TSTP Solution File: SYO481^6 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO481^6 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n022.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 09:05:23 EDT 2024
% Result : Theorem 0.15s 0.38s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO481^6 : TPTP v8.2.0. Released v4.0.0.
% 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
% 0.15/0.35 % Computer : n022.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 20 10:16:53 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 This is a TH0_THM_EQU_NAR problem
% 0.15/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.37 % (29162)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.37 % (29162)Instruction limit reached!
% 0.15/0.37 % (29162)------------------------------
% 0.15/0.37 % (29162)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (29162)Termination reason: Unknown
% 0.15/0.37 % (29162)Termination phase: Property scanning
% 0.15/0.37
% 0.15/0.37 % (29162)Memory used [KB]: 1023
% 0.15/0.37 % (29162)Time elapsed: 0.003 s
% 0.15/0.37 % (29162)Instructions burned: 5 (million)
% 0.15/0.37 % (29162)------------------------------
% 0.15/0.37 % (29162)------------------------------
% 0.15/0.37 % (29158)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.37 % (29159)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)
% 0.15/0.37 % (29160)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)
% 0.15/0.37 % (29163)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)
% 0.15/0.37 % (29164)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)
% 0.15/0.37 % (29165)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.37 % (29166)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)
% 0.15/0.37 % (29163)Instruction limit reached!
% 0.15/0.37 % (29163)------------------------------
% 0.15/0.37 % (29163)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (29163)Termination reason: Unknown
% 0.15/0.37 % (29163)Termination phase: shuffling
% 0.15/0.37
% 0.15/0.37 % (29163)Memory used [KB]: 1023
% 0.15/0.37 % (29163)Time elapsed: 0.004 s
% 0.15/0.37 % (29163)Instructions burned: 3 (million)
% 0.15/0.37 % (29163)------------------------------
% 0.15/0.37 % (29163)------------------------------
% 0.15/0.37 % (29166)Instruction limit reached!
% 0.15/0.37 % (29166)------------------------------
% 0.15/0.37 % (29166)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (29166)Termination reason: Unknown
% 0.15/0.37 % (29166)Termination phase: shuffling
% 0.15/0.37
% 0.15/0.37 % (29166)Memory used [KB]: 1023
% 0.15/0.37 % (29166)Time elapsed: 0.004 s
% 0.15/0.37 % (29166)Instructions burned: 3 (million)
% 0.15/0.37 % (29166)------------------------------
% 0.15/0.37 % (29166)------------------------------
% 0.15/0.38 % (29159)Instruction limit reached!
% 0.15/0.38 % (29159)------------------------------
% 0.15/0.38 % (29159)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (29159)Termination reason: Unknown
% 0.15/0.38 % (29159)Termination phase: Property scanning
% 0.15/0.38
% 0.15/0.38 % (29159)Memory used [KB]: 1023
% 0.15/0.38 % (29159)Time elapsed: 0.005 s
% 0.15/0.38 % (29159)Instructions burned: 5 (million)
% 0.15/0.38 % (29159)------------------------------
% 0.15/0.38 % (29159)------------------------------
% 0.15/0.38 % (29171)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.15/0.38 % (29164)First to succeed.
% 0.15/0.38 % (29158)Also succeeded, but the first one will report.
% 0.15/0.38 % (29164)Refutation found. Thanks to Tanya!
% 0.15/0.38 % SZS status Theorem for theBenchmark
% 0.15/0.38 % SZS output start Proof for theBenchmark
% 0.15/0.38 thf(type_def_5, type, mu: $tType).
% 0.15/0.38 thf(func_def_0, type, mu: $tType).
% 0.15/0.38 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.15/0.38 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_15, type, mtrue: $i > $o).
% 0.15/0.38 thf(func_def_16, type, mfalse: $i > $o).
% 0.15/0.38 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.15/0.38 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.15/0.38 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.15/0.38 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.15/0.38 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.15/0.38 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.15/0.38 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.15/0.38 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.15/0.38 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.15/0.38 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.15/0.38 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.15/0.38 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.15/0.38 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.15/0.38 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.15/0.38 thf(func_def_33, type, rel_s5: $i > $i > $o).
% 0.15/0.38 thf(func_def_34, type, mbox_s5: ($i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_35, type, mdia_s5: ($i > $o) > $i > $o).
% 0.15/0.38 thf(func_def_53, type, sK2: mu).
% 0.15/0.38 thf(func_def_54, type, sK3: mu).
% 0.15/0.38 thf(f139,plain,(
% 0.15/0.38 $false),
% 0.15/0.38 inference(subsumption_resolution,[],[f131,f138])).
% 0.15/0.38 thf(f138,plain,(
% 0.15/0.38 (sK2 = sK3)),
% 0.15/0.38 inference(equality_proxy_clausification,[],[f137])).
% 0.15/0.38 thf(f137,plain,(
% 0.15/0.38 ((sK2 = sK3) = $true)),
% 0.15/0.38 inference(not_proxy_clausification,[],[f134])).
% 0.15/0.38 thf(f134,plain,(
% 0.15/0.38 ((~ (sK2 = sK3)) = $false)),
% 0.15/0.38 inference(binary_proxy_clausification,[],[f133])).
% 0.15/0.38 thf(f133,plain,(
% 0.15/0.38 ($false = ((~ (rel_s5 @ sK1 @ sK4)) | (~ (sK2 = sK3))))),
% 0.15/0.38 inference(beta_eta_normalization,[],[f132])).
% 0.15/0.38 thf(f132,plain,(
% 0.15/0.38 ($false = ((^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (~ (sK2 = sK3)))) @ sK4))),
% 0.15/0.38 inference(sigma_clausification,[],[f129])).
% 0.15/0.38 thf(f129,plain,(
% 0.15/0.38 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (~ (sK2 = sK3))))))),
% 0.15/0.38 inference(binary_proxy_clausification,[],[f128])).
% 0.15/0.38 thf(f128,plain,(
% 0.15/0.38 (((sK2 = sK3) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (~ (sK2 = sK3)))))) = $false)),
% 0.15/0.38 inference(beta_eta_normalization,[],[f127])).
% 0.15/0.38 thf(f127,plain,(
% 0.15/0.38 ($false = ((^[Y0 : mu]: ((sK2 = Y0) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ sK1 @ Y1)) | (~ (sK2 = Y0))))))) @ sK3))),
% 0.15/0.38 inference(sigma_clausification,[],[f126])).
% 0.15/0.38 thf(f126,plain,(
% 0.15/0.38 ((!! @ mu @ (^[Y0 : mu]: ((sK2 = Y0) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ sK1 @ Y1)) | (~ (sK2 = Y0)))))))) = $false)),
% 0.15/0.38 inference(beta_eta_normalization,[],[f125])).
% 0.15/0.38 thf(f125,plain,(
% 0.15/0.38 (((^[Y0 : mu]: (!! @ mu @ (^[Y1 : mu]: ((Y0 = Y1) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ sK1 @ Y2)) | (~ (Y0 = Y1))))))))) @ sK2) = $false)),
% 0.15/0.38 inference(sigma_clausification,[],[f124])).
% 0.15/0.38 thf(f124,plain,(
% 0.15/0.38 ($false = (!! @ mu @ (^[Y0 : mu]: (!! @ mu @ (^[Y1 : mu]: ((Y0 = Y1) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ sK1 @ Y2)) | (~ (Y0 = Y1)))))))))))),
% 0.15/0.38 inference(beta_eta_normalization,[],[f123])).
% 0.15/0.38 thf(f123,plain,(
% 0.15/0.38 (((^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: (!! @ mu @ (^[Y2 : mu]: ((Y1 = Y2) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y0 @ Y3)) | (~ (Y1 = Y2))))))))))) @ sK1) = $false)),
% 0.15/0.38 inference(sigma_clausification,[],[f122])).
% 0.15/0.38 thf(f122,plain,(
% 0.15/0.38 ((!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: (!! @ mu @ (^[Y2 : mu]: ((Y1 = Y2) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y0 @ Y3)) | (~ (Y1 = Y2)))))))))))) != $true)),
% 0.15/0.38 inference(boolean_simplification,[],[f121])).
% 0.15/0.38 thf(f121,plain,(
% 0.15/0.38 ((!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: (!! @ mu @ (^[Y2 : mu]: ((~ (~ (Y1 = Y2))) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y0 @ Y3)) | (~ (Y1 = Y2)))))))))))) != $true)),
% 0.15/0.38 inference(beta_eta_normalization,[],[f120])).
% 0.15/0.38 thf(f120,plain,(
% 0.15/0.38 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : mu]: ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : mu]: ((^[Y3 : mu]: ((^[Y4 : $i]: (Y2 = Y3)))))) @ Y0 @ Y1)) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s5 @ Y3 @ Y4)) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : mu]: ((^[Y3 : mu]: ((^[Y4 : $i]: (Y2 = Y3)))))) @ Y0 @ Y1))))))))) != $true)),
% 0.15/0.38 inference(definition_unfolding,[],[f113,f115,f111,f111,f119,f114,f116,f117,f114,f116])).
% 0.15/0.38 thf(f117,plain,(
% 0.15/0.38 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.15/0.38 inference(cnf_transformation,[],[f64])).
% 0.15/0.38 thf(f64,plain,(
% 0.15/0.38 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.15/0.38 inference(fool_elimination,[],[f63])).
% 0.15/0.38 thf(f63,plain,(
% 0.15/0.38 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_s5 @ X1 @ X2)))) = mbox_s5)),
% 0.15/0.38 inference(rectify,[],[f32])).
% 0.15/0.38 thf(f32,axiom,(
% 0.15/0.38 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_s5 @ X2 @ X7)))) = mbox_s5)),
% 0.15/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s5)).
% 0.15/0.38 thf(f116,plain,(
% 0.15/0.38 (meq_ind = (^[Y0 : mu]: ((^[Y1 : mu]: ((^[Y2 : $i]: (Y0 = Y1)))))))),
% 0.15/0.38 inference(cnf_transformation,[],[f40])).
% 0.15/0.38 thf(f40,plain,(
% 0.15/0.38 (meq_ind = (^[Y0 : mu]: ((^[Y1 : mu]: ((^[Y2 : $i]: (Y0 = Y1)))))))),
% 0.15/0.38 inference(fool_elimination,[],[f1])).
% 0.15/0.38 thf(f1,axiom,(
% 0.15/0.38 (meq_ind = (^[X0 : mu, X1 : mu, X2 : $i] : ((X0 = X1))))),
% 0.15/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meq_ind)).
% 0.15/0.38 thf(f114,plain,(
% 0.15/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.15/0.38 inference(cnf_transformation,[],[f66])).
% 0.15/0.38 thf(f66,plain,(
% 0.15/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.15/0.38 inference(fool_elimination,[],[f65])).
% 0.15/0.38 thf(f65,plain,(
% 0.15/0.38 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.15/0.38 inference(rectify,[],[f3])).
% 0.15/0.38 thf(f3,axiom,(
% 0.15/0.38 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.15/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.15/0.38 thf(f119,plain,(
% 0.15/0.38 (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)))))),
% 0.15/0.38 inference(definition_unfolding,[],[f112,f118,f114])).
% 0.15/0.38 thf(f118,plain,(
% 0.15/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.15/0.38 inference(cnf_transformation,[],[f107])).
% 0.15/0.38 thf(f107,plain,(
% 0.15/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.15/0.38 inference(fool_elimination,[],[f106])).
% 0.15/0.38 thf(f106,plain,(
% 0.15/0.38 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.15/0.38 inference(rectify,[],[f4])).
% 0.15/0.38 thf(f4,axiom,(
% 0.15/0.38 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))))),
% 0.15/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.15/0.38 thf(f112,plain,(
% 0.15/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.15/0.38 inference(cnf_transformation,[],[f103])).
% 0.15/0.38 thf(f103,plain,(
% 0.15/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.15/0.38 inference(fool_elimination,[],[f102])).
% 0.15/0.38 thf(f102,plain,(
% 0.15/0.38 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.15/0.38 inference(rectify,[],[f6])).
% 0.15/0.38 thf(f6,axiom,(
% 0.15/0.38 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.15/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.15/0.38 thf(f111,plain,(
% 0.15/0.38 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.15/0.38 inference(cnf_transformation,[],[f105])).
% 0.15/0.38 thf(f105,plain,(
% 0.15/0.38 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.15/0.38 inference(fool_elimination,[],[f104])).
% 0.15/0.38 thf(f104,plain,(
% 0.15/0.38 (mforall_ind = (^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : (X0 @ X2 @ X1))))),
% 0.15/0.38 inference(rectify,[],[f10])).
% 0.15/0.38 thf(f10,axiom,(
% 0.15/0.38 (mforall_ind = (^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : (X3 @ X0 @ X2))))),
% 0.15/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind)).
% 0.15/0.38 thf(f115,plain,(
% 0.15/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.15/0.38 inference(cnf_transformation,[],[f109])).
% 0.15/0.38 thf(f109,plain,(
% 0.15/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.15/0.38 inference(fool_elimination,[],[f108])).
% 0.15/0.38 thf(f108,plain,(
% 0.15/0.38 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.15/0.38 inference(rectify,[],[f28])).
% 0.15/0.38 thf(f28,axiom,(
% 0.15/0.38 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.15/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.15/0.38 thf(f113,plain,(
% 0.15/0.38 ((mvalid @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mimplies @ (mnot @ (meq_ind @ Y0 @ Y1)) @ (mbox_s5 @ (mnot @ (meq_ind @ Y0 @ Y1))))))))) != $true)),
% 0.15/0.38 inference(cnf_transformation,[],[f110])).
% 0.15/0.38 thf(f110,plain,(
% 0.15/0.38 ((mvalid @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mimplies @ (mnot @ (meq_ind @ Y0 @ Y1)) @ (mbox_s5 @ (mnot @ (meq_ind @ Y0 @ Y1))))))))) != $true)),
% 0.15/0.38 inference(flattening,[],[f72])).
% 0.15/0.38 thf(f72,plain,(
% 0.15/0.38 ~((mvalid @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mimplies @ (mnot @ (meq_ind @ Y0 @ Y1)) @ (mbox_s5 @ (mnot @ (meq_ind @ Y0 @ Y1))))))))) = $true)),
% 0.15/0.38 inference(fool_elimination,[],[f71])).
% 0.15/0.38 thf(f71,plain,(
% 0.15/0.38 ~(mvalid @ (mforall_ind @ (^[X0 : mu] : (mforall_ind @ (^[X1 : mu] : (mimplies @ (mnot @ (meq_ind @ X0 @ X1)) @ (mbox_s5 @ (mnot @ (meq_ind @ X0 @ X1)))))))))),
% 0.15/0.38 inference(rectify,[],[f38])).
% 0.15/0.38 thf(f38,negated_conjecture,(
% 0.15/0.38 ~(mvalid @ (mforall_ind @ (^[X0 : mu] : (mforall_ind @ (^[X1 : mu] : (mimplies @ (mnot @ (meq_ind @ X0 @ X1)) @ (mbox_s5 @ (mnot @ (meq_ind @ X0 @ X1)))))))))),
% 0.15/0.38 inference(negated_conjecture,[],[f37])).
% 0.15/0.38 thf(f37,conjecture,(
% 0.15/0.38 (mvalid @ (mforall_ind @ (^[X0 : mu] : (mforall_ind @ (^[X1 : mu] : (mimplies @ (mnot @ (meq_ind @ X0 @ X1)) @ (mbox_s5 @ (mnot @ (meq_ind @ X0 @ X1)))))))))),
% 0.15/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.15/0.38 thf(f131,plain,(
% 0.15/0.38 (sK2 != sK3)),
% 0.15/0.38 inference(equality_proxy_clausification,[],[f130])).
% 0.15/0.38 thf(f130,plain,(
% 0.15/0.38 ((sK2 = sK3) = $false)),
% 0.15/0.38 inference(binary_proxy_clausification,[],[f128])).
% 0.15/0.38 % SZS output end Proof for theBenchmark
% 0.15/0.38 % (29164)------------------------------
% 0.15/0.38 % (29164)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (29164)Termination reason: Refutation
% 0.15/0.38
% 0.15/0.38 % (29164)Memory used [KB]: 5628
% 0.15/0.38 % (29164)Time elapsed: 0.009 s
% 0.15/0.38 % (29164)Instructions burned: 9 (million)
% 0.15/0.38 % (29164)------------------------------
% 0.15/0.38 % (29164)------------------------------
% 0.15/0.38 % (29155)Success in time 0.014 s
% 0.15/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------