TSTP Solution File: SYO487^6 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO487^6 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n010.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 09:05:24 EDT 2024
% Result : Theorem 0.20s 0.38s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO487^6 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 09:05:08 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 This is a TH0_THM_EQU_NAR problem
% 0.13/0.35 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/sandbox/benchmark/theBenchmark.p
% 0.13/0.37 % (22561)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.37 % (22562)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)
% 0.13/0.37 % (22562)Instruction limit reached!
% 0.13/0.37 % (22562)------------------------------
% 0.13/0.37 % (22562)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (22562)Termination reason: Unknown
% 0.13/0.37 % (22562)Termination phase: shuffling
% 0.13/0.37
% 0.13/0.37 % (22562)Memory used [KB]: 1023
% 0.13/0.37 % (22562)Time elapsed: 0.004 s
% 0.13/0.37 % (22562)Instructions burned: 4 (million)
% 0.13/0.37 % (22562)------------------------------
% 0.13/0.37 % (22562)------------------------------
% 0.13/0.38 % (22564)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.38 % (22561)First to succeed.
% 0.13/0.38 % (22564)Instruction limit reached!
% 0.13/0.38 % (22564)------------------------------
% 0.13/0.38 % (22564)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (22564)Termination reason: Unknown
% 0.13/0.38 % (22564)Termination phase: shuffling
% 0.13/0.38
% 0.13/0.38 % (22564)Memory used [KB]: 1023
% 0.13/0.38 % (22564)Time elapsed: 0.003 s
% 0.13/0.38 % (22564)Instructions burned: 3 (million)
% 0.13/0.38 % (22564)------------------------------
% 0.13/0.38 % (22564)------------------------------
% 0.20/0.38 % (22567)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.38 % (22561)Refutation found. Thanks to Tanya!
% 0.20/0.38 % SZS status Theorem for theBenchmark
% 0.20/0.38 % SZS output start Proof for theBenchmark
% 0.20/0.38 thf(type_def_5, type, mu: $tType).
% 0.20/0.38 thf(func_def_0, type, mu: $tType).
% 0.20/0.38 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.20/0.38 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.38 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.20/0.38 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.38 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.38 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.38 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.38 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.38 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.38 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.20/0.38 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.20/0.38 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.20/0.38 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.20/0.38 thf(func_def_15, type, mtrue: $i > $o).
% 0.20/0.38 thf(func_def_16, type, mfalse: $i > $o).
% 0.20/0.38 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.20/0.38 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.20/0.38 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.20/0.38 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.20/0.38 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.20/0.38 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.20/0.38 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.20/0.38 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.20/0.38 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.20/0.38 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.20/0.38 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.20/0.38 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.20/0.38 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.20/0.38 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.20/0.38 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.20/0.38 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.20/0.38 thf(func_def_33, type, rel_s5: $i > $i > $o).
% 0.20/0.38 thf(func_def_34, type, mbox_s5: ($i > $o) > $i > $o).
% 0.20/0.38 thf(func_def_35, type, mdia_s5: ($i > $o) > $i > $o).
% 0.20/0.38 thf(func_def_36, type, f: mu > $i > $o).
% 0.20/0.38 thf(f214,plain,(
% 0.20/0.38 $false),
% 0.20/0.38 inference(trivial_inequality_removal,[],[f208])).
% 0.20/0.38 thf(f208,plain,(
% 0.20/0.38 ($true = $false)),
% 0.20/0.38 inference(superposition,[],[f207,f176])).
% 0.20/0.38 thf(f176,plain,(
% 0.20/0.38 ($true = (rel_s5 @ sK1 @ sK2))),
% 0.20/0.38 inference(not_proxy_clausification,[],[f175])).
% 0.20/0.38 thf(f175,plain,(
% 0.20/0.38 ((~ (rel_s5 @ sK1 @ sK2)) = $false)),
% 0.20/0.38 inference(binary_proxy_clausification,[],[f173])).
% 0.20/0.38 thf(f173,plain,(
% 0.20/0.38 (((~ (rel_s5 @ sK1 @ sK2)) | (~ (!! @ mu @ (^[Y0 : mu]: (f @ Y0 @ sK2))))) = $false)),
% 0.20/0.38 inference(beta_eta_normalization,[],[f172])).
% 0.20/0.38 thf(f172,plain,(
% 0.20/0.38 (((^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (~ (!! @ mu @ (^[Y1 : mu]: (f @ Y1 @ Y0)))))) @ sK2) = $false)),
% 0.20/0.38 inference(sigma_clausification,[],[f171])).
% 0.20/0.38 thf(f171,plain,(
% 0.20/0.38 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (~ (!! @ mu @ (^[Y1 : mu]: (f @ Y1 @ Y0))))))) = $false)),
% 0.20/0.38 inference(binary_proxy_clausification,[],[f169])).
% 0.20/0.38 thf(f169,plain,(
% 0.20/0.38 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (~ (!! @ mu @ (^[Y1 : mu]: (f @ Y1 @ Y0))))))) | (~ (!! @ mu @ (^[Y0 : mu]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ sK1 @ Y1)) | (~ (f @ Y0 @ Y1))))))))))),
% 0.20/0.38 inference(beta_eta_normalization,[],[f168])).
% 0.20/0.38 thf(f168,plain,(
% 0.20/0.38 (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ mu @ (^[Y2 : mu]: (f @ Y2 @ Y1))))))) | (~ (!! @ mu @ (^[Y1 : mu]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y0 @ Y2)) | (~ (f @ Y1 @ Y2)))))))))) @ sK1) = $false)),
% 0.20/0.38 inference(sigma_clausification,[],[f167])).
% 0.20/0.38 thf(f167,plain,(
% 0.20/0.38 ($true != (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ mu @ (^[Y2 : mu]: (f @ Y2 @ Y1))))))) | (~ (!! @ mu @ (^[Y1 : mu]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y0 @ Y2)) | (~ (f @ Y1 @ Y2))))))))))))),
% 0.20/0.38 inference(boolean_simplification,[],[f166])).
% 0.20/0.38 thf(f166,plain,(
% 0.20/0.38 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ mu @ (^[Y2 : mu]: (f @ Y2 @ Y1))))))))) | (~ (!! @ mu @ (^[Y1 : mu]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y0 @ Y2)) | (~ (f @ Y1 @ Y2))))))))))))),
% 0.20/0.38 inference(boolean_simplification,[],[f165])).
% 0.20/0.38 thf(f165,plain,(
% 0.20/0.38 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ mu @ (^[Y2 : mu]: (f @ Y2 @ Y1))))))))) | (~ (!! @ mu @ (^[Y1 : mu]: (~ (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y0 @ Y2)) | (~ (f @ Y1 @ Y2))))))))))))))),
% 0.20/0.38 inference(beta_eta_normalization,[],[f158])).
% 0.20/0.38 thf(f158,plain,(
% 0.20/0.38 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : mu]: (f @ Y0)))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ (Y0 @ Y1)))))) @ (^[Y0 : mu]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s5 @ Y3 @ Y4)) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))) @ (f @ Y0)))))))),
% 0.20/0.38 inference(definition_unfolding,[],[f115,f147,f149,f157,f131,f153,f157])).
% 0.20/0.38 thf(f153,plain,(
% 0.20/0.38 (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ (Y0 @ Y1)))))))),
% 0.20/0.38 inference(definition_unfolding,[],[f134,f120,f131,f120])).
% 0.20/0.38 thf(f120,plain,(
% 0.20/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.38 inference(cnf_transformation,[],[f75])).
% 0.20/0.38 thf(f75,plain,(
% 0.20/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.38 inference(fool_elimination,[],[f74])).
% 0.20/0.38 thf(f74,plain,(
% 0.20/0.38 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.20/0.38 inference(rectify,[],[f3])).
% 0.20/0.38 thf(f3,axiom,(
% 0.20/0.38 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.20/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.20/0.38 thf(f134,plain,(
% 0.20/0.38 (mexists_ind = (^[Y0 : mu > $i > $o]: (mnot @ (mforall_ind @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))))))),
% 0.20/0.38 inference(cnf_transformation,[],[f71])).
% 0.20/0.38 thf(f71,plain,(
% 0.20/0.38 (mexists_ind = (^[Y0 : mu > $i > $o]: (mnot @ (mforall_ind @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))))))),
% 0.20/0.38 inference(fool_elimination,[],[f70])).
% 0.20/0.38 thf(f70,plain,(
% 0.20/0.38 ((^[X0 : mu > $i > $o] : (mnot @ (mforall_ind @ (^[X1 : mu] : (mnot @ (X0 @ X1)))))) = mexists_ind)),
% 0.20/0.38 inference(rectify,[],[f12])).
% 0.20/0.38 thf(f12,axiom,(
% 0.20/0.38 ((^[X3 : mu > $i > $o] : (mnot @ (mforall_ind @ (^[X0 : mu] : (mnot @ (X3 @ X0)))))) = mexists_ind)),
% 0.20/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_ind)).
% 0.20/0.38 thf(f131,plain,(
% 0.20/0.38 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.20/0.38 inference(cnf_transformation,[],[f95])).
% 0.20/0.38 thf(f95,plain,(
% 0.20/0.38 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.20/0.38 inference(fool_elimination,[],[f94])).
% 0.20/0.38 thf(f94,plain,(
% 0.20/0.38 (mforall_ind = (^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : (X0 @ X2 @ X1))))),
% 0.20/0.38 inference(rectify,[],[f10])).
% 0.20/0.38 thf(f10,axiom,(
% 0.20/0.38 (mforall_ind = (^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : (X3 @ X0 @ X2))))),
% 0.20/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_ind)).
% 0.20/0.38 thf(f157,plain,(
% 0.20/0.38 (mdia_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.20/0.38 inference(definition_unfolding,[],[f114,f120,f132,f120])).
% 0.20/0.38 thf(f132,plain,(
% 0.20/0.38 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.20/0.38 inference(cnf_transformation,[],[f47])).
% 0.20/0.38 thf(f47,plain,(
% 0.20/0.38 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.20/0.38 inference(fool_elimination,[],[f46])).
% 0.20/0.38 thf(f46,plain,(
% 0.20/0.38 (mbox_s5 = (^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_s5 @ X1 @ X2)))))),
% 0.20/0.38 inference(rectify,[],[f32])).
% 0.20/0.38 thf(f32,axiom,(
% 0.20/0.38 (mbox_s5 = (^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_s5 @ X2 @ X7)))))),
% 0.20/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s5)).
% 0.20/0.38 thf(f114,plain,(
% 0.20/0.38 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.20/0.38 inference(cnf_transformation,[],[f100])).
% 0.20/0.38 thf(f100,plain,(
% 0.20/0.38 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.20/0.38 inference(fool_elimination,[],[f99])).
% 0.20/0.38 thf(f99,plain,(
% 0.20/0.38 ((^[X0 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X0)))) = mdia_s5)),
% 0.20/0.38 inference(rectify,[],[f33])).
% 0.20/0.38 thf(f33,axiom,(
% 0.20/0.38 ((^[X3 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X3)))) = mdia_s5)),
% 0.20/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_s5)).
% 0.20/0.38 thf(f149,plain,(
% 0.20/0.38 (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)))))),
% 0.20/0.38 inference(definition_unfolding,[],[f116,f119,f120])).
% 0.20/0.38 thf(f119,plain,(
% 0.20/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.20/0.38 inference(cnf_transformation,[],[f85])).
% 0.20/0.38 thf(f85,plain,(
% 0.20/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.20/0.38 inference(fool_elimination,[],[f84])).
% 0.20/0.38 thf(f84,plain,(
% 0.20/0.38 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 0.20/0.38 inference(rectify,[],[f4])).
% 0.20/0.38 thf(f4,axiom,(
% 0.20/0.38 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))) = mor)),
% 0.20/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.20/0.38 thf(f116,plain,(
% 0.20/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.38 inference(cnf_transformation,[],[f67])).
% 0.20/0.38 thf(f67,plain,(
% 0.20/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.38 inference(fool_elimination,[],[f66])).
% 0.20/0.38 thf(f66,plain,(
% 0.20/0.38 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.20/0.38 inference(rectify,[],[f6])).
% 0.20/0.38 thf(f6,axiom,(
% 0.20/0.38 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.20/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.20/0.38 thf(f147,plain,(
% 0.20/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.38 inference(cnf_transformation,[],[f51])).
% 0.20/0.38 thf(f51,plain,(
% 0.20/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.38 inference(fool_elimination,[],[f50])).
% 0.20/0.38 thf(f50,plain,(
% 0.20/0.38 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.20/0.38 inference(rectify,[],[f28])).
% 0.20/0.38 thf(f28,axiom,(
% 0.20/0.38 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.20/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.20/0.38 thf(f115,plain,(
% 0.20/0.38 ($true != (mvalid @ (mimplies @ (mdia_s5 @ (mforall_ind @ (^[Y0 : mu]: (f @ Y0)))) @ (mexists_ind @ (^[Y0 : mu]: (mdia_s5 @ (f @ Y0)))))))),
% 0.20/0.38 inference(cnf_transformation,[],[f110])).
% 0.20/0.38 thf(f110,plain,(
% 0.20/0.38 ($true != (mvalid @ (mimplies @ (mdia_s5 @ (mforall_ind @ (^[Y0 : mu]: (f @ Y0)))) @ (mexists_ind @ (^[Y0 : mu]: (mdia_s5 @ (f @ Y0)))))))),
% 0.20/0.38 inference(flattening,[],[f63])).
% 0.20/0.38 thf(f63,plain,(
% 0.20/0.38 ~($true = (mvalid @ (mimplies @ (mdia_s5 @ (mforall_ind @ (^[Y0 : mu]: (f @ Y0)))) @ (mexists_ind @ (^[Y0 : mu]: (mdia_s5 @ (f @ Y0)))))))),
% 0.20/0.38 inference(fool_elimination,[],[f62])).
% 0.20/0.38 thf(f62,plain,(
% 0.20/0.38 ~(mvalid @ (mimplies @ (mdia_s5 @ (mforall_ind @ (^[X0 : mu] : (f @ X0)))) @ (mexists_ind @ (^[X1 : mu] : (mdia_s5 @ (f @ X1))))))),
% 0.20/0.38 inference(rectify,[],[f38])).
% 0.20/0.38 thf(f38,negated_conjecture,(
% 0.20/0.38 ~(mvalid @ (mimplies @ (mdia_s5 @ (mforall_ind @ (^[X0 : mu] : (f @ X0)))) @ (mexists_ind @ (^[X0 : mu] : (mdia_s5 @ (f @ X0))))))),
% 0.20/0.38 inference(negated_conjecture,[],[f37])).
% 0.20/0.38 thf(f37,conjecture,(
% 0.20/0.38 (mvalid @ (mimplies @ (mdia_s5 @ (mforall_ind @ (^[X0 : mu] : (f @ X0)))) @ (mexists_ind @ (^[X0 : mu] : (mdia_s5 @ (f @ X0))))))),
% 0.20/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.20/0.38 thf(f207,plain,(
% 0.20/0.38 ((rel_s5 @ sK1 @ sK2) = $false)),
% 0.20/0.38 inference(trivial_inequality_removal,[],[f205])).
% 0.20/0.38 thf(f205,plain,(
% 0.20/0.38 ($true = $false) | ((rel_s5 @ sK1 @ sK2) = $false)),
% 0.20/0.38 inference(superposition,[],[f179,f187])).
% 0.20/0.38 thf(f187,plain,(
% 0.20/0.38 ( ! [X2 : $i,X1 : mu] : (((f @ X1 @ X2) = $false) | ((rel_s5 @ sK1 @ X2) = $false)) )),
% 0.20/0.38 inference(not_proxy_clausification,[],[f186])).
% 0.20/0.38 thf(f186,plain,(
% 0.20/0.38 ( ! [X2 : $i,X1 : mu] : (((f @ X1 @ X2) = $false) | ($true = (~ (rel_s5 @ sK1 @ X2)))) )),
% 0.20/0.38 inference(not_proxy_clausification,[],[f185])).
% 0.20/0.38 thf(f185,plain,(
% 0.20/0.38 ( ! [X2 : $i,X1 : mu] : (($true = (~ (f @ X1 @ X2))) | ($true = (~ (rel_s5 @ sK1 @ X2)))) )),
% 0.20/0.38 inference(binary_proxy_clausification,[],[f184])).
% 0.20/0.38 thf(f184,plain,(
% 0.20/0.38 ( ! [X2 : $i,X1 : mu] : ((((~ (rel_s5 @ sK1 @ X2)) | (~ (f @ X1 @ X2))) = $true)) )),
% 0.20/0.38 inference(beta_eta_normalization,[],[f183])).
% 0.20/0.38 thf(f183,plain,(
% 0.20/0.38 ( ! [X2 : $i,X1 : mu] : ((((^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (~ (f @ X1 @ Y0)))) @ X2) = $true)) )),
% 0.20/0.38 inference(pi_clausification,[],[f182])).
% 0.20/0.38 thf(f182,plain,(
% 0.20/0.38 ( ! [X1 : mu] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (~ (f @ X1 @ Y0))))))) )),
% 0.20/0.38 inference(beta_eta_normalization,[],[f181])).
% 0.20/0.38 thf(f181,plain,(
% 0.20/0.38 ( ! [X1 : mu] : ((((^[Y0 : mu]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ sK1 @ Y1)) | (~ (f @ Y0 @ Y1)))))) @ X1) = $true)) )),
% 0.20/0.38 inference(pi_clausification,[],[f180])).
% 0.20/0.38 thf(f180,plain,(
% 0.20/0.38 ((!! @ mu @ (^[Y0 : mu]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ sK1 @ Y1)) | (~ (f @ Y0 @ Y1))))))) = $true)),
% 0.20/0.38 inference(not_proxy_clausification,[],[f170])).
% 0.20/0.38 thf(f170,plain,(
% 0.20/0.38 ((~ (!! @ mu @ (^[Y0 : mu]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ sK1 @ Y1)) | (~ (f @ Y0 @ Y1)))))))) = $false)),
% 0.20/0.38 inference(binary_proxy_clausification,[],[f169])).
% 0.20/0.38 thf(f179,plain,(
% 0.20/0.38 ( ! [X1 : mu] : (($true = (f @ X1 @ sK2))) )),
% 0.20/0.38 inference(beta_eta_normalization,[],[f178])).
% 0.20/0.38 thf(f178,plain,(
% 0.20/0.38 ( ! [X1 : mu] : (($true = ((^[Y0 : mu]: (f @ Y0 @ sK2)) @ X1))) )),
% 0.20/0.38 inference(pi_clausification,[],[f177])).
% 0.20/0.38 thf(f177,plain,(
% 0.20/0.38 ($true = (!! @ mu @ (^[Y0 : mu]: (f @ Y0 @ sK2))))),
% 0.20/0.38 inference(not_proxy_clausification,[],[f174])).
% 0.20/0.38 thf(f174,plain,(
% 0.20/0.38 ((~ (!! @ mu @ (^[Y0 : mu]: (f @ Y0 @ sK2)))) = $false)),
% 0.20/0.38 inference(binary_proxy_clausification,[],[f173])).
% 0.20/0.38 % SZS output end Proof for theBenchmark
% 0.20/0.38 % (22561)------------------------------
% 0.20/0.38 % (22561)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (22561)Termination reason: Refutation
% 0.20/0.38
% 0.20/0.38 % (22561)Memory used [KB]: 5628
% 0.20/0.38 % (22561)Time elapsed: 0.012 s
% 0.20/0.38 % (22561)Instructions burned: 13 (million)
% 0.20/0.38 % (22561)------------------------------
% 0.20/0.38 % (22561)------------------------------
% 0.20/0.38 % (22560)Success in time 0.025 s
% 0.20/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------