TSTP Solution File: LCL715^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL715^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 00:22:21 EDT 2024
% Result : Theorem 0.21s 0.41s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL715^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 0.06/0.13 % 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
% 0.15/0.34 % Computer : n020.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Mon May 20 02:55:38 EDT 2024
% 0.15/0.34 % CPUTime :
% 0.15/0.34 This is a TH0_THM_EQU_NAR problem
% 0.15/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.37 % (10073)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.15/0.37 % (10078)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.37 % (10076)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.15/0.37 % (10078)Instruction limit reached!
% 0.15/0.37 % (10078)------------------------------
% 0.15/0.37 % (10078)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (10078)Termination reason: Unknown
% 0.15/0.37 % (10078)Termination phase: shuffling
% 0.15/0.37
% 0.15/0.37 % (10078)Memory used [KB]: 1023
% 0.15/0.37 % (10078)Time elapsed: 0.004 s
% 0.15/0.37 % (10078)Instructions burned: 4 (million)
% 0.15/0.37 % (10078)------------------------------
% 0.15/0.37 % (10078)------------------------------
% 0.15/0.37 % (10077)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.37 % (10076)Refutation not found, incomplete strategy
% 0.15/0.37 % (10076)------------------------------
% 0.15/0.37 % (10076)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (10076)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.37
% 0.15/0.37
% 0.15/0.37 % (10076)Memory used [KB]: 5628
% 0.15/0.37 % (10076)Time elapsed: 0.008 s
% 0.15/0.37 % (10076)Instructions burned: 9 (million)
% 0.15/0.37 % (10076)------------------------------
% 0.15/0.37 % (10076)------------------------------
% 0.15/0.37 % (10071)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.38 % (10072)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)
% 0.15/0.38 % (10075)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)
% 0.15/0.38 % (10075)Instruction limit reached!
% 0.15/0.38 % (10075)------------------------------
% 0.15/0.38 % (10075)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (10075)Termination reason: Unknown
% 0.15/0.38 % (10075)Termination phase: shuffling
% 0.15/0.38
% 0.15/0.38 % (10075)Memory used [KB]: 1023
% 0.15/0.38 % (10075)Time elapsed: 0.003 s
% 0.15/0.38 % (10075)Instructions burned: 2 (million)
% 0.15/0.38 % (10075)------------------------------
% 0.15/0.38 % (10075)------------------------------
% 0.15/0.38 % (10072)Instruction limit reached!
% 0.15/0.38 % (10072)------------------------------
% 0.15/0.38 % (10072)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (10072)Termination reason: Unknown
% 0.15/0.38 % (10072)Termination phase: shuffling
% 0.15/0.38
% 0.15/0.38 % (10072)Memory used [KB]: 1023
% 0.15/0.38 % (10072)Time elapsed: 0.004 s
% 0.15/0.38 % (10072)Instructions burned: 4 (million)
% 0.15/0.38 % (10072)------------------------------
% 0.15/0.38 % (10072)------------------------------
% 0.15/0.38 % (10074)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.38 % (10073)Instruction limit reached!
% 0.15/0.38 % (10073)------------------------------
% 0.15/0.38 % (10073)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (10079)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)
% 0.15/0.38 % (10074)Instruction limit reached!
% 0.15/0.38 % (10074)------------------------------
% 0.15/0.38 % (10074)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (10074)Termination reason: Unknown
% 0.15/0.38 % (10074)Termination phase: shuffling
% 0.15/0.38
% 0.15/0.38 % (10074)Memory used [KB]: 1023
% 0.15/0.38 % (10074)Time elapsed: 0.003 s
% 0.15/0.38 % (10074)Instructions burned: 2 (million)
% 0.15/0.38 % (10074)------------------------------
% 0.15/0.38 % (10074)------------------------------
% 0.15/0.38 % (10073)Termination reason: Unknown
% 0.15/0.38 % (10073)Termination phase: Saturation
% 0.15/0.38
% 0.15/0.38 % (10073)Memory used [KB]: 5756
% 0.15/0.38 % (10073)Time elapsed: 0.018 s
% 0.15/0.38 % (10073)Instructions burned: 27 (million)
% 0.15/0.38 % (10073)------------------------------
% 0.15/0.38 % (10073)------------------------------
% 0.15/0.38 % (10077)Instruction limit reached!
% 0.15/0.38 % (10077)------------------------------
% 0.15/0.38 % (10077)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (10077)Termination reason: Unknown
% 0.15/0.38 % (10077)Termination phase: Saturation
% 0.15/0.38
% 0.15/0.38 % (10077)Memory used [KB]: 5756
% 0.15/0.38 % (10077)Time elapsed: 0.013 s
% 0.15/0.38 % (10077)Instructions burned: 18 (million)
% 0.15/0.38 % (10077)------------------------------
% 0.15/0.38 % (10077)------------------------------
% 0.15/0.39 % (10080)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)
% 0.21/0.39 % (10081)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)
% 0.21/0.39 % (10082)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)
% 0.21/0.39 % (10083)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.40 % (10081)Instruction limit reached!
% 0.21/0.40 % (10081)------------------------------
% 0.21/0.40 % (10081)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (10081)Termination reason: Unknown
% 0.21/0.40 % (10081)Termination phase: Property scanning
% 0.21/0.40
% 0.21/0.40 % (10081)Memory used [KB]: 1023
% 0.21/0.40 % (10081)Time elapsed: 0.004 s
% 0.21/0.40 % (10081)Instructions burned: 4 (million)
% 0.21/0.40 % (10081)------------------------------
% 0.21/0.40 % (10081)------------------------------
% 0.21/0.40 % (10084)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.21/0.40 % (10080)Instruction limit reached!
% 0.21/0.40 % (10080)------------------------------
% 0.21/0.40 % (10080)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (10080)Termination reason: Unknown
% 0.21/0.40 % (10080)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (10080)Memory used [KB]: 5628
% 0.21/0.40 % (10080)Time elapsed: 0.010 s
% 0.21/0.40 % (10080)Instructions burned: 15 (million)
% 0.21/0.40 % (10080)------------------------------
% 0.21/0.40 % (10080)------------------------------
% 0.21/0.40 % (10079)Instruction limit reached!
% 0.21/0.40 % (10079)------------------------------
% 0.21/0.40 % (10079)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (10079)Termination reason: Unknown
% 0.21/0.40 % (10079)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (10079)Memory used [KB]: 5756
% 0.21/0.40 % (10079)Time elapsed: 0.018 s
% 0.21/0.40 % (10079)Instructions burned: 38 (million)
% 0.21/0.40 % (10079)------------------------------
% 0.21/0.40 % (10079)------------------------------
% 0.21/0.40 % (10083)Instruction limit reached!
% 0.21/0.40 % (10083)------------------------------
% 0.21/0.40 % (10083)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (10083)Termination reason: Unknown
% 0.21/0.40 % (10083)Termination phase: Property scanning
% 0.21/0.40
% 0.21/0.40 % (10083)Memory used [KB]: 1023
% 0.21/0.40 % (10083)Time elapsed: 0.005 s
% 0.21/0.40 % (10083)Instructions burned: 7 (million)
% 0.21/0.40 % (10083)------------------------------
% 0.21/0.40 % (10083)------------------------------
% 0.21/0.40 % (10085)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.40 % (10085)Instruction limit reached!
% 0.21/0.40 % (10085)------------------------------
% 0.21/0.40 % (10085)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (10085)Termination reason: Unknown
% 0.21/0.40 % (10085)Termination phase: Property scanning
% 0.21/0.40
% 0.21/0.40 % (10085)Memory used [KB]: 1023
% 0.21/0.40 % (10085)Time elapsed: 0.004 s
% 0.21/0.40 % (10085)Instructions burned: 4 (million)
% 0.21/0.40 % (10085)------------------------------
% 0.21/0.40 % (10085)------------------------------
% 0.21/0.41 % (10084)Instruction limit reached!
% 0.21/0.41 % (10084)------------------------------
% 0.21/0.41 % (10084)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (10084)Termination reason: Unknown
% 0.21/0.41 % (10084)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (10084)Memory used [KB]: 5884
% 0.21/0.41 % (10084)Time elapsed: 0.012 s
% 0.21/0.41 % (10084)Instructions burned: 16 (million)
% 0.21/0.41 % (10084)------------------------------
% 0.21/0.41 % (10084)------------------------------
% 0.21/0.41 % (10071)First to succeed.
% 0.21/0.41 % (10086)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.41 % (10089)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.41 % (10087)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.41 % (10086)Instruction limit reached!
% 0.21/0.41 % (10086)------------------------------
% 0.21/0.41 % (10086)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (10086)Termination reason: Unknown
% 0.21/0.41 % (10086)Termination phase: Property scanning
% 0.21/0.41
% 0.21/0.41 % (10086)Memory used [KB]: 1023
% 0.21/0.41 % (10086)Time elapsed: 0.004 s
% 0.21/0.41 % (10086)Instructions burned: 4 (million)
% 0.21/0.41 % (10086)------------------------------
% 0.21/0.41 % (10086)------------------------------
% 0.21/0.41 % (10071)Refutation found. Thanks to Tanya!
% 0.21/0.41 % SZS status Theorem for theBenchmark
% 0.21/0.41 % SZS output start Proof for theBenchmark
% 0.21/0.41 thf(type_def_5, type, mu: $tType).
% 0.21/0.41 thf(func_def_0, type, mu: $tType).
% 0.21/0.41 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.21/0.41 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_15, type, mtrue: $i > $o).
% 0.21/0.41 thf(func_def_16, type, mfalse: $i > $o).
% 0.21/0.41 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.21/0.41 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.21/0.41 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.21/0.41 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.21/0.41 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.21/0.41 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.21/0.41 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.21/0.41 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.21/0.41 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.21/0.41 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.21/0.41 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.21/0.41 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.21/0.41 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.21/0.41 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.21/0.41 thf(func_def_48, type, sK0: $i > $i > $o).
% 0.21/0.41 thf(func_def_51, type, sK3: $i > $i).
% 0.21/0.41 thf(func_def_52, type, sK4: $i > ($i > $o) > $i).
% 0.21/0.41 thf(func_def_53, type, sK5: $i > ($i > $o) > $i).
% 0.21/0.41 thf(func_def_54, type, ph6: !>[X0: $tType]:(X0)).
% 0.21/0.41 thf(f333,plain,(
% 0.21/0.41 $false),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f332])).
% 0.21/0.41 thf(f332,plain,(
% 0.21/0.41 ($false = $true)),
% 0.21/0.41 inference(beta_eta_normalization,[],[f322])).
% 0.21/0.41 thf(f322,plain,(
% 0.21/0.41 ($false = ((^[Y0 : $i]: ($true)) @ (sK4 @ sK2 @ (^[Y0 : $i]: ($true)))))),
% 0.21/0.41 inference(primitive_instantiation,[],[f311])).
% 0.21/0.41 thf(f311,plain,(
% 0.21/0.41 ( ! [X0 : $i > $o] : (($false = (X0 @ (sK4 @ sK2 @ X0)))) )),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f284])).
% 0.21/0.41 thf(f284,plain,(
% 0.21/0.41 ( ! [X0 : $i > $o] : (($false = $true) | ($false = (X0 @ (sK4 @ sK2 @ X0)))) )),
% 0.21/0.41 inference(superposition,[],[f186,f232])).
% 0.21/0.41 thf(f232,plain,(
% 0.21/0.41 ( ! [X0 : $i] : (($false = (sK0 @ sK2 @ X0))) )),
% 0.21/0.41 inference(subsumption_resolution,[],[f231,f152])).
% 0.21/0.41 thf(f152,plain,(
% 0.21/0.41 ( ! [X1 : $i] : (($false = (sK0 @ sK2 @ X1)) | ((sK3 @ X1) != X1)) )),
% 0.21/0.41 inference(equality_proxy_clausification,[],[f150])).
% 0.21/0.41 thf(f150,plain,(
% 0.21/0.41 ( ! [X1 : $i] : (($false = (sK0 @ sK2 @ X1)) | ($false = (X1 = (sK3 @ X1)))) )),
% 0.21/0.41 inference(binary_proxy_clausification,[],[f149])).
% 0.21/0.41 thf(f149,plain,(
% 0.21/0.41 ( ! [X1 : $i] : (($false = (sK0 @ sK2 @ X1)) | ($false = ((sK0 @ sK2 @ (sK3 @ X1)) => (X1 = (sK3 @ X1))))) )),
% 0.21/0.41 inference(beta_eta_normalization,[],[f148])).
% 0.21/0.41 thf(f148,plain,(
% 0.21/0.41 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((sK0 @ sK2 @ Y0) => (X1 = Y0))) @ (sK3 @ X1))) | ($false = (sK0 @ sK2 @ X1))) )),
% 0.21/0.41 inference(sigma_clausification,[],[f147])).
% 0.21/0.41 thf(f147,plain,(
% 0.21/0.41 ( ! [X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK2 @ Y0) => (X1 = Y0))))) | ($false = (sK0 @ sK2 @ X1))) )),
% 0.21/0.41 inference(binary_proxy_clausification,[],[f146])).
% 0.21/0.41 thf(f146,plain,(
% 0.21/0.41 ( ! [X1 : $i] : (($false = ((sK0 @ sK2 @ X1) & (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK2 @ Y0) => (X1 = Y0))))))) )),
% 0.21/0.41 inference(beta_eta_normalization,[],[f145])).
% 0.21/0.41 thf(f145,plain,(
% 0.21/0.41 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((sK0 @ sK2 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ sK2 @ Y1) => (Y0 = Y1)))))) @ X1))) )),
% 0.21/0.41 inference(pi_clausification,[],[f144])).
% 0.21/0.41 thf(f144,plain,(
% 0.21/0.41 ($false = (?? @ $i @ (^[Y0 : $i]: ((sK0 @ sK2 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ sK2 @ Y1) => (Y0 = Y1))))))))),
% 0.21/0.41 inference(beta_eta_normalization,[],[f143])).
% 0.21/0.41 thf(f143,plain,(
% 0.21/0.41 ($false = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((sK0 @ Y0 @ Y2) => (Y1 = Y2)))))))) @ sK2))),
% 0.21/0.41 inference(sigma_clausification,[],[f142])).
% 0.21/0.41 thf(f142,plain,(
% 0.21/0.41 ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((sK0 @ Y0 @ Y2) => (Y1 = Y2))))))))) != $true)),
% 0.21/0.41 inference(beta_eta_normalization,[],[f140])).
% 0.21/0.41 thf(f140,plain,(
% 0.21/0.41 ($true != ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y1 @ Y3) => (Y2 = Y3)))))))))) @ sK0))),
% 0.21/0.41 inference(definition_unfolding,[],[f102,f126])).
% 0.21/0.41 thf(f126,plain,(
% 0.21/0.41 (mfunctional = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y1 @ Y3) => (Y2 = Y3)))))))))))),
% 0.21/0.41 inference(cnf_transformation,[],[f38])).
% 0.21/0.41 thf(f38,plain,(
% 0.21/0.41 (mfunctional = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y1 @ Y3) => (Y2 = Y3)))))))))))),
% 0.21/0.41 inference(fool_elimination,[],[f37])).
% 0.21/0.41 thf(f37,plain,(
% 0.21/0.41 (mfunctional = (^[X0 : $i > $i > $o] : (! [X1] : ? [X2] : (! [X3] : ((X0 @ X1 @ X3) => (X2 = X3)) & (X0 @ X1 @ X2)))))),
% 0.21/0.41 inference(rectify,[],[f24])).
% 0.21/0.41 thf(f24,axiom,(
% 0.21/0.41 (mfunctional = (^[X6 : $i > $i > $o] : (! [X8] : ? [X9] : (! [X10] : ((X6 @ X8 @ X10) => (X9 = X10)) & (X6 @ X8 @ X9)))))),
% 0.21/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfunctional)).
% 0.21/0.41 thf(f102,plain,(
% 0.21/0.41 ($true != (mfunctional @ sK0))),
% 0.21/0.41 inference(cnf_transformation,[],[f97])).
% 0.21/0.41 thf(f97,plain,(
% 0.21/0.41 ($true != (mfunctional @ sK0)) & ($true = (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mequiv @ (mdia @ sK0 @ Y0) @ (mbox @ sK0 @ Y0))))))),
% 0.21/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f95,f96])).
% 0.21/0.41 thf(f96,plain,(
% 0.21/0.41 ? [X0 : $i > $i > $o] : (((mfunctional @ X0) != $true) & ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mequiv @ (mdia @ X0 @ Y0) @ (mbox @ X0 @ Y0))))) = $true)) => (($true != (mfunctional @ sK0)) & ($true = (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mequiv @ (mdia @ sK0 @ Y0) @ (mbox @ sK0 @ Y0)))))))),
% 0.21/0.41 introduced(choice_axiom,[])).
% 0.21/0.41 thf(f95,plain,(
% 0.21/0.41 ? [X0 : $i > $i > $o] : (((mfunctional @ X0) != $true) & ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mequiv @ (mdia @ X0 @ Y0) @ (mbox @ X0 @ Y0))))) = $true))),
% 0.21/0.41 inference(ennf_transformation,[],[f78])).
% 0.21/0.41 thf(f78,plain,(
% 0.21/0.41 ~! [X0 : $i > $i > $o] : (((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mequiv @ (mdia @ X0 @ Y0) @ (mbox @ X0 @ Y0))))) = $true) => ((mfunctional @ X0) = $true))),
% 0.21/0.41 inference(fool_elimination,[],[f77])).
% 0.21/0.41 thf(f77,plain,(
% 0.21/0.41 ~! [X0 : $i > $i > $o] : ((mvalid @ (mforall_prop @ (^[X1 : $i > $o] : (mequiv @ (mdia @ X0 @ X1) @ (mbox @ X0 @ X1))))) => (mfunctional @ X0))),
% 0.21/0.41 inference(rectify,[],[f33])).
% 0.21/0.41 thf(f33,negated_conjecture,(
% 0.21/0.41 ~! [X6 : $i > $i > $o] : ((mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mequiv @ (mdia @ X6 @ X11) @ (mbox @ X6 @ X11))))) => (mfunctional @ X6))),
% 0.21/0.41 inference(negated_conjecture,[],[f32])).
% 0.21/0.41 thf(f32,conjecture,(
% 0.21/0.41 ! [X6 : $i > $i > $o] : ((mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mequiv @ (mdia @ X6 @ X11) @ (mbox @ X6 @ X11))))) => (mfunctional @ X6))),
% 0.21/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 0.21/0.41 thf(f231,plain,(
% 0.21/0.41 ( ! [X0 : $i] : (((sK3 @ X0) = X0) | ($false = (sK0 @ sK2 @ X0))) )),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f228])).
% 0.21/0.41 thf(f228,plain,(
% 0.21/0.41 ( ! [X0 : $i] : (($false != $false) | ((sK3 @ X0) = X0) | ($false = (sK0 @ sK2 @ X0))) )),
% 0.21/0.41 inference(equality_factoring,[],[f225])).
% 0.21/0.41 thf(f225,plain,(
% 0.21/0.41 ( ! [X0 : $i,X1 : $i] : (($false = (sK0 @ sK2 @ X1)) | ((sK3 @ X0) = X1) | ($false = (sK0 @ sK2 @ X0))) )),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f221])).
% 0.21/0.41 thf(f221,plain,(
% 0.21/0.41 ( ! [X0 : $i,X1 : $i] : (($false = (sK0 @ sK2 @ X1)) | ($false = $true) | ($false = (sK0 @ sK2 @ X0)) | ((sK3 @ X0) = X1)) )),
% 0.21/0.41 inference(superposition,[],[f197,f151])).
% 0.21/0.41 thf(f151,plain,(
% 0.21/0.41 ( ! [X1 : $i] : (((sK0 @ sK2 @ (sK3 @ X1)) = $true) | ($false = (sK0 @ sK2 @ X1))) )),
% 0.21/0.41 inference(binary_proxy_clausification,[],[f149])).
% 0.21/0.41 thf(f197,plain,(
% 0.21/0.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (sK0 @ X2 @ X1)) | ($false = (sK0 @ X2 @ X0)) | (X0 = X1)) )),
% 0.21/0.41 inference(leibniz_equality_elimination,[],[f172])).
% 0.21/0.41 thf(f172,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X3 : $i,X1 : $i,X4 : $i] : (($false = (sK0 @ X1 @ X4)) | ($false = (sK0 @ X1 @ X3)) | ($false = (X2 @ X4)) | ((X2 @ X3) = $true)) )),
% 0.21/0.41 inference(not_proxy_clausification,[],[f171])).
% 0.21/0.41 thf(f171,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X3 : $i,X1 : $i,X4 : $i] : (((X2 @ X3) = $true) | ((~ (X2 @ X4)) = $true) | ($false = (sK0 @ X1 @ X4)) | ($false = (sK0 @ X1 @ X3))) )),
% 0.21/0.41 inference(not_proxy_clausification,[],[f170])).
% 0.21/0.41 thf(f170,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X3 : $i,X1 : $i,X4 : $i] : (((X2 @ X3) = $true) | ($false = (sK0 @ X1 @ X3)) | ((~ (sK0 @ X1 @ X4)) = $true) | ((~ (X2 @ X4)) = $true)) )),
% 0.21/0.41 inference(not_proxy_clausification,[],[f169])).
% 0.21/0.41 thf(f169,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X3 : $i,X1 : $i,X4 : $i] : (((X2 @ X3) = $true) | ((~ (sK0 @ X1 @ X3)) = $true) | ((~ (X2 @ X4)) = $true) | ((~ (sK0 @ X1 @ X4)) = $true)) )),
% 0.21/0.41 inference(binary_proxy_clausification,[],[f168])).
% 0.21/0.41 thf(f168,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X3 : $i,X1 : $i,X4 : $i] : (((X2 @ X3) = $true) | (((~ (X2 @ X4)) | (~ (sK0 @ X1 @ X4))) = $true) | ((~ (sK0 @ X1 @ X3)) = $true)) )),
% 0.21/0.41 inference(beta_eta_normalization,[],[f167])).
% 0.21/0.41 thf(f167,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X3 : $i,X1 : $i,X4 : $i] : (((X2 @ X3) = $true) | (((^[Y0 : $i]: ((~ (X2 @ Y0)) | (~ (sK0 @ X1 @ Y0)))) @ X4) = $true) | ((~ (sK0 @ X1 @ X3)) = $true)) )),
% 0.21/0.41 inference(pi_clausification,[],[f166])).
% 0.21/0.41 thf(f166,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (X2 @ Y0)) | (~ (sK0 @ X1 @ Y0)))))) | ((X2 @ X3) = $true) | ((~ (sK0 @ X1 @ X3)) = $true)) )),
% 0.21/0.41 inference(binary_proxy_clausification,[],[f165])).
% 0.21/0.41 thf(f165,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = ((X2 @ X3) | (~ (sK0 @ X1 @ X3)))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (X2 @ Y0)) | (~ (sK0 @ X1 @ Y0))))))) )),
% 0.21/0.41 inference(beta_eta_normalization,[],[f164])).
% 0.21/0.41 thf(f164,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (X2 @ Y0)) | (~ (sK0 @ X1 @ Y0)))))) | (((^[Y0 : $i]: ((X2 @ Y0) | (~ (sK0 @ X1 @ Y0)))) @ X3) = $true)) )),
% 0.21/0.41 inference(pi_clausification,[],[f163])).
% 0.21/0.41 thf(f163,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) | (~ (sK0 @ X1 @ Y0))))) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (X2 @ Y0)) | (~ (sK0 @ X1 @ Y0))))))) )),
% 0.21/0.41 inference(binary_proxy_clausification,[],[f162])).
% 0.21/0.41 thf(f162,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((~ (X2 @ Y0)) | (~ (sK0 @ X1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) | (~ (sK0 @ X1 @ Y0)))))) = $true)) )),
% 0.21/0.41 inference(not_proxy_clausification,[],[f161])).
% 0.21/0.41 thf(f161,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X1 : $i] : (($false = (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (X2 @ Y0)) | (~ (sK0 @ X1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) | (~ (sK0 @ X1 @ Y0))))))))) )),
% 0.21/0.41 inference(binary_proxy_clausification,[],[f159])).
% 0.21/0.41 thf(f159,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X1 : $i] : (($false = ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (X2 @ Y0)) | (~ (sK0 @ X1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) | (~ (sK0 @ X1 @ Y0))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) | (~ (sK0 @ X1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (X2 @ Y0)) | (~ (sK0 @ X1 @ Y0))))))))))) )),
% 0.21/0.41 inference(not_proxy_clausification,[],[f158])).
% 0.21/0.41 thf(f158,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X1 : $i] : (((~ ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (X2 @ Y0)) | (~ (sK0 @ X1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) | (~ (sK0 @ X1 @ Y0))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) | (~ (sK0 @ X1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (X2 @ Y0)) | (~ (sK0 @ X1 @ Y0)))))))))) = $true)) )),
% 0.21/0.41 inference(beta_eta_normalization,[],[f157])).
% 0.21/0.41 thf(f157,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (Y0 @ Y1)) | (~ (sK0 @ X1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) | (~ (sK0 @ X1 @ Y1))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) | (~ (sK0 @ X1 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (Y0 @ Y1)) | (~ (sK0 @ X1 @ Y1))))))))))) @ X2) = $true)) )),
% 0.21/0.41 inference(pi_clausification,[],[f156])).
% 0.21/0.41 thf(f156,plain,(
% 0.21/0.41 ( ! [X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (Y0 @ Y1)) | (~ (sK0 @ X1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) | (~ (sK0 @ X1 @ Y1))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) | (~ (sK0 @ X1 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (Y0 @ Y1)) | (~ (sK0 @ X1 @ Y1)))))))))))) = $true)) )),
% 0.21/0.41 inference(beta_eta_normalization,[],[f155])).
% 0.21/0.41 thf(f155,plain,(
% 0.21/0.41 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (~ ((~ ((!! @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) | (~ (sK0 @ Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (sK0 @ Y0 @ Y2))))))) | (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (sK0 @ Y0 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) | (~ (sK0 @ Y0 @ Y2))))))))))))) @ X1))) )),
% 0.21/0.41 inference(pi_clausification,[],[f154])).
% 0.21/0.41 thf(f154,plain,(
% 0.21/0.41 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (~ ((~ ((!! @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) | (~ (sK0 @ Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (sK0 @ Y0 @ Y2))))))) | (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (sK0 @ Y0 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) | (~ (sK0 @ Y0 @ Y2)))))))))))))) = $true)),
% 0.21/0.41 inference(boolean_simplification,[],[f153])).
% 0.21/0.41 thf(f153,plain,(
% 0.21/0.41 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (~ ((~ ((~ (~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) | (~ (sK0 @ Y0 @ Y2))))))) | (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (sK0 @ Y0 @ Y2))))))) | (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (sK0 @ Y0 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) | (~ (sK0 @ Y0 @ Y2)))))))))))))) = $true)),
% 0.21/0.41 inference(beta_eta_normalization,[],[f141])).
% 0.21/0.41 thf(f141,plain,(
% 0.21/0.41 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: ((Y5 @ Y7) | (Y6 @ Y7))))))) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ Y3) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ Y4)))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: ((Y5 @ Y7) | (Y6 @ Y7))))))) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ Y3) @ Y4)))) @ Y1 @ Y2) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: ((Y5 @ Y7) | (Y6 @ Y7))))))) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ Y3) @ Y4)))) @ Y2 @ Y1))))) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6) | (~ (Y3 @ Y5 @ Y6)))))))))) @ Y1 @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y2)))))) @ sK0 @ Y0) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (Y1 @ Y3 @ Y4)))))))))) @ sK0 @ Y0))))))),
% 0.21/0.41 inference(definition_unfolding,[],[f101,f123,f121,f134,f139,f109])).
% 0.21/0.41 thf(f109,plain,(
% 0.21/0.41 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))))),
% 0.21/0.41 inference(cnf_transformation,[],[f53])).
% 0.21/0.41 thf(f53,plain,(
% 0.21/0.41 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))))),
% 0.21/0.41 inference(fool_elimination,[],[f52])).
% 0.21/0.41 thf(f52,plain,(
% 0.21/0.41 ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : (~(X0 @ X2 @ X3) | (X1 @ X3)))) = mbox)),
% 0.21/0.41 inference(rectify,[],[f16])).
% 0.21/0.41 thf(f16,axiom,(
% 0.21/0.41 ((^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7] : (~(X6 @ X2 @ X7) | (X3 @ X7)))) = mbox)),
% 0.21/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox)).
% 0.21/0.41 thf(f139,plain,(
% 0.21/0.41 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5) | (~ (Y2 @ Y4 @ Y5)))))))))) @ Y0 @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.21/0.41 inference(definition_unfolding,[],[f115,f124,f109,f124])).
% 0.21/0.41 thf(f124,plain,(
% 0.21/0.41 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.41 inference(cnf_transformation,[],[f86])).
% 0.21/0.41 thf(f86,plain,(
% 0.21/0.41 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.41 inference(fool_elimination,[],[f85])).
% 0.21/0.41 thf(f85,plain,(
% 0.21/0.41 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.21/0.41 inference(rectify,[],[f3])).
% 0.21/0.41 thf(f3,axiom,(
% 0.21/0.41 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.21/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.21/0.41 thf(f115,plain,(
% 0.21/0.41 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mbox @ Y0 @ (mnot @ Y1)))))))),
% 0.21/0.41 inference(cnf_transformation,[],[f84])).
% 0.21/0.41 thf(f84,plain,(
% 0.21/0.41 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mbox @ Y0 @ (mnot @ Y1)))))))),
% 0.21/0.41 inference(fool_elimination,[],[f83])).
% 0.21/0.41 thf(f83,plain,(
% 0.21/0.41 (mdia = (^[X0 : $i > $i > $o, X1 : $i > $o] : (mnot @ (mbox @ X0 @ (mnot @ X1)))))),
% 0.21/0.41 inference(rectify,[],[f17])).
% 0.21/0.41 thf(f17,axiom,(
% 0.21/0.41 (mdia = (^[X6 : $i > $i > $o, X3 : $i > $o] : (mnot @ (mbox @ X6 @ (mnot @ X3)))))),
% 0.21/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia)).
% 0.21/0.41 thf(f134,plain,(
% 0.21/0.41 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))))),
% 0.21/0.41 inference(definition_unfolding,[],[f120,f131,f132,f132])).
% 0.21/0.41 thf(f132,plain,(
% 0.21/0.41 (mimplies = (^[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)))))),
% 0.21/0.41 inference(definition_unfolding,[],[f106,f125,f124])).
% 0.21/0.41 thf(f125,plain,(
% 0.21/0.41 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.21/0.41 inference(cnf_transformation,[],[f60])).
% 0.21/0.41 thf(f60,plain,(
% 0.21/0.41 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.21/0.41 inference(fool_elimination,[],[f59])).
% 0.21/0.41 thf(f59,plain,(
% 0.21/0.41 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 0.21/0.41 inference(rectify,[],[f4])).
% 0.21/0.41 thf(f4,axiom,(
% 0.21/0.41 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))) = mor)),
% 0.21/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.21/0.41 thf(f106,plain,(
% 0.21/0.41 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.41 inference(cnf_transformation,[],[f90])).
% 0.21/0.41 thf(f90,plain,(
% 0.21/0.41 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.41 inference(fool_elimination,[],[f89])).
% 0.21/0.41 thf(f89,plain,(
% 0.21/0.41 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.21/0.41 inference(rectify,[],[f6])).
% 0.21/0.41 thf(f6,axiom,(
% 0.21/0.41 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.21/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.21/0.41 thf(f131,plain,(
% 0.21/0.41 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.21/0.41 inference(definition_unfolding,[],[f99,f124,f125,f124,f124])).
% 0.21/0.41 thf(f99,plain,(
% 0.21/0.41 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.21/0.41 inference(cnf_transformation,[],[f92])).
% 0.21/0.41 thf(f92,plain,(
% 0.21/0.41 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.21/0.41 inference(fool_elimination,[],[f91])).
% 0.21/0.41 thf(f91,plain,(
% 0.21/0.41 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.21/0.41 inference(rectify,[],[f5])).
% 0.21/0.41 thf(f5,axiom,(
% 0.21/0.41 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.21/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)).
% 0.21/0.41 thf(f120,plain,(
% 0.21/0.41 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.21/0.41 inference(cnf_transformation,[],[f68])).
% 0.21/0.41 thf(f68,plain,(
% 0.21/0.41 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.21/0.41 inference(fool_elimination,[],[f67])).
% 0.21/0.41 thf(f67,plain,(
% 0.21/0.41 ((^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))) = mequiv)),
% 0.21/0.41 inference(rectify,[],[f8])).
% 0.21/0.41 thf(f8,axiom,(
% 0.21/0.41 ((^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))) = mequiv)),
% 0.21/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv)).
% 0.21/0.41 thf(f121,plain,(
% 0.21/0.41 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.21/0.41 inference(cnf_transformation,[],[f58])).
% 0.21/0.41 thf(f58,plain,(
% 0.21/0.41 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.21/0.41 inference(fool_elimination,[],[f57])).
% 0.21/0.41 thf(f57,plain,(
% 0.21/0.41 ((^[X0 : ($i > $o) > $i > $o, X1 : $i] : (! [X2 : $i > $o] : (X0 @ X2 @ X1))) = mforall_prop)),
% 0.21/0.41 inference(rectify,[],[f11])).
% 0.21/0.41 thf(f11,axiom,(
% 0.21/0.41 ((^[X3 : ($i > $o) > $i > $o, X2 : $i] : (! [X5 : $i > $o] : (X3 @ X5 @ X2))) = mforall_prop)),
% 0.21/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_prop)).
% 0.21/0.41 thf(f123,plain,(
% 0.21/0.41 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.41 inference(cnf_transformation,[],[f43])).
% 0.21/0.41 thf(f43,plain,(
% 0.21/0.41 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.41 inference(fool_elimination,[],[f42])).
% 0.21/0.41 thf(f42,plain,(
% 0.21/0.41 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.21/0.41 inference(rectify,[],[f28])).
% 0.21/0.41 thf(f28,axiom,(
% 0.21/0.41 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.21/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.21/0.41 thf(f101,plain,(
% 0.21/0.41 ($true = (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mequiv @ (mdia @ sK0 @ Y0) @ (mbox @ sK0 @ Y0))))))),
% 0.21/0.41 inference(cnf_transformation,[],[f97])).
% 0.21/0.41 thf(f186,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X1 : $i] : (((sK0 @ X1 @ (sK5 @ X1 @ X2)) = $true) | ($false = (X2 @ (sK4 @ X1 @ X2)))) )),
% 0.21/0.41 inference(not_proxy_clausification,[],[f183])).
% 0.21/0.41 thf(f183,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X1 : $i] : (($false = (X2 @ (sK4 @ X1 @ X2))) | ($false = (~ (sK0 @ X1 @ (sK5 @ X1 @ X2))))) )),
% 0.21/0.41 inference(binary_proxy_clausification,[],[f182])).
% 0.21/0.41 thf(f182,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X1 : $i] : (($false = ((~ (X2 @ (sK5 @ X1 @ X2))) | (~ (sK0 @ X1 @ (sK5 @ X1 @ X2))))) | ($false = (X2 @ (sK4 @ X1 @ X2)))) )),
% 0.21/0.41 inference(binary_proxy_clausification,[],[f180])).
% 0.21/0.41 thf(f180,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X1 : $i] : (($false = ((X2 @ (sK4 @ X1 @ X2)) | (~ (sK0 @ X1 @ (sK4 @ X1 @ X2))))) | ($false = ((~ (X2 @ (sK5 @ X1 @ X2))) | (~ (sK0 @ X1 @ (sK5 @ X1 @ X2)))))) )),
% 0.21/0.41 inference(beta_eta_normalization,[],[f179])).
% 0.21/0.41 thf(f179,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X1 : $i] : (($false = ((X2 @ (sK4 @ X1 @ X2)) | (~ (sK0 @ X1 @ (sK4 @ X1 @ X2))))) | ($false = ((^[Y0 : $i]: ((~ (X2 @ Y0)) | (~ (sK0 @ X1 @ Y0)))) @ (sK5 @ X1 @ X2)))) )),
% 0.21/0.41 inference(sigma_clausification,[],[f178])).
% 0.21/0.41 thf(f178,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((~ (X2 @ Y0)) | (~ (sK0 @ X1 @ Y0)))))) | ($false = ((X2 @ (sK4 @ X1 @ X2)) | (~ (sK0 @ X1 @ (sK4 @ X1 @ X2)))))) )),
% 0.21/0.41 inference(beta_eta_normalization,[],[f177])).
% 0.21/0.41 thf(f177,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X1 : $i] : (($false = ((^[Y0 : $i]: ((X2 @ Y0) | (~ (sK0 @ X1 @ Y0)))) @ (sK4 @ X1 @ X2))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (X2 @ Y0)) | (~ (sK0 @ X1 @ Y0))))))) )),
% 0.21/0.41 inference(sigma_clausification,[],[f176])).
% 0.21/0.41 thf(f176,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) | (~ (sK0 @ X1 @ Y0)))))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (X2 @ Y0)) | (~ (sK0 @ X1 @ Y0))))))) )),
% 0.21/0.41 inference(not_proxy_clausification,[],[f175])).
% 0.21/0.41 thf(f175,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) | (~ (sK0 @ X1 @ Y0))))))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (X2 @ Y0)) | (~ (sK0 @ X1 @ Y0))))))) )),
% 0.21/0.41 inference(not_proxy_clausification,[],[f174])).
% 0.21/0.41 thf(f174,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (X2 @ Y0)) | (~ (sK0 @ X1 @ Y0))))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) | (~ (sK0 @ X1 @ Y0)))))))) )),
% 0.21/0.41 inference(binary_proxy_clausification,[],[f173])).
% 0.21/0.41 thf(f173,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X1 : $i] : ((((~ (!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) | (~ (sK0 @ X1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (X2 @ Y0)) | (~ (sK0 @ X1 @ Y0))))))) = $true)) )),
% 0.21/0.41 inference(not_proxy_clausification,[],[f160])).
% 0.21/0.41 thf(f160,plain,(
% 0.21/0.41 ( ! [X2 : $i > $o,X1 : $i] : (($false = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) | (~ (sK0 @ X1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (X2 @ Y0)) | (~ (sK0 @ X1 @ Y0)))))))))) )),
% 0.21/0.41 inference(binary_proxy_clausification,[],[f159])).
% 0.21/0.41 % SZS output end Proof for theBenchmark
% 0.21/0.41 % (10071)------------------------------
% 0.21/0.41 % (10071)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (10071)Termination reason: Refutation
% 0.21/0.41
% 0.21/0.41 % (10071)Memory used [KB]: 6012
% 0.21/0.41 % (10071)Time elapsed: 0.039 s
% 0.21/0.41 % (10071)Instructions burned: 80 (million)
% 0.21/0.41 % (10071)------------------------------
% 0.21/0.41 % (10071)------------------------------
% 0.21/0.41 % (10070)Success in time 0.055 s
% 0.21/0.41 % Vampire---4.8 exiting
%------------------------------------------------------------------------------