TSTP Solution File: PHI005^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : PHI005^2 : TPTP v8.2.0. Released v6.1.0.
% 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 : n007.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 02:18:43 EDT 2024
% Result : Theorem 0.20s 0.41s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : PHI005^2 : TPTP v8.2.0. Released v6.1.0.
% 0.11/0.14 % 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
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat May 18 14:48:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.35 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
% 0.14/0.37 % (3089)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.37 % (3083)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.37 % (3085)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)
% 0.14/0.37 % (3086)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37 % (3084)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)
% 0.14/0.37 % (3087)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)
% 0.14/0.37 % (3088)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)
% 0.14/0.37 % (3090)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)
% 0.14/0.37 % (3086)Instruction limit reached!
% 0.14/0.37 % (3086)------------------------------
% 0.14/0.37 % (3086)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (3086)Termination reason: Unknown
% 0.14/0.37 % (3086)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (3087)Instruction limit reached!
% 0.14/0.37 % (3087)------------------------------
% 0.14/0.37 % (3087)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (3087)Termination reason: Unknown
% 0.14/0.37 % (3087)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (3087)Memory used [KB]: 1023
% 0.14/0.37 % (3087)Time elapsed: 0.003 s
% 0.14/0.37 % (3087)Instructions burned: 2 (million)
% 0.14/0.37 % (3087)------------------------------
% 0.14/0.37 % (3087)------------------------------
% 0.14/0.37 % (3086)Memory used [KB]: 1023
% 0.14/0.37 % (3086)Time elapsed: 0.003 s
% 0.14/0.37 % (3086)Instructions burned: 2 (million)
% 0.14/0.37 % (3086)------------------------------
% 0.14/0.37 % (3086)------------------------------
% 0.14/0.37 % (3084)Instruction limit reached!
% 0.14/0.37 % (3084)------------------------------
% 0.14/0.37 % (3084)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (3084)Termination reason: Unknown
% 0.14/0.37 % (3084)Termination phase: Property scanning
% 0.14/0.37
% 0.14/0.37 % (3084)Memory used [KB]: 1023
% 0.14/0.37 % (3084)Time elapsed: 0.004 s
% 0.14/0.37 % (3084)Instructions burned: 4 (million)
% 0.14/0.37 % (3084)------------------------------
% 0.14/0.37 % (3084)------------------------------
% 0.14/0.37 % (3090)Instruction limit reached!
% 0.14/0.37 % (3090)------------------------------
% 0.14/0.37 % (3090)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (3090)Termination reason: Unknown
% 0.14/0.37 % (3090)Termination phase: Property scanning
% 0.14/0.37
% 0.14/0.37 % (3090)Memory used [KB]: 1023
% 0.14/0.37 % (3090)Time elapsed: 0.004 s
% 0.14/0.37 % (3090)Instructions burned: 3 (million)
% 0.14/0.37 % (3090)------------------------------
% 0.14/0.37 % (3090)------------------------------
% 0.14/0.38 % (3088)Refutation not found, incomplete strategy
% 0.14/0.38 % (3088)------------------------------
% 0.14/0.38 % (3088)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (3088)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.38
% 0.14/0.38
% 0.14/0.38 % (3088)Memory used [KB]: 5628
% 0.14/0.38 % (3088)Time elapsed: 0.006 s
% 0.14/0.38 % (3088)Instructions burned: 7 (million)
% 0.14/0.38 % (3088)------------------------------
% 0.14/0.38 % (3088)------------------------------
% 0.14/0.38 % (3089)Instruction limit reached!
% 0.14/0.38 % (3089)------------------------------
% 0.14/0.38 % (3089)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (3089)Termination reason: Unknown
% 0.14/0.38 % (3089)Termination phase: Saturation
% 0.14/0.38
% 0.14/0.38 % (3089)Memory used [KB]: 5756
% 0.14/0.38 % (3089)Time elapsed: 0.010 s
% 0.14/0.38 % (3089)Instructions burned: 18 (million)
% 0.14/0.38 % (3089)------------------------------
% 0.14/0.38 % (3089)------------------------------
% 0.14/0.39 % (3091)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)
% 0.14/0.39 % (3092)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)
% 0.14/0.39 % (3094)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)
% 0.14/0.39 % (3085)Instruction limit reached!
% 0.14/0.39 % (3085)------------------------------
% 0.14/0.39 % (3085)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (3085)Termination reason: Unknown
% 0.14/0.39 % (3085)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (3085)Memory used [KB]: 5756
% 0.14/0.39 % (3085)Time elapsed: 0.019 s
% 0.14/0.39 % (3085)Instructions burned: 28 (million)
% 0.14/0.39 % (3085)------------------------------
% 0.14/0.39 % (3085)------------------------------
% 0.14/0.39 % (3096)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.14/0.39 % (3095)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.39 % (3093)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)
% 0.14/0.39 % (3093)Instruction limit reached!
% 0.14/0.39 % (3093)------------------------------
% 0.14/0.39 % (3093)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (3093)Termination reason: Unknown
% 0.14/0.39 % (3093)Termination phase: Property scanning
% 0.14/0.39
% 0.14/0.39 % (3093)Memory used [KB]: 1023
% 0.14/0.39 % (3093)Time elapsed: 0.004 s
% 0.14/0.39 % (3093)Instructions burned: 4 (million)
% 0.14/0.39 % (3093)------------------------------
% 0.14/0.39 % (3093)------------------------------
% 0.14/0.39 % (3095)Instruction limit reached!
% 0.14/0.39 % (3095)------------------------------
% 0.14/0.39 % (3095)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (3095)Termination reason: Unknown
% 0.14/0.39 % (3095)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (3095)Memory used [KB]: 1023
% 0.14/0.39 % (3095)Time elapsed: 0.006 s
% 0.14/0.39 % (3095)Instructions burned: 8 (million)
% 0.14/0.39 % (3095)------------------------------
% 0.14/0.39 % (3095)------------------------------
% 0.14/0.39 % (3096)Instruction limit reached!
% 0.14/0.39 % (3096)------------------------------
% 0.14/0.39 % (3096)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (3092)Instruction limit reached!
% 0.14/0.39 % (3092)------------------------------
% 0.14/0.39 % (3092)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (3092)Termination reason: Unknown
% 0.14/0.39 % (3092)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (3092)Memory used [KB]: 5628
% 0.14/0.39 % (3092)Time elapsed: 0.011 s
% 0.14/0.39 % (3092)Instructions burned: 15 (million)
% 0.14/0.39 % (3092)------------------------------
% 0.14/0.39 % (3092)------------------------------
% 0.14/0.39 % (3096)Termination reason: Unknown
% 0.14/0.39 % (3096)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (3096)Memory used [KB]: 5628
% 0.14/0.39 % (3096)Time elapsed: 0.008 s
% 0.14/0.39 % (3096)Instructions burned: 16 (million)
% 0.14/0.39 % (3096)------------------------------
% 0.14/0.39 % (3096)------------------------------
% 0.14/0.40 % (3097)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)
% 0.14/0.40 % (3097)Instruction limit reached!
% 0.14/0.40 % (3097)------------------------------
% 0.14/0.40 % (3097)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (3097)Termination reason: Unknown
% 0.14/0.40 % (3097)Termination phase: Property scanning
% 0.14/0.40
% 0.14/0.40 % (3097)Memory used [KB]: 1023
% 0.14/0.40 % (3097)Time elapsed: 0.004 s
% 0.14/0.40 % (3097)Instructions burned: 4 (million)
% 0.14/0.40 % (3097)------------------------------
% 0.14/0.40 % (3097)------------------------------
% 0.14/0.41 % (3091)Instruction limit reached!
% 0.14/0.41 % (3091)------------------------------
% 0.14/0.41 % (3091)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41 % (3091)Termination reason: Unknown
% 0.14/0.41 % (3091)Termination phase: Saturation
% 0.14/0.41
% 0.14/0.41 % (3091)Memory used [KB]: 6140
% 0.14/0.41 % (3091)Time elapsed: 0.022 s
% 0.14/0.41 % (3091)Instructions burned: 37 (million)
% 0.14/0.41 % (3091)------------------------------
% 0.14/0.41 % (3091)------------------------------
% 0.14/0.41 % (3098)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)
% 0.20/0.41 % (3101)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.20/0.41 % (3094)First to succeed.
% 0.20/0.41 % (3099)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)
% 0.20/0.41 % (3098)Instruction limit reached!
% 0.20/0.41 % (3098)------------------------------
% 0.20/0.41 % (3098)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (3098)Termination reason: Unknown
% 0.20/0.41 % (3098)Termination phase: shuffling
% 0.20/0.41
% 0.20/0.41 % (3098)Memory used [KB]: 1023
% 0.20/0.41 % (3098)Time elapsed: 0.004 s
% 0.20/0.41 % (3098)Instructions burned: 4 (million)
% 0.20/0.41 % (3098)------------------------------
% 0.20/0.41 % (3098)------------------------------
% 0.20/0.41 % (3101)Instruction limit reached!
% 0.20/0.41 % (3101)------------------------------
% 0.20/0.41 % (3101)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (3101)Termination reason: Unknown
% 0.20/0.41 % (3101)Termination phase: Function definition elimination
% 0.20/0.41
% 0.20/0.41 % (3101)Memory used [KB]: 1023
% 0.20/0.41 % (3101)Time elapsed: 0.003 s
% 0.20/0.41 % (3101)Instructions burned: 5 (million)
% 0.20/0.41 % (3101)------------------------------
% 0.20/0.41 % (3101)------------------------------
% 0.20/0.41 % (3100)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.41 % (3100)Instruction limit reached!
% 0.20/0.41 % (3100)------------------------------
% 0.20/0.41 % (3100)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (3100)Termination reason: Unknown
% 0.20/0.41 % (3100)Termination phase: Property scanning
% 0.20/0.41
% 0.20/0.41 % (3100)Memory used [KB]: 1023
% 0.20/0.41 % (3100)Time elapsed: 0.004 s
% 0.20/0.41 % (3100)Instructions burned: 4 (million)
% 0.20/0.41 % (3100)------------------------------
% 0.20/0.41 % (3100)------------------------------
% 0.20/0.41 % (3099)Instruction limit reached!
% 0.20/0.41 % (3099)------------------------------
% 0.20/0.41 % (3099)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (3099)Termination reason: Unknown
% 0.20/0.41 % (3099)Termination phase: Saturation
% 0.20/0.41
% 0.20/0.41 % (3099)Memory used [KB]: 1023
% 0.20/0.41 % (3099)Time elapsed: 0.005 s
% 0.20/0.41 % (3099)Instructions burned: 7 (million)
% 0.20/0.41 % (3099)------------------------------
% 0.20/0.41 % (3099)------------------------------
% 0.20/0.41 % (3094)Refutation found. Thanks to Tanya!
% 0.20/0.41 % SZS status Theorem for theBenchmark
% 0.20/0.41 % SZS output start Proof for theBenchmark
% 0.20/0.41 thf(type_def_5, type, mu: $tType).
% 0.20/0.41 thf(func_def_0, type, mu: $tType).
% 0.20/0.41 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.20/0.41 thf(func_def_2, type, mtrue: $i > $o).
% 0.20/0.41 thf(func_def_3, type, mfalse: $i > $o).
% 0.20/0.41 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_6, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_7, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_8, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_9, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_10, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_11, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_12, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_13, type, mforall_indset: ((mu > $i > $o) > $i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_14, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_15, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_16, type, mexists_indset: ((mu > $i > $o) > $i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_17, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_18, type, mbox_generic: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_19, type, mdia_generic: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_20, type, rel: $i > $i > $o).
% 0.20/0.41 thf(func_def_21, type, mbox: ($i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_22, type, mdia: ($i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_23, type, mvalid: ($i > $o) > $o).
% 0.20/0.41 thf(func_def_24, type, minvalid: ($i > $o) > $o).
% 0.20/0.41 thf(func_def_25, type, msymmetric: ($i > $i > $o) > $o).
% 0.20/0.41 thf(func_def_26, type, positive: (mu > $i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_27, type, god: mu > $i > $o).
% 0.20/0.41 thf(func_def_28, type, essence: (mu > $i > $o) > mu > $i > $o).
% 0.20/0.41 thf(func_def_29, type, necessary_existence: mu > $i > $o).
% 0.20/0.41 thf(func_def_47, type, ph1: !>[X0: $tType]:(X0)).
% 0.20/0.41 thf(func_def_48, type, sK2: $i > $i).
% 0.20/0.41 thf(func_def_49, type, sK3: $i > mu).
% 0.20/0.41 thf(func_def_52, type, sK6: mu > mu > $i > $o).
% 0.20/0.41 thf(f231,plain,(
% 0.20/0.41 $false),
% 0.20/0.41 inference(trivial_inequality_removal,[],[f230])).
% 0.20/0.41 thf(f230,plain,(
% 0.20/0.41 ($true = $false)),
% 0.20/0.41 inference(boolean_simplification,[],[f229])).
% 0.20/0.41 thf(f229,plain,(
% 0.20/0.41 ($true = (~ $true))),
% 0.20/0.41 inference(superposition,[],[f223,f151])).
% 0.20/0.41 thf(f151,plain,(
% 0.20/0.41 ( ! [X0 : $i] : (($true = (rel @ (sK2 @ X0) @ X0))) )),
% 0.20/0.41 inference(boolean_simplification,[],[f149])).
% 0.20/0.41 thf(f149,plain,(
% 0.20/0.41 ( ! [X0 : $i] : (($true = ($true => (rel @ (sK2 @ X0) @ X0)))) )),
% 0.20/0.41 inference(superposition,[],[f137,f144])).
% 0.20/0.41 thf(f144,plain,(
% 0.20/0.41 ( ! [X1 : $i] : (($true = (rel @ X1 @ (sK2 @ X1)))) )),
% 0.20/0.41 inference(binary_proxy_clausification,[],[f142])).
% 0.20/0.41 thf(f142,plain,(
% 0.20/0.41 ( ! [X1 : $i] : (($true = ((rel @ X1 @ (sK2 @ X1)) & (?? @ mu @ (^[Y0 : mu]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ (sK2 @ X1)) => (Y1 @ Y0 @ (sK2 @ X1)))))))))) )),
% 0.20/0.41 inference(beta_eta_normalization,[],[f141])).
% 0.20/0.41 thf(f141,plain,(
% 0.20/0.41 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((rel @ X1 @ Y0) & (?? @ mu @ (^[Y1 : mu]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))))))) @ (sK2 @ X1)))) )),
% 0.20/0.41 inference(sigma_clausification,[],[f140])).
% 0.20/0.41 thf(f140,plain,(
% 0.20/0.41 ( ! [X1 : $i] : (($true = (?? @ $i @ (^[Y0 : $i]: ((rel @ X1 @ Y0) & (?? @ mu @ (^[Y1 : mu]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0))))))))))) )),
% 0.20/0.41 inference(beta_eta_normalization,[],[f139])).
% 0.20/0.41 thf(f139,plain,(
% 0.20/0.41 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((rel @ Y0 @ Y1) & (?? @ mu @ (^[Y2 : mu]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((positive @ Y3 @ Y1) => (Y3 @ Y2 @ Y1)))))))))) @ X1))) )),
% 0.20/0.41 inference(pi_clausification,[],[f133])).
% 0.20/0.41 thf(f133,plain,(
% 0.20/0.41 ($true = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((rel @ Y0 @ Y1) & (?? @ mu @ (^[Y2 : mu]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((positive @ Y3 @ Y1) => (Y3 @ Y2 @ Y1))))))))))))),
% 0.20/0.41 inference(beta_eta_normalization,[],[f124])).
% 0.20/0.41 thf(f124,plain,(
% 0.20/0.41 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))) @ rel @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : mu]: ((^[Y1 : mu]: ((^[Y2 : (mu > $i > $o) > $i > $o]: ((^[Y3 : $i]: (!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : mu > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y3 @ Y5) => (Y4 @ Y5))))))) @ (positive @ Y2) @ (Y2 @ Y1))))) @ Y0))))))),
% 0.20/0.41 inference(definition_unfolding,[],[f102,f96,f121,f103,f122])).
% 0.20/0.41 thf(f122,plain,(
% 0.20/0.41 (god = (^[Y0 : mu]: ((^[Y1 : (mu > $i > $o) > $i > $o]: ((^[Y2 : $i]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : mu > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) => (Y3 @ Y4))))))) @ (positive @ Y1) @ (Y1 @ Y0))))))),
% 0.20/0.41 inference(definition_unfolding,[],[f101,f91,f95])).
% 0.20/0.41 thf(f95,plain,(
% 0.20/0.41 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.20/0.41 inference(cnf_transformation,[],[f55])).
% 0.20/0.41 thf(f55,plain,(
% 0.20/0.41 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.20/0.41 inference(fool_elimination,[],[f54])).
% 0.20/0.41 thf(f54,plain,(
% 0.20/0.41 (mimplies = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) => (X1 @ X2))))),
% 0.20/0.41 inference(rectify,[],[f7])).
% 0.20/0.41 thf(f7,axiom,(
% 0.20/0.41 (mimplies = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) => (X4 @ X2))))),
% 0.20/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.20/0.41 thf(f91,plain,(
% 0.20/0.41 (mforall_indset = (^[Y0 : (mu > $i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.20/0.41 inference(cnf_transformation,[],[f38])).
% 0.20/0.41 thf(f38,plain,(
% 0.20/0.41 (mforall_indset = (^[Y0 : (mu > $i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.20/0.41 inference(fool_elimination,[],[f37])).
% 0.20/0.41 thf(f37,plain,(
% 0.20/0.41 ((^[X0 : (mu > $i > $o) > $i > $o, X1 : $i] : (! [X2 : mu > $i > $o] : (X0 @ X2 @ X1))) = mforall_indset)),
% 0.20/0.41 inference(rectify,[],[f12])).
% 0.20/0.41 thf(f12,axiom,(
% 0.20/0.41 ((^[X3 : (mu > $i > $o) > $i > $o, X2 : $i] : (! [X0 : mu > $i > $o] : (X3 @ X0 @ X2))) = mforall_indset)),
% 0.20/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_indset)).
% 0.20/0.41 thf(f101,plain,(
% 0.20/0.41 (god = (^[Y0 : mu]: (mforall_indset @ (^[Y1 : mu > $i > $o]: (mimplies @ (positive @ Y1) @ (Y1 @ Y0))))))),
% 0.20/0.41 inference(cnf_transformation,[],[f59])).
% 0.20/0.41 thf(f59,plain,(
% 0.20/0.41 (god = (^[Y0 : mu]: (mforall_indset @ (^[Y1 : mu > $i > $o]: (mimplies @ (positive @ Y1) @ (Y1 @ Y0))))))),
% 0.20/0.41 inference(fool_elimination,[],[f58])).
% 0.20/0.41 thf(f58,plain,(
% 0.20/0.41 (god = (^[X0 : mu] : (mforall_indset @ (^[X1 : mu > $i > $o] : (mimplies @ (positive @ X1) @ (X1 @ X0))))))),
% 0.20/0.41 inference(rectify,[],[f25])).
% 0.20/0.41 thf(f25,axiom,(
% 0.20/0.41 (god = (^[X0 : mu] : (mforall_indset @ (^[X3 : mu > $i > $o] : (mimplies @ (positive @ X3) @ (X3 @ X0))))))),
% 0.20/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',defD1)).
% 0.20/0.41 thf(f103,plain,(
% 0.20/0.41 (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.20/0.41 inference(cnf_transformation,[],[f36])).
% 0.20/0.41 thf(f36,plain,(
% 0.20/0.41 (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.20/0.41 inference(fool_elimination,[],[f35])).
% 0.20/0.41 thf(f35,plain,(
% 0.20/0.41 ((^[X0 : mu > $i > $o, X1 : $i] : (? [X2 : mu] : (X0 @ X2 @ X1))) = mexists_ind)),
% 0.20/0.41 inference(rectify,[],[f14])).
% 0.20/0.41 thf(f14,axiom,(
% 0.20/0.41 ((^[X3 : mu > $i > $o, X2 : $i] : (? [X0 : mu] : (X3 @ X0 @ X2))) = mexists_ind)),
% 0.20/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_ind)).
% 0.20/0.41 thf(f121,plain,(
% 0.20/0.41 (mdia = ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))) @ rel))),
% 0.20/0.41 inference(definition_unfolding,[],[f117,f105])).
% 0.20/0.41 thf(f105,plain,(
% 0.20/0.41 (mdia_generic = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))))),
% 0.20/0.41 inference(cnf_transformation,[],[f70])).
% 0.20/0.41 thf(f70,plain,(
% 0.20/0.41 (mdia_generic = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))))),
% 0.20/0.41 inference(fool_elimination,[],[f69])).
% 0.20/0.41 thf(f69,plain,(
% 0.20/0.41 ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (? [X3] : ((X1 @ X3) & (X0 @ X2 @ X3)))) = mdia_generic)),
% 0.20/0.41 inference(rectify,[],[f18])).
% 0.20/0.41 thf(f18,axiom,(
% 0.20/0.41 ((^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (? [X7] : ((X3 @ X7) & (X6 @ X2 @ X7)))) = mdia_generic)),
% 0.20/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_generic)).
% 0.20/0.41 thf(f117,plain,(
% 0.20/0.41 (mdia = (mdia_generic @ rel))),
% 0.20/0.41 inference(cnf_transformation,[],[f83])).
% 0.20/0.41 thf(f83,plain,(
% 0.20/0.41 (mdia = (mdia_generic @ rel))),
% 0.20/0.41 inference(fool_elimination,[],[f20])).
% 0.20/0.41 thf(f20,axiom,(
% 0.20/0.41 (mdia = (mdia_generic @ rel))),
% 0.20/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia)).
% 0.20/0.41 thf(f96,plain,(
% 0.20/0.41 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.41 inference(cnf_transformation,[],[f82])).
% 0.20/0.41 thf(f82,plain,(
% 0.20/0.41 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.41 inference(fool_elimination,[],[f81])).
% 0.20/0.41 thf(f81,plain,(
% 0.20/0.42 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.20/0.42 inference(rectify,[],[f21])).
% 0.20/0.42 thf(f21,axiom,(
% 0.20/0.42 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.20/0.42 thf(f102,plain,(
% 0.20/0.42 ($true = (mvalid @ (mdia @ (mexists_ind @ (^[Y0 : mu]: (god @ Y0))))))),
% 0.20/0.42 inference(cnf_transformation,[],[f44])).
% 0.20/0.42 thf(f44,plain,(
% 0.20/0.42 ($true = (mvalid @ (mdia @ (mexists_ind @ (^[Y0 : mu]: (god @ Y0))))))),
% 0.20/0.42 inference(fool_elimination,[],[f43])).
% 0.20/0.42 thf(f43,plain,(
% 0.20/0.42 (mvalid @ (mdia @ (mexists_ind @ (^[X0 : mu] : (god @ X0)))))),
% 0.20/0.42 inference(rectify,[],[f28])).
% 0.20/0.42 thf(f28,axiom,(
% 0.20/0.42 (mvalid @ (mdia @ (mexists_ind @ (^[X0 : mu] : (god @ X0)))))),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corC)).
% 0.20/0.42 thf(f137,plain,(
% 0.20/0.42 ( ! [X2 : $i,X1 : $i] : (($true = ((rel @ X2 @ X1) => (rel @ X1 @ X2)))) )),
% 0.20/0.42 inference(beta_eta_normalization,[],[f136])).
% 0.20/0.42 thf(f136,plain,(
% 0.20/0.42 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((rel @ Y0 @ X1) => (rel @ X1 @ Y0))) @ X2))) )),
% 0.20/0.42 inference(pi_clausification,[],[f135])).
% 0.20/0.42 thf(f135,plain,(
% 0.20/0.42 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((rel @ Y0 @ X1) => (rel @ X1 @ Y0)))))) )),
% 0.20/0.42 inference(beta_eta_normalization,[],[f134])).
% 0.20/0.42 thf(f134,plain,(
% 0.20/0.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel @ Y1 @ Y0) => (rel @ Y0 @ Y1))))) @ X1))) )),
% 0.20/0.42 inference(pi_clausification,[],[f129])).
% 0.20/0.42 thf(f129,plain,(
% 0.20/0.42 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel @ Y1 @ Y0) => (rel @ Y0 @ Y1)))))))),
% 0.20/0.42 inference(beta_eta_normalization,[],[f128])).
% 0.20/0.42 thf(f128,plain,(
% 0.20/0.42 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))) @ rel))),
% 0.20/0.42 inference(definition_unfolding,[],[f119,f116])).
% 0.20/0.42 thf(f116,plain,(
% 0.20/0.42 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))))),
% 0.20/0.42 inference(cnf_transformation,[],[f78])).
% 0.20/0.42 thf(f78,plain,(
% 0.20/0.42 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))))),
% 0.20/0.42 inference(fool_elimination,[],[f77])).
% 0.20/0.42 thf(f77,plain,(
% 0.20/0.42 (msymmetric = (^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X1 @ X2) => (X0 @ X2 @ X1)))))),
% 0.20/0.42 inference(rectify,[],[f23])).
% 0.20/0.42 thf(f23,axiom,(
% 0.20/0.42 (msymmetric = (^[X6 : $i > $i > $o] : (! [X8,X9] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))))),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msymmetric)).
% 0.20/0.42 thf(f119,plain,(
% 0.20/0.42 ((msymmetric @ rel) = $true)),
% 0.20/0.42 inference(cnf_transformation,[],[f61])).
% 0.20/0.42 thf(f61,plain,(
% 0.20/0.42 ((msymmetric @ rel) = $true)),
% 0.20/0.42 inference(fool_elimination,[],[f60])).
% 0.20/0.42 thf(f60,plain,(
% 0.20/0.42 (msymmetric @ rel)),
% 0.20/0.42 inference(rectify,[],[f24])).
% 0.20/0.42 thf(f24,axiom,(
% 0.20/0.42 (msymmetric @ rel)),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sym)).
% 0.20/0.42 thf(f223,plain,(
% 0.20/0.42 ( ! [X0 : $i] : (($true = (~ (rel @ (sK2 @ X0) @ sK5)))) )),
% 0.20/0.42 inference(boolean_simplification,[],[f216])).
% 0.20/0.42 thf(f216,plain,(
% 0.20/0.42 ( ! [X0 : $i] : (($true = ((~ (rel @ (sK2 @ X0) @ sK5)) | $false))) )),
% 0.20/0.42 inference(superposition,[],[f214,f170])).
% 0.20/0.42 thf(f170,plain,(
% 0.20/0.42 ($false = (?? @ mu @ (^[Y0 : mu]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ sK5) => (Y1 @ Y0 @ sK5)))))))),
% 0.20/0.42 inference(boolean_simplification,[],[f169])).
% 0.20/0.42 thf(f169,plain,(
% 0.20/0.42 ($false = ($false | (?? @ mu @ (^[Y0 : mu]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ sK5) => (Y1 @ Y0 @ sK5))))))))),
% 0.20/0.42 inference(backward_demodulation,[],[f166,f168])).
% 0.20/0.42 thf(f168,plain,(
% 0.20/0.42 ($false = (~ (rel @ sK4 @ sK5)))),
% 0.20/0.42 inference(binary_proxy_clausification,[],[f166])).
% 0.20/0.42 thf(f166,plain,(
% 0.20/0.42 ($false = ((~ (rel @ sK4 @ sK5)) | (?? @ mu @ (^[Y0 : mu]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ sK5) => (Y1 @ Y0 @ sK5))))))))),
% 0.20/0.42 inference(beta_eta_normalization,[],[f165])).
% 0.20/0.42 thf(f165,plain,(
% 0.20/0.42 ($false = ((^[Y0 : $i]: ((~ (rel @ sK4 @ Y0)) | (?? @ mu @ (^[Y1 : mu]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))))))) @ sK5))),
% 0.20/0.42 inference(sigma_clausification,[],[f164])).
% 0.20/0.42 thf(f164,plain,(
% 0.20/0.42 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel @ sK4 @ Y0)) | (?? @ mu @ (^[Y1 : mu]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0))))))))))),
% 0.20/0.42 inference(beta_eta_normalization,[],[f163])).
% 0.20/0.42 thf(f163,plain,(
% 0.20/0.42 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel @ Y0 @ Y1)) | (?? @ mu @ (^[Y2 : mu]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((positive @ Y3 @ Y1) => (Y3 @ Y2 @ Y1)))))))))) @ sK4))),
% 0.20/0.42 inference(sigma_clausification,[],[f160])).
% 0.20/0.42 thf(f160,plain,(
% 0.20/0.42 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel @ Y0 @ Y1)) | (?? @ mu @ (^[Y2 : mu]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((positive @ Y3 @ Y1) => (Y3 @ Y2 @ Y1))))))))))) = $false)),
% 0.20/0.42 inference(not_proxy_clausification,[],[f132])).
% 0.20/0.42 thf(f132,plain,(
% 0.20/0.42 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel @ Y0 @ Y1)) | (?? @ mu @ (^[Y2 : mu]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((positive @ Y3 @ Y1) => (Y3 @ Y2 @ Y1)))))))))))))),
% 0.20/0.42 inference(beta_eta_normalization,[],[f125])).
% 0.20/0.42 thf(f125,plain,(
% 0.20/0.42 ($true = (~ ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))) @ rel @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : mu]: ((^[Y1 : mu]: ((^[Y2 : (mu > $i > $o) > $i > $o]: ((^[Y3 : $i]: (!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : mu > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y3 @ Y5) => (Y4 @ Y5))))))) @ (positive @ Y2) @ (Y2 @ Y1))))) @ Y0)))))))),
% 0.20/0.42 inference(definition_unfolding,[],[f109,f96,f120,f103,f122])).
% 0.20/0.42 thf(f120,plain,(
% 0.20/0.42 (mbox = ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))) @ rel))),
% 0.20/0.42 inference(definition_unfolding,[],[f115,f111])).
% 0.20/0.42 thf(f111,plain,(
% 0.20/0.42 (mbox_generic = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.20/0.42 inference(cnf_transformation,[],[f87])).
% 0.20/0.42 thf(f87,plain,(
% 0.20/0.42 (mbox_generic = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.20/0.42 inference(fool_elimination,[],[f86])).
% 0.20/0.42 thf(f86,plain,(
% 0.20/0.42 (mbox_generic = (^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))))),
% 0.20/0.42 inference(rectify,[],[f17])).
% 0.20/0.42 thf(f17,axiom,(
% 0.20/0.42 (mbox_generic = (^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(X6 @ X2 @ X7)))))),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_generic)).
% 0.20/0.42 thf(f115,plain,(
% 0.20/0.42 (mbox = (mbox_generic @ rel))),
% 0.20/0.42 inference(cnf_transformation,[],[f68])).
% 0.20/0.42 thf(f68,plain,(
% 0.20/0.42 (mbox = (mbox_generic @ rel))),
% 0.20/0.42 inference(fool_elimination,[],[f19])).
% 0.20/0.42 thf(f19,axiom,(
% 0.20/0.42 (mbox = (mbox_generic @ rel))),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox)).
% 0.20/0.42 thf(f109,plain,(
% 0.20/0.42 ($true = (~ (mvalid @ (mbox @ (mexists_ind @ (^[Y0 : mu]: (god @ Y0)))))))),
% 0.20/0.42 inference(cnf_transformation,[],[f85])).
% 0.20/0.42 thf(f85,plain,(
% 0.20/0.42 ($true = (~ (mvalid @ (mbox @ (mexists_ind @ (^[Y0 : mu]: (god @ Y0)))))))),
% 0.20/0.42 inference(fool_elimination,[],[f84])).
% 0.20/0.42 thf(f84,plain,(
% 0.20/0.42 ~(mvalid @ (mbox @ (mexists_ind @ (^[X0 : mu] : (god @ X0)))))),
% 0.20/0.42 inference(rectify,[],[f31])).
% 0.20/0.42 thf(f31,negated_conjecture,(
% 0.20/0.42 ~(mvalid @ (mbox @ (mexists_ind @ (^[X0 : mu] : (god @ X0)))))),
% 0.20/0.42 inference(negated_conjecture,[],[f30])).
% 0.20/0.42 thf(f30,conjecture,(
% 0.20/0.42 (mvalid @ (mbox @ (mexists_ind @ (^[X0 : mu] : (god @ X0)))))),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thmT3)).
% 0.20/0.42 thf(f214,plain,(
% 0.20/0.42 ( ! [X0 : $i,X1 : $i] : (($true = ((~ (rel @ (sK2 @ X0) @ X1)) | (?? @ mu @ (^[Y0 : mu]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ X1) => (Y1 @ Y0 @ X1))))))))) )),
% 0.20/0.42 inference(beta_eta_normalization,[],[f213])).
% 0.20/0.42 thf(f213,plain,(
% 0.20/0.42 ( ! [X0 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel @ (sK2 @ X0) @ Y0)) | (?? @ mu @ (^[Y1 : mu]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))))))) @ X1))) )),
% 0.20/0.42 inference(pi_clausification,[],[f210])).
% 0.20/0.42 thf(f210,plain,(
% 0.20/0.42 ( ! [X0 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel @ (sK2 @ X0) @ Y0)) | (?? @ mu @ (^[Y1 : mu]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0))))))))))) )),
% 0.20/0.42 inference(boolean_simplification,[],[f209])).
% 0.20/0.42 thf(f209,plain,(
% 0.20/0.42 ( ! [X0 : $i] : (($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((~ (rel @ (sK2 @ X0) @ Y0)) | (?? @ mu @ (^[Y1 : mu]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))))))))))) )),
% 0.20/0.42 inference(beta_eta_normalization,[],[f206])).
% 0.20/0.42 thf(f206,plain,(
% 0.20/0.42 ( ! [X0 : $i] : (($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((~ (rel @ (sK2 @ X0) @ Y0)) | (?? @ mu @ (^[Y1 : mu]: ((^[Y2 : mu]: ((^[Y3 : $i]: (!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: ((positive @ Y4 @ Y3) => (Y4 @ Y2 @ Y3))))))) @ Y1 @ Y0))))))))) )),
% 0.20/0.42 inference(superposition,[],[f195,f204])).
% 0.20/0.42 thf(f204,plain,(
% 0.20/0.42 ( ! [X0 : $i] : (($true = (essence @ (^[Y0 : mu]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y1) => (Y2 @ Y0 @ Y1))))))) @ (sK3 @ X0) @ (sK2 @ X0)))) )),
% 0.20/0.42 inference(boolean_simplification,[],[f203])).
% 0.20/0.42 thf(f203,plain,(
% 0.20/0.42 ( ! [X0 : $i] : (($true = ($true => (essence @ (^[Y0 : mu]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y1) => (Y2 @ Y0 @ Y1))))))) @ (sK3 @ X0) @ (sK2 @ X0))))) )),
% 0.20/0.42 inference(superposition,[],[f200,f148])).
% 0.20/0.42 thf(f148,plain,(
% 0.20/0.42 ( ! [X1 : $i] : (($true = (!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((positive @ Y0 @ (sK2 @ X1)) => (Y0 @ (sK3 @ X1) @ (sK2 @ X1))))))) )),
% 0.20/0.42 inference(beta_eta_normalization,[],[f147])).
% 0.20/0.42 thf(f147,plain,(
% 0.20/0.42 ( ! [X1 : $i] : (($true = ((^[Y0 : mu]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ (sK2 @ X1)) => (Y1 @ Y0 @ (sK2 @ X1)))))) @ (sK3 @ X1)))) )),
% 0.20/0.42 inference(sigma_clausification,[],[f146])).
% 0.20/0.42 thf(f146,plain,(
% 0.20/0.42 ( ! [X1 : $i] : (($true = (?? @ mu @ (^[Y0 : mu]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ (sK2 @ X1)) => (Y1 @ Y0 @ (sK2 @ X1))))))))) )),
% 0.20/0.42 inference(boolean_simplification,[],[f145])).
% 0.20/0.42 thf(f145,plain,(
% 0.20/0.42 ( ! [X1 : $i] : (($true = ($true & (?? @ mu @ (^[Y0 : mu]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ (sK2 @ X1)) => (Y1 @ Y0 @ (sK2 @ X1)))))))))) )),
% 0.20/0.42 inference(backward_demodulation,[],[f142,f144])).
% 0.20/0.42 thf(f200,plain,(
% 0.20/0.42 ( ! [X2 : mu,X1 : $i] : (($true = ((!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((positive @ Y0 @ X1) => (Y0 @ X2 @ X1)))) => (essence @ (^[Y0 : mu]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y1) => (Y2 @ Y0 @ Y1))))))) @ X2 @ X1)))) )),
% 0.20/0.42 inference(beta_eta_normalization,[],[f199])).
% 0.20/0.42 thf(f199,plain,(
% 0.20/0.42 ( ! [X2 : mu,X1 : $i] : (($true = ((^[Y0 : mu]: ((!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ X1) => (Y1 @ Y0 @ X1)))) => (essence @ (^[Y1 : mu]: ((^[Y2 : $i]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((positive @ Y3 @ Y2) => (Y3 @ Y1 @ Y2))))))) @ Y0 @ X1))) @ X2))) )),
% 0.20/0.42 inference(pi_clausification,[],[f197])).
% 0.20/0.42 thf(f197,plain,(
% 0.20/0.42 ( ! [X1 : $i] : (($true = (!! @ mu @ (^[Y0 : mu]: ((!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ X1) => (Y1 @ Y0 @ X1)))) => (essence @ (^[Y1 : mu]: ((^[Y2 : $i]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((positive @ Y3 @ Y2) => (Y3 @ Y1 @ Y2))))))) @ Y0 @ X1)))))) )),
% 0.20/0.42 inference(beta_eta_normalization,[],[f196])).
% 0.20/0.42 thf(f196,plain,(
% 0.20/0.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))) => (essence @ (^[Y2 : mu]: ((^[Y3 : $i]: (!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: ((positive @ Y4 @ Y3) => (Y4 @ Y2 @ Y3))))))) @ Y1 @ Y0))))) @ X1))) )),
% 0.20/0.42 inference(pi_clausification,[],[f130])).
% 0.20/0.42 thf(f130,plain,(
% 0.20/0.42 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))) => (essence @ (^[Y2 : mu]: ((^[Y3 : $i]: (!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: ((positive @ Y4 @ Y3) => (Y4 @ Y2 @ Y3))))))) @ Y1 @ Y0)))))))),
% 0.20/0.42 inference(beta_eta_normalization,[],[f127])).
% 0.20/0.42 thf(f127,plain,(
% 0.20/0.42 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : mu]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: ((Y1 @ Y3) => (Y2 @ Y3))))))) @ ((^[Y1 : mu]: ((^[Y2 : (mu > $i > $o) > $i > $o]: ((^[Y3 : $i]: (!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : mu > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y3 @ Y5) => (Y4 @ Y5))))))) @ (positive @ Y2) @ (Y2 @ Y1))))) @ Y0) @ (essence @ (^[Y1 : mu]: ((^[Y2 : (mu > $i > $o) > $i > $o]: ((^[Y3 : $i]: (!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : mu > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y3 @ Y5) => (Y4 @ Y5))))))) @ (positive @ Y2) @ (Y2 @ Y1))))) @ Y0))))))),
% 0.20/0.42 inference(definition_unfolding,[],[f113,f96,f99,f95,f122,f122])).
% 0.20/0.42 thf(f99,plain,(
% 0.20/0.42 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.20/0.42 inference(cnf_transformation,[],[f80])).
% 0.20/0.42 thf(f80,plain,(
% 0.20/0.42 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.20/0.42 inference(fool_elimination,[],[f79])).
% 0.20/0.42 thf(f79,plain,(
% 0.20/0.42 (mforall_ind = (^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : (X0 @ X2 @ X1))))),
% 0.20/0.42 inference(rectify,[],[f11])).
% 0.20/0.42 thf(f11,axiom,(
% 0.20/0.42 (mforall_ind = (^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : (X3 @ X0 @ X2))))),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind)).
% 0.20/0.42 thf(f113,plain,(
% 0.20/0.42 ($true = (mvalid @ (mforall_ind @ (^[Y0 : mu]: (mimplies @ (god @ Y0) @ (essence @ god @ Y0))))))),
% 0.20/0.42 inference(cnf_transformation,[],[f47])).
% 0.20/0.42 thf(f47,plain,(
% 0.20/0.42 ($true = (mvalid @ (mforall_ind @ (^[Y0 : mu]: (mimplies @ (god @ Y0) @ (essence @ god @ Y0))))))),
% 0.20/0.42 inference(fool_elimination,[],[f46])).
% 0.20/0.42 thf(f46,plain,(
% 0.20/0.42 (mvalid @ (mforall_ind @ (^[X0 : mu] : (mimplies @ (god @ X0) @ (essence @ god @ X0)))))),
% 0.20/0.42 inference(rectify,[],[f29])).
% 0.20/0.42 thf(f29,axiom,(
% 0.20/0.42 (mvalid @ (mforall_ind @ (^[X0 : mu] : (mimplies @ (god @ X0) @ (essence @ god @ X0)))))),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thmT2)).
% 0.20/0.42 thf(f195,plain,(
% 0.20/0.42 ( ! [X0 : $i,X1 : mu > $i > $o] : (($true = ((essence @ X1 @ (sK3 @ X0) @ (sK2 @ X0)) => (!! @ $i @ (^[Y0 : $i]: ((~ (rel @ (sK2 @ X0) @ Y0)) | (?? @ mu @ (^[Y1 : mu]: (X1 @ Y1 @ Y0))))))))) )),
% 0.20/0.42 inference(beta_eta_normalization,[],[f194])).
% 0.20/0.42 thf(f194,plain,(
% 0.20/0.42 ( ! [X0 : $i,X1 : mu > $i > $o] : (($true = ((^[Y0 : mu > $i > $o]: ((essence @ Y0 @ (sK3 @ X0) @ (sK2 @ X0)) => (!! @ $i @ (^[Y1 : $i]: ((~ (rel @ (sK2 @ X0) @ Y1)) | (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))) @ X1))) )),
% 0.20/0.42 inference(pi_clausification,[],[f193])).
% 0.20/0.42 thf(f193,plain,(
% 0.20/0.42 ( ! [X0 : $i] : (($true = (!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((essence @ Y0 @ (sK3 @ X0) @ (sK2 @ X0)) => (!! @ $i @ (^[Y1 : $i]: ((~ (rel @ (sK2 @ X0) @ Y1)) | (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1))))))))))) )),
% 0.20/0.42 inference(boolean_simplification,[],[f192])).
% 0.20/0.42 thf(f192,plain,(
% 0.20/0.42 ( ! [X0 : $i] : (($true = ($true => (!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((essence @ Y0 @ (sK3 @ X0) @ (sK2 @ X0)) => (!! @ $i @ (^[Y1 : $i]: ((~ (rel @ (sK2 @ X0) @ Y1)) | (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))))))) )),
% 0.20/0.42 inference(beta_eta_normalization,[],[f191])).
% 0.20/0.42 thf(f191,plain,(
% 0.20/0.42 ( ! [X0 : $i] : (($true = ($true => ((^[Y0 : mu]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((essence @ Y2 @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel @ Y1 @ Y3)) | (?? @ mu @ (^[Y4 : mu]: (Y2 @ Y4 @ Y3)))))))))))) @ (sK3 @ X0) @ (sK2 @ X0))))) )),
% 0.20/0.42 inference(superposition,[],[f154,f190])).
% 0.20/0.42 thf(f190,plain,(
% 0.20/0.42 ( ! [X1 : $i] : (($true = (positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((essence @ Y2 @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel @ Y1 @ Y3)) | (?? @ mu @ (^[Y4 : mu]: (Y2 @ Y4 @ Y3)))))))))))) @ X1))) )),
% 0.20/0.42 inference(pi_clausification,[],[f131])).
% 0.20/0.42 thf(f131,plain,(
% 0.20/0.42 ($true = (!! @ $i @ (positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((essence @ Y2 @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel @ Y1 @ Y3)) | (?? @ mu @ (^[Y4 : mu]: (Y2 @ Y4 @ Y3)))))))))))))))),
% 0.20/0.42 inference(beta_eta_normalization,[],[f126])).
% 0.20/0.42 thf(f126,plain,(
% 0.20/0.42 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ (positive @ (^[Y0 : mu]: ((^[Y1 : (mu > $i > $o) > $i > $o]: ((^[Y2 : $i]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : mu > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) => (Y3 @ Y4))))))) @ (essence @ Y1 @ Y0) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y2 @ Y4 @ Y5)) | (Y3 @ Y5))))))))) @ rel @ ((^[Y2 : mu > $i > $o]: ((^[Y3 : $i]: (?? @ mu @ (^[Y4 : mu]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : mu]: (Y1 @ Y2)))))))))))),
% 0.20/0.42 inference(definition_unfolding,[],[f110,f96,f123])).
% 0.20/0.42 thf(f123,plain,(
% 0.20/0.42 (necessary_existence = (^[Y0 : mu]: ((^[Y1 : (mu > $i > $o) > $i > $o]: ((^[Y2 : $i]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : mu > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) => (Y3 @ Y4))))))) @ (essence @ Y1 @ Y0) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y2 @ Y4 @ Y5)) | (Y3 @ Y5))))))))) @ rel @ ((^[Y2 : mu > $i > $o]: ((^[Y3 : $i]: (?? @ mu @ (^[Y4 : mu]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : mu]: (Y1 @ Y2)))))))))),
% 0.20/0.42 inference(definition_unfolding,[],[f104,f91,f95,f120,f103])).
% 0.20/0.42 thf(f104,plain,(
% 0.20/0.42 (necessary_existence = (^[Y0 : mu]: (mforall_indset @ (^[Y1 : mu > $i > $o]: (mimplies @ (essence @ Y1 @ Y0) @ (mbox @ (mexists_ind @ (^[Y2 : mu]: (Y1 @ Y2)))))))))),
% 0.20/0.42 inference(cnf_transformation,[],[f42])).
% 0.20/0.42 thf(f42,plain,(
% 0.20/0.42 (necessary_existence = (^[Y0 : mu]: (mforall_indset @ (^[Y1 : mu > $i > $o]: (mimplies @ (essence @ Y1 @ Y0) @ (mbox @ (mexists_ind @ (^[Y2 : mu]: (Y1 @ Y2)))))))))),
% 0.20/0.42 inference(fool_elimination,[],[f41])).
% 0.20/0.42 thf(f41,plain,(
% 0.20/0.42 (necessary_existence = (^[X0 : mu] : (mforall_indset @ (^[X1 : mu > $i > $o] : (mimplies @ (essence @ X1 @ X0) @ (mbox @ (mexists_ind @ (^[X2 : mu] : (X1 @ X2)))))))))),
% 0.20/0.42 inference(rectify,[],[f26])).
% 0.20/0.42 thf(f26,axiom,(
% 0.20/0.42 (necessary_existence = (^[X0 : mu] : (mforall_indset @ (^[X3 : mu > $i > $o] : (mimplies @ (essence @ X3 @ X0) @ (mbox @ (mexists_ind @ (^[X1 : mu] : (X3 @ X1)))))))))),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',defD3)).
% 0.20/0.42 thf(f110,plain,(
% 0.20/0.42 ((mvalid @ (positive @ necessary_existence)) = $true)),
% 0.20/0.42 inference(cnf_transformation,[],[f76])).
% 0.20/0.42 thf(f76,plain,(
% 0.20/0.42 ((mvalid @ (positive @ necessary_existence)) = $true)),
% 0.20/0.42 inference(fool_elimination,[],[f75])).
% 0.20/0.42 thf(f75,plain,(
% 0.20/0.42 (mvalid @ (positive @ necessary_existence))),
% 0.20/0.42 inference(rectify,[],[f27])).
% 0.20/0.42 thf(f27,axiom,(
% 0.20/0.42 (mvalid @ (positive @ necessary_existence))),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axA5)).
% 0.20/0.42 thf(f154,plain,(
% 0.20/0.42 ( ! [X2 : mu > $i > $o,X1 : $i] : (($true = ((positive @ X2 @ (sK2 @ X1)) => (X2 @ (sK3 @ X1) @ (sK2 @ X1))))) )),
% 0.20/0.42 inference(beta_eta_normalization,[],[f153])).
% 0.20/0.42 thf(f153,plain,(
% 0.20/0.42 ( ! [X2 : mu > $i > $o,X1 : $i] : (($true = ((^[Y0 : mu > $i > $o]: ((positive @ Y0 @ (sK2 @ X1)) => (Y0 @ (sK3 @ X1) @ (sK2 @ X1)))) @ X2))) )),
% 0.20/0.42 inference(pi_clausification,[],[f148])).
% 0.20/0.42 % SZS output end Proof for theBenchmark
% 0.20/0.42 % (3094)------------------------------
% 0.20/0.42 % (3094)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (3094)Termination reason: Refutation
% 0.20/0.42
% 0.20/0.42 % (3094)Memory used [KB]: 5884
% 0.20/0.42 % (3094)Time elapsed: 0.028 s
% 0.20/0.42 % (3094)Instructions burned: 34 (million)
% 0.20/0.42 % (3094)------------------------------
% 0.20/0.42 % (3094)------------------------------
% 0.20/0.42 % (3082)Success in time 0.052 s
% 0.20/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------