TSTP Solution File: SYO455^4 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO455^4 : 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 : n015.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 09:04:41 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 : SYO455^4 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.14 % 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 : n015.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 10:42:08 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
% 0.22/0.37 % (21253)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)
% 0.22/0.37 % (21253)Instruction limit reached!
% 0.22/0.37 % (21253)------------------------------
% 0.22/0.37 % (21253)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.37 % (21253)Termination reason: Unknown
% 0.22/0.37 % (21253)Termination phase: shuffling
% 0.22/0.37
% 0.22/0.37 % (21253)Memory used [KB]: 1023
% 0.22/0.37 % (21253)Time elapsed: 0.002 s
% 0.22/0.37 % (21253)Instructions burned: 3 (million)
% 0.22/0.37 % (21253)------------------------------
% 0.22/0.37 % (21253)------------------------------
% 0.22/0.38 % (21248)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 % (21250)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 % (21249)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 % (21251)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.38 % (21255)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 % (21254)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 % (21251)Instruction limit reached!
% 0.22/0.38 % (21251)------------------------------
% 0.22/0.38 % (21251)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38 % (21251)Termination reason: Unknown
% 0.22/0.38 % (21251)Termination phase: shuffling
% 0.22/0.38
% 0.22/0.38 % (21251)Memory used [KB]: 1023
% 0.22/0.38 % (21251)Time elapsed: 0.004 s
% 0.22/0.38 % (21251)Instructions burned: 3 (million)
% 0.22/0.38 % (21251)------------------------------
% 0.22/0.38 % (21251)------------------------------
% 0.22/0.38 % (21249)Instruction limit reached!
% 0.22/0.38 % (21249)------------------------------
% 0.22/0.38 % (21249)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38 % (21249)Termination reason: Unknown
% 0.22/0.38 % (21249)Termination phase: Property scanning
% 0.22/0.38
% 0.22/0.38 % (21249)Memory used [KB]: 1023
% 0.22/0.38 % (21249)Time elapsed: 0.004 s
% 0.22/0.38 % (21249)Instructions burned: 5 (million)
% 0.22/0.38 % (21249)------------------------------
% 0.22/0.38 % (21249)------------------------------
% 0.22/0.38 % (21260)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)
% 0.22/0.38 % (21256)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 % (21256)Instruction limit reached!
% 0.22/0.38 % (21256)------------------------------
% 0.22/0.38 % (21256)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38 % (21256)Termination reason: Unknown
% 0.22/0.38 % (21256)Termination phase: shuffling
% 0.22/0.38
% 0.22/0.38 % (21256)Memory used [KB]: 1023
% 0.22/0.38 % (21256)Time elapsed: 0.003 s
% 0.22/0.38 % (21256)Instructions burned: 3 (million)
% 0.22/0.38 % (21256)------------------------------
% 0.22/0.38 % (21256)------------------------------
% 0.22/0.38 % (21254)Refutation not found, incomplete strategy
% 0.22/0.38 % (21254)------------------------------
% 0.22/0.38 % (21254)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38 % (21254)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.38
% 0.22/0.38
% 0.22/0.38 % (21254)Memory used [KB]: 5628
% 0.22/0.38 % (21254)Time elapsed: 0.008 s
% 0.22/0.38 % (21254)Instructions burned: 9 (million)
% 0.22/0.38 % (21254)------------------------------
% 0.22/0.38 % (21254)------------------------------
% 0.22/0.39 % (21250)First to succeed.
% 0.22/0.39 % (21255)Also succeeded, but the first one will report.
% 0.22/0.39 % (21248)Also succeeded, but the first one will report.
% 0.22/0.39 % (21250)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_33, type, rel_b: $i > $i > $o).
% 0.22/0.39 thf(func_def_34, type, mbox_b: ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_35, type, mdia_b: ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_36, type, p: $i > $o).
% 0.22/0.39 thf(func_def_37, type, q: $i > $o).
% 0.22/0.39 thf(func_def_38, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.22/0.39 thf(f213,plain,(
% 0.22/0.39 $false),
% 0.22/0.39 inference(trivial_inequality_removal,[],[f212])).
% 0.22/0.39 thf(f212,plain,(
% 0.22/0.39 ($false = $true)),
% 0.22/0.39 inference(backward_demodulation,[],[f202,f209])).
% 0.22/0.39 thf(f209,plain,(
% 0.22/0.39 ((p @ sK1) = $false)),
% 0.22/0.39 inference(trivial_inequality_removal,[],[f208])).
% 0.22/0.39 thf(f208,plain,(
% 0.22/0.39 ($false = $true) | ((p @ sK1) = $false)),
% 0.22/0.39 inference(forward_demodulation,[],[f207,f194])).
% 0.22/0.39 thf(f194,plain,(
% 0.22/0.39 ((q @ sK1) = $false)),
% 0.22/0.39 inference(trivial_inequality_removal,[],[f193])).
% 0.22/0.39 thf(f193,plain,(
% 0.22/0.39 ((q @ sK1) = $false) | ($false = $true)),
% 0.22/0.39 inference(superposition,[],[f191,f182])).
% 0.22/0.39 thf(f182,plain,(
% 0.22/0.39 ( ! [X1 : $i] : (((rel_b @ sK1 @ X1) = $false) | ((q @ X1) = $false)) )),
% 0.22/0.39 inference(not_proxy_clausification,[],[f181])).
% 0.22/0.39 thf(f181,plain,(
% 0.22/0.39 ( ! [X1 : $i] : (((~ (q @ X1)) = $true) | ((rel_b @ sK1 @ X1) = $false)) )),
% 0.22/0.39 inference(not_proxy_clausification,[],[f180])).
% 0.22/0.39 thf(f180,plain,(
% 0.22/0.39 ( ! [X1 : $i] : (((~ (rel_b @ sK1 @ X1)) = $true) | ((~ (q @ X1)) = $true)) )),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f179])).
% 0.22/0.39 thf(f179,plain,(
% 0.22/0.39 ( ! [X1 : $i] : ((((~ (q @ X1)) | (~ (rel_b @ sK1 @ X1))) = $true)) )),
% 0.22/0.39 inference(beta_eta_normalization,[],[f178])).
% 0.22/0.39 thf(f178,plain,(
% 0.22/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_b @ sK1 @ Y0)))) @ X1) = $true)) )),
% 0.22/0.39 inference(pi_clausification,[],[f177])).
% 0.22/0.39 thf(f177,plain,(
% 0.22/0.39 ((!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_b @ sK1 @ Y0))))) = $true)),
% 0.22/0.39 inference(not_proxy_clausification,[],[f161])).
% 0.22/0.39 thf(f161,plain,(
% 0.22/0.39 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_b @ sK1 @ Y0)))))) = $false)),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f160])).
% 0.22/0.39 thf(f160,plain,(
% 0.22/0.39 ((((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (q @ Y0)) | (~ (rel_b @ sK1 @ Y0))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_b @ sK1 @ Y0))))))) = $false)),
% 0.22/0.39 inference(beta_eta_normalization,[],[f159])).
% 0.22/0.39 thf(f159,plain,(
% 0.22/0.39 (((^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (q @ Y1)) | (~ (rel_b @ Y0 @ Y1))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_b @ Y0 @ Y1)))))))) @ sK1) = $false)),
% 0.22/0.39 inference(sigma_clausification,[],[f158])).
% 0.22/0.39 thf(f158,plain,(
% 0.22/0.39 ((!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (q @ Y1)) | (~ (rel_b @ Y0 @ Y1))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_b @ Y0 @ Y1))))))))) != $true)),
% 0.22/0.39 inference(boolean_simplification,[],[f157])).
% 0.22/0.39 thf(f157,plain,(
% 0.22/0.39 ((!! @ $i @ (^[Y0 : $i]: ((~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (q @ Y1)) | (~ (rel_b @ Y0 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_b @ Y0 @ Y1))))))))) != $true)),
% 0.22/0.39 inference(beta_eta_normalization,[],[f154])).
% 0.22/0.39 thf(f154,plain,(
% 0.22/0.39 (((^[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 > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_b @ Y1 @ Y2)))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_b @ Y1 @ Y2)))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))) @ p) @ q))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_b @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ q))) != $true)),
% 0.22/0.39 inference(definition_unfolding,[],[f120,f110,f145,f144,f121,f121,f128,f142,f153])).
% 0.22/0.39 thf(f153,plain,(
% 0.22/0.39 (mdia_b = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_b @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.22/0.39 inference(definition_unfolding,[],[f134,f142,f121,f142])).
% 0.22/0.39 thf(f134,plain,(
% 0.22/0.39 (mdia_b = (^[Y0 : $i > $o]: (mnot @ (mbox_b @ (mnot @ Y0)))))),
% 0.22/0.39 inference(cnf_transformation,[],[f44])).
% 0.22/0.39 thf(f44,plain,(
% 0.22/0.39 (mdia_b = (^[Y0 : $i > $o]: (mnot @ (mbox_b @ (mnot @ Y0)))))),
% 0.22/0.39 inference(fool_elimination,[],[f43])).
% 0.22/0.39 thf(f43,plain,(
% 0.22/0.39 (mdia_b = (^[X0 : $i > $o] : (mnot @ (mbox_b @ (mnot @ X0)))))),
% 0.22/0.39 inference(rectify,[],[f33])).
% 0.22/0.39 thf(f33,axiom,(
% 0.22/0.39 (mdia_b = (^[X3 : $i > $o] : (mnot @ (mbox_b @ (mnot @ X3)))))),
% 0.22/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_b)).
% 0.22/0.39 thf(f142,plain,(
% 0.22/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.22/0.39 inference(cnf_transformation,[],[f52])).
% 0.22/0.39 thf(f52,plain,(
% 0.22/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.22/0.39 inference(fool_elimination,[],[f51])).
% 0.22/0.39 thf(f51,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/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.22/0.39 thf(f128,plain,(
% 0.22/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.22/0.39 inference(cnf_transformation,[],[f94])).
% 0.22/0.39 thf(f94,plain,(
% 0.22/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.22/0.39 inference(fool_elimination,[],[f93])).
% 0.22/0.39 thf(f93,plain,(
% 0.22/0.39 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 0.22/0.39 inference(rectify,[],[f4])).
% 0.22/0.39 thf(f4,axiom,(
% 0.22/0.39 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))) = mor)),
% 0.22/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.22/0.39 thf(f121,plain,(
% 0.22/0.39 (mbox_b = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_b @ Y1 @ Y2)))))))))),
% 0.22/0.39 inference(cnf_transformation,[],[f81])).
% 0.22/0.39 thf(f81,plain,(
% 0.22/0.39 (mbox_b = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_b @ Y1 @ Y2)))))))))),
% 0.22/0.39 inference(fool_elimination,[],[f80])).
% 0.22/0.39 thf(f80,plain,(
% 0.22/0.39 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_b @ X1 @ X2) | (X0 @ X2)))) = mbox_b)),
% 0.22/0.39 inference(rectify,[],[f32])).
% 0.22/0.39 thf(f32,axiom,(
% 0.22/0.39 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_b @ X2 @ X7) | (X3 @ X7)))) = mbox_b)),
% 0.22/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_b)).
% 0.22/0.39 thf(f144,plain,(
% 0.22/0.39 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.22/0.39 inference(definition_unfolding,[],[f139,f142,f128,f142,f142])).
% 0.22/0.39 thf(f139,plain,(
% 0.22/0.39 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.22/0.39 inference(cnf_transformation,[],[f69])).
% 0.22/0.39 thf(f69,plain,(
% 0.22/0.39 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.22/0.39 inference(fool_elimination,[],[f68])).
% 0.22/0.39 thf(f68,plain,(
% 0.22/0.39 ((^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))) = mand)),
% 0.22/0.39 inference(rectify,[],[f5])).
% 0.22/0.39 thf(f5,axiom,(
% 0.22/0.39 ((^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))) = mand)),
% 0.22/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)).
% 0.22/0.39 thf(f145,plain,(
% 0.22/0.39 (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)))))),
% 0.22/0.39 inference(definition_unfolding,[],[f127,f128,f142])).
% 0.22/0.39 thf(f127,plain,(
% 0.22/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.22/0.39 inference(cnf_transformation,[],[f92])).
% 0.22/0.39 thf(f92,plain,(
% 0.22/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.22/0.39 inference(fool_elimination,[],[f91])).
% 0.22/0.39 thf(f91,plain,(
% 0.22/0.39 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.22/0.39 inference(rectify,[],[f6])).
% 0.22/0.39 thf(f6,axiom,(
% 0.22/0.39 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.22/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.22/0.39 thf(f110,plain,(
% 0.22/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.22/0.39 inference(cnf_transformation,[],[f71])).
% 0.22/0.39 thf(f71,plain,(
% 0.22/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.22/0.39 inference(fool_elimination,[],[f70])).
% 0.22/0.39 thf(f70,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/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.22/0.39 thf(f120,plain,(
% 0.22/0.39 ((mvalid @ (mimplies @ (mand @ (mbox_b @ p) @ (mbox_b @ (mor @ (mnot @ p) @ q))) @ (mdia_b @ q))) != $true)),
% 0.22/0.39 inference(cnf_transformation,[],[f107])).
% 0.22/0.39 thf(f107,plain,(
% 0.22/0.39 ((mvalid @ (mimplies @ (mand @ (mbox_b @ p) @ (mbox_b @ (mor @ (mnot @ p) @ q))) @ (mdia_b @ q))) != $true)),
% 0.22/0.39 inference(flattening,[],[f96])).
% 0.22/0.39 thf(f96,plain,(
% 0.22/0.39 ~((mvalid @ (mimplies @ (mand @ (mbox_b @ p) @ (mbox_b @ (mor @ (mnot @ p) @ q))) @ (mdia_b @ q))) = $true)),
% 0.22/0.39 inference(fool_elimination,[],[f95])).
% 0.22/0.39 thf(f95,plain,(
% 0.22/0.39 ~(mvalid @ (mimplies @ (mand @ (mbox_b @ p) @ (mbox_b @ (mor @ (mnot @ p) @ q))) @ (mdia_b @ q)))),
% 0.22/0.39 inference(rectify,[],[f37])).
% 0.22/0.39 thf(f37,negated_conjecture,(
% 0.22/0.39 ~(mvalid @ (mimplies @ (mand @ (mbox_b @ p) @ (mbox_b @ (mor @ (mnot @ p) @ q))) @ (mdia_b @ q)))),
% 0.22/0.39 inference(negated_conjecture,[],[f36])).
% 0.22/0.39 thf(f36,conjecture,(
% 0.22/0.39 (mvalid @ (mimplies @ (mand @ (mbox_b @ p) @ (mbox_b @ (mor @ (mnot @ p) @ q))) @ (mdia_b @ q)))),
% 0.22/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.22/0.39 thf(f191,plain,(
% 0.22/0.39 ( ! [X1 : $i] : (((rel_b @ X1 @ X1) = $true)) )),
% 0.22/0.39 inference(beta_eta_normalization,[],[f190])).
% 0.22/0.39 thf(f190,plain,(
% 0.22/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: (rel_b @ Y0 @ Y0)) @ X1) = $true)) )),
% 0.22/0.39 inference(pi_clausification,[],[f189])).
% 0.22/0.39 thf(f189,plain,(
% 0.22/0.39 ((!! @ $i @ (^[Y0 : $i]: (rel_b @ Y0 @ Y0))) = $true)),
% 0.22/0.39 inference(beta_eta_normalization,[],[f156])).
% 0.22/0.39 thf(f156,plain,(
% 0.22/0.39 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ rel_b) = $true)),
% 0.22/0.39 inference(definition_unfolding,[],[f143,f141])).
% 0.22/0.39 thf(f141,plain,(
% 0.22/0.39 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.22/0.39 inference(cnf_transformation,[],[f67])).
% 0.22/0.39 thf(f67,plain,(
% 0.22/0.39 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.22/0.39 inference(fool_elimination,[],[f66])).
% 0.22/0.39 thf(f66,plain,(
% 0.22/0.39 ((^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))) = mreflexive)),
% 0.22/0.39 inference(rectify,[],[f18])).
% 0.22/0.39 thf(f18,axiom,(
% 0.22/0.39 ((^[X6 : $i > $i > $o] : (! [X8] : (X6 @ X8 @ X8))) = mreflexive)),
% 0.22/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive)).
% 0.22/0.39 thf(f143,plain,(
% 0.22/0.39 ((mreflexive @ rel_b) = $true)),
% 0.22/0.39 inference(cnf_transformation,[],[f89])).
% 0.22/0.39 thf(f89,plain,(
% 0.22/0.39 ((mreflexive @ rel_b) = $true)),
% 0.22/0.39 inference(fool_elimination,[],[f88])).
% 0.22/0.39 thf(f88,plain,(
% 0.22/0.39 (mreflexive @ rel_b)),
% 0.22/0.39 inference(rectify,[],[f34])).
% 0.22/0.39 thf(f34,axiom,(
% 0.22/0.39 (mreflexive @ rel_b)),
% 0.22/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
% 0.22/0.39 thf(f207,plain,(
% 0.22/0.39 ((q @ sK1) = $true) | ((p @ sK1) = $false)),
% 0.22/0.39 inference(trivial_inequality_removal,[],[f205])).
% 0.22/0.39 thf(f205,plain,(
% 0.22/0.39 ((q @ sK1) = $true) | ($false = $true) | ((p @ sK1) = $false)),
% 0.22/0.39 inference(superposition,[],[f191,f176])).
% 0.22/0.39 thf(f176,plain,(
% 0.22/0.39 ( ! [X1 : $i] : (((rel_b @ sK1 @ X1) = $false) | ((p @ X1) = $false) | ((q @ X1) = $true)) )),
% 0.22/0.39 inference(not_proxy_clausification,[],[f175])).
% 0.22/0.39 thf(f175,plain,(
% 0.22/0.39 ( ! [X1 : $i] : (((q @ X1) = $true) | ((rel_b @ sK1 @ X1) = $false) | ((~ (p @ X1)) = $true)) )),
% 0.22/0.39 inference(not_proxy_clausification,[],[f174])).
% 0.22/0.39 thf(f174,plain,(
% 0.22/0.39 ( ! [X1 : $i] : (((~ (rel_b @ sK1 @ X1)) = $true) | ((~ (p @ X1)) = $true) | ((q @ X1) = $true)) )),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f173])).
% 0.22/0.39 thf(f173,plain,(
% 0.22/0.39 ( ! [X1 : $i] : ((((~ (p @ X1)) | (q @ X1)) = $true) | ((~ (rel_b @ sK1 @ X1)) = $true)) )),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f172])).
% 0.22/0.39 thf(f172,plain,(
% 0.22/0.39 ( ! [X1 : $i] : (((((~ (p @ X1)) | (q @ X1)) | (~ (rel_b @ sK1 @ X1))) = $true)) )),
% 0.22/0.39 inference(beta_eta_normalization,[],[f171])).
% 0.22/0.39 thf(f171,plain,(
% 0.22/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: (((~ (p @ Y0)) | (q @ Y0)) | (~ (rel_b @ sK1 @ Y0)))) @ X1) = $true)) )),
% 0.22/0.39 inference(pi_clausification,[],[f170])).
% 0.22/0.39 thf(f170,plain,(
% 0.22/0.39 ((!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (q @ Y0)) | (~ (rel_b @ sK1 @ Y0))))) = $true)),
% 0.22/0.39 inference(not_proxy_clausification,[],[f163])).
% 0.22/0.39 thf(f163,plain,(
% 0.22/0.39 ((~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (q @ Y0)) | (~ (rel_b @ sK1 @ Y0)))))) = $false)),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f162])).
% 0.22/0.39 thf(f162,plain,(
% 0.22/0.39 (((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (q @ Y0)) | (~ (rel_b @ sK1 @ Y0))))))) = $false)),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f160])).
% 0.22/0.39 thf(f202,plain,(
% 0.22/0.39 ((p @ sK1) = $true)),
% 0.22/0.39 inference(trivial_inequality_removal,[],[f200])).
% 0.22/0.39 thf(f200,plain,(
% 0.22/0.39 ($false = $true) | ((p @ sK1) = $true)),
% 0.22/0.39 inference(superposition,[],[f169,f191])).
% 0.22/0.39 thf(f169,plain,(
% 0.22/0.39 ( ! [X1 : $i] : (((rel_b @ sK1 @ X1) = $false) | ((p @ X1) = $true)) )),
% 0.22/0.39 inference(not_proxy_clausification,[],[f168])).
% 0.22/0.39 thf(f168,plain,(
% 0.22/0.39 ( ! [X1 : $i] : (((~ (rel_b @ sK1 @ X1)) = $true) | ((p @ X1) = $true)) )),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f167])).
% 0.22/0.39 thf(f167,plain,(
% 0.22/0.39 ( ! [X1 : $i] : ((((p @ X1) | (~ (rel_b @ sK1 @ X1))) = $true)) )),
% 0.22/0.39 inference(beta_eta_normalization,[],[f166])).
% 0.22/0.39 thf(f166,plain,(
% 0.22/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))) @ X1) = $true)) )),
% 0.22/0.39 inference(pi_clausification,[],[f165])).
% 0.22/0.39 thf(f165,plain,(
% 0.22/0.39 ((!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0))))) = $true)),
% 0.22/0.39 inference(not_proxy_clausification,[],[f164])).
% 0.22/0.39 thf(f164,plain,(
% 0.22/0.39 ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) = $false)),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f162])).
% 0.22/0.39 % SZS output end Proof for theBenchmark
% 0.22/0.39 % (21250)------------------------------
% 0.22/0.39 % (21250)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39 % (21250)Termination reason: Refutation
% 0.22/0.39
% 0.22/0.39 % (21250)Memory used [KB]: 5628
% 0.22/0.39 % (21250)Time elapsed: 0.012 s
% 0.22/0.39 % (21250)Instructions burned: 13 (million)
% 0.22/0.39 % (21250)------------------------------
% 0.22/0.39 % (21250)------------------------------
% 0.22/0.39 % (21245)Success in time 0.027 s
% 0.22/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------