% 0.15/0.39 thf(f6,axiom,(
% 0.15/0.39 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.15/0.39 thf(f107,plain,(
% 0.15/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.15/0.39 inference(cnf_transformation,[],[f56])).
% 0.15/0.39 thf(f56,plain,(
% 0.15/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.15/0.39 inference(fool_elimination,[],[f55])).
% 0.15/0.39 thf(f55,plain,(
% 0.15/0.39 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.15/0.39 inference(rectify,[],[f28])).
% 0.15/0.39 thf(f28,axiom,(
% 0.15/0.39 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.15/0.39 thf(f104,plain,(
% 0.15/0.39 ((mvalid @ (mimplies @ (mdia_k @ p) @ (mimplies @ (mbox_k @ q) @ (mdia_k @ q)))) != $true)),
% 0.15/0.39 inference(cnf_transformation,[],[f101])).
% 0.15/0.39 thf(f101,plain,(
% 0.15/0.39 ((mvalid @ (mimplies @ (mdia_k @ p) @ (mimplies @ (mbox_k @ q) @ (mdia_k @ q)))) != $true)),
% 0.15/0.39 inference(flattening,[],[f96])).
% 0.15/0.39 thf(f96,plain,(
% 0.15/0.39 ~((mvalid @ (mimplies @ (mdia_k @ p) @ (mimplies @ (mbox_k @ q) @ (mdia_k @ q)))) = $true)),
% 0.15/0.39 inference(fool_elimination,[],[f95])).
% 0.15/0.39 thf(f95,plain,(
% 0.15/0.39 ~(mvalid @ (mimplies @ (mdia_k @ p) @ (mimplies @ (mbox_k @ q) @ (mdia_k @ q))))),
% 0.15/0.39 inference(rectify,[],[f35])).
% 0.15/0.39 thf(f35,negated_conjecture,(
% 0.15/0.39 ~(mvalid @ (mimplies @ (mdia_k @ p) @ (mimplies @ (mbox_k @ q) @ (mdia_k @ q))))),
% 0.15/0.39 inference(negated_conjecture,[],[f34])).
% 0.15/0.39 thf(f34,conjecture,(
% 0.15/0.39 (mvalid @ (mimplies @ (mdia_k @ p) @ (mimplies @ (mbox_k @ q) @ (mdia_k @ q))))),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.15/0.39 thf(f160,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ((q @ X1) = $false)) )),
% 0.15/0.39 inference(not_proxy_clausification,[],[f159])).
% 0.15/0.39 thf(f159,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (((~ (rel_k @ sK1 @ X1)) = $true) | ((q @ X1) = $false)) )),
% 0.15/0.39 inference(not_proxy_clausification,[],[f158])).
% 0.15/0.39 thf(f158,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (((~ (q @ X1)) = $true) | ((~ (rel_k @ sK1 @ X1)) = $true)) )),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f157])).
% 0.15/0.39 thf(f157,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (($true = ((~ (q @ X1)) | (~ (rel_k @ sK1 @ X1))))) )),
% 0.15/0.39 inference(beta_eta_normalization,[],[f156])).
% 0.15/0.39 thf(f156,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))) @ X1))) )),
% 0.15/0.39 inference(pi_clausification,[],[f155])).
% 0.15/0.39 thf(f155,plain,(
% 0.15/0.39 ((!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0))))) = $true)),
% 0.15/0.39 inference(not_proxy_clausification,[],[f154])).
% 0.15/0.39 thf(f154,plain,(
% 0.15/0.39 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) = $false)),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f152])).
% 0.15/0.39 thf(f152,plain,(
% 0.15/0.39 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_k @ sK1 @ Y0))))))) = $false)),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f150])).
% 0.15/0.39 thf(f179,plain,(
% 0.15/0.39 ($true = (q @ sK2))),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f176])).
% 0.15/0.39 thf(f176,plain,(
% 0.15/0.39 ($true = (q @ sK2)) | ($true = $false)),
% 0.15/0.39 inference(superposition,[],[f165,f171])).
% 0.15/0.39 thf(f165,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ($true = (q @ X1))) )),
% 0.15/0.39 inference(not_proxy_clausification,[],[f164])).
% 0.15/0.39 thf(f164,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (((~ (rel_k @ sK1 @ X1)) = $true) | ($true = (q @ X1))) )),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f163])).
% 0.15/0.39 thf(f163,plain,(
% 0.15/0.39 ( ! [X1 : $i] : ((((q @ X1) | (~ (rel_k @ sK1 @ X1))) = $true)) )),
% 0.15/0.39 inference(beta_eta_normalization,[],[f162])).
% 0.15/0.39 thf(f162,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((q @ Y0) | (~ (rel_k @ sK1 @ Y0)))) @ X1))) )),
% 0.15/0.39 inference(pi_clausification,[],[f161])).
% 0.15/0.39 thf(f161,plain,(
% 0.15/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_k @ sK1 @ Y0))))))),
% 0.15/0.39 inference(not_proxy_clausification,[],[f153])).
% 0.15/0.39 thf(f153,plain,(
% 0.15/0.39 ((~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_k @ sK1 @ Y0)))))) = $false)),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f152])).
% 0.15/0.39 % SZS output end Proof for theBenchmark
% 0.15/0.39 % (26225)------------------------------
% 0.15/0.39 % (26225)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (26225)Termination reason: Refutation
% 0.15/0.39
% 0.15/0.39 % (26225)Memory used [KB]: 5628
% 0.15/0.39 % (26225)Time elapsed: 0.010 s
% 0.15/0.39 % (26225)Instructions burned: 11 (million)
% 0.15/0.39 % (26225)------------------------------
% 0.15/0.39 % (26225)------------------------------
% 0.15/0.39 % (26224)Success in time 0.012 s
% 0.15/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------