TSTP Solution File: SEU462^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU462^1 : 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 : n022.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 03:49:00 EDT 2024
% Result : Theorem 0.22s 0.44s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.14 % Problem : SEU462^1 : TPTP v8.2.0. Released v3.6.0.
% 0.06/0.15 % 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
% 0.15/0.37 % Computer : n022.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sun May 19 17:45:08 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.15/0.37 This is a TH0_THM_EQU_NAR problem
% 0.15/0.37 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
% 0.22/0.40 % (21626)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.40 % (21622)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)
% 0.22/0.40 % (21623)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.40 % (21627)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)
% 0.22/0.40 % (21625)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)
% 0.22/0.40 % (21620)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.22/0.40 % (21624)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)
% 0.22/0.40 % (21621)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)
% 0.22/0.40 % (21623)Instruction limit reached!
% 0.22/0.40 % (21623)------------------------------
% 0.22/0.40 % (21623)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (21623)Termination reason: Unknown
% 0.22/0.40 % (21623)Termination phase: shuffling
% 0.22/0.40
% 0.22/0.40 % (21623)Memory used [KB]: 1023
% 0.22/0.40 % (21624)Instruction limit reached!
% 0.22/0.40 % (21624)------------------------------
% 0.22/0.40 % (21624)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (21623)Time elapsed: 0.003 s
% 0.22/0.40 % (21623)Instructions burned: 3 (million)
% 0.22/0.40 % (21623)------------------------------
% 0.22/0.40 % (21623)------------------------------
% 0.22/0.40 % (21624)Termination reason: Unknown
% 0.22/0.40 % (21624)Termination phase: shuffling
% 0.22/0.40
% 0.22/0.40 % (21624)Memory used [KB]: 1023
% 0.22/0.40 % (21624)Time elapsed: 0.003 s
% 0.22/0.40 % (21624)Instructions burned: 3 (million)
% 0.22/0.40 % (21624)------------------------------
% 0.22/0.40 % (21624)------------------------------
% 0.22/0.40 % (21627)Instruction limit reached!
% 0.22/0.40 % (21627)------------------------------
% 0.22/0.40 % (21627)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (21627)Termination reason: Unknown
% 0.22/0.40 % (21627)Termination phase: shuffling
% 0.22/0.40
% 0.22/0.40 % (21627)Memory used [KB]: 1023
% 0.22/0.40 % (21627)Time elapsed: 0.003 s
% 0.22/0.40 % (21627)Instructions burned: 4 (million)
% 0.22/0.40 % (21627)------------------------------
% 0.22/0.40 % (21627)------------------------------
% 0.22/0.40 % (21621)Instruction limit reached!
% 0.22/0.40 % (21621)------------------------------
% 0.22/0.40 % (21621)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (21621)Termination reason: Unknown
% 0.22/0.40 % (21621)Termination phase: Property scanning
% 0.22/0.40
% 0.22/0.40 % (21621)Memory used [KB]: 1023
% 0.22/0.40 % (21621)Time elapsed: 0.005 s
% 0.22/0.40 % (21621)Instructions burned: 5 (million)
% 0.22/0.40 % (21621)------------------------------
% 0.22/0.40 % (21621)------------------------------
% 0.22/0.41 % (21626)Instruction limit reached!
% 0.22/0.41 % (21626)------------------------------
% 0.22/0.41 % (21626)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (21626)Termination reason: Unknown
% 0.22/0.41 % (21626)Termination phase: Saturation
% 0.22/0.41
% 0.22/0.41 % (21626)Memory used [KB]: 5756
% 0.22/0.41 % (21626)Time elapsed: 0.012 s
% 0.22/0.41 % (21626)Instructions burned: 18 (million)
% 0.22/0.41 % (21626)------------------------------
% 0.22/0.41 % (21626)------------------------------
% 0.22/0.41 % (21622)Instruction limit reached!
% 0.22/0.41 % (21622)------------------------------
% 0.22/0.41 % (21622)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (21622)Termination reason: Unknown
% 0.22/0.41 % (21622)Termination phase: Saturation
% 0.22/0.41
% 0.22/0.41 % (21622)Memory used [KB]: 5756
% 0.22/0.41 % (21622)Time elapsed: 0.018 s
% 0.22/0.41 % (21622)Instructions burned: 28 (million)
% 0.22/0.41 % (21622)------------------------------
% 0.22/0.41 % (21622)------------------------------
% 0.22/0.41 % (21628)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)
% 0.22/0.41 % (21630)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)
% 0.22/0.41 % (21629)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)
% 0.22/0.41 % (21630)Instruction limit reached!
% 0.22/0.41 % (21630)------------------------------
% 0.22/0.41 % (21630)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (21630)Termination reason: Unknown
% 0.22/0.41 % (21630)Termination phase: shuffling
% 0.22/0.41
% 0.22/0.41 % (21630)Memory used [KB]: 1023
% 0.22/0.41 % (21630)Time elapsed: 0.003 s
% 0.22/0.41 % (21630)Instructions burned: 3 (million)
% 0.22/0.41 % (21630)------------------------------
% 0.22/0.41 % (21630)------------------------------
% 0.22/0.42 % (21631)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)
% 0.22/0.42 % (21629)Instruction limit reached!
% 0.22/0.42 % (21629)------------------------------
% 0.22/0.42 % (21629)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (21629)Termination reason: Unknown
% 0.22/0.42 % (21629)Termination phase: Saturation
% 0.22/0.42
% 0.22/0.42 % (21629)Memory used [KB]: 5628
% 0.22/0.42 % (21629)Time elapsed: 0.010 s
% 0.22/0.42 % (21629)Instructions burned: 15 (million)
% 0.22/0.42 % (21629)------------------------------
% 0.22/0.42 % (21629)------------------------------
% 0.22/0.42 % (21632)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.43 % (21632)Instruction limit reached!
% 0.22/0.43 % (21632)------------------------------
% 0.22/0.43 % (21632)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (21632)Termination reason: Unknown
% 0.22/0.43 % (21632)Termination phase: Property scanning
% 0.22/0.43
% 0.22/0.43 % (21632)Memory used [KB]: 1023
% 0.22/0.43 % (21632)Time elapsed: 0.006 s
% 0.22/0.43 % (21632)Instructions burned: 7 (million)
% 0.22/0.43 % (21632)------------------------------
% 0.22/0.43 % (21632)------------------------------
% 0.22/0.43 % (21631)First to succeed.
% 0.22/0.43 % (21633)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.22/0.43 % (21634)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)
% 0.22/0.43 % (21628)Instruction limit reached!
% 0.22/0.43 % (21628)------------------------------
% 0.22/0.43 % (21628)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (21628)Termination reason: Unknown
% 0.22/0.43 % (21628)Termination phase: Saturation
% 0.22/0.43
% 0.22/0.43 % (21628)Memory used [KB]: 5884
% 0.22/0.43 % (21628)Time elapsed: 0.023 s
% 0.22/0.43 % (21628)Instructions burned: 37 (million)
% 0.22/0.43 % (21628)------------------------------
% 0.22/0.43 % (21628)------------------------------
% 0.22/0.43 % (21634)Instruction limit reached!
% 0.22/0.43 % (21634)------------------------------
% 0.22/0.43 % (21634)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (21634)Termination reason: Unknown
% 0.22/0.43 % (21634)Termination phase: shuffling
% 0.22/0.43
% 0.22/0.43 % (21634)Memory used [KB]: 1023
% 0.22/0.43 % (21634)Time elapsed: 0.004 s
% 0.22/0.43 % (21634)Instructions burned: 4 (million)
% 0.22/0.43 % (21634)------------------------------
% 0.22/0.43 % (21634)------------------------------
% 0.22/0.44 % (21635)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)
% 0.22/0.44 % (21631)Refutation found. Thanks to Tanya!
% 0.22/0.44 % SZS status Theorem for theBenchmark
% 0.22/0.44 % SZS output start Proof for theBenchmark
% 0.22/0.44 thf(func_def_0, type, subrel: ($i > $i > $o) > ($i > $i > $o) > $o).
% 0.22/0.44 thf(func_def_2, type, inv: ($i > $i > $o) > $i > $i > $o).
% 0.22/0.44 thf(func_def_3, type, idem: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.22/0.44 thf(func_def_4, type, infl: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.22/0.44 thf(func_def_5, type, mono: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.22/0.44 thf(func_def_6, type, refl: ($i > $i > $o) > $o).
% 0.22/0.44 thf(func_def_7, type, irrefl: ($i > $i > $o) > $o).
% 0.22/0.44 thf(func_def_8, type, rc: ($i > $i > $o) > $i > $i > $o).
% 0.22/0.44 thf(func_def_9, type, symm: ($i > $i > $o) > $o).
% 0.22/0.44 thf(func_def_10, type, antisymm: ($i > $i > $o) > $o).
% 0.22/0.44 thf(func_def_11, type, asymm: ($i > $i > $o) > $o).
% 0.22/0.44 thf(func_def_12, type, sc: ($i > $i > $o) > $i > $i > $o).
% 0.22/0.44 thf(func_def_13, type, trans: ($i > $i > $o) > $o).
% 0.22/0.44 thf(func_def_14, type, tc: ($i > $i > $o) > $i > $i > $o).
% 0.22/0.44 thf(func_def_15, type, trc: ($i > $i > $o) > $i > $i > $o).
% 0.22/0.44 thf(func_def_16, type, trsc: ($i > $i > $o) > $i > $i > $o).
% 0.22/0.44 thf(func_def_17, type, po: ($i > $i > $o) > $o).
% 0.22/0.44 thf(func_def_18, type, so: ($i > $i > $o) > $o).
% 0.22/0.44 thf(func_def_19, type, total: ($i > $i > $o) > $o).
% 0.22/0.44 thf(func_def_20, type, term: ($i > $i > $o) > $o).
% 0.22/0.44 thf(func_def_21, type, ind: ($i > $i > $o) > $o).
% 0.22/0.44 thf(func_def_22, type, innf: ($i > $i > $o) > $i > $o).
% 0.22/0.44 thf(func_def_23, type, nfof: ($i > $i > $o) > $i > $i > $o).
% 0.22/0.44 thf(func_def_24, type, norm: ($i > $i > $o) > $o).
% 0.22/0.44 thf(func_def_25, type, join: ($i > $i > $o) > $i > $i > $o).
% 0.22/0.44 thf(func_def_26, type, lconfl: ($i > $i > $o) > $o).
% 0.22/0.44 thf(func_def_27, type, sconfl: ($i > $i > $o) > $o).
% 0.22/0.44 thf(func_def_28, type, confl: ($i > $i > $o) > $o).
% 0.22/0.44 thf(func_def_29, type, cr: ($i > $i > $o) > $o).
% 0.22/0.44 thf(func_def_47, type, ph1: !>[X0: $tType]:(X0)).
% 0.22/0.44 thf(func_def_49, type, sK3: $i > $i > $o).
% 0.22/0.44 thf(func_def_50, type, sK4: $i > $i > $o).
% 0.22/0.44 thf(f170,plain,(
% 0.22/0.44 $false),
% 0.22/0.44 inference(trivial_inequality_removal,[],[f169])).
% 0.22/0.44 thf(f169,plain,(
% 0.22/0.44 ($true = $false)),
% 0.22/0.44 inference(boolean_simplification,[],[f168])).
% 0.22/0.44 thf(f168,plain,(
% 0.22/0.44 ($true = (~ $true))),
% 0.22/0.44 inference(forward_demodulation,[],[f167,f160])).
% 0.22/0.44 thf(f160,plain,(
% 0.22/0.44 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ Y1)))))))),
% 0.22/0.44 inference(binary_proxy_clausification,[],[f154])).
% 0.22/0.44 thf(f154,plain,(
% 0.22/0.44 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK3 @ Y2 @ Y1) & (sK3 @ Y1 @ Y0)) => (sK3 @ Y2 @ Y0))))))))))),
% 0.22/0.44 inference(binary_proxy_clausification,[],[f150])).
% 0.22/0.44 thf(f150,plain,(
% 0.22/0.44 ($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK3 @ Y2 @ Y1) & (sK3 @ Y1 @ Y0)) => (sK3 @ Y2 @ Y0))))))))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK4 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK5 @ sK2))))))),
% 0.22/0.44 inference(binary_proxy_clausification,[],[f148])).
% 0.22/0.44 thf(f148,plain,(
% 0.22/0.44 ($false = ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK3 @ Y2 @ Y1) & (sK3 @ Y1 @ Y0)) => (sK3 @ Y2 @ Y0))))))))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK4 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK5 @ sK2))))) => (sK3 @ sK5 @ sK2)))),
% 0.22/0.44 inference(beta_eta_normalization,[],[f147])).
% 0.22/0.44 thf(f147,plain,(
% 0.22/0.44 ($false = ((^[Y0 : $i]: ((((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK4 @ Y1 @ Y2) => (sK3 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((sK3 @ Y3 @ Y2) & (sK3 @ Y2 @ Y1)) => (sK3 @ Y3 @ Y1))))))))) & (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y4 @ Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ Y0 @ sK2))))) => (sK3 @ Y0 @ sK2))) @ sK5))),
% 0.22/0.44 inference(sigma_clausification,[],[f146])).
% 0.22/0.44 thf(f146,plain,(
% 0.22/0.44 ($false = (!! @ $i @ (^[Y0 : $i]: ((((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK4 @ Y1 @ Y2) => (sK3 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((sK3 @ Y3 @ Y2) & (sK3 @ Y2 @ Y1)) => (sK3 @ Y3 @ Y1))))))))) & (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y4 @ Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ Y0 @ sK2))))) => (sK3 @ Y0 @ sK2)))))),
% 0.22/0.44 inference(beta_eta_normalization,[],[f145])).
% 0.22/0.44 thf(f145,plain,(
% 0.22/0.44 ($false = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (sK3 @ Y2 @ Y3)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((sK3 @ Y4 @ Y3) & (sK3 @ Y3 @ Y2)) => (sK3 @ Y4 @ Y2))))))))) & (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y1 @ sK2))))) => (sK3 @ Y1 @ sK2))))) @ sK4))),
% 0.22/0.44 inference(sigma_clausification,[],[f144])).
% 0.22/0.44 thf(f144,plain,(
% 0.22/0.44 ($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (sK3 @ Y2 @ Y3)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((sK3 @ Y4 @ Y3) & (sK3 @ Y3 @ Y2)) => (sK3 @ Y4 @ Y2))))))))) & (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y1 @ sK2))))) => (sK3 @ Y1 @ sK2)))))))),
% 0.22/0.44 inference(beta_eta_normalization,[],[f143])).
% 0.22/0.44 thf(f143,plain,(
% 0.22/0.44 (((^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y3 @ Y4) => (Y0 @ Y3 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y0 @ Y5 @ Y4) & (Y0 @ Y4 @ Y3)) => (Y0 @ Y5 @ Y3))))))))) & (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y1 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ sK2))))) => (Y0 @ Y2 @ sK2))))))) @ sK3) = $false)),
% 0.22/0.44 inference(sigma_clausification,[],[f142])).
% 0.22/0.44 thf(f142,plain,(
% 0.22/0.44 ($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y3 @ Y4) => (Y0 @ Y3 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y0 @ Y5 @ Y4) & (Y0 @ Y4 @ Y3)) => (Y0 @ Y5 @ Y3))))))))) & (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y1 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ sK2))))) => (Y0 @ Y2 @ sK2)))))))))),
% 0.22/0.44 inference(beta_eta_normalization,[],[f141])).
% 0.22/0.44 thf(f141,plain,(
% 0.22/0.44 (((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y2 @ Y4 @ Y5) => (Y1 @ Y4 @ Y5)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y1 @ Y6 @ Y5) & (Y1 @ Y5 @ Y4)) => (Y1 @ Y6 @ Y4))))))))) & (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y6) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y7 @ Y5)))))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y3 @ Y0))))) => (Y1 @ Y3 @ Y0))))))))) @ sK2) = $false)),
% 0.22/0.44 inference(sigma_clausification,[],[f138])).
% 0.22/0.44 thf(f138,plain,(
% 0.22/0.44 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y2 @ Y4 @ Y5) => (Y1 @ Y4 @ Y5)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y1 @ Y6 @ Y5) & (Y1 @ Y5 @ Y4)) => (Y1 @ Y6 @ Y4))))))))) & (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y6) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y7 @ Y5)))))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y3 @ Y0))))) => (Y1 @ Y3 @ Y0)))))))))))),
% 0.22/0.44 inference(not_proxy_clausification,[],[f137])).
% 0.22/0.44 thf(f137,plain,(
% 0.22/0.44 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y2 @ Y4 @ Y5) => (Y1 @ Y4 @ Y5)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y1 @ Y6 @ Y5) & (Y1 @ Y5 @ Y4)) => (Y1 @ Y6 @ Y4))))))))) & (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y6) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y7 @ Y5)))))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y3 @ Y0))))) => (Y1 @ Y3 @ Y0))))))))))))),
% 0.22/0.44 inference(beta_eta_normalization,[],[f136])).
% 0.22/0.44 thf(f136,plain,(
% 0.22/0.44 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (((((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7))))))))) @ Y2 @ Y1) & ((^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y6) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y7 @ Y5))))))))) @ Y1)) & ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: ((((^[Y8 : $i > $i > $o]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: (((Y8 @ Y11 @ Y10) & (Y8 @ Y10 @ Y9)) => (Y8 @ Y11 @ Y9))))))))) @ Y7) & ((^[Y8 : $i > $i > $o]: ((^[Y9 : $i > $i > $o]: (!! @ $i @ (^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: ((Y8 @ Y10 @ Y11) => (Y9 @ Y10 @ Y11))))))))) @ Y4 @ Y7)) => (Y7 @ Y5 @ Y6))))))))) @ Y2 @ Y3 @ Y0)) => (Y1 @ Y3 @ Y0))))))))))))),
% 0.22/0.44 inference(definition_unfolding,[],[f95,f120,f108,f123])).
% 0.22/0.44 thf(f123,plain,(
% 0.22/0.44 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((((^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y6) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y7 @ Y5))))))))) @ Y3) & ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7))))))))) @ Y0 @ Y3)) => (Y3 @ Y1 @ Y2))))))))))),
% 0.22/0.44 inference(definition_unfolding,[],[f97,f108,f120])).
% 0.22/0.44 thf(f97,plain,(
% 0.22/0.44 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((trans @ Y3) & (subrel @ Y0 @ Y3)) => (Y3 @ Y1 @ Y2))))))))))),
% 0.22/0.44 inference(cnf_transformation,[],[f46])).
% 0.22/0.44 thf(f46,plain,(
% 0.22/0.44 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((trans @ Y3) & (subrel @ Y0 @ Y3)) => (Y3 @ Y1 @ Y2))))))))))),
% 0.22/0.44 inference(fool_elimination,[],[f45])).
% 0.22/0.44 thf(f45,plain,(
% 0.22/0.44 (tc = (^[X0 : $i > $i > $o, X1 : $i, X2 : $i] : (! [X3 : $i > $i > $o] : (((subrel @ X0 @ X3) & (trans @ X3)) => (X3 @ X1 @ X2)))))),
% 0.22/0.44 inference(rectify,[],[f14])).
% 0.22/0.44 thf(f14,axiom,(
% 0.22/0.44 (tc = (^[X0 : $i > $i > $o, X2 : $i, X3 : $i] : (! [X1 : $i > $i > $o] : (((subrel @ X0 @ X1) & (trans @ X1)) => (X1 @ X2 @ X3)))))),
% 0.22/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive_closure)).
% 0.22/0.44 thf(f108,plain,(
% 0.22/0.44 (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))))),
% 0.22/0.44 inference(cnf_transformation,[],[f34])).
% 0.22/0.44 thf(f34,plain,(
% 0.22/0.44 (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))))),
% 0.22/0.44 inference(fool_elimination,[],[f33])).
% 0.22/0.44 thf(f33,plain,(
% 0.22/0.44 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X2 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X1 @ X3)))) = trans)),
% 0.22/0.44 inference(rectify,[],[f13])).
% 0.22/0.44 thf(f13,axiom,(
% 0.22/0.44 ((^[X0 : $i > $i > $o] : (! [X2,X3,X5] : (((X0 @ X3 @ X5) & (X0 @ X2 @ X3)) => (X0 @ X2 @ X5)))) = trans)),
% 0.22/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive)).
% 0.22/0.44 thf(f120,plain,(
% 0.22/0.44 (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))))))),
% 0.22/0.44 inference(cnf_transformation,[],[f72])).
% 0.22/0.44 thf(f72,plain,(
% 0.22/0.44 (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))))))),
% 0.22/0.44 inference(fool_elimination,[],[f71])).
% 0.22/0.44 thf(f71,plain,(
% 0.22/0.44 (subrel = (^[X0 : $i > $i > $o, X1 : $i > $i > $o] : (! [X2,X3] : ((X0 @ X3 @ X2) => (X1 @ X3 @ X2)))))),
% 0.22/0.44 inference(rectify,[],[f1])).
% 0.22/0.44 thf(f1,axiom,(
% 0.22/0.44 (subrel = (^[X0 : $i > $i > $o, X1 : $i > $i > $o] : (! [X3,X2] : ((X0 @ X2 @ X3) => (X1 @ X2 @ X3)))))),
% 0.22/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subrel)).
% 0.22/0.44 thf(f95,plain,(
% 0.22/0.44 ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((((subrel @ Y2 @ Y1) & (trans @ Y1)) & (tc @ Y2 @ Y3 @ Y0)) => (Y1 @ Y3 @ Y0))))))))))) = $true)),
% 0.22/0.44 inference(cnf_transformation,[],[f44])).
% 0.22/0.44 thf(f44,plain,(
% 0.22/0.44 ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((((subrel @ Y2 @ Y1) & (trans @ Y1)) & (tc @ Y2 @ Y3 @ Y0)) => (Y1 @ Y3 @ Y0))))))))))) = $true)),
% 0.22/0.44 inference(fool_elimination,[],[f43])).
% 0.22/0.44 thf(f43,plain,(
% 0.22/0.44 ~! [X0,X1 : $i > $i > $o,X2 : $i > $i > $o,X3] : (((tc @ X1 @ X0 @ X3) & (trans @ X2) & (subrel @ X1 @ X2)) => (X2 @ X0 @ X3))),
% 0.22/0.44 inference(rectify,[],[f31])).
% 0.22/0.44 thf(f31,negated_conjecture,(
% 0.22/0.44 ~! [X2,X0 : $i > $i > $o,X1 : $i > $i > $o,X3] : (((tc @ X0 @ X2 @ X3) & (trans @ X1) & (subrel @ X0 @ X1)) => (X1 @ X2 @ X3))),
% 0.22/0.44 inference(negated_conjecture,[],[f30])).
% 0.22/0.44 thf(f30,conjecture,(
% 0.22/0.44 ! [X2,X0 : $i > $i > $o,X1 : $i > $i > $o,X3] : (((tc @ X0 @ X2 @ X3) & (trans @ X1) & (subrel @ X0 @ X1)) => (X1 @ X2 @ X3))),
% 0.22/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive_closure_is_transitive2)).
% 0.22/0.44 thf(f167,plain,(
% 0.22/0.44 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ Y1))))))))),
% 0.22/0.44 inference(boolean_simplification,[],[f166])).
% 0.22/0.44 thf(f166,plain,(
% 0.22/0.44 ($true = (~ ($true & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ Y1)))))))))),
% 0.22/0.44 inference(forward_demodulation,[],[f165,f162])).
% 0.22/0.44 thf(f162,plain,(
% 0.22/0.44 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK3 @ Y2 @ Y1) & (sK3 @ Y1 @ Y0)) => (sK3 @ Y2 @ Y0)))))))))),
% 0.22/0.44 inference(boolean_simplification,[],[f161])).
% 0.22/0.44 thf(f161,plain,(
% 0.22/0.44 ($true = ($true & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK3 @ Y2 @ Y1) & (sK3 @ Y1 @ Y0)) => (sK3 @ Y2 @ Y0))))))))))),
% 0.22/0.44 inference(backward_demodulation,[],[f154,f160])).
% 0.22/0.44 thf(f165,plain,(
% 0.22/0.44 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK3 @ Y2 @ Y1) & (sK3 @ Y1 @ Y0)) => (sK3 @ Y2 @ Y0)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ Y1)))))))) = $true)),
% 0.22/0.44 inference(boolean_simplification,[],[f164])).
% 0.22/0.44 thf(f164,plain,(
% 0.22/0.44 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK3 @ Y2 @ Y1) & (sK3 @ Y1 @ Y0)) => (sK3 @ Y2 @ Y0)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ Y1))))))) => $false) = $true)),
% 0.22/0.44 inference(superposition,[],[f158,f152])).
% 0.22/0.44 thf(f152,plain,(
% 0.22/0.44 ((sK3 @ sK5 @ sK2) = $false)),
% 0.22/0.44 inference(boolean_simplification,[],[f151])).
% 0.22/0.44 thf(f151,plain,(
% 0.22/0.44 (($true => (sK3 @ sK5 @ sK2)) = $false)),
% 0.22/0.44 inference(backward_demodulation,[],[f148,f150])).
% 0.22/0.44 thf(f158,plain,(
% 0.22/0.44 ( ! [X1 : $i > $i > $o] : (($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X1 @ Y2 @ Y1) & (X1 @ Y1 @ Y0)) => (X1 @ Y2 @ Y0)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y0 @ Y1) => (X1 @ Y0 @ Y1))))))) => (X1 @ sK5 @ sK2)))) )),
% 0.22/0.44 inference(beta_eta_normalization,[],[f157])).
% 0.22/0.44 thf(f157,plain,(
% 0.22/0.44 ( ! [X1 : $i > $i > $o] : (($true = ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK4 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK5 @ sK2))) @ X1))) )),
% 0.22/0.44 inference(pi_clausification,[],[f156])).
% 0.22/0.44 thf(f156,plain,(
% 0.22/0.44 ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK4 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK5 @ sK2)))))),
% 0.22/0.44 inference(boolean_simplification,[],[f155])).
% 0.22/0.44 thf(f155,plain,(
% 0.22/0.44 ($true = ($true & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK4 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK5 @ sK2))))))),
% 0.22/0.44 inference(backward_demodulation,[],[f150,f154])).
% 0.22/0.44 % SZS output end Proof for theBenchmark
% 0.22/0.44 % (21631)------------------------------
% 0.22/0.44 % (21631)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (21631)Termination reason: Refutation
% 0.22/0.44
% 0.22/0.44 % (21631)Memory used [KB]: 5884
% 0.22/0.44 % (21631)Time elapsed: 0.040 s
% 0.22/0.44 % (21631)Instructions burned: 23 (million)
% 0.22/0.44 % (21631)------------------------------
% 0.22/0.44 % (21631)------------------------------
% 0.22/0.44 % (21619)Success in time 0.042 s
% 0.22/0.44 % Vampire---4.8 exiting
%------------------------------------------------------------------------------