TSTP Solution File: LCL595^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL595^1 : 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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n022.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 00:16:07 EDT 2024
% Result : Theorem 0.18s 0.37s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LCL595^1 : TPTP v8.2.0. Released v3.6.0.
% 0.11/0.11 % 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
% 0.12/0.32 % Computer : n022.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon May 20 01:10:08 EDT 2024
% 0.12/0.32 % CPUTime :
% 0.12/0.32 This is a TH0_THM_EQU_NAR problem
% 0.18/0.32 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/sandbox2/benchmark/theBenchmark.p
% 0.18/0.35 % (24187)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)
% 0.18/0.35 % (24186)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)
% 0.18/0.35 % (24187)Refutation not found, incomplete strategy
% 0.18/0.35 % (24187)------------------------------
% 0.18/0.35 % (24187)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.35 % (24187)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.35
% 0.18/0.35
% 0.18/0.35 % (24187)Memory used [KB]: 5628
% 0.18/0.35 % (24187)Time elapsed: 0.006 s
% 0.18/0.35 % (24187)Instructions burned: 8 (million)
% 0.18/0.35 % (24187)------------------------------
% 0.18/0.35 % (24187)------------------------------
% 0.18/0.35 % (24186)Instruction limit reached!
% 0.18/0.35 % (24186)------------------------------
% 0.18/0.35 % (24186)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.35 % (24186)Termination reason: Unknown
% 0.18/0.35 % (24186)Termination phase: shuffling
% 0.18/0.35
% 0.18/0.35 % (24186)Memory used [KB]: 1023
% 0.18/0.35 % (24186)Time elapsed: 0.002 s
% 0.18/0.35 % (24186)Instructions burned: 2 (million)
% 0.18/0.35 % (24186)------------------------------
% 0.18/0.35 % (24186)------------------------------
% 0.18/0.36 % (24185)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.18/0.36 % (24189)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)
% 0.18/0.36 % (24183)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)
% 0.18/0.36 % (24182)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.18/0.36 % (24185)Instruction limit reached!
% 0.18/0.36 % (24185)------------------------------
% 0.18/0.36 % (24185)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.36 % (24185)Termination reason: Unknown
% 0.18/0.36 % (24185)Termination phase: shuffling
% 0.18/0.36
% 0.18/0.36 % (24185)Memory used [KB]: 1023
% 0.18/0.36 % (24185)Time elapsed: 0.004 s
% 0.18/0.36 % (24185)Instructions burned: 3 (million)
% 0.18/0.36 % (24185)------------------------------
% 0.18/0.36 % (24185)------------------------------
% 0.18/0.36 % (24188)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.18/0.36 % (24189)Instruction limit reached!
% 0.18/0.36 % (24189)------------------------------
% 0.18/0.36 % (24189)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.36 % (24189)Termination reason: Unknown
% 0.18/0.36 % (24189)Termination phase: shuffling
% 0.18/0.36
% 0.18/0.36 % (24189)Memory used [KB]: 1023
% 0.18/0.36 % (24189)Time elapsed: 0.004 s
% 0.18/0.36 % (24189)Instructions burned: 3 (million)
% 0.18/0.36 % (24189)------------------------------
% 0.18/0.36 % (24189)------------------------------
% 0.18/0.36 % (24184)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)
% 0.18/0.36 % (24183)Instruction limit reached!
% 0.18/0.36 % (24183)------------------------------
% 0.18/0.36 % (24183)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.36 % (24183)Termination reason: Unknown
% 0.18/0.36 % (24183)Termination phase: Property scanning
% 0.18/0.36
% 0.18/0.36 % (24183)Memory used [KB]: 1023
% 0.18/0.36 % (24183)Time elapsed: 0.005 s
% 0.18/0.36 % (24183)Instructions burned: 4 (million)
% 0.18/0.36 % (24183)------------------------------
% 0.18/0.36 % (24183)------------------------------
% 0.18/0.37 % (24190)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)
% 0.18/0.37 % (24191)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.18/0.37 % (24184)First to succeed.
% 0.18/0.37 % (24188)Instruction limit reached!
% 0.18/0.37 % (24188)------------------------------
% 0.18/0.37 % (24188)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37 % (24188)Termination reason: Unknown
% 0.18/0.37 % (24188)Termination phase: Saturation
% 0.18/0.37
% 0.18/0.37 % (24188)Memory used [KB]: 5756
% 0.18/0.37 % (24188)Time elapsed: 0.011 s
% 0.18/0.37 % (24188)Instructions burned: 19 (million)
% 0.18/0.37 % (24188)------------------------------
% 0.18/0.37 % (24188)------------------------------
% 0.18/0.37 % (24192)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.18/0.37 % (24184)Refutation found. Thanks to Tanya!
% 0.18/0.37 % SZS status Theorem for theBenchmark
% 0.18/0.37 % SZS output start Proof for theBenchmark
% 0.18/0.37 thf(type_def_6, type, individuals: $tType).
% 0.18/0.37 thf(func_def_1, type, prop_a: $i > $o).
% 0.18/0.37 thf(func_def_2, type, prop_b: $i > $o).
% 0.18/0.37 thf(func_def_3, type, prop_c: $i > $o).
% 0.18/0.37 thf(func_def_4, type, mfalse: $i > $o).
% 0.18/0.37 thf(func_def_5, type, mtrue: $i > $o).
% 0.18/0.37 thf(func_def_6, type, mnot: ($i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_8, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_9, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_10, type, mimpl: ($i > $o) > ($i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_11, type, miff: ($i > $o) > ($i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_12, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_13, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_14, type, individuals: $tType).
% 0.18/0.37 thf(func_def_15, type, mall: (individuals > $i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_16, type, mexists: (individuals > $i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_17, type, mvalid: ($i > $o) > $o).
% 0.18/0.37 thf(func_def_18, type, msatisfiable: ($i > $o) > $o).
% 0.18/0.37 thf(func_def_19, type, mcountersatisfiable: ($i > $o) > $o).
% 0.18/0.37 thf(func_def_20, type, minvalid: ($i > $o) > $o).
% 0.18/0.37 thf(func_def_21, type, cartesian_product: ($i > $o) > ($i > $o) > $i > $i > $o).
% 0.18/0.37 thf(func_def_22, type, pair_rel: $i > $i > $i > $i > $o).
% 0.18/0.37 thf(func_def_23, type, id_rel: ($i > $o) > $i > $i > $o).
% 0.18/0.37 thf(func_def_24, type, sub_rel: ($i > $i > $o) > ($i > $i > $o) > $o).
% 0.18/0.37 thf(func_def_25, type, is_rel_on: ($i > $i > $o) > ($i > $o) > ($i > $o) > $o).
% 0.18/0.37 thf(func_def_26, type, restrict_rel_domain: ($i > $i > $o) > ($i > $o) > $i > $i > $o).
% 0.18/0.37 thf(func_def_27, type, rel_diagonal: $i > $i > $o).
% 0.18/0.37 thf(func_def_28, type, rel_composition: ($i > $i > $o) > ($i > $i > $o) > $i > $i > $o).
% 0.18/0.37 thf(func_def_29, type, reflexive: ($i > $i > $o) > $o).
% 0.18/0.37 thf(func_def_30, type, irreflexive: ($i > $i > $o) > $o).
% 0.18/0.37 thf(func_def_31, type, symmetric: ($i > $i > $o) > $o).
% 0.18/0.37 thf(func_def_32, type, transitive: ($i > $i > $o) > $o).
% 0.18/0.37 thf(func_def_33, type, equiv_rel: ($i > $i > $o) > $o).
% 0.18/0.37 thf(func_def_34, type, rel_codomain: ($i > $i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_35, type, rel_domain: ($i > $i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_36, type, rel_inverse: ($i > $i > $o) > $i > $i > $o).
% 0.18/0.37 thf(func_def_37, type, equiv_classes: ($i > $i > $o) > ($i > $o) > $o).
% 0.18/0.37 thf(func_def_38, type, restrict_rel_codomain: ($i > $i > $o) > ($i > $o) > $i > $i > $o).
% 0.18/0.37 thf(func_def_39, type, rel_field: ($i > $i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_40, type, well_founded: ($i > $i > $o) > $o).
% 0.18/0.37 thf(func_def_41, type, upwards_well_founded: ($i > $i > $o) > $o).
% 0.18/0.37 thf(func_def_42, type, r: $i > $i > $o).
% 0.18/0.37 thf(func_def_43, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.18/0.37 thf(func_def_60, type, sK0: $i > $o).
% 0.18/0.37 thf(func_def_62, type, sK2: ($i > $o) > $i > $i).
% 0.18/0.37 thf(func_def_66, type, ph6: !>[X0: $tType]:(X0)).
% 0.18/0.37 thf(f247,plain,(
% 0.18/0.37 $false),
% 0.18/0.37 inference(avatar_sat_refutation,[],[f193,f201,f208,f212,f222,f234,f240,f246])).
% 0.18/0.37 thf(f246,plain,(
% 0.18/0.37 ~spl1_1 | ~spl1_5),
% 0.18/0.37 inference(avatar_contradiction_clause,[],[f245])).
% 0.18/0.37 thf(f245,plain,(
% 0.18/0.37 $false | (~spl1_1 | ~spl1_5)),
% 0.18/0.37 inference(trivial_inequality_removal,[],[f241])).
% 0.18/0.37 thf(f241,plain,(
% 0.18/0.37 ($true = $false) | (~spl1_1 | ~spl1_5)),
% 0.18/0.37 inference(superposition,[],[f188,f204])).
% 0.18/0.37 thf(f204,plain,(
% 0.18/0.37 ( ! [X3 : $i] : (($true = (r @ X3 @ X3))) ) | ~spl1_5),
% 0.18/0.37 inference(avatar_component_clause,[],[f203])).
% 0.18/0.37 thf(f203,plain,(
% 0.18/0.37 spl1_5 <=> ! [X3] : ($true = (r @ X3 @ X3))),
% 0.18/0.37 introduced(avatar_definition,[new_symbols(naming,[spl1_5])])).
% 0.18/0.37 thf(f188,plain,(
% 0.18/0.37 ((r @ sK5 @ sK5) = $false) | ~spl1_1),
% 0.18/0.37 inference(avatar_component_clause,[],[f186])).
% 0.18/0.37 thf(f186,plain,(
% 0.18/0.37 spl1_1 <=> ((r @ sK5 @ sK5) = $false)),
% 0.18/0.37 introduced(avatar_definition,[new_symbols(naming,[spl1_1])])).
% 0.18/0.37 thf(f240,plain,(
% 0.18/0.37 ~spl1_4 | ~spl1_5),
% 0.18/0.37 inference(avatar_contradiction_clause,[],[f239])).
% 0.18/0.37 thf(f239,plain,(
% 0.18/0.37 $false | (~spl1_4 | ~spl1_5)),
% 0.18/0.37 inference(trivial_inequality_removal,[],[f236])).
% 0.18/0.37 thf(f236,plain,(
% 0.18/0.37 ($true = $false) | (~spl1_4 | ~spl1_5)),
% 0.18/0.37 inference(superposition,[],[f200,f204])).
% 0.18/0.37 thf(f200,plain,(
% 0.18/0.37 ((r @ sK4 @ sK4) = $false) | ~spl1_4),
% 0.18/0.37 inference(avatar_component_clause,[],[f198])).
% 0.18/0.37 thf(f198,plain,(
% 0.18/0.37 spl1_4 <=> ((r @ sK4 @ sK4) = $false)),
% 0.18/0.37 introduced(avatar_definition,[new_symbols(naming,[spl1_4])])).
% 0.18/0.37 thf(f234,plain,(
% 0.18/0.37 spl1_5 | ~spl1_6 | ~spl1_7),
% 0.18/0.37 inference(avatar_split_clause,[],[f229,f210,f206,f203])).
% 0.18/0.37 thf(f206,plain,(
% 0.18/0.37 spl1_6 <=> ! [X2,X1 : $i > $o] : (($true = (X1 @ X2)) | ($false = (X1 @ (sK2 @ X1 @ X2))))),
% 0.18/0.37 introduced(avatar_definition,[new_symbols(naming,[spl1_6])])).
% 0.18/0.37 thf(f210,plain,(
% 0.18/0.37 spl1_7 <=> ! [X2,X1 : $i > $o] : (($true = (X1 @ X2)) | ($true = (r @ X2 @ (sK2 @ X1 @ X2))))),
% 0.18/0.37 introduced(avatar_definition,[new_symbols(naming,[spl1_7])])).
% 0.18/0.37 thf(f229,plain,(
% 0.18/0.37 ( ! [X0 : $i] : (($true = (r @ X0 @ X0))) ) | (~spl1_6 | ~spl1_7)),
% 0.18/0.37 inference(trivial_inequality_removal,[],[f228])).
% 0.18/0.37 thf(f228,plain,(
% 0.18/0.37 ( ! [X0 : $i] : (($true = $false) | ($true = (r @ X0 @ X0))) ) | (~spl1_6 | ~spl1_7)),
% 0.18/0.37 inference(duplicate_literal_removal,[],[f226])).
% 0.18/0.37 thf(f226,plain,(
% 0.18/0.37 ( ! [X0 : $i] : (($true = (r @ X0 @ X0)) | ($true = (r @ X0 @ X0)) | ($true = $false)) ) | (~spl1_6 | ~spl1_7)),
% 0.18/0.37 inference(superposition,[],[f207,f211])).
% 0.18/0.37 thf(f211,plain,(
% 0.18/0.37 ( ! [X2 : $i,X1 : $i > $o] : (($true = (r @ X2 @ (sK2 @ X1 @ X2))) | ($true = (X1 @ X2))) ) | ~spl1_7),
% 0.18/0.37 inference(avatar_component_clause,[],[f210])).
% 0.18/0.37 thf(f207,plain,(
% 0.18/0.37 ( ! [X2 : $i,X1 : $i > $o] : (($false = (X1 @ (sK2 @ X1 @ X2))) | ($true = (X1 @ X2))) ) | ~spl1_6),
% 0.18/0.37 inference(avatar_component_clause,[],[f206])).
% 0.18/0.37 thf(f222,plain,(
% 0.18/0.37 ~spl1_2 | ~spl1_3 | ~spl1_5),
% 0.18/0.37 inference(avatar_contradiction_clause,[],[f221])).
% 0.18/0.37 thf(f221,plain,(
% 0.18/0.37 $false | (~spl1_2 | ~spl1_3 | ~spl1_5)),
% 0.18/0.37 inference(trivial_inequality_removal,[],[f220])).
% 0.18/0.37 thf(f220,plain,(
% 0.18/0.37 ($true = $false) | (~spl1_2 | ~spl1_3 | ~spl1_5)),
% 0.18/0.37 inference(forward_demodulation,[],[f215,f192])).
% 0.18/0.37 thf(f192,plain,(
% 0.18/0.37 ((sK0 @ sK3) = $false) | ~spl1_2),
% 0.18/0.37 inference(avatar_component_clause,[],[f190])).
% 0.18/0.37 thf(f190,plain,(
% 0.18/0.37 spl1_2 <=> ((sK0 @ sK3) = $false)),
% 0.18/0.37 introduced(avatar_definition,[new_symbols(naming,[spl1_2])])).
% 0.18/0.37 thf(f215,plain,(
% 0.18/0.37 ((sK0 @ sK3) = $true) | (~spl1_3 | ~spl1_5)),
% 0.18/0.37 inference(trivial_inequality_removal,[],[f213])).
% 0.18/0.37 thf(f213,plain,(
% 0.18/0.37 ((sK0 @ sK3) = $true) | ($true = $false) | (~spl1_3 | ~spl1_5)),
% 0.18/0.37 inference(superposition,[],[f196,f204])).
% 0.18/0.37 thf(f196,plain,(
% 0.18/0.37 ( ! [X1 : $i] : (((r @ sK3 @ X1) = $false) | ($true = (sK0 @ X1))) ) | ~spl1_3),
% 0.18/0.37 inference(avatar_component_clause,[],[f195])).
% 0.18/0.37 thf(f195,plain,(
% 0.18/0.37 spl1_3 <=> ! [X1] : (((r @ sK3 @ X1) = $false) | ($true = (sK0 @ X1)))),
% 0.18/0.37 introduced(avatar_definition,[new_symbols(naming,[spl1_3])])).
% 0.18/0.37 thf(f212,plain,(
% 0.18/0.37 spl1_5 | spl1_7),
% 0.18/0.37 inference(avatar_split_clause,[],[f171,f210,f203])).
% 0.18/0.37 thf(f171,plain,(
% 0.18/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($true = (r @ X3 @ X3)) | ($true = (X1 @ X2)) | ($true = (r @ X2 @ (sK2 @ X1 @ X2)))) )),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f169])).
% 0.18/0.37 thf(f169,plain,(
% 0.18/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($true = (r @ X3 @ X3)) | (((r @ X2 @ (sK2 @ X1 @ X2)) => (X1 @ (sK2 @ X1 @ X2))) = $false) | ($true = (X1 @ X2))) )),
% 0.18/0.37 inference(beta_eta_normalization,[],[f168])).
% 0.18/0.37 thf(f168,plain,(
% 0.18/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($true = (X1 @ X2)) | ($true = (r @ X3 @ X3)) | (((^[Y0 : $i]: ((r @ X2 @ Y0) => (X1 @ Y0))) @ (sK2 @ X1 @ X2)) = $false)) )),
% 0.18/0.37 inference(sigma_clausification,[],[f167])).
% 0.18/0.37 thf(f167,plain,(
% 0.18/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($true = (X1 @ X2)) | ((!! @ $i @ (^[Y0 : $i]: ((r @ X2 @ Y0) => (X1 @ Y0)))) = $false) | ($true = (r @ X3 @ X3))) )),
% 0.18/0.37 inference(not_proxy_clausification,[],[f166])).
% 0.18/0.37 thf(f166,plain,(
% 0.18/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($true = (r @ X3 @ X3)) | ($true = (X1 @ X2)) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((r @ X2 @ Y0) => (X1 @ Y0))))))) )),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f165])).
% 0.18/0.37 thf(f165,plain,(
% 0.18/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($true = (r @ X3 @ X3)) | (((~ (!! @ $i @ (^[Y0 : $i]: ((r @ X2 @ Y0) => (X1 @ Y0))))) | (X1 @ X2)) = $true)) )),
% 0.18/0.37 inference(beta_eta_normalization,[],[f164])).
% 0.18/0.37 thf(f164,plain,(
% 0.18/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : ((((~ (!! @ $i @ (^[Y0 : $i]: ((r @ X2 @ Y0) => (X1 @ Y0))))) | (X1 @ X2)) = $true) | ($true = ((^[Y0 : $i]: (r @ Y0 @ Y0)) @ X3))) )),
% 0.18/0.37 inference(pi_clausification,[],[f163])).
% 0.18/0.37 thf(f163,plain,(
% 0.18/0.37 ( ! [X2 : $i,X1 : $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: (r @ Y0 @ Y0)))) | (((~ (!! @ $i @ (^[Y0 : $i]: ((r @ X2 @ Y0) => (X1 @ Y0))))) | (X1 @ X2)) = $true)) )),
% 0.18/0.37 inference(beta_eta_normalization,[],[f162])).
% 0.18/0.37 thf(f162,plain,(
% 0.18/0.37 ( ! [X2 : $i,X1 : $i > $o] : ((((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((r @ Y0 @ Y1) => (X1 @ Y1))))) | (X1 @ Y0))) @ X2) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: (r @ Y0 @ Y0))))) )),
% 0.18/0.37 inference(pi_clausification,[],[f161])).
% 0.18/0.37 thf(f161,plain,(
% 0.18/0.37 ( ! [X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((r @ Y0 @ Y1) => (X1 @ Y1))))) | (X1 @ Y0)))) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: (r @ Y0 @ Y0))))) )),
% 0.18/0.37 inference(beta_eta_normalization,[],[f160])).
% 0.18/0.37 thf(f160,plain,(
% 0.18/0.37 ( ! [X1 : $i > $o] : (($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ r)) | ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))) @ r @ X1) @ X1)))) )),
% 0.18/0.37 inference(definition_unfolding,[],[f142,f118,f150,f155,f136])).
% 0.18/0.37 thf(f136,plain,(
% 0.18/0.37 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))))),
% 0.18/0.37 inference(cnf_transformation,[],[f109])).
% 0.18/0.37 thf(f109,plain,(
% 0.18/0.37 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))))),
% 0.18/0.37 inference(fool_elimination,[],[f108])).
% 0.18/0.37 thf(f108,plain,(
% 0.18/0.37 (mbox = (^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : ((X0 @ X2 @ X3) => (X1 @ X3)))))),
% 0.18/0.37 inference(rectify,[],[f8])).
% 0.18/0.37 thf(f8,axiom,(
% 0.18/0.37 (mbox = (^[X4 : $i > $i > $o, X5 : $i > $o, X0 : $i] : (! [X2] : ((X4 @ X0 @ X2) => (X5 @ X2)))))),
% 0.18/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox)).
% 0.18/0.37 thf(f155,plain,(
% 0.18/0.37 (mimpl = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.18/0.37 inference(definition_unfolding,[],[f127,f148,f134])).
% 0.18/0.37 thf(f134,plain,(
% 0.18/0.37 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.18/0.37 inference(cnf_transformation,[],[f51])).
% 0.18/0.37 thf(f51,plain,(
% 0.18/0.37 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.18/0.37 inference(fool_elimination,[],[f50])).
% 0.18/0.37 thf(f50,plain,(
% 0.18/0.37 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.18/0.37 inference(rectify,[],[f3])).
% 0.18/0.37 thf(f3,axiom,(
% 0.18/0.37 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.18/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.18/0.37 thf(f148,plain,(
% 0.18/0.37 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.18/0.37 inference(cnf_transformation,[],[f82])).
% 0.18/0.37 thf(f82,plain,(
% 0.18/0.37 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.18/0.37 inference(fool_elimination,[],[f81])).
% 0.18/0.37 thf(f81,plain,(
% 0.18/0.37 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.18/0.37 inference(rectify,[],[f4])).
% 0.18/0.37 thf(f4,axiom,(
% 0.18/0.37 (mor = (^[X0 : $i > $o, X2 : $i > $o, X1 : $i] : ((X2 @ X1) | (X0 @ X1))))),
% 0.18/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.18/0.37 thf(f127,plain,(
% 0.18/0.37 (mimpl = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.18/0.37 inference(cnf_transformation,[],[f71])).
% 0.18/0.37 thf(f71,plain,(
% 0.18/0.37 (mimpl = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.18/0.37 inference(fool_elimination,[],[f70])).
% 0.18/0.37 thf(f70,plain,(
% 0.18/0.37 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimpl)),
% 0.18/0.37 inference(rectify,[],[f6])).
% 0.18/0.37 thf(f6,axiom,(
% 0.18/0.37 ((^[X1 : $i > $o, X3 : $i > $o] : (mor @ (mnot @ X1) @ X3)) = mimpl)),
% 0.18/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimpl)).
% 0.18/0.37 thf(f150,plain,(
% 0.18/0.37 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.18/0.37 inference(cnf_transformation,[],[f65])).
% 0.18/0.37 thf(f65,plain,(
% 0.18/0.37 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.18/0.37 inference(fool_elimination,[],[f64])).
% 0.18/0.37 thf(f64,plain,(
% 0.18/0.37 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.18/0.37 inference(rectify,[],[f12])).
% 0.18/0.37 thf(f12,axiom,(
% 0.18/0.37 ((^[X5 : $i > $o] : (! [X6] : (X5 @ X6))) = mvalid)),
% 0.18/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.18/0.37 thf(f118,plain,(
% 0.18/0.37 (reflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.18/0.37 inference(cnf_transformation,[],[f69])).
% 0.18/0.37 thf(f69,plain,(
% 0.18/0.37 (reflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.18/0.37 inference(fool_elimination,[],[f68])).
% 0.18/0.37 thf(f68,plain,(
% 0.18/0.37 (reflexive = (^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))))),
% 0.18/0.37 inference(rectify,[],[f24])).
% 0.18/0.37 thf(f24,axiom,(
% 0.18/0.37 (reflexive = (^[X4 : $i > $i > $o] : (! [X0] : (X4 @ X0 @ X0))))),
% 0.18/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexive)).
% 0.18/0.37 thf(f142,plain,(
% 0.18/0.37 ( ! [X1 : $i > $o] : (((reflexive @ r) = $true) | ((mvalid @ (mimpl @ (mbox @ r @ X1) @ X1)) = $true)) )),
% 0.18/0.37 inference(cnf_transformation,[],[f116])).
% 0.18/0.37 thf(f116,plain,(
% 0.18/0.37 (((reflexive @ r) != $true) | ($true != (mvalid @ (mimpl @ (mbox @ r @ sK0) @ sK0)))) & (((reflexive @ r) = $true) | ! [X1 : $i > $o] : ((mvalid @ (mimpl @ (mbox @ r @ X1) @ X1)) = $true))),
% 0.18/0.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f114,f115])).
% 0.18/0.37 thf(f115,plain,(
% 0.18/0.37 ? [X0 : $i > $o] : ((mvalid @ (mimpl @ (mbox @ r @ X0) @ X0)) != $true) => ($true != (mvalid @ (mimpl @ (mbox @ r @ sK0) @ sK0)))),
% 0.18/0.37 introduced(choice_axiom,[])).
% 0.18/0.37 thf(f114,plain,(
% 0.18/0.37 (((reflexive @ r) != $true) | ? [X0 : $i > $o] : ((mvalid @ (mimpl @ (mbox @ r @ X0) @ X0)) != $true)) & (((reflexive @ r) = $true) | ! [X1 : $i > $o] : ((mvalid @ (mimpl @ (mbox @ r @ X1) @ X1)) = $true))),
% 0.18/0.37 inference(rectify,[],[f113])).
% 0.18/0.37 thf(f113,plain,(
% 0.18/0.37 (((reflexive @ r) != $true) | ? [X0 : $i > $o] : ((mvalid @ (mimpl @ (mbox @ r @ X0) @ X0)) != $true)) & (((reflexive @ r) = $true) | ! [X0 : $i > $o] : ((mvalid @ (mimpl @ (mbox @ r @ X0) @ X0)) = $true))),
% 0.18/0.37 inference(nnf_transformation,[],[f112])).
% 0.18/0.37 thf(f112,plain,(
% 0.18/0.37 ! [X0 : $i > $o] : ((mvalid @ (mimpl @ (mbox @ r @ X0) @ X0)) = $true) <~> ((reflexive @ r) = $true)),
% 0.18/0.37 inference(ennf_transformation,[],[f78])).
% 0.18/0.37 thf(f78,plain,(
% 0.18/0.37 ~(((reflexive @ r) = $true) <=> ! [X0 : $i > $o] : ((mvalid @ (mimpl @ (mbox @ r @ X0) @ X0)) = $true))),
% 0.18/0.37 inference(fool_elimination,[],[f77])).
% 0.18/0.37 thf(f77,plain,(
% 0.18/0.37 ~(! [X0 : $i > $o] : (mvalid @ (mimpl @ (mbox @ r @ X0) @ X0)) <=> (reflexive @ r))),
% 0.18/0.37 inference(rectify,[],[f38])).
% 0.18/0.37 thf(f38,negated_conjecture,(
% 0.18/0.37 ~(! [X10 : $i > $o] : (mvalid @ (mimpl @ (mbox @ r @ X10) @ X10)) <=> (reflexive @ r))),
% 0.18/0.37 inference(negated_conjecture,[],[f37])).
% 0.18/0.37 thf(f37,conjecture,(
% 0.18/0.37 ! [X10 : $i > $o] : (mvalid @ (mimpl @ (mbox @ r @ X10) @ X10)) <=> (reflexive @ r)),
% 0.18/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm)).
% 0.18/0.37 thf(f208,plain,(
% 0.18/0.37 spl1_5 | spl1_6),
% 0.18/0.37 inference(avatar_split_clause,[],[f170,f206,f203])).
% 0.18/0.37 thf(f170,plain,(
% 0.18/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($true = (r @ X3 @ X3)) | ($true = (X1 @ X2)) | ($false = (X1 @ (sK2 @ X1 @ X2)))) )),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f169])).
% 0.18/0.37 thf(f201,plain,(
% 0.18/0.37 spl1_3 | spl1_4),
% 0.18/0.37 inference(avatar_split_clause,[],[f182,f198,f195])).
% 0.18/0.37 thf(f182,plain,(
% 0.18/0.37 ( ! [X1 : $i] : (((r @ sK4 @ sK4) = $false) | ((r @ sK3 @ X1) = $false) | ($true = (sK0 @ X1))) )),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f181])).
% 0.18/0.37 thf(f181,plain,(
% 0.18/0.37 ( ! [X1 : $i] : ((((r @ sK3 @ X1) => (sK0 @ X1)) = $true) | ((r @ sK4 @ sK4) = $false)) )),
% 0.18/0.37 inference(beta_eta_normalization,[],[f180])).
% 0.18/0.37 thf(f180,plain,(
% 0.18/0.37 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((r @ sK3 @ Y0) => (sK0 @ Y0))) @ X1) = $true) | ((r @ sK4 @ sK4) = $false)) )),
% 0.18/0.37 inference(pi_clausification,[],[f179])).
% 0.18/0.37 thf(f179,plain,(
% 0.18/0.37 ((r @ sK4 @ sK4) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((r @ sK3 @ Y0) => (sK0 @ Y0)))) = $true)),
% 0.18/0.37 inference(beta_eta_normalization,[],[f178])).
% 0.18/0.37 thf(f178,plain,(
% 0.18/0.37 (((^[Y0 : $i]: (r @ Y0 @ Y0)) @ sK4) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((r @ sK3 @ Y0) => (sK0 @ Y0)))) = $true)),
% 0.18/0.37 inference(sigma_clausification,[],[f177])).
% 0.18/0.37 thf(f177,plain,(
% 0.18/0.37 ($true != (!! @ $i @ (^[Y0 : $i]: (r @ Y0 @ Y0)))) | ((!! @ $i @ (^[Y0 : $i]: ((r @ sK3 @ Y0) => (sK0 @ Y0)))) = $true)),
% 0.18/0.37 inference(not_proxy_clausification,[],[f176])).
% 0.18/0.37 thf(f176,plain,(
% 0.18/0.37 ((~ (!! @ $i @ (^[Y0 : $i]: ((r @ sK3 @ Y0) => (sK0 @ Y0))))) = $false) | ($true != (!! @ $i @ (^[Y0 : $i]: (r @ Y0 @ Y0))))),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f174])).
% 0.18/0.37 thf(f174,plain,(
% 0.18/0.37 (((~ (!! @ $i @ (^[Y0 : $i]: ((r @ sK3 @ Y0) => (sK0 @ Y0))))) | (sK0 @ sK3)) = $false) | ($true != (!! @ $i @ (^[Y0 : $i]: (r @ Y0 @ Y0))))),
% 0.18/0.37 inference(beta_eta_normalization,[],[f173])).
% 0.18/0.37 thf(f173,plain,(
% 0.18/0.37 ($true != (!! @ $i @ (^[Y0 : $i]: (r @ Y0 @ Y0)))) | (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((r @ Y0 @ Y1) => (sK0 @ Y1))))) | (sK0 @ Y0))) @ sK3) = $false)),
% 0.18/0.37 inference(sigma_clausification,[],[f172])).
% 0.18/0.37 thf(f172,plain,(
% 0.18/0.37 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((r @ Y0 @ Y1) => (sK0 @ Y1))))) | (sK0 @ Y0)))) != $true) | ($true != (!! @ $i @ (^[Y0 : $i]: (r @ Y0 @ Y0))))),
% 0.18/0.37 inference(beta_eta_normalization,[],[f159])).
% 0.18/0.37 thf(f159,plain,(
% 0.18/0.37 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))) @ r @ sK0) @ sK0)) != $true) | ($true != ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ r))),
% 0.18/0.37 inference(definition_unfolding,[],[f143,f118,f150,f155,f136])).
% 0.18/0.37 thf(f143,plain,(
% 0.18/0.37 ((reflexive @ r) != $true) | ($true != (mvalid @ (mimpl @ (mbox @ r @ sK0) @ sK0)))),
% 0.18/0.37 inference(cnf_transformation,[],[f116])).
% 0.18/0.37 thf(f193,plain,(
% 0.18/0.37 spl1_1 | spl1_2),
% 0.18/0.37 inference(avatar_split_clause,[],[f184,f190,f186])).
% 0.18/0.37 thf(f184,plain,(
% 0.18/0.37 ((r @ sK5 @ sK5) = $false) | ((sK0 @ sK3) = $false)),
% 0.18/0.37 inference(beta_eta_normalization,[],[f183])).
% 0.18/0.37 thf(f183,plain,(
% 0.18/0.37 ((sK0 @ sK3) = $false) | (((^[Y0 : $i]: (r @ Y0 @ Y0)) @ sK5) = $false)),
% 0.18/0.37 inference(sigma_clausification,[],[f175])).
% 0.18/0.37 thf(f175,plain,(
% 0.18/0.37 ($true != (!! @ $i @ (^[Y0 : $i]: (r @ Y0 @ Y0)))) | ((sK0 @ sK3) = $false)),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f174])).
% 0.18/0.37 % SZS output end Proof for theBenchmark
% 0.18/0.37 % (24184)------------------------------
% 0.18/0.37 % (24184)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37 % (24184)Termination reason: Refutation
% 0.18/0.37
% 0.18/0.37 % (24184)Memory used [KB]: 5756
% 0.18/0.37 % (24184)Time elapsed: 0.039 s
% 0.18/0.37 % (24184)Instructions burned: 13 (million)
% 0.18/0.37 % (24184)------------------------------
% 0.18/0.37 % (24184)------------------------------
% 0.18/0.37 % (24181)Success in time 0.04 s
% 0.18/0.37 % Vampire---4.8 exiting
%------------------------------------------------------------------------------