TSTP Solution File: SYO418^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO418^1 : 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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n004.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 09:04:22 EDT 2024
% Result : Theorem 0.20s 0.37s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO418^1 : TPTP v8.2.0. Released v4.0.0.
% 0.13/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon May 20 11:02:23 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.34 This is a TH0_THM_EQU_NAR problem
% 0.20/0.35 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
% 0.20/0.36 % (28722)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)
% 0.20/0.36 % (28723)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)
% 0.20/0.36 % (28724)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.36 % (28722)Instruction limit reached!
% 0.20/0.36 % (28722)------------------------------
% 0.20/0.36 % (28722)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.36 % (28722)Termination reason: Unknown
% 0.20/0.36 % (28722)Termination phase: shuffling
% 0.20/0.36
% 0.20/0.36 % (28722)Memory used [KB]: 1023
% 0.20/0.36 % (28722)Time elapsed: 0.002 s
% 0.20/0.36 % (28722)Instructions burned: 2 (million)
% 0.20/0.36 % (28722)------------------------------
% 0.20/0.36 % (28722)------------------------------
% 0.20/0.37 % (28725)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)
% 0.20/0.37 % (28718)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.20/0.37 % (28725)Instruction limit reached!
% 0.20/0.37 % (28725)------------------------------
% 0.20/0.37 % (28725)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.37 % (28725)Termination reason: Unknown
% 0.20/0.37 % (28725)Termination phase: Property scanning
% 0.20/0.37
% 0.20/0.37 % (28725)Memory used [KB]: 1023
% 0.20/0.37 % (28725)Time elapsed: 0.003 s
% 0.20/0.37 % (28725)Instructions burned: 4 (million)
% 0.20/0.37 % (28725)------------------------------
% 0.20/0.37 % (28725)------------------------------
% 0.20/0.37 % (28721)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.37 % (28723)Refutation not found, incomplete strategy
% 0.20/0.37 % (28723)------------------------------
% 0.20/0.37 % (28723)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.37 % (28723)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.37
% 0.20/0.37
% 0.20/0.37 % (28723)Memory used [KB]: 5628
% 0.20/0.37 % (28723)Time elapsed: 0.004 s
% 0.20/0.37 % (28723)Instructions burned: 7 (million)
% 0.20/0.37 % (28723)------------------------------
% 0.20/0.37 % (28723)------------------------------
% 0.20/0.37 % (28721)Instruction limit reached!
% 0.20/0.37 % (28721)------------------------------
% 0.20/0.37 % (28721)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.37 % (28721)Termination reason: Unknown
% 0.20/0.37 % (28721)Termination phase: shuffling
% 0.20/0.37
% 0.20/0.37 % (28721)Memory used [KB]: 1023
% 0.20/0.37 % (28721)Time elapsed: 0.003 s
% 0.20/0.37 % (28721)Instructions burned: 2 (million)
% 0.20/0.37 % (28721)------------------------------
% 0.20/0.37 % (28721)------------------------------
% 0.20/0.37 % (28719)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)
% 0.20/0.37 % (28724)First to succeed.
% 0.20/0.37 % (28719)Instruction limit reached!
% 0.20/0.37 % (28719)------------------------------
% 0.20/0.37 % (28719)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.37 % (28719)Termination reason: Unknown
% 0.20/0.37 % (28719)Termination phase: Property scanning
% 0.20/0.37
% 0.20/0.37 % (28719)Memory used [KB]: 1023
% 0.20/0.37 % (28719)Time elapsed: 0.003 s
% 0.20/0.37 % (28719)Instructions burned: 5 (million)
% 0.20/0.37 % (28719)------------------------------
% 0.20/0.37 % (28719)------------------------------
% 0.20/0.37 % (28724)Refutation found. Thanks to Tanya!
% 0.20/0.37 % SZS status Theorem for theBenchmark
% 0.20/0.37 % SZS output start Proof for theBenchmark
% 0.20/0.37 thf(type_def_5, type, mu: $tType).
% 0.20/0.37 thf(func_def_0, type, mu: $tType).
% 0.20/0.37 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.20/0.37 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.37 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.20/0.37 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.37 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.37 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.37 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.37 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.37 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.37 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.20/0.37 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.20/0.37 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.20/0.37 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.20/0.37 thf(func_def_15, type, mtrue: $i > $o).
% 0.20/0.37 thf(func_def_16, type, mfalse: $i > $o).
% 0.20/0.37 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.20/0.37 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.20/0.37 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.20/0.37 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.20/0.37 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.20/0.37 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.20/0.37 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.20/0.37 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.20/0.37 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.20/0.37 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.20/0.37 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.20/0.37 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.20/0.37 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.20/0.37 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.20/0.37 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.20/0.37 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.20/0.37 thf(func_def_33, type, rel_d: $i > $i > $o).
% 0.20/0.37 thf(func_def_34, type, mbox_d: ($i > $o) > $i > $o).
% 0.20/0.37 thf(func_def_35, type, mdia_d: ($i > $o) > $i > $o).
% 0.20/0.37 thf(func_def_36, type, p: $i > $o).
% 0.20/0.37 thf(func_def_37, type, q: $i > $o).
% 0.20/0.37 thf(func_def_54, type, sK1: $i > $i).
% 0.20/0.37 thf(f184,plain,(
% 0.20/0.37 $false),
% 0.20/0.37 inference(trivial_inequality_removal,[],[f183])).
% 0.20/0.37 thf(f183,plain,(
% 0.20/0.37 ($false = $true)),
% 0.20/0.37 inference(backward_demodulation,[],[f178,f182])).
% 0.20/0.37 thf(f182,plain,(
% 0.20/0.37 ($false = (p @ (sK1 @ sK2)))),
% 0.20/0.37 inference(trivial_inequality_removal,[],[f179])).
% 0.20/0.37 thf(f179,plain,(
% 0.20/0.37 ($false = (p @ (sK1 @ sK2))) | ($false = $true)),
% 0.20/0.37 inference(superposition,[],[f168,f155])).
% 0.20/0.37 thf(f155,plain,(
% 0.20/0.37 ( ! [X1 : $i] : (((rel_d @ X1 @ (sK1 @ X1)) = $true)) )),
% 0.20/0.37 inference(sigma_clausification,[],[f154])).
% 0.20/0.37 thf(f154,plain,(
% 0.20/0.37 ( ! [X1 : $i] : (((?? @ $i @ (rel_d @ X1)) = $true)) )),
% 0.20/0.37 inference(beta_eta_normalization,[],[f153])).
% 0.20/0.37 thf(f153,plain,(
% 0.20/0.37 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (?? @ $i @ (rel_d @ Y0))) @ X1))) )),
% 0.20/0.37 inference(pi_clausification,[],[f152])).
% 0.20/0.37 thf(f152,plain,(
% 0.20/0.37 ($true = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (rel_d @ Y0)))))),
% 0.20/0.37 inference(beta_eta_normalization,[],[f151])).
% 0.20/0.37 thf(f151,plain,(
% 0.20/0.37 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))) @ rel_d) = $true)),
% 0.20/0.37 inference(definition_unfolding,[],[f129,f121])).
% 0.20/0.37 thf(f121,plain,(
% 0.20/0.37 (mserial = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.20/0.37 inference(cnf_transformation,[],[f86])).
% 0.20/0.37 thf(f86,plain,(
% 0.20/0.37 (mserial = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.20/0.37 inference(fool_elimination,[],[f85])).
% 0.20/0.37 thf(f85,plain,(
% 0.20/0.37 ((^[X0 : $i > $i > $o] : (! [X1] : ? [X2] : (X0 @ X1 @ X2))) = mserial)),
% 0.20/0.37 inference(rectify,[],[f20])).
% 0.20/0.37 thf(f20,axiom,(
% 0.20/0.37 ((^[X6 : $i > $i > $o] : (! [X8] : ? [X9] : (X6 @ X8 @ X9))) = mserial)),
% 0.20/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mserial)).
% 0.20/0.37 thf(f129,plain,(
% 0.20/0.37 ((mserial @ rel_d) = $true)),
% 0.20/0.37 inference(cnf_transformation,[],[f100])).
% 0.20/0.37 thf(f100,plain,(
% 0.20/0.37 ((mserial @ rel_d) = $true)),
% 0.20/0.37 inference(fool_elimination,[],[f99])).
% 0.20/0.37 thf(f99,plain,(
% 0.20/0.37 (mserial @ rel_d)),
% 0.20/0.37 inference(rectify,[],[f34])).
% 0.20/0.37 thf(f34,axiom,(
% 0.20/0.37 (mserial @ rel_d)),
% 0.20/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
% 0.20/0.37 thf(f168,plain,(
% 0.20/0.37 ( ! [X1 : $i] : (($false = (rel_d @ sK2 @ X1)) | ($false = (p @ X1))) )),
% 0.20/0.37 inference(binary_proxy_clausification,[],[f166])).
% 0.20/0.37 thf(f166,plain,(
% 0.20/0.37 ( ! [X1 : $i] : (($false = ((p @ X1) | (~ (q @ X1)))) | ($false = (rel_d @ sK2 @ X1))) )),
% 0.20/0.37 inference(not_proxy_clausification,[],[f165])).
% 0.20/0.37 thf(f165,plain,(
% 0.20/0.37 ( ! [X1 : $i] : (($true = (~ (rel_d @ sK2 @ X1))) | ($false = ((p @ X1) | (~ (q @ X1))))) )),
% 0.20/0.37 inference(not_proxy_clausification,[],[f164])).
% 0.20/0.37 thf(f164,plain,(
% 0.20/0.37 ( ! [X1 : $i] : (((~ ((p @ X1) | (~ (q @ X1)))) = $true) | ($true = (~ (rel_d @ sK2 @ X1)))) )),
% 0.20/0.37 inference(binary_proxy_clausification,[],[f163])).
% 0.20/0.37 thf(f163,plain,(
% 0.20/0.37 ( ! [X1 : $i] : ((((~ ((p @ X1) | (~ (q @ X1)))) | (~ (rel_d @ sK2 @ X1))) = $true)) )),
% 0.20/0.37 inference(beta_eta_normalization,[],[f162])).
% 0.20/0.37 thf(f162,plain,(
% 0.20/0.37 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ ((p @ Y0) | (~ (q @ Y0)))) | (~ (rel_d @ sK2 @ Y0)))) @ X1))) )),
% 0.20/0.37 inference(pi_clausification,[],[f161])).
% 0.20/0.37 thf(f161,plain,(
% 0.20/0.37 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ ((p @ Y0) | (~ (q @ Y0)))) | (~ (rel_d @ sK2 @ Y0))))))),
% 0.20/0.37 inference(not_proxy_clausification,[],[f160])).
% 0.20/0.37 thf(f160,plain,(
% 0.20/0.37 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((p @ Y0) | (~ (q @ Y0)))) | (~ (rel_d @ sK2 @ Y0)))))) = $false)),
% 0.20/0.37 inference(binary_proxy_clausification,[],[f158])).
% 0.20/0.37 thf(f158,plain,(
% 0.20/0.37 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((p @ Y0) | (~ (q @ Y0)))) | (~ (rel_d @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0))))))))),
% 0.20/0.37 inference(beta_eta_normalization,[],[f157])).
% 0.20/0.37 thf(f157,plain,(
% 0.20/0.37 ($false = ((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ ((p @ Y1) | (~ (q @ Y1)))) | (~ (rel_d @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_d @ Y0 @ Y1)))))))) @ sK2))),
% 0.20/0.37 inference(sigma_clausification,[],[f156])).
% 0.20/0.37 thf(f156,plain,(
% 0.20/0.37 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ ((p @ Y1) | (~ (q @ Y1)))) | (~ (rel_d @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_d @ Y0 @ Y1))))))))))),
% 0.20/0.37 inference(beta_eta_normalization,[],[f150])).
% 0.20/0.37 thf(f150,plain,(
% 0.20/0.37 (((^[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]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_d @ Y1 @ Y2)))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_d @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[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)))) @ q @ p)))) != $true)),
% 0.20/0.37 inference(definition_unfolding,[],[f125,f110,f141,f111,f149,f141])).
% 0.20/0.37 thf(f149,plain,(
% 0.20/0.37 (mdia_d = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_d @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.20/0.37 inference(definition_unfolding,[],[f123,f139,f111,f139])).
% 0.20/0.37 thf(f139,plain,(
% 0.20/0.37 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.37 inference(cnf_transformation,[],[f53])).
% 0.20/0.37 thf(f53,plain,(
% 0.20/0.37 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.37 inference(fool_elimination,[],[f52])).
% 0.20/0.37 thf(f52,plain,(
% 0.20/0.37 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.20/0.37 inference(rectify,[],[f3])).
% 0.20/0.37 thf(f3,axiom,(
% 0.20/0.37 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.20/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.20/0.37 thf(f123,plain,(
% 0.20/0.37 (mdia_d = (^[Y0 : $i > $o]: (mnot @ (mbox_d @ (mnot @ Y0)))))),
% 0.20/0.37 inference(cnf_transformation,[],[f82])).
% 0.20/0.37 thf(f82,plain,(
% 0.20/0.37 (mdia_d = (^[Y0 : $i > $o]: (mnot @ (mbox_d @ (mnot @ Y0)))))),
% 0.20/0.37 inference(fool_elimination,[],[f81])).
% 0.20/0.37 thf(f81,plain,(
% 0.20/0.37 ((^[X0 : $i > $o] : (mnot @ (mbox_d @ (mnot @ X0)))) = mdia_d)),
% 0.20/0.37 inference(rectify,[],[f33])).
% 0.20/0.37 thf(f33,axiom,(
% 0.20/0.37 ((^[X3 : $i > $o] : (mnot @ (mbox_d @ (mnot @ X3)))) = mdia_d)),
% 0.20/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_d)).
% 0.20/0.37 thf(f111,plain,(
% 0.20/0.37 (mbox_d = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_d @ Y1 @ Y2)))))))))),
% 0.20/0.37 inference(cnf_transformation,[],[f43])).
% 0.20/0.37 thf(f43,plain,(
% 0.20/0.37 (mbox_d = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_d @ Y1 @ Y2)))))))))),
% 0.20/0.37 inference(fool_elimination,[],[f42])).
% 0.20/0.37 thf(f42,plain,(
% 0.20/0.37 (mbox_d = (^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_d @ X1 @ X2) | (X0 @ X2)))))),
% 0.20/0.37 inference(rectify,[],[f32])).
% 0.20/0.37 thf(f32,axiom,(
% 0.20/0.37 (mbox_d = (^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_d @ X2 @ X7) | (X3 @ X7)))))),
% 0.20/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_d)).
% 0.20/0.37 thf(f141,plain,(
% 0.20/0.37 (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)))))),
% 0.20/0.37 inference(definition_unfolding,[],[f120,f132,f139])).
% 0.20/0.37 thf(f132,plain,(
% 0.20/0.37 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.20/0.37 inference(cnf_transformation,[],[f55])).
% 0.20/0.37 thf(f55,plain,(
% 0.20/0.37 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.20/0.37 inference(fool_elimination,[],[f54])).
% 0.20/0.37 thf(f54,plain,(
% 0.20/0.37 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor)),
% 0.20/0.37 inference(rectify,[],[f4])).
% 0.20/0.37 thf(f4,axiom,(
% 0.20/0.37 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))) = mor)),
% 0.20/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.20/0.37 thf(f120,plain,(
% 0.20/0.37 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.37 inference(cnf_transformation,[],[f71])).
% 0.20/0.37 thf(f71,plain,(
% 0.20/0.37 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.37 inference(fool_elimination,[],[f70])).
% 0.20/0.37 thf(f70,plain,(
% 0.20/0.37 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.20/0.37 inference(rectify,[],[f6])).
% 0.20/0.37 thf(f6,axiom,(
% 0.20/0.37 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.20/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.20/0.37 thf(f110,plain,(
% 0.20/0.37 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.37 inference(cnf_transformation,[],[f98])).
% 0.20/0.37 thf(f98,plain,(
% 0.20/0.37 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.37 inference(fool_elimination,[],[f97])).
% 0.20/0.37 thf(f97,plain,(
% 0.20/0.37 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.20/0.37 inference(rectify,[],[f28])).
% 0.20/0.37 thf(f28,axiom,(
% 0.20/0.37 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.20/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.20/0.37 thf(f125,plain,(
% 0.20/0.37 ((mvalid @ (mimplies @ (mbox_d @ p) @ (mdia_d @ (mimplies @ q @ p)))) != $true)),
% 0.20/0.37 inference(cnf_transformation,[],[f104])).
% 0.20/0.37 thf(f104,plain,(
% 0.20/0.37 ((mvalid @ (mimplies @ (mbox_d @ p) @ (mdia_d @ (mimplies @ q @ p)))) != $true)),
% 0.20/0.37 inference(flattening,[],[f69])).
% 0.20/0.37 thf(f69,plain,(
% 0.20/0.37 ~((mvalid @ (mimplies @ (mbox_d @ p) @ (mdia_d @ (mimplies @ q @ p)))) = $true)),
% 0.20/0.37 inference(fool_elimination,[],[f68])).
% 0.20/0.37 thf(f68,plain,(
% 0.20/0.37 ~(mvalid @ (mimplies @ (mbox_d @ p) @ (mdia_d @ (mimplies @ q @ p))))),
% 0.20/0.37 inference(rectify,[],[f36])).
% 0.20/0.37 thf(f36,negated_conjecture,(
% 0.20/0.37 ~(mvalid @ (mimplies @ (mbox_d @ p) @ (mdia_d @ (mimplies @ q @ p))))),
% 0.20/0.37 inference(negated_conjecture,[],[f35])).
% 0.20/0.37 thf(f35,conjecture,(
% 0.20/0.37 (mvalid @ (mimplies @ (mbox_d @ p) @ (mdia_d @ (mimplies @ q @ p))))),
% 0.20/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.20/0.37 thf(f178,plain,(
% 0.20/0.37 ($true = (p @ (sK1 @ sK2)))),
% 0.20/0.37 inference(trivial_inequality_removal,[],[f176])).
% 0.20/0.37 thf(f176,plain,(
% 0.20/0.37 ($true = (p @ (sK1 @ sK2))) | ($false = $true)),
% 0.20/0.37 inference(superposition,[],[f155,f174])).
% 0.20/0.37 thf(f174,plain,(
% 0.20/0.37 ( ! [X1 : $i] : (($false = (rel_d @ sK2 @ X1)) | ($true = (p @ X1))) )),
% 0.20/0.37 inference(not_proxy_clausification,[],[f173])).
% 0.20/0.37 thf(f173,plain,(
% 0.20/0.37 ( ! [X1 : $i] : (($true = (p @ X1)) | ($true = (~ (rel_d @ sK2 @ X1)))) )),
% 0.20/0.37 inference(binary_proxy_clausification,[],[f172])).
% 0.20/0.37 thf(f172,plain,(
% 0.20/0.37 ( ! [X1 : $i] : (($true = ((p @ X1) | (~ (rel_d @ sK2 @ X1))))) )),
% 0.20/0.37 inference(beta_eta_normalization,[],[f171])).
% 0.20/0.37 thf(f171,plain,(
% 0.20/0.37 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))) @ X1) = $true)) )),
% 0.20/0.37 inference(pi_clausification,[],[f170])).
% 0.20/0.37 thf(f170,plain,(
% 0.20/0.37 ($true = (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0))))))),
% 0.20/0.37 inference(not_proxy_clausification,[],[f159])).
% 0.20/0.37 thf(f159,plain,(
% 0.20/0.37 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))))))),
% 0.20/0.37 inference(binary_proxy_clausification,[],[f158])).
% 0.20/0.37 % SZS output end Proof for theBenchmark
% 0.20/0.37 % (28724)------------------------------
% 0.20/0.37 % (28724)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.37 % (28724)Termination reason: Refutation
% 0.20/0.37
% 0.20/0.37 % (28724)Memory used [KB]: 5628
% 0.20/0.37 % (28724)Time elapsed: 0.008 s
% 0.20/0.37 % (28724)Instructions burned: 11 (million)
% 0.20/0.37 % (28724)------------------------------
% 0.20/0.37 % (28724)------------------------------
% 0.20/0.37 % (28717)Success in time 0.03 s
% 0.20/0.37 % Vampire---4.8 exiting
%------------------------------------------------------------------------------