TSTP Solution File: SEU464^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU464^1 : TPTP v8.2.0. Released v3.6.0.
% 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 : n012.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 03:49:01 EDT 2024
% Result : Theorem 0.18s 0.38s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SEU464^1 : TPTP v8.2.0. Released v3.6.0.
% 0.05/0.11 % 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
% 0.11/0.31 % Computer : n012.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sun May 19 16:58:23 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.11/0.31 This is a TH0_THM_EQU_NAR problem
% 0.17/0.31 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
% 0.17/0.33 % (12726)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)
% 0.17/0.33 % (12729)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)
% 0.17/0.33 % (12724)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)
% 0.17/0.33 % (12729)Instruction limit reached!
% 0.17/0.33 % (12729)------------------------------
% 0.17/0.33 % (12729)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.33 % (12729)Termination reason: Unknown
% 0.17/0.33 % (12729)Termination phase: shuffling
% 0.17/0.33
% 0.17/0.33 % (12729)Memory used [KB]: 1023
% 0.17/0.33 % (12729)Time elapsed: 0.003 s
% 0.17/0.33 % (12729)Instructions burned: 3 (million)
% 0.17/0.33 % (12729)------------------------------
% 0.17/0.33 % (12729)------------------------------
% 0.17/0.33 % (12726)Instruction limit reached!
% 0.17/0.33 % (12726)------------------------------
% 0.17/0.33 % (12726)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.33 % (12727)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)
% 0.17/0.33 % (12726)Termination reason: Unknown
% 0.17/0.33 % (12726)Termination phase: shuffling
% 0.17/0.33
% 0.17/0.33 % (12726)Memory used [KB]: 1023
% 0.17/0.33 % (12726)Time elapsed: 0.003 s
% 0.17/0.33 % (12726)Instructions burned: 3 (million)
% 0.17/0.33 % (12726)------------------------------
% 0.17/0.33 % (12726)------------------------------
% 0.17/0.34 % (12728)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.17/0.34 % (12722)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.17/0.34 % (12725)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.17/0.34 % (12725)Instruction limit reached!
% 0.17/0.34 % (12725)------------------------------
% 0.17/0.34 % (12725)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.34 % (12725)Termination reason: Unknown
% 0.17/0.34 % (12725)Termination phase: shuffling
% 0.17/0.34
% 0.17/0.34 % (12725)Memory used [KB]: 1023
% 0.17/0.34 % (12725)Time elapsed: 0.003 s
% 0.17/0.34 % (12725)Instructions burned: 3 (million)
% 0.17/0.34 % (12725)------------------------------
% 0.17/0.34 % (12725)------------------------------
% 0.17/0.34 % (12723)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)
% 0.17/0.35 % (12723)Instruction limit reached!
% 0.17/0.35 % (12723)------------------------------
% 0.17/0.35 % (12723)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.35 % (12723)Termination reason: Unknown
% 0.17/0.35 % (12723)Termination phase: Property scanning
% 0.17/0.35
% 0.17/0.35 % (12723)Memory used [KB]: 1023
% 0.17/0.35 % (12723)Time elapsed: 0.004 s
% 0.17/0.35 % (12723)Instructions burned: 5 (million)
% 0.17/0.35 % (12723)------------------------------
% 0.17/0.35 % (12723)------------------------------
% 0.17/0.35 % (12728)Instruction limit reached!
% 0.17/0.35 % (12728)------------------------------
% 0.17/0.35 % (12728)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.35 % (12728)Termination reason: Unknown
% 0.17/0.35 % (12728)Termination phase: Saturation
% 0.17/0.35
% 0.17/0.35 % (12728)Memory used [KB]: 5756
% 0.17/0.35 % (12728)Time elapsed: 0.013 s
% 0.17/0.35 % (12728)Instructions burned: 19 (million)
% 0.17/0.35 % (12728)------------------------------
% 0.17/0.35 % (12728)------------------------------
% 0.17/0.35 % (12730)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)
% 0.17/0.35 % (12724)Instruction limit reached!
% 0.17/0.35 % (12724)------------------------------
% 0.17/0.35 % (12724)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.35 % (12724)Termination reason: Unknown
% 0.17/0.35 % (12724)Termination phase: Saturation
% 0.17/0.35
% 0.17/0.35 % (12724)Memory used [KB]: 5756
% 0.17/0.35 % (12724)Time elapsed: 0.017 s
% 0.17/0.35 % (12724)Instructions burned: 28 (million)
% 0.17/0.35 % (12724)------------------------------
% 0.17/0.35 % (12724)------------------------------
% 0.17/0.36 % (12733)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)
% 0.17/0.36 % (12731)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)
% 0.17/0.36 % (12734)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.17/0.36 % (12734)Instruction limit reached!
% 0.17/0.36 % (12734)------------------------------
% 0.17/0.36 % (12734)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.36 % (12734)Termination reason: Unknown
% 0.17/0.36 % (12734)Termination phase: Property scanning
% 0.17/0.36
% 0.17/0.36 % (12734)Memory used [KB]: 1023
% 0.17/0.36 % (12734)Time elapsed: 0.005 s
% 0.17/0.36 % (12734)Instructions burned: 7 (million)
% 0.17/0.36 % (12734)------------------------------
% 0.17/0.36 % (12734)------------------------------
% 0.17/0.37 % (12730)Instruction limit reached!
% 0.17/0.37 % (12730)------------------------------
% 0.17/0.37 % (12730)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.37 % (12730)Termination reason: Unknown
% 0.17/0.37 % (12730)Termination phase: Saturation
% 0.17/0.37
% 0.17/0.37 % (12730)Memory used [KB]: 5884
% 0.17/0.37 % (12730)Time elapsed: 0.020 s
% 0.17/0.37 % (12730)Instructions burned: 37 (million)
% 0.17/0.37 % (12730)------------------------------
% 0.17/0.37 % (12730)------------------------------
% 0.17/0.37 % (12731)Instruction limit reached!
% 0.17/0.37 % (12731)------------------------------
% 0.17/0.37 % (12731)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.37 % (12731)Termination reason: Unknown
% 0.17/0.37 % (12731)Termination phase: Saturation
% 0.17/0.37
% 0.17/0.37 % (12731)Memory used [KB]: 5628
% 0.17/0.37 % (12731)Time elapsed: 0.035 s
% 0.17/0.37 % (12731)Instructions burned: 16 (million)
% 0.17/0.37 % (12731)------------------------------
% 0.17/0.37 % (12731)------------------------------
% 0.17/0.37 % (12732)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)
% 0.17/0.37 % (12732)Instruction limit reached!
% 0.17/0.37 % (12732)------------------------------
% 0.17/0.37 % (12732)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.37 % (12732)Termination reason: Unknown
% 0.17/0.37 % (12732)Termination phase: shuffling
% 0.17/0.37
% 0.17/0.37 % (12732)Memory used [KB]: 1023
% 0.17/0.37 % (12732)Time elapsed: 0.004 s
% 0.17/0.37 % (12732)Instructions burned: 4 (million)
% 0.17/0.37 % (12732)------------------------------
% 0.17/0.37 % (12732)------------------------------
% 0.18/0.37 % (12733)First to succeed.
% 0.18/0.38 % (12733)Refutation found. Thanks to Tanya!
% 0.18/0.38 % SZS status Theorem for theBenchmark
% 0.18/0.38 % SZS output start Proof for theBenchmark
% 0.18/0.38 thf(func_def_0, type, subrel: ($i > $i > $o) > ($i > $i > $o) > $o).
% 0.18/0.38 thf(func_def_2, type, inv: ($i > $i > $o) > $i > $i > $o).
% 0.18/0.38 thf(func_def_3, type, idem: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.18/0.38 thf(func_def_4, type, infl: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.18/0.38 thf(func_def_5, type, mono: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.18/0.38 thf(func_def_6, type, refl: ($i > $i > $o) > $o).
% 0.18/0.38 thf(func_def_7, type, irrefl: ($i > $i > $o) > $o).
% 0.18/0.38 thf(func_def_8, type, rc: ($i > $i > $o) > $i > $i > $o).
% 0.18/0.38 thf(func_def_9, type, symm: ($i > $i > $o) > $o).
% 0.18/0.38 thf(func_def_10, type, antisymm: ($i > $i > $o) > $o).
% 0.18/0.38 thf(func_def_11, type, asymm: ($i > $i > $o) > $o).
% 0.18/0.38 thf(func_def_12, type, sc: ($i > $i > $o) > $i > $i > $o).
% 0.18/0.38 thf(func_def_13, type, trans: ($i > $i > $o) > $o).
% 0.18/0.38 thf(func_def_14, type, tc: ($i > $i > $o) > $i > $i > $o).
% 0.18/0.38 thf(func_def_15, type, trc: ($i > $i > $o) > $i > $i > $o).
% 0.18/0.38 thf(func_def_16, type, trsc: ($i > $i > $o) > $i > $i > $o).
% 0.18/0.38 thf(func_def_17, type, po: ($i > $i > $o) > $o).
% 0.18/0.38 thf(func_def_18, type, so: ($i > $i > $o) > $o).
% 0.18/0.38 thf(func_def_19, type, total: ($i > $i > $o) > $o).
% 0.18/0.38 thf(func_def_20, type, term: ($i > $i > $o) > $o).
% 0.18/0.38 thf(func_def_21, type, ind: ($i > $i > $o) > $o).
% 0.18/0.38 thf(func_def_22, type, innf: ($i > $i > $o) > $i > $o).
% 0.18/0.38 thf(func_def_23, type, nfof: ($i > $i > $o) > $i > $i > $o).
% 0.18/0.38 thf(func_def_24, type, norm: ($i > $i > $o) > $o).
% 0.18/0.38 thf(func_def_25, type, join: ($i > $i > $o) > $i > $i > $o).
% 0.18/0.38 thf(func_def_26, type, lconfl: ($i > $i > $o) > $o).
% 0.18/0.38 thf(func_def_27, type, sconfl: ($i > $i > $o) > $o).
% 0.18/0.38 thf(func_def_28, type, confl: ($i > $i > $o) > $o).
% 0.18/0.38 thf(func_def_29, type, cr: ($i > $i > $o) > $o).
% 0.18/0.38 thf(func_def_48, type, ph1: !>[X0: $tType]:(X0)).
% 0.18/0.38 thf(func_def_49, type, sK2: $i > $i > $o).
% 0.18/0.38 thf(func_def_50, type, sK3: $i > $i > $o).
% 0.18/0.38 thf(f190,plain,(
% 0.18/0.38 $false),
% 0.18/0.38 inference(trivial_inequality_removal,[],[f189])).
% 0.18/0.38 thf(f189,plain,(
% 0.18/0.38 ($true = $false)),
% 0.18/0.38 inference(forward_demodulation,[],[f188,f152])).
% 0.18/0.38 thf(f152,plain,(
% 0.18/0.38 ($false = (sK2 @ sK4 @ sK5))),
% 0.18/0.38 inference(boolean_simplification,[],[f151])).
% 0.18/0.38 thf(f151,plain,(
% 0.18/0.38 ($false = ($true => (sK2 @ sK4 @ sK5)))),
% 0.18/0.38 inference(backward_demodulation,[],[f148,f150])).
% 0.18/0.38 thf(f150,plain,(
% 0.18/0.38 ($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y0) & (sK2 @ Y1 @ Y2)) => (sK2 @ Y1 @ Y0)))))))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK5))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1 @ Y0) => (sK2 @ Y1 @ Y0))))))))),
% 0.18/0.38 inference(binary_proxy_clausification,[],[f148])).
% 0.18/0.38 thf(f148,plain,(
% 0.18/0.38 ($false = ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y0) & (sK2 @ Y1 @ Y2)) => (sK2 @ Y1 @ Y0)))))))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK5))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1 @ Y0) => (sK2 @ Y1 @ Y0))))))) => (sK2 @ sK4 @ sK5)))),
% 0.18/0.38 inference(beta_eta_normalization,[],[f147])).
% 0.18/0.38 thf(f147,plain,(
% 0.18/0.38 ($false = ((^[Y0 : $i]: ((((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((sK2 @ Y3 @ Y1) & (sK2 @ Y2 @ Y3)) => (sK2 @ Y2 @ Y1)))))))) & (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y3 @ Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ sK4 @ Y0))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2 @ Y1) => (sK2 @ Y2 @ Y1))))))) => (sK2 @ sK4 @ Y0))) @ sK5))),
% 0.18/0.38 inference(sigma_clausification,[],[f146])).
% 0.18/0.38 thf(f146,plain,(
% 0.18/0.38 ((!! @ $i @ (^[Y0 : $i]: ((((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((sK2 @ Y3 @ Y1) & (sK2 @ Y2 @ Y3)) => (sK2 @ Y2 @ Y1)))))))) & (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y3 @ Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ sK4 @ Y0))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2 @ Y1) => (sK2 @ Y2 @ Y1))))))) => (sK2 @ sK4 @ Y0)))) = $false)),
% 0.18/0.38 inference(beta_eta_normalization,[],[f145])).
% 0.18/0.38 thf(f145,plain,(
% 0.18/0.38 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((sK2 @ Y4 @ Y2) & (sK2 @ Y3 @ Y4)) => (sK2 @ Y3 @ Y2)))))))) & (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK3 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3 @ Y2) => (sK2 @ Y3 @ Y2))))))) => (sK2 @ Y0 @ Y1))))) @ sK4))),
% 0.18/0.38 inference(sigma_clausification,[],[f144])).
% 0.18/0.38 thf(f144,plain,(
% 0.18/0.38 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((sK2 @ Y4 @ Y2) & (sK2 @ Y3 @ Y4)) => (sK2 @ Y3 @ Y2)))))))) & (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK3 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3 @ Y2) => (sK2 @ Y3 @ Y2))))))) => (sK2 @ Y0 @ Y1)))))))),
% 0.18/0.38 inference(beta_eta_normalization,[],[f143])).
% 0.18/0.38 thf(f143,plain,(
% 0.18/0.38 ($false = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((sK2 @ Y5 @ Y3) & (sK2 @ Y4 @ Y5)) => (sK2 @ Y4 @ Y3)))))))) & (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y5 @ Y4)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y1 @ Y2))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) => (sK2 @ Y4 @ Y3))))))) => (sK2 @ Y1 @ Y2))))))) @ sK3))),
% 0.18/0.38 inference(sigma_clausification,[],[f142])).
% 0.18/0.38 thf(f142,plain,(
% 0.18/0.38 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((sK2 @ Y5 @ Y3) & (sK2 @ Y4 @ Y5)) => (sK2 @ Y4 @ Y3)))))))) & (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y5 @ Y4)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y1 @ Y2))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) => (sK2 @ Y4 @ Y3))))))) => (sK2 @ Y1 @ Y2)))))))) = $false)),
% 0.18/0.38 inference(beta_eta_normalization,[],[f141])).
% 0.18/0.38 thf(f141,plain,(
% 0.18/0.38 ($false = ((^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y0 @ Y6 @ Y4) & (Y0 @ Y5 @ Y6)) => (Y0 @ Y5 @ Y4)))))))) & (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y6 @ Y7)) => (Y4 @ Y6 @ Y5)))))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y2 @ Y3))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y1 @ Y5 @ Y4) => (Y0 @ Y5 @ Y4))))))) => (Y0 @ Y2 @ Y3))))))))) @ sK2))),
% 0.18/0.38 inference(sigma_clausification,[],[f138])).
% 0.18/0.38 thf(f138,plain,(
% 0.18/0.38 ($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y0 @ Y6 @ Y4) & (Y0 @ Y5 @ Y6)) => (Y0 @ Y5 @ Y4)))))))) & (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y6 @ Y7)) => (Y4 @ Y6 @ Y5)))))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y2 @ Y3))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y1 @ Y5 @ Y4) => (Y0 @ Y5 @ Y4))))))) => (Y0 @ Y2 @ Y3)))))))))))),
% 0.18/0.38 inference(not_proxy_clausification,[],[f137])).
% 0.18/0.38 thf(f137,plain,(
% 0.18/0.38 ($true = (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y0 @ Y6 @ Y4) & (Y0 @ Y5 @ Y6)) => (Y0 @ Y5 @ Y4)))))))) & (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y6 @ Y7)) => (Y4 @ Y6 @ Y5)))))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y2 @ Y3))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y1 @ Y5 @ Y4) => (Y0 @ Y5 @ Y4))))))) => (Y0 @ Y2 @ Y3))))))))))))),
% 0.18/0.38 inference(beta_eta_normalization,[],[f136])).
% 0.18/0.38 thf(f136,plain,(
% 0.18/0.38 ($true = (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((((^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y6 @ Y7)) => (Y4 @ Y6 @ Y5))))))))) @ Y0) & (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((((^[Y5 : $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y6) & (Y5 @ Y7 @ Y8)) => (Y5 @ Y7 @ Y6))))))))) @ Y4) & ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i > $i > $o]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y5 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7))))))))) @ Y1 @ Y4)) => (Y4 @ Y2 @ Y3))))) & ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6))))))))) @ Y1 @ Y0)) => (Y0 @ Y2 @ Y3))))))))))))),
% 0.18/0.38 inference(definition_unfolding,[],[f104,f119,f119,f108,f108])).
% 0.18/0.38 thf(f108,plain,(
% 0.18/0.38 (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))))))),
% 0.18/0.38 inference(cnf_transformation,[],[f82])).
% 0.18/0.38 thf(f82,plain,(
% 0.18/0.38 (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))))))),
% 0.18/0.38 inference(fool_elimination,[],[f81])).
% 0.18/0.38 thf(f81,plain,(
% 0.18/0.38 (subrel = (^[X0 : $i > $i > $o, X1 : $i > $i > $o] : (! [X2,X3] : ((X0 @ X2 @ X3) => (X1 @ X2 @ X3)))))),
% 0.18/0.38 inference(rectify,[],[f1])).
% 0.18/0.38 thf(f1,axiom,(
% 0.18/0.38 (subrel = (^[X0 : $i > $i > $o, X1 : $i > $i > $o] : (! [X2,X3] : ((X0 @ X2 @ X3) => (X1 @ X2 @ X3)))))),
% 0.18/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subrel)).
% 0.18/0.38 thf(f119,plain,(
% 0.18/0.38 (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))))),
% 0.18/0.38 inference(cnf_transformation,[],[f78])).
% 0.18/0.38 thf(f78,plain,(
% 0.18/0.38 (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))))),
% 0.18/0.38 inference(fool_elimination,[],[f77])).
% 0.18/0.38 thf(f77,plain,(
% 0.18/0.38 (trans = (^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X2 @ X1) & (X0 @ X1 @ X3)) => (X0 @ X2 @ X3)))))),
% 0.18/0.38 inference(rectify,[],[f13])).
% 0.18/0.38 thf(f13,axiom,(
% 0.18/0.38 (trans = (^[X0 : $i > $i > $o] : (! [X3,X2,X5] : (((X0 @ X2 @ X3) & (X0 @ X3 @ X5)) => (X0 @ X2 @ X5)))))),
% 0.18/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive)).
% 0.18/0.38 thf(f104,plain,(
% 0.18/0.38 ($true = (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((trans @ Y0) & (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((trans @ Y4) & (subrel @ Y1 @ Y4)) => (Y4 @ Y2 @ Y3))))) & (subrel @ Y1 @ Y0)) => (Y0 @ Y2 @ Y3))))))))))))),
% 0.18/0.38 inference(cnf_transformation,[],[f57])).
% 0.18/0.38 thf(f57,plain,(
% 0.18/0.38 ($true = (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((trans @ Y0) & (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((trans @ Y4) & (subrel @ Y1 @ Y4)) => (Y4 @ Y2 @ Y3))))) & (subrel @ Y1 @ Y0)) => (Y0 @ Y2 @ Y3))))))))))))),
% 0.18/0.38 inference(fool_elimination,[],[f56])).
% 0.18/0.38 thf(f56,plain,(
% 0.18/0.38 ~! [X0,X1,X2 : $i > $i > $o,X3 : $i > $i > $o] : (((subrel @ X2 @ X3) & ! [X4 : $i > $i > $o] : (((subrel @ X2 @ X4) & (trans @ X4)) => (X4 @ X1 @ X0)) & (trans @ X3)) => (X3 @ X1 @ X0))),
% 0.18/0.38 inference(rectify,[],[f31])).
% 0.18/0.38 thf(f31,negated_conjecture,(
% 0.18/0.38 ~! [X3,X2,X0 : $i > $i > $o,X1 : $i > $i > $o] : (((subrel @ X0 @ X1) & ! [X1 : $i > $i > $o] : (((subrel @ X0 @ X1) & (trans @ X1)) => (X1 @ X2 @ X3)) & (trans @ X1)) => (X1 @ X2 @ X3))),
% 0.18/0.38 inference(negated_conjecture,[],[f30])).
% 0.18/0.38 thf(f30,conjecture,(
% 0.18/0.38 ! [X3,X2,X0 : $i > $i > $o,X1 : $i > $i > $o] : (((subrel @ X0 @ X1) & ! [X1 : $i > $i > $o] : (((subrel @ X0 @ X1) & (trans @ X1)) => (X1 @ X2 @ X3)) & (trans @ X1)) => (X1 @ X2 @ X3))),
% 0.18/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive_closure_is_transitive4)).
% 0.18/0.38 thf(f188,plain,(
% 0.18/0.38 ($true = (sK2 @ sK4 @ sK5))),
% 0.18/0.38 inference(boolean_simplification,[],[f187])).
% 0.18/0.38 thf(f187,plain,(
% 0.18/0.38 ($true = ($true => (sK2 @ sK4 @ sK5)))),
% 0.18/0.38 inference(forward_demodulation,[],[f186,f170])).
% 0.18/0.38 thf(f170,plain,(
% 0.18/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y0) & (sK2 @ Y1 @ Y2)) => (sK2 @ Y1 @ Y0)))))))))),
% 0.18/0.38 inference(binary_proxy_clausification,[],[f154])).
% 0.18/0.38 thf(f154,plain,(
% 0.18/0.38 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y0) & (sK2 @ Y1 @ Y2)) => (sK2 @ Y1 @ Y0)))))))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK5))))))),
% 0.18/0.38 inference(binary_proxy_clausification,[],[f150])).
% 0.18/0.38 thf(f186,plain,(
% 0.18/0.38 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y0) & (sK2 @ Y1 @ Y2)) => (sK2 @ Y1 @ Y0)))))))) => (sK2 @ sK4 @ sK5)))),
% 0.18/0.38 inference(boolean_simplification,[],[f180])).
% 0.18/0.38 thf(f180,plain,(
% 0.18/0.38 ($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y0) & (sK2 @ Y1 @ Y2)) => (sK2 @ Y1 @ Y0)))))))) & $true) => (sK2 @ sK4 @ sK5)))),
% 0.18/0.38 inference(superposition,[],[f174,f156])).
% 0.18/0.38 thf(f156,plain,(
% 0.18/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1 @ Y0) => (sK2 @ Y1 @ Y0)))))))),
% 0.18/0.38 inference(boolean_simplification,[],[f155])).
% 0.18/0.38 thf(f155,plain,(
% 0.18/0.38 ($true = ($true & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1 @ Y0) => (sK2 @ Y1 @ Y0))))))))),
% 0.18/0.38 inference(backward_demodulation,[],[f150,f154])).
% 0.18/0.38 thf(f174,plain,(
% 0.18/0.38 ( ! [X1 : $i > $i > $o] : (($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X1 @ Y2 @ Y0) & (X1 @ Y1 @ Y2)) => (X1 @ Y1 @ Y0)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1 @ Y0) => (X1 @ Y1 @ Y0))))))) => (X1 @ sK4 @ sK5)))) )),
% 0.18/0.38 inference(beta_eta_normalization,[],[f173])).
% 0.18/0.38 thf(f173,plain,(
% 0.18/0.38 ( ! [X1 : $i > $i > $o] : (($true = ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK5))) @ X1))) )),
% 0.18/0.38 inference(pi_clausification,[],[f172])).
% 0.18/0.38 thf(f172,plain,(
% 0.18/0.38 ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK5)))))),
% 0.18/0.38 inference(boolean_simplification,[],[f171])).
% 0.18/0.38 thf(f171,plain,(
% 0.18/0.38 ($true = ($true & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK5))))))),
% 0.18/0.38 inference(backward_demodulation,[],[f154,f170])).
% 0.18/0.38 % SZS output end Proof for theBenchmark
% 0.18/0.38 % (12733)------------------------------
% 0.18/0.38 % (12733)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.38 % (12733)Termination reason: Refutation
% 0.18/0.38
% 0.18/0.38 % (12733)Memory used [KB]: 5884
% 0.18/0.38 % (12733)Time elapsed: 0.018 s
% 0.18/0.38 % (12733)Instructions burned: 26 (million)
% 0.18/0.38 % (12733)------------------------------
% 0.18/0.38 % (12733)------------------------------
% 0.18/0.38 % (12721)Success in time 0.043 s
% 0.18/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------