TSTP Solution File: LCL709^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL709^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 00:22:19 EDT 2024
% Result : Theorem 0.21s 0.39s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL709^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 0.07/0.14 % 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 : n025.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 00:53:38 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 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
% 0.14/0.38 % (2285)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.39 % (2286)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)
% 0.14/0.39 % (2288)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.39 % (2290)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)
% 0.14/0.39 % (2292)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)
% 0.14/0.39 % (2288)Instruction limit reached!
% 0.14/0.39 % (2288)------------------------------
% 0.14/0.39 % (2288)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (2288)Termination reason: Unknown
% 0.14/0.39 % (2288)Termination phase: shuffling
% 0.21/0.39
% 0.21/0.39 % (2288)Memory used [KB]: 1023
% 0.21/0.39 % (2288)Time elapsed: 0.004 s
% 0.21/0.39 % (2288)Instructions burned: 2 (million)
% 0.21/0.39 % (2288)------------------------------
% 0.21/0.39 % (2288)------------------------------
% 0.21/0.39 % (2289)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)
% 0.21/0.39 % (2287)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)
% 0.21/0.39 % (2291)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.39 % (2292)Instruction limit reached!
% 0.21/0.39 % (2292)------------------------------
% 0.21/0.39 % (2292)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (2292)Termination reason: Unknown
% 0.21/0.39 % (2292)Termination phase: shuffling
% 0.21/0.39
% 0.21/0.39 % (2292)Memory used [KB]: 1023
% 0.21/0.39 % (2292)Time elapsed: 0.004 s
% 0.21/0.39 % (2292)Instructions burned: 4 (million)
% 0.21/0.39 % (2292)------------------------------
% 0.21/0.39 % (2292)------------------------------
% 0.21/0.39 % (2286)Instruction limit reached!
% 0.21/0.39 % (2286)------------------------------
% 0.21/0.39 % (2286)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (2286)Termination reason: Unknown
% 0.21/0.39 % (2286)Termination phase: Property scanning
% 0.21/0.39
% 0.21/0.39 % (2286)Memory used [KB]: 1023
% 0.21/0.39 % (2286)Time elapsed: 0.005 s
% 0.21/0.39 % (2286)Instructions burned: 5 (million)
% 0.21/0.39 % (2286)------------------------------
% 0.21/0.39 % (2286)------------------------------
% 0.21/0.39 % (2289)Instruction limit reached!
% 0.21/0.39 % (2289)------------------------------
% 0.21/0.39 % (2289)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (2289)Termination reason: Unknown
% 0.21/0.39 % (2289)Termination phase: shuffling
% 0.21/0.39
% 0.21/0.39 % (2289)Memory used [KB]: 1023
% 0.21/0.39 % (2289)Time elapsed: 0.004 s
% 0.21/0.39 % (2289)Instructions burned: 2 (million)
% 0.21/0.39 % (2289)------------------------------
% 0.21/0.39 % (2289)------------------------------
% 0.21/0.39 % (2285)First to succeed.
% 0.21/0.39 % (2285)Refutation found. Thanks to Tanya!
% 0.21/0.39 % SZS status Theorem for theBenchmark
% 0.21/0.39 % SZS output start Proof for theBenchmark
% 0.21/0.39 thf(type_def_5, type, mu: $tType).
% 0.21/0.39 thf(func_def_0, type, mu: $tType).
% 0.21/0.39 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.21/0.39 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_15, type, mtrue: $i > $o).
% 0.21/0.39 thf(func_def_16, type, mfalse: $i > $o).
% 0.21/0.39 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.21/0.39 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.21/0.39 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.21/0.39 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.21/0.39 thf(func_def_48, type, sK0: $i > $i > $o).
% 0.21/0.39 thf(func_def_51, type, sK3: $i > ($i > $o) > $i).
% 0.21/0.39 thf(func_def_52, type, ph4: !>[X0: $tType]:(X0)).
% 0.21/0.39 thf(f202,plain,(
% 0.21/0.39 $false),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f198])).
% 0.21/0.39 thf(f198,plain,(
% 0.21/0.39 ($true = $false)),
% 0.21/0.39 inference(superposition,[],[f191,f144])).
% 0.21/0.39 thf(f144,plain,(
% 0.21/0.39 ((sK0 @ sK2 @ sK2) = $false)),
% 0.21/0.39 inference(beta_eta_normalization,[],[f143])).
% 0.21/0.39 thf(f143,plain,(
% 0.21/0.39 (((^[Y0 : $i]: (sK0 @ Y0 @ Y0)) @ sK2) = $false)),
% 0.21/0.39 inference(sigma_clausification,[],[f142])).
% 0.21/0.39 thf(f142,plain,(
% 0.21/0.39 ($true != (!! @ $i @ (^[Y0 : $i]: (sK0 @ Y0 @ Y0))))),
% 0.21/0.39 inference(beta_eta_normalization,[],[f140])).
% 0.21/0.39 thf(f140,plain,(
% 0.21/0.39 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ sK0) != $true)),
% 0.21/0.39 inference(definition_unfolding,[],[f124,f119])).
% 0.21/0.39 thf(f119,plain,(
% 0.21/0.39 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.21/0.39 inference(cnf_transformation,[],[f74])).
% 0.21/0.39 thf(f74,plain,(
% 0.21/0.39 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.21/0.39 inference(fool_elimination,[],[f73])).
% 0.21/0.39 thf(f73,plain,(
% 0.21/0.39 ((^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))) = mreflexive)),
% 0.21/0.39 inference(rectify,[],[f18])).
% 0.21/0.39 thf(f18,axiom,(
% 0.21/0.39 ((^[X6 : $i > $i > $o] : (! [X8] : (X6 @ X8 @ X8))) = mreflexive)),
% 0.21/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive)).
% 0.21/0.39 thf(f124,plain,(
% 0.21/0.39 ((mreflexive @ sK0) != $true)),
% 0.21/0.39 inference(cnf_transformation,[],[f97])).
% 0.21/0.39 thf(f97,plain,(
% 0.21/0.39 ((mreflexive @ sK0) != $true) & ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ sK0 @ Y0) @ Y0)))) = $true)),
% 0.21/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f95,f96])).
% 0.21/0.39 thf(f96,plain,(
% 0.21/0.39 ? [X0 : $i > $i > $o] : (($true != (mreflexive @ X0)) & ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ X0 @ Y0) @ Y0)))) = $true)) => (((mreflexive @ sK0) != $true) & ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ sK0 @ Y0) @ Y0)))) = $true))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f95,plain,(
% 0.21/0.39 ? [X0 : $i > $i > $o] : (($true != (mreflexive @ X0)) & ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ X0 @ Y0) @ Y0)))) = $true))),
% 0.21/0.39 inference(ennf_transformation,[],[f70])).
% 0.21/0.39 thf(f70,plain,(
% 0.21/0.39 ~! [X0 : $i > $i > $o] : (((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ X0 @ Y0) @ Y0)))) = $true) => ($true = (mreflexive @ X0)))),
% 0.21/0.39 inference(fool_elimination,[],[f69])).
% 0.21/0.39 thf(f69,plain,(
% 0.21/0.39 ~! [X0 : $i > $i > $o] : ((mvalid @ (mforall_prop @ (^[X1 : $i > $o] : (mimplies @ (mbox @ X0 @ X1) @ X1)))) => (mreflexive @ X0))),
% 0.21/0.39 inference(rectify,[],[f33])).
% 0.21/0.39 thf(f33,negated_conjecture,(
% 0.21/0.39 ~! [X6 : $i > $i > $o] : ((mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mimplies @ (mbox @ X6 @ X11) @ X11)))) => (mreflexive @ X6))),
% 0.21/0.39 inference(negated_conjecture,[],[f32])).
% 0.21/0.39 thf(f32,conjecture,(
% 0.21/0.39 ! [X6 : $i > $i > $o] : ((mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mimplies @ (mbox @ X6 @ X11) @ X11)))) => (mreflexive @ X6))),
% 0.21/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 0.21/0.39 thf(f191,plain,(
% 0.21/0.39 ( ! [X0 : $i] : (((sK0 @ X0 @ X0) = $true)) )),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f190])).
% 0.21/0.39 thf(f190,plain,(
% 0.21/0.39 ( ! [X0 : $i] : (($true = $false) | ((sK0 @ X0 @ X0) = $true)) )),
% 0.21/0.39 inference(boolean_simplification,[],[f189])).
% 0.21/0.39 thf(f189,plain,(
% 0.21/0.39 ( ! [X0 : $i] : (((~ $true) = $true) | ((sK0 @ X0 @ X0) = $true)) )),
% 0.21/0.39 inference(boolean_simplification,[],[f188])).
% 0.21/0.39 thf(f188,plain,(
% 0.21/0.39 ( ! [X0 : $i] : (((sK0 @ X0 @ X0) = $true) | ((~ (X0 = X0)) = $true)) )),
% 0.21/0.39 inference(beta_eta_normalization,[],[f186])).
% 0.21/0.39 thf(f186,plain,(
% 0.21/0.39 ( ! [X0 : $i] : (((sK0 @ X0 @ X0) = $true) | (((^[Y0 : $i]: (~ (X0 = Y0))) @ X0) = $true)) )),
% 0.21/0.39 inference(superposition,[],[f156,f157])).
% 0.21/0.39 thf(f157,plain,(
% 0.21/0.39 ( ! [X0 : $i] : (((sK3 @ X0 @ (^[Y0 : $i]: (~ (X0 = Y0)))) = X0)) )),
% 0.21/0.39 inference(leibniz_equality_elimination,[],[f154])).
% 0.21/0.39 thf(f154,plain,(
% 0.21/0.39 ( ! [X2 : $i > $o,X1 : $i] : (((X2 @ (sK3 @ X1 @ X2)) = $false) | ((X2 @ X1) = $true)) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f153])).
% 0.21/0.39 thf(f153,plain,(
% 0.21/0.39 ( ! [X2 : $i > $o,X1 : $i] : (((X2 @ X1) = $true) | (((~ (sK0 @ X1 @ (sK3 @ X1 @ X2))) | (X2 @ (sK3 @ X1 @ X2))) = $false)) )),
% 0.21/0.39 inference(beta_eta_normalization,[],[f152])).
% 0.21/0.39 thf(f152,plain,(
% 0.21/0.39 ( ! [X2 : $i > $o,X1 : $i] : ((((^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (X2 @ Y0))) @ (sK3 @ X1 @ X2)) = $false) | ((X2 @ X1) = $true)) )),
% 0.21/0.39 inference(sigma_clausification,[],[f151])).
% 0.21/0.39 thf(f151,plain,(
% 0.21/0.39 ( ! [X2 : $i > $o,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (X2 @ Y0)))) = $false) | ((X2 @ X1) = $true)) )),
% 0.21/0.39 inference(not_proxy_clausification,[],[f150])).
% 0.21/0.39 thf(f150,plain,(
% 0.21/0.39 ( ! [X2 : $i > $o,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (X2 @ Y0))))) = $true) | ((X2 @ X1) = $true)) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f149])).
% 0.21/0.39 thf(f149,plain,(
% 0.21/0.39 ( ! [X2 : $i > $o,X1 : $i] : ((((X2 @ X1) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (X2 @ Y0)))))) = $true)) )),
% 0.21/0.39 inference(beta_eta_normalization,[],[f148])).
% 0.21/0.39 thf(f148,plain,(
% 0.21/0.39 ( ! [X2 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: ((Y0 @ X1) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ X1 @ Y1)) | (Y0 @ Y1))))))) @ X2))) )),
% 0.21/0.39 inference(pi_clausification,[],[f147])).
% 0.21/0.39 thf(f147,plain,(
% 0.21/0.39 ( ! [X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ X1) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ X1 @ Y1)) | (Y0 @ Y1)))))))) = $true)) )),
% 0.21/0.39 inference(beta_eta_normalization,[],[f146])).
% 0.21/0.39 thf(f146,plain,(
% 0.21/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y0 @ Y2)) | (Y1 @ Y2))))))))) @ X1) = $true)) )),
% 0.21/0.39 inference(pi_clausification,[],[f145])).
% 0.21/0.39 thf(f145,plain,(
% 0.21/0.39 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y0 @ Y2)) | (Y1 @ Y2)))))))))) = $true)),
% 0.21/0.39 inference(beta_eta_normalization,[],[f141])).
% 0.21/0.39 thf(f141,plain,(
% 0.21/0.39 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y4 @ Y5) | (Y3 @ Y5))))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y1) @ Y2)))) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (Y1 @ Y3 @ Y4)) | (Y2 @ Y4))))))))) @ sK0 @ Y0) @ Y0)))) = $true)),
% 0.21/0.39 inference(definition_unfolding,[],[f123,f117,f99,f132,f121])).
% 0.21/0.39 thf(f121,plain,(
% 0.21/0.39 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.21/0.39 inference(cnf_transformation,[],[f46])).
% 0.21/0.39 thf(f46,plain,(
% 0.21/0.39 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.21/0.39 inference(fool_elimination,[],[f45])).
% 0.21/0.39 thf(f45,plain,(
% 0.21/0.39 ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))) = mbox)),
% 0.21/0.39 inference(rectify,[],[f16])).
% 0.21/0.39 thf(f16,axiom,(
% 0.21/0.39 ((^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(X6 @ X2 @ X7)))) = mbox)),
% 0.21/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox)).
% 0.21/0.39 thf(f132,plain,(
% 0.21/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.21/0.39 inference(definition_unfolding,[],[f120,f125,f115])).
% 0.21/0.39 thf(f115,plain,(
% 0.21/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.39 inference(cnf_transformation,[],[f48])).
% 0.21/0.39 thf(f48,plain,(
% 0.21/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.39 inference(fool_elimination,[],[f47])).
% 0.21/0.39 thf(f47,plain,(
% 0.21/0.39 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.21/0.39 inference(rectify,[],[f3])).
% 0.21/0.39 thf(f3,axiom,(
% 0.21/0.39 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.21/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.21/0.39 thf(f125,plain,(
% 0.21/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.21/0.39 inference(cnf_transformation,[],[f64])).
% 0.21/0.39 thf(f64,plain,(
% 0.21/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.21/0.39 inference(fool_elimination,[],[f63])).
% 0.21/0.39 thf(f63,plain,(
% 0.21/0.39 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.21/0.39 inference(rectify,[],[f4])).
% 0.21/0.39 thf(f4,axiom,(
% 0.21/0.39 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))),
% 0.21/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.21/0.39 thf(f120,plain,(
% 0.21/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.39 inference(cnf_transformation,[],[f68])).
% 0.21/0.39 thf(f68,plain,(
% 0.21/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.39 inference(fool_elimination,[],[f67])).
% 0.21/0.39 thf(f67,plain,(
% 0.21/0.39 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.21/0.39 inference(rectify,[],[f6])).
% 0.21/0.39 thf(f6,axiom,(
% 0.21/0.39 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.21/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.21/0.39 thf(f99,plain,(
% 0.21/0.39 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.21/0.39 inference(cnf_transformation,[],[f92])).
% 0.21/0.39 thf(f92,plain,(
% 0.21/0.39 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.21/0.39 inference(fool_elimination,[],[f91])).
% 0.21/0.39 thf(f91,plain,(
% 0.21/0.39 ((^[X0 : ($i > $o) > $i > $o, X1 : $i] : (! [X2 : $i > $o] : (X0 @ X2 @ X1))) = mforall_prop)),
% 0.21/0.39 inference(rectify,[],[f11])).
% 0.21/0.39 thf(f11,axiom,(
% 0.21/0.39 ((^[X3 : ($i > $o) > $i > $o, X2 : $i] : (! [X5 : $i > $o] : (X3 @ X5 @ X2))) = mforall_prop)),
% 0.21/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_prop)).
% 0.21/0.39 thf(f117,plain,(
% 0.21/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.39 inference(cnf_transformation,[],[f90])).
% 0.21/0.39 thf(f90,plain,(
% 0.21/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.39 inference(fool_elimination,[],[f89])).
% 0.21/0.39 thf(f89,plain,(
% 0.21/0.39 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.21/0.39 inference(rectify,[],[f28])).
% 0.21/0.39 thf(f28,axiom,(
% 0.21/0.39 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.21/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.21/0.39 thf(f123,plain,(
% 0.21/0.39 ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ sK0 @ Y0) @ Y0)))) = $true)),
% 0.21/0.39 inference(cnf_transformation,[],[f97])).
% 0.21/0.39 thf(f156,plain,(
% 0.21/0.39 ( ! [X2 : $i > $o,X1 : $i] : (((sK0 @ X1 @ (sK3 @ X1 @ X2)) = $true) | ((X2 @ X1) = $true)) )),
% 0.21/0.39 inference(not_proxy_clausification,[],[f155])).
% 0.21/0.39 thf(f155,plain,(
% 0.21/0.39 ( ! [X2 : $i > $o,X1 : $i] : (((X2 @ X1) = $true) | ((~ (sK0 @ X1 @ (sK3 @ X1 @ X2))) = $false)) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f153])).
% 0.21/0.39 % SZS output end Proof for theBenchmark
% 0.21/0.39 % (2285)------------------------------
% 0.21/0.39 % (2285)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (2285)Termination reason: Refutation
% 0.21/0.39
% 0.21/0.39 % (2285)Memory used [KB]: 5756
% 0.21/0.39 % (2285)Time elapsed: 0.014 s
% 0.21/0.39 % (2285)Instructions burned: 14 (million)
% 0.21/0.39 % (2285)------------------------------
% 0.21/0.39 % (2285)------------------------------
% 0.21/0.39 % (2284)Success in time 0.029 s
% 0.21/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------