TSTP Solution File: PHI003^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : PHI003^2 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n027.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 02:18:41 EDT 2024
% Result : Theorem 0.14s 0.40s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : PHI003^2 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n027.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 14:48:53 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/sandbox/benchmark/theBenchmark.p
% 0.14/0.36 % (19277)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)
% 0.14/0.36 % (19277)Instruction limit reached!
% 0.14/0.36 % (19277)------------------------------
% 0.14/0.36 % (19277)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.36 % (19277)Termination reason: Unknown
% 0.14/0.36 % (19277)Termination phase: Preprocessing 3
% 0.14/0.36
% 0.14/0.36 % (19277)Memory used [KB]: 1023
% 0.14/0.36 % (19277)Time elapsed: 0.002 s
% 0.14/0.36 % (19277)Instructions burned: 3 (million)
% 0.14/0.36 % (19277)------------------------------
% 0.14/0.36 % (19277)------------------------------
% 0.14/0.37 % (19273)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 % (19274)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 % (19276)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37 % (19279)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 % (19278)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 % (19280)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 % (19276)Instruction limit reached!
% 0.14/0.37 % (19276)------------------------------
% 0.14/0.37 % (19276)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (19276)Termination reason: Unknown
% 0.14/0.37 % (19276)Termination phase: Property scanning
% 0.14/0.37
% 0.14/0.37 % (19276)Memory used [KB]: 1023
% 0.14/0.37 % (19276)Time elapsed: 0.004 s
% 0.14/0.37 % (19276)Instructions burned: 3 (million)
% 0.14/0.37 % (19276)------------------------------
% 0.14/0.37 % (19276)------------------------------
% 0.14/0.37 % (19275)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 % (19280)Instruction limit reached!
% 0.14/0.37 % (19280)------------------------------
% 0.14/0.37 % (19280)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (19280)Termination reason: Unknown
% 0.14/0.37 % (19280)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (19280)Memory used [KB]: 1023
% 0.14/0.37 % (19280)Time elapsed: 0.003 s
% 0.14/0.37 % (19280)Instructions burned: 3 (million)
% 0.14/0.37 % (19280)------------------------------
% 0.14/0.37 % (19280)------------------------------
% 0.14/0.37 % (19274)Instruction limit reached!
% 0.14/0.37 % (19274)------------------------------
% 0.14/0.37 % (19274)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (19274)Termination reason: Unknown
% 0.14/0.37 % (19274)Termination phase: Property scanning
% 0.14/0.37
% 0.14/0.37 % (19274)Memory used [KB]: 1023
% 0.14/0.37 % (19274)Time elapsed: 0.004 s
% 0.14/0.37 % (19274)Instructions burned: 5 (million)
% 0.14/0.37 % (19274)------------------------------
% 0.14/0.37 % (19274)------------------------------
% 0.14/0.37 % (19281)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)
% 0.14/0.37 % (19278)Refutation not found, incomplete strategy
% 0.14/0.37 % (19278)------------------------------
% 0.14/0.37 % (19278)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (19278)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.37
% 0.14/0.37
% 0.14/0.37 % (19278)Memory used [KB]: 5500
% 0.14/0.37 % (19278)Time elapsed: 0.005 s
% 0.14/0.37 % (19278)Instructions burned: 6 (million)
% 0.14/0.37 % (19278)------------------------------
% 0.14/0.37 % (19278)------------------------------
% 0.14/0.38 % (19275)Refutation not found, incomplete strategy
% 0.14/0.38 % (19275)------------------------------
% 0.14/0.38 % (19275)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (19275)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.38
% 0.14/0.38
% 0.14/0.38 % (19275)Memory used [KB]: 5628
% 0.14/0.38 % (19275)Time elapsed: 0.010 s
% 0.14/0.38 % (19275)Instructions burned: 10 (million)
% 0.14/0.38 % (19275)------------------------------
% 0.14/0.38 % (19275)------------------------------
% 0.14/0.38 % (19279)Instruction limit reached!
% 0.14/0.38 % (19279)------------------------------
% 0.14/0.38 % (19279)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (19279)Termination reason: Unknown
% 0.14/0.38 % (19279)Termination phase: Saturation
% 0.14/0.38
% 0.14/0.38 % (19279)Memory used [KB]: 5628
% 0.14/0.38 % (19279)Time elapsed: 0.013 s
% 0.14/0.38 % (19279)Instructions burned: 18 (million)
% 0.14/0.38 % (19279)------------------------------
% 0.14/0.38 % (19279)------------------------------
% 0.14/0.39 % (19281)Instruction limit reached!
% 0.14/0.39 % (19281)------------------------------
% 0.14/0.39 % (19281)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (19281)Termination reason: Unknown
% 0.14/0.39 % (19281)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (19281)Memory used [KB]: 5884
% 0.14/0.39 % (19281)Time elapsed: 0.015 s
% 0.14/0.39 % (19281)Instructions burned: 38 (million)
% 0.14/0.39 % (19281)------------------------------
% 0.14/0.39 % (19281)------------------------------
% 0.14/0.39 % (19282)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 % (19284)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 % (19283)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 % (19283)Instruction limit reached!
% 0.14/0.39 % (19283)------------------------------
% 0.14/0.39 % (19283)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (19283)Termination reason: Unknown
% 0.14/0.39 % (19283)Termination phase: Property scanning
% 0.14/0.39
% 0.14/0.39 % (19283)Memory used [KB]: 1023
% 0.14/0.39 % (19283)Time elapsed: 0.003 s
% 0.14/0.39 % (19283)Instructions burned: 3 (million)
% 0.14/0.39 % (19283)------------------------------
% 0.14/0.39 % (19283)------------------------------
% 0.14/0.39 % (19285)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 % (19285)Instruction limit reached!
% 0.14/0.39 % (19285)------------------------------
% 0.14/0.39 % (19285)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (19285)Termination reason: Unknown
% 0.14/0.39 % (19285)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (19285)Memory used [KB]: 1023
% 0.14/0.39 % (19285)Time elapsed: 0.006 s
% 0.14/0.39 % (19285)Instructions burned: 8 (million)
% 0.14/0.39 % (19285)------------------------------
% 0.14/0.39 % (19285)------------------------------
% 0.14/0.39 % (19282)Refutation not found, incomplete strategy
% 0.14/0.39 % (19282)------------------------------
% 0.14/0.39 % (19282)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (19286)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 % (19282)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.39
% 0.14/0.39
% 0.14/0.39 % (19282)Memory used [KB]: 5628
% 0.14/0.39 % (19282)Time elapsed: 0.010 s
% 0.14/0.39 % (19282)Instructions burned: 12 (million)
% 0.14/0.39 % (19282)------------------------------
% 0.14/0.39 % (19282)------------------------------
% 0.14/0.39 % (19291)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)
% 0.14/0.40 % (19284)First to succeed.
% 0.14/0.40 % (19288)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 % (19291)Instruction limit reached!
% 0.14/0.40 % (19291)------------------------------
% 0.14/0.40 % (19291)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (19291)Termination reason: Unknown
% 0.14/0.40 % (19291)Termination phase: Property scanning
% 0.14/0.40
% 0.14/0.40 % (19291)Memory used [KB]: 1023
% 0.14/0.40 % (19291)Time elapsed: 0.002 s
% 0.14/0.40 % (19291)Instructions burned: 4 (million)
% 0.14/0.40 % (19291)------------------------------
% 0.14/0.40 % (19291)------------------------------
% 0.14/0.40 % (19288)Instruction limit reached!
% 0.14/0.40 % (19288)------------------------------
% 0.14/0.40 % (19288)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (19288)Termination reason: Unknown
% 0.14/0.40 % (19288)Termination phase: SInE selection
% 0.14/0.40
% 0.14/0.40 % (19288)Memory used [KB]: 1023
% 0.14/0.40 % (19288)Time elapsed: 0.004 s
% 0.14/0.40 % (19288)Instructions burned: 3 (million)
% 0.14/0.40 % (19288)------------------------------
% 0.14/0.40 % (19288)------------------------------
% 0.14/0.40 % (19284)Refutation found. Thanks to Tanya!
% 0.14/0.40 % SZS status Theorem for theBenchmark
% 0.14/0.40 % SZS output start Proof for theBenchmark
% 0.14/0.40 thf(type_def_5, type, mu: $tType).
% 0.14/0.40 thf(func_def_0, type, mu: $tType).
% 0.14/0.40 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.14/0.40 thf(func_def_2, type, mtrue: $i > $o).
% 0.14/0.40 thf(func_def_3, type, mfalse: $i > $o).
% 0.14/0.40 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_6, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_7, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_8, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_9, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_10, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_11, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_12, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_13, type, mforall_indset: ((mu > $i > $o) > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_14, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_15, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_16, type, mexists_indset: ((mu > $i > $o) > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_17, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_18, type, mbox_generic: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_19, type, mdia_generic: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_20, type, rel: $i > $i > $o).
% 0.14/0.40 thf(func_def_21, type, mbox: ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_22, type, mdia: ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_23, type, mvalid: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_24, type, minvalid: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_25, type, positive: (mu > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_26, type, god: mu > $i > $o).
% 0.14/0.40 thf(func_def_44, type, ph1: !>[X0: $tType]:(X0)).
% 0.14/0.40 thf(func_def_45, type, sK2: $i > $i).
% 0.14/0.40 thf(f137,plain,(
% 0.14/0.40 $false),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f135])).
% 0.14/0.40 thf(f135,plain,(
% 0.14/0.40 ($false = $true)),
% 0.14/0.40 inference(superposition,[],[f121,f132])).
% 0.14/0.40 thf(f132,plain,(
% 0.14/0.40 ($false = (?? @ $i @ (^[Y0 : $i]: ((?? @ mu @ (^[Y1 : mu]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))))) & (rel @ sK3 @ Y0)))))),
% 0.14/0.40 inference(beta_eta_normalization,[],[f131])).
% 0.14/0.40 thf(f131,plain,(
% 0.14/0.40 (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ mu @ (^[Y2 : mu]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((positive @ Y3 @ Y1) => (Y3 @ Y2 @ Y1)))))) & (rel @ Y0 @ Y1))))) @ sK3) = $false)),
% 0.14/0.40 inference(sigma_clausification,[],[f124])).
% 0.14/0.40 thf(f124,plain,(
% 0.14/0.40 ($false = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ mu @ (^[Y2 : mu]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((positive @ Y3 @ Y1) => (Y3 @ Y2 @ Y1)))))) & (rel @ Y0 @ Y1)))))))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f111])).
% 0.14/0.40 thf(f111,plain,(
% 0.14/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ mu @ (^[Y2 : mu]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((positive @ Y3 @ Y1) => (Y3 @ Y2 @ Y1)))))) & (rel @ Y0 @ Y1))))))) = $true)),
% 0.14/0.40 inference(beta_eta_normalization,[],[f108])).
% 0.14/0.40 thf(f108,plain,(
% 0.14/0.40 ((~ ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) & (Y0 @ Y2 @ 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)))))) = $true)),
% 0.14/0.40 inference(definition_unfolding,[],[f92,f82,f105,f84,f106])).
% 0.14/0.40 thf(f106,plain,(
% 0.14/0.40 (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))))))),
% 0.14/0.40 inference(definition_unfolding,[],[f85,f91,f80])).
% 0.14/0.40 thf(f80,plain,(
% 0.14/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f51])).
% 0.14/0.40 thf(f51,plain,(
% 0.14/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.14/0.40 inference(fool_elimination,[],[f50])).
% 0.14/0.40 thf(f50,plain,(
% 0.14/0.40 (mimplies = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) => (X1 @ X2))))),
% 0.14/0.40 inference(rectify,[],[f7])).
% 0.14/0.40 thf(f7,axiom,(
% 0.14/0.40 (mimplies = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) => (X4 @ X2))))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.14/0.40 thf(f91,plain,(
% 0.14/0.40 (mforall_indset = (^[Y0 : (mu > $i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f30])).
% 0.14/0.40 thf(f30,plain,(
% 0.14/0.40 (mforall_indset = (^[Y0 : (mu > $i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.14/0.40 inference(fool_elimination,[],[f29])).
% 0.14/0.40 thf(f29,plain,(
% 0.14/0.40 (mforall_indset = (^[X0 : (mu > $i > $o) > $i > $o, X1 : $i] : (! [X2 : mu > $i > $o] : (X0 @ X2 @ X1))))),
% 0.14/0.40 inference(rectify,[],[f12])).
% 0.14/0.40 thf(f12,axiom,(
% 0.14/0.40 (mforall_indset = (^[X3 : (mu > $i > $o) > $i > $o, X2 : $i] : (! [X0 : mu > $i > $o] : (X3 @ X0 @ X2))))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_indset)).
% 0.14/0.40 thf(f85,plain,(
% 0.14/0.40 (god = (^[Y0 : mu]: (mforall_indset @ (^[Y1 : mu > $i > $o]: (mimplies @ (positive @ Y1) @ (Y1 @ Y0))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f77])).
% 0.14/0.40 thf(f77,plain,(
% 0.14/0.40 (god = (^[Y0 : mu]: (mforall_indset @ (^[Y1 : mu > $i > $o]: (mimplies @ (positive @ Y1) @ (Y1 @ Y0))))))),
% 0.14/0.40 inference(fool_elimination,[],[f76])).
% 0.14/0.40 thf(f76,plain,(
% 0.14/0.40 (god = (^[X0 : mu] : (mforall_indset @ (^[X1 : mu > $i > $o] : (mimplies @ (positive @ X1) @ (X1 @ X0))))))),
% 0.14/0.40 inference(rectify,[],[f23])).
% 0.14/0.40 thf(f23,axiom,(
% 0.14/0.40 (god = (^[X0 : mu] : (mforall_indset @ (^[X3 : mu > $i > $o] : (mimplies @ (positive @ X3) @ (X3 @ X0))))))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',defD1)).
% 0.14/0.40 thf(f84,plain,(
% 0.14/0.40 (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f47])).
% 0.14/0.40 thf(f47,plain,(
% 0.14/0.40 (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.14/0.40 inference(fool_elimination,[],[f46])).
% 0.14/0.40 thf(f46,plain,(
% 0.14/0.40 (mexists_ind = (^[X0 : mu > $i > $o, X1 : $i] : (? [X2 : mu] : (X0 @ X2 @ X1))))),
% 0.14/0.40 inference(rectify,[],[f14])).
% 0.14/0.40 thf(f14,axiom,(
% 0.14/0.40 (mexists_ind = (^[X3 : mu > $i > $o, X2 : $i] : (? [X0 : mu] : (X3 @ X0 @ X2))))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_ind)).
% 0.14/0.40 thf(f105,plain,(
% 0.14/0.40 (mdia = ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) & (Y0 @ Y2 @ Y3))))))))) @ rel))),
% 0.14/0.40 inference(definition_unfolding,[],[f96,f78])).
% 0.14/0.40 thf(f78,plain,(
% 0.14/0.40 (mdia_generic = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) & (Y0 @ Y2 @ Y3))))))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f71])).
% 0.14/0.40 thf(f71,plain,(
% 0.14/0.40 (mdia_generic = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) & (Y0 @ Y2 @ Y3))))))))))),
% 0.14/0.40 inference(fool_elimination,[],[f70])).
% 0.14/0.40 thf(f70,plain,(
% 0.14/0.40 ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (? [X3] : ((X0 @ X2 @ X3) & (X1 @ X3)))) = mdia_generic)),
% 0.14/0.40 inference(rectify,[],[f18])).
% 0.14/0.40 thf(f18,axiom,(
% 0.14/0.40 ((^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (? [X7] : ((X6 @ X2 @ X7) & (X3 @ X7)))) = mdia_generic)),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_generic)).
% 0.14/0.40 thf(f96,plain,(
% 0.14/0.40 (mdia = (mdia_generic @ rel))),
% 0.14/0.40 inference(cnf_transformation,[],[f67])).
% 0.14/0.40 thf(f67,plain,(
% 0.14/0.40 (mdia = (mdia_generic @ rel))),
% 0.14/0.40 inference(fool_elimination,[],[f20])).
% 0.14/0.40 thf(f20,axiom,(
% 0.14/0.40 (mdia = (mdia_generic @ rel))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia)).
% 0.14/0.40 thf(f82,plain,(
% 0.14/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.40 inference(cnf_transformation,[],[f63])).
% 0.14/0.40 thf(f63,plain,(
% 0.14/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.40 inference(fool_elimination,[],[f62])).
% 0.14/0.40 thf(f62,plain,(
% 0.14/0.40 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.14/0.40 inference(rectify,[],[f21])).
% 0.14/0.40 thf(f21,axiom,(
% 0.14/0.40 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.14/0.40 thf(f92,plain,(
% 0.14/0.40 ((~ (mvalid @ (mdia @ (mexists_ind @ (^[Y0 : mu]: (god @ Y0)))))) = $true)),
% 0.14/0.40 inference(cnf_transformation,[],[f66])).
% 0.14/0.40 thf(f66,plain,(
% 0.14/0.40 ((~ (mvalid @ (mdia @ (mexists_ind @ (^[Y0 : mu]: (god @ Y0)))))) = $true)),
% 0.14/0.40 inference(fool_elimination,[],[f65])).
% 0.14/0.40 thf(f65,plain,(
% 0.14/0.40 ~(mvalid @ (mdia @ (mexists_ind @ (^[X0 : mu] : (god @ X0)))))),
% 0.14/0.40 inference(rectify,[],[f27])).
% 0.14/0.40 thf(f27,negated_conjecture,(
% 0.14/0.40 ~(mvalid @ (mdia @ (mexists_ind @ (^[X0 : mu] : (god @ X0)))))),
% 0.14/0.40 inference(negated_conjecture,[],[f26])).
% 0.14/0.40 thf(f26,conjecture,(
% 0.14/0.40 (mvalid @ (mdia @ (mexists_ind @ (^[X0 : mu] : (god @ X0)))))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',corC)).
% 0.14/0.40 thf(f121,plain,(
% 0.14/0.40 ( ! [X0 : $i] : (((?? @ $i @ (^[Y0 : $i]: ((?? @ mu @ (^[Y1 : mu]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))))) & (rel @ X0 @ Y0)))) = $true)) )),
% 0.14/0.40 inference(boolean_simplification,[],[f120])).
% 0.14/0.40 thf(f120,plain,(
% 0.14/0.40 ( ! [X0 : $i] : ((($true => (?? @ $i @ (^[Y0 : $i]: ((?? @ mu @ (^[Y1 : mu]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))))) & (rel @ X0 @ Y0))))) = $true)) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f119])).
% 0.14/0.40 thf(f119,plain,(
% 0.14/0.40 ( ! [X0 : $i] : (($true = ($true => (?? @ $i @ (^[Y0 : $i]: ((?? @ mu @ (^[Y1 : mu]: ((^[Y2 : mu]: ((^[Y3 : $i]: (!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: ((positive @ Y4 @ Y3) => (Y4 @ Y2 @ Y3))))))) @ Y1 @ Y0))) & (rel @ X0 @ Y0))))))) )),
% 0.14/0.40 inference(superposition,[],[f117,f113])).
% 0.14/0.40 thf(f113,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = (positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y1) => (Y2 @ Y0 @ Y1))))))) @ X1))) )),
% 0.14/0.40 inference(pi_clausification,[],[f110])).
% 0.14/0.40 thf(f110,plain,(
% 0.14/0.40 ((!! @ $i @ (positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y1) => (Y2 @ Y0 @ Y1))))))))) = $true)),
% 0.14/0.40 inference(beta_eta_normalization,[],[f109])).
% 0.14/0.40 thf(f109,plain,(
% 0.14/0.40 (((^[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))))))) @ (positive @ Y1) @ (Y1 @ Y0))))))) = $true)),
% 0.14/0.40 inference(definition_unfolding,[],[f101,f82,f106])).
% 0.14/0.40 thf(f101,plain,(
% 0.14/0.40 ((mvalid @ (positive @ god)) = $true)),
% 0.14/0.40 inference(cnf_transformation,[],[f69])).
% 0.14/0.40 thf(f69,plain,(
% 0.14/0.40 ((mvalid @ (positive @ god)) = $true)),
% 0.14/0.40 inference(fool_elimination,[],[f68])).
% 0.14/0.40 thf(f68,plain,(
% 0.14/0.40 (mvalid @ (positive @ god))),
% 0.14/0.40 inference(rectify,[],[f24])).
% 0.14/0.40 thf(f24,axiom,(
% 0.14/0.40 (mvalid @ (positive @ god))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axA3)).
% 0.14/0.40 thf(f117,plain,(
% 0.14/0.40 ( ! [X2 : mu > $i > $o,X1 : $i] : (($true = ((positive @ X2 @ X1) => (?? @ $i @ (^[Y0 : $i]: ((?? @ mu @ (^[Y1 : mu]: (X2 @ Y1 @ Y0))) & (rel @ X1 @ Y0))))))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f116])).
% 0.14/0.40 thf(f116,plain,(
% 0.14/0.40 ( ! [X2 : mu > $i > $o,X1 : $i] : ((((^[Y0 : mu > $i > $o]: ((positive @ Y0 @ X1) => (?? @ $i @ (^[Y1 : $i]: ((?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1))) & (rel @ X1 @ Y1)))))) @ X2) = $true)) )),
% 0.14/0.40 inference(pi_clausification,[],[f115])).
% 0.14/0.40 thf(f115,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((positive @ Y0 @ X1) => (?? @ $i @ (^[Y1 : $i]: ((?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1))) & (rel @ X1 @ Y1))))))) = $true)) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f114])).
% 0.14/0.40 thf(f114,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ Y0) => (?? @ $i @ (^[Y2 : $i]: ((?? @ mu @ (^[Y3 : mu]: (Y1 @ Y3 @ Y2))) & (rel @ Y0 @ Y2)))))))) @ X1))) )),
% 0.14/0.40 inference(pi_clausification,[],[f112])).
% 0.14/0.40 thf(f112,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ Y0) => (?? @ $i @ (^[Y2 : $i]: ((?? @ mu @ (^[Y3 : mu]: (Y1 @ Y3 @ Y2))) & (rel @ Y0 @ Y2))))))))) = $true)),
% 0.14/0.40 inference(beta_eta_normalization,[],[f107])).
% 0.14/0.40 thf(f107,plain,(
% 0.14/0.40 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : (mu > $i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: ((Y1 @ Y3) => (Y2 @ Y3))))))) @ (positive @ Y0) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) & (Y1 @ Y3 @ Y4))))))))) @ rel @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (?? @ mu @ (^[Y3 : mu]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : mu]: (Y0 @ Y1)))))))) = $true)),
% 0.14/0.40 inference(definition_unfolding,[],[f81,f82,f91,f80,f105,f84])).
% 0.14/0.40 thf(f81,plain,(
% 0.14/0.40 ((mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mimplies @ (positive @ Y0) @ (mdia @ (mexists_ind @ (^[Y1 : mu]: (Y0 @ Y1)))))))) = $true)),
% 0.14/0.40 inference(cnf_transformation,[],[f53])).
% 0.14/0.40 thf(f53,plain,(
% 0.14/0.40 ((mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mimplies @ (positive @ Y0) @ (mdia @ (mexists_ind @ (^[Y1 : mu]: (Y0 @ Y1)))))))) = $true)),
% 0.14/0.40 inference(fool_elimination,[],[f52])).
% 0.14/0.40 thf(f52,plain,(
% 0.14/0.40 (mvalid @ (mforall_indset @ (^[X0 : mu > $i > $o] : (mimplies @ (positive @ X0) @ (mdia @ (mexists_ind @ (^[X1 : mu] : (X0 @ X1))))))))),
% 0.14/0.40 inference(rectify,[],[f25])).
% 0.14/0.40 thf(f25,axiom,(
% 0.14/0.40 (mvalid @ (mforall_indset @ (^[X3 : mu > $i > $o] : (mimplies @ (positive @ X3) @ (mdia @ (mexists_ind @ (^[X0 : mu] : (X3 @ X0))))))))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thmT1)).
% 0.14/0.40 % SZS output end Proof for theBenchmark
% 0.14/0.40 % (19284)------------------------------
% 0.14/0.40 % (19284)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (19284)Termination reason: Refutation
% 0.14/0.40
% 0.14/0.40 % (19284)Memory used [KB]: 5628
% 0.14/0.40 % (19284)Time elapsed: 0.013 s
% 0.14/0.40 % (19284)Instructions burned: 13 (million)
% 0.14/0.40 % (19284)------------------------------
% 0.14/0.40 % (19284)------------------------------
% 0.14/0.40 % (19272)Success in time 0.034 s
% 0.14/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------