TSTP Solution File: SET684^3 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET684^3 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:12:50 EDT 2024
% Result : Theorem 0.15s 0.34s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET684^3 : TPTP v8.2.0. Released v3.6.0.
% 0.09/0.11 % 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
% 0.10/0.31 % Computer : n010.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon May 20 12:47:53 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.10/0.31 This is a TH0_THM_EQU_NAR problem
% 0.10/0.32 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
% 0.15/0.33 % (1745)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)
% 0.15/0.33 % (1743)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.33 % (1744)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)
% 0.15/0.33 % (1743)Instruction limit reached!
% 0.15/0.33 % (1743)------------------------------
% 0.15/0.33 % (1743)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (1743)Termination reason: Unknown
% 0.15/0.33 % (1743)Termination phase: shuffling
% 0.15/0.33
% 0.15/0.33 % (1743)Memory used [KB]: 1023
% 0.15/0.33 % (1743)Time elapsed: 0.003 s
% 0.15/0.33 % (1743)Instructions burned: 3 (million)
% 0.15/0.33 % (1743)------------------------------
% 0.15/0.33 % (1743)------------------------------
% 0.15/0.33 % (1744)Instruction limit reached!
% 0.15/0.33 % (1744)------------------------------
% 0.15/0.33 % (1744)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (1744)Termination reason: Unknown
% 0.15/0.34 % (1744)Termination phase: shuffling
% 0.15/0.34
% 0.15/0.34 % (1744)Memory used [KB]: 1023
% 0.15/0.34 % (1744)Time elapsed: 0.003 s
% 0.15/0.34 % (1744)Instructions burned: 2 (million)
% 0.15/0.34 % (1744)------------------------------
% 0.15/0.34 % (1744)------------------------------
% 0.15/0.34 % (1745)First to succeed.
% 0.15/0.34 % (1745)Refutation found. Thanks to Tanya!
% 0.15/0.34 % SZS status Theorem for theBenchmark
% 0.15/0.34 % SZS output start Proof for theBenchmark
% 0.15/0.34 thf(func_def_0, type, in: $i > ($i > $o) > $o).
% 0.15/0.34 thf(func_def_2, type, is_a: $i > ($i > $o) > $o).
% 0.15/0.34 thf(func_def_3, type, emptyset: $i > $o).
% 0.15/0.34 thf(func_def_4, type, unord_pair: $i > $i > $i > $o).
% 0.15/0.34 thf(func_def_5, type, singleton: $i > $i > $o).
% 0.15/0.34 thf(func_def_6, type, union: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.34 thf(func_def_7, type, excl_union: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.34 thf(func_def_8, type, intersection: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.34 thf(func_def_9, type, setminus: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.34 thf(func_def_10, type, complement: ($i > $o) > $i > $o).
% 0.15/0.34 thf(func_def_11, type, disjoint: ($i > $o) > ($i > $o) > $o).
% 0.15/0.34 thf(func_def_12, type, subset: ($i > $o) > ($i > $o) > $o).
% 0.15/0.34 thf(func_def_13, type, meets: ($i > $o) > ($i > $o) > $o).
% 0.15/0.34 thf(func_def_14, type, misses: ($i > $o) > ($i > $o) > $o).
% 0.15/0.34 thf(func_def_15, type, cartesian_product: ($i > $o) > ($i > $o) > $i > $i > $o).
% 0.15/0.34 thf(func_def_16, type, pair_rel: $i > $i > $i > $i > $o).
% 0.15/0.34 thf(func_def_17, type, id_rel: ($i > $o) > $i > $i > $o).
% 0.15/0.34 thf(func_def_18, type, sub_rel: ($i > $i > $o) > ($i > $i > $o) > $o).
% 0.15/0.34 thf(func_def_19, type, is_rel_on: ($i > $i > $o) > ($i > $o) > ($i > $o) > $o).
% 0.15/0.34 thf(func_def_20, type, restrict_rel_domain: ($i > $i > $o) > ($i > $o) > $i > $i > $o).
% 0.15/0.34 thf(func_def_21, type, rel_diagonal: $i > $i > $o).
% 0.15/0.34 thf(func_def_22, type, rel_composition: ($i > $i > $o) > ($i > $i > $o) > $i > $i > $o).
% 0.15/0.34 thf(func_def_23, type, reflexive: ($i > $i > $o) > $o).
% 0.15/0.34 thf(func_def_24, type, irreflexive: ($i > $i > $o) > $o).
% 0.15/0.34 thf(func_def_25, type, symmetric: ($i > $i > $o) > $o).
% 0.15/0.34 thf(func_def_26, type, transitive: ($i > $i > $o) > $o).
% 0.15/0.34 thf(func_def_27, type, equiv_rel: ($i > $i > $o) > $o).
% 0.15/0.34 thf(func_def_28, type, rel_codomain: ($i > $i > $o) > $i > $o).
% 0.15/0.34 thf(func_def_29, type, rel_domain: ($i > $i > $o) > $i > $o).
% 0.15/0.34 thf(func_def_30, type, rel_inverse: ($i > $i > $o) > $i > $i > $o).
% 0.15/0.34 thf(func_def_31, type, equiv_classes: ($i > $i > $o) > ($i > $o) > $o).
% 0.15/0.34 thf(func_def_32, type, restrict_rel_codomain: ($i > $i > $o) > ($i > $o) > $i > $i > $o).
% 0.15/0.34 thf(func_def_33, type, rel_field: ($i > $i > $o) > $i > $o).
% 0.15/0.34 thf(func_def_34, type, well_founded: ($i > $i > $o) > $o).
% 0.15/0.34 thf(func_def_35, type, upwards_well_founded: ($i > $i > $o) > $o).
% 0.15/0.34 thf(func_def_52, type, sK0: $i > $i > $o).
% 0.15/0.34 thf(func_def_54, type, sK2: $i > $i > $o).
% 0.15/0.34 thf(f214,plain,(
% 0.15/0.34 $false),
% 0.15/0.34 inference(avatar_sat_refutation,[],[f144,f149,f156,f165,f170,f184,f187,f199,f206,f211,f213])).
% 0.15/0.34 thf(f213,plain,(
% 0.15/0.34 ~spl5_2 | ~spl5_3 | ~spl5_5),
% 0.15/0.34 inference(avatar_contradiction_clause,[],[f212])).
% 0.15/0.34 thf(f212,plain,(
% 0.15/0.34 $false | (~spl5_2 | ~spl5_3 | ~spl5_5)),
% 0.15/0.34 inference(subsumption_resolution,[],[f202,f143])).
% 0.15/0.34 thf(f143,plain,(
% 0.15/0.34 ((sK0 @ sK1 @ sK7) = $true) | ~spl5_2),
% 0.15/0.34 inference(avatar_component_clause,[],[f141])).
% 0.15/0.34 thf(f141,plain,(
% 0.15/0.34 spl5_2 <=> ((sK0 @ sK1 @ sK7) = $true)),
% 0.15/0.34 introduced(avatar_definition,[new_symbols(naming,[spl5_2])])).
% 0.15/0.34 thf(f202,plain,(
% 0.15/0.34 ((sK0 @ sK1 @ sK7) != $true) | (~spl5_3 | ~spl5_5)),
% 0.15/0.34 inference(trivial_inequality_removal,[],[f201])).
% 0.15/0.34 thf(f201,plain,(
% 0.15/0.34 ($true != $true) | ((sK0 @ sK1 @ sK7) != $true) | (~spl5_3 | ~spl5_5)),
% 0.15/0.34 inference(superposition,[],[f155,f148])).
% 0.15/0.34 thf(f148,plain,(
% 0.15/0.34 ($true = (sK2 @ sK7 @ sK3)) | ~spl5_3),
% 0.15/0.34 inference(avatar_component_clause,[],[f146])).
% 0.15/0.34 thf(f146,plain,(
% 0.15/0.34 spl5_3 <=> ($true = (sK2 @ sK7 @ sK3))),
% 0.15/0.34 introduced(avatar_definition,[new_symbols(naming,[spl5_3])])).
% 0.15/0.34 thf(f155,plain,(
% 0.15/0.34 ( ! [X4 : $i] : (($true != (sK2 @ X4 @ sK3)) | ((sK0 @ sK1 @ X4) != $true)) ) | ~spl5_5),
% 0.15/0.34 inference(avatar_component_clause,[],[f154])).
% 0.15/0.34 thf(f154,plain,(
% 0.15/0.34 spl5_5 <=> ! [X4] : (((sK0 @ sK1 @ X4) != $true) | ($true != (sK2 @ X4 @ sK3)))),
% 0.15/0.34 introduced(avatar_definition,[new_symbols(naming,[spl5_5])])).
% 0.15/0.34 thf(f211,plain,(
% 0.15/0.34 ~spl5_1 | ~spl5_5 | ~spl5_6),
% 0.15/0.34 inference(avatar_split_clause,[],[f208,f158,f154,f137])).
% 0.15/0.34 thf(f137,plain,(
% 0.15/0.34 spl5_1 <=> ($true = (sK0 @ sK1 @ sK4))),
% 0.15/0.34 introduced(avatar_definition,[new_symbols(naming,[spl5_1])])).
% 0.15/0.34 thf(f158,plain,(
% 0.15/0.34 spl5_6 <=> ((sK2 @ sK4 @ sK3) = $true)),
% 0.15/0.34 introduced(avatar_definition,[new_symbols(naming,[spl5_6])])).
% 0.15/0.34 thf(f208,plain,(
% 0.15/0.34 ($true != (sK0 @ sK1 @ sK4)) | (~spl5_5 | ~spl5_6)),
% 0.15/0.34 inference(trivial_inequality_removal,[],[f207])).
% 0.15/0.34 thf(f207,plain,(
% 0.15/0.34 ($true != (sK0 @ sK1 @ sK4)) | ($true != $true) | (~spl5_5 | ~spl5_6)),
% 0.15/0.34 inference(superposition,[],[f155,f160])).
% 0.15/0.34 thf(f160,plain,(
% 0.15/0.34 ((sK2 @ sK4 @ sK3) = $true) | ~spl5_6),
% 0.15/0.34 inference(avatar_component_clause,[],[f158])).
% 0.15/0.34 thf(f206,plain,(
% 0.15/0.34 ~spl5_7 | ~spl5_5 | ~spl5_8),
% 0.15/0.34 inference(avatar_split_clause,[],[f203,f167,f154,f162])).
% 0.15/0.34 thf(f162,plain,(
% 0.15/0.34 spl5_7 <=> ($true = (sK0 @ sK1 @ sK6))),
% 0.15/0.34 introduced(avatar_definition,[new_symbols(naming,[spl5_7])])).
% 0.15/0.34 thf(f167,plain,(
% 0.15/0.34 spl5_8 <=> ($true = (sK2 @ sK6 @ sK3))),
% 0.15/0.34 introduced(avatar_definition,[new_symbols(naming,[spl5_8])])).
% 0.15/0.34 thf(f203,plain,(
% 0.15/0.34 ($true != (sK0 @ sK1 @ sK6)) | (~spl5_5 | ~spl5_8)),
% 0.15/0.34 inference(trivial_inequality_removal,[],[f200])).
% 0.15/0.34 thf(f200,plain,(
% 0.15/0.34 ($true != $true) | ($true != (sK0 @ sK1 @ sK6)) | (~spl5_5 | ~spl5_8)),
% 0.15/0.34 inference(superposition,[],[f155,f169])).
% 0.15/0.34 thf(f169,plain,(
% 0.15/0.34 ($true = (sK2 @ sK6 @ sK3)) | ~spl5_8),
% 0.15/0.34 inference(avatar_component_clause,[],[f167])).
% 0.15/0.34 thf(f199,plain,(
% 0.15/0.34 ~spl5_4 | ~spl5_7 | ~spl5_8),
% 0.15/0.34 inference(avatar_contradiction_clause,[],[f198])).
% 0.15/0.34 thf(f198,plain,(
% 0.15/0.34 $false | (~spl5_4 | ~spl5_7 | ~spl5_8)),
% 0.15/0.34 inference(trivial_inequality_removal,[],[f194])).
% 0.15/0.34 thf(f194,plain,(
% 0.15/0.34 ($true = $false) | (~spl5_4 | ~spl5_7 | ~spl5_8)),
% 0.15/0.34 inference(superposition,[],[f193,f164])).
% 0.15/0.34 thf(f164,plain,(
% 0.15/0.34 ($true = (sK0 @ sK1 @ sK6)) | ~spl5_7),
% 0.15/0.34 inference(avatar_component_clause,[],[f162])).
% 0.15/0.34 thf(f193,plain,(
% 0.15/0.34 ((sK0 @ sK1 @ sK6) = $false) | (~spl5_4 | ~spl5_8)),
% 0.15/0.34 inference(trivial_inequality_removal,[],[f190])).
% 0.15/0.34 thf(f190,plain,(
% 0.15/0.34 ((sK0 @ sK1 @ sK6) = $false) | ($true = $false) | (~spl5_4 | ~spl5_8)),
% 0.15/0.34 inference(superposition,[],[f169,f152])).
% 0.15/0.34 thf(f152,plain,(
% 0.15/0.34 ( ! [X5 : $i] : (((sK2 @ X5 @ sK3) = $false) | ((sK0 @ sK1 @ X5) = $false)) ) | ~spl5_4),
% 0.15/0.34 inference(avatar_component_clause,[],[f151])).
% 0.15/0.34 thf(f151,plain,(
% 0.15/0.34 spl5_4 <=> ! [X5] : (((sK0 @ sK1 @ X5) = $false) | ((sK2 @ X5 @ sK3) = $false))),
% 0.15/0.34 introduced(avatar_definition,[new_symbols(naming,[spl5_4])])).
% 0.15/0.34 thf(f187,plain,(
% 0.15/0.34 ~spl5_1 | ~spl5_4 | ~spl5_6),
% 0.15/0.34 inference(avatar_contradiction_clause,[],[f186])).
% 0.15/0.34 thf(f186,plain,(
% 0.15/0.34 $false | (~spl5_1 | ~spl5_4 | ~spl5_6)),
% 0.15/0.34 inference(trivial_inequality_removal,[],[f185])).
% 0.15/0.34 thf(f185,plain,(
% 0.15/0.34 ($true = $false) | (~spl5_1 | ~spl5_4 | ~spl5_6)),
% 0.15/0.34 inference(forward_demodulation,[],[f139,f178])).
% 0.15/0.34 thf(f178,plain,(
% 0.15/0.34 ($false = (sK0 @ sK1 @ sK4)) | (~spl5_4 | ~spl5_6)),
% 0.15/0.34 inference(trivial_inequality_removal,[],[f175])).
% 0.15/0.34 thf(f175,plain,(
% 0.15/0.34 ($true = $false) | ($false = (sK0 @ sK1 @ sK4)) | (~spl5_4 | ~spl5_6)),
% 0.15/0.34 inference(superposition,[],[f160,f152])).
% 0.15/0.34 thf(f139,plain,(
% 0.15/0.34 ($true = (sK0 @ sK1 @ sK4)) | ~spl5_1),
% 0.15/0.34 inference(avatar_component_clause,[],[f137])).
% 0.15/0.34 thf(f184,plain,(
% 0.15/0.34 ~spl5_2 | ~spl5_3 | ~spl5_4),
% 0.15/0.34 inference(avatar_contradiction_clause,[],[f183])).
% 0.15/0.34 thf(f183,plain,(
% 0.15/0.34 $false | (~spl5_2 | ~spl5_3 | ~spl5_4)),
% 0.15/0.34 inference(trivial_inequality_removal,[],[f180])).
% 0.15/0.34 thf(f180,plain,(
% 0.15/0.34 ($true = $false) | (~spl5_2 | ~spl5_3 | ~spl5_4)),
% 0.15/0.34 inference(superposition,[],[f143,f174])).
% 0.15/0.34 thf(f174,plain,(
% 0.15/0.34 ((sK0 @ sK1 @ sK7) = $false) | (~spl5_3 | ~spl5_4)),
% 0.15/0.34 inference(trivial_inequality_removal,[],[f171])).
% 0.15/0.34 thf(f171,plain,(
% 0.15/0.34 ((sK0 @ sK1 @ sK7) = $false) | ($true = $false) | (~spl5_3 | ~spl5_4)),
% 0.15/0.34 inference(superposition,[],[f148,f152])).
% 0.15/0.34 thf(f170,plain,(
% 0.15/0.34 spl5_6 | spl5_8),
% 0.15/0.34 inference(avatar_split_clause,[],[f126,f167,f158])).
% 0.15/0.34 thf(f126,plain,(
% 0.15/0.34 ($true = (sK2 @ sK6 @ sK3)) | ((sK2 @ sK4 @ sK3) = $true)),
% 0.15/0.34 inference(binary_proxy_clausification,[],[f124])).
% 0.15/0.34 thf(f124,plain,(
% 0.15/0.34 ($true = ((sK2 @ sK6 @ sK3) & (sK0 @ sK1 @ sK6))) | ((sK2 @ sK4 @ sK3) = $true)),
% 0.15/0.34 inference(beta_eta_normalization,[],[f123])).
% 0.15/0.34 thf(f123,plain,(
% 0.15/0.34 ((sK2 @ sK4 @ sK3) = $true) | ($true = ((^[Y0 : $i]: ((sK2 @ Y0 @ sK3) & (sK0 @ sK1 @ Y0))) @ sK6))),
% 0.15/0.34 inference(sigma_clausification,[],[f122])).
% 0.15/0.34 thf(f122,plain,(
% 0.15/0.34 ($true = (?? @ $i @ (^[Y0 : $i]: ((sK2 @ Y0 @ sK3) & (sK0 @ sK1 @ Y0))))) | ((sK2 @ sK4 @ sK3) = $true)),
% 0.15/0.34 inference(beta_eta_normalization,[],[f120])).
% 0.15/0.34 thf(f120,plain,(
% 0.15/0.34 ((sK2 @ sK4 @ sK3) = $true) | ($true = ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((Y1 @ Y4 @ Y3) & (Y0 @ Y2 @ Y4))))))))))) @ sK0 @ sK2 @ sK1 @ sK3))),
% 0.15/0.34 inference(definition_unfolding,[],[f117,f114])).
% 0.15/0.34 thf(f114,plain,(
% 0.15/0.34 (rel_composition = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((Y1 @ Y4 @ Y3) & (Y0 @ Y2 @ Y4))))))))))))),
% 0.15/0.34 inference(cnf_transformation,[],[f80])).
% 0.15/0.34 thf(f80,plain,(
% 0.15/0.34 (rel_composition = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((Y1 @ Y4 @ Y3) & (Y0 @ Y2 @ Y4))))))))))))),
% 0.15/0.34 inference(fool_elimination,[],[f79])).
% 0.15/0.34 thf(f79,plain,(
% 0.15/0.34 (rel_composition = (^[X0 : $i > $i > $o, X1 : $i > $i > $o, X2 : $i, X3 : $i] : (? [X4] : ((X0 @ X2 @ X4) & (X1 @ X4 @ X3)))))),
% 0.15/0.34 inference(rectify,[],[f22])).
% 0.15/0.34 thf(f22,axiom,(
% 0.15/0.34 (rel_composition = (^[X6 : $i > $i > $o, X7 : $i > $i > $o, X0 : $i, X11 : $i] : (? [X2] : ((X6 @ X0 @ X2) & (X7 @ X2 @ X11)))))),
% 0.15/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p',rel_composition)).
% 0.15/0.34 thf(f117,plain,(
% 0.15/0.34 ($true = (rel_composition @ sK0 @ sK2 @ sK1 @ sK3)) | ((sK2 @ sK4 @ sK3) = $true)),
% 0.15/0.34 inference(cnf_transformation,[],[f113])).
% 0.15/0.34 thf(f113,plain,(
% 0.15/0.34 (($true != (rel_composition @ sK0 @ sK2 @ sK1 @ sK3)) | ! [X4] : (($true != (sK2 @ X4 @ sK3)) | ((sK0 @ sK1 @ X4) != $true))) & (($true = (rel_composition @ sK0 @ sK2 @ sK1 @ sK3)) | (((sK2 @ sK4 @ sK3) = $true) & ($true = (sK0 @ sK1 @ sK4))))),
% 0.15/0.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f110,f112,f111])).
% 0.15/0.34 thf(f111,plain,(
% 0.15/0.34 ? [X0 : $i > $i > $o,X1,X2 : $i > $i > $o,X3] : ((($true != (rel_composition @ X0 @ X2 @ X1 @ X3)) | ! [X4] : (($true != (X2 @ X4 @ X3)) | ($true != (X0 @ X1 @ X4)))) & (($true = (rel_composition @ X0 @ X2 @ X1 @ X3)) | ? [X5] : (($true = (X2 @ X5 @ X3)) & ($true = (X0 @ X1 @ X5))))) => ((($true != (rel_composition @ sK0 @ sK2 @ sK1 @ sK3)) | ! [X4] : (($true != (sK2 @ X4 @ sK3)) | ((sK0 @ sK1 @ X4) != $true))) & (($true = (rel_composition @ sK0 @ sK2 @ sK1 @ sK3)) | ? [X5] : (((sK2 @ X5 @ sK3) = $true) & ((sK0 @ sK1 @ X5) = $true))))),
% 0.15/0.34 introduced(choice_axiom,[])).
% 0.15/0.34 thf(f112,plain,(
% 0.15/0.34 ? [X5] : (((sK2 @ X5 @ sK3) = $true) & ((sK0 @ sK1 @ X5) = $true)) => (((sK2 @ sK4 @ sK3) = $true) & ($true = (sK0 @ sK1 @ sK4)))),
% 0.15/0.34 introduced(choice_axiom,[])).
% 0.15/0.34 thf(f110,plain,(
% 0.15/0.34 ? [X0 : $i > $i > $o,X1,X2 : $i > $i > $o,X3] : ((($true != (rel_composition @ X0 @ X2 @ X1 @ X3)) | ! [X4] : (($true != (X2 @ X4 @ X3)) | ($true != (X0 @ X1 @ X4)))) & (($true = (rel_composition @ X0 @ X2 @ X1 @ X3)) | ? [X5] : (($true = (X2 @ X5 @ X3)) & ($true = (X0 @ X1 @ X5)))))),
% 0.15/0.34 inference(rectify,[],[f109])).
% 0.15/0.34 thf(f109,plain,(
% 0.15/0.34 ? [X0 : $i > $i > $o,X1,X2 : $i > $i > $o,X3] : ((($true != (rel_composition @ X0 @ X2 @ X1 @ X3)) | ! [X4] : (($true != (X2 @ X4 @ X3)) | ($true != (X0 @ X1 @ X4)))) & (($true = (rel_composition @ X0 @ X2 @ X1 @ X3)) | ? [X4] : (($true = (X2 @ X4 @ X3)) & ($true = (X0 @ X1 @ X4)))))),
% 0.15/0.34 inference(nnf_transformation,[],[f108])).
% 0.15/0.34 thf(f108,plain,(
% 0.15/0.34 ? [X0 : $i > $i > $o,X1,X2 : $i > $i > $o,X3] : (? [X4] : (($true = (X2 @ X4 @ X3)) & ($true = (X0 @ X1 @ X4))) <~> ($true = (rel_composition @ X0 @ X2 @ X1 @ X3)))),
% 0.15/0.34 inference(ennf_transformation,[],[f40])).
% 0.15/0.34 thf(f40,plain,(
% 0.15/0.34 ~! [X0 : $i > $i > $o,X1,X2 : $i > $i > $o,X3] : (($true = (rel_composition @ X0 @ X2 @ X1 @ X3)) <=> ? [X4] : (($true = (X2 @ X4 @ X3)) & ($true = (X0 @ X1 @ X4))))),
% 0.15/0.34 inference(fool_elimination,[],[f39])).
% 0.15/0.34 thf(f39,plain,(
% 0.15/0.34 ~! [X0 : $i > $i > $o,X1,X2 : $i > $i > $o,X3] : (? [X4] : ((X0 @ X1 @ X4) & (X2 @ X4 @ X3)) <=> (rel_composition @ X0 @ X2 @ X1 @ X3))),
% 0.15/0.34 inference(rectify,[],[f37])).
% 0.15/0.34 thf(f37,negated_conjecture,(
% 0.15/0.34 ~! [X14 : $i > $i > $o,X0,X8 : $i > $i > $o,X11] : (? [X2] : ((X14 @ X0 @ X2) & (X8 @ X2 @ X11)) <=> (rel_composition @ X14 @ X8 @ X0 @ X11))),
% 0.15/0.34 inference(negated_conjecture,[],[f36])).
% 0.15/0.34 thf(f36,conjecture,(
% 0.15/0.34 ! [X14 : $i > $i > $o,X0,X8 : $i > $i > $o,X11] : (? [X2] : ((X14 @ X0 @ X2) & (X8 @ X2 @ X11)) <=> (rel_composition @ X14 @ X8 @ X0 @ X11))),
% 0.15/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm)).
% 0.15/0.34 thf(f165,plain,(
% 0.15/0.34 spl5_6 | spl5_7),
% 0.15/0.34 inference(avatar_split_clause,[],[f125,f162,f158])).
% 0.15/0.34 thf(f125,plain,(
% 0.15/0.34 ((sK2 @ sK4 @ sK3) = $true) | ($true = (sK0 @ sK1 @ sK6))),
% 0.15/0.34 inference(binary_proxy_clausification,[],[f124])).
% 0.15/0.34 thf(f156,plain,(
% 0.15/0.34 spl5_4 | spl5_5),
% 0.15/0.34 inference(avatar_split_clause,[],[f130,f154,f151])).
% 0.15/0.34 thf(f130,plain,(
% 0.15/0.34 ( ! [X4 : $i,X5 : $i] : (((sK0 @ sK1 @ X4) != $true) | ((sK0 @ sK1 @ X5) = $false) | ($true != (sK2 @ X4 @ sK3)) | ((sK2 @ X5 @ sK3) = $false)) )),
% 0.15/0.34 inference(binary_proxy_clausification,[],[f129])).
% 0.15/0.34 thf(f129,plain,(
% 0.15/0.34 ( ! [X4 : $i,X5 : $i] : (($true != (sK2 @ X4 @ sK3)) | ($false = ((sK2 @ X5 @ sK3) & (sK0 @ sK1 @ X5))) | ((sK0 @ sK1 @ X4) != $true)) )),
% 0.15/0.34 inference(beta_eta_normalization,[],[f128])).
% 0.15/0.34 thf(f128,plain,(
% 0.15/0.34 ( ! [X4 : $i,X5 : $i] : (((sK0 @ sK1 @ X4) != $true) | ($false = ((^[Y0 : $i]: ((sK2 @ Y0 @ sK3) & (sK0 @ sK1 @ Y0))) @ X5)) | ($true != (sK2 @ X4 @ sK3))) )),
% 0.15/0.34 inference(pi_clausification,[],[f127])).
% 0.15/0.34 thf(f127,plain,(
% 0.15/0.34 ( ! [X4 : $i] : (((sK0 @ sK1 @ X4) != $true) | ($true != (sK2 @ X4 @ sK3)) | ($true != (?? @ $i @ (^[Y0 : $i]: ((sK2 @ Y0 @ sK3) & (sK0 @ sK1 @ Y0)))))) )),
% 0.15/0.34 inference(beta_eta_normalization,[],[f119])).
% 0.15/0.34 thf(f119,plain,(
% 0.15/0.34 ( ! [X4 : $i] : (((sK0 @ sK1 @ X4) != $true) | ($true != ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((Y1 @ Y4 @ Y3) & (Y0 @ Y2 @ Y4))))))))))) @ sK0 @ sK2 @ sK1 @ sK3)) | ($true != (sK2 @ X4 @ sK3))) )),
% 0.15/0.34 inference(definition_unfolding,[],[f118,f114])).
% 0.15/0.34 thf(f118,plain,(
% 0.15/0.34 ( ! [X4 : $i] : (($true != (rel_composition @ sK0 @ sK2 @ sK1 @ sK3)) | ($true != (sK2 @ X4 @ sK3)) | ((sK0 @ sK1 @ X4) != $true)) )),
% 0.15/0.34 inference(cnf_transformation,[],[f113])).
% 0.15/0.34 thf(f149,plain,(
% 0.15/0.34 spl5_3 | spl5_1),
% 0.15/0.34 inference(avatar_split_clause,[],[f135,f137,f146])).
% 0.15/0.34 thf(f135,plain,(
% 0.15/0.34 ($true = (sK0 @ sK1 @ sK4)) | ($true = (sK2 @ sK7 @ sK3))),
% 0.15/0.34 inference(binary_proxy_clausification,[],[f133])).
% 0.15/0.34 thf(f133,plain,(
% 0.15/0.34 ($true = (sK0 @ sK1 @ sK4)) | (((sK2 @ sK7 @ sK3) & (sK0 @ sK1 @ sK7)) = $true)),
% 0.15/0.34 inference(beta_eta_normalization,[],[f132])).
% 0.15/0.34 thf(f132,plain,(
% 0.15/0.34 (((^[Y0 : $i]: ((sK2 @ Y0 @ sK3) & (sK0 @ sK1 @ Y0))) @ sK7) = $true) | ($true = (sK0 @ sK1 @ sK4))),
% 0.15/0.34 inference(sigma_clausification,[],[f131])).
% 0.15/0.34 thf(f131,plain,(
% 0.15/0.34 ($true = (?? @ $i @ (^[Y0 : $i]: ((sK2 @ Y0 @ sK3) & (sK0 @ sK1 @ Y0))))) | ($true = (sK0 @ sK1 @ sK4))),
% 0.15/0.34 inference(beta_eta_normalization,[],[f121])).
% 0.15/0.34 thf(f121,plain,(
% 0.15/0.34 ($true = ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((Y1 @ Y4 @ Y3) & (Y0 @ Y2 @ Y4))))))))))) @ sK0 @ sK2 @ sK1 @ sK3)) | ($true = (sK0 @ sK1 @ sK4))),
% 0.15/0.34 inference(definition_unfolding,[],[f116,f114])).
% 0.15/0.34 thf(f116,plain,(
% 0.15/0.34 ($true = (rel_composition @ sK0 @ sK2 @ sK1 @ sK3)) | ($true = (sK0 @ sK1 @ sK4))),
% 0.15/0.34 inference(cnf_transformation,[],[f113])).
% 0.15/0.34 thf(f144,plain,(
% 0.15/0.34 spl5_1 | spl5_2),
% 0.15/0.34 inference(avatar_split_clause,[],[f134,f141,f137])).
% 0.15/0.34 thf(f134,plain,(
% 0.15/0.34 ((sK0 @ sK1 @ sK7) = $true) | ($true = (sK0 @ sK1 @ sK4))),
% 0.15/0.34 inference(binary_proxy_clausification,[],[f133])).
% 0.15/0.34 % SZS output end Proof for theBenchmark
% 0.15/0.34 % (1745)------------------------------
% 0.15/0.34 % (1745)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.34 % (1745)Termination reason: Refutation
% 0.15/0.34
% 0.15/0.34 % (1745)Memory used [KB]: 5628
% 0.15/0.34 % (1745)Time elapsed: 0.010 s
% 0.15/0.34 % (1745)Instructions burned: 10 (million)
% 0.15/0.34 % (1745)------------------------------
% 0.15/0.34 % (1745)------------------------------
% 0.15/0.34 % (1739)Success in time 0.023 s
% 0.15/0.34 % Vampire---4.8 exiting
%------------------------------------------------------------------------------