TSTP Solution File: PHI043^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : PHI043^1 : TPTP v8.2.0. Released v7.5.0.
% 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 : n018.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 02:18:53 EDT 2024
% Result : Theorem 0.24s 0.45s
% Output : Refutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : PHI043^1 : TPTP v8.2.0. Released v7.5.0.
% 0.14/0.16 % 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
% 0.16/0.37 % Computer : n018.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Sat May 18 14:49:23 EDT 2024
% 0.16/0.38 % CPUTime :
% 0.16/0.38 This is a TH0_THM_EQU_NAR problem
% 0.16/0.38 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
% 0.16/0.40 % (16275)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.16/0.40 % (16276)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)
% 0.16/0.40 % (16272)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.16/0.40 % (16273)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)
% 0.16/0.40 % (16276)Instruction limit reached!
% 0.16/0.40 % (16276)------------------------------
% 0.16/0.40 % (16276)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.40 % (16276)Termination reason: Unknown
% 0.16/0.40 % (16276)Termination phase: Property scanning
% 0.16/0.40
% 0.16/0.40 % (16276)Memory used [KB]: 1023
% 0.16/0.40 % (16276)Time elapsed: 0.003 s
% 0.16/0.40 % (16276)Instructions burned: 3 (million)
% 0.16/0.40 % (16276)------------------------------
% 0.16/0.40 % (16276)------------------------------
% 0.16/0.40 % (16272)Instruction limit reached!
% 0.16/0.40 % (16272)------------------------------
% 0.16/0.40 % (16272)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.40 % (16272)Termination reason: Unknown
% 0.16/0.40 % (16272)Termination phase: shuffling
% 0.16/0.40
% 0.16/0.40 % (16272)Memory used [KB]: 1023
% 0.16/0.40 % (16272)Time elapsed: 0.003 s
% 0.16/0.40 % (16272)Instructions burned: 2 (million)
% 0.16/0.40 % (16272)------------------------------
% 0.16/0.40 % (16272)------------------------------
% 0.16/0.40 % (16273)Instruction limit reached!
% 0.16/0.40 % (16273)------------------------------
% 0.16/0.40 % (16273)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.40 % (16273)Termination reason: Unknown
% 0.16/0.40 % (16273)Termination phase: shuffling
% 0.16/0.40
% 0.16/0.40 % (16273)Memory used [KB]: 1023
% 0.16/0.40 % (16273)Time elapsed: 0.002 s
% 0.16/0.40 % (16273)Instructions burned: 2 (million)
% 0.16/0.40 % (16273)------------------------------
% 0.16/0.40 % (16273)------------------------------
% 0.16/0.40 % (16269)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.16/0.40 % (16271)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)
% 0.16/0.41 % (16275)Instruction limit reached!
% 0.16/0.41 % (16275)------------------------------
% 0.16/0.41 % (16275)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.41 % (16274)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)
% 0.16/0.41 % (16275)Termination reason: Unknown
% 0.16/0.41 % (16275)Termination phase: Saturation
% 0.16/0.41
% 0.16/0.41 % (16275)Memory used [KB]: 5756
% 0.16/0.41 % (16275)Time elapsed: 0.014 s
% 0.16/0.41 % (16275)Instructions burned: 18 (million)
% 0.16/0.41 % (16275)------------------------------
% 0.16/0.41 % (16275)------------------------------
% 0.16/0.41 % (16270)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)
% 0.16/0.41 % (16270)Instruction limit reached!
% 0.16/0.41 % (16270)------------------------------
% 0.16/0.41 % (16270)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.41 % (16270)Termination reason: Unknown
% 0.16/0.41 % (16270)Termination phase: Function definition elimination
% 0.16/0.41
% 0.16/0.41 % (16270)Memory used [KB]: 1023
% 0.16/0.41 % (16270)Time elapsed: 0.004 s
% 0.16/0.41 % (16270)Instructions burned: 4 (million)
% 0.16/0.41 % (16270)------------------------------
% 0.16/0.41 % (16270)------------------------------
% 0.16/0.41 % (16274)Refutation not found, incomplete strategy
% 0.16/0.41 % (16274)------------------------------
% 0.16/0.41 % (16274)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.41 % (16274)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.41
% 0.16/0.41
% 0.16/0.41 % (16274)Memory used [KB]: 5500
% 0.16/0.41 % (16274)Time elapsed: 0.005 s
% 0.16/0.41 % (16274)Instructions burned: 5 (million)
% 0.16/0.41 % (16274)------------------------------
% 0.16/0.41 % (16274)------------------------------
% 0.16/0.42 % (16277)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)
% 0.16/0.42 % (16279)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)
% 0.16/0.42 % (16279)Instruction limit reached!
% 0.16/0.42 % (16279)------------------------------
% 0.16/0.42 % (16279)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.42 % (16279)Termination reason: Unknown
% 0.16/0.42 % (16279)Termination phase: Property scanning
% 0.16/0.42
% 0.16/0.42 % (16279)Memory used [KB]: 1023
% 0.16/0.42 % (16279)Time elapsed: 0.003 s
% 0.16/0.42 % (16279)Instructions burned: 3 (million)
% 0.16/0.42 % (16279)------------------------------
% 0.16/0.42 % (16279)------------------------------
% 0.16/0.42 % (16271)Instruction limit reached!
% 0.16/0.42 % (16271)------------------------------
% 0.16/0.42 % (16271)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.42 % (16271)Termination reason: Unknown
% 0.16/0.42 % (16271)Termination phase: Saturation
% 0.16/0.42
% 0.16/0.42 % (16271)Memory used [KB]: 5756
% 0.16/0.42 % (16271)Time elapsed: 0.017 s
% 0.16/0.42 % (16271)Instructions burned: 27 (million)
% 0.16/0.42 % (16271)------------------------------
% 0.16/0.42 % (16271)------------------------------
% 0.16/0.43 % (16280)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)
% 0.16/0.43 % (16281)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.16/0.43 % (16278)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)
% 0.16/0.43 % (16282)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.16/0.43 % (16281)Instruction limit reached!
% 0.16/0.43 % (16281)------------------------------
% 0.16/0.43 % (16281)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.43 % (16281)Termination reason: Unknown
% 0.16/0.43 % (16281)Termination phase: Saturation
% 0.16/0.43
% 0.16/0.43 % (16281)Memory used [KB]: 1023
% 0.16/0.43 % (16281)Time elapsed: 0.006 s
% 0.16/0.43 % (16281)Instructions burned: 7 (million)
% 0.16/0.43 % (16281)------------------------------
% 0.16/0.43 % (16281)------------------------------
% 0.16/0.43 % (16278)Refutation not found, incomplete strategy
% 0.16/0.43 % (16278)------------------------------
% 0.16/0.43 % (16278)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.43 % (16278)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.43
% 0.16/0.43
% 0.16/0.43 % (16278)Memory used [KB]: 5628
% 0.16/0.43 % (16278)Time elapsed: 0.031 s
% 0.16/0.43 % (16278)Instructions burned: 9 (million)
% 0.16/0.43 % (16278)------------------------------
% 0.16/0.43 % (16278)------------------------------
% 0.16/0.44 % (16277)Instruction limit reached!
% 0.16/0.44 % (16277)------------------------------
% 0.16/0.44 % (16277)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.44 % (16277)Termination reason: Unknown
% 0.16/0.44 % (16277)Termination phase: Saturation
% 0.16/0.44
% 0.16/0.44 % (16277)Memory used [KB]: 5884
% 0.16/0.44 % (16277)Time elapsed: 0.023 s
% 0.16/0.44 % (16277)Instructions burned: 37 (million)
% 0.16/0.44 % (16277)------------------------------
% 0.16/0.44 % (16277)------------------------------
% 0.24/0.44 % (16283)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)
% 0.24/0.44 % (16282)Instruction limit reached!
% 0.24/0.44 % (16282)------------------------------
% 0.24/0.44 % (16282)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.44 % (16282)Termination reason: Unknown
% 0.24/0.44 % (16282)Termination phase: Saturation
% 0.24/0.44
% 0.24/0.44 % (16282)Memory used [KB]: 5628
% 0.24/0.44 % (16282)Time elapsed: 0.011 s
% 0.24/0.44 % (16282)Instructions burned: 17 (million)
% 0.24/0.44 % (16282)------------------------------
% 0.24/0.44 % (16282)------------------------------
% 0.24/0.44 % (16283)Instruction limit reached!
% 0.24/0.44 % (16283)------------------------------
% 0.24/0.44 % (16283)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.44 % (16283)Termination reason: Unknown
% 0.24/0.44 % (16283)Termination phase: Property scanning
% 0.24/0.44
% 0.24/0.44 % (16283)Memory used [KB]: 1023
% 0.24/0.44 % (16283)Time elapsed: 0.003 s
% 0.24/0.44 % (16283)Instructions burned: 3 (million)
% 0.24/0.44 % (16283)------------------------------
% 0.24/0.44 % (16283)------------------------------
% 0.24/0.44 % (16280)First to succeed.
% 0.24/0.45 % (16284)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)
% 0.24/0.45 % (16285)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)
% 0.24/0.45 % (16280)Refutation found. Thanks to Tanya!
% 0.24/0.45 % SZS status Theorem for theBenchmark
% 0.24/0.45 % SZS output start Proof for theBenchmark
% 0.24/0.45 thf(type_def_5, type, mu: $tType).
% 0.24/0.45 thf(func_def_0, type, mu: $tType).
% 0.24/0.45 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.24/0.45 thf(func_def_2, type, mtrue: $i > $o).
% 0.24/0.45 thf(func_def_3, type, mfalse: $i > $o).
% 0.24/0.45 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.24/0.45 thf(func_def_6, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.24/0.45 thf(func_def_7, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.24/0.45 thf(func_def_8, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.24/0.45 thf(func_def_9, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.24/0.45 thf(func_def_10, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.24/0.45 thf(func_def_11, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.24/0.45 thf(func_def_12, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.24/0.45 thf(func_def_13, type, mforall_indset: ((mu > $i > $o) > $i > $o) > $i > $o).
% 0.24/0.45 thf(func_def_14, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.24/0.45 thf(func_def_15, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.24/0.45 thf(func_def_16, type, mexists_indset: ((mu > $i > $o) > $i > $o) > $i > $o).
% 0.24/0.45 thf(func_def_17, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.24/0.45 thf(func_def_18, type, mbox_generic: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.24/0.45 thf(func_def_19, type, mdia_generic: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.24/0.45 thf(func_def_20, type, rel: $i > $i > $o).
% 0.24/0.45 thf(func_def_21, type, mbox: ($i > $o) > $i > $o).
% 0.24/0.45 thf(func_def_22, type, mdia: ($i > $o) > $i > $o).
% 0.24/0.45 thf(func_def_23, type, mvalid: ($i > $o) > $o).
% 0.24/0.45 thf(func_def_24, type, minvalid: ($i > $o) > $o).
% 0.24/0.45 thf(func_def_25, type, p: (mu > $i > $o) > $i > $o).
% 0.24/0.45 thf(func_def_44, type, ph1: !>[X0: $tType]:(X0)).
% 0.24/0.45 thf(func_def_46, type, sK3: mu > $i > $o).
% 0.24/0.45 thf(func_def_48, type, sK5: mu).
% 0.24/0.45 thf(f199,plain,(
% 0.24/0.45 $false),
% 0.24/0.45 inference(trivial_inequality_removal,[],[f198])).
% 0.24/0.45 thf(f198,plain,(
% 0.24/0.45 ($false = $true)),
% 0.24/0.45 inference(boolean_simplification,[],[f197])).
% 0.24/0.45 thf(f197,plain,(
% 0.24/0.45 ($false = (~ $false))),
% 0.24/0.45 inference(forward_demodulation,[],[f196,f185])).
% 0.24/0.45 thf(f185,plain,(
% 0.24/0.45 ( ! [X1 : mu] : (($false = (sK3 @ X1 @ sK4))) )),
% 0.24/0.45 inference(beta_eta_normalization,[],[f182])).
% 0.24/0.45 thf(f182,plain,(
% 0.24/0.45 ( ! [X1 : mu] : (($false = ((^[Y0 : mu]: (sK3 @ Y0 @ sK4)) @ X1))) )),
% 0.24/0.45 inference(pi_clausification,[],[f172])).
% 0.24/0.45 thf(f172,plain,(
% 0.24/0.45 ($false = (?? @ mu @ (^[Y0 : mu]: (sK3 @ Y0 @ sK4))))),
% 0.24/0.45 inference(boolean_simplification,[],[f171])).
% 0.24/0.45 thf(f171,plain,(
% 0.24/0.45 ($false = ($true & (?? @ mu @ (^[Y0 : mu]: (sK3 @ Y0 @ sK4)))))),
% 0.24/0.45 inference(superposition,[],[f127,f168])).
% 0.24/0.45 thf(f168,plain,(
% 0.24/0.45 ($true = (rel @ sK2 @ sK4))),
% 0.24/0.45 inference(not_proxy_clausification,[],[f167])).
% 0.24/0.45 thf(f167,plain,(
% 0.24/0.45 ($false = (~ (rel @ sK2 @ sK4)))),
% 0.24/0.45 inference(boolean_simplification,[],[f166])).
% 0.24/0.45 thf(f166,plain,(
% 0.24/0.45 ($false = ((~ (rel @ sK2 @ sK4)) | $false))),
% 0.24/0.45 inference(backward_demodulation,[],[f162,f164])).
% 0.24/0.45 thf(f164,plain,(
% 0.24/0.45 ($false = (!! @ mu @ (^[Y0 : mu]: (~ (sK3 @ Y0 @ sK4)))))),
% 0.24/0.45 inference(binary_proxy_clausification,[],[f162])).
% 0.24/0.45 thf(f162,plain,(
% 0.24/0.45 (((~ (rel @ sK2 @ sK4)) | (!! @ mu @ (^[Y0 : mu]: (~ (sK3 @ Y0 @ sK4))))) = $false)),
% 0.24/0.45 inference(beta_eta_normalization,[],[f160])).
% 0.24/0.45 thf(f160,plain,(
% 0.24/0.45 ($false = ((^[Y0 : $i]: ((~ (rel @ sK2 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: (~ (sK3 @ Y1 @ Y0)))))) @ sK4))),
% 0.24/0.45 inference(sigma_clausification,[],[f157])).
% 0.24/0.45 thf(f157,plain,(
% 0.24/0.45 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel @ sK2 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: (~ (sK3 @ Y1 @ Y0))))))))),
% 0.24/0.45 inference(not_proxy_clausification,[],[f153])).
% 0.24/0.45 thf(f153,plain,(
% 0.24/0.45 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel @ sK2 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: (~ (sK3 @ Y1 @ Y0)))))))))),
% 0.24/0.45 inference(boolean_simplification,[],[f152])).
% 0.24/0.45 thf(f152,plain,(
% 0.24/0.45 ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel @ sK2 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: (~ (sK3 @ Y1 @ Y0))))))) => $false))),
% 0.24/0.45 inference(boolean_simplification,[],[f151])).
% 0.24/0.45 thf(f151,plain,(
% 0.24/0.45 ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel @ sK2 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: (~ (sK3 @ Y1 @ Y0))))))) => (~ $true)))),
% 0.24/0.45 inference(superposition,[],[f147,f123])).
% 0.24/0.45 thf(f123,plain,(
% 0.24/0.45 ($true = (p @ sK3 @ sK2))),
% 0.24/0.45 inference(binary_proxy_clausification,[],[f121])).
% 0.24/0.45 thf(f121,plain,(
% 0.24/0.45 ($false = ((p @ sK3 @ sK2) => (?? @ $i @ (^[Y0 : $i]: ((rel @ sK2 @ Y0) & (?? @ mu @ (^[Y1 : mu]: (sK3 @ Y1 @ Y0))))))))),
% 0.24/0.45 inference(beta_eta_normalization,[],[f120])).
% 0.24/0.45 thf(f120,plain,(
% 0.24/0.45 ($false = ((^[Y0 : mu > $i > $o]: ((p @ Y0 @ sK2) => (?? @ $i @ (^[Y1 : $i]: ((rel @ sK2 @ Y1) & (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))) @ sK3))),
% 0.24/0.45 inference(sigma_clausification,[],[f119])).
% 0.24/0.45 thf(f119,plain,(
% 0.24/0.45 ((!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((p @ Y0 @ sK2) => (?? @ $i @ (^[Y1 : $i]: ((rel @ sK2 @ Y1) & (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1))))))))) = $false)),
% 0.24/0.45 inference(beta_eta_normalization,[],[f118])).
% 0.24/0.45 thf(f118,plain,(
% 0.24/0.45 ($false = ((^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((p @ Y1 @ Y0) => (?? @ $i @ (^[Y2 : $i]: ((rel @ Y0 @ Y2) & (?? @ mu @ (^[Y3 : mu]: (Y1 @ Y3 @ Y2)))))))))) @ sK2))),
% 0.24/0.45 inference(sigma_clausification,[],[f115])).
% 0.24/0.45 thf(f115,plain,(
% 0.24/0.45 ((!! @ $i @ (^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((p @ Y1 @ Y0) => (?? @ $i @ (^[Y2 : $i]: ((rel @ Y0 @ Y2) & (?? @ mu @ (^[Y3 : mu]: (Y1 @ Y3 @ Y2))))))))))) = $false)),
% 0.24/0.45 inference(not_proxy_clausification,[],[f109])).
% 0.24/0.45 thf(f109,plain,(
% 0.24/0.45 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((p @ Y1 @ Y0) => (?? @ $i @ (^[Y2 : $i]: ((rel @ Y0 @ Y2) & (?? @ mu @ (^[Y3 : mu]: (Y1 @ Y3 @ Y2)))))))))))))),
% 0.24/0.45 inference(beta_eta_normalization,[],[f103])).
% 0.24/0.45 thf(f103,plain,(
% 0.24/0.45 ((~ ((^[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))))))) @ (p @ Y0) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((Y1 @ Y3 @ Y4) & (Y2 @ Y4))))))))) @ rel @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (?? @ mu @ (^[Y3 : mu]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : mu]: (Y0 @ Y1))))))))) = $true)),
% 0.24/0.45 inference(definition_unfolding,[],[f83,f90,f80,f79,f101,f99])).
% 0.24/0.45 thf(f99,plain,(
% 0.24/0.45 (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.24/0.45 inference(cnf_transformation,[],[f71])).
% 0.24/0.45 thf(f71,plain,(
% 0.24/0.45 (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.24/0.45 inference(fool_elimination,[],[f70])).
% 0.24/0.45 thf(f70,plain,(
% 0.24/0.45 (mexists_ind = (^[X0 : mu > $i > $o, X1 : $i] : (? [X2 : mu] : (X0 @ X2 @ X1))))),
% 0.24/0.45 inference(rectify,[],[f14])).
% 0.24/0.45 thf(f14,axiom,(
% 0.24/0.45 (mexists_ind = (^[X3 : mu > $i > $o, X2 : $i] : (? [X0 : mu] : (X3 @ X0 @ X2))))),
% 0.24/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_ind)).
% 0.24/0.45 thf(f101,plain,(
% 0.24/0.45 (mdia = ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))) @ rel))),
% 0.24/0.45 inference(definition_unfolding,[],[f81,f82])).
% 0.24/0.45 thf(f82,plain,(
% 0.24/0.45 (mdia_generic = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))))),
% 0.24/0.45 inference(cnf_transformation,[],[f58])).
% 0.24/0.45 thf(f58,plain,(
% 0.24/0.45 (mdia_generic = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))))),
% 0.24/0.45 inference(fool_elimination,[],[f57])).
% 0.24/0.45 thf(f57,plain,(
% 0.24/0.45 ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (? [X3] : ((X1 @ X3) & (X0 @ X2 @ X3)))) = mdia_generic)),
% 0.24/0.45 inference(rectify,[],[f18])).
% 0.24/0.45 thf(f18,axiom,(
% 0.24/0.45 ((^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (? [X7] : ((X3 @ X7) & (X6 @ X2 @ X7)))) = mdia_generic)),
% 0.24/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_generic)).
% 0.24/0.45 thf(f81,plain,(
% 0.24/0.45 (mdia = (mdia_generic @ rel))),
% 0.24/0.45 inference(cnf_transformation,[],[f72])).
% 0.24/0.45 thf(f72,plain,(
% 0.24/0.45 (mdia = (mdia_generic @ rel))),
% 0.24/0.45 inference(fool_elimination,[],[f20])).
% 0.24/0.45 thf(f20,axiom,(
% 0.24/0.45 (mdia = (mdia_generic @ rel))),
% 0.24/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia)).
% 0.24/0.45 thf(f79,plain,(
% 0.24/0.45 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.24/0.45 inference(cnf_transformation,[],[f63])).
% 0.24/0.45 thf(f63,plain,(
% 0.24/0.45 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.24/0.45 inference(fool_elimination,[],[f62])).
% 0.24/0.45 thf(f62,plain,(
% 0.24/0.45 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) => (X1 @ X2))) = mimplies)),
% 0.24/0.45 inference(rectify,[],[f7])).
% 0.24/0.45 thf(f7,axiom,(
% 0.24/0.45 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) => (X4 @ X2))) = mimplies)),
% 0.24/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.24/0.45 thf(f80,plain,(
% 0.24/0.45 (mforall_indset = (^[Y0 : (mu > $i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.24/0.45 inference(cnf_transformation,[],[f52])).
% 0.24/0.45 thf(f52,plain,(
% 0.24/0.45 (mforall_indset = (^[Y0 : (mu > $i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.24/0.45 inference(fool_elimination,[],[f51])).
% 0.24/0.45 thf(f51,plain,(
% 0.24/0.45 ((^[X0 : (mu > $i > $o) > $i > $o, X1 : $i] : (! [X2 : mu > $i > $o] : (X0 @ X2 @ X1))) = mforall_indset)),
% 0.24/0.45 inference(rectify,[],[f12])).
% 0.24/0.45 thf(f12,axiom,(
% 0.24/0.45 ((^[X3 : (mu > $i > $o) > $i > $o, X2 : $i] : (! [X0 : mu > $i > $o] : (X3 @ X0 @ X2))) = mforall_indset)),
% 0.24/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_indset)).
% 0.24/0.45 thf(f90,plain,(
% 0.24/0.45 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.24/0.45 inference(cnf_transformation,[],[f65])).
% 0.24/0.45 thf(f65,plain,(
% 0.24/0.45 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.24/0.45 inference(fool_elimination,[],[f64])).
% 0.24/0.45 thf(f64,plain,(
% 0.24/0.45 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.24/0.45 inference(rectify,[],[f21])).
% 0.24/0.45 thf(f21,axiom,(
% 0.24/0.45 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.24/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.24/0.45 thf(f83,plain,(
% 0.24/0.45 ($true = (~ (mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mimplies @ (p @ Y0) @ (mdia @ (mexists_ind @ (^[Y1 : mu]: (Y0 @ Y1))))))))))),
% 0.24/0.45 inference(cnf_transformation,[],[f69])).
% 0.24/0.45 thf(f69,plain,(
% 0.24/0.45 ($true = (~ (mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mimplies @ (p @ Y0) @ (mdia @ (mexists_ind @ (^[Y1 : mu]: (Y0 @ Y1))))))))))),
% 0.24/0.45 inference(fool_elimination,[],[f68])).
% 0.24/0.45 thf(f68,plain,(
% 0.24/0.45 ~(mvalid @ (mforall_indset @ (^[X0 : mu > $i > $o] : (mimplies @ (p @ X0) @ (mdia @ (mexists_ind @ (^[X1 : mu] : (X0 @ X1))))))))),
% 0.24/0.45 inference(rectify,[],[f26])).
% 0.24/0.45 thf(f26,negated_conjecture,(
% 0.24/0.45 ~(mvalid @ (mforall_indset @ (^[X3 : mu > $i > $o] : (mimplies @ (p @ X3) @ (mdia @ (mexists_ind @ (^[X0 : mu] : (X3 @ X0))))))))),
% 0.24/0.45 inference(negated_conjecture,[],[f25])).
% 0.24/0.45 thf(f25,conjecture,(
% 0.24/0.45 (mvalid @ (mforall_indset @ (^[X3 : mu > $i > $o] : (mimplies @ (p @ X3) @ (mdia @ (mexists_ind @ (^[X0 : mu] : (X3 @ X0))))))))),
% 0.24/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',possible_instantiation_of_the_positive)).
% 0.24/0.45 thf(f147,plain,(
% 0.24/0.45 ( ! [X0 : $i,X1 : mu > $i > $o] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel @ X0 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: (~ (X1 @ Y1 @ Y0))))))) => (~ (p @ X1 @ X0))))) )),
% 0.24/0.45 inference(boolean_simplification,[],[f146])).
% 0.24/0.45 thf(f146,plain,(
% 0.24/0.45 ( ! [X0 : $i,X1 : mu > $i > $o] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel @ X0 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ($false = (X1 @ Y1 @ Y0))))))) => (~ (p @ X1 @ X0))))) )),
% 0.24/0.45 inference(boolean_simplification,[],[f145])).
% 0.24/0.45 thf(f145,plain,(
% 0.24/0.45 ( ! [X0 : $i,X1 : mu > $i > $o] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel @ X0 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ($false = (X1 @ Y1 @ Y0))))))) => ($false = (p @ X1 @ X0))))) )),
% 0.24/0.45 inference(beta_eta_normalization,[],[f138])).
% 0.24/0.45 thf(f138,plain,(
% 0.24/0.45 ( ! [X0 : $i,X1 : mu > $i > $o] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel @ X0 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: (((^[Y2 : mu]: ((^[Y3 : $i]: ($false)))) @ Y1 @ Y0) = (X1 @ Y1 @ Y0))))))) => ($false = (p @ X1 @ X0))))) )),
% 0.24/0.45 inference(superposition,[],[f134,f112])).
% 0.24/0.45 thf(f112,plain,(
% 0.24/0.45 ( ! [X1 : $i] : (($false = (p @ (^[Y0 : mu]: ((^[Y1 : $i]: ($false)))) @ X1))) )),
% 0.24/0.45 inference(not_proxy_clausification,[],[f111])).
% 0.24/0.45 thf(f111,plain,(
% 0.24/0.45 ( ! [X1 : $i] : (($true = (~ (p @ (^[Y0 : mu]: ((^[Y1 : $i]: ($false)))) @ X1)))) )),
% 0.24/0.45 inference(beta_eta_normalization,[],[f110])).
% 0.24/0.45 thf(f110,plain,(
% 0.24/0.45 ( ! [X1 : $i] : ((((^[Y0 : $i]: (~ (p @ (^[Y1 : mu]: ((^[Y2 : $i]: ($false)))) @ Y0))) @ X1) = $true)) )),
% 0.24/0.45 inference(pi_clausification,[],[f108])).
% 0.24/0.45 thf(f108,plain,(
% 0.24/0.45 ($true = (!! @ $i @ (^[Y0 : $i]: (~ (p @ (^[Y1 : mu]: ((^[Y2 : $i]: ($false)))) @ Y0)))))),
% 0.24/0.45 inference(boolean_simplification,[],[f107])).
% 0.24/0.45 thf(f107,plain,(
% 0.24/0.45 ($true = (!! @ $i @ (^[Y0 : $i]: (~ (p @ (^[Y1 : mu]: ((^[Y2 : $i]: (~ $true)))) @ Y0)))))),
% 0.24/0.45 inference(boolean_simplification,[],[f106])).
% 0.24/0.45 thf(f106,plain,(
% 0.24/0.45 ((!! @ $i @ (^[Y0 : $i]: (~ (p @ (^[Y1 : mu]: ((^[Y2 : $i]: (~ (Y1 = Y1))))) @ Y0)))) = $true)),
% 0.24/0.45 inference(beta_eta_normalization,[],[f104])).
% 0.24/0.45 thf(f104,plain,(
% 0.24/0.45 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))) @ (p @ (^[Y0 : mu]: ((^[Y1 : $i]: (~ (Y0 = Y0)))))))))),
% 0.24/0.45 inference(definition_unfolding,[],[f89,f90,f75])).
% 0.24/0.45 thf(f75,plain,(
% 0.24/0.45 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.24/0.45 inference(cnf_transformation,[],[f33])).
% 0.24/0.45 thf(f33,plain,(
% 0.24/0.45 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.24/0.45 inference(fool_elimination,[],[f32])).
% 0.24/0.45 thf(f32,plain,(
% 0.24/0.45 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.24/0.45 inference(rectify,[],[f4])).
% 0.24/0.45 thf(f4,axiom,(
% 0.24/0.45 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.24/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.24/0.45 thf(f89,plain,(
% 0.24/0.45 ($true = (mvalid @ (mnot @ (p @ (^[Y0 : mu]: ((^[Y1 : $i]: (~ (Y0 = Y0)))))))))),
% 0.24/0.45 inference(cnf_transformation,[],[f50])).
% 0.24/0.45 thf(f50,plain,(
% 0.24/0.45 ($true = (mvalid @ (mnot @ (p @ (^[Y0 : mu]: ((^[Y1 : $i]: (~ (Y0 = Y0)))))))))),
% 0.24/0.45 inference(fool_elimination,[],[f49])).
% 0.24/0.45 thf(f49,plain,(
% 0.24/0.45 (mvalid @ (mnot @ (p @ (^[X0 : mu, X1 : $i] : ((X0 != X0))))))),
% 0.24/0.45 inference(rectify,[],[f23])).
% 0.24/0.45 thf(f23,axiom,(
% 0.24/0.45 (mvalid @ (mnot @ (p @ (^[X0 : mu, X2 : $i] : ((X0 != X0))))))),
% 0.24/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16)).
% 0.24/0.45 thf(f134,plain,(
% 0.24/0.45 ( ! [X2 : mu > $i > $o,X3 : mu > $i > $o,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((~ (rel @ X1 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((X2 @ Y1 @ Y0) = (X3 @ Y1 @ Y0))))))) => ((p @ X2 @ X1) = (p @ X3 @ X1))) = $true)) )),
% 0.24/0.45 inference(beta_eta_normalization,[],[f133])).
% 0.24/0.45 thf(f133,plain,(
% 0.24/0.45 ( ! [X2 : mu > $i > $o,X3 : mu > $i > $o,X1 : $i] : (($true = ((^[Y0 : mu > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((~ (rel @ X1 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((X2 @ Y2 @ Y1) = (Y0 @ Y2 @ Y1))))))) => ((p @ X2 @ X1) = (p @ Y0 @ X1)))) @ X3))) )),
% 0.24/0.45 inference(pi_clausification,[],[f132])).
% 0.24/0.45 thf(f132,plain,(
% 0.24/0.45 ( ! [X2 : mu > $i > $o,X1 : $i] : (($true = (!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((~ (rel @ X1 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((X2 @ Y2 @ Y1) = (Y0 @ Y2 @ Y1))))))) => ((p @ X2 @ X1) = (p @ Y0 @ X1))))))) )),
% 0.24/0.45 inference(beta_eta_normalization,[],[f131])).
% 0.24/0.45 thf(f131,plain,(
% 0.24/0.45 ( ! [X2 : mu > $i > $o,X1 : $i] : (($true = ((^[Y0 : mu > $i > $o]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((~ (rel @ X1 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((Y0 @ Y3 @ Y2) = (Y1 @ Y3 @ Y2))))))) => ((p @ Y0 @ X1) = (p @ Y1 @ X1)))))) @ X2))) )),
% 0.24/0.45 inference(pi_clausification,[],[f130])).
% 0.24/0.45 thf(f130,plain,(
% 0.24/0.45 ( ! [X1 : $i] : (($true = (!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((~ (rel @ X1 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((Y0 @ Y3 @ Y2) = (Y1 @ Y3 @ Y2))))))) => ((p @ Y0 @ X1) = (p @ Y1 @ X1))))))))) )),
% 0.24/0.45 inference(beta_eta_normalization,[],[f129])).
% 0.24/0.45 thf(f129,plain,(
% 0.24/0.45 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((~ (rel @ Y0 @ Y3)) | (!! @ mu @ (^[Y4 : mu]: ((Y1 @ Y4 @ Y3) = (Y2 @ Y4 @ Y3))))))) => ((p @ Y1 @ Y0) = (p @ Y2 @ Y0)))))))) @ X1) = $true)) )),
% 0.24/0.45 inference(pi_clausification,[],[f105])).
% 0.24/0.45 thf(f105,plain,(
% 0.24/0.45 ((!! @ $i @ (^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((~ (rel @ Y0 @ Y3)) | (!! @ mu @ (^[Y4 : mu]: ((Y1 @ Y4 @ Y3) = (Y2 @ Y4 @ Y3))))))) => ((p @ Y1 @ Y0) = (p @ Y2 @ Y0))))))))) = $true)),
% 0.24/0.45 inference(beta_eta_normalization,[],[f102])).
% 0.24/0.45 thf(f102,plain,(
% 0.24/0.45 ($true = ((^[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 : (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))))))) @ ((^[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]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y3 @ Y5) = (Y4 @ Y5))))))) @ (Y0 @ Y2) @ (Y1 @ Y2))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) = (Y3 @ Y4))))))) @ (p @ Y0) @ (p @ Y1)))))))))),
% 0.24/0.45 inference(definition_unfolding,[],[f77,f90,f80,f80,f79,f100,f96,f85,f85])).
% 0.24/0.45 thf(f85,plain,(
% 0.24/0.45 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 0.24/0.45 inference(cnf_transformation,[],[f43])).
% 0.24/0.45 thf(f43,plain,(
% 0.24/0.45 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 0.24/0.45 inference(fool_elimination,[],[f42])).
% 0.24/0.45 thf(f42,plain,(
% 0.24/0.45 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) <=> (X1 @ X2))) = mequiv)),
% 0.24/0.45 inference(rectify,[],[f9])).
% 0.24/0.45 thf(f9,axiom,(
% 0.24/0.45 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) <=> (X4 @ X2))) = mequiv)),
% 0.24/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv)).
% 0.24/0.45 thf(f96,plain,(
% 0.24/0.45 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.24/0.45 inference(cnf_transformation,[],[f39])).
% 0.24/0.45 thf(f39,plain,(
% 0.24/0.45 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.24/0.45 inference(fool_elimination,[],[f38])).
% 0.24/0.45 thf(f38,plain,(
% 0.24/0.45 ((^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : (X0 @ X2 @ X1))) = mforall_ind)),
% 0.24/0.45 inference(rectify,[],[f11])).
% 0.24/0.45 thf(f11,axiom,(
% 0.24/0.45 ((^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : (X3 @ X0 @ X2))) = mforall_ind)),
% 0.24/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind)).
% 0.24/0.45 thf(f100,plain,(
% 0.24/0.45 (mbox = ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))) @ rel))),
% 0.24/0.45 inference(definition_unfolding,[],[f98,f95])).
% 0.24/0.45 thf(f95,plain,(
% 0.24/0.45 (mbox_generic = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.24/0.45 inference(cnf_transformation,[],[f74])).
% 0.24/0.45 thf(f74,plain,(
% 0.24/0.45 (mbox_generic = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.24/0.45 inference(fool_elimination,[],[f73])).
% 0.24/0.45 thf(f73,plain,(
% 0.24/0.45 (mbox_generic = (^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))))),
% 0.24/0.45 inference(rectify,[],[f17])).
% 0.24/0.45 thf(f17,axiom,(
% 0.24/0.45 (mbox_generic = (^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(X6 @ X2 @ X7)))))),
% 0.24/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_generic)).
% 0.24/0.45 thf(f98,plain,(
% 0.24/0.45 (mbox = (mbox_generic @ rel))),
% 0.24/0.45 inference(cnf_transformation,[],[f44])).
% 0.24/0.45 thf(f44,plain,(
% 0.24/0.45 (mbox = (mbox_generic @ rel))),
% 0.24/0.45 inference(fool_elimination,[],[f19])).
% 0.24/0.45 thf(f19,axiom,(
% 0.24/0.45 (mbox = (mbox_generic @ rel))),
% 0.24/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox)).
% 0.24/0.45 thf(f77,plain,(
% 0.24/0.45 ($true = (mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mforall_indset @ (^[Y1 : mu > $i > $o]: (mimplies @ (mbox @ (mforall_ind @ (^[Y2 : mu]: (mequiv @ (Y0 @ Y2) @ (Y1 @ Y2))))) @ (mequiv @ (p @ Y0) @ (p @ Y1)))))))))),
% 0.24/0.45 inference(cnf_transformation,[],[f54])).
% 0.24/0.45 thf(f54,plain,(
% 0.24/0.45 ($true = (mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mforall_indset @ (^[Y1 : mu > $i > $o]: (mimplies @ (mbox @ (mforall_ind @ (^[Y2 : mu]: (mequiv @ (Y0 @ Y2) @ (Y1 @ Y2))))) @ (mequiv @ (p @ Y0) @ (p @ Y1)))))))))),
% 0.24/0.45 inference(fool_elimination,[],[f53])).
% 0.24/0.45 thf(f53,plain,(
% 0.24/0.45 (mvalid @ (mforall_indset @ (^[X0 : mu > $i > $o] : (mforall_indset @ (^[X1 : mu > $i > $o] : (mimplies @ (mbox @ (mforall_ind @ (^[X2 : mu] : (mequiv @ (X0 @ X2) @ (X1 @ X2))))) @ (mequiv @ (p @ X0) @ (p @ X1))))))))),
% 0.24/0.45 inference(rectify,[],[f24])).
% 0.24/0.45 thf(f24,axiom,(
% 0.24/0.45 (mvalid @ (mforall_indset @ (^[X3 : mu > $i > $o] : (mforall_indset @ (^[X4 : mu > $i > $o] : (mimplies @ (mbox @ (mforall_ind @ (^[X0 : mu] : (mequiv @ (X3 @ X0) @ (X4 @ X0))))) @ (mequiv @ (p @ X3) @ (p @ X4))))))))),
% 0.24/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17)).
% 0.24/0.45 thf(f127,plain,(
% 0.24/0.45 ( ! [X1 : $i] : ((((rel @ sK2 @ X1) & (?? @ mu @ (^[Y0 : mu]: (sK3 @ Y0 @ X1)))) = $false)) )),
% 0.24/0.45 inference(beta_eta_normalization,[],[f126])).
% 0.24/0.45 thf(f126,plain,(
% 0.24/0.45 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((rel @ sK2 @ Y0) & (?? @ mu @ (^[Y1 : mu]: (sK3 @ Y1 @ Y0))))) @ X1) = $false)) )),
% 0.24/0.45 inference(pi_clausification,[],[f125])).
% 0.24/0.45 thf(f125,plain,(
% 0.24/0.45 ((?? @ $i @ (^[Y0 : $i]: ((rel @ sK2 @ Y0) & (?? @ mu @ (^[Y1 : mu]: (sK3 @ Y1 @ Y0)))))) = $false)),
% 0.24/0.45 inference(boolean_simplification,[],[f124])).
% 0.24/0.45 thf(f124,plain,(
% 0.24/0.45 ($false = ($true => (?? @ $i @ (^[Y0 : $i]: ((rel @ sK2 @ Y0) & (?? @ mu @ (^[Y1 : mu]: (sK3 @ Y1 @ Y0))))))))),
% 0.24/0.45 inference(backward_demodulation,[],[f121,f123])).
% 0.24/0.45 thf(f196,plain,(
% 0.24/0.45 ((~ (sK3 @ sK5 @ sK4)) = $false)),
% 0.24/0.45 inference(beta_eta_normalization,[],[f195])).
% 0.24/0.45 thf(f195,plain,(
% 0.24/0.45 (((^[Y0 : mu]: (~ (sK3 @ Y0 @ sK4))) @ sK5) = $false)),
% 0.24/0.45 inference(sigma_clausification,[],[f164])).
% 0.24/0.45 % SZS output end Proof for theBenchmark
% 0.24/0.45 % (16280)------------------------------
% 0.24/0.45 % (16280)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.45 % (16280)Termination reason: Refutation
% 0.24/0.45
% 0.24/0.45 % (16280)Memory used [KB]: 5756
% 0.24/0.45 % (16280)Time elapsed: 0.023 s
% 0.24/0.45 % (16280)Instructions burned: 26 (million)
% 0.24/0.45 % (16280)------------------------------
% 0.24/0.45 % (16280)------------------------------
% 0.24/0.45 % (16268)Success in time 0.048 s
% 0.24/0.45 % Vampire---4.8 exiting
%------------------------------------------------------------------------------