TSTP Solution File: SYO399^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO399^1 : 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 : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 09:04:17 EDT 2024
% Result : Theorem 0.14s 0.39s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO399^1 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 09:52:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.36 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
% 0.14/0.37 % (26406)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37 % (26406)Instruction limit reached!
% 0.14/0.37 % (26406)------------------------------
% 0.14/0.37 % (26406)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (26406)Termination reason: Unknown
% 0.14/0.37 % (26406)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (26406)Memory used [KB]: 1023
% 0.14/0.37 % (26406)Time elapsed: 0.003 s
% 0.14/0.37 % (26406)Instructions burned: 2 (million)
% 0.14/0.37 % (26406)------------------------------
% 0.14/0.37 % (26406)------------------------------
% 0.14/0.38 % (26403)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.38 % (26405)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)
% 0.14/0.38 % (26404)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)
% 0.14/0.38 % (26407)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)
% 0.14/0.38 % (26409)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.38 % (26408)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)
% 0.14/0.38 % (26407)Instruction limit reached!
% 0.14/0.38 % (26407)------------------------------
% 0.14/0.38 % (26407)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (26407)Termination reason: Unknown
% 0.14/0.38 % (26407)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (26407)Memory used [KB]: 1023
% 0.14/0.38 % (26407)Time elapsed: 0.003 s
% 0.14/0.38 % (26407)Instructions burned: 2 (million)
% 0.14/0.38 % (26407)------------------------------
% 0.14/0.38 % (26407)------------------------------
% 0.14/0.38 % (26410)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)
% 0.14/0.38 % (26404)Instruction limit reached!
% 0.14/0.38 % (26404)------------------------------
% 0.14/0.38 % (26404)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (26404)Termination reason: Unknown
% 0.14/0.38 % (26404)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (26404)Memory used [KB]: 1023
% 0.14/0.38 % (26404)Time elapsed: 0.005 s
% 0.14/0.38 % (26404)Instructions burned: 5 (million)
% 0.14/0.38 % (26404)------------------------------
% 0.14/0.38 % (26404)------------------------------
% 0.14/0.38 % (26410)Instruction limit reached!
% 0.14/0.38 % (26410)------------------------------
% 0.14/0.38 % (26410)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (26410)Termination reason: Unknown
% 0.14/0.38 % (26410)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (26410)Memory used [KB]: 1023
% 0.14/0.38 % (26410)Time elapsed: 0.005 s
% 0.14/0.38 % (26410)Instructions burned: 4 (million)
% 0.14/0.38 % (26410)------------------------------
% 0.14/0.38 % (26410)------------------------------
% 0.14/0.38 % (26403)First to succeed.
% 0.14/0.38 % (26408)Refutation not found, incomplete strategy
% 0.14/0.38 % (26408)------------------------------
% 0.14/0.38 % (26408)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (26408)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.38
% 0.14/0.38
% 0.14/0.38 % (26408)Memory used [KB]: 5628
% 0.14/0.38 % (26408)Time elapsed: 0.007 s
% 0.14/0.38 % (26408)Instructions burned: 9 (million)
% 0.14/0.38 % (26408)------------------------------
% 0.14/0.38 % (26408)------------------------------
% 0.14/0.39 % (26409)Also succeeded, but the first one will report.
% 0.14/0.39 % (26411)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.14/0.39 % (26403)Refutation found. Thanks to Tanya!
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39 % SZS output start Proof for theBenchmark
% 0.14/0.39 thf(type_def_5, type, mu: $tType).
% 0.14/0.39 thf(func_def_0, type, mu: $tType).
% 0.14/0.39 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.14/0.39 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_15, type, mtrue: $i > $o).
% 0.14/0.39 thf(func_def_16, type, mfalse: $i > $o).
% 0.14/0.39 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.14/0.39 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.14/0.39 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.14/0.39 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.14/0.39 thf(func_def_33, type, rel_k: $i > $i > $o).
% 0.14/0.39 thf(func_def_34, type, mbox_k: ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_35, type, mdia_k: ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_36, type, p: $i > $o).
% 0.14/0.39 thf(func_def_37, type, q: $i > $o).
% 0.14/0.39 thf(func_def_38, type, r: $i > $o).
% 0.14/0.39 thf(f155,plain,(
% 0.14/0.39 $false),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f154])).
% 0.14/0.39 thf(f154,plain,(
% 0.14/0.39 ($false = $true)),
% 0.14/0.39 inference(beta_eta_normalization,[],[f153])).
% 0.14/0.39 thf(f153,plain,(
% 0.14/0.39 ($false = ((^[Y0 : $i]: ($true)) @ sK1))),
% 0.14/0.39 inference(sigma_clausification,[],[f152])).
% 0.14/0.39 thf(f152,plain,(
% 0.14/0.39 ($true != (!! @ $i @ (^[Y0 : $i]: ($true))))),
% 0.14/0.39 inference(boolean_simplification,[],[f151])).
% 0.14/0.39 thf(f151,plain,(
% 0.14/0.39 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((~ (q @ Y1)) | (~ (r @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((~ (q @ Y1)) | (~ (r @ Y1))))))))))),
% 0.14/0.39 inference(boolean_simplification,[],[f150])).
% 0.14/0.39 thf(f150,plain,(
% 0.14/0.39 ($true != (!! @ $i @ (^[Y0 : $i]: (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((~ (q @ Y1)) | (~ (r @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((~ (q @ Y1)) | (~ (r @ Y1))))))))))))),
% 0.14/0.39 inference(boolean_simplification,[],[f149])).
% 0.14/0.39 thf(f149,plain,(
% 0.14/0.39 ((!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((~ (q @ Y1)) | (~ (r @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((~ (q @ Y1)) | (~ (r @ Y1)))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((~ (q @ Y1)) | (~ (r @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((~ (q @ Y1)) | (~ (r @ Y1)))))))))))) != $true)),
% 0.14/0.39 inference(boolean_simplification,[],[f148])).
% 0.14/0.39 thf(f148,plain,(
% 0.14/0.39 ($true != (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (~ ((~ (q @ Y1)) | (~ (r @ Y1))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((~ (q @ Y1)) | (~ (r @ Y1)))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((~ (q @ Y1)) | (~ (r @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (~ ((~ (q @ Y1)) | (~ (r @ Y1)))))))))))))))),
% 0.14/0.39 inference(boolean_simplification,[],[f147])).
% 0.14/0.39 thf(f147,plain,(
% 0.14/0.39 ($true != (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (~ ((~ (q @ Y1)) | (~ (r @ Y1))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((~ (q @ Y1)) | (~ (r @ Y1)))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((~ (q @ Y1)) | (~ (r @ Y1))))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (~ ((~ (q @ Y1)) | (~ (r @ Y1)))))))))))))))))),
% 0.14/0.39 inference(beta_eta_normalization,[],[f146])).
% 0.14/0.39 thf(f146,plain,(
% 0.14/0.39 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_k @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ q @ r))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[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)))) @ q @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))) @ r))))))),
% 0.14/0.39 inference(definition_unfolding,[],[f132,f120,f139,f118,f145,f136,f107,f137,f118])).
% 0.14/0.39 thf(f137,plain,(
% 0.14/0.39 (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)))))),
% 0.14/0.39 inference(definition_unfolding,[],[f129,f127,f118])).
% 0.14/0.39 thf(f127,plain,(
% 0.14/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.14/0.39 inference(cnf_transformation,[],[f42])).
% 0.14/0.39 thf(f42,plain,(
% 0.14/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.14/0.39 inference(fool_elimination,[],[f41])).
% 0.14/0.39 thf(f41,plain,(
% 0.14/0.39 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 0.14/0.39 inference(rectify,[],[f4])).
% 0.14/0.39 thf(f4,axiom,(
% 0.14/0.39 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))) = mor)),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.14/0.39 thf(f129,plain,(
% 0.14/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.39 inference(cnf_transformation,[],[f87])).
% 0.14/0.39 thf(f87,plain,(
% 0.14/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.39 inference(fool_elimination,[],[f86])).
% 0.14/0.39 thf(f86,plain,(
% 0.14/0.39 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.14/0.39 inference(rectify,[],[f6])).
% 0.14/0.39 thf(f6,axiom,(
% 0.14/0.39 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.14/0.39 thf(f107,plain,(
% 0.14/0.39 (mbox_k = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.14/0.39 inference(cnf_transformation,[],[f63])).
% 0.14/0.39 thf(f63,plain,(
% 0.14/0.39 (mbox_k = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.14/0.39 inference(fool_elimination,[],[f62])).
% 0.14/0.39 thf(f62,plain,(
% 0.14/0.39 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_k @ X1 @ X2)))) = mbox_k)),
% 0.14/0.39 inference(rectify,[],[f32])).
% 0.14/0.39 thf(f32,axiom,(
% 0.14/0.39 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_k @ X2 @ X7)))) = mbox_k)),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_k)).
% 0.14/0.39 thf(f136,plain,(
% 0.14/0.39 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.14/0.39 inference(definition_unfolding,[],[f108,f118,f127,f118,f118])).
% 0.14/0.39 thf(f108,plain,(
% 0.14/0.39 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.14/0.39 inference(cnf_transformation,[],[f60])).
% 0.14/0.39 thf(f60,plain,(
% 0.14/0.39 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.14/0.39 inference(fool_elimination,[],[f59])).
% 0.14/0.39 thf(f59,plain,(
% 0.14/0.39 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.14/0.39 inference(rectify,[],[f5])).
% 0.14/0.39 thf(f5,axiom,(
% 0.14/0.39 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.14/0.39 thf(f145,plain,(
% 0.14/0.39 (mdia_k = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_k @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.14/0.39 inference(definition_unfolding,[],[f117,f118,f107,f118])).
% 0.14/0.39 thf(f117,plain,(
% 0.14/0.39 (mdia_k = (^[Y0 : $i > $o]: (mnot @ (mbox_k @ (mnot @ Y0)))))),
% 0.14/0.39 inference(cnf_transformation,[],[f93])).
% 0.14/0.39 thf(f93,plain,(
% 0.14/0.39 (mdia_k = (^[Y0 : $i > $o]: (mnot @ (mbox_k @ (mnot @ Y0)))))),
% 0.14/0.39 inference(fool_elimination,[],[f92])).
% 0.14/0.39 thf(f92,plain,(
% 0.14/0.39 ((^[X0 : $i > $o] : (mnot @ (mbox_k @ (mnot @ X0)))) = mdia_k)),
% 0.14/0.39 inference(rectify,[],[f33])).
% 0.14/0.39 thf(f33,axiom,(
% 0.14/0.39 ((^[X3 : $i > $o] : (mnot @ (mbox_k @ (mnot @ X3)))) = mdia_k)),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_k)).
% 0.14/0.39 thf(f118,plain,(
% 0.14/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.39 inference(cnf_transformation,[],[f65])).
% 0.14/0.39 thf(f65,plain,(
% 0.14/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.39 inference(fool_elimination,[],[f64])).
% 0.14/0.39 thf(f64,plain,(
% 0.14/0.39 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.14/0.39 inference(rectify,[],[f3])).
% 0.14/0.39 thf(f3,axiom,(
% 0.14/0.39 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.14/0.39 thf(f139,plain,(
% 0.14/0.39 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))))),
% 0.14/0.39 inference(definition_unfolding,[],[f109,f136,f137,f137])).
% 0.14/0.39 thf(f109,plain,(
% 0.14/0.39 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.14/0.39 inference(cnf_transformation,[],[f50])).
% 0.14/0.39 thf(f50,plain,(
% 0.14/0.39 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.14/0.39 inference(fool_elimination,[],[f49])).
% 0.14/0.39 thf(f49,plain,(
% 0.14/0.39 (mequiv = (^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))))),
% 0.14/0.39 inference(rectify,[],[f8])).
% 0.14/0.39 thf(f8,axiom,(
% 0.14/0.39 (mequiv = (^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))))),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv)).
% 0.14/0.39 thf(f120,plain,(
% 0.14/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.39 inference(cnf_transformation,[],[f97])).
% 0.14/0.39 thf(f97,plain,(
% 0.14/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.39 inference(fool_elimination,[],[f96])).
% 0.14/0.39 thf(f96,plain,(
% 0.14/0.39 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.14/0.39 inference(rectify,[],[f28])).
% 0.14/0.39 thf(f28,axiom,(
% 0.14/0.39 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.14/0.39 thf(f132,plain,(
% 0.14/0.39 ((mvalid @ (mequiv @ (mnot @ (mdia_k @ (mand @ q @ r))) @ (mbox_k @ (mimplies @ q @ (mnot @ r))))) != $true)),
% 0.14/0.39 inference(cnf_transformation,[],[f101])).
% 0.14/0.39 thf(f101,plain,(
% 0.14/0.39 ((mvalid @ (mequiv @ (mnot @ (mdia_k @ (mand @ q @ r))) @ (mbox_k @ (mimplies @ q @ (mnot @ r))))) != $true)),
% 0.14/0.39 inference(flattening,[],[f48])).
% 0.14/0.39 thf(f48,plain,(
% 0.14/0.39 ~((mvalid @ (mequiv @ (mnot @ (mdia_k @ (mand @ q @ r))) @ (mbox_k @ (mimplies @ q @ (mnot @ r))))) = $true)),
% 0.14/0.39 inference(fool_elimination,[],[f47])).
% 0.14/0.39 thf(f47,plain,(
% 0.14/0.39 ~(mvalid @ (mequiv @ (mnot @ (mdia_k @ (mand @ q @ r))) @ (mbox_k @ (mimplies @ q @ (mnot @ r)))))),
% 0.14/0.39 inference(rectify,[],[f35])).
% 0.14/0.39 thf(f35,negated_conjecture,(
% 0.14/0.39 ~(mvalid @ (mequiv @ (mnot @ (mdia_k @ (mand @ q @ r))) @ (mbox_k @ (mimplies @ q @ (mnot @ r)))))),
% 0.14/0.39 inference(negated_conjecture,[],[f34])).
% 0.14/0.39 thf(f34,conjecture,(
% 0.14/0.39 (mvalid @ (mequiv @ (mnot @ (mdia_k @ (mand @ q @ r))) @ (mbox_k @ (mimplies @ q @ (mnot @ r)))))),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.14/0.39 % SZS output end Proof for theBenchmark
% 0.14/0.39 % (26403)------------------------------
% 0.14/0.39 % (26403)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (26403)Termination reason: Refutation
% 0.14/0.39
% 0.14/0.39 % (26403)Memory used [KB]: 5628
% 0.14/0.39 % (26403)Time elapsed: 0.011 s
% 0.14/0.39 % (26403)Instructions burned: 11 (million)
% 0.14/0.39 % (26403)------------------------------
% 0.14/0.39 % (26403)------------------------------
% 0.14/0.39 % (26402)Success in time 0.011 s
% 0.14/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------