TSTP Solution File: SYO497^6 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO497^6 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n019.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 09:05:27 EDT 2024
% Result : Theorem 0.21s 0.40s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO497^6 : TPTP v8.2.0. Released v4.0.0.
% 0.14/0.14 % 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
% 0.15/0.34 % Computer : n019.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
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 20 09:40:53 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 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/sandbox/benchmark/theBenchmark.p
% 0.21/0.36 % (24580)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.37 % (24580)Instruction limit reached!
% 0.21/0.37 % (24580)------------------------------
% 0.21/0.37 % (24580)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (24580)Termination reason: Unknown
% 0.21/0.37 % (24580)Termination phase: shuffling
% 0.21/0.37
% 0.21/0.37 % (24580)Memory used [KB]: 1023
% 0.21/0.37 % (24580)Time elapsed: 0.003 s
% 0.21/0.37 % (24580)Instructions burned: 4 (million)
% 0.21/0.37 % (24580)------------------------------
% 0.21/0.37 % (24580)------------------------------
% 0.21/0.37 % (24577)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.21/0.37 % (24579)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)
% 0.21/0.37 % (24578)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)
% 0.21/0.37 % (24581)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)
% 0.21/0.37 % (24582)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)
% 0.21/0.37 % (24583)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.37 % (24584)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)
% 0.21/0.37 % (24581)Instruction limit reached!
% 0.21/0.37 % (24581)------------------------------
% 0.21/0.37 % (24581)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (24581)Termination reason: Unknown
% 0.21/0.37 % (24581)Termination phase: shuffling
% 0.21/0.37
% 0.21/0.37 % (24581)Memory used [KB]: 1023
% 0.21/0.37 % (24581)Time elapsed: 0.003 s
% 0.21/0.37 % (24581)Instructions burned: 2 (million)
% 0.21/0.37 % (24581)------------------------------
% 0.21/0.37 % (24581)------------------------------
% 0.21/0.37 % (24584)Instruction limit reached!
% 0.21/0.37 % (24584)------------------------------
% 0.21/0.37 % (24584)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (24584)Termination reason: Unknown
% 0.21/0.37 % (24584)Termination phase: shuffling
% 0.21/0.37
% 0.21/0.37 % (24584)Memory used [KB]: 1023
% 0.21/0.37 % (24584)Time elapsed: 0.004 s
% 0.21/0.37 % (24584)Instructions burned: 3 (million)
% 0.21/0.37 % (24584)------------------------------
% 0.21/0.37 % (24584)------------------------------
% 0.21/0.37 % (24578)Instruction limit reached!
% 0.21/0.37 % (24578)------------------------------
% 0.21/0.37 % (24578)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (24578)Termination reason: Unknown
% 0.21/0.37 % (24578)Termination phase: Property scanning
% 0.21/0.37
% 0.21/0.37 % (24578)Memory used [KB]: 1023
% 0.21/0.37 % (24578)Time elapsed: 0.004 s
% 0.21/0.37 % (24578)Instructions burned: 5 (million)
% 0.21/0.37 % (24578)------------------------------
% 0.21/0.37 % (24578)------------------------------
% 0.21/0.37 % (24585)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)
% 0.21/0.38 % (24582)Refutation not found, incomplete strategy
% 0.21/0.38 % (24582)------------------------------
% 0.21/0.38 % (24582)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (24582)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.38
% 0.21/0.38
% 0.21/0.38 % (24582)Memory used [KB]: 5628
% 0.21/0.38 % (24582)Time elapsed: 0.012 s
% 0.21/0.38 % (24582)Instructions burned: 15 (million)
% 0.21/0.38 % (24582)------------------------------
% 0.21/0.38 % (24582)------------------------------
% 0.21/0.38 % (24583)Instruction limit reached!
% 0.21/0.38 % (24583)------------------------------
% 0.21/0.38 % (24583)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (24583)Termination reason: Unknown
% 0.21/0.38 % (24583)Termination phase: Saturation
% 0.21/0.38
% 0.21/0.38 % (24583)Memory used [KB]: 5756
% 0.21/0.38 % (24583)Time elapsed: 0.013 s
% 0.21/0.38 % (24583)Instructions burned: 19 (million)
% 0.21/0.38 % (24583)------------------------------
% 0.21/0.38 % (24583)------------------------------
% 0.21/0.39 % (24579)Instruction limit reached!
% 0.21/0.39 % (24579)------------------------------
% 0.21/0.39 % (24579)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (24579)Termination reason: Unknown
% 0.21/0.39 % (24579)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (24579)Memory used [KB]: 5756
% 0.21/0.39 % (24579)Time elapsed: 0.018 s
% 0.21/0.39 % (24579)Instructions burned: 27 (million)
% 0.21/0.39 % (24579)------------------------------
% 0.21/0.39 % (24579)------------------------------
% 0.21/0.39 % (24586)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 % (24587)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 % (24585)Instruction limit reached!
% 0.21/0.39 % (24585)------------------------------
% 0.21/0.39 % (24585)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (24585)Termination reason: Unknown
% 0.21/0.39 % (24585)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (24585)Memory used [KB]: 5756
% 0.21/0.39 % (24585)Time elapsed: 0.014 s
% 0.21/0.39 % (24585)Instructions burned: 38 (million)
% 0.21/0.39 % (24585)------------------------------
% 0.21/0.39 % (24585)------------------------------
% 0.21/0.39 % (24588)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 % (24587)Instruction limit reached!
% 0.21/0.39 % (24587)------------------------------
% 0.21/0.39 % (24587)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (24587)Termination reason: Unknown
% 0.21/0.39 % (24587)Termination phase: shuffling
% 0.21/0.39
% 0.21/0.39 % (24587)Memory used [KB]: 1023
% 0.21/0.39 % (24587)Time elapsed: 0.004 s
% 0.21/0.39 % (24587)Instructions burned: 4 (million)
% 0.21/0.39 % (24587)------------------------------
% 0.21/0.39 % (24587)------------------------------
% 0.21/0.39 % (24586)Instruction limit reached!
% 0.21/0.39 % (24586)------------------------------
% 0.21/0.39 % (24586)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (24586)Termination reason: Unknown
% 0.21/0.39 % (24586)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (24586)Memory used [KB]: 5628
% 0.21/0.39 % (24586)Time elapsed: 0.009 s
% 0.21/0.39 % (24586)Instructions burned: 15 (million)
% 0.21/0.39 % (24586)------------------------------
% 0.21/0.39 % (24586)------------------------------
% 0.21/0.39 % (24589)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.39 % (24577)First to succeed.
% 0.21/0.40 % (24590)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 % (24592)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)
% 0.21/0.40 % (24592)Instruction limit reached!
% 0.21/0.40 % (24592)------------------------------
% 0.21/0.40 % (24592)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (24592)Termination reason: Unknown
% 0.21/0.40 % (24592)Termination phase: shuffling
% 0.21/0.40
% 0.21/0.40 % (24592)Memory used [KB]: 1023
% 0.21/0.40 % (24592)Time elapsed: 0.002 s
% 0.21/0.40 % (24592)Instructions burned: 3 (million)
% 0.21/0.40 % (24592)------------------------------
% 0.21/0.40 % (24592)------------------------------
% 0.21/0.40 % (24589)Instruction limit reached!
% 0.21/0.40 % (24589)------------------------------
% 0.21/0.40 % (24589)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (24589)Termination reason: Unknown
% 0.21/0.40 % (24589)Termination phase: Property scanning
% 0.21/0.40
% 0.21/0.40 % (24589)Memory used [KB]: 1023
% 0.21/0.40 % (24589)Time elapsed: 0.006 s
% 0.21/0.40 % (24589)Instructions burned: 8 (million)
% 0.21/0.40 % (24589)------------------------------
% 0.21/0.40 % (24589)------------------------------
% 0.21/0.40 % (24591)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 % (24577)Refutation found. Thanks to Tanya!
% 0.21/0.40 % SZS status Theorem for theBenchmark
% 0.21/0.40 % SZS output start Proof for theBenchmark
% 0.21/0.40 thf(type_def_5, type, mu: $tType).
% 0.21/0.40 thf(func_def_0, type, mu: $tType).
% 0.21/0.40 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.21/0.40 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_15, type, mtrue: $i > $o).
% 0.21/0.40 thf(func_def_16, type, mfalse: $i > $o).
% 0.21/0.40 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.21/0.40 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.21/0.40 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.21/0.40 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.21/0.40 thf(func_def_33, type, rel_s5: $i > $i > $o).
% 0.21/0.40 thf(func_def_34, type, mbox_s5: ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_35, type, mdia_s5: ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_36, type, f: mu > $i > $o).
% 0.21/0.40 thf(func_def_56, type, sK4: mu).
% 0.21/0.40 thf(f520,plain,(
% 0.21/0.40 $false),
% 0.21/0.40 inference(avatar_sat_refutation,[],[f485,f501,f518])).
% 0.21/0.40 thf(f518,plain,(
% 0.21/0.40 ~spl0_1),
% 0.21/0.40 inference(avatar_contradiction_clause,[],[f517])).
% 0.21/0.40 thf(f517,plain,(
% 0.21/0.40 $false | ~spl0_1),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f502])).
% 0.21/0.40 thf(f502,plain,(
% 0.21/0.40 ($true = $false) | ~spl0_1),
% 0.21/0.40 inference(superposition,[],[f465,f197])).
% 0.21/0.40 thf(f197,plain,(
% 0.21/0.40 ((rel_s5 @ sK1 @ sK3) = $true)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f192])).
% 0.21/0.40 thf(f192,plain,(
% 0.21/0.40 ((~ (rel_s5 @ sK1 @ sK3)) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f191])).
% 0.21/0.40 thf(f191,plain,(
% 0.21/0.40 ($false = ((!! @ mu @ (^[Y0 : mu]: (~ (f @ Y0 @ sK3)))) | (~ (rel_s5 @ sK1 @ sK3))))),
% 0.21/0.40 inference(beta_eta_normalization,[],[f190])).
% 0.21/0.40 thf(f190,plain,(
% 0.21/0.40 (((^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: (~ (f @ Y1 @ Y0)))) | (~ (rel_s5 @ sK1 @ Y0)))) @ sK3) = $false)),
% 0.21/0.40 inference(sigma_clausification,[],[f189])).
% 0.21/0.40 thf(f189,plain,(
% 0.21/0.40 ((!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: (~ (f @ Y1 @ Y0)))) | (~ (rel_s5 @ sK1 @ Y0))))) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f177])).
% 0.21/0.40 thf(f177,plain,(
% 0.21/0.40 (((!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: (~ (f @ Y1 @ Y0)))) | (~ (rel_s5 @ sK1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s5 @ Y0 @ Y2))))) | (~ (f @ Y1 @ Y0))))) | (~ (rel_s5 @ sK1 @ Y0))))))) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f176])).
% 0.21/0.40 thf(f176,plain,(
% 0.21/0.40 (((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ mu @ (^[Y1 : mu]: (~ (f @ Y1 @ Y0))))) | (~ (rel_s5 @ sK1 @ Y0))))) | ((!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: (~ (f @ Y1 @ Y0)))) | (~ (rel_s5 @ sK1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s5 @ Y0 @ Y2))))) | (~ (f @ Y1 @ Y0))))) | (~ (rel_s5 @ sK1 @ Y0)))))))) = $false)),
% 0.21/0.40 inference(beta_eta_normalization,[],[f175])).
% 0.21/0.40 thf(f175,plain,(
% 0.21/0.40 (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ mu @ (^[Y2 : mu]: (~ (f @ Y2 @ Y1))))) | (~ (rel_s5 @ Y0 @ Y1))))) | ((!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: (~ (f @ Y2 @ Y1)))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((!! @ $i @ (^[Y3 : $i]: ((f @ Y2 @ Y3) | (~ (rel_s5 @ Y1 @ Y3))))) | (~ (f @ Y2 @ Y1))))) | (~ (rel_s5 @ Y0 @ Y1))))))))) @ sK1) = $false)),
% 0.21/0.40 inference(sigma_clausification,[],[f174])).
% 0.21/0.40 thf(f174,plain,(
% 0.21/0.40 ($true != (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ mu @ (^[Y2 : mu]: (~ (f @ Y2 @ Y1))))) | (~ (rel_s5 @ Y0 @ Y1))))) | ((!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: (~ (f @ Y2 @ Y1)))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((!! @ $i @ (^[Y3 : $i]: ((f @ Y2 @ Y3) | (~ (rel_s5 @ Y1 @ Y3))))) | (~ (f @ Y2 @ Y1))))) | (~ (rel_s5 @ Y0 @ Y1)))))))))))),
% 0.21/0.40 inference(boolean_simplification,[],[f173])).
% 0.21/0.40 thf(f173,plain,(
% 0.21/0.40 ($true != (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ mu @ (^[Y2 : mu]: (~ (f @ Y2 @ Y1))))) | (~ (rel_s5 @ Y0 @ Y1))))) | ((!! @ $i @ (^[Y1 : $i]: ((~ (~ (!! @ mu @ (^[Y2 : mu]: (~ (f @ Y2 @ Y1)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((!! @ $i @ (^[Y3 : $i]: ((f @ Y2 @ Y3) | (~ (rel_s5 @ Y1 @ Y3))))) | (~ (f @ Y2 @ Y1))))) | (~ (rel_s5 @ Y0 @ Y1)))))))))))),
% 0.21/0.40 inference(boolean_simplification,[],[f172])).
% 0.21/0.40 thf(f172,plain,(
% 0.21/0.40 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ mu @ (^[Y2 : mu]: (~ (f @ Y2 @ Y1))))) | (~ (rel_s5 @ Y0 @ Y1))))) | ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (~ (!! @ mu @ (^[Y2 : mu]: (~ (f @ Y2 @ Y1)))))) | (~ (rel_s5 @ Y0 @ Y1))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((!! @ $i @ (^[Y3 : $i]: ((f @ Y2 @ Y3) | (~ (rel_s5 @ Y1 @ Y3))))) | (~ (f @ Y2 @ Y1))))) | (~ (rel_s5 @ Y0 @ Y1)))))))))) != $true)),
% 0.21/0.40 inference(boolean_simplification,[],[f171])).
% 0.21/0.40 thf(f171,plain,(
% 0.21/0.40 ($true != (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ mu @ (^[Y2 : mu]: (~ (f @ Y2 @ Y1))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (~ (!! @ mu @ (^[Y2 : mu]: (~ (f @ Y2 @ Y1)))))) | (~ (rel_s5 @ Y0 @ Y1))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((!! @ $i @ (^[Y3 : $i]: ((f @ Y2 @ Y3) | (~ (rel_s5 @ Y1 @ Y3))))) | (~ (f @ Y2 @ Y1))))) | (~ (rel_s5 @ Y0 @ Y1)))))))))))))),
% 0.21/0.40 inference(beta_eta_normalization,[],[f158])).
% 0.21/0.40 thf(f158,plain,(
% 0.21/0.40 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : mu]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y4 @ Y5) | (Y3 @ Y5))))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y1) @ Y2)))) @ (f @ Y0) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))))) @ (f @ Y0)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ (Y0 @ Y1)))))) @ (^[Y0 : mu]: (f @ Y0))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ (Y0 @ Y1)))))) @ (^[Y0 : mu]: (f @ Y0)))))))),
% 0.21/0.40 inference(definition_unfolding,[],[f120,f132,f149,f148,f123,f112,f149,f123,f157,f153,f123,f153])).
% 0.21/0.40 thf(f153,plain,(
% 0.21/0.40 (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ (Y0 @ Y1)))))))),
% 0.21/0.40 inference(definition_unfolding,[],[f136,f114,f112,f114])).
% 0.21/0.40 thf(f114,plain,(
% 0.21/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f84])).
% 0.21/0.40 thf(f84,plain,(
% 0.21/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.40 inference(fool_elimination,[],[f83])).
% 0.21/0.40 thf(f83,plain,(
% 0.21/0.40 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.21/0.40 inference(rectify,[],[f3])).
% 0.21/0.40 thf(f3,axiom,(
% 0.21/0.40 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.21/0.40 thf(f136,plain,(
% 0.21/0.40 (mexists_ind = (^[Y0 : mu > $i > $o]: (mnot @ (mforall_ind @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f96])).
% 0.21/0.40 thf(f96,plain,(
% 0.21/0.40 (mexists_ind = (^[Y0 : mu > $i > $o]: (mnot @ (mforall_ind @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))))))),
% 0.21/0.40 inference(fool_elimination,[],[f95])).
% 0.21/0.40 thf(f95,plain,(
% 0.21/0.40 ((^[X0 : mu > $i > $o] : (mnot @ (mforall_ind @ (^[X1 : mu] : (mnot @ (X0 @ X1)))))) = mexists_ind)),
% 0.21/0.40 inference(rectify,[],[f12])).
% 0.21/0.40 thf(f12,axiom,(
% 0.21/0.40 ((^[X3 : mu > $i > $o] : (mnot @ (mforall_ind @ (^[X0 : mu] : (mnot @ (X3 @ X0)))))) = mexists_ind)),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_ind)).
% 0.21/0.40 thf(f157,plain,(
% 0.21/0.40 (mdia_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.21/0.40 inference(definition_unfolding,[],[f111,f114,f123,f114])).
% 0.21/0.40 thf(f111,plain,(
% 0.21/0.40 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.21/0.40 inference(cnf_transformation,[],[f55])).
% 0.21/0.40 thf(f55,plain,(
% 0.21/0.40 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.21/0.40 inference(fool_elimination,[],[f54])).
% 0.21/0.40 thf(f54,plain,(
% 0.21/0.40 (mdia_s5 = (^[X0 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X0)))))),
% 0.21/0.40 inference(rectify,[],[f33])).
% 0.21/0.40 thf(f33,axiom,(
% 0.21/0.40 (mdia_s5 = (^[X3 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X3)))))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_s5)).
% 0.21/0.40 thf(f112,plain,(
% 0.21/0.40 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f62])).
% 0.21/0.40 thf(f62,plain,(
% 0.21/0.40 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.21/0.40 inference(fool_elimination,[],[f61])).
% 0.21/0.40 thf(f61,plain,(
% 0.21/0.40 (mforall_ind = (^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : (X0 @ X2 @ X1))))),
% 0.21/0.40 inference(rectify,[],[f10])).
% 0.21/0.40 thf(f10,axiom,(
% 0.21/0.40 (mforall_ind = (^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : (X3 @ X0 @ X2))))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_ind)).
% 0.21/0.40 thf(f123,plain,(
% 0.21/0.40 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f80])).
% 0.21/0.40 thf(f80,plain,(
% 0.21/0.40 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))))),
% 0.21/0.40 inference(fool_elimination,[],[f79])).
% 0.21/0.40 thf(f79,plain,(
% 0.21/0.40 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_s5 @ X1 @ X2) | (X0 @ X2)))) = mbox_s5)),
% 0.21/0.40 inference(rectify,[],[f32])).
% 0.21/0.40 thf(f32,axiom,(
% 0.21/0.40 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_s5 @ X2 @ X7) | (X3 @ X7)))) = mbox_s5)),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s5)).
% 0.21/0.40 thf(f148,plain,(
% 0.21/0.40 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.21/0.40 inference(definition_unfolding,[],[f139,f114,f138,f114,f114])).
% 0.21/0.40 thf(f138,plain,(
% 0.21/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f76])).
% 0.21/0.40 thf(f76,plain,(
% 0.21/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.21/0.40 inference(fool_elimination,[],[f75])).
% 0.21/0.40 thf(f75,plain,(
% 0.21/0.40 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.21/0.40 inference(rectify,[],[f4])).
% 0.21/0.40 thf(f4,axiom,(
% 0.21/0.40 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.21/0.40 thf(f139,plain,(
% 0.21/0.40 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f104])).
% 0.21/0.40 thf(f104,plain,(
% 0.21/0.40 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.21/0.40 inference(fool_elimination,[],[f103])).
% 0.21/0.40 thf(f103,plain,(
% 0.21/0.40 ((^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))) = mand)),
% 0.21/0.40 inference(rectify,[],[f5])).
% 0.21/0.40 thf(f5,axiom,(
% 0.21/0.40 ((^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))) = mand)),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.21/0.40 thf(f149,plain,(
% 0.21/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.21/0.40 inference(definition_unfolding,[],[f115,f138,f114])).
% 0.21/0.40 thf(f115,plain,(
% 0.21/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.40 inference(cnf_transformation,[],[f45])).
% 0.21/0.40 thf(f45,plain,(
% 0.21/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.40 inference(fool_elimination,[],[f44])).
% 0.21/0.40 thf(f44,plain,(
% 0.21/0.40 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.21/0.40 inference(rectify,[],[f6])).
% 0.21/0.40 thf(f6,axiom,(
% 0.21/0.40 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.21/0.40 thf(f132,plain,(
% 0.21/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.40 inference(cnf_transformation,[],[f72])).
% 0.21/0.40 thf(f72,plain,(
% 0.21/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.40 inference(fool_elimination,[],[f71])).
% 0.21/0.40 thf(f71,plain,(
% 0.21/0.40 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.21/0.40 inference(rectify,[],[f28])).
% 0.21/0.40 thf(f28,axiom,(
% 0.21/0.40 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.21/0.40 thf(f120,plain,(
% 0.21/0.40 ($true != (mvalid @ (mimplies @ (mand @ (mbox_s5 @ (mforall_ind @ (^[Y0 : mu]: (mimplies @ (f @ Y0) @ (mbox_s5 @ (f @ Y0)))))) @ (mdia_s5 @ (mexists_ind @ (^[Y0 : mu]: (f @ Y0))))) @ (mbox_s5 @ (mexists_ind @ (^[Y0 : mu]: (f @ Y0)))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f110])).
% 0.21/0.40 thf(f110,plain,(
% 0.21/0.40 ($true != (mvalid @ (mimplies @ (mand @ (mbox_s5 @ (mforall_ind @ (^[Y0 : mu]: (mimplies @ (f @ Y0) @ (mbox_s5 @ (f @ Y0)))))) @ (mdia_s5 @ (mexists_ind @ (^[Y0 : mu]: (f @ Y0))))) @ (mbox_s5 @ (mexists_ind @ (^[Y0 : mu]: (f @ Y0)))))))),
% 0.21/0.40 inference(flattening,[],[f94])).
% 0.21/0.40 thf(f94,plain,(
% 0.21/0.40 ~($true = (mvalid @ (mimplies @ (mand @ (mbox_s5 @ (mforall_ind @ (^[Y0 : mu]: (mimplies @ (f @ Y0) @ (mbox_s5 @ (f @ Y0)))))) @ (mdia_s5 @ (mexists_ind @ (^[Y0 : mu]: (f @ Y0))))) @ (mbox_s5 @ (mexists_ind @ (^[Y0 : mu]: (f @ Y0)))))))),
% 0.21/0.40 inference(fool_elimination,[],[f93])).
% 0.21/0.40 thf(f93,plain,(
% 0.21/0.40 ~(mvalid @ (mimplies @ (mand @ (mbox_s5 @ (mforall_ind @ (^[X0 : mu] : (mimplies @ (f @ X0) @ (mbox_s5 @ (f @ X0)))))) @ (mdia_s5 @ (mexists_ind @ (^[X1 : mu] : (f @ X1))))) @ (mbox_s5 @ (mexists_ind @ (^[X2 : mu] : (f @ X2))))))),
% 0.21/0.40 inference(rectify,[],[f38])).
% 0.21/0.40 thf(f38,negated_conjecture,(
% 0.21/0.40 ~(mvalid @ (mimplies @ (mand @ (mbox_s5 @ (mforall_ind @ (^[X0 : mu] : (mimplies @ (f @ X0) @ (mbox_s5 @ (f @ X0)))))) @ (mdia_s5 @ (mexists_ind @ (^[X0 : mu] : (f @ X0))))) @ (mbox_s5 @ (mexists_ind @ (^[X0 : mu] : (f @ X0))))))),
% 0.21/0.40 inference(negated_conjecture,[],[f37])).
% 0.21/0.40 thf(f37,conjecture,(
% 0.21/0.40 (mvalid @ (mimplies @ (mand @ (mbox_s5 @ (mforall_ind @ (^[X0 : mu] : (mimplies @ (f @ X0) @ (mbox_s5 @ (f @ X0)))))) @ (mdia_s5 @ (mexists_ind @ (^[X0 : mu] : (f @ X0))))) @ (mbox_s5 @ (mexists_ind @ (^[X0 : mu] : (f @ X0))))))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.21/0.40 thf(f465,plain,(
% 0.21/0.40 ((rel_s5 @ sK1 @ sK3) = $false) | ~spl0_1),
% 0.21/0.40 inference(avatar_component_clause,[],[f463])).
% 0.21/0.40 thf(f463,plain,(
% 0.21/0.40 spl0_1 <=> ((rel_s5 @ sK1 @ sK3) = $false)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.21/0.40 thf(f501,plain,(
% 0.21/0.40 ~spl0_2),
% 0.21/0.40 inference(avatar_contradiction_clause,[],[f500])).
% 0.21/0.40 thf(f500,plain,(
% 0.21/0.40 $false | ~spl0_2),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f495])).
% 0.21/0.40 thf(f495,plain,(
% 0.21/0.40 ($true = $false) | ~spl0_2),
% 0.21/0.40 inference(superposition,[],[f196,f468])).
% 0.21/0.40 thf(f468,plain,(
% 0.21/0.40 ( ! [X0 : mu] : (($false = (f @ X0 @ sK3))) ) | ~spl0_2),
% 0.21/0.40 inference(avatar_component_clause,[],[f467])).
% 0.21/0.40 thf(f467,plain,(
% 0.21/0.40 spl0_2 <=> ! [X0 : mu] : ($false = (f @ X0 @ sK3))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.21/0.40 thf(f196,plain,(
% 0.21/0.40 ((f @ sK4 @ sK3) = $true)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f195])).
% 0.21/0.40 thf(f195,plain,(
% 0.21/0.40 ((~ (f @ sK4 @ sK3)) = $false)),
% 0.21/0.40 inference(beta_eta_normalization,[],[f194])).
% 0.21/0.40 thf(f194,plain,(
% 0.21/0.40 ($false = ((^[Y0 : mu]: (~ (f @ Y0 @ sK3))) @ sK4))),
% 0.21/0.40 inference(sigma_clausification,[],[f193])).
% 0.21/0.40 thf(f193,plain,(
% 0.21/0.40 ((!! @ mu @ (^[Y0 : mu]: (~ (f @ Y0 @ sK3)))) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f191])).
% 0.21/0.40 thf(f485,plain,(
% 0.21/0.40 spl0_2 | spl0_1),
% 0.21/0.40 inference(avatar_split_clause,[],[f452,f463,f467])).
% 0.21/0.40 thf(f452,plain,(
% 0.21/0.40 ( ! [X0 : mu] : (($false = (f @ X0 @ sK3)) | ((rel_s5 @ sK1 @ sK3) = $false)) )),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f442])).
% 0.21/0.40 thf(f442,plain,(
% 0.21/0.40 ( ! [X0 : mu] : (($true = $false) | ((rel_s5 @ sK1 @ sK3) = $false) | ($false = (f @ X0 @ sK3))) )),
% 0.21/0.40 inference(superposition,[],[f397,f294])).
% 0.21/0.40 thf(f294,plain,(
% 0.21/0.40 ((rel_s5 @ sK3 @ sK2) = $true)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f292])).
% 0.21/0.40 thf(f292,plain,(
% 0.21/0.40 ($true = $false) | ((rel_s5 @ sK3 @ sK2) = $true)),
% 0.21/0.40 inference(superposition,[],[f219,f287])).
% 0.21/0.40 thf(f287,plain,(
% 0.21/0.40 ($true = (rel_s5 @ sK2 @ sK3))),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f276])).
% 0.21/0.40 thf(f276,plain,(
% 0.21/0.40 ($true = (rel_s5 @ sK2 @ sK3)) | ($true = $false)),
% 0.21/0.40 inference(superposition,[],[f271,f231])).
% 0.21/0.40 thf(f231,plain,(
% 0.21/0.40 ((rel_s5 @ sK3 @ sK1) = $true)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f222])).
% 0.21/0.40 thf(f222,plain,(
% 0.21/0.40 ((rel_s5 @ sK3 @ sK1) = $true) | ($true = $false)),
% 0.21/0.40 inference(superposition,[],[f219,f197])).
% 0.21/0.40 thf(f271,plain,(
% 0.21/0.40 ( ! [X0 : $i] : (($false = (rel_s5 @ X0 @ sK1)) | ((rel_s5 @ sK2 @ X0) = $true)) )),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f254])).
% 0.21/0.40 thf(f254,plain,(
% 0.21/0.40 ( ! [X0 : $i] : (($false = (rel_s5 @ X0 @ sK1)) | ((rel_s5 @ sK2 @ X0) = $true) | ($true = $false)) )),
% 0.21/0.40 inference(superposition,[],[f187,f245])).
% 0.21/0.40 thf(f245,plain,(
% 0.21/0.40 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (rel_s5 @ X2 @ X1)) | ((rel_s5 @ X0 @ X2) = $false) | ((rel_s5 @ X1 @ X0) = $true)) )),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f241])).
% 0.21/0.40 thf(f241,plain,(
% 0.21/0.40 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((rel_s5 @ X1 @ X0) = $true) | ($false = (rel_s5 @ X2 @ X1)) | ((rel_s5 @ X0 @ X2) = $false) | ($true = $false)) )),
% 0.21/0.40 inference(superposition,[],[f219,f170])).
% 0.21/0.40 thf(f170,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (rel_s5 @ X3 @ X1)) | ($false = (rel_s5 @ X2 @ X1)) | ($false = (rel_s5 @ X3 @ X2))) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f169])).
% 0.21/0.40 thf(f169,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (rel_s5 @ X3 @ X1)) | ($false = ((rel_s5 @ X3 @ X2) & (rel_s5 @ X2 @ X1)))) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f168])).
% 0.21/0.40 thf(f168,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((rel_s5 @ X3 @ X2) & (rel_s5 @ X2 @ X1)) => (rel_s5 @ X3 @ X1)) = $true)) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f167])).
% 0.21/0.40 thf(f167,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((rel_s5 @ Y0 @ X2) & (rel_s5 @ X2 @ X1)) => (rel_s5 @ Y0 @ X1))) @ X3))) )),
% 0.21/0.40 inference(pi_clausification,[],[f166])).
% 0.21/0.40 thf(f166,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((rel_s5 @ Y0 @ X2) & (rel_s5 @ X2 @ X1)) => (rel_s5 @ Y0 @ X1)))))) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f165])).
% 0.21/0.40 thf(f165,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ Y1 @ Y0) & (rel_s5 @ Y0 @ X1)) => (rel_s5 @ Y1 @ X1))))) @ X2))) )),
% 0.21/0.40 inference(pi_clausification,[],[f164])).
% 0.21/0.40 thf(f164,plain,(
% 0.21/0.40 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ Y1 @ Y0) & (rel_s5 @ Y0 @ X1)) => (rel_s5 @ Y1 @ X1)))))) = $true)) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f163])).
% 0.21/0.40 thf(f163,plain,(
% 0.21/0.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y2 @ Y1) & (rel_s5 @ Y1 @ Y0)) => (rel_s5 @ Y2 @ Y0))))))) @ X1) = $true)) )),
% 0.21/0.40 inference(pi_clausification,[],[f162])).
% 0.21/0.40 thf(f162,plain,(
% 0.21/0.40 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y2 @ Y1) & (rel_s5 @ Y1 @ Y0)) => (rel_s5 @ Y2 @ Y0)))))))) = $true)),
% 0.21/0.40 inference(beta_eta_normalization,[],[f159])).
% 0.21/0.40 thf(f159,plain,(
% 0.21/0.40 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) @ rel_s5))),
% 0.21/0.40 inference(definition_unfolding,[],[f122,f124])).
% 0.21/0.40 thf(f124,plain,(
% 0.21/0.40 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f82])).
% 0.21/0.40 thf(f82,plain,(
% 0.21/0.40 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))))),
% 0.21/0.40 inference(fool_elimination,[],[f81])).
% 0.21/0.40 thf(f81,plain,(
% 0.21/0.40 (mtransitive = (^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X2 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X1 @ X3)))))),
% 0.21/0.40 inference(rectify,[],[f21])).
% 0.21/0.40 thf(f21,axiom,(
% 0.21/0.40 (mtransitive = (^[X6 : $i > $i > $o] : (! [X8,X9,X10] : (((X6 @ X9 @ X10) & (X6 @ X8 @ X9)) => (X6 @ X8 @ X10)))))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtransitive)).
% 0.21/0.40 thf(f122,plain,(
% 0.21/0.40 ((mtransitive @ rel_s5) = $true)),
% 0.21/0.40 inference(cnf_transformation,[],[f58])).
% 0.21/0.40 thf(f58,plain,(
% 0.21/0.40 ((mtransitive @ rel_s5) = $true)),
% 0.21/0.40 inference(fool_elimination,[],[f57])).
% 0.21/0.40 thf(f57,plain,(
% 0.21/0.40 (mtransitive @ rel_s5)),
% 0.21/0.40 inference(rectify,[],[f35])).
% 0.21/0.40 thf(f35,axiom,(
% 0.21/0.40 (mtransitive @ rel_s5)),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2)).
% 0.21/0.40 thf(f187,plain,(
% 0.21/0.40 ((rel_s5 @ sK1 @ sK2) = $true)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f181])).
% 0.21/0.40 thf(f181,plain,(
% 0.21/0.40 ($false = (~ (rel_s5 @ sK1 @ sK2)))),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f180])).
% 0.21/0.40 thf(f180,plain,(
% 0.21/0.40 (((~ (!! @ mu @ (^[Y0 : mu]: (~ (f @ Y0 @ sK2))))) | (~ (rel_s5 @ sK1 @ sK2))) = $false)),
% 0.21/0.40 inference(beta_eta_normalization,[],[f179])).
% 0.21/0.40 thf(f179,plain,(
% 0.21/0.40 (((^[Y0 : $i]: ((~ (!! @ mu @ (^[Y1 : mu]: (~ (f @ Y1 @ Y0))))) | (~ (rel_s5 @ sK1 @ Y0)))) @ sK2) = $false)),
% 0.21/0.40 inference(sigma_clausification,[],[f178])).
% 0.21/0.40 thf(f178,plain,(
% 0.21/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ mu @ (^[Y1 : mu]: (~ (f @ Y1 @ Y0))))) | (~ (rel_s5 @ sK1 @ Y0))))) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f176])).
% 0.21/0.40 thf(f219,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (rel_s5 @ X2 @ X1)) | ((rel_s5 @ X1 @ X2) = $true)) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f218])).
% 0.21/0.40 thf(f218,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : ((((rel_s5 @ X2 @ X1) => (rel_s5 @ X1 @ X2)) = $true)) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f217])).
% 0.21/0.40 thf(f217,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((rel_s5 @ Y0 @ X1) => (rel_s5 @ X1 @ Y0))) @ X2) = $true)) )),
% 0.21/0.40 inference(pi_clausification,[],[f216])).
% 0.21/0.40 thf(f216,plain,(
% 0.21/0.40 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((rel_s5 @ Y0 @ X1) => (rel_s5 @ X1 @ Y0)))) = $true)) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f215])).
% 0.21/0.40 thf(f215,plain,(
% 0.21/0.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y1 @ Y0) => (rel_s5 @ Y0 @ Y1))))) @ X1))) )),
% 0.21/0.40 inference(pi_clausification,[],[f214])).
% 0.21/0.40 thf(f214,plain,(
% 0.21/0.40 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y1 @ Y0) => (rel_s5 @ Y0 @ Y1)))))))),
% 0.21/0.40 inference(beta_eta_normalization,[],[f160])).
% 0.21/0.40 thf(f160,plain,(
% 0.21/0.40 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))) @ rel_s5))),
% 0.21/0.40 inference(definition_unfolding,[],[f129,f128])).
% 0.21/0.40 thf(f128,plain,(
% 0.21/0.40 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f74])).
% 0.21/0.40 thf(f74,plain,(
% 0.21/0.40 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))))),
% 0.21/0.40 inference(fool_elimination,[],[f73])).
% 0.21/0.40 thf(f73,plain,(
% 0.21/0.40 ((^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X1 @ X2) => (X0 @ X2 @ X1)))) = msymmetric)),
% 0.21/0.40 inference(rectify,[],[f19])).
% 0.21/0.40 thf(f19,axiom,(
% 0.21/0.40 ((^[X6 : $i > $i > $o] : (! [X8,X9] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))) = msymmetric)),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',msymmetric)).
% 0.21/0.40 thf(f129,plain,(
% 0.21/0.40 ((msymmetric @ rel_s5) = $true)),
% 0.21/0.40 inference(cnf_transformation,[],[f68])).
% 0.21/0.40 thf(f68,plain,(
% 0.21/0.40 ((msymmetric @ rel_s5) = $true)),
% 0.21/0.40 inference(fool_elimination,[],[f67])).
% 0.21/0.40 thf(f67,plain,(
% 0.21/0.40 (msymmetric @ rel_s5)),
% 0.21/0.40 inference(rectify,[],[f36])).
% 0.21/0.40 thf(f36,axiom,(
% 0.21/0.40 (msymmetric @ rel_s5)),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3)).
% 0.21/0.40 thf(f397,plain,(
% 0.21/0.40 ( ! [X0 : mu,X1 : $i] : (($false = (rel_s5 @ X1 @ sK2)) | ((rel_s5 @ sK1 @ X1) = $false) | ((f @ X0 @ X1) = $false)) )),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f394])).
% 0.21/0.40 thf(f394,plain,(
% 0.21/0.40 ( ! [X0 : mu,X1 : $i] : (((f @ X0 @ X1) = $false) | ($false = (rel_s5 @ X1 @ sK2)) | ($true = $false) | ((rel_s5 @ sK1 @ X1) = $false)) )),
% 0.21/0.40 inference(superposition,[],[f186,f210])).
% 0.21/0.40 thf(f210,plain,(
% 0.21/0.40 ( ! [X2 : mu,X3 : $i,X1 : $i] : (($true = (f @ X2 @ X3)) | ((rel_s5 @ X1 @ X3) = $false) | ((rel_s5 @ sK1 @ X1) = $false) | ((f @ X2 @ X1) = $false)) )),
% 0.21/0.40 inference(not_proxy_clausification,[],[f209])).
% 0.21/0.40 thf(f209,plain,(
% 0.21/0.40 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((~ (rel_s5 @ X1 @ X3)) = $true) | ($true = (f @ X2 @ X3)) | ((f @ X2 @ X1) = $false) | ((rel_s5 @ sK1 @ X1) = $false)) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f208])).
% 0.21/0.40 thf(f208,plain,(
% 0.21/0.40 ( ! [X2 : mu,X3 : $i,X1 : $i] : (($true = ((f @ X2 @ X3) | (~ (rel_s5 @ X1 @ X3)))) | ((rel_s5 @ sK1 @ X1) = $false) | ((f @ X2 @ X1) = $false)) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f207])).
% 0.21/0.40 thf(f207,plain,(
% 0.21/0.40 ( ! [X2 : mu,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s5 @ X1 @ Y0)))) @ X3) = $true) | ((f @ X2 @ X1) = $false) | ((rel_s5 @ sK1 @ X1) = $false)) )),
% 0.21/0.40 inference(pi_clausification,[],[f206])).
% 0.21/0.40 thf(f206,plain,(
% 0.21/0.40 ( ! [X2 : mu,X1 : $i] : (((f @ X2 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s5 @ X1 @ Y0))))) = $true) | ((rel_s5 @ sK1 @ X1) = $false)) )),
% 0.21/0.40 inference(not_proxy_clausification,[],[f205])).
% 0.21/0.40 thf(f205,plain,(
% 0.21/0.40 ( ! [X2 : mu,X1 : $i] : (((~ (f @ X2 @ X1)) = $true) | ((rel_s5 @ sK1 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s5 @ X1 @ Y0))))) = $true)) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f204])).
% 0.21/0.40 thf(f204,plain,(
% 0.21/0.40 ( ! [X2 : mu,X1 : $i] : (((rel_s5 @ sK1 @ X1) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s5 @ X1 @ Y0))))) | (~ (f @ X2 @ X1))))) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f203])).
% 0.21/0.40 thf(f203,plain,(
% 0.21/0.40 ( ! [X2 : mu,X1 : $i] : (((rel_s5 @ sK1 @ X1) = $false) | (((^[Y0 : mu]: ((!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s5 @ X1 @ Y1))))) | (~ (f @ Y0 @ X1)))) @ X2) = $true)) )),
% 0.21/0.40 inference(pi_clausification,[],[f202])).
% 0.21/0.40 thf(f202,plain,(
% 0.21/0.40 ( ! [X1 : $i] : (($true = (!! @ mu @ (^[Y0 : mu]: ((!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s5 @ X1 @ Y1))))) | (~ (f @ Y0 @ X1)))))) | ((rel_s5 @ sK1 @ X1) = $false)) )),
% 0.21/0.40 inference(not_proxy_clausification,[],[f201])).
% 0.21/0.40 thf(f201,plain,(
% 0.21/0.40 ( ! [X1 : $i] : (($true = (~ (rel_s5 @ sK1 @ X1))) | ($true = (!! @ mu @ (^[Y0 : mu]: ((!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s5 @ X1 @ Y1))))) | (~ (f @ Y0 @ X1))))))) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f200])).
% 0.21/0.40 thf(f200,plain,(
% 0.21/0.40 ( ! [X1 : $i] : (($true = ((!! @ mu @ (^[Y0 : mu]: ((!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s5 @ X1 @ Y1))))) | (~ (f @ Y0 @ X1))))) | (~ (rel_s5 @ sK1 @ X1))))) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f199])).
% 0.21/0.40 thf(f199,plain,(
% 0.21/0.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s5 @ Y0 @ Y2))))) | (~ (f @ Y1 @ Y0))))) | (~ (rel_s5 @ sK1 @ Y0)))) @ X1) = $true)) )),
% 0.21/0.40 inference(pi_clausification,[],[f198])).
% 0.21/0.40 thf(f198,plain,(
% 0.21/0.40 ((!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s5 @ Y0 @ Y2))))) | (~ (f @ Y1 @ Y0))))) | (~ (rel_s5 @ sK1 @ Y0))))) = $true)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f188])).
% 0.21/0.40 thf(f188,plain,(
% 0.21/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s5 @ Y0 @ Y2))))) | (~ (f @ Y1 @ Y0))))) | (~ (rel_s5 @ sK1 @ Y0)))))) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f177])).
% 0.21/0.40 thf(f186,plain,(
% 0.21/0.40 ( ! [X1 : mu] : (((f @ X1 @ sK2) = $false)) )),
% 0.21/0.40 inference(not_proxy_clausification,[],[f185])).
% 0.21/0.40 thf(f185,plain,(
% 0.21/0.40 ( ! [X1 : mu] : (($true = (~ (f @ X1 @ sK2)))) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f184])).
% 0.21/0.40 thf(f184,plain,(
% 0.21/0.40 ( ! [X1 : mu] : (($true = ((^[Y0 : mu]: (~ (f @ Y0 @ sK2))) @ X1))) )),
% 0.21/0.40 inference(pi_clausification,[],[f183])).
% 0.21/0.40 thf(f183,plain,(
% 0.21/0.40 ($true = (!! @ mu @ (^[Y0 : mu]: (~ (f @ Y0 @ sK2)))))),
% 0.21/0.40 inference(not_proxy_clausification,[],[f182])).
% 0.21/0.40 thf(f182,plain,(
% 0.21/0.40 ($false = (~ (!! @ mu @ (^[Y0 : mu]: (~ (f @ Y0 @ sK2))))))),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f180])).
% 0.21/0.40 % SZS output end Proof for theBenchmark
% 0.21/0.40 % (24577)------------------------------
% 0.21/0.40 % (24577)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (24577)Termination reason: Refutation
% 0.21/0.40
% 0.21/0.40 % (24577)Memory used [KB]: 5884
% 0.21/0.40 % (24577)Time elapsed: 0.033 s
% 0.21/0.40 % (24577)Instructions burned: 41 (million)
% 0.21/0.40 % (24577)------------------------------
% 0.21/0.40 % (24577)------------------------------
% 0.21/0.40 % (24576)Success in time 0.054 s
% 0.21/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------