TSTP Solution File: LCL702^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL702^1 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n027.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 0.22s 0.39s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL702^1 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n027.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 01:52:23 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a TH0_THM_EQU_NAR problem
% 0.22/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.38 % (4362)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.22/0.38 % (4365)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.38 % (4364)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)
% 0.22/0.38 % (4363)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)
% 0.22/0.38 % (4366)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)
% 0.22/0.38 % (4367)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)
% 0.22/0.38 % (4368)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.38 % (4369)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)
% 0.22/0.38 % (4365)Instruction limit reached!
% 0.22/0.38 % (4365)------------------------------
% 0.22/0.38 % (4365)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38 % (4365)Termination reason: Unknown
% 0.22/0.38 % (4365)Termination phase: shuffling
% 0.22/0.38 % (4366)Instruction limit reached!
% 0.22/0.38 % (4366)------------------------------
% 0.22/0.38 % (4366)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38 % (4366)Termination reason: Unknown
% 0.22/0.38 % (4366)Termination phase: shuffling
% 0.22/0.38
% 0.22/0.38 % (4366)Memory used [KB]: 1023
% 0.22/0.38 % (4366)Time elapsed: 0.003 s
% 0.22/0.38 % (4366)Instructions burned: 2 (million)
% 0.22/0.38 % (4366)------------------------------
% 0.22/0.38 % (4366)------------------------------
% 0.22/0.38
% 0.22/0.38 % (4365)Memory used [KB]: 1023
% 0.22/0.38 % (4365)Time elapsed: 0.003 s
% 0.22/0.38 % (4365)Instructions burned: 2 (million)
% 0.22/0.38 % (4365)------------------------------
% 0.22/0.38 % (4365)------------------------------
% 0.22/0.38 % (4369)Instruction limit reached!
% 0.22/0.38 % (4369)------------------------------
% 0.22/0.38 % (4369)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38 % (4369)Termination reason: Unknown
% 0.22/0.38 % (4369)Termination phase: shuffling
% 0.22/0.38
% 0.22/0.38 % (4369)Memory used [KB]: 1023
% 0.22/0.38 % (4369)Time elapsed: 0.004 s
% 0.22/0.38 % (4369)Instructions burned: 3 (million)
% 0.22/0.38 % (4369)------------------------------
% 0.22/0.38 % (4369)------------------------------
% 0.22/0.38 % (4363)Instruction limit reached!
% 0.22/0.38 % (4363)------------------------------
% 0.22/0.38 % (4363)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38 % (4363)Termination reason: Unknown
% 0.22/0.38 % (4363)Termination phase: Property scanning
% 0.22/0.38
% 0.22/0.38 % (4363)Memory used [KB]: 1023
% 0.22/0.38 % (4363)Time elapsed: 0.004 s
% 0.22/0.38 % (4363)Instructions burned: 5 (million)
% 0.22/0.38 % (4363)------------------------------
% 0.22/0.38 % (4363)------------------------------
% 0.22/0.39 % (4367)First to succeed.
% 0.22/0.39 % (4362)Also succeeded, but the first one will report.
% 0.22/0.39 % (4364)Also succeeded, but the first one will report.
% 0.22/0.39 % (4367)Refutation found. Thanks to Tanya!
% 0.22/0.39 % SZS status Theorem for theBenchmark
% 0.22/0.39 % SZS output start Proof for theBenchmark
% 0.22/0.39 thf(type_def_5, type, mu: $tType).
% 0.22/0.39 thf(func_def_0, type, mu: $tType).
% 0.22/0.39 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.22/0.39 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_15, type, mtrue: $i > $o).
% 0.22/0.39 thf(func_def_16, type, mfalse: $i > $o).
% 0.22/0.39 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.22/0.39 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.22/0.39 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.22/0.39 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.22/0.39 thf(func_def_48, type, sK0: $i > $i > $o).
% 0.22/0.39 thf(func_def_51, type, sK3: $i > $o).
% 0.22/0.39 thf(f178,plain,(
% 0.22/0.39 $false),
% 0.22/0.39 inference(trivial_inequality_removal,[],[f177])).
% 0.22/0.39 thf(f177,plain,(
% 0.22/0.39 ($false = $true)),
% 0.22/0.39 inference(forward_demodulation,[],[f175,f124])).
% 0.22/0.39 thf(f124,plain,(
% 0.22/0.39 ((sK3 @ sK5) = $false)),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f123])).
% 0.22/0.39 thf(f123,plain,(
% 0.22/0.39 ($false = ((~ (sK0 @ sK4 @ sK5)) | (sK3 @ sK5)))),
% 0.22/0.39 inference(beta_eta_normalization,[],[f122])).
% 0.22/0.39 thf(f122,plain,(
% 0.22/0.39 (((^[Y0 : $i]: ((~ (sK0 @ sK4 @ Y0)) | (sK3 @ Y0))) @ sK5) = $false)),
% 0.22/0.39 inference(sigma_clausification,[],[f119])).
% 0.22/0.39 thf(f119,plain,(
% 0.22/0.39 ((!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ sK4 @ Y0)) | (sK3 @ Y0)))) = $false)),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f118])).
% 0.22/0.39 thf(f118,plain,(
% 0.22/0.39 ($false = ((~ (sK0 @ sK2 @ sK4)) | (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ sK4 @ Y0)) | (sK3 @ Y0))))))),
% 0.22/0.39 inference(beta_eta_normalization,[],[f117])).
% 0.22/0.39 thf(f117,plain,(
% 0.22/0.39 ($false = ((^[Y0 : $i]: ((~ (sK0 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ Y0 @ Y1)) | (sK3 @ Y1)))))) @ sK4))),
% 0.22/0.39 inference(sigma_clausification,[],[f116])).
% 0.22/0.39 thf(f116,plain,(
% 0.22/0.39 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ Y0 @ Y1)) | (sK3 @ Y1))))))))),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f114])).
% 0.22/0.39 thf(f114,plain,(
% 0.22/0.39 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ Y0 @ Y1)) | (sK3 @ Y1))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ sK2 @ Y0)) | (sK3 @ Y0)))))))),
% 0.22/0.39 inference(beta_eta_normalization,[],[f113])).
% 0.22/0.39 thf(f113,plain,(
% 0.22/0.39 (((^[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) = $false)),
% 0.22/0.39 inference(sigma_clausification,[],[f112])).
% 0.22/0.39 thf(f112,plain,(
% 0.22/0.39 ($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)))))))))),
% 0.22/0.39 inference(beta_eta_normalization,[],[f111])).
% 0.22/0.39 thf(f111,plain,(
% 0.22/0.39 (((^[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)),
% 0.22/0.39 inference(sigma_clausification,[],[f110])).
% 0.22/0.39 thf(f110,plain,(
% 0.22/0.39 ((!! @ $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)))))))))) != $true)),
% 0.22/0.39 inference(beta_eta_normalization,[],[f108])).
% 0.22/0.39 thf(f108,plain,(
% 0.22/0.39 ($true != ((^[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]: (!! @ $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 @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (Y1 @ Y3 @ Y4)) | (Y2 @ Y4))))))))) @ sK0 @ Y0)))))))),
% 0.22/0.39 inference(definition_unfolding,[],[f102,f98,f99,f107,f106,f106,f106])).
% 0.22/0.39 thf(f106,plain,(
% 0.22/0.39 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.22/0.39 inference(cnf_transformation,[],[f82])).
% 0.22/0.39 thf(f82,plain,(
% 0.22/0.39 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.22/0.39 inference(fool_elimination,[],[f81])).
% 0.22/0.39 thf(f81,plain,(
% 0.22/0.39 ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))) = mbox)),
% 0.22/0.39 inference(rectify,[],[f16])).
% 0.22/0.39 thf(f16,axiom,(
% 0.22/0.39 ((^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(X6 @ X2 @ X7)))) = mbox)),
% 0.22/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox)).
% 0.22/0.39 thf(f107,plain,(
% 0.22/0.39 (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)))))),
% 0.22/0.39 inference(definition_unfolding,[],[f104,f105,f103])).
% 0.22/0.39 thf(f103,plain,(
% 0.22/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.22/0.39 inference(cnf_transformation,[],[f46])).
% 0.22/0.39 thf(f46,plain,(
% 0.22/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.22/0.39 inference(fool_elimination,[],[f45])).
% 0.22/0.39 thf(f45,plain,(
% 0.22/0.39 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.22/0.39 inference(rectify,[],[f3])).
% 0.22/0.39 thf(f3,axiom,(
% 0.22/0.39 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.22/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.22/0.39 thf(f105,plain,(
% 0.22/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.22/0.39 inference(cnf_transformation,[],[f78])).
% 0.22/0.39 thf(f78,plain,(
% 0.22/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.22/0.39 inference(fool_elimination,[],[f77])).
% 0.22/0.39 thf(f77,plain,(
% 0.22/0.39 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.22/0.39 inference(rectify,[],[f4])).
% 0.22/0.39 thf(f4,axiom,(
% 0.22/0.39 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))),
% 0.22/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.22/0.39 thf(f104,plain,(
% 0.22/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.22/0.39 inference(cnf_transformation,[],[f60])).
% 0.22/0.39 thf(f60,plain,(
% 0.22/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.22/0.39 inference(fool_elimination,[],[f59])).
% 0.22/0.39 thf(f59,plain,(
% 0.22/0.39 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.22/0.39 inference(rectify,[],[f6])).
% 0.22/0.39 thf(f6,axiom,(
% 0.22/0.39 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.22/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.22/0.39 thf(f99,plain,(
% 0.22/0.39 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.22/0.39 inference(cnf_transformation,[],[f64])).
% 0.22/0.39 thf(f64,plain,(
% 0.22/0.39 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.22/0.39 inference(fool_elimination,[],[f63])).
% 0.22/0.39 thf(f63,plain,(
% 0.22/0.39 (mforall_prop = (^[X0 : ($i > $o) > $i > $o, X1 : $i] : (! [X2 : $i > $o] : (X0 @ X2 @ X1))))),
% 0.22/0.39 inference(rectify,[],[f11])).
% 0.22/0.39 thf(f11,axiom,(
% 0.22/0.39 (mforall_prop = (^[X3 : ($i > $o) > $i > $o, X2 : $i] : (! [X5 : $i > $o] : (X3 @ X5 @ X2))))),
% 0.22/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_prop)).
% 0.22/0.39 thf(f98,plain,(
% 0.22/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.22/0.39 inference(cnf_transformation,[],[f52])).
% 0.22/0.39 thf(f52,plain,(
% 0.22/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.22/0.39 inference(fool_elimination,[],[f51])).
% 0.22/0.39 thf(f51,plain,(
% 0.22/0.39 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.22/0.39 inference(rectify,[],[f28])).
% 0.22/0.39 thf(f28,axiom,(
% 0.22/0.39 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.22/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.22/0.39 thf(f102,plain,(
% 0.22/0.39 ($true != (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ sK0 @ Y0) @ (mbox @ sK0 @ (mbox @ sK0 @ Y0)))))))),
% 0.22/0.39 inference(cnf_transformation,[],[f97])).
% 0.22/0.39 thf(f97,plain,(
% 0.22/0.39 ($true != (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ sK0 @ Y0) @ (mbox @ sK0 @ (mbox @ sK0 @ Y0))))))) & ($true = (mtransitive @ sK0))),
% 0.22/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f95,f96])).
% 0.22/0.39 thf(f96,plain,(
% 0.22/0.39 ? [X0 : $i > $i > $o] : (($true != (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ X0 @ Y0) @ (mbox @ X0 @ (mbox @ X0 @ Y0))))))) & ((mtransitive @ X0) = $true)) => (($true != (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ sK0 @ Y0) @ (mbox @ sK0 @ (mbox @ sK0 @ Y0))))))) & ($true = (mtransitive @ sK0)))),
% 0.22/0.39 introduced(choice_axiom,[])).
% 0.22/0.39 thf(f95,plain,(
% 0.22/0.39 ? [X0 : $i > $i > $o] : (($true != (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ X0 @ Y0) @ (mbox @ X0 @ (mbox @ X0 @ Y0))))))) & ((mtransitive @ X0) = $true))),
% 0.22/0.39 inference(ennf_transformation,[],[f88])).
% 0.22/0.39 thf(f88,plain,(
% 0.22/0.39 ~! [X0 : $i > $i > $o] : (((mtransitive @ X0) = $true) => ($true = (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ X0 @ Y0) @ (mbox @ X0 @ (mbox @ X0 @ Y0))))))))),
% 0.22/0.39 inference(fool_elimination,[],[f87])).
% 0.22/0.39 thf(f87,plain,(
% 0.22/0.39 ~! [X0 : $i > $i > $o] : ((mtransitive @ X0) => (mvalid @ (mforall_prop @ (^[X1 : $i > $o] : (mimplies @ (mbox @ X0 @ X1) @ (mbox @ X0 @ (mbox @ X0 @ X1)))))))),
% 0.22/0.39 inference(rectify,[],[f33])).
% 0.22/0.39 thf(f33,negated_conjecture,(
% 0.22/0.39 ~! [X6 : $i > $i > $o] : ((mtransitive @ X6) => (mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mimplies @ (mbox @ X6 @ X11) @ (mbox @ X6 @ (mbox @ X6 @ X11)))))))),
% 0.22/0.39 inference(negated_conjecture,[],[f32])).
% 0.22/0.39 thf(f32,conjecture,(
% 0.22/0.39 ! [X6 : $i > $i > $o] : ((mtransitive @ X6) => (mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mimplies @ (mbox @ X6 @ X11) @ (mbox @ X6 @ (mbox @ X6 @ X11)))))))),
% 0.22/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 0.22/0.39 thf(f175,plain,(
% 0.22/0.39 ((sK3 @ sK5) = $true)),
% 0.22/0.39 inference(trivial_inequality_removal,[],[f171])).
% 0.22/0.39 thf(f171,plain,(
% 0.22/0.39 ((sK3 @ sK5) = $true) | ($false = $true)),
% 0.22/0.39 inference(superposition,[],[f131,f168])).
% 0.22/0.39 thf(f168,plain,(
% 0.22/0.39 ((sK0 @ sK2 @ sK5) = $true)),
% 0.22/0.39 inference(trivial_inequality_removal,[],[f165])).
% 0.22/0.39 thf(f165,plain,(
% 0.22/0.39 ((sK0 @ sK2 @ sK5) = $true) | ($false = $true)),
% 0.22/0.39 inference(superposition,[],[f164,f121])).
% 0.22/0.39 thf(f121,plain,(
% 0.22/0.39 ((sK0 @ sK2 @ sK4) = $true)),
% 0.22/0.39 inference(not_proxy_clausification,[],[f120])).
% 0.22/0.39 thf(f120,plain,(
% 0.22/0.39 ((~ (sK0 @ sK2 @ sK4)) = $false)),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f118])).
% 0.22/0.39 thf(f164,plain,(
% 0.22/0.39 ( ! [X0 : $i] : (($false = (sK0 @ X0 @ sK4)) | ((sK0 @ X0 @ sK5) = $true)) )),
% 0.22/0.39 inference(trivial_inequality_removal,[],[f162])).
% 0.22/0.39 thf(f162,plain,(
% 0.22/0.39 ( ! [X0 : $i] : (((sK0 @ X0 @ sK5) = $true) | ($false = (sK0 @ X0 @ sK4)) | ($false = $true)) )),
% 0.22/0.39 inference(superposition,[],[f140,f126])).
% 0.22/0.39 thf(f126,plain,(
% 0.22/0.39 ((sK0 @ sK4 @ sK5) = $true)),
% 0.22/0.39 inference(not_proxy_clausification,[],[f125])).
% 0.22/0.39 thf(f125,plain,(
% 0.22/0.39 ($false = (~ (sK0 @ sK4 @ sK5)))),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f123])).
% 0.22/0.39 thf(f140,plain,(
% 0.22/0.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (sK0 @ X1 @ X2)) | ((sK0 @ X3 @ X1) = $false) | ((sK0 @ X3 @ X2) = $true)) )),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f139])).
% 0.22/0.39 thf(f139,plain,(
% 0.22/0.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((sK0 @ X3 @ X2) = $true) | ($false = ((sK0 @ X3 @ X1) & (sK0 @ X1 @ X2)))) )),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f138])).
% 0.22/0.39 thf(f138,plain,(
% 0.22/0.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((sK0 @ X3 @ X1) & (sK0 @ X1 @ X2)) => (sK0 @ X3 @ X2)) = $true)) )),
% 0.22/0.39 inference(beta_eta_normalization,[],[f137])).
% 0.22/0.39 thf(f137,plain,(
% 0.22/0.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((sK0 @ Y0 @ X1) & (sK0 @ X1 @ X2)) => (sK0 @ Y0 @ X2))) @ X3))) )),
% 0.22/0.39 inference(pi_clausification,[],[f136])).
% 0.22/0.39 thf(f136,plain,(
% 0.22/0.39 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (((sK0 @ Y0 @ X1) & (sK0 @ X1 @ X2)) => (sK0 @ Y0 @ X2)))) = $true)) )),
% 0.22/0.39 inference(beta_eta_normalization,[],[f135])).
% 0.22/0.39 thf(f135,plain,(
% 0.22/0.39 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ Y1 @ X1) & (sK0 @ X1 @ Y0)) => (sK0 @ Y1 @ Y0))))) @ X2) = $true)) )),
% 0.22/0.39 inference(pi_clausification,[],[f134])).
% 0.22/0.39 thf(f134,plain,(
% 0.22/0.39 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ Y1 @ X1) & (sK0 @ X1 @ Y0)) => (sK0 @ Y1 @ Y0)))))) = $true)) )),
% 0.22/0.39 inference(beta_eta_normalization,[],[f133])).
% 0.22/0.39 thf(f133,plain,(
% 0.22/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y2 @ Y0) & (sK0 @ Y0 @ Y1)) => (sK0 @ Y2 @ Y1))))))) @ X1) = $true)) )),
% 0.22/0.39 inference(pi_clausification,[],[f132])).
% 0.22/0.39 thf(f132,plain,(
% 0.22/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y2 @ Y0) & (sK0 @ Y0 @ Y1)) => (sK0 @ Y2 @ Y1)))))))))),
% 0.22/0.39 inference(beta_eta_normalization,[],[f109])).
% 0.22/0.39 thf(f109,plain,(
% 0.22/0.39 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) @ sK0) = $true)),
% 0.22/0.39 inference(definition_unfolding,[],[f101,f100])).
% 0.22/0.39 thf(f100,plain,(
% 0.22/0.39 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))))),
% 0.22/0.39 inference(cnf_transformation,[],[f38])).
% 0.22/0.39 thf(f38,plain,(
% 0.22/0.39 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))))),
% 0.22/0.39 inference(fool_elimination,[],[f37])).
% 0.22/0.39 thf(f37,plain,(
% 0.22/0.39 (mtransitive = (^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X3 @ X2) & (X0 @ X1 @ X3)) => (X0 @ X1 @ X2)))))),
% 0.22/0.39 inference(rectify,[],[f21])).
% 0.22/0.39 thf(f21,axiom,(
% 0.22/0.39 (mtransitive = (^[X6 : $i > $i > $o] : (! [X8,X10,X9] : (((X6 @ X9 @ X10) & (X6 @ X8 @ X9)) => (X6 @ X8 @ X10)))))),
% 0.22/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtransitive)).
% 0.22/0.39 thf(f101,plain,(
% 0.22/0.39 ($true = (mtransitive @ sK0))),
% 0.22/0.39 inference(cnf_transformation,[],[f97])).
% 0.22/0.39 thf(f131,plain,(
% 0.22/0.39 ( ! [X1 : $i] : (((sK0 @ sK2 @ X1) = $false) | ((sK3 @ X1) = $true)) )),
% 0.22/0.39 inference(not_proxy_clausification,[],[f130])).
% 0.22/0.39 thf(f130,plain,(
% 0.22/0.39 ( ! [X1 : $i] : (((~ (sK0 @ sK2 @ X1)) = $true) | ((sK3 @ X1) = $true)) )),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f129])).
% 0.22/0.39 thf(f129,plain,(
% 0.22/0.39 ( ! [X1 : $i] : ((((~ (sK0 @ sK2 @ X1)) | (sK3 @ X1)) = $true)) )),
% 0.22/0.39 inference(beta_eta_normalization,[],[f128])).
% 0.22/0.39 thf(f128,plain,(
% 0.22/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (sK0 @ sK2 @ Y0)) | (sK3 @ Y0))) @ X1) = $true)) )),
% 0.22/0.39 inference(pi_clausification,[],[f127])).
% 0.22/0.39 thf(f127,plain,(
% 0.22/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ sK2 @ Y0)) | (sK3 @ Y0)))))),
% 0.22/0.39 inference(not_proxy_clausification,[],[f115])).
% 0.22/0.39 thf(f115,plain,(
% 0.22/0.39 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ sK2 @ Y0)) | (sK3 @ Y0))))))),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f114])).
% 0.22/0.39 % SZS output end Proof for theBenchmark
% 0.22/0.39 % (4367)------------------------------
% 0.22/0.39 % (4367)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39 % (4367)Termination reason: Refutation
% 0.22/0.39
% 0.22/0.39 % (4367)Memory used [KB]: 5628
% 0.22/0.39 % (4367)Time elapsed: 0.013 s
% 0.22/0.39 % (4367)Instructions burned: 12 (million)
% 0.22/0.39 % (4367)------------------------------
% 0.22/0.39 % (4367)------------------------------
% 0.22/0.39 % (4361)Success in time 0.016 s
% 0.22/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------