TSTP Solution File: LCL604^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL604^1 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n032.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 00:16:10 EDT 2024
% Result : Theorem 0.15s 0.33s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : LCL604^1 : TPTP v8.2.0. Released v3.6.0.
% 0.05/0.10 % 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
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon May 20 02:40:22 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.10/0.30 This is a TH0_THM_EQU_NAR problem
% 0.10/0.30 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
% 0.15/0.31 % (1401)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)
% 0.15/0.31 % (1401)Instruction limit reached!
% 0.15/0.31 % (1401)------------------------------
% 0.15/0.31 % (1401)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.31 % (1401)Termination reason: Unknown
% 0.15/0.31 % (1401)Termination phase: shuffling
% 0.15/0.31
% 0.15/0.31 % (1401)Memory used [KB]: 1023
% 0.15/0.31 % (1401)Time elapsed: 0.002 s
% 0.15/0.31 % (1401)Instructions burned: 2 (million)
% 0.15/0.31 % (1401)------------------------------
% 0.15/0.31 % (1401)------------------------------
% 0.15/0.31 % (1400)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.31 % (1400)Instruction limit reached!
% 0.15/0.31 % (1400)------------------------------
% 0.15/0.31 % (1400)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.31 % (1400)Termination reason: Unknown
% 0.15/0.31 % (1400)Termination phase: shuffling
% 0.15/0.31
% 0.15/0.31 % (1400)Memory used [KB]: 1023
% 0.15/0.31 % (1400)Time elapsed: 0.002 s
% 0.15/0.31 % (1400)Instructions burned: 3 (million)
% 0.15/0.31 % (1400)------------------------------
% 0.15/0.31 % (1400)------------------------------
% 0.15/0.32 % (1397)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.32 % (1399)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)
% 0.15/0.32 % (1402)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)
% 0.15/0.32 % (1403)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.32 % (1398)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)
% 0.15/0.32 % (1404)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)
% 0.15/0.32 % (1398)Instruction limit reached!
% 0.15/0.32 % (1398)------------------------------
% 0.15/0.32 % (1398)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.32 % (1398)Termination reason: Unknown
% 0.15/0.32 % (1398)Termination phase: Property scanning
% 0.15/0.32
% 0.15/0.32 % (1398)Memory used [KB]: 1023
% 0.15/0.32 % (1398)Time elapsed: 0.004 s
% 0.15/0.32 % (1398)Instructions burned: 4 (million)
% 0.15/0.32 % (1398)------------------------------
% 0.15/0.32 % (1398)------------------------------
% 0.15/0.32 % (1404)Instruction limit reached!
% 0.15/0.32 % (1404)------------------------------
% 0.15/0.32 % (1404)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.32 % (1404)Termination reason: Unknown
% 0.15/0.32 % (1404)Termination phase: shuffling
% 0.15/0.32
% 0.15/0.32 % (1404)Memory used [KB]: 1023
% 0.15/0.32 % (1404)Time elapsed: 0.002 s
% 0.15/0.32 % (1404)Instructions burned: 3 (million)
% 0.15/0.32 % (1404)------------------------------
% 0.15/0.32 % (1404)------------------------------
% 0.15/0.32 % (1406)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)
% 0.15/0.32 % (1402)Refutation not found, incomplete strategy
% 0.15/0.32 % (1402)------------------------------
% 0.15/0.32 % (1402)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.32 % (1402)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.32
% 0.15/0.32
% 0.15/0.32 % (1402)Memory used [KB]: 5628
% 0.15/0.32 % (1402)Time elapsed: 0.007 s
% 0.15/0.32 % (1402)Instructions burned: 10 (million)
% 0.15/0.32 % (1402)------------------------------
% 0.15/0.32 % (1402)------------------------------
% 0.15/0.33 % (1405)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)
% 0.15/0.33 % (1403)Instruction limit reached!
% 0.15/0.33 % (1403)------------------------------
% 0.15/0.33 % (1403)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (1403)Termination reason: Unknown
% 0.15/0.33 % (1403)Termination phase: Saturation
% 0.15/0.33
% 0.15/0.33 % (1403)Memory used [KB]: 5756
% 0.15/0.33 % (1403)Time elapsed: 0.011 s
% 0.15/0.33 % (1403)Instructions burned: 18 (million)
% 0.15/0.33 % (1403)------------------------------
% 0.15/0.33 % (1403)------------------------------
% 0.15/0.33 % (1406)Instruction limit reached!
% 0.15/0.33 % (1406)------------------------------
% 0.15/0.33 % (1406)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (1406)Termination reason: Unknown
% 0.15/0.33 % (1406)Termination phase: Saturation
% 0.15/0.33
% 0.15/0.33 % (1406)Memory used [KB]: 5756
% 0.15/0.33 % (1406)Time elapsed: 0.006 s
% 0.15/0.33 % (1406)Instructions burned: 16 (million)
% 0.15/0.33 % (1406)------------------------------
% 0.15/0.33 % (1406)------------------------------
% 0.15/0.33 % (1397)First to succeed.
% 0.15/0.33 % (1408)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.15/0.33 % (1399)Also succeeded, but the first one will report.
% 0.15/0.33 % (1397)Refutation found. Thanks to Tanya!
% 0.15/0.33 % SZS status Theorem for theBenchmark
% 0.15/0.33 % SZS output start Proof for theBenchmark
% 0.15/0.33 thf(type_def_6, type, individuals: $tType).
% 0.15/0.33 thf(func_def_1, type, prop_a: $i > $o).
% 0.15/0.33 thf(func_def_2, type, prop_b: $i > $o).
% 0.15/0.33 thf(func_def_3, type, prop_c: $i > $o).
% 0.15/0.33 thf(func_def_4, type, mfalse: $i > $o).
% 0.15/0.33 thf(func_def_5, type, mtrue: $i > $o).
% 0.15/0.33 thf(func_def_6, type, mnot: ($i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_8, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_9, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_10, type, mimpl: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_11, type, miff: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_12, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_13, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_14, type, individuals: $tType).
% 0.15/0.33 thf(func_def_15, type, mall: (individuals > $i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_16, type, mexists: (individuals > $i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_17, type, mvalid: ($i > $o) > $o).
% 0.15/0.33 thf(func_def_18, type, msatisfiable: ($i > $o) > $o).
% 0.15/0.33 thf(func_def_19, type, mcountersatisfiable: ($i > $o) > $o).
% 0.15/0.33 thf(func_def_20, type, minvalid: ($i > $o) > $o).
% 0.15/0.33 thf(func_def_21, type, cartesian_product: ($i > $o) > ($i > $o) > $i > $i > $o).
% 0.15/0.33 thf(func_def_22, type, pair_rel: $i > $i > $i > $i > $o).
% 0.15/0.33 thf(func_def_23, type, id_rel: ($i > $o) > $i > $i > $o).
% 0.15/0.33 thf(func_def_24, type, sub_rel: ($i > $i > $o) > ($i > $i > $o) > $o).
% 0.15/0.33 thf(func_def_25, type, is_rel_on: ($i > $i > $o) > ($i > $o) > ($i > $o) > $o).
% 0.15/0.33 thf(func_def_26, type, restrict_rel_domain: ($i > $i > $o) > ($i > $o) > $i > $i > $o).
% 0.15/0.33 thf(func_def_27, type, rel_diagonal: $i > $i > $o).
% 0.15/0.33 thf(func_def_28, type, rel_composition: ($i > $i > $o) > ($i > $i > $o) > $i > $i > $o).
% 0.15/0.33 thf(func_def_29, type, reflexive: ($i > $i > $o) > $o).
% 0.15/0.33 thf(func_def_30, type, irreflexive: ($i > $i > $o) > $o).
% 0.15/0.33 thf(func_def_31, type, symmetric: ($i > $i > $o) > $o).
% 0.15/0.33 thf(func_def_32, type, transitive: ($i > $i > $o) > $o).
% 0.15/0.33 thf(func_def_33, type, equiv_rel: ($i > $i > $o) > $o).
% 0.15/0.33 thf(func_def_34, type, rel_codomain: ($i > $i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_35, type, rel_domain: ($i > $i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_36, type, rel_inverse: ($i > $i > $o) > $i > $i > $o).
% 0.15/0.33 thf(func_def_37, type, equiv_classes: ($i > $i > $o) > ($i > $o) > $o).
% 0.15/0.33 thf(func_def_38, type, restrict_rel_codomain: ($i > $i > $o) > ($i > $o) > $i > $i > $o).
% 0.15/0.33 thf(func_def_39, type, rel_field: ($i > $i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_40, type, well_founded: ($i > $i > $o) > $o).
% 0.15/0.33 thf(func_def_41, type, upwards_well_founded: ($i > $i > $o) > $o).
% 0.15/0.33 thf(func_def_58, type, sK0: $i > $i > $o).
% 0.15/0.33 thf(func_def_59, type, sK1: $i > $o).
% 0.15/0.33 thf(f377,plain,(
% 0.15/0.33 $false),
% 0.15/0.33 inference(avatar_sat_refutation,[],[f228,f233,f238,f242,f250,f255,f260,f264,f326,f332,f376])).
% 0.15/0.33 thf(f376,plain,(
% 0.15/0.33 ~spl2_7 | ~spl2_8 | ~spl2_9 | ~spl2_10),
% 0.15/0.33 inference(avatar_contradiction_clause,[],[f375])).
% 0.15/0.33 thf(f375,plain,(
% 0.15/0.33 $false | (~spl2_7 | ~spl2_8 | ~spl2_9 | ~spl2_10)),
% 0.15/0.33 inference(trivial_inequality_removal,[],[f372])).
% 0.15/0.33 thf(f372,plain,(
% 0.15/0.33 ($true = $false) | (~spl2_7 | ~spl2_8 | ~spl2_9 | ~spl2_10)),
% 0.15/0.33 inference(superposition,[],[f249,f369])).
% 0.15/0.33 thf(f369,plain,(
% 0.15/0.33 ((sK1 @ sK6) = $true) | (~spl2_8 | ~spl2_9 | ~spl2_10)),
% 0.15/0.33 inference(trivial_inequality_removal,[],[f363])).
% 0.15/0.33 thf(f363,plain,(
% 0.15/0.33 ((sK1 @ sK6) = $true) | ($true = $false) | (~spl2_8 | ~spl2_9 | ~spl2_10)),
% 0.15/0.33 inference(superposition,[],[f361,f263])).
% 0.15/0.33 thf(f263,plain,(
% 0.15/0.33 ( ! [X2 : $i] : (((sK0 @ sK4 @ X2) = $false) | ((sK1 @ X2) = $true)) ) | ~spl2_10),
% 0.15/0.33 inference(avatar_component_clause,[],[f262])).
% 0.15/0.33 thf(f262,plain,(
% 0.15/0.33 spl2_10 <=> ! [X2] : (((sK0 @ sK4 @ X2) = $false) | ((sK1 @ X2) = $true))),
% 0.15/0.33 introduced(avatar_definition,[new_symbols(naming,[spl2_10])])).
% 0.15/0.33 thf(f361,plain,(
% 0.15/0.33 ((sK0 @ sK4 @ sK6) = $true) | (~spl2_8 | ~spl2_9)),
% 0.15/0.33 inference(trivial_inequality_removal,[],[f354])).
% 0.15/0.33 thf(f354,plain,(
% 0.15/0.33 ((sK0 @ sK4 @ sK6) = $true) | ($true = $false) | (~spl2_8 | ~spl2_9)),
% 0.15/0.33 inference(superposition,[],[f336,f254])).
% 0.15/0.33 thf(f254,plain,(
% 0.15/0.33 ((sK0 @ sK5 @ sK6) = $true) | ~spl2_8),
% 0.15/0.33 inference(avatar_component_clause,[],[f252])).
% 0.15/0.33 thf(f252,plain,(
% 0.15/0.33 spl2_8 <=> ((sK0 @ sK5 @ sK6) = $true)),
% 0.15/0.33 introduced(avatar_definition,[new_symbols(naming,[spl2_8])])).
% 0.15/0.33 thf(f336,plain,(
% 0.15/0.33 ( ! [X0 : $i] : (($false = (sK0 @ sK5 @ X0)) | ((sK0 @ sK4 @ X0) = $true)) ) | ~spl2_9),
% 0.15/0.33 inference(trivial_inequality_removal,[],[f333])).
% 0.15/0.33 thf(f333,plain,(
% 0.15/0.33 ( ! [X0 : $i] : (($true = $false) | ($false = (sK0 @ sK5 @ X0)) | ((sK0 @ sK4 @ X0) = $true)) ) | ~spl2_9),
% 0.15/0.33 inference(superposition,[],[f259,f174])).
% 0.15/0.33 thf(f174,plain,(
% 0.15/0.33 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (sK0 @ X3 @ X2)) | ((sK0 @ X2 @ X1) = $false) | ((sK0 @ X3 @ X1) = $true)) )),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f173])).
% 0.15/0.33 thf(f173,plain,(
% 0.15/0.33 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((sK0 @ X3 @ X1) = $true) | (((sK0 @ X3 @ X2) & (sK0 @ X2 @ X1)) = $false)) )),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f172])).
% 0.15/0.33 thf(f172,plain,(
% 0.15/0.33 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((sK0 @ X3 @ X2) & (sK0 @ X2 @ X1)) => (sK0 @ X3 @ X1)) = $true)) )),
% 0.15/0.33 inference(beta_eta_normalization,[],[f171])).
% 0.15/0.33 thf(f171,plain,(
% 0.15/0.33 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((sK0 @ Y0 @ X2) & (sK0 @ X2 @ X1)) => (sK0 @ Y0 @ X1))) @ X3) = $true)) )),
% 0.15/0.33 inference(pi_clausification,[],[f170])).
% 0.15/0.33 thf(f170,plain,(
% 0.15/0.33 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (((sK0 @ Y0 @ X2) & (sK0 @ X2 @ X1)) => (sK0 @ Y0 @ X1)))) = $true)) )),
% 0.15/0.33 inference(beta_eta_normalization,[],[f169])).
% 0.15/0.33 thf(f169,plain,(
% 0.15/0.33 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ Y1 @ Y0) & (sK0 @ Y0 @ X1)) => (sK0 @ Y1 @ X1))))) @ X2) = $true)) )),
% 0.15/0.33 inference(pi_clausification,[],[f168])).
% 0.15/0.33 thf(f168,plain,(
% 0.15/0.33 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ Y1 @ Y0) & (sK0 @ Y0 @ X1)) => (sK0 @ Y1 @ X1)))))) = $true)) )),
% 0.15/0.33 inference(beta_eta_normalization,[],[f167])).
% 0.15/0.33 thf(f167,plain,(
% 0.15/0.33 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y2 @ Y1) & (sK0 @ Y1 @ Y0)) => (sK0 @ Y2 @ Y0))))))) @ X1) = $true)) )),
% 0.15/0.33 inference(pi_clausification,[],[f166])).
% 0.15/0.33 thf(f166,plain,(
% 0.15/0.33 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y2 @ Y1) & (sK0 @ Y1 @ Y0)) => (sK0 @ Y2 @ Y0)))))))) = $true)),
% 0.15/0.33 inference(beta_eta_normalization,[],[f161])).
% 0.15/0.33 thf(f161,plain,(
% 0.15/0.33 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) @ sK0) = $true)),
% 0.15/0.33 inference(definition_unfolding,[],[f142,f118])).
% 0.15/0.33 thf(f118,plain,(
% 0.15/0.33 (transitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))))),
% 0.15/0.33 inference(cnf_transformation,[],[f77])).
% 0.15/0.33 thf(f77,plain,(
% 0.15/0.33 (transitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))))),
% 0.15/0.33 inference(fool_elimination,[],[f76])).
% 0.15/0.33 thf(f76,plain,(
% 0.15/0.33 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X2 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X1 @ X3)))) = transitive)),
% 0.15/0.33 inference(rectify,[],[f27])).
% 0.15/0.33 thf(f27,axiom,(
% 0.15/0.33 ((^[X4 : $i > $i > $o] : (! [X0,X2,X12] : (((X4 @ X2 @ X12) & (X4 @ X0 @ X2)) => (X4 @ X0 @ X12)))) = transitive)),
% 0.15/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive)).
% 0.15/0.33 thf(f142,plain,(
% 0.15/0.33 ((transitive @ sK0) = $true)),
% 0.15/0.33 inference(cnf_transformation,[],[f116])).
% 0.15/0.33 thf(f116,plain,(
% 0.15/0.33 (((mvalid @ (mimpl @ (mbox @ sK0 @ sK1) @ sK1)) != $true) | ((mvalid @ (mimpl @ (mbox @ sK0 @ sK1) @ (mbox @ sK0 @ (mbox @ sK0 @ sK1)))) != $true)) & ((transitive @ sK0) = $true) & ((reflexive @ sK0) = $true)),
% 0.15/0.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f113,f115,f114])).
% 0.15/0.33 thf(f114,plain,(
% 0.15/0.33 ? [X0 : $i > $i > $o] : (? [X1 : $i > $o] : (($true != (mvalid @ (mimpl @ (mbox @ X0 @ X1) @ X1))) | ((mvalid @ (mimpl @ (mbox @ X0 @ X1) @ (mbox @ X0 @ (mbox @ X0 @ X1)))) != $true)) & ($true = (transitive @ X0)) & ((reflexive @ X0) = $true)) => (? [X1 : $i > $o] : (((mvalid @ (mimpl @ (mbox @ sK0 @ X1) @ X1)) != $true) | ($true != (mvalid @ (mimpl @ (mbox @ sK0 @ X1) @ (mbox @ sK0 @ (mbox @ sK0 @ X1)))))) & ((transitive @ sK0) = $true) & ((reflexive @ sK0) = $true))),
% 0.15/0.33 introduced(choice_axiom,[])).
% 0.15/0.33 thf(f115,plain,(
% 0.15/0.33 ? [X1 : $i > $o] : (((mvalid @ (mimpl @ (mbox @ sK0 @ X1) @ X1)) != $true) | ($true != (mvalid @ (mimpl @ (mbox @ sK0 @ X1) @ (mbox @ sK0 @ (mbox @ sK0 @ X1)))))) => (((mvalid @ (mimpl @ (mbox @ sK0 @ sK1) @ sK1)) != $true) | ((mvalid @ (mimpl @ (mbox @ sK0 @ sK1) @ (mbox @ sK0 @ (mbox @ sK0 @ sK1)))) != $true))),
% 0.15/0.33 introduced(choice_axiom,[])).
% 0.15/0.33 thf(f113,plain,(
% 0.15/0.33 ? [X0 : $i > $i > $o] : (? [X1 : $i > $o] : (($true != (mvalid @ (mimpl @ (mbox @ X0 @ X1) @ X1))) | ((mvalid @ (mimpl @ (mbox @ X0 @ X1) @ (mbox @ X0 @ (mbox @ X0 @ X1)))) != $true)) & ($true = (transitive @ X0)) & ((reflexive @ X0) = $true))),
% 0.15/0.33 inference(flattening,[],[f112])).
% 0.15/0.33 thf(f112,plain,(
% 0.15/0.33 ? [X0 : $i > $i > $o] : (? [X1 : $i > $o] : (($true != (mvalid @ (mimpl @ (mbox @ X0 @ X1) @ X1))) | ((mvalid @ (mimpl @ (mbox @ X0 @ X1) @ (mbox @ X0 @ (mbox @ X0 @ X1)))) != $true)) & (($true = (transitive @ X0)) & ((reflexive @ X0) = $true)))),
% 0.15/0.33 inference(ennf_transformation,[],[f45])).
% 0.15/0.33 thf(f45,plain,(
% 0.15/0.33 ~! [X0 : $i > $i > $o] : ((($true = (transitive @ X0)) & ((reflexive @ X0) = $true)) => ! [X1 : $i > $o] : (((mvalid @ (mimpl @ (mbox @ X0 @ X1) @ (mbox @ X0 @ (mbox @ X0 @ X1)))) = $true) & ($true = (mvalid @ (mimpl @ (mbox @ X0 @ X1) @ X1)))))),
% 0.15/0.33 inference(fool_elimination,[],[f44])).
% 0.15/0.33 thf(f44,plain,(
% 0.15/0.33 ~! [X0 : $i > $i > $o] : (((transitive @ X0) & (reflexive @ X0)) => ! [X1 : $i > $o] : ((mvalid @ (mimpl @ (mbox @ X0 @ X1) @ X1)) & (mvalid @ (mimpl @ (mbox @ X0 @ X1) @ (mbox @ X0 @ (mbox @ X0 @ X1))))))),
% 0.15/0.33 inference(rectify,[],[f38])).
% 0.15/0.33 thf(f38,negated_conjecture,(
% 0.15/0.33 ~! [X4 : $i > $i > $o] : (((transitive @ X4) & (reflexive @ X4)) => ! [X10 : $i > $o] : ((mvalid @ (mimpl @ (mbox @ X4 @ X10) @ X10)) & (mvalid @ (mimpl @ (mbox @ X4 @ X10) @ (mbox @ X4 @ (mbox @ X4 @ X10))))))),
% 0.15/0.33 inference(negated_conjecture,[],[f37])).
% 0.15/0.33 thf(f37,conjecture,(
% 0.15/0.33 ! [X4 : $i > $i > $o] : (((transitive @ X4) & (reflexive @ X4)) => ! [X10 : $i > $o] : ((mvalid @ (mimpl @ (mbox @ X4 @ X10) @ X10)) & (mvalid @ (mimpl @ (mbox @ X4 @ X10) @ (mbox @ X4 @ (mbox @ X4 @ X10))))))),
% 0.15/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm)).
% 0.15/0.33 thf(f259,plain,(
% 0.15/0.33 ((sK0 @ sK4 @ sK5) = $true) | ~spl2_9),
% 0.15/0.33 inference(avatar_component_clause,[],[f257])).
% 0.15/0.33 thf(f257,plain,(
% 0.15/0.33 spl2_9 <=> ((sK0 @ sK4 @ sK5) = $true)),
% 0.15/0.33 introduced(avatar_definition,[new_symbols(naming,[spl2_9])])).
% 0.15/0.33 thf(f249,plain,(
% 0.15/0.33 ((sK1 @ sK6) = $false) | ~spl2_7),
% 0.15/0.33 inference(avatar_component_clause,[],[f247])).
% 0.15/0.33 thf(f247,plain,(
% 0.15/0.33 spl2_7 <=> ((sK1 @ sK6) = $false)),
% 0.15/0.33 introduced(avatar_definition,[new_symbols(naming,[spl2_7])])).
% 0.15/0.33 thf(f332,plain,(
% 0.15/0.33 ~spl2_1 | ~spl2_6),
% 0.15/0.33 inference(avatar_contradiction_clause,[],[f331])).
% 0.15/0.33 thf(f331,plain,(
% 0.15/0.33 $false | (~spl2_1 | ~spl2_6)),
% 0.15/0.33 inference(trivial_inequality_removal,[],[f328])).
% 0.15/0.33 thf(f328,plain,(
% 0.15/0.33 ($true = $false) | (~spl2_1 | ~spl2_6)),
% 0.15/0.33 inference(superposition,[],[f276,f223])).
% 0.15/0.33 thf(f223,plain,(
% 0.15/0.33 ((sK1 @ sK3) = $false) | ~spl2_1),
% 0.15/0.33 inference(avatar_component_clause,[],[f221])).
% 0.15/0.33 thf(f221,plain,(
% 0.15/0.33 spl2_1 <=> ((sK1 @ sK3) = $false)),
% 0.15/0.33 introduced(avatar_definition,[new_symbols(naming,[spl2_1])])).
% 0.15/0.33 thf(f276,plain,(
% 0.15/0.33 ((sK1 @ sK3) = $true) | ~spl2_6),
% 0.15/0.33 inference(trivial_inequality_removal,[],[f273])).
% 0.15/0.33 thf(f273,plain,(
% 0.15/0.33 ($true = $false) | ((sK1 @ sK3) = $true) | ~spl2_6),
% 0.15/0.33 inference(superposition,[],[f245,f165])).
% 0.15/0.33 thf(f165,plain,(
% 0.15/0.33 ( ! [X1 : $i] : (((sK0 @ X1 @ X1) = $true)) )),
% 0.15/0.33 inference(beta_eta_normalization,[],[f164])).
% 0.15/0.33 thf(f164,plain,(
% 0.15/0.33 ( ! [X1 : $i] : ((((^[Y0 : $i]: (sK0 @ Y0 @ Y0)) @ X1) = $true)) )),
% 0.15/0.33 inference(pi_clausification,[],[f163])).
% 0.15/0.33 thf(f163,plain,(
% 0.15/0.33 ((!! @ $i @ (^[Y0 : $i]: (sK0 @ Y0 @ Y0))) = $true)),
% 0.15/0.33 inference(beta_eta_normalization,[],[f162])).
% 0.15/0.33 thf(f162,plain,(
% 0.15/0.33 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ sK0) = $true)),
% 0.15/0.33 inference(definition_unfolding,[],[f141,f131])).
% 0.15/0.33 thf(f131,plain,(
% 0.15/0.33 (reflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.15/0.33 inference(cnf_transformation,[],[f95])).
% 0.15/0.33 thf(f95,plain,(
% 0.15/0.33 (reflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.15/0.33 inference(fool_elimination,[],[f94])).
% 0.15/0.33 thf(f94,plain,(
% 0.15/0.33 ((^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))) = reflexive)),
% 0.15/0.33 inference(rectify,[],[f24])).
% 0.15/0.33 thf(f24,axiom,(
% 0.15/0.33 ((^[X4 : $i > $i > $o] : (! [X0] : (X4 @ X0 @ X0))) = reflexive)),
% 0.15/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexive)).
% 0.15/0.33 thf(f141,plain,(
% 0.15/0.33 ((reflexive @ sK0) = $true)),
% 0.15/0.33 inference(cnf_transformation,[],[f116])).
% 0.15/0.33 thf(f245,plain,(
% 0.15/0.33 ( ! [X1 : $i] : (((sK0 @ sK3 @ X1) = $false) | ((sK1 @ X1) = $true)) ) | ~spl2_6),
% 0.15/0.33 inference(avatar_component_clause,[],[f244])).
% 0.15/0.33 thf(f244,plain,(
% 0.15/0.33 spl2_6 <=> ! [X1] : (((sK1 @ X1) = $true) | ((sK0 @ sK3 @ X1) = $false))),
% 0.15/0.33 introduced(avatar_definition,[new_symbols(naming,[spl2_6])])).
% 0.15/0.33 thf(f326,plain,(
% 0.15/0.33 ~spl2_2 | ~spl2_3 | ~spl2_4 | ~spl2_5),
% 0.15/0.33 inference(avatar_contradiction_clause,[],[f325])).
% 0.15/0.33 thf(f325,plain,(
% 0.15/0.33 $false | (~spl2_2 | ~spl2_3 | ~spl2_4 | ~spl2_5)),
% 0.15/0.33 inference(trivial_inequality_removal,[],[f322])).
% 0.15/0.33 thf(f322,plain,(
% 0.15/0.33 ($true = $false) | (~spl2_2 | ~spl2_3 | ~spl2_4 | ~spl2_5)),
% 0.15/0.33 inference(superposition,[],[f227,f319])).
% 0.15/0.33 thf(f319,plain,(
% 0.15/0.33 ($true = (sK1 @ sK9)) | (~spl2_3 | ~spl2_4 | ~spl2_5)),
% 0.15/0.33 inference(trivial_inequality_removal,[],[f315])).
% 0.15/0.33 thf(f315,plain,(
% 0.15/0.33 ($true = $false) | ($true = (sK1 @ sK9)) | (~spl2_3 | ~spl2_4 | ~spl2_5)),
% 0.15/0.33 inference(superposition,[],[f241,f310])).
% 0.15/0.33 thf(f310,plain,(
% 0.15/0.33 ($true = (sK0 @ sK7 @ sK9)) | (~spl2_3 | ~spl2_4)),
% 0.15/0.33 inference(trivial_inequality_removal,[],[f304])).
% 0.15/0.33 thf(f304,plain,(
% 0.15/0.33 ($true = $false) | ($true = (sK0 @ sK7 @ sK9)) | (~spl2_3 | ~spl2_4)),
% 0.15/0.33 inference(superposition,[],[f286,f232])).
% 0.15/0.33 thf(f232,plain,(
% 0.15/0.33 ((sK0 @ sK8 @ sK9) = $true) | ~spl2_3),
% 0.15/0.33 inference(avatar_component_clause,[],[f230])).
% 0.15/0.33 thf(f230,plain,(
% 0.15/0.33 spl2_3 <=> ((sK0 @ sK8 @ sK9) = $true)),
% 0.15/0.33 introduced(avatar_definition,[new_symbols(naming,[spl2_3])])).
% 0.15/0.33 thf(f286,plain,(
% 0.15/0.33 ( ! [X0 : $i] : (((sK0 @ sK8 @ X0) = $false) | ((sK0 @ sK7 @ X0) = $true)) ) | ~spl2_4),
% 0.15/0.33 inference(trivial_inequality_removal,[],[f281])).
% 0.15/0.33 thf(f281,plain,(
% 0.15/0.33 ( ! [X0 : $i] : (((sK0 @ sK8 @ X0) = $false) | ($true = $false) | ((sK0 @ sK7 @ X0) = $true)) ) | ~spl2_4),
% 0.15/0.33 inference(superposition,[],[f237,f174])).
% 0.15/0.33 thf(f237,plain,(
% 0.15/0.33 ((sK0 @ sK7 @ sK8) = $true) | ~spl2_4),
% 0.15/0.33 inference(avatar_component_clause,[],[f235])).
% 0.15/0.33 thf(f235,plain,(
% 0.15/0.33 spl2_4 <=> ((sK0 @ sK7 @ sK8) = $true)),
% 0.15/0.33 introduced(avatar_definition,[new_symbols(naming,[spl2_4])])).
% 0.15/0.33 thf(f241,plain,(
% 0.15/0.33 ( ! [X1 : $i] : (((sK0 @ sK7 @ X1) = $false) | ((sK1 @ X1) = $true)) ) | ~spl2_5),
% 0.15/0.33 inference(avatar_component_clause,[],[f240])).
% 0.15/0.33 thf(f240,plain,(
% 0.15/0.33 spl2_5 <=> ! [X1] : (((sK1 @ X1) = $true) | ((sK0 @ sK7 @ X1) = $false))),
% 0.15/0.33 introduced(avatar_definition,[new_symbols(naming,[spl2_5])])).
% 0.15/0.33 thf(f227,plain,(
% 0.15/0.33 ($false = (sK1 @ sK9)) | ~spl2_2),
% 0.15/0.33 inference(avatar_component_clause,[],[f225])).
% 0.15/0.33 thf(f225,plain,(
% 0.15/0.33 spl2_2 <=> ($false = (sK1 @ sK9))),
% 0.15/0.33 introduced(avatar_definition,[new_symbols(naming,[spl2_2])])).
% 0.15/0.33 thf(f264,plain,(
% 0.15/0.33 spl2_6 | spl2_10),
% 0.15/0.33 inference(avatar_split_clause,[],[f191,f262,f244])).
% 0.15/0.33 thf(f191,plain,(
% 0.15/0.33 ( ! [X2 : $i,X1 : $i] : (((sK0 @ sK4 @ X2) = $false) | ((sK1 @ X2) = $true) | ((sK1 @ X1) = $true) | ((sK0 @ sK3 @ X1) = $false)) )),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f190])).
% 0.15/0.33 thf(f190,plain,(
% 0.15/0.33 ( ! [X2 : $i,X1 : $i] : ((((sK0 @ sK3 @ X1) => (sK1 @ X1)) = $true) | ((sK1 @ X2) = $true) | ((sK0 @ sK4 @ X2) = $false)) )),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f189])).
% 0.15/0.33 thf(f189,plain,(
% 0.15/0.33 ( ! [X2 : $i,X1 : $i] : ((((sK0 @ sK4 @ X2) => (sK1 @ X2)) = $true) | (((sK0 @ sK3 @ X1) => (sK1 @ X1)) = $true)) )),
% 0.15/0.33 inference(beta_eta_normalization,[],[f188])).
% 0.15/0.33 thf(f188,plain,(
% 0.15/0.33 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((sK0 @ sK4 @ Y0) => (sK1 @ Y0))) @ X2)) | (((sK0 @ sK3 @ X1) => (sK1 @ X1)) = $true)) )),
% 0.15/0.33 inference(pi_clausification,[],[f187])).
% 0.15/0.33 thf(f187,plain,(
% 0.15/0.33 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK4 @ Y0) => (sK1 @ Y0))))) | (((sK0 @ sK3 @ X1) => (sK1 @ X1)) = $true)) )),
% 0.15/0.33 inference(beta_eta_normalization,[],[f186])).
% 0.15/0.33 thf(f186,plain,(
% 0.15/0.33 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((sK0 @ sK3 @ Y0) => (sK1 @ Y0))) @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK4 @ Y0) => (sK1 @ Y0)))))) )),
% 0.15/0.33 inference(pi_clausification,[],[f185])).
% 0.15/0.33 thf(f185,plain,(
% 0.15/0.33 ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK3 @ Y0) => (sK1 @ Y0)))) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK4 @ Y0) => (sK1 @ Y0)))))),
% 0.15/0.33 inference(not_proxy_clausification,[],[f184])).
% 0.15/0.33 thf(f184,plain,(
% 0.15/0.33 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK4 @ Y0) => (sK1 @ Y0)))))) | ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK3 @ Y0) => (sK1 @ Y0)))) = $true)),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f182])).
% 0.15/0.33 thf(f182,plain,(
% 0.15/0.33 (((~ (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK4 @ Y0) => (sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK4 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK1 @ Y1)))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK3 @ Y0) => (sK1 @ Y0)))) = $true)),
% 0.15/0.33 inference(not_proxy_clausification,[],[f181])).
% 0.15/0.33 thf(f181,plain,(
% 0.15/0.33 ((~ (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK3 @ Y0) => (sK1 @ Y0))))) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK4 @ Y0) => (sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK4 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK1 @ Y1)))))))) = $false)),
% 0.15/0.33 inference(beta_eta_normalization,[],[f180])).
% 0.15/0.33 thf(f180,plain,(
% 0.15/0.33 ((~ (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK3 @ Y0) => (sK1 @ Y0))))) = $false) | (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((sK0 @ Y1 @ Y2) => (sK1 @ Y2))))))))) @ sK4) = $false)),
% 0.15/0.33 inference(sigma_clausification,[],[f179])).
% 0.15/0.33 thf(f179,plain,(
% 0.15/0.33 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((sK0 @ Y1 @ Y2) => (sK1 @ Y2)))))))))) != $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK3 @ Y0) => (sK1 @ Y0))))) = $false)),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f177])).
% 0.15/0.33 thf(f177,plain,(
% 0.15/0.33 (((~ (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK3 @ Y0) => (sK1 @ Y0))))) | (sK1 @ sK3)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((sK0 @ Y1 @ Y2) => (sK1 @ Y2)))))))))) != $true)),
% 0.15/0.33 inference(beta_eta_normalization,[],[f176])).
% 0.15/0.33 thf(f176,plain,(
% 0.15/0.33 (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK1 @ Y1))))) | (sK1 @ Y0))) @ sK3) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((sK0 @ Y1 @ Y2) => (sK1 @ Y2)))))))))) != $true)),
% 0.15/0.33 inference(sigma_clausification,[],[f175])).
% 0.15/0.33 thf(f175,plain,(
% 0.15/0.33 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK1 @ Y1))))) | (sK1 @ Y0))))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((sK0 @ Y1 @ Y2) => (sK1 @ Y2)))))))))) != $true)),
% 0.15/0.33 inference(beta_eta_normalization,[],[f160])).
% 0.15/0.33 thf(f160,plain,(
% 0.15/0.33 ($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))))))))) @ sK0 @ sK1) @ sK1))) | (((^[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))))))))) @ sK0 @ sK1) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))) @ sK0 @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))) @ sK0 @ sK1)))) != $true)),
% 0.15/0.33 inference(definition_unfolding,[],[f143,f127,f156,f126,f127,f156,f126,f126,f126])).
% 0.15/0.33 thf(f126,plain,(
% 0.15/0.33 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))))),
% 0.15/0.33 inference(cnf_transformation,[],[f107])).
% 0.15/0.33 thf(f107,plain,(
% 0.15/0.33 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))))),
% 0.15/0.33 inference(fool_elimination,[],[f106])).
% 0.15/0.33 thf(f106,plain,(
% 0.15/0.33 (mbox = (^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : ((X0 @ X2 @ X3) => (X1 @ X3)))))),
% 0.15/0.33 inference(rectify,[],[f8])).
% 0.15/0.33 thf(f8,axiom,(
% 0.15/0.33 (mbox = (^[X4 : $i > $i > $o, X5 : $i > $o, X0 : $i] : (! [X2] : ((X4 @ X0 @ X2) => (X5 @ X2)))))),
% 0.15/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox)).
% 0.15/0.33 thf(f156,plain,(
% 0.15/0.33 (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)))))),
% 0.15/0.33 inference(definition_unfolding,[],[f146,f129,f136])).
% 0.15/0.33 thf(f136,plain,(
% 0.15/0.33 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.15/0.33 inference(cnf_transformation,[],[f43])).
% 0.15/0.33 thf(f43,plain,(
% 0.15/0.33 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.15/0.33 inference(fool_elimination,[],[f42])).
% 0.15/0.33 thf(f42,plain,(
% 0.15/0.33 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.15/0.33 inference(rectify,[],[f3])).
% 0.15/0.33 thf(f3,axiom,(
% 0.15/0.33 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.15/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.15/0.33 thf(f129,plain,(
% 0.15/0.33 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.15/0.33 inference(cnf_transformation,[],[f83])).
% 0.15/0.33 thf(f83,plain,(
% 0.15/0.33 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.15/0.33 inference(fool_elimination,[],[f82])).
% 0.15/0.33 thf(f82,plain,(
% 0.15/0.33 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 0.15/0.33 inference(rectify,[],[f4])).
% 0.15/0.33 thf(f4,axiom,(
% 0.15/0.33 ((^[X0 : $i > $o, X2 : $i > $o, X1 : $i] : ((X2 @ X1) | (X0 @ X1))) = mor)),
% 0.15/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.15/0.33 thf(f146,plain,(
% 0.15/0.33 (mimpl = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.15/0.33 inference(cnf_transformation,[],[f48])).
% 0.15/0.33 thf(f48,plain,(
% 0.15/0.33 (mimpl = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.15/0.33 inference(fool_elimination,[],[f47])).
% 0.15/0.33 thf(f47,plain,(
% 0.15/0.33 (mimpl = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.15/0.33 inference(rectify,[],[f6])).
% 0.15/0.33 thf(f6,axiom,(
% 0.15/0.33 (mimpl = (^[X1 : $i > $o, X3 : $i > $o] : (mor @ (mnot @ X1) @ X3)))),
% 0.15/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimpl)).
% 0.15/0.33 thf(f127,plain,(
% 0.15/0.33 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.15/0.33 inference(cnf_transformation,[],[f89])).
% 0.15/0.33 thf(f89,plain,(
% 0.15/0.33 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.15/0.33 inference(fool_elimination,[],[f88])).
% 0.15/0.33 thf(f88,plain,(
% 0.15/0.33 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.15/0.33 inference(rectify,[],[f12])).
% 0.15/0.33 thf(f12,axiom,(
% 0.15/0.33 ((^[X5 : $i > $o] : (! [X6] : (X5 @ X6))) = mvalid)),
% 0.15/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.15/0.33 thf(f143,plain,(
% 0.15/0.33 ((mvalid @ (mimpl @ (mbox @ sK0 @ sK1) @ sK1)) != $true) | ((mvalid @ (mimpl @ (mbox @ sK0 @ sK1) @ (mbox @ sK0 @ (mbox @ sK0 @ sK1)))) != $true)),
% 0.15/0.33 inference(cnf_transformation,[],[f116])).
% 0.15/0.33 thf(f260,plain,(
% 0.15/0.33 spl2_6 | spl2_9),
% 0.15/0.33 inference(avatar_split_clause,[],[f198,f257,f244])).
% 0.15/0.33 thf(f198,plain,(
% 0.15/0.33 ( ! [X1 : $i] : (((sK0 @ sK4 @ sK5) = $true) | ((sK1 @ X1) = $true) | ((sK0 @ sK3 @ X1) = $false)) )),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f197])).
% 0.15/0.33 thf(f197,plain,(
% 0.15/0.33 ( ! [X1 : $i] : ((((sK0 @ sK3 @ X1) => (sK1 @ X1)) = $true) | ((sK0 @ sK4 @ sK5) = $true)) )),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f195])).
% 0.15/0.33 thf(f195,plain,(
% 0.15/0.33 ( ! [X1 : $i] : ((((sK0 @ sK4 @ sK5) => (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK5 @ Y0) => (sK1 @ Y0))))) = $false) | (((sK0 @ sK3 @ X1) => (sK1 @ X1)) = $true)) )),
% 0.15/0.33 inference(beta_eta_normalization,[],[f194])).
% 0.15/0.33 thf(f194,plain,(
% 0.15/0.33 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK0 @ sK4 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK1 @ Y1)))))) @ sK5) = $false) | (((sK0 @ sK3 @ X1) => (sK1 @ X1)) = $true)) )),
% 0.15/0.33 inference(sigma_clausification,[],[f193])).
% 0.15/0.33 thf(f193,plain,(
% 0.15/0.33 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK4 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK1 @ Y1))))))) = $false) | (((sK0 @ sK3 @ X1) => (sK1 @ X1)) = $true)) )),
% 0.15/0.33 inference(beta_eta_normalization,[],[f192])).
% 0.15/0.33 thf(f192,plain,(
% 0.15/0.33 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK4 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK1 @ Y1))))))) = $false) | ($true = ((^[Y0 : $i]: ((sK0 @ sK3 @ Y0) => (sK1 @ Y0))) @ X1))) )),
% 0.15/0.33 inference(pi_clausification,[],[f183])).
% 0.15/0.33 thf(f183,plain,(
% 0.15/0.33 ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK3 @ Y0) => (sK1 @ Y0)))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK4 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK1 @ Y1))))))) = $false)),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f182])).
% 0.15/0.33 thf(f255,plain,(
% 0.15/0.33 spl2_6 | spl2_8),
% 0.15/0.33 inference(avatar_split_clause,[],[f203,f252,f244])).
% 0.15/0.33 thf(f203,plain,(
% 0.15/0.33 ( ! [X1 : $i] : (((sK0 @ sK3 @ X1) = $false) | ((sK1 @ X1) = $true) | ((sK0 @ sK5 @ sK6) = $true)) )),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f201])).
% 0.15/0.33 thf(f201,plain,(
% 0.15/0.33 ( ! [X1 : $i] : (($false = ((sK0 @ sK5 @ sK6) => (sK1 @ sK6))) | ((sK1 @ X1) = $true) | ((sK0 @ sK3 @ X1) = $false)) )),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f200])).
% 0.15/0.33 thf(f200,plain,(
% 0.15/0.33 ( ! [X1 : $i] : ((((sK0 @ sK3 @ X1) => (sK1 @ X1)) = $true) | ($false = ((sK0 @ sK5 @ sK6) => (sK1 @ sK6)))) )),
% 0.15/0.33 inference(beta_eta_normalization,[],[f199])).
% 0.15/0.33 thf(f199,plain,(
% 0.15/0.33 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK0 @ sK5 @ Y0) => (sK1 @ Y0))) @ sK6) = $false) | (((sK0 @ sK3 @ X1) => (sK1 @ X1)) = $true)) )),
% 0.15/0.33 inference(sigma_clausification,[],[f196])).
% 0.15/0.33 thf(f196,plain,(
% 0.15/0.33 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK5 @ Y0) => (sK1 @ Y0)))) = $false) | (((sK0 @ sK3 @ X1) => (sK1 @ X1)) = $true)) )),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f195])).
% 0.15/0.33 thf(f250,plain,(
% 0.15/0.33 spl2_6 | spl2_7),
% 0.15/0.33 inference(avatar_split_clause,[],[f202,f247,f244])).
% 0.15/0.33 thf(f202,plain,(
% 0.15/0.33 ( ! [X1 : $i] : (((sK1 @ X1) = $true) | ((sK0 @ sK3 @ X1) = $false) | ((sK1 @ sK6) = $false)) )),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f201])).
% 0.15/0.33 thf(f242,plain,(
% 0.15/0.33 spl2_5 | spl2_1),
% 0.15/0.33 inference(avatar_split_clause,[],[f211,f221,f240])).
% 0.15/0.33 thf(f211,plain,(
% 0.15/0.33 ( ! [X1 : $i] : (((sK1 @ X1) = $true) | ((sK0 @ sK7 @ X1) = $false) | ((sK1 @ sK3) = $false)) )),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f210])).
% 0.15/0.33 thf(f210,plain,(
% 0.15/0.33 ( ! [X1 : $i] : ((((sK0 @ sK7 @ X1) => (sK1 @ X1)) = $true) | ((sK1 @ sK3) = $false)) )),
% 0.15/0.33 inference(beta_eta_normalization,[],[f209])).
% 0.15/0.33 thf(f209,plain,(
% 0.15/0.33 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK0 @ sK7 @ Y0) => (sK1 @ Y0))) @ X1) = $true) | ((sK1 @ sK3) = $false)) )),
% 0.15/0.33 inference(pi_clausification,[],[f208])).
% 0.15/0.33 thf(f208,plain,(
% 0.15/0.33 ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK7 @ Y0) => (sK1 @ Y0)))) = $true) | ((sK1 @ sK3) = $false)),
% 0.15/0.33 inference(not_proxy_clausification,[],[f207])).
% 0.15/0.33 thf(f207,plain,(
% 0.15/0.33 ((sK1 @ sK3) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK7 @ Y0) => (sK1 @ Y0))))) = $false)),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f205])).
% 0.15/0.33 thf(f205,plain,(
% 0.15/0.33 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK7 @ Y0) => (sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK7 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK1 @ Y1))))))))) | ((sK1 @ sK3) = $false)),
% 0.15/0.33 inference(beta_eta_normalization,[],[f204])).
% 0.15/0.33 thf(f204,plain,(
% 0.15/0.33 (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((sK0 @ Y1 @ Y2) => (sK1 @ Y2))))))))) @ sK7) = $false) | ((sK1 @ sK3) = $false)),
% 0.15/0.33 inference(sigma_clausification,[],[f178])).
% 0.15/0.33 thf(f178,plain,(
% 0.15/0.33 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((sK0 @ Y1 @ Y2) => (sK1 @ Y2)))))))))) != $true) | ((sK1 @ sK3) = $false)),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f177])).
% 0.15/0.33 thf(f238,plain,(
% 0.15/0.33 spl2_4 | spl2_1),
% 0.15/0.33 inference(avatar_split_clause,[],[f215,f221,f235])).
% 0.15/0.33 thf(f215,plain,(
% 0.15/0.33 ((sK1 @ sK3) = $false) | ((sK0 @ sK7 @ sK8) = $true)),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f213])).
% 0.15/0.33 thf(f213,plain,(
% 0.15/0.33 ((sK1 @ sK3) = $false) | ($false = ((sK0 @ sK7 @ sK8) => (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK8 @ Y0) => (sK1 @ Y0))))))),
% 0.15/0.33 inference(beta_eta_normalization,[],[f212])).
% 0.15/0.33 thf(f212,plain,(
% 0.15/0.33 (((^[Y0 : $i]: ((sK0 @ sK7 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK1 @ Y1)))))) @ sK8) = $false) | ((sK1 @ sK3) = $false)),
% 0.15/0.33 inference(sigma_clausification,[],[f206])).
% 0.15/0.33 thf(f206,plain,(
% 0.15/0.33 ((sK1 @ sK3) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK7 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK1 @ Y1))))))) = $false)),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f205])).
% 0.15/0.33 thf(f233,plain,(
% 0.15/0.33 spl2_1 | spl2_3),
% 0.15/0.33 inference(avatar_split_clause,[],[f219,f230,f221])).
% 0.15/0.33 thf(f219,plain,(
% 0.15/0.33 ((sK0 @ sK8 @ sK9) = $true) | ((sK1 @ sK3) = $false)),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f217])).
% 0.15/0.33 thf(f217,plain,(
% 0.15/0.33 ((sK1 @ sK3) = $false) | (((sK0 @ sK8 @ sK9) => (sK1 @ sK9)) = $false)),
% 0.15/0.33 inference(beta_eta_normalization,[],[f216])).
% 0.15/0.33 thf(f216,plain,(
% 0.15/0.33 ((sK1 @ sK3) = $false) | (((^[Y0 : $i]: ((sK0 @ sK8 @ Y0) => (sK1 @ Y0))) @ sK9) = $false)),
% 0.15/0.33 inference(sigma_clausification,[],[f214])).
% 0.15/0.33 thf(f214,plain,(
% 0.15/0.33 ($false = (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK8 @ Y0) => (sK1 @ Y0))))) | ((sK1 @ sK3) = $false)),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f213])).
% 0.15/0.33 thf(f228,plain,(
% 0.15/0.33 spl2_1 | spl2_2),
% 0.15/0.33 inference(avatar_split_clause,[],[f218,f225,f221])).
% 0.15/0.33 thf(f218,plain,(
% 0.15/0.33 ((sK1 @ sK3) = $false) | ($false = (sK1 @ sK9))),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f217])).
% 0.15/0.33 % SZS output end Proof for theBenchmark
% 0.15/0.33 % (1397)------------------------------
% 0.15/0.33 % (1397)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (1397)Termination reason: Refutation
% 0.15/0.33
% 0.15/0.33 % (1397)Memory used [KB]: 5756
% 0.15/0.33 % (1397)Time elapsed: 0.016 s
% 0.15/0.33 % (1397)Instructions burned: 20 (million)
% 0.15/0.33 % (1397)------------------------------
% 0.15/0.33 % (1397)------------------------------
% 0.15/0.33 % (1396)Success in time 0.018 s
% 0.15/0.33 % Vampire---4.8 exiting
%------------------------------------------------------------------------------