TSTP Solution File: LCL703^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL703^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 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 : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 00:22:18 EDT 2024
% Result : Theorem 0.14s 0.40s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL703^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 0.11/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n021.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
% 0.14/0.36 % DateTime : Mon May 20 02:03:08 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 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/sandbox2/benchmark/theBenchmark.p
% 0.14/0.38 % (2067)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.39 % (2073)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.39 % (2070)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.39 % (2068)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)
% 0.14/0.39 % (2071)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)
% 0.14/0.39 % (2072)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)
% 0.14/0.39 % (2070)Instruction limit reached!
% 0.14/0.39 % (2070)------------------------------
% 0.14/0.39 % (2070)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (2074)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)
% 0.14/0.39 % (2070)Termination reason: Unknown
% 0.14/0.39 % (2070)Termination phase: shuffling
% 0.14/0.39
% 0.14/0.39 % (2070)Memory used [KB]: 1023
% 0.14/0.39 % (2070)Time elapsed: 0.003 s
% 0.14/0.39 % (2069)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)
% 0.14/0.39 % (2070)Instructions burned: 2 (million)
% 0.14/0.39 % (2070)------------------------------
% 0.14/0.39 % (2070)------------------------------
% 0.14/0.39 % (2067)First to succeed.
% 0.14/0.39 % (2071)Instruction limit reached!
% 0.14/0.39 % (2071)------------------------------
% 0.14/0.39 % (2071)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (2071)Termination reason: Unknown
% 0.14/0.39 % (2071)Termination phase: shuffling
% 0.14/0.39
% 0.14/0.39 % (2071)Memory used [KB]: 1023
% 0.14/0.39 % (2071)Time elapsed: 0.004 s
% 0.14/0.39 % (2071)Instructions burned: 2 (million)
% 0.14/0.39 % (2071)------------------------------
% 0.14/0.39 % (2071)------------------------------
% 0.14/0.39 % (2068)Instruction limit reached!
% 0.14/0.39 % (2068)------------------------------
% 0.14/0.39 % (2068)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (2068)Termination reason: Unknown
% 0.14/0.39 % (2068)Termination phase: shuffling
% 0.14/0.39
% 0.14/0.39 % (2068)Memory used [KB]: 1023
% 0.14/0.39 % (2068)Time elapsed: 0.005 s
% 0.14/0.39 % (2068)Instructions burned: 4 (million)
% 0.14/0.39 % (2068)------------------------------
% 0.14/0.39 % (2068)------------------------------
% 0.14/0.39 % (2074)Instruction limit reached!
% 0.14/0.39 % (2074)------------------------------
% 0.14/0.39 % (2074)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (2074)Termination reason: Unknown
% 0.14/0.39 % (2074)Termination phase: shuffling
% 0.14/0.39
% 0.14/0.39 % (2074)Memory used [KB]: 1023
% 0.14/0.39 % (2074)Time elapsed: 0.005 s
% 0.14/0.39 % (2074)Instructions burned: 4 (million)
% 0.14/0.39 % (2074)------------------------------
% 0.14/0.39 % (2074)------------------------------
% 0.14/0.40 % (2067)Refutation found. Thanks to Tanya!
% 0.14/0.40 % SZS status Theorem for theBenchmark
% 0.14/0.40 % SZS output start Proof for theBenchmark
% 0.14/0.40 thf(type_def_5, type, mu: $tType).
% 0.14/0.40 thf(func_def_0, type, mu: $tType).
% 0.14/0.40 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.14/0.40 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_15, type, mtrue: $i > $o).
% 0.14/0.40 thf(func_def_16, type, mfalse: $i > $o).
% 0.14/0.40 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_48, type, sK0: $i > $i > $o).
% 0.14/0.40 thf(func_def_51, type, sK3: $i > $o).
% 0.14/0.40 thf(f215,plain,(
% 0.14/0.40 $false),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f213])).
% 0.14/0.40 thf(f213,plain,(
% 0.14/0.40 ($true = $false)),
% 0.14/0.40 inference(superposition,[],[f209,f174])).
% 0.14/0.40 thf(f174,plain,(
% 0.14/0.40 ($true = (sK3 @ sK5))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f173])).
% 0.14/0.40 thf(f173,plain,(
% 0.14/0.40 ($false = (~ (sK3 @ sK5)))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f171])).
% 0.14/0.40 thf(f171,plain,(
% 0.14/0.40 (((~ (sK3 @ sK5)) | (~ (sK0 @ sK2 @ sK5))) = $false)),
% 0.14/0.40 inference(beta_eta_normalization,[],[f170])).
% 0.14/0.40 thf(f170,plain,(
% 0.14/0.40 ($false = ((^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))) @ sK5))),
% 0.14/0.40 inference(sigma_clausification,[],[f157])).
% 0.14/0.40 thf(f157,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f156])).
% 0.14/0.40 thf(f156,plain,(
% 0.14/0.40 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK3 @ Y1)) | (~ (sK0 @ Y0 @ Y1)))))) | (~ (sK0 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))))),
% 0.14/0.40 inference(beta_eta_normalization,[],[f155])).
% 0.14/0.40 thf(f155,plain,(
% 0.14/0.40 (((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) | (~ (sK0 @ Y1 @ Y2)))))) | (~ (sK0 @ sK2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (Y0 @ Y1)) | (~ (sK0 @ sK2 @ Y1))))))) @ sK3) = $false)),
% 0.14/0.40 inference(sigma_clausification,[],[f154])).
% 0.14/0.40 thf(f154,plain,(
% 0.14/0.40 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) | (~ (sK0 @ Y1 @ Y2)))))) | (~ (sK0 @ sK2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (Y0 @ Y1)) | (~ (sK0 @ sK2 @ Y1)))))))) = $false)),
% 0.14/0.40 inference(beta_eta_normalization,[],[f153])).
% 0.14/0.40 thf(f153,plain,(
% 0.14/0.40 (((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (sK0 @ Y2 @ Y3)))))) | (~ (sK0 @ Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) | (~ (sK0 @ Y0 @ Y2))))))))) @ sK2) = $false)),
% 0.14/0.40 inference(sigma_clausification,[],[f152])).
% 0.14/0.40 thf(f152,plain,(
% 0.14/0.40 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (sK0 @ Y2 @ Y3)))))) | (~ (sK0 @ Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) | (~ (sK0 @ Y0 @ Y2)))))))))))),
% 0.14/0.40 inference(boolean_simplification,[],[f151])).
% 0.14/0.40 thf(f151,plain,(
% 0.14/0.40 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (sK0 @ Y2 @ Y3)))))) | (~ (sK0 @ Y0 @ Y2))))) | (~ (~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) | (~ (sK0 @ Y0 @ Y2)))))))))))))),
% 0.14/0.40 inference(beta_eta_normalization,[],[f140])).
% 0.14/0.40 thf(f140,plain,(
% 0.14/0.40 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y4 @ Y5) | (Y3 @ Y5))))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y1) @ Y2)))) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6) | (~ (Y3 @ Y5 @ Y6)))))))))) @ Y1 @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y2)))))) @ sK0 @ Y0) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (Y1 @ Y3 @ Y4)))))))))) @ sK0 @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6) | (~ (Y3 @ Y5 @ Y6)))))))))) @ Y1 @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y2)))))) @ sK0 @ Y0)))))) != $true)),
% 0.14/0.40 inference(definition_unfolding,[],[f116,f121,f98,f132,f139,f106,f139])).
% 0.14/0.40 thf(f106,plain,(
% 0.14/0.40 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f47])).
% 0.14/0.40 thf(f47,plain,(
% 0.14/0.40 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))))),
% 0.14/0.40 inference(fool_elimination,[],[f46])).
% 0.14/0.40 thf(f46,plain,(
% 0.14/0.40 ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : (~(X0 @ X2 @ X3) | (X1 @ X3)))) = mbox)),
% 0.14/0.40 inference(rectify,[],[f16])).
% 0.14/0.40 thf(f16,axiom,(
% 0.14/0.40 ((^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7] : (~(X6 @ X2 @ X7) | (X3 @ X7)))) = mbox)),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox)).
% 0.14/0.40 thf(f139,plain,(
% 0.14/0.40 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5) | (~ (Y2 @ Y4 @ Y5)))))))))) @ Y0 @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.14/0.40 inference(definition_unfolding,[],[f108,f126,f106,f126])).
% 0.14/0.40 thf(f126,plain,(
% 0.14/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f55])).
% 0.14/0.40 thf(f55,plain,(
% 0.14/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.40 inference(fool_elimination,[],[f54])).
% 0.14/0.40 thf(f54,plain,(
% 0.14/0.40 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.14/0.40 inference(rectify,[],[f3])).
% 0.14/0.40 thf(f3,axiom,(
% 0.14/0.40 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.14/0.40 thf(f108,plain,(
% 0.14/0.40 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mbox @ Y0 @ (mnot @ Y1)))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f44])).
% 0.14/0.40 thf(f44,plain,(
% 0.14/0.40 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mbox @ Y0 @ (mnot @ Y1)))))))),
% 0.14/0.40 inference(fool_elimination,[],[f43])).
% 0.14/0.40 thf(f43,plain,(
% 0.14/0.40 ((^[X0 : $i > $i > $o, X1 : $i > $o] : (mnot @ (mbox @ X0 @ (mnot @ X1)))) = mdia)),
% 0.14/0.40 inference(rectify,[],[f17])).
% 0.14/0.40 thf(f17,axiom,(
% 0.14/0.40 ((^[X6 : $i > $i > $o, X3 : $i > $o] : (mnot @ (mbox @ X6 @ (mnot @ X3)))) = mdia)),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia)).
% 0.14/0.40 thf(f132,plain,(
% 0.14/0.40 (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)))))),
% 0.14/0.40 inference(definition_unfolding,[],[f124,f122,f126])).
% 0.14/0.40 thf(f122,plain,(
% 0.14/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f92])).
% 0.14/0.40 thf(f92,plain,(
% 0.14/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.14/0.40 inference(fool_elimination,[],[f91])).
% 0.14/0.40 thf(f91,plain,(
% 0.14/0.40 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.14/0.40 inference(rectify,[],[f4])).
% 0.14/0.40 thf(f4,axiom,(
% 0.14/0.40 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.14/0.40 thf(f124,plain,(
% 0.14/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.40 inference(cnf_transformation,[],[f57])).
% 0.14/0.40 thf(f57,plain,(
% 0.14/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.40 inference(fool_elimination,[],[f56])).
% 0.14/0.40 thf(f56,plain,(
% 0.14/0.40 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.14/0.40 inference(rectify,[],[f6])).
% 0.14/0.40 thf(f6,axiom,(
% 0.14/0.40 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.14/0.40 thf(f98,plain,(
% 0.14/0.40 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f61])).
% 0.14/0.40 thf(f61,plain,(
% 0.14/0.40 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.14/0.40 inference(fool_elimination,[],[f60])).
% 0.14/0.40 thf(f60,plain,(
% 0.14/0.40 (mforall_prop = (^[X0 : ($i > $o) > $i > $o, X1 : $i] : (! [X2 : $i > $o] : (X0 @ X2 @ X1))))),
% 0.14/0.40 inference(rectify,[],[f11])).
% 0.14/0.40 thf(f11,axiom,(
% 0.14/0.40 (mforall_prop = (^[X3 : ($i > $o) > $i > $o, X2 : $i] : (! [X5 : $i > $o] : (X3 @ X5 @ X2))))),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_prop)).
% 0.14/0.40 thf(f121,plain,(
% 0.14/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.40 inference(cnf_transformation,[],[f71])).
% 0.14/0.40 thf(f71,plain,(
% 0.14/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.40 inference(fool_elimination,[],[f70])).
% 0.14/0.40 thf(f70,plain,(
% 0.14/0.40 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.14/0.40 inference(rectify,[],[f28])).
% 0.14/0.40 thf(f28,axiom,(
% 0.14/0.40 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.14/0.40 thf(f116,plain,(
% 0.14/0.40 ($true != (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mdia @ sK0 @ Y0) @ (mbox @ sK0 @ (mdia @ sK0 @ Y0)))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f97])).
% 0.14/0.40 thf(f97,plain,(
% 0.14/0.40 ($true != (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mdia @ sK0 @ Y0) @ (mbox @ sK0 @ (mdia @ sK0 @ Y0))))))) & ((meuclidean @ sK0) = $true)),
% 0.14/0.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f95,f96])).
% 0.14/0.40 thf(f96,plain,(
% 0.14/0.40 ? [X0 : $i > $i > $o] : (($true != (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mdia @ X0 @ Y0) @ (mbox @ X0 @ (mdia @ X0 @ Y0))))))) & ((meuclidean @ X0) = $true)) => (($true != (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mdia @ sK0 @ Y0) @ (mbox @ sK0 @ (mdia @ sK0 @ Y0))))))) & ((meuclidean @ sK0) = $true))),
% 0.14/0.40 introduced(choice_axiom,[])).
% 0.14/0.40 thf(f95,plain,(
% 0.14/0.40 ? [X0 : $i > $i > $o] : (($true != (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mdia @ X0 @ Y0) @ (mbox @ X0 @ (mdia @ X0 @ Y0))))))) & ((meuclidean @ X0) = $true))),
% 0.14/0.40 inference(ennf_transformation,[],[f79])).
% 0.14/0.40 thf(f79,plain,(
% 0.14/0.40 ~! [X0 : $i > $i > $o] : (((meuclidean @ X0) = $true) => ($true = (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mdia @ X0 @ Y0) @ (mbox @ X0 @ (mdia @ X0 @ Y0))))))))),
% 0.14/0.40 inference(fool_elimination,[],[f78])).
% 0.14/0.40 thf(f78,plain,(
% 0.14/0.40 ~! [X0 : $i > $i > $o] : ((meuclidean @ X0) => (mvalid @ (mforall_prop @ (^[X1 : $i > $o] : (mimplies @ (mdia @ X0 @ X1) @ (mbox @ X0 @ (mdia @ X0 @ X1)))))))),
% 0.14/0.40 inference(rectify,[],[f33])).
% 0.14/0.40 thf(f33,negated_conjecture,(
% 0.14/0.40 ~! [X6 : $i > $i > $o] : ((meuclidean @ X6) => (mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mimplies @ (mdia @ X6 @ X11) @ (mbox @ X6 @ (mdia @ X6 @ X11)))))))),
% 0.14/0.40 inference(negated_conjecture,[],[f32])).
% 0.14/0.40 thf(f32,conjecture,(
% 0.14/0.40 ! [X6 : $i > $i > $o] : ((meuclidean @ X6) => (mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mimplies @ (mdia @ X6 @ X11) @ (mbox @ X6 @ (mdia @ X6 @ X11)))))))),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 0.14/0.40 thf(f209,plain,(
% 0.14/0.40 ((sK3 @ sK5) = $false)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f203])).
% 0.14/0.40 thf(f203,plain,(
% 0.14/0.40 ($true = $false) | ((sK3 @ sK5) = $false)),
% 0.14/0.40 inference(superposition,[],[f192,f175])).
% 0.14/0.40 thf(f175,plain,(
% 0.14/0.40 ($true = (sK0 @ sK2 @ sK5))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f172])).
% 0.14/0.40 thf(f172,plain,(
% 0.14/0.40 ((~ (sK0 @ sK2 @ sK5)) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f171])).
% 0.14/0.40 thf(f192,plain,(
% 0.14/0.40 ( ! [X0 : $i] : (((sK0 @ sK2 @ X0) = $false) | ((sK3 @ X0) = $false)) )),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f185])).
% 0.14/0.40 thf(f185,plain,(
% 0.14/0.40 ( ! [X0 : $i] : (($true = $false) | ((sK0 @ sK2 @ X0) = $false) | ((sK3 @ X0) = $false)) )),
% 0.14/0.40 inference(superposition,[],[f169,f182])).
% 0.14/0.40 thf(f182,plain,(
% 0.14/0.40 ( ! [X0 : $i,X1 : $i] : (((sK0 @ X1 @ sK4) = $false) | ((sK3 @ X0) = $false) | ((sK0 @ X1 @ X0) = $false)) )),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f179])).
% 0.14/0.40 thf(f179,plain,(
% 0.14/0.40 ( ! [X0 : $i,X1 : $i] : (((sK0 @ X1 @ sK4) = $false) | ($true = $false) | ((sK3 @ X0) = $false) | ((sK0 @ X1 @ X0) = $false)) )),
% 0.14/0.40 inference(superposition,[],[f168,f150])).
% 0.14/0.40 thf(f150,plain,(
% 0.14/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK0 @ X2 @ X3)) | ((sK0 @ X1 @ X2) = $false) | ($false = (sK0 @ X1 @ X3))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f149])).
% 0.14/0.40 thf(f149,plain,(
% 0.14/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK0 @ X2 @ X3)) | (((sK0 @ X1 @ X3) & (sK0 @ X1 @ X2)) = $false)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f148])).
% 0.14/0.40 thf(f148,plain,(
% 0.14/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((sK0 @ X1 @ X3) & (sK0 @ X1 @ X2)) => (sK0 @ X2 @ X3)) = $true)) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f147])).
% 0.14/0.40 thf(f147,plain,(
% 0.14/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((sK0 @ X1 @ Y0) & (sK0 @ X1 @ X2)) => (sK0 @ X2 @ Y0))) @ X3))) )),
% 0.14/0.40 inference(pi_clausification,[],[f146])).
% 0.14/0.40 thf(f146,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((sK0 @ X1 @ Y0) & (sK0 @ X1 @ X2)) => (sK0 @ X2 @ Y0)))))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f145])).
% 0.14/0.40 thf(f145,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ X1 @ Y1) & (sK0 @ X1 @ Y0)) => (sK0 @ Y0 @ Y1))))) @ X2) = $true)) )),
% 0.14/0.40 inference(pi_clausification,[],[f144])).
% 0.14/0.40 thf(f144,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ X1 @ Y1) & (sK0 @ X1 @ Y0)) => (sK0 @ Y0 @ Y1)))))))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f143])).
% 0.14/0.40 thf(f143,plain,(
% 0.14/0.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y0 @ Y2) & (sK0 @ Y0 @ Y1)) => (sK0 @ Y1 @ Y2))))))) @ X1) = $true)) )),
% 0.14/0.40 inference(pi_clausification,[],[f142])).
% 0.14/0.40 thf(f142,plain,(
% 0.14/0.40 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y0 @ Y2) & (sK0 @ Y0 @ Y1)) => (sK0 @ Y1 @ Y2)))))))))),
% 0.14/0.40 inference(beta_eta_normalization,[],[f141])).
% 0.14/0.40 thf(f141,plain,(
% 0.14/0.40 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y2 @ Y3))))))))) @ sK0))),
% 0.14/0.40 inference(definition_unfolding,[],[f115,f120])).
% 0.14/0.40 thf(f120,plain,(
% 0.14/0.40 (meuclidean = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y2 @ Y3))))))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f36])).
% 0.14/0.40 thf(f36,plain,(
% 0.14/0.40 (meuclidean = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y2 @ Y3))))))))))),
% 0.14/0.40 inference(fool_elimination,[],[f35])).
% 0.14/0.40 thf(f35,plain,(
% 0.14/0.40 (meuclidean = (^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X3 @ X2) & (X0 @ X3 @ X1)) => (X0 @ X2 @ X1)))))),
% 0.14/0.40 inference(rectify,[],[f22])).
% 0.14/0.40 thf(f22,axiom,(
% 0.14/0.40 (meuclidean = (^[X6 : $i > $i > $o] : (! [X10,X9,X8] : (((X6 @ X8 @ X9) & (X6 @ X8 @ X10)) => (X6 @ X9 @ X10)))))),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meuclidean)).
% 0.14/0.40 thf(f115,plain,(
% 0.14/0.40 ((meuclidean @ sK0) = $true)),
% 0.14/0.40 inference(cnf_transformation,[],[f97])).
% 0.14/0.40 thf(f168,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((sK0 @ sK4 @ X1) = $false) | ((sK3 @ X1) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f167])).
% 0.14/0.40 thf(f167,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = (~ (sK3 @ X1))) | ((sK0 @ sK4 @ X1) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f166])).
% 0.14/0.40 thf(f166,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((~ (sK0 @ sK4 @ X1)) = $true) | ($true = (~ (sK3 @ X1)))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f165])).
% 0.14/0.40 thf(f165,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = ((~ (sK3 @ X1)) | (~ (sK0 @ sK4 @ X1))))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f164])).
% 0.14/0.40 thf(f164,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK4 @ Y0)))) @ X1))) )),
% 0.14/0.40 inference(pi_clausification,[],[f163])).
% 0.14/0.40 thf(f163,plain,(
% 0.14/0.40 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK4 @ Y0))))))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f162])).
% 0.14/0.40 thf(f162,plain,(
% 0.14/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK4 @ Y0)))))) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f160])).
% 0.14/0.40 thf(f160,plain,(
% 0.14/0.40 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK4 @ Y0)))))) | (~ (sK0 @ sK2 @ sK4))) = $false)),
% 0.14/0.40 inference(beta_eta_normalization,[],[f159])).
% 0.14/0.40 thf(f159,plain,(
% 0.14/0.40 ($false = ((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK3 @ Y1)) | (~ (sK0 @ Y0 @ Y1)))))) | (~ (sK0 @ sK2 @ Y0)))) @ sK4))),
% 0.14/0.40 inference(sigma_clausification,[],[f158])).
% 0.14/0.40 thf(f158,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK3 @ Y1)) | (~ (sK0 @ Y0 @ Y1)))))) | (~ (sK0 @ sK2 @ Y0))))) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f156])).
% 0.14/0.40 thf(f169,plain,(
% 0.14/0.40 ($true = (sK0 @ sK2 @ sK4))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f161])).
% 0.14/0.40 thf(f161,plain,(
% 0.14/0.40 ((~ (sK0 @ sK2 @ sK4)) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f160])).
% 0.14/0.40 % SZS output end Proof for theBenchmark
% 0.14/0.40 % (2067)------------------------------
% 0.14/0.40 % (2067)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (2067)Termination reason: Refutation
% 0.14/0.40
% 0.14/0.40 % (2067)Memory used [KB]: 5756
% 0.14/0.40 % (2067)Time elapsed: 0.015 s
% 0.14/0.40 % (2067)Instructions burned: 14 (million)
% 0.14/0.40 % (2067)------------------------------
% 0.14/0.40 % (2067)------------------------------
% 0.14/0.40 % (2066)Success in time 0.029 s
% 0.14/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------