TSTP Solution File: SYO431^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO431^1 : 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 : n029.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 09:04:24 EDT 2024
% Result : Theorem 0.15s 0.40s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO431^1 : 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
% 0.15/0.35 % Computer : n029.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 20 09:37:08 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 This is a TH0_THM_EQU_NAR problem
% 0.15/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.37 % (29000)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.37 % (29000)Instruction limit reached!
% 0.15/0.37 % (29000)------------------------------
% 0.15/0.37 % (29000)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (29000)Termination reason: Unknown
% 0.15/0.37 % (29000)Termination phase: shuffling
% 0.15/0.37
% 0.15/0.37 % (29000)Memory used [KB]: 1023
% 0.15/0.37 % (29000)Time elapsed: 0.003 s
% 0.15/0.37 % (29000)Instructions burned: 2 (million)
% 0.15/0.37 % (29000)------------------------------
% 0.15/0.37 % (29000)------------------------------
% 0.15/0.37 % (28998)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.15/0.37 % (28999)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.15/0.37 % (29001)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.37 % (28997)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.37 % (29002)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.15/0.37 % (29005)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.37 % (29001)Instruction limit reached!
% 0.15/0.37 % (29001)------------------------------
% 0.15/0.37 % (29001)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (29004)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.37 % (29001)Termination reason: Unknown
% 0.15/0.37 % (29001)Termination phase: shuffling
% 0.15/0.37
% 0.15/0.37 % (29001)Memory used [KB]: 1023
% 0.15/0.38 % (29001)Time elapsed: 0.004 s
% 0.15/0.38 % (29001)Instructions burned: 3 (million)
% 0.15/0.38 % (29001)------------------------------
% 0.15/0.38 % (29001)------------------------------
% 0.15/0.38 % (28998)Instruction limit reached!
% 0.15/0.38 % (28998)------------------------------
% 0.15/0.38 % (28998)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (28998)Termination reason: Unknown
% 0.15/0.38 % (28998)Termination phase: Property scanning
% 0.15/0.38
% 0.15/0.38 % (28998)Memory used [KB]: 1023
% 0.15/0.38 % (28998)Time elapsed: 0.005 s
% 0.15/0.38 % (28998)Instructions burned: 5 (million)
% 0.15/0.38 % (28998)------------------------------
% 0.15/0.38 % (28998)------------------------------
% 0.15/0.38 % (29005)Instruction limit reached!
% 0.15/0.38 % (29005)------------------------------
% 0.15/0.38 % (29005)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (29005)Termination reason: Unknown
% 0.15/0.38 % (29005)Termination phase: shuffling
% 0.15/0.38
% 0.15/0.38 % (29005)Memory used [KB]: 1023
% 0.15/0.38 % (29005)Time elapsed: 0.005 s
% 0.15/0.38 % (29005)Instructions burned: 3 (million)
% 0.15/0.38 % (29005)------------------------------
% 0.15/0.38 % (29005)------------------------------
% 0.15/0.39 % (29002)Refutation not found, incomplete strategy
% 0.15/0.39 % (29002)------------------------------
% 0.15/0.39 % (29002)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (29002)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.39
% 0.15/0.39
% 0.15/0.39 % (29002)Memory used [KB]: 5628
% 0.15/0.39 % (29002)Time elapsed: 0.014 s
% 0.15/0.39 % (29002)Instructions burned: 13 (million)
% 0.15/0.39 % (29002)------------------------------
% 0.15/0.39 % (29002)------------------------------
% 0.15/0.39 % (28997)First to succeed.
% 0.15/0.39 % (29004)Instruction limit reached!
% 0.15/0.39 % (29004)------------------------------
% 0.15/0.39 % (29004)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (29004)Termination reason: Unknown
% 0.15/0.39 % (29004)Termination phase: Saturation
% 0.15/0.39
% 0.15/0.39 % (29004)Memory used [KB]: 5628
% 0.15/0.39 % (29004)Time elapsed: 0.018 s
% 0.15/0.39 % (29004)Instructions burned: 18 (million)
% 0.15/0.39 % (29004)------------------------------
% 0.15/0.39 % (29004)------------------------------
% 0.15/0.39 % (29010)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.15/0.40 % (28999)Also succeeded, but the first one will report.
% 0.15/0.40 % (28997)Refutation found. Thanks to Tanya!
% 0.15/0.40 % SZS status Theorem for theBenchmark
% 0.15/0.40 % SZS output start Proof for theBenchmark
% 0.15/0.40 thf(type_def_5, type, mu: $tType).
% 0.15/0.40 thf(func_def_0, type, mu: $tType).
% 0.15/0.40 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.15/0.40 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_15, type, mtrue: $i > $o).
% 0.15/0.40 thf(func_def_16, type, mfalse: $i > $o).
% 0.15/0.40 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.15/0.40 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.15/0.40 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.15/0.40 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.15/0.40 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.15/0.40 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.15/0.40 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.15/0.40 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.15/0.40 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.15/0.40 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.15/0.40 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.15/0.40 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.15/0.40 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.15/0.40 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.15/0.40 thf(func_def_33, type, rel_b: $i > $i > $o).
% 0.15/0.40 thf(func_def_34, type, mbox_b: ($i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_35, type, mdia_b: ($i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_36, type, p: $i > $o).
% 0.15/0.40 thf(func_def_56, type, sK4: $i > $i).
% 0.15/0.40 thf(f287,plain,(
% 0.15/0.40 $false),
% 0.15/0.40 inference(avatar_sat_refutation,[],[f272,f279,f286])).
% 0.15/0.40 thf(f286,plain,(
% 0.15/0.40 ~spl0_1),
% 0.15/0.40 inference(avatar_contradiction_clause,[],[f285])).
% 0.15/0.40 thf(f285,plain,(
% 0.15/0.40 $false | ~spl0_1),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f282])).
% 0.15/0.40 thf(f282,plain,(
% 0.15/0.40 ($false = $true) | ~spl0_1),
% 0.15/0.40 inference(superposition,[],[f224,f257])).
% 0.15/0.40 thf(f257,plain,(
% 0.15/0.40 ($false = (rel_b @ sK3 @ sK2)) | ~spl0_1),
% 0.15/0.40 inference(avatar_component_clause,[],[f255])).
% 0.15/0.40 thf(f255,plain,(
% 0.15/0.40 spl0_1 <=> ($false = (rel_b @ sK3 @ sK2))),
% 0.15/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.15/0.40 thf(f224,plain,(
% 0.15/0.40 ($true = (rel_b @ sK3 @ sK2))),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f219])).
% 0.15/0.40 thf(f219,plain,(
% 0.15/0.40 ($true = (rel_b @ sK3 @ sK2)) | ($false = $true)),
% 0.15/0.40 inference(superposition,[],[f180,f198])).
% 0.15/0.40 thf(f198,plain,(
% 0.15/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (rel_b @ X1 @ X2)) | ((rel_b @ X2 @ X1) = $true)) )),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f197])).
% 0.15/0.40 thf(f197,plain,(
% 0.15/0.40 ( ! [X2 : $i,X1 : $i] : (($true = ((rel_b @ X1 @ X2) => (rel_b @ X2 @ X1)))) )),
% 0.15/0.40 inference(beta_eta_normalization,[],[f196])).
% 0.15/0.40 thf(f196,plain,(
% 0.15/0.40 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((rel_b @ X1 @ Y0) => (rel_b @ Y0 @ X1))) @ X2))) )),
% 0.15/0.40 inference(pi_clausification,[],[f195])).
% 0.15/0.40 thf(f195,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((rel_b @ X1 @ Y0) => (rel_b @ Y0 @ X1)))) = $true)) )),
% 0.15/0.40 inference(beta_eta_normalization,[],[f194])).
% 0.15/0.40 thf(f194,plain,(
% 0.15/0.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_b @ Y0 @ Y1) => (rel_b @ Y1 @ Y0))))) @ X1) = $true)) )),
% 0.15/0.40 inference(pi_clausification,[],[f193])).
% 0.15/0.40 thf(f193,plain,(
% 0.15/0.40 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_b @ Y0 @ Y1) => (rel_b @ Y1 @ Y0)))))))),
% 0.15/0.40 inference(beta_eta_normalization,[],[f155])).
% 0.15/0.40 thf(f155,plain,(
% 0.15/0.40 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) @ rel_b) = $true)),
% 0.15/0.40 inference(definition_unfolding,[],[f132,f122])).
% 0.15/0.40 thf(f122,plain,(
% 0.15/0.40 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.15/0.40 inference(cnf_transformation,[],[f76])).
% 0.15/0.40 thf(f76,plain,(
% 0.15/0.40 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.15/0.40 inference(fool_elimination,[],[f75])).
% 0.15/0.40 thf(f75,plain,(
% 0.15/0.40 (msymmetric = (^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X2 @ X1) => (X0 @ X1 @ X2)))))),
% 0.15/0.40 inference(rectify,[],[f19])).
% 0.15/0.40 thf(f19,axiom,(
% 0.15/0.40 (msymmetric = (^[X6 : $i > $i > $o] : (! [X9,X8] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))))),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',msymmetric)).
% 0.15/0.40 thf(f132,plain,(
% 0.15/0.40 ((msymmetric @ rel_b) = $true)),
% 0.15/0.40 inference(cnf_transformation,[],[f70])).
% 0.15/0.40 thf(f70,plain,(
% 0.15/0.40 ((msymmetric @ rel_b) = $true)),
% 0.15/0.40 inference(fool_elimination,[],[f69])).
% 0.15/0.40 thf(f69,plain,(
% 0.15/0.40 (msymmetric @ rel_b)),
% 0.15/0.40 inference(rectify,[],[f35])).
% 0.15/0.40 thf(f35,axiom,(
% 0.15/0.40 (msymmetric @ rel_b)),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2)).
% 0.15/0.40 thf(f180,plain,(
% 0.15/0.40 ((rel_b @ sK2 @ sK3) = $true)),
% 0.15/0.40 inference(not_proxy_clausification,[],[f179])).
% 0.15/0.40 thf(f179,plain,(
% 0.15/0.40 ($false = (~ (rel_b @ sK2 @ sK3)))),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f177])).
% 0.15/0.40 thf(f177,plain,(
% 0.15/0.40 ($false = ((~ (rel_b @ sK2 @ sK3)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (p @ Y1))))))))))))),
% 0.15/0.40 inference(beta_eta_normalization,[],[f176])).
% 0.15/0.40 thf(f176,plain,(
% 0.15/0.40 ($false = ((^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (p @ Y2)))))))))))) @ sK3))),
% 0.15/0.40 inference(sigma_clausification,[],[f168])).
% 0.15/0.40 thf(f168,plain,(
% 0.15/0.40 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (p @ Y2))))))))))))))),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f165])).
% 0.15/0.40 thf(f165,plain,(
% 0.15/0.40 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (p @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (p @ Y2)))))))))))))))),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f164])).
% 0.15/0.40 thf(f164,plain,(
% 0.15/0.40 ($false = ((~ (rel_b @ sK1 @ sK2)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (p @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (p @ Y2))))))))))))))))),
% 0.15/0.40 inference(beta_eta_normalization,[],[f163])).
% 0.15/0.40 thf(f163,plain,(
% 0.15/0.40 ($false = ((^[Y0 : $i]: ((~ (rel_b @ sK1 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (p @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (~ (p @ Y3)))))))))))))))) @ sK2))),
% 0.15/0.40 inference(sigma_clausification,[],[f162])).
% 0.15/0.40 thf(f162,plain,(
% 0.15/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK1 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (p @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (~ (p @ Y3))))))))))))))))) = $false)),
% 0.15/0.40 inference(beta_eta_normalization,[],[f161])).
% 0.15/0.40 thf(f161,plain,(
% 0.15/0.40 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (p @ Y2)))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_b @ Y3 @ Y4)) | (~ (p @ Y4)))))))))))))))))) @ sK1))),
% 0.15/0.40 inference(sigma_clausification,[],[f160])).
% 0.15/0.40 thf(f160,plain,(
% 0.15/0.40 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (p @ Y2)))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_b @ Y3 @ Y4)) | (~ (p @ Y4))))))))))))))))))))),
% 0.15/0.40 inference(boolean_simplification,[],[f159])).
% 0.15/0.40 thf(f159,plain,(
% 0.15/0.40 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (p @ Y2)))))) | (~ (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_b @ Y3 @ Y4)) | (~ (p @ Y4))))))))))))))))))))))),
% 0.15/0.40 inference(boolean_simplification,[],[f158])).
% 0.15/0.40 thf(f158,plain,(
% 0.15/0.40 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (p @ Y2)))))) | (~ (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_b @ Y3 @ Y4)) | (~ (p @ Y4))))))))))))))))))))))) != $true)),
% 0.15/0.40 inference(boolean_simplification,[],[f157])).
% 0.15/0.40 thf(f157,plain,(
% 0.15/0.40 ((!! @ $i @ (^[Y0 : $i]: (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (p @ Y2)))))) | (~ (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_b @ Y3 @ Y4)) | (~ (p @ Y4))))))))))))))))))))))))) != $true)),
% 0.15/0.40 inference(beta_eta_normalization,[],[f154])).
% 0.15/0.40 thf(f154,plain,(
% 0.15/0.40 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[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 > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ p))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))) @ p)))))) != $true)),
% 0.15/0.40 inference(definition_unfolding,[],[f112,f141,f121,f153,f144,f153,f133,f153,f133,f121])).
% 0.15/0.40 thf(f133,plain,(
% 0.15/0.40 (mbox_b = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.15/0.40 inference(cnf_transformation,[],[f42])).
% 0.15/0.40 thf(f42,plain,(
% 0.15/0.40 (mbox_b = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.15/0.40 inference(fool_elimination,[],[f41])).
% 0.15/0.40 thf(f41,plain,(
% 0.15/0.40 (mbox_b = (^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_b @ X1 @ X2)))))),
% 0.15/0.40 inference(rectify,[],[f32])).
% 0.15/0.40 thf(f32,axiom,(
% 0.15/0.40 (mbox_b = (^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_b @ X2 @ X7)))))),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_b)).
% 0.15/0.40 thf(f144,plain,(
% 0.15/0.40 (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)))))))),
% 0.15/0.40 inference(definition_unfolding,[],[f111,f121,f120,f121,f121])).
% 0.15/0.40 thf(f120,plain,(
% 0.15/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.15/0.40 inference(cnf_transformation,[],[f61])).
% 0.15/0.40 thf(f61,plain,(
% 0.15/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.15/0.40 inference(fool_elimination,[],[f60])).
% 0.15/0.40 thf(f60,plain,(
% 0.15/0.40 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.15/0.40 inference(rectify,[],[f4])).
% 0.15/0.40 thf(f4,axiom,(
% 0.15/0.40 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.15/0.40 thf(f111,plain,(
% 0.15/0.40 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.15/0.40 inference(cnf_transformation,[],[f53])).
% 0.15/0.40 thf(f53,plain,(
% 0.15/0.40 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.15/0.40 inference(fool_elimination,[],[f52])).
% 0.15/0.40 thf(f52,plain,(
% 0.15/0.40 ((^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))) = mand)),
% 0.15/0.40 inference(rectify,[],[f5])).
% 0.15/0.40 thf(f5,axiom,(
% 0.15/0.40 ((^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))) = mand)),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.15/0.40 thf(f153,plain,(
% 0.15/0.40 (mdia_b = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.15/0.40 inference(definition_unfolding,[],[f117,f121,f133,f121])).
% 0.15/0.40 thf(f117,plain,(
% 0.15/0.40 (mdia_b = (^[Y0 : $i > $o]: (mnot @ (mbox_b @ (mnot @ Y0)))))),
% 0.15/0.40 inference(cnf_transformation,[],[f44])).
% 0.15/0.40 thf(f44,plain,(
% 0.15/0.40 (mdia_b = (^[Y0 : $i > $o]: (mnot @ (mbox_b @ (mnot @ Y0)))))),
% 0.15/0.40 inference(fool_elimination,[],[f43])).
% 0.15/0.40 thf(f43,plain,(
% 0.15/0.40 (mdia_b = (^[X0 : $i > $o] : (mnot @ (mbox_b @ (mnot @ X0)))))),
% 0.15/0.40 inference(rectify,[],[f33])).
% 0.15/0.40 thf(f33,axiom,(
% 0.15/0.40 (mdia_b = (^[X3 : $i > $o] : (mnot @ (mbox_b @ (mnot @ X3)))))),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_b)).
% 0.15/0.40 thf(f121,plain,(
% 0.15/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.15/0.40 inference(cnf_transformation,[],[f66])).
% 0.15/0.40 thf(f66,plain,(
% 0.15/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.15/0.40 inference(fool_elimination,[],[f65])).
% 0.15/0.40 thf(f65,plain,(
% 0.15/0.40 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.15/0.40 inference(rectify,[],[f3])).
% 0.15/0.40 thf(f3,axiom,(
% 0.15/0.40 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.15/0.40 thf(f141,plain,(
% 0.15/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.15/0.40 inference(cnf_transformation,[],[f51])).
% 0.15/0.40 thf(f51,plain,(
% 0.15/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.15/0.40 inference(fool_elimination,[],[f50])).
% 0.15/0.40 thf(f50,plain,(
% 0.15/0.40 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.15/0.40 inference(rectify,[],[f28])).
% 0.15/0.40 thf(f28,axiom,(
% 0.15/0.40 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.15/0.40 thf(f112,plain,(
% 0.15/0.40 ((mvalid @ (mnot @ (mdia_b @ (mand @ (mdia_b @ (mbox_b @ (mdia_b @ p))) @ (mbox_b @ (mnot @ p)))))) != $true)),
% 0.15/0.40 inference(cnf_transformation,[],[f107])).
% 0.15/0.40 thf(f107,plain,(
% 0.15/0.40 ((mvalid @ (mnot @ (mdia_b @ (mand @ (mdia_b @ (mbox_b @ (mdia_b @ p))) @ (mbox_b @ (mnot @ p)))))) != $true)),
% 0.15/0.40 inference(flattening,[],[f92])).
% 0.15/0.40 thf(f92,plain,(
% 0.15/0.40 ~((mvalid @ (mnot @ (mdia_b @ (mand @ (mdia_b @ (mbox_b @ (mdia_b @ p))) @ (mbox_b @ (mnot @ p)))))) = $true)),
% 0.15/0.40 inference(fool_elimination,[],[f91])).
% 0.15/0.40 thf(f91,plain,(
% 0.15/0.40 ~(mvalid @ (mnot @ (mdia_b @ (mand @ (mdia_b @ (mbox_b @ (mdia_b @ p))) @ (mbox_b @ (mnot @ p))))))),
% 0.15/0.40 inference(rectify,[],[f37])).
% 0.15/0.40 thf(f37,negated_conjecture,(
% 0.15/0.40 ~(mvalid @ (mnot @ (mdia_b @ (mand @ (mdia_b @ (mbox_b @ (mdia_b @ p))) @ (mbox_b @ (mnot @ p))))))),
% 0.15/0.40 inference(negated_conjecture,[],[f36])).
% 0.15/0.40 thf(f36,conjecture,(
% 0.15/0.40 (mvalid @ (mnot @ (mdia_b @ (mand @ (mdia_b @ (mbox_b @ (mdia_b @ p))) @ (mbox_b @ (mnot @ p))))))),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.15/0.40 thf(f279,plain,(
% 0.15/0.40 ~spl0_2),
% 0.15/0.40 inference(avatar_contradiction_clause,[],[f278])).
% 0.15/0.40 thf(f278,plain,(
% 0.15/0.40 $false | ~spl0_2),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f275])).
% 0.15/0.40 thf(f275,plain,(
% 0.15/0.40 ($false = $true) | ~spl0_2),
% 0.15/0.40 inference(superposition,[],[f239,f261])).
% 0.15/0.40 thf(f261,plain,(
% 0.15/0.40 ($false = (p @ (sK4 @ sK2))) | ~spl0_2),
% 0.15/0.40 inference(avatar_component_clause,[],[f259])).
% 0.15/0.40 thf(f259,plain,(
% 0.15/0.40 spl0_2 <=> ($false = (p @ (sK4 @ sK2)))),
% 0.15/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.15/0.40 thf(f239,plain,(
% 0.15/0.40 ($true = (p @ (sK4 @ sK2)))),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f234])).
% 0.15/0.40 thf(f234,plain,(
% 0.15/0.40 ($false = $true) | ($true = (p @ (sK4 @ sK2)))),
% 0.15/0.40 inference(superposition,[],[f224,f192])).
% 0.15/0.40 thf(f192,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (((rel_b @ sK3 @ X1) = $false) | ((p @ (sK4 @ X1)) = $true)) )),
% 0.15/0.40 inference(not_proxy_clausification,[],[f189])).
% 0.15/0.40 thf(f189,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (((rel_b @ sK3 @ X1) = $false) | ($false = (~ (p @ (sK4 @ X1))))) )),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f188])).
% 0.15/0.40 thf(f188,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (((rel_b @ sK3 @ X1) = $false) | ($false = ((~ (rel_b @ X1 @ (sK4 @ X1))) | (~ (p @ (sK4 @ X1)))))) )),
% 0.15/0.40 inference(beta_eta_normalization,[],[f187])).
% 0.15/0.40 thf(f187,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((~ (rel_b @ X1 @ Y0)) | (~ (p @ Y0)))) @ (sK4 @ X1))) | ((rel_b @ sK3 @ X1) = $false)) )),
% 0.15/0.40 inference(sigma_clausification,[],[f186])).
% 0.15/0.40 thf(f186,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (((rel_b @ sK3 @ X1) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ X1 @ Y0)) | (~ (p @ Y0))))))) )),
% 0.15/0.40 inference(not_proxy_clausification,[],[f185])).
% 0.15/0.40 thf(f185,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (((rel_b @ sK3 @ X1) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ X1 @ Y0)) | (~ (p @ Y0)))))) = $true)) )),
% 0.15/0.40 inference(not_proxy_clausification,[],[f184])).
% 0.15/0.40 thf(f184,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (((~ (rel_b @ sK3 @ X1)) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ X1 @ Y0)) | (~ (p @ Y0)))))) = $true)) )),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f183])).
% 0.15/0.40 thf(f183,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($true = ((~ (rel_b @ sK3 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ X1 @ Y0)) | (~ (p @ Y0))))))))) )),
% 0.15/0.40 inference(beta_eta_normalization,[],[f182])).
% 0.15/0.40 thf(f182,plain,(
% 0.15/0.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_b @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (p @ Y1)))))))) @ X1) = $true)) )),
% 0.15/0.40 inference(pi_clausification,[],[f181])).
% 0.15/0.40 thf(f181,plain,(
% 0.15/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (p @ Y1))))))))) = $true)),
% 0.15/0.40 inference(not_proxy_clausification,[],[f178])).
% 0.15/0.40 thf(f178,plain,(
% 0.15/0.40 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (p @ Y1)))))))))))),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f177])).
% 0.15/0.40 thf(f272,plain,(
% 0.15/0.40 spl0_1 | spl0_2),
% 0.15/0.40 inference(avatar_split_clause,[],[f250,f259,f255])).
% 0.15/0.40 thf(f250,plain,(
% 0.15/0.40 ($false = (p @ (sK4 @ sK2))) | ($false = (rel_b @ sK3 @ sK2))),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f246])).
% 0.15/0.40 thf(f246,plain,(
% 0.15/0.40 ($false = $true) | ($false = (p @ (sK4 @ sK2))) | ($false = (rel_b @ sK3 @ sK2))),
% 0.15/0.40 inference(superposition,[],[f175,f191])).
% 0.15/0.40 thf(f191,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (((rel_b @ X1 @ (sK4 @ X1)) = $true) | ((rel_b @ sK3 @ X1) = $false)) )),
% 0.15/0.40 inference(not_proxy_clausification,[],[f190])).
% 0.15/0.40 thf(f190,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($false = (~ (rel_b @ X1 @ (sK4 @ X1)))) | ((rel_b @ sK3 @ X1) = $false)) )),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f188])).
% 0.15/0.40 thf(f175,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($false = (rel_b @ sK2 @ X1)) | ($false = (p @ X1))) )),
% 0.15/0.40 inference(not_proxy_clausification,[],[f174])).
% 0.15/0.40 thf(f174,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($false = (p @ X1)) | ((~ (rel_b @ sK2 @ X1)) = $true)) )),
% 0.15/0.40 inference(not_proxy_clausification,[],[f173])).
% 0.15/0.40 thf(f173,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (((~ (p @ X1)) = $true) | ((~ (rel_b @ sK2 @ X1)) = $true)) )),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f172])).
% 0.15/0.40 thf(f172,plain,(
% 0.15/0.40 ( ! [X1 : $i] : ((((~ (rel_b @ sK2 @ X1)) | (~ (p @ X1))) = $true)) )),
% 0.15/0.40 inference(beta_eta_normalization,[],[f171])).
% 0.15/0.40 thf(f171,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (p @ Y0)))) @ X1))) )),
% 0.15/0.40 inference(pi_clausification,[],[f170])).
% 0.15/0.40 thf(f170,plain,(
% 0.15/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (p @ Y0))))) = $true)),
% 0.15/0.40 inference(not_proxy_clausification,[],[f169])).
% 0.15/0.40 thf(f169,plain,(
% 0.15/0.40 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (p @ Y0)))))))),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f165])).
% 0.15/0.40 % SZS output end Proof for theBenchmark
% 0.15/0.40 % (28997)------------------------------
% 0.15/0.40 % (28997)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (28997)Termination reason: Refutation
% 0.15/0.40
% 0.15/0.40 % (28997)Memory used [KB]: 5756
% 0.15/0.40 % (28997)Time elapsed: 0.024 s
% 0.15/0.40 % (28997)Instructions burned: 18 (million)
% 0.15/0.40 % (28997)------------------------------
% 0.15/0.40 % (28997)------------------------------
% 0.15/0.40 % (28993)Success in time 0.026 s
% 0.15/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------