TSTP Solution File: LCL706^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL706^1 : 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 : n014.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 00:22:19 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
% 0.04/0.12 % Problem : LCL706^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 0.14/0.14 % 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 : n014.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 01:48:08 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/sandbox2/benchmark/theBenchmark.p
% 0.14/0.38 % (17374)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 % (17375)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 % (17376)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 % (17378)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 % (17377)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.39 % (17379)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 % (17380)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 % (17381)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 % (17374)First to succeed.
% 0.14/0.39 % (17378)Instruction limit reached!
% 0.14/0.39 % (17378)------------------------------
% 0.14/0.39 % (17378)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (17378)Termination reason: Unknown
% 0.14/0.39 % (17378)Termination phase: shuffling
% 0.14/0.39
% 0.14/0.39 % (17378)Memory used [KB]: 1023
% 0.14/0.39 % (17378)Time elapsed: 0.004 s
% 0.14/0.39 % (17378)Instructions burned: 2 (million)
% 0.14/0.39 % (17378)------------------------------
% 0.14/0.39 % (17378)------------------------------
% 0.14/0.39 % (17377)Instruction limit reached!
% 0.14/0.39 % (17377)------------------------------
% 0.14/0.39 % (17377)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (17377)Termination reason: Unknown
% 0.14/0.39 % (17377)Termination phase: shuffling
% 0.14/0.39
% 0.14/0.39 % (17377)Memory used [KB]: 1023
% 0.14/0.39 % (17377)Time elapsed: 0.005 s
% 0.14/0.39 % (17377)Instructions burned: 3 (million)
% 0.14/0.39 % (17377)------------------------------
% 0.14/0.39 % (17377)------------------------------
% 0.14/0.39 % (17381)Instruction limit reached!
% 0.14/0.39 % (17381)------------------------------
% 0.14/0.39 % (17381)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (17381)Termination reason: Unknown
% 0.14/0.39 % (17381)Termination phase: shuffling
% 0.14/0.39
% 0.14/0.39 % (17381)Memory used [KB]: 1023
% 0.14/0.39 % (17381)Time elapsed: 0.005 s
% 0.14/0.39 % (17381)Instructions burned: 3 (million)
% 0.14/0.39 % (17381)------------------------------
% 0.14/0.39 % (17381)------------------------------
% 0.14/0.39 % (17375)Instruction limit reached!
% 0.14/0.39 % (17375)------------------------------
% 0.14/0.39 % (17375)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (17375)Termination reason: Unknown
% 0.14/0.39 % (17375)Termination phase: Property scanning
% 0.14/0.39
% 0.14/0.39 % (17375)Memory used [KB]: 1023
% 0.14/0.39 % (17375)Time elapsed: 0.006 s
% 0.14/0.39 % (17375)Instructions burned: 4 (million)
% 0.14/0.39 % (17375)------------------------------
% 0.14/0.39 % (17375)------------------------------
% 0.14/0.39 % (17374)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_48, type, sK0: $i > $i > $o).
% 0.14/0.39 thf(func_def_51, type, sK3: $i > $o).
% 0.14/0.39 thf(func_def_53, type, sK5: $i > $i > $i).
% 0.14/0.39 thf(f216,plain,(
% 0.14/0.39 $false),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f215])).
% 0.14/0.39 thf(f215,plain,(
% 0.14/0.39 ($false = $true)),
% 0.14/0.39 inference(superposition,[],[f160,f213])).
% 0.14/0.39 thf(f213,plain,(
% 0.14/0.39 ($true = (sK3 @ sK4))),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f206])).
% 0.14/0.39 thf(f206,plain,(
% 0.14/0.39 ($true = (sK3 @ sK4)) | ($false = $true)),
% 0.14/0.39 inference(superposition,[],[f204,f162])).
% 0.14/0.39 thf(f162,plain,(
% 0.14/0.39 ((sK0 @ sK2 @ sK4) = $true)),
% 0.14/0.39 inference(not_proxy_clausification,[],[f161])).
% 0.14/0.39 thf(f161,plain,(
% 0.14/0.39 ((~ (sK0 @ sK2 @ sK4)) = $false)),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f159])).
% 0.14/0.39 thf(f159,plain,(
% 0.14/0.39 ($false = ((~ (sK0 @ sK2 @ sK4)) | (sK3 @ sK4)))),
% 0.14/0.39 inference(beta_eta_normalization,[],[f158])).
% 0.14/0.39 thf(f158,plain,(
% 0.14/0.39 (((^[Y0 : $i]: ((~ (sK0 @ sK2 @ Y0)) | (sK3 @ Y0))) @ sK4) = $false)),
% 0.14/0.39 inference(sigma_clausification,[],[f147])).
% 0.14/0.39 thf(f147,plain,(
% 0.14/0.39 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ sK2 @ Y0)) | (sK3 @ Y0)))))),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f146])).
% 0.14/0.39 thf(f146,plain,(
% 0.14/0.39 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ Y0 @ Y1)) | (sK3 @ Y1)))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ sK2 @ Y0)) | (sK3 @ Y0))))) = $false)),
% 0.14/0.39 inference(beta_eta_normalization,[],[f145])).
% 0.14/0.39 thf(f145,plain,(
% 0.14/0.39 ($false = ((^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ sK2 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y1 @ Y2)) | (Y0 @ Y2)))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ sK2 @ Y1)) | (Y0 @ Y1)))))) @ sK3))),
% 0.14/0.39 inference(sigma_clausification,[],[f144])).
% 0.14/0.39 thf(f144,plain,(
% 0.14/0.39 ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ sK2 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y1 @ Y2)) | (Y0 @ Y2)))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ sK2 @ Y1)) | (Y0 @ Y1))))))))),
% 0.14/0.39 inference(beta_eta_normalization,[],[f143])).
% 0.14/0.39 thf(f143,plain,(
% 0.14/0.39 (((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y0 @ Y2)) | (!! @ $i @ (^[Y3 : $i]: ((~ (sK0 @ Y2 @ Y3)) | (Y1 @ Y3)))))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y0 @ Y2)) | (Y1 @ Y2)))))))) @ sK2) = $false)),
% 0.14/0.39 inference(sigma_clausification,[],[f142])).
% 0.14/0.39 thf(f142,plain,(
% 0.14/0.39 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y0 @ Y2)) | (!! @ $i @ (^[Y3 : $i]: ((~ (sK0 @ Y2 @ Y3)) | (Y1 @ Y3)))))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y0 @ Y2)) | (Y1 @ Y2))))))))) != $true)),
% 0.14/0.39 inference(beta_eta_normalization,[],[f141])).
% 0.14/0.39 thf(f141,plain,(
% 0.14/0.39 (((^[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]: ((Y3 @ Y5) | (Y4 @ Y5))))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y1) @ Y2)))) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (Y1 @ Y3 @ Y4)) | (Y2 @ Y4))))))))) @ sK0 @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (Y1 @ Y3 @ Y4)) | (Y2 @ Y4))))))))) @ sK0 @ Y0)) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (Y1 @ Y3 @ Y4)) | (Y2 @ Y4))))))))) @ sK0 @ Y0))))) != $true)),
% 0.14/0.39 inference(definition_unfolding,[],[f116,f108,f110,f132,f113,f113,f113])).
% 0.14/0.39 thf(f113,plain,(
% 0.14/0.39 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.14/0.39 inference(cnf_transformation,[],[f50])).
% 0.14/0.39 thf(f50,plain,(
% 0.14/0.39 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.14/0.39 inference(fool_elimination,[],[f49])).
% 0.14/0.39 thf(f49,plain,(
% 0.14/0.39 ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))) = mbox)),
% 0.14/0.39 inference(rectify,[],[f16])).
% 0.14/0.39 thf(f16,axiom,(
% 0.14/0.39 ((^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(X6 @ X2 @ X7)))) = mbox)),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox)).
% 0.14/0.39 thf(f132,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,[],[f119,f121,f100])).
% 0.14/0.39 thf(f100,plain,(
% 0.14/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.39 inference(cnf_transformation,[],[f64])).
% 0.14/0.39 thf(f64,plain,(
% 0.14/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.39 inference(fool_elimination,[],[f63])).
% 0.14/0.39 thf(f63,plain,(
% 0.14/0.39 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.14/0.39 inference(rectify,[],[f3])).
% 0.14/0.39 thf(f3,axiom,(
% 0.14/0.39 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.14/0.39 thf(f121,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,[],[f92])).
% 0.14/0.39 thf(f92,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,[],[f91])).
% 0.14/0.39 thf(f91,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/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.14/0.39 thf(f119,plain,(
% 0.14/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.39 inference(cnf_transformation,[],[f46])).
% 0.14/0.39 thf(f46,plain,(
% 0.14/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.39 inference(fool_elimination,[],[f45])).
% 0.14/0.39 thf(f45,plain,(
% 0.14/0.39 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.14/0.39 inference(rectify,[],[f6])).
% 0.14/0.39 thf(f6,axiom,(
% 0.14/0.39 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.14/0.39 thf(f110,plain,(
% 0.14/0.39 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.14/0.39 inference(cnf_transformation,[],[f73])).
% 0.14/0.39 thf(f73,plain,(
% 0.14/0.39 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.14/0.39 inference(fool_elimination,[],[f72])).
% 0.14/0.39 thf(f72,plain,(
% 0.14/0.39 ((^[X0 : ($i > $o) > $i > $o, X1 : $i] : (! [X2 : $i > $o] : (X0 @ X2 @ X1))) = mforall_prop)),
% 0.14/0.39 inference(rectify,[],[f11])).
% 0.14/0.39 thf(f11,axiom,(
% 0.14/0.39 ((^[X3 : ($i > $o) > $i > $o, X2 : $i] : (! [X5 : $i > $o] : (X3 @ X5 @ X2))) = mforall_prop)),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_prop)).
% 0.14/0.39 thf(f108,plain,(
% 0.14/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.39 inference(cnf_transformation,[],[f38])).
% 0.14/0.39 thf(f38,plain,(
% 0.14/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.39 inference(fool_elimination,[],[f37])).
% 0.14/0.39 thf(f37,plain,(
% 0.14/0.39 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.14/0.39 inference(rectify,[],[f28])).
% 0.14/0.39 thf(f28,axiom,(
% 0.14/0.39 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.14/0.39 thf(f116,plain,(
% 0.14/0.39 ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ sK0 @ (mbox @ sK0 @ Y0)) @ (mbox @ sK0 @ Y0))))) != $true)),
% 0.14/0.39 inference(cnf_transformation,[],[f97])).
% 0.14/0.39 thf(f97,plain,(
% 0.14/0.39 ((mweakly_dense @ sK0) = $true) & ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ sK0 @ (mbox @ sK0 @ Y0)) @ (mbox @ sK0 @ Y0))))) != $true)),
% 0.14/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f95,f96])).
% 0.14/0.39 thf(f96,plain,(
% 0.14/0.39 ? [X0 : $i > $i > $o] : (((mweakly_dense @ X0) = $true) & ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ X0 @ (mbox @ X0 @ Y0)) @ (mbox @ X0 @ Y0))))) != $true)) => (((mweakly_dense @ sK0) = $true) & ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ sK0 @ (mbox @ sK0 @ Y0)) @ (mbox @ sK0 @ Y0))))) != $true))),
% 0.14/0.39 introduced(choice_axiom,[])).
% 0.14/0.39 thf(f95,plain,(
% 0.14/0.39 ? [X0 : $i > $i > $o] : (((mweakly_dense @ X0) = $true) & ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ X0 @ (mbox @ X0 @ Y0)) @ (mbox @ X0 @ Y0))))) != $true))),
% 0.14/0.39 inference(ennf_transformation,[],[f90])).
% 0.14/0.39 thf(f90,plain,(
% 0.14/0.39 ~! [X0 : $i > $i > $o] : (((mweakly_dense @ X0) = $true) => ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ X0 @ (mbox @ X0 @ Y0)) @ (mbox @ X0 @ Y0))))) = $true))),
% 0.14/0.39 inference(fool_elimination,[],[f89])).
% 0.14/0.39 thf(f89,plain,(
% 0.14/0.39 ~! [X0 : $i > $i > $o] : ((mweakly_dense @ X0) => (mvalid @ (mforall_prop @ (^[X1 : $i > $o] : (mimplies @ (mbox @ X0 @ (mbox @ X0 @ X1)) @ (mbox @ X0 @ X1))))))),
% 0.14/0.39 inference(rectify,[],[f33])).
% 0.14/0.39 thf(f33,negated_conjecture,(
% 0.14/0.39 ~! [X6 : $i > $i > $o] : ((mweakly_dense @ X6) => (mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mimplies @ (mbox @ X6 @ (mbox @ X6 @ X11)) @ (mbox @ X6 @ X11))))))),
% 0.14/0.39 inference(negated_conjecture,[],[f32])).
% 0.14/0.39 thf(f32,conjecture,(
% 0.14/0.39 ! [X6 : $i > $i > $o] : ((mweakly_dense @ X6) => (mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mimplies @ (mbox @ X6 @ (mbox @ X6 @ X11)) @ (mbox @ X6 @ X11))))))),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 0.14/0.39 thf(f204,plain,(
% 0.14/0.39 ( ! [X0 : $i] : (($false = (sK0 @ sK2 @ X0)) | ((sK3 @ X0) = $true)) )),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f203])).
% 0.14/0.39 thf(f203,plain,(
% 0.14/0.39 ( ! [X0 : $i] : (((sK3 @ X0) = $true) | ($false = (sK0 @ sK2 @ X0)) | ($false = $true)) )),
% 0.14/0.39 inference(duplicate_literal_removal,[],[f198])).
% 0.14/0.39 thf(f198,plain,(
% 0.14/0.39 ( ! [X0 : $i] : (((sK3 @ X0) = $true) | ($false = (sK0 @ sK2 @ X0)) | ($false = (sK0 @ sK2 @ X0)) | ($false = $true)) )),
% 0.14/0.39 inference(superposition,[],[f172,f195])).
% 0.14/0.39 thf(f195,plain,(
% 0.14/0.39 ( ! [X0 : $i,X1 : $i] : (($false = (sK0 @ (sK5 @ X0 @ sK2) @ X1)) | ((sK3 @ X1) = $true) | ($false = (sK0 @ sK2 @ X0))) )),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f190])).
% 0.14/0.39 thf(f190,plain,(
% 0.14/0.39 ( ! [X0 : $i,X1 : $i] : (($false = (sK0 @ (sK5 @ X0 @ sK2) @ X1)) | ($false = $true) | ($false = (sK0 @ sK2 @ X0)) | ((sK3 @ X1) = $true)) )),
% 0.14/0.39 inference(superposition,[],[f157,f171])).
% 0.14/0.39 thf(f171,plain,(
% 0.14/0.39 ( ! [X2 : $i,X1 : $i] : (((sK0 @ X2 @ (sK5 @ X1 @ X2)) = $true) | ((sK0 @ X2 @ X1) = $false)) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f170])).
% 0.14/0.39 thf(f170,plain,(
% 0.14/0.39 ( ! [X2 : $i,X1 : $i] : ((((sK0 @ (sK5 @ X1 @ X2) @ X1) & (sK0 @ X2 @ (sK5 @ X1 @ X2))) = $true) | ((sK0 @ X2 @ X1) = $false)) )),
% 0.14/0.39 inference(beta_eta_normalization,[],[f169])).
% 0.14/0.39 thf(f169,plain,(
% 0.14/0.39 ( ! [X2 : $i,X1 : $i] : (((sK0 @ X2 @ X1) = $false) | ($true = ((^[Y0 : $i]: ((sK0 @ Y0 @ X1) & (sK0 @ X2 @ Y0))) @ (sK5 @ X1 @ X2)))) )),
% 0.14/0.39 inference(sigma_clausification,[],[f168])).
% 0.14/0.39 thf(f168,plain,(
% 0.14/0.39 ( ! [X2 : $i,X1 : $i] : (((?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0 @ X1) & (sK0 @ X2 @ Y0)))) = $true) | ((sK0 @ X2 @ X1) = $false)) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f167])).
% 0.14/0.39 thf(f167,plain,(
% 0.14/0.39 ( ! [X2 : $i,X1 : $i] : ((((sK0 @ X2 @ X1) => (?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0 @ X1) & (sK0 @ X2 @ Y0))))) = $true)) )),
% 0.14/0.39 inference(beta_eta_normalization,[],[f166])).
% 0.14/0.39 thf(f166,plain,(
% 0.14/0.39 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((sK0 @ Y0 @ X1) => (?? @ $i @ (^[Y1 : $i]: ((sK0 @ Y1 @ X1) & (sK0 @ Y0 @ Y1)))))) @ X2) = $true)) )),
% 0.14/0.39 inference(pi_clausification,[],[f165])).
% 0.14/0.39 thf(f165,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0 @ X1) => (?? @ $i @ (^[Y1 : $i]: ((sK0 @ Y1 @ X1) & (sK0 @ Y0 @ Y1))))))) = $true)) )),
% 0.14/0.39 inference(beta_eta_normalization,[],[f164])).
% 0.14/0.39 thf(f164,plain,(
% 0.14/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1 @ Y0) => (?? @ $i @ (^[Y2 : $i]: ((sK0 @ Y2 @ Y0) & (sK0 @ Y1 @ Y2)))))))) @ X1) = $true)) )),
% 0.14/0.39 inference(pi_clausification,[],[f163])).
% 0.14/0.39 thf(f163,plain,(
% 0.14/0.39 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1 @ Y0) => (?? @ $i @ (^[Y2 : $i]: ((sK0 @ Y2 @ Y0) & (sK0 @ Y1 @ Y2))))))))) = $true)),
% 0.14/0.39 inference(beta_eta_normalization,[],[f140])).
% 0.14/0.39 thf(f140,plain,(
% 0.14/0.39 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)))))))))) @ sK0))),
% 0.14/0.39 inference(definition_unfolding,[],[f117,f126])).
% 0.14/0.39 thf(f126,plain,(
% 0.14/0.39 (mweakly_dense = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)))))))))))),
% 0.14/0.39 inference(cnf_transformation,[],[f83])).
% 0.14/0.39 thf(f83,plain,(
% 0.14/0.39 (mweakly_dense = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)))))))))))),
% 0.14/0.39 inference(fool_elimination,[],[f82])).
% 0.14/0.39 thf(f82,plain,(
% 0.14/0.39 ((^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X1 @ X2) => ? [X4] : ((X0 @ X1 @ X4) & (X0 @ X4 @ X2))))) = mweakly_dense)),
% 0.14/0.39 inference(rectify,[],[f25])).
% 0.14/0.39 thf(f25,axiom,(
% 0.14/0.39 ((^[X6 : $i > $i > $o] : (! [X8,X9,X10] : ((X6 @ X8 @ X9) => ? [X10] : ((X6 @ X8 @ X10) & (X6 @ X10 @ X9))))) = mweakly_dense)),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_dense)).
% 0.14/0.39 thf(f117,plain,(
% 0.14/0.39 ((mweakly_dense @ sK0) = $true)),
% 0.14/0.39 inference(cnf_transformation,[],[f97])).
% 0.14/0.39 thf(f157,plain,(
% 0.14/0.39 ( ! [X2 : $i,X1 : $i] : (($false = (sK0 @ sK2 @ X1)) | ((sK3 @ X2) = $true) | ((sK0 @ X1 @ X2) = $false)) )),
% 0.14/0.39 inference(not_proxy_clausification,[],[f156])).
% 0.14/0.39 thf(f156,plain,(
% 0.14/0.39 ( ! [X2 : $i,X1 : $i] : (((sK3 @ X2) = $true) | ((~ (sK0 @ sK2 @ X1)) = $true) | ((sK0 @ X1 @ X2) = $false)) )),
% 0.14/0.39 inference(not_proxy_clausification,[],[f155])).
% 0.14/0.39 thf(f155,plain,(
% 0.14/0.39 ( ! [X2 : $i,X1 : $i] : (((~ (sK0 @ X1 @ X2)) = $true) | ((~ (sK0 @ sK2 @ X1)) = $true) | ((sK3 @ X2) = $true)) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f154])).
% 0.14/0.39 thf(f154,plain,(
% 0.14/0.39 ( ! [X2 : $i,X1 : $i] : ((((~ (sK0 @ X1 @ X2)) | (sK3 @ X2)) = $true) | ((~ (sK0 @ sK2 @ X1)) = $true)) )),
% 0.14/0.39 inference(beta_eta_normalization,[],[f153])).
% 0.14/0.39 thf(f153,plain,(
% 0.14/0.39 ( ! [X2 : $i,X1 : $i] : (((~ (sK0 @ sK2 @ X1)) = $true) | (((^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (sK3 @ Y0))) @ X2) = $true)) )),
% 0.14/0.39 inference(pi_clausification,[],[f152])).
% 0.14/0.39 thf(f152,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (sK3 @ Y0)))) = $true) | ((~ (sK0 @ sK2 @ X1)) = $true)) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f151])).
% 0.14/0.39 thf(f151,plain,(
% 0.14/0.39 ( ! [X1 : $i] : ((((~ (sK0 @ sK2 @ X1)) | (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (sK3 @ Y0))))) = $true)) )),
% 0.14/0.39 inference(beta_eta_normalization,[],[f150])).
% 0.14/0.39 thf(f150,plain,(
% 0.14/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (sK0 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ Y0 @ Y1)) | (sK3 @ Y1)))))) @ X1) = $true)) )),
% 0.14/0.39 inference(pi_clausification,[],[f149])).
% 0.14/0.39 thf(f149,plain,(
% 0.14/0.39 ((!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ Y0 @ Y1)) | (sK3 @ Y1))))))) = $true)),
% 0.14/0.39 inference(not_proxy_clausification,[],[f148])).
% 0.14/0.39 thf(f148,plain,(
% 0.14/0.39 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ Y0 @ Y1)) | (sK3 @ Y1)))))))) = $false)),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f146])).
% 0.14/0.39 thf(f172,plain,(
% 0.14/0.39 ( ! [X2 : $i,X1 : $i] : (((sK0 @ (sK5 @ X1 @ X2) @ X1) = $true) | ((sK0 @ X2 @ X1) = $false)) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f170])).
% 0.14/0.39 thf(f160,plain,(
% 0.14/0.39 ($false = (sK3 @ sK4))),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f159])).
% 0.14/0.39 % SZS output end Proof for theBenchmark
% 0.14/0.39 % (17374)------------------------------
% 0.14/0.39 % (17374)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (17374)Termination reason: Refutation
% 0.14/0.39
% 0.14/0.39 % (17374)Memory used [KB]: 5628
% 0.14/0.39 % (17374)Time elapsed: 0.016 s
% 0.14/0.39 % (17374)Instructions burned: 15 (million)
% 0.14/0.39 % (17374)------------------------------
% 0.14/0.39 % (17374)------------------------------
% 0.14/0.39 % (17373)Success in time 0.03 s
% 0.14/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------