TSTP Solution File: SYO455^2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO455^2 : 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 : n003.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 09:04:41 EDT 2024
% Result : Theorem 0.11s 0.35s
% Output : Refutation 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SYO455^2 : TPTP v8.2.0. Released v4.0.0.
% 0.09/0.12 % 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
% 0.11/0.33 % Computer : n003.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon May 20 08:33:23 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 This is a TH0_THM_EQU_NAR problem
% 0.11/0.33 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
% 0.11/0.34 % (23491)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.11/0.34 % (23487)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)
% 0.11/0.34 % (23486)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)
% 0.11/0.34 % (23486)Instruction limit reached!
% 0.11/0.34 % (23486)------------------------------
% 0.11/0.34 % (23486)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.34 % (23486)Termination reason: Unknown
% 0.11/0.34 % (23486)Termination phase: Clausification
% 0.11/0.34
% 0.11/0.34 % (23486)Memory used [KB]: 1023
% 0.11/0.34 % (23486)Time elapsed: 0.004 s
% 0.11/0.34 % (23486)Instructions burned: 6 (million)
% 0.11/0.34 % (23486)------------------------------
% 0.11/0.34 % (23486)------------------------------
% 0.11/0.34 % (23485)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.11/0.35 % (23490)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)
% 0.11/0.35 % (23489)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)
% 0.11/0.35 % (23491)First to succeed.
% 0.11/0.35 % (23488)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.11/0.35 % (23488)Instruction limit reached!
% 0.11/0.35 % (23488)------------------------------
% 0.11/0.35 % (23488)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35 % (23488)Termination reason: Unknown
% 0.11/0.35 % (23489)Instruction limit reached!
% 0.11/0.35 % (23489)------------------------------
% 0.11/0.35 % (23489)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35 % (23489)Termination reason: Unknown
% 0.11/0.35 % (23489)Termination phase: shuffling
% 0.11/0.35
% 0.11/0.35 % (23489)Memory used [KB]: 1023
% 0.11/0.35 % (23489)Time elapsed: 0.003 s
% 0.11/0.35 % (23489)Instructions burned: 3 (million)
% 0.11/0.35 % (23489)------------------------------
% 0.11/0.35 % (23489)------------------------------
% 0.11/0.35 % (23488)Termination phase: shuffling
% 0.11/0.35
% 0.11/0.35 % (23488)Memory used [KB]: 1023
% 0.11/0.35 % (23488)Time elapsed: 0.003 s
% 0.11/0.35 % (23488)Instructions burned: 3 (million)
% 0.11/0.35 % (23488)------------------------------
% 0.11/0.35 % (23488)------------------------------
% 0.11/0.35 % (23487)Also succeeded, but the first one will report.
% 0.11/0.35 % (23491)Refutation found. Thanks to Tanya!
% 0.11/0.35 % SZS status Theorem for theBenchmark
% 0.11/0.35 % SZS output start Proof for theBenchmark
% 0.11/0.35 thf(type_def_5, type, mu: $tType).
% 0.11/0.35 thf(func_def_0, type, mu: $tType).
% 0.11/0.35 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.11/0.35 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.11/0.35 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.11/0.35 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.11/0.35 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.11/0.35 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.11/0.35 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.11/0.35 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.11/0.35 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.11/0.35 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.11/0.35 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.11/0.35 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.11/0.35 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.11/0.35 thf(func_def_15, type, mtrue: $i > $o).
% 0.11/0.35 thf(func_def_16, type, mfalse: $i > $o).
% 0.11/0.35 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.11/0.35 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.11/0.35 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.11/0.35 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.11/0.35 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.11/0.35 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.11/0.35 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.11/0.35 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.11/0.35 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.11/0.35 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.11/0.35 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.11/0.35 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.11/0.35 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.11/0.35 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.11/0.35 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.11/0.35 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.11/0.35 thf(func_def_33, type, rel_d: $i > $i > $o).
% 0.11/0.35 thf(func_def_34, type, mbox_d: ($i > $o) > $i > $o).
% 0.11/0.35 thf(func_def_35, type, mdia_d: ($i > $o) > $i > $o).
% 0.11/0.35 thf(func_def_36, type, p: $i > $o).
% 0.11/0.35 thf(func_def_37, type, q: $i > $o).
% 0.11/0.35 thf(func_def_55, type, sK2: $i > $i).
% 0.11/0.35 thf(f197,plain,(
% 0.11/0.35 $false),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f196])).
% 0.11/0.35 thf(f196,plain,(
% 0.11/0.35 ($true = $false)),
% 0.11/0.35 inference(backward_demodulation,[],[f189,f195])).
% 0.11/0.35 thf(f195,plain,(
% 0.11/0.35 ($false = (p @ (sK2 @ sK1)))),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f194])).
% 0.11/0.35 thf(f194,plain,(
% 0.11/0.35 ($false = (p @ (sK2 @ sK1))) | ($true = $false)),
% 0.11/0.35 inference(forward_demodulation,[],[f193,f185])).
% 0.11/0.35 thf(f185,plain,(
% 0.11/0.35 ($false = (q @ (sK2 @ sK1)))),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f183])).
% 0.11/0.35 thf(f183,plain,(
% 0.11/0.35 ($false = (q @ (sK2 @ sK1))) | ($true = $false)),
% 0.11/0.35 inference(superposition,[],[f181,f177])).
% 0.11/0.35 thf(f177,plain,(
% 0.11/0.35 ( ! [X1 : $i] : (($false = (rel_d @ sK1 @ X1)) | ((q @ X1) = $false)) )),
% 0.11/0.35 inference(not_proxy_clausification,[],[f176])).
% 0.11/0.35 thf(f176,plain,(
% 0.11/0.35 ( ! [X1 : $i] : (($true = (~ (q @ X1))) | ($false = (rel_d @ sK1 @ X1))) )),
% 0.11/0.35 inference(not_proxy_clausification,[],[f175])).
% 0.11/0.35 thf(f175,plain,(
% 0.11/0.35 ( ! [X1 : $i] : (($true = (~ (rel_d @ sK1 @ X1))) | ($true = (~ (q @ X1)))) )),
% 0.11/0.35 inference(binary_proxy_clausification,[],[f174])).
% 0.11/0.35 thf(f174,plain,(
% 0.11/0.35 ( ! [X1 : $i] : (($true = ((~ (rel_d @ sK1 @ X1)) | (~ (q @ X1))))) )),
% 0.11/0.35 inference(beta_eta_normalization,[],[f173])).
% 0.11/0.35 thf(f173,plain,(
% 0.11/0.35 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_d @ sK1 @ Y0)) | (~ (q @ Y0)))) @ X1))) )),
% 0.11/0.35 inference(pi_clausification,[],[f172])).
% 0.11/0.35 thf(f172,plain,(
% 0.11/0.35 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_d @ sK1 @ Y0)) | (~ (q @ Y0))))))),
% 0.11/0.35 inference(not_proxy_clausification,[],[f156])).
% 0.11/0.35 thf(f156,plain,(
% 0.11/0.35 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_d @ sK1 @ Y0)) | (~ (q @ Y0)))))))),
% 0.11/0.35 inference(binary_proxy_clausification,[],[f155])).
% 0.11/0.35 thf(f155,plain,(
% 0.11/0.35 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_d @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_d @ sK1 @ Y0)) | ((~ (p @ Y0)) | (q @ Y0))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_d @ sK1 @ Y0)) | (~ (q @ Y0))))))))),
% 0.11/0.35 inference(beta_eta_normalization,[],[f154])).
% 0.11/0.35 thf(f154,plain,(
% 0.11/0.35 ($false = ((^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_d @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_d @ Y0 @ Y1)) | ((~ (p @ Y1)) | (q @ Y1))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_d @ Y0 @ Y1)) | (~ (q @ Y1)))))))) @ sK1))),
% 0.11/0.35 inference(sigma_clausification,[],[f153])).
% 0.11/0.35 thf(f153,plain,(
% 0.11/0.35 ($true != (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_d @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_d @ Y0 @ Y1)) | ((~ (p @ Y1)) | (q @ Y1))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_d @ Y0 @ Y1)) | (~ (q @ Y1))))))))))),
% 0.11/0.35 inference(boolean_simplification,[],[f152])).
% 0.11/0.35 thf(f152,plain,(
% 0.11/0.35 ((!! @ $i @ (^[Y0 : $i]: ((~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_d @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_d @ Y0 @ Y1)) | ((~ (p @ Y1)) | (q @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_d @ Y0 @ Y1)) | (~ (q @ Y1))))))))) != $true)),
% 0.11/0.35 inference(beta_eta_normalization,[],[f150])).
% 0.11/0.35 thf(f150,plain,(
% 0.11/0.35 ($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 > $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)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_d @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_d @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))) @ p) @ q))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_d @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ q))))),
% 0.11/0.35 inference(definition_unfolding,[],[f113,f127,f141,f140,f136,f136,f138,f106,f149])).
% 0.11/0.35 thf(f149,plain,(
% 0.11/0.35 (mdia_d = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_d @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.11/0.35 inference(definition_unfolding,[],[f124,f106,f136,f106])).
% 0.11/0.35 thf(f124,plain,(
% 0.11/0.35 (mdia_d = (^[Y0 : $i > $o]: (mnot @ (mbox_d @ (mnot @ Y0)))))),
% 0.11/0.35 inference(cnf_transformation,[],[f82])).
% 0.11/0.35 thf(f82,plain,(
% 0.11/0.35 (mdia_d = (^[Y0 : $i > $o]: (mnot @ (mbox_d @ (mnot @ Y0)))))),
% 0.11/0.35 inference(fool_elimination,[],[f81])).
% 0.11/0.35 thf(f81,plain,(
% 0.11/0.35 ((^[X0 : $i > $o] : (mnot @ (mbox_d @ (mnot @ X0)))) = mdia_d)),
% 0.11/0.35 inference(rectify,[],[f33])).
% 0.11/0.35 thf(f33,axiom,(
% 0.11/0.35 ((^[X3 : $i > $o] : (mnot @ (mbox_d @ (mnot @ X3)))) = mdia_d)),
% 0.11/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_d)).
% 0.11/0.35 thf(f106,plain,(
% 0.11/0.35 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.11/0.35 inference(cnf_transformation,[],[f95])).
% 0.11/0.35 thf(f95,plain,(
% 0.11/0.35 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.11/0.35 inference(fool_elimination,[],[f94])).
% 0.11/0.35 thf(f94,plain,(
% 0.11/0.35 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.11/0.35 inference(rectify,[],[f3])).
% 0.11/0.35 thf(f3,axiom,(
% 0.11/0.35 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.11/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.11/0.35 thf(f138,plain,(
% 0.11/0.35 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.11/0.35 inference(cnf_transformation,[],[f103])).
% 0.11/0.35 thf(f103,plain,(
% 0.11/0.35 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.11/0.35 inference(fool_elimination,[],[f102])).
% 0.11/0.35 thf(f102,plain,(
% 0.11/0.35 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 0.11/0.35 inference(rectify,[],[f4])).
% 0.11/0.35 thf(f4,axiom,(
% 0.11/0.35 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))) = mor)),
% 0.11/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.11/0.35 thf(f136,plain,(
% 0.11/0.35 (mbox_d = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_d @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.11/0.35 inference(cnf_transformation,[],[f56])).
% 0.11/0.35 thf(f56,plain,(
% 0.11/0.35 (mbox_d = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_d @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.11/0.35 inference(fool_elimination,[],[f55])).
% 0.11/0.35 thf(f55,plain,(
% 0.11/0.35 (mbox_d = (^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_d @ X1 @ X2)))))),
% 0.11/0.35 inference(rectify,[],[f32])).
% 0.11/0.35 thf(f32,axiom,(
% 0.11/0.35 (mbox_d = (^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_d @ X2 @ X7)))))),
% 0.11/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_d)).
% 0.11/0.35 thf(f140,plain,(
% 0.11/0.35 (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)))))))),
% 0.11/0.35 inference(definition_unfolding,[],[f125,f106,f138,f106,f106])).
% 0.11/0.35 thf(f125,plain,(
% 0.11/0.35 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.11/0.35 inference(cnf_transformation,[],[f99])).
% 0.11/0.35 thf(f99,plain,(
% 0.11/0.35 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.11/0.35 inference(fool_elimination,[],[f98])).
% 0.11/0.35 thf(f98,plain,(
% 0.11/0.35 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.11/0.35 inference(rectify,[],[f5])).
% 0.11/0.35 thf(f5,axiom,(
% 0.11/0.35 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.11/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.11/0.35 thf(f141,plain,(
% 0.11/0.35 (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)))))),
% 0.11/0.35 inference(definition_unfolding,[],[f128,f138,f106])).
% 0.11/0.35 thf(f128,plain,(
% 0.11/0.35 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.11/0.35 inference(cnf_transformation,[],[f101])).
% 0.11/0.35 thf(f101,plain,(
% 0.11/0.35 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.11/0.35 inference(fool_elimination,[],[f100])).
% 0.11/0.35 thf(f100,plain,(
% 0.11/0.35 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.11/0.35 inference(rectify,[],[f6])).
% 0.11/0.35 thf(f6,axiom,(
% 0.11/0.35 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.11/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.11/0.35 thf(f127,plain,(
% 0.11/0.35 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.11/0.35 inference(cnf_transformation,[],[f41])).
% 0.11/0.35 thf(f41,plain,(
% 0.11/0.35 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.11/0.35 inference(fool_elimination,[],[f40])).
% 0.11/0.35 thf(f40,plain,(
% 0.11/0.35 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.11/0.35 inference(rectify,[],[f28])).
% 0.11/0.35 thf(f28,axiom,(
% 0.11/0.35 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.11/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.11/0.35 thf(f113,plain,(
% 0.11/0.35 ((mvalid @ (mimplies @ (mand @ (mbox_d @ p) @ (mbox_d @ (mor @ (mnot @ p) @ q))) @ (mdia_d @ q))) != $true)),
% 0.11/0.35 inference(cnf_transformation,[],[f104])).
% 0.11/0.35 thf(f104,plain,(
% 0.11/0.35 ((mvalid @ (mimplies @ (mand @ (mbox_d @ p) @ (mbox_d @ (mor @ (mnot @ p) @ q))) @ (mdia_d @ q))) != $true)),
% 0.11/0.35 inference(flattening,[],[f84])).
% 0.11/0.35 thf(f84,plain,(
% 0.11/0.35 ~((mvalid @ (mimplies @ (mand @ (mbox_d @ p) @ (mbox_d @ (mor @ (mnot @ p) @ q))) @ (mdia_d @ q))) = $true)),
% 0.11/0.35 inference(fool_elimination,[],[f83])).
% 0.11/0.35 thf(f83,plain,(
% 0.11/0.35 ~(mvalid @ (mimplies @ (mand @ (mbox_d @ p) @ (mbox_d @ (mor @ (mnot @ p) @ q))) @ (mdia_d @ q)))),
% 0.11/0.35 inference(rectify,[],[f36])).
% 0.11/0.35 thf(f36,negated_conjecture,(
% 0.11/0.35 ~(mvalid @ (mimplies @ (mand @ (mbox_d @ p) @ (mbox_d @ (mor @ (mnot @ p) @ q))) @ (mdia_d @ q)))),
% 0.11/0.35 inference(negated_conjecture,[],[f35])).
% 0.11/0.35 thf(f35,conjecture,(
% 0.11/0.35 (mvalid @ (mimplies @ (mand @ (mbox_d @ p) @ (mbox_d @ (mor @ (mnot @ p) @ q))) @ (mdia_d @ q)))),
% 0.11/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.11/0.35 thf(f181,plain,(
% 0.11/0.35 ( ! [X1 : $i] : (($true = (rel_d @ X1 @ (sK2 @ X1)))) )),
% 0.11/0.35 inference(sigma_clausification,[],[f180])).
% 0.11/0.35 thf(f180,plain,(
% 0.11/0.35 ( ! [X1 : $i] : (($true = (?? @ $i @ (rel_d @ X1)))) )),
% 0.11/0.35 inference(beta_eta_normalization,[],[f179])).
% 0.11/0.35 thf(f179,plain,(
% 0.11/0.35 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (?? @ $i @ (rel_d @ Y0))) @ X1))) )),
% 0.11/0.35 inference(pi_clausification,[],[f178])).
% 0.11/0.35 thf(f178,plain,(
% 0.11/0.35 ($true = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (rel_d @ Y0)))))),
% 0.11/0.35 inference(beta_eta_normalization,[],[f151])).
% 0.11/0.35 thf(f151,plain,(
% 0.11/0.35 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))) @ rel_d))),
% 0.11/0.35 inference(definition_unfolding,[],[f115,f139])).
% 0.11/0.35 thf(f139,plain,(
% 0.11/0.35 (mserial = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.11/0.35 inference(cnf_transformation,[],[f78])).
% 0.11/0.35 thf(f78,plain,(
% 0.11/0.35 (mserial = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.11/0.35 inference(fool_elimination,[],[f77])).
% 0.11/0.35 thf(f77,plain,(
% 0.11/0.35 ((^[X0 : $i > $i > $o] : (! [X1] : ? [X2] : (X0 @ X1 @ X2))) = mserial)),
% 0.11/0.35 inference(rectify,[],[f20])).
% 0.11/0.35 thf(f20,axiom,(
% 0.11/0.35 ((^[X6 : $i > $i > $o] : (! [X8] : ? [X9] : (X6 @ X8 @ X9))) = mserial)),
% 0.11/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mserial)).
% 0.11/0.35 thf(f115,plain,(
% 0.11/0.35 ((mserial @ rel_d) = $true)),
% 0.11/0.35 inference(cnf_transformation,[],[f93])).
% 0.11/0.35 thf(f93,plain,(
% 0.11/0.35 ((mserial @ rel_d) = $true)),
% 0.11/0.35 inference(fool_elimination,[],[f92])).
% 0.11/0.35 thf(f92,plain,(
% 0.11/0.35 (mserial @ rel_d)),
% 0.11/0.35 inference(rectify,[],[f34])).
% 0.11/0.35 thf(f34,axiom,(
% 0.11/0.35 (mserial @ rel_d)),
% 0.11/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1)).
% 0.11/0.35 thf(f193,plain,(
% 0.11/0.35 ($true = (q @ (sK2 @ sK1))) | ($false = (p @ (sK2 @ sK1)))),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f191])).
% 0.11/0.35 thf(f191,plain,(
% 0.11/0.35 ($true = $false) | ($false = (p @ (sK2 @ sK1))) | ($true = (q @ (sK2 @ sK1)))),
% 0.11/0.35 inference(superposition,[],[f181,f171])).
% 0.11/0.35 thf(f171,plain,(
% 0.11/0.35 ( ! [X1 : $i] : (($false = (rel_d @ sK1 @ X1)) | ($false = (p @ X1)) | ($true = (q @ X1))) )),
% 0.11/0.35 inference(not_proxy_clausification,[],[f170])).
% 0.11/0.35 thf(f170,plain,(
% 0.11/0.35 ( ! [X1 : $i] : (($true = (q @ X1)) | ($false = (rel_d @ sK1 @ X1)) | ((~ (p @ X1)) = $true)) )),
% 0.11/0.35 inference(not_proxy_clausification,[],[f169])).
% 0.11/0.35 thf(f169,plain,(
% 0.11/0.35 ( ! [X1 : $i] : (($true = (q @ X1)) | ($true = (~ (rel_d @ sK1 @ X1))) | ((~ (p @ X1)) = $true)) )),
% 0.11/0.35 inference(binary_proxy_clausification,[],[f168])).
% 0.11/0.35 thf(f168,plain,(
% 0.11/0.35 ( ! [X1 : $i] : (($true = ((~ (p @ X1)) | (q @ X1))) | ($true = (~ (rel_d @ sK1 @ X1)))) )),
% 0.11/0.35 inference(binary_proxy_clausification,[],[f167])).
% 0.11/0.35 thf(f167,plain,(
% 0.11/0.35 ( ! [X1 : $i] : (($true = ((~ (rel_d @ sK1 @ X1)) | ((~ (p @ X1)) | (q @ X1))))) )),
% 0.11/0.35 inference(beta_eta_normalization,[],[f166])).
% 0.11/0.35 thf(f166,plain,(
% 0.11/0.35 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_d @ sK1 @ Y0)) | ((~ (p @ Y0)) | (q @ Y0)))) @ X1))) )),
% 0.11/0.35 inference(pi_clausification,[],[f165])).
% 0.11/0.35 thf(f165,plain,(
% 0.11/0.35 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_d @ sK1 @ Y0)) | ((~ (p @ Y0)) | (q @ Y0))))))),
% 0.11/0.35 inference(not_proxy_clausification,[],[f158])).
% 0.11/0.35 thf(f158,plain,(
% 0.11/0.35 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_d @ sK1 @ Y0)) | ((~ (p @ Y0)) | (q @ Y0)))))))),
% 0.11/0.35 inference(binary_proxy_clausification,[],[f157])).
% 0.11/0.35 thf(f157,plain,(
% 0.11/0.35 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_d @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_d @ sK1 @ Y0)) | ((~ (p @ Y0)) | (q @ Y0))))))) = $false)),
% 0.11/0.35 inference(binary_proxy_clausification,[],[f155])).
% 0.11/0.35 thf(f189,plain,(
% 0.11/0.35 ($true = (p @ (sK2 @ sK1)))),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f186])).
% 0.11/0.35 thf(f186,plain,(
% 0.11/0.35 ($true = (p @ (sK2 @ sK1))) | ($true = $false)),
% 0.11/0.35 inference(superposition,[],[f164,f181])).
% 0.11/0.35 thf(f164,plain,(
% 0.11/0.35 ( ! [X1 : $i] : (($false = (rel_d @ sK1 @ X1)) | ($true = (p @ X1))) )),
% 0.11/0.35 inference(not_proxy_clausification,[],[f163])).
% 0.11/0.35 thf(f163,plain,(
% 0.11/0.35 ( ! [X1 : $i] : (($true = (p @ X1)) | ($true = (~ (rel_d @ sK1 @ X1)))) )),
% 0.11/0.35 inference(binary_proxy_clausification,[],[f162])).
% 0.11/0.35 thf(f162,plain,(
% 0.11/0.35 ( ! [X1 : $i] : ((((~ (rel_d @ sK1 @ X1)) | (p @ X1)) = $true)) )),
% 0.11/0.35 inference(beta_eta_normalization,[],[f161])).
% 0.11/0.35 thf(f161,plain,(
% 0.11/0.35 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_d @ sK1 @ Y0)) | (p @ Y0))) @ X1))) )),
% 0.11/0.35 inference(pi_clausification,[],[f160])).
% 0.11/0.35 thf(f160,plain,(
% 0.11/0.35 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_d @ sK1 @ Y0)) | (p @ Y0)))))),
% 0.11/0.35 inference(not_proxy_clausification,[],[f159])).
% 0.11/0.35 thf(f159,plain,(
% 0.11/0.35 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_d @ sK1 @ Y0)) | (p @ Y0))))))),
% 0.11/0.35 inference(binary_proxy_clausification,[],[f157])).
% 0.11/0.35 % SZS output end Proof for theBenchmark
% 0.11/0.35 % (23491)------------------------------
% 0.11/0.35 % (23491)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35 % (23491)Termination reason: Refutation
% 0.11/0.35
% 0.11/0.35 % (23491)Memory used [KB]: 5628
% 0.11/0.35 % (23491)Time elapsed: 0.007 s
% 0.11/0.35 % (23491)Instructions burned: 12 (million)
% 0.11/0.35 % (23491)------------------------------
% 0.11/0.35 % (23491)------------------------------
% 0.11/0.35 % (23484)Success in time 0.014 s
% 0.11/0.35 % Vampire---4.8 exiting
%------------------------------------------------------------------------------