TSTP Solution File: SYO420^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO420^1 : 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 : n002.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 09:04:22 EDT 2024
% Result : Theorem 0.13s 0.38s
% Output : Refutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO420^1 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.14 % 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
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon May 20 10:17:23 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 % (11745)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.37 % (11744)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)
% 0.13/0.37 % (11745)Instruction limit reached!
% 0.13/0.37 % (11745)------------------------------
% 0.13/0.37 % (11745)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (11745)Termination reason: Unknown
% 0.13/0.37 % (11745)Termination phase: shuffling
% 0.13/0.37
% 0.13/0.37 % (11745)Memory used [KB]: 1023
% 0.13/0.37 % (11745)Time elapsed: 0.003 s
% 0.13/0.37 % (11745)Instructions burned: 2 (million)
% 0.13/0.37 % (11745)------------------------------
% 0.13/0.37 % (11745)------------------------------
% 0.13/0.37 % (11746)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)
% 0.13/0.37 % (11748)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.37 % (11746)Instruction limit reached!
% 0.13/0.37 % (11746)------------------------------
% 0.13/0.37 % (11746)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (11746)Termination reason: Unknown
% 0.13/0.37 % (11746)Termination phase: shuffling
% 0.13/0.37
% 0.13/0.37 % (11746)Memory used [KB]: 1023
% 0.13/0.37 % (11746)Time elapsed: 0.003 s
% 0.13/0.37 % (11746)Instructions burned: 2 (million)
% 0.13/0.37 % (11746)------------------------------
% 0.13/0.37 % (11746)------------------------------
% 0.13/0.37 % (11749)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)
% 0.13/0.38 % (11749)Instruction limit reached!
% 0.13/0.38 % (11749)------------------------------
% 0.13/0.38 % (11749)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (11749)Termination reason: Unknown
% 0.13/0.38 % (11749)Termination phase: shuffling
% 0.13/0.38
% 0.13/0.38 % (11749)Memory used [KB]: 1023
% 0.13/0.38 % (11749)Time elapsed: 0.004 s
% 0.13/0.38 % (11749)Instructions burned: 4 (million)
% 0.13/0.38 % (11749)------------------------------
% 0.13/0.38 % (11749)------------------------------
% 0.13/0.38 % (11743)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)
% 0.13/0.38 % (11742)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.38 % (11744)First to succeed.
% 0.13/0.38 % (11747)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)
% 0.13/0.38 % (11743)Instruction limit reached!
% 0.13/0.38 % (11743)------------------------------
% 0.13/0.38 % (11743)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (11743)Termination reason: Unknown
% 0.13/0.38 % (11743)Termination phase: Property scanning
% 0.13/0.38
% 0.13/0.38 % (11743)Memory used [KB]: 1023
% 0.13/0.38 % (11743)Time elapsed: 0.004 s
% 0.13/0.38 % (11743)Instructions burned: 5 (million)
% 0.13/0.38 % (11743)------------------------------
% 0.13/0.38 % (11743)------------------------------
% 0.13/0.38 % (11748)Also succeeded, but the first one will report.
% 0.13/0.38 % (11744)Refutation found. Thanks to Tanya!
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38 % SZS output start Proof for theBenchmark
% 0.13/0.38 thf(type_def_5, type, mu: $tType).
% 0.13/0.38 thf(func_def_0, type, mu: $tType).
% 0.13/0.38 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.13/0.38 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_15, type, mtrue: $i > $o).
% 0.13/0.38 thf(func_def_16, type, mfalse: $i > $o).
% 0.13/0.38 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.13/0.38 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.13/0.38 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.13/0.38 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.13/0.38 thf(func_def_33, type, rel_d: $i > $i > $o).
% 0.13/0.38 thf(func_def_34, type, mbox_d: ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_35, type, mdia_d: ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_36, type, p: $i > $o).
% 0.13/0.38 thf(func_def_37, type, q: $i > $o).
% 0.13/0.38 thf(func_def_38, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.13/0.38 thf(func_def_56, type, sK2: $i > $i).
% 0.13/0.38 thf(f197,plain,(
% 0.13/0.38 $false),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f196])).
% 0.13/0.38 thf(f196,plain,(
% 0.13/0.38 ($true = $false)),
% 0.13/0.38 inference(forward_demodulation,[],[f195,f184])).
% 0.13/0.38 thf(f184,plain,(
% 0.13/0.38 ((q @ (sK2 @ sK1)) = $false)),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f182])).
% 0.13/0.38 thf(f182,plain,(
% 0.13/0.38 ((q @ (sK2 @ sK1)) = $false) | ($true = $false)),
% 0.13/0.38 inference(superposition,[],[f163,f181])).
% 0.13/0.38 thf(f181,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($true = (rel_d @ X1 @ (sK2 @ X1)))) )),
% 0.13/0.38 inference(sigma_clausification,[],[f180])).
% 0.13/0.38 thf(f180,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (((?? @ $i @ (rel_d @ X1)) = $true)) )),
% 0.13/0.38 inference(beta_eta_normalization,[],[f179])).
% 0.13/0.38 thf(f179,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (?? @ $i @ (rel_d @ Y0))) @ X1))) )),
% 0.13/0.38 inference(pi_clausification,[],[f178])).
% 0.13/0.38 thf(f178,plain,(
% 0.13/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (rel_d @ Y0)))))),
% 0.13/0.38 inference(beta_eta_normalization,[],[f151])).
% 0.13/0.38 thf(f151,plain,(
% 0.13/0.38 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))) @ rel_d))),
% 0.13/0.38 inference(definition_unfolding,[],[f130,f109])).
% 0.13/0.38 thf(f109,plain,(
% 0.13/0.38 (mserial = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.13/0.38 inference(cnf_transformation,[],[f101])).
% 0.13/0.38 thf(f101,plain,(
% 0.13/0.38 (mserial = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.13/0.38 inference(fool_elimination,[],[f100])).
% 0.13/0.38 thf(f100,plain,(
% 0.13/0.38 ((^[X0 : $i > $i > $o] : (! [X1] : ? [X2] : (X0 @ X1 @ X2))) = mserial)),
% 0.13/0.38 inference(rectify,[],[f20])).
% 0.13/0.38 thf(f20,axiom,(
% 0.13/0.38 ((^[X6 : $i > $i > $o] : (! [X8] : ? [X9] : (X6 @ X8 @ X9))) = mserial)),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mserial)).
% 0.13/0.38 thf(f130,plain,(
% 0.13/0.38 ((mserial @ rel_d) = $true)),
% 0.13/0.38 inference(cnf_transformation,[],[f57])).
% 0.13/0.38 thf(f57,plain,(
% 0.13/0.38 ((mserial @ rel_d) = $true)),
% 0.13/0.38 inference(fool_elimination,[],[f56])).
% 0.13/0.38 thf(f56,plain,(
% 0.13/0.38 (mserial @ rel_d)),
% 0.13/0.38 inference(rectify,[],[f34])).
% 0.13/0.38 thf(f34,axiom,(
% 0.13/0.38 (mserial @ rel_d)),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1)).
% 0.13/0.38 thf(f163,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($false = (rel_d @ sK1 @ X1)) | ((q @ X1) = $false)) )),
% 0.13/0.38 inference(not_proxy_clausification,[],[f162])).
% 0.13/0.38 thf(f162,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (((q @ X1) = $false) | ($true = (~ (rel_d @ sK1 @ X1)))) )),
% 0.13/0.38 inference(not_proxy_clausification,[],[f161])).
% 0.13/0.38 thf(f161,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($true = (~ (q @ X1))) | ($true = (~ (rel_d @ sK1 @ X1)))) )),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f160])).
% 0.13/0.38 thf(f160,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($true = ((~ (q @ X1)) | (~ (rel_d @ sK1 @ X1))))) )),
% 0.13/0.38 inference(beta_eta_normalization,[],[f159])).
% 0.13/0.38 thf(f159,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_d @ sK1 @ Y0)))) @ X1))) )),
% 0.13/0.38 inference(pi_clausification,[],[f158])).
% 0.13/0.38 thf(f158,plain,(
% 0.13/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_d @ sK1 @ Y0))))))),
% 0.13/0.38 inference(not_proxy_clausification,[],[f157])).
% 0.13/0.38 thf(f157,plain,(
% 0.13/0.38 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_d @ sK1 @ Y0)))))) = $false)),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f155])).
% 0.13/0.38 thf(f155,plain,(
% 0.13/0.38 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_d @ sK1 @ Y0)))))) | ((~ (!! @ $i @ (^[Y0 : $i]: (((q @ Y0) | (~ (p @ Y0))) | (~ (rel_d @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK1 @ Y0)))))))) = $false)),
% 0.13/0.38 inference(beta_eta_normalization,[],[f154])).
% 0.13/0.38 thf(f154,plain,(
% 0.13/0.38 ($false = ((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_d @ Y0 @ Y1)))))) | ((~ (!! @ $i @ (^[Y1 : $i]: (((q @ Y1) | (~ (p @ Y1))) | (~ (rel_d @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_d @ Y0 @ Y1))))))))) @ sK1))),
% 0.13/0.38 inference(sigma_clausification,[],[f153])).
% 0.13/0.38 thf(f153,plain,(
% 0.13/0.38 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_d @ Y0 @ Y1)))))) | ((~ (!! @ $i @ (^[Y1 : $i]: (((q @ Y1) | (~ (p @ Y1))) | (~ (rel_d @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_d @ Y0 @ Y1)))))))))))),
% 0.13/0.38 inference(boolean_simplification,[],[f152])).
% 0.13/0.38 thf(f152,plain,(
% 0.13/0.38 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_d @ Y0 @ Y1)))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: (((q @ Y1) | (~ (p @ Y1))) | (~ (rel_d @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_d @ Y0 @ Y1)))))))))))))),
% 0.13/0.38 inference(beta_eta_normalization,[],[f150])).
% 0.13/0.38 thf(f150,plain,(
% 0.13/0.38 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ 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]: ((Y3 @ Y4) | (Y2 @ 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_d @ Y1 @ Y2)))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_d @ Y1 @ Y2)))))))) @ ((^[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)))) @ p @ q))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_d @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ q))))),
% 0.13/0.38 inference(definition_unfolding,[],[f111,f105,f141,f140,f110,f110,f141,f149])).
% 0.13/0.38 thf(f149,plain,(
% 0.13/0.38 (mdia_d = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_d @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.13/0.38 inference(definition_unfolding,[],[f117,f127,f110,f127])).
% 0.13/0.38 thf(f127,plain,(
% 0.13/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.13/0.38 inference(cnf_transformation,[],[f78])).
% 0.13/0.38 thf(f78,plain,(
% 0.13/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.13/0.38 inference(fool_elimination,[],[f77])).
% 0.13/0.38 thf(f77,plain,(
% 0.13/0.38 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.13/0.38 inference(rectify,[],[f3])).
% 0.13/0.38 thf(f3,axiom,(
% 0.13/0.38 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.13/0.38 thf(f117,plain,(
% 0.13/0.38 (mdia_d = (^[Y0 : $i > $o]: (mnot @ (mbox_d @ (mnot @ Y0)))))),
% 0.13/0.38 inference(cnf_transformation,[],[f41])).
% 0.13/0.38 thf(f41,plain,(
% 0.13/0.38 (mdia_d = (^[Y0 : $i > $o]: (mnot @ (mbox_d @ (mnot @ Y0)))))),
% 0.13/0.38 inference(fool_elimination,[],[f40])).
% 0.13/0.38 thf(f40,plain,(
% 0.13/0.38 (mdia_d = (^[X0 : $i > $o] : (mnot @ (mbox_d @ (mnot @ X0)))))),
% 0.13/0.38 inference(rectify,[],[f33])).
% 0.13/0.38 thf(f33,axiom,(
% 0.13/0.38 (mdia_d = (^[X3 : $i > $o] : (mnot @ (mbox_d @ (mnot @ X3)))))),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_d)).
% 0.13/0.38 thf(f110,plain,(
% 0.13/0.38 (mbox_d = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_d @ Y1 @ Y2)))))))))),
% 0.13/0.38 inference(cnf_transformation,[],[f45])).
% 0.13/0.38 thf(f45,plain,(
% 0.13/0.38 (mbox_d = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_d @ Y1 @ Y2)))))))))),
% 0.13/0.38 inference(fool_elimination,[],[f44])).
% 0.13/0.38 thf(f44,plain,(
% 0.13/0.38 (mbox_d = (^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_d @ X1 @ X2) | (X0 @ X2)))))),
% 0.13/0.38 inference(rectify,[],[f32])).
% 0.13/0.38 thf(f32,axiom,(
% 0.13/0.38 (mbox_d = (^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_d @ X2 @ X7) | (X3 @ X7)))))),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_d)).
% 0.13/0.38 thf(f140,plain,(
% 0.13/0.38 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.13/0.38 inference(definition_unfolding,[],[f134,f127,f131,f127,f127])).
% 0.13/0.38 thf(f131,plain,(
% 0.13/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.13/0.38 inference(cnf_transformation,[],[f47])).
% 0.13/0.38 thf(f47,plain,(
% 0.13/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.13/0.38 inference(fool_elimination,[],[f46])).
% 0.13/0.38 thf(f46,plain,(
% 0.13/0.38 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.13/0.38 inference(rectify,[],[f4])).
% 0.13/0.38 thf(f4,axiom,(
% 0.13/0.38 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.13/0.38 thf(f134,plain,(
% 0.13/0.38 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.13/0.38 inference(cnf_transformation,[],[f93])).
% 0.13/0.38 thf(f93,plain,(
% 0.13/0.38 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.13/0.38 inference(fool_elimination,[],[f92])).
% 0.13/0.38 thf(f92,plain,(
% 0.13/0.38 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.13/0.38 inference(rectify,[],[f5])).
% 0.13/0.38 thf(f5,axiom,(
% 0.13/0.38 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.13/0.38 thf(f141,plain,(
% 0.13/0.38 (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)))))),
% 0.13/0.38 inference(definition_unfolding,[],[f137,f131,f127])).
% 0.13/0.38 thf(f137,plain,(
% 0.13/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.13/0.38 inference(cnf_transformation,[],[f66])).
% 0.13/0.38 thf(f66,plain,(
% 0.13/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.13/0.38 inference(fool_elimination,[],[f65])).
% 0.13/0.38 thf(f65,plain,(
% 0.13/0.38 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.13/0.38 inference(rectify,[],[f6])).
% 0.13/0.38 thf(f6,axiom,(
% 0.13/0.38 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.13/0.38 thf(f105,plain,(
% 0.13/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.13/0.38 inference(cnf_transformation,[],[f43])).
% 0.13/0.38 thf(f43,plain,(
% 0.13/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.13/0.38 inference(fool_elimination,[],[f42])).
% 0.13/0.38 thf(f42,plain,(
% 0.13/0.38 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.13/0.38 inference(rectify,[],[f28])).
% 0.13/0.38 thf(f28,axiom,(
% 0.13/0.38 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.13/0.38 thf(f111,plain,(
% 0.13/0.38 ((mvalid @ (mimplies @ (mand @ (mbox_d @ p) @ (mbox_d @ (mimplies @ p @ q))) @ (mdia_d @ q))) != $true)),
% 0.13/0.38 inference(cnf_transformation,[],[f104])).
% 0.13/0.38 thf(f104,plain,(
% 0.13/0.38 ((mvalid @ (mimplies @ (mand @ (mbox_d @ p) @ (mbox_d @ (mimplies @ p @ q))) @ (mdia_d @ q))) != $true)),
% 0.13/0.38 inference(flattening,[],[f51])).
% 0.13/0.38 thf(f51,plain,(
% 0.13/0.38 ~((mvalid @ (mimplies @ (mand @ (mbox_d @ p) @ (mbox_d @ (mimplies @ p @ q))) @ (mdia_d @ q))) = $true)),
% 0.13/0.38 inference(fool_elimination,[],[f50])).
% 0.13/0.38 thf(f50,plain,(
% 0.13/0.38 ~(mvalid @ (mimplies @ (mand @ (mbox_d @ p) @ (mbox_d @ (mimplies @ p @ q))) @ (mdia_d @ q)))),
% 0.13/0.38 inference(rectify,[],[f36])).
% 0.13/0.38 thf(f36,negated_conjecture,(
% 0.13/0.38 ~(mvalid @ (mimplies @ (mand @ (mbox_d @ p) @ (mbox_d @ (mimplies @ p @ q))) @ (mdia_d @ q)))),
% 0.13/0.38 inference(negated_conjecture,[],[f35])).
% 0.13/0.38 thf(f35,conjecture,(
% 0.13/0.38 (mvalid @ (mimplies @ (mand @ (mbox_d @ p) @ (mbox_d @ (mimplies @ p @ q))) @ (mdia_d @ q)))),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.13/0.38 thf(f195,plain,(
% 0.13/0.38 ($true = (q @ (sK2 @ sK1)))),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f194])).
% 0.13/0.38 thf(f194,plain,(
% 0.13/0.38 ($true = (q @ (sK2 @ sK1))) | ($true = $false)),
% 0.13/0.38 inference(forward_demodulation,[],[f193,f188])).
% 0.13/0.38 thf(f188,plain,(
% 0.13/0.38 ($true = (p @ (sK2 @ sK1)))),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f187])).
% 0.13/0.38 thf(f187,plain,(
% 0.13/0.38 ($true = $false) | ($true = (p @ (sK2 @ sK1)))),
% 0.13/0.38 inference(superposition,[],[f181,f177])).
% 0.13/0.38 thf(f177,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($false = (rel_d @ sK1 @ X1)) | ($true = (p @ X1))) )),
% 0.13/0.38 inference(not_proxy_clausification,[],[f176])).
% 0.13/0.38 thf(f176,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($true = (p @ X1)) | ($true = (~ (rel_d @ sK1 @ X1)))) )),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f175])).
% 0.13/0.38 thf(f175,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($true = ((p @ X1) | (~ (rel_d @ sK1 @ X1))))) )),
% 0.13/0.38 inference(beta_eta_normalization,[],[f174])).
% 0.13/0.38 thf(f174,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK1 @ Y0)))) @ X1))) )),
% 0.13/0.38 inference(pi_clausification,[],[f173])).
% 0.13/0.38 thf(f173,plain,(
% 0.13/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK1 @ Y0))))))),
% 0.13/0.38 inference(not_proxy_clausification,[],[f164])).
% 0.13/0.38 thf(f164,plain,(
% 0.13/0.38 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK1 @ Y0)))))))),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f156])).
% 0.13/0.38 thf(f156,plain,(
% 0.13/0.38 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: (((q @ Y0) | (~ (p @ Y0))) | (~ (rel_d @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK1 @ Y0))))))))),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f155])).
% 0.13/0.38 thf(f193,plain,(
% 0.13/0.38 ($false = (p @ (sK2 @ sK1))) | ($true = (q @ (sK2 @ sK1)))),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f190])).
% 0.13/0.38 thf(f190,plain,(
% 0.13/0.38 ($true = $false) | ($false = (p @ (sK2 @ sK1))) | ($true = (q @ (sK2 @ sK1)))),
% 0.13/0.38 inference(superposition,[],[f172,f181])).
% 0.13/0.38 thf(f172,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($false = (rel_d @ sK1 @ X1)) | ($false = (p @ X1)) | ((q @ X1) = $true)) )),
% 0.13/0.38 inference(not_proxy_clausification,[],[f171])).
% 0.13/0.38 thf(f171,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (((q @ X1) = $true) | ((~ (p @ X1)) = $true) | ($false = (rel_d @ sK1 @ X1))) )),
% 0.13/0.38 inference(not_proxy_clausification,[],[f170])).
% 0.13/0.38 thf(f170,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($true = (~ (rel_d @ sK1 @ X1))) | ((q @ X1) = $true) | ((~ (p @ X1)) = $true)) )),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f169])).
% 0.13/0.38 thf(f169,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($true = ((q @ X1) | (~ (p @ X1)))) | ($true = (~ (rel_d @ sK1 @ X1)))) )),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f168])).
% 0.13/0.38 thf(f168,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($true = (((q @ X1) | (~ (p @ X1))) | (~ (rel_d @ sK1 @ X1))))) )),
% 0.13/0.38 inference(beta_eta_normalization,[],[f167])).
% 0.13/0.38 thf(f167,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (((q @ Y0) | (~ (p @ Y0))) | (~ (rel_d @ sK1 @ Y0)))) @ X1))) )),
% 0.13/0.38 inference(pi_clausification,[],[f166])).
% 0.13/0.38 thf(f166,plain,(
% 0.13/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: (((q @ Y0) | (~ (p @ Y0))) | (~ (rel_d @ sK1 @ Y0))))))),
% 0.13/0.38 inference(not_proxy_clausification,[],[f165])).
% 0.13/0.38 thf(f165,plain,(
% 0.13/0.38 ($false = (~ (!! @ $i @ (^[Y0 : $i]: (((q @ Y0) | (~ (p @ Y0))) | (~ (rel_d @ sK1 @ Y0)))))))),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f156])).
% 0.13/0.38 % SZS output end Proof for theBenchmark
% 0.13/0.38 % (11744)------------------------------
% 0.13/0.38 % (11744)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (11744)Termination reason: Refutation
% 0.13/0.38
% 0.13/0.38 % (11744)Memory used [KB]: 5628
% 0.13/0.38 % (11744)Time elapsed: 0.010 s
% 0.13/0.38 % (11744)Instructions burned: 13 (million)
% 0.13/0.38 % (11744)------------------------------
% 0.13/0.38 % (11744)------------------------------
% 0.13/0.38 % (11741)Success in time 0.024 s
% 0.13/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------