TSTP Solution File: SEV292^5 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV292^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% 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 : n026.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 04:12:41 EDT 2024
% Result : Theorem 0.18s 0.40s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV292^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% 0.11/0.12 % 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
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun May 19 18:45:53 EDT 2024
% 0.18/0.33 % CPUTime :
% 0.18/0.33 This is a TH0_THM_EQU_NAR problem
% 0.18/0.34 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
% 0.18/0.35 % (11224)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)
% 0.18/0.35 % (11226)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.18/0.35 % (11226)Instruction limit reached!
% 0.18/0.35 % (11226)------------------------------
% 0.18/0.35 % (11226)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.35 % (11226)Termination reason: Unknown
% 0.18/0.35 % (11226)Termination phase: Saturation
% 0.18/0.35
% 0.18/0.35 % (11226)Memory used [KB]: 5500
% 0.18/0.35 % (11226)Time elapsed: 0.002 s
% 0.18/0.35 % (11226)Instructions burned: 3 (million)
% 0.18/0.35 % (11226)------------------------------
% 0.18/0.35 % (11226)------------------------------
% 0.18/0.35 % (11224)Instruction limit reached!
% 0.18/0.35 % (11224)------------------------------
% 0.18/0.35 % (11224)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.35 % (11224)Termination reason: Unknown
% 0.18/0.35 % (11224)Termination phase: Saturation
% 0.18/0.35
% 0.18/0.35 % (11224)Memory used [KB]: 5500
% 0.18/0.35 % (11224)Time elapsed: 0.003 s
% 0.18/0.35 % (11224)Instructions burned: 5 (million)
% 0.18/0.35 % (11224)------------------------------
% 0.18/0.35 % (11224)------------------------------
% 0.18/0.35 % (11223)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.18/0.35 % (11227)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)
% 0.18/0.36 % (11229)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.18/0.36 % (11228)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)
% 0.18/0.36 % (11230)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)
% 0.18/0.36 % (11227)Instruction limit reached!
% 0.18/0.36 % (11227)------------------------------
% 0.18/0.36 % (11227)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.36 % (11227)Termination reason: Unknown
% 0.18/0.36 % (11227)Termination phase: Property scanning
% 0.18/0.36
% 0.18/0.36 % (11227)Memory used [KB]: 895
% 0.18/0.36 % (11227)Time elapsed: 0.003 s
% 0.18/0.36 % (11227)Instructions burned: 2 (million)
% 0.18/0.36 % (11227)------------------------------
% 0.18/0.36 % (11227)------------------------------
% 0.18/0.36 % (11225)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)
% 0.18/0.36 % (11230)Instruction limit reached!
% 0.18/0.36 % (11230)------------------------------
% 0.18/0.36 % (11230)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.36 % (11230)Termination reason: Unknown
% 0.18/0.36 % (11230)Termination phase: Property scanning
% 0.18/0.36 % (11228)Refutation not found, incomplete strategy
% 0.18/0.36 % (11228)------------------------------
% 0.18/0.36 % (11228)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.36 % (11228)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.36
% 0.18/0.36
% 0.18/0.36 % (11228)Memory used [KB]: 5500
% 0.18/0.36 % (11228)Time elapsed: 0.004 s
% 0.18/0.36 % (11228)Instructions burned: 2 (million)
% 0.18/0.36 % (11228)------------------------------
% 0.18/0.36 % (11228)------------------------------
% 0.18/0.36
% 0.18/0.36 % (11235)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)
% 0.18/0.36 % (11230)Memory used [KB]: 895
% 0.18/0.36 % (11230)Time elapsed: 0.003 s
% 0.18/0.36 % (11230)Instructions burned: 3 (million)
% 0.18/0.36 % (11230)------------------------------
% 0.18/0.36 % (11230)------------------------------
% 0.18/0.36 % (11236)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)
% 0.18/0.36 % (11236)Instruction limit reached!
% 0.18/0.36 % (11236)------------------------------
% 0.18/0.36 % (11236)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.36 % (11236)Termination reason: Unknown
% 0.18/0.36 % (11236)Termination phase: Saturation
% 0.18/0.36
% 0.18/0.36 % (11236)Memory used [KB]: 5628
% 0.18/0.36 % (11236)Time elapsed: 0.007 s
% 0.18/0.36 % (11236)Instructions burned: 17 (million)
% 0.18/0.36 % (11236)------------------------------
% 0.18/0.36 % (11236)------------------------------
% 0.18/0.37 % (11229)Instruction limit reached!
% 0.18/0.37 % (11229)------------------------------
% 0.18/0.37 % (11229)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37 % (11229)Termination reason: Unknown
% 0.18/0.37 % (11229)Termination phase: Saturation
% 0.18/0.37
% 0.18/0.37 % (11229)Memory used [KB]: 5500
% 0.18/0.37 % (11229)Time elapsed: 0.013 s
% 0.18/0.37 % (11229)Instructions burned: 19 (million)
% 0.18/0.37 % (11229)------------------------------
% 0.18/0.37 % (11229)------------------------------
% 0.18/0.37 % (11235)Instruction limit reached!
% 0.18/0.37 % (11235)------------------------------
% 0.18/0.37 % (11235)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37 % (11235)Termination reason: Unknown
% 0.18/0.37 % (11235)Termination phase: Saturation
% 0.18/0.37
% 0.18/0.37 % (11235)Memory used [KB]: 5628
% 0.18/0.37 % (11235)Time elapsed: 0.012 s
% 0.18/0.37 % (11235)Instructions burned: 37 (million)
% 0.18/0.37 % (11235)------------------------------
% 0.18/0.37 % (11235)------------------------------
% 0.18/0.37 % (11225)Refutation not found, incomplete strategy
% 0.18/0.37 % (11225)------------------------------
% 0.18/0.37 % (11225)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37 % (11225)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.37
% 0.18/0.37
% 0.18/0.37 % (11225)Memory used [KB]: 5628
% 0.18/0.37 % (11225)Time elapsed: 0.016 s
% 0.18/0.37 % (11225)Instructions burned: 21 (million)
% 0.18/0.37 % (11225)------------------------------
% 0.18/0.37 % (11225)------------------------------
% 0.18/0.37 % (11237)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)
% 0.18/0.37 % (11240)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.18/0.37 % (11237)Instruction limit reached!
% 0.18/0.37 % (11237)------------------------------
% 0.18/0.37 % (11237)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37 % (11239)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.18/0.37 % (11237)Termination reason: Unknown
% 0.18/0.37 % (11238)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)
% 0.18/0.37 % (11237)Termination phase: Saturation
% 0.18/0.37
% 0.18/0.37 % (11237)Memory used [KB]: 5500
% 0.18/0.37 % (11237)Time elapsed: 0.004 s
% 0.18/0.37 % (11237)Instructions burned: 4 (million)
% 0.18/0.37 % (11237)------------------------------
% 0.18/0.37 % (11237)------------------------------
% 0.18/0.38 % (11242)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)
% 0.18/0.38 % (11239)Instruction limit reached!
% 0.18/0.38 % (11239)------------------------------
% 0.18/0.38 % (11239)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.38 % (11239)Termination reason: Unknown
% 0.18/0.38 % (11239)Termination phase: Saturation
% 0.18/0.38
% 0.18/0.38 % (11239)Memory used [KB]: 1023
% 0.18/0.38 % (11239)Time elapsed: 0.006 s
% 0.18/0.38 % (11239)Instructions burned: 7 (million)
% 0.18/0.38 % (11239)------------------------------
% 0.18/0.38 % (11239)------------------------------
% 0.18/0.38 % (11242)Instruction limit reached!
% 0.18/0.38 % (11242)------------------------------
% 0.18/0.38 % (11242)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.38 % (11242)Termination reason: Unknown
% 0.18/0.38 % (11242)Termination phase: Saturation
% 0.18/0.38
% 0.18/0.38 % (11242)Memory used [KB]: 1023
% 0.18/0.38 % (11242)Time elapsed: 0.003 s
% 0.18/0.38 % (11242)Instructions burned: 5 (million)
% 0.18/0.38 % (11242)------------------------------
% 0.18/0.38 % (11242)------------------------------
% 0.18/0.38 % (11240)Instruction limit reached!
% 0.18/0.38 % (11240)------------------------------
% 0.18/0.38 % (11240)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.38 % (11240)Termination reason: Unknown
% 0.18/0.38 % (11240)Termination phase: Saturation
% 0.18/0.38
% 0.18/0.38 % (11240)Memory used [KB]: 5756
% 0.18/0.38 % (11240)Time elapsed: 0.008 s
% 0.18/0.38 % (11240)Instructions burned: 17 (million)
% 0.18/0.38 % (11240)------------------------------
% 0.18/0.38 % (11240)------------------------------
% 0.18/0.38 % (11241)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)
% 0.18/0.38 % (11241)Instruction limit reached!
% 0.18/0.38 % (11241)------------------------------
% 0.18/0.38 % (11241)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.38 % (11241)Termination reason: Unknown
% 0.18/0.38 % (11241)Termination phase: Property scanning
% 0.18/0.38
% 0.18/0.38 % (11241)Memory used [KB]: 1023
% 0.18/0.38 % (11241)Time elapsed: 0.004 s
% 0.18/0.38 % (11241)Instructions burned: 3 (million)
% 0.18/0.38 % (11241)------------------------------
% 0.18/0.38 % (11241)------------------------------
% 0.18/0.39 % (11249)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.18/0.39 % (11244)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)
% 0.18/0.39 % (11250)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.18/0.39 % (11246)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.18/0.39 % (11244)Refutation not found, incomplete strategy
% 0.18/0.39 % (11244)------------------------------
% 0.18/0.39 % (11244)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.39 % (11244)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.39
% 0.18/0.39
% 0.18/0.39 % (11244)Memory used [KB]: 5500
% 0.18/0.39 % (11244)Time elapsed: 0.005 s
% 0.18/0.39 % (11244)Instructions burned: 4 (million)
% 0.18/0.39 % (11244)------------------------------
% 0.18/0.39 % (11244)------------------------------
% 0.18/0.39 % (11246)Instruction limit reached!
% 0.18/0.39 % (11246)------------------------------
% 0.18/0.39 % (11246)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.39 % (11246)Termination reason: Unknown
% 0.18/0.39 % (11246)Termination phase: Saturation
% 0.18/0.39
% 0.18/0.39 % (11246)Memory used [KB]: 5500
% 0.18/0.39 % (11246)Time elapsed: 0.004 s
% 0.18/0.39 % (11246)Instructions burned: 4 (million)
% 0.18/0.39 % (11246)------------------------------
% 0.18/0.39 % (11246)------------------------------
% 0.18/0.39 % (11248)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.18/0.39 % (11249)Instruction limit reached!
% 0.18/0.39 % (11249)------------------------------
% 0.18/0.39 % (11249)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.39 % (11249)Termination reason: Unknown
% 0.18/0.39 % (11249)Termination phase: Saturation
% 0.18/0.39
% 0.18/0.39 % (11249)Memory used [KB]: 5628
% 0.18/0.39 % (11249)Time elapsed: 0.008 s
% 0.18/0.39 % (11249)Instructions burned: 19 (million)
% 0.18/0.39 % (11249)------------------------------
% 0.18/0.39 % (11249)------------------------------
% 0.18/0.39 % (11238)First to succeed.
% 0.18/0.39 % (11248)Instruction limit reached!
% 0.18/0.39 % (11248)------------------------------
% 0.18/0.39 % (11248)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.39 % (11248)Termination reason: Unknown
% 0.18/0.39 % (11248)Termination phase: Saturation
% 0.18/0.39
% 0.18/0.39 % (11248)Memory used [KB]: 5500
% 0.18/0.39 % (11248)Time elapsed: 0.005 s
% 0.18/0.39 % (11248)Instructions burned: 5 (million)
% 0.18/0.39 % (11248)------------------------------
% 0.18/0.39 % (11248)------------------------------
% 0.18/0.40 % (11253)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.18/0.40 % (11238)Refutation found. Thanks to Tanya!
% 0.18/0.40 % SZS status Theorem for theBenchmark
% 0.18/0.40 % SZS output start Proof for theBenchmark
% 0.18/0.40 thf(func_def_0, type, cP: (($i > $o) > $o) > $o).
% 0.18/0.40 thf(func_def_1, type, cONE: ($i > $o) > $o).
% 0.18/0.40 thf(func_def_2, type, cSUCC: (($i > $o) > $o) > ($i > $o) > $o).
% 0.18/0.40 thf(func_def_3, type, cZERO: ($i > $o) > $o).
% 0.18/0.40 thf(func_def_4, type, c_less__eq_: (($i > $o) > $o) > (($i > $o) > $o) > $o).
% 0.18/0.40 thf(func_def_22, type, ph1: !>[X0: $tType]:(X0)).
% 0.18/0.40 thf(func_def_23, type, sK2: (($i > $o) > $o) > $o).
% 0.18/0.40 thf(func_def_24, type, sK3: (($i > $o) > $o) > $o).
% 0.18/0.40 thf(f105,plain,(
% 0.18/0.40 $false),
% 0.18/0.40 inference(avatar_sat_refutation,[],[f47,f75,f104])).
% 0.18/0.40 thf(f104,plain,(
% 0.18/0.40 ~spl0_1),
% 0.18/0.40 inference(avatar_contradiction_clause,[],[f103])).
% 0.18/0.40 thf(f103,plain,(
% 0.18/0.40 $false | ~spl0_1),
% 0.18/0.40 inference(trivial_inequality_removal,[],[f102])).
% 0.18/0.40 thf(f102,plain,(
% 0.18/0.40 ($true = $false) | ~spl0_1),
% 0.18/0.40 inference(forward_demodulation,[],[f99,f83])).
% 0.18/0.40 thf(f83,plain,(
% 0.18/0.40 ((sK3 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: (((~ (Y1 = Y2)) & (Y0 @ Y2)) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3)))))))))))))) = $false) | ~spl0_1),
% 0.18/0.40 inference(binary_proxy_clausification,[],[f80])).
% 0.18/0.40 thf(f80,plain,(
% 0.18/0.40 ((((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK3 @ Y0) => (sK3 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) & (sK3 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))) => (sK3 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: (((~ (Y1 = Y2)) & (Y0 @ Y2)) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3))))))))))))))) = $false) | ~spl0_1),
% 0.18/0.40 inference(beta_eta_normalization,[],[f78])).
% 0.18/0.40 thf(f78,plain,(
% 0.18/0.40 (((^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (?? @ $i @ (^[Y3 : $i]: (((~ (Y2 = Y3)) & (Y1 @ Y3)) & (~ (?? @ $i @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & ((~ (Y2 = Y4)) & (Y1 @ Y4)))))))))))))))) @ sK3) = $false) | ~spl0_1),
% 0.18/0.40 inference(sigma_clausification,[],[f43])).
% 0.18/0.40 thf(f43,plain,(
% 0.18/0.40 ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (?? @ $i @ (^[Y3 : $i]: (((~ (Y2 = Y3)) & (Y1 @ Y3)) & (~ (?? @ $i @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & ((~ (Y2 = Y4)) & (Y1 @ Y4))))))))))))))))) = $false) | ~spl0_1),
% 0.18/0.40 inference(avatar_component_clause,[],[f42])).
% 0.18/0.40 thf(f42,plain,(
% 0.18/0.40 spl0_1 <=> ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (?? @ $i @ (^[Y3 : $i]: (((~ (Y2 = Y3)) & (Y1 @ Y3)) & (~ (?? @ $i @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & ((~ (Y2 = Y4)) & (Y1 @ Y4))))))))))))))))) = $false)),
% 0.18/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.18/0.40 thf(f99,plain,(
% 0.18/0.40 ((sK3 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: (((~ (Y1 = Y2)) & (Y0 @ Y2)) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3)))))))))))))) = $true) | ~spl0_1),
% 0.18/0.40 inference(boolean_simplification,[],[f98])).
% 0.18/0.40 thf(f98,plain,(
% 0.18/0.40 (($true => (sK3 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: (((~ (Y1 = Y2)) & (Y0 @ Y2)) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3))))))))))))))) = $true) | ~spl0_1),
% 0.18/0.40 inference(beta_eta_normalization,[],[f96])).
% 0.18/0.40 thf(f96,plain,(
% 0.18/0.40 (($true => (sK3 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & ((^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (~ (?? @ $i @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4))))))))) @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))) = $true) | ~spl0_1),
% 0.18/0.40 inference(superposition,[],[f94,f92])).
% 0.18/0.40 thf(f92,plain,(
% 0.18/0.40 ((sK3 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))) = $true) | ~spl0_1),
% 0.18/0.40 inference(boolean_simplification,[],[f91])).
% 0.18/0.40 thf(f91,plain,(
% 0.18/0.40 (($true & (sK3 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))) = $true) | ~spl0_1),
% 0.18/0.40 inference(backward_demodulation,[],[f84,f90])).
% 0.18/0.40 thf(f90,plain,(
% 0.18/0.40 ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK3 @ Y0) => (sK3 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) = $true) | ~spl0_1),
% 0.18/0.40 inference(binary_proxy_clausification,[],[f84])).
% 0.18/0.40 thf(f84,plain,(
% 0.18/0.40 (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK3 @ Y0) => (sK3 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) & (sK3 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))) = $true) | ~spl0_1),
% 0.18/0.40 inference(binary_proxy_clausification,[],[f80])).
% 0.18/0.40 thf(f94,plain,(
% 0.18/0.40 ( ! [X1 : ($i > $o) > $o] : ((((sK3 @ X1) => (sK3 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))) = $true)) ) | ~spl0_1),
% 0.18/0.40 inference(beta_eta_normalization,[],[f93])).
% 0.18/0.40 thf(f93,plain,(
% 0.18/0.40 ( ! [X1 : ($i > $o) > $o] : (($true = ((^[Y0 : ($i > $o) > $o]: ((sK3 @ Y0) => (sK3 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) @ X1))) ) | ~spl0_1),
% 0.18/0.40 inference(pi_clausification,[],[f90])).
% 0.18/0.40 thf(f75,plain,(
% 0.18/0.40 ~spl0_2),
% 0.18/0.40 inference(avatar_contradiction_clause,[],[f74])).
% 0.18/0.40 thf(f74,plain,(
% 0.18/0.40 $false | ~spl0_2),
% 0.18/0.40 inference(trivial_inequality_removal,[],[f73])).
% 0.18/0.40 thf(f73,plain,(
% 0.18/0.40 ($true = $false) | ~spl0_2),
% 0.18/0.40 inference(forward_demodulation,[],[f70,f54])).
% 0.18/0.40 thf(f54,plain,(
% 0.18/0.40 ((sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))) = $false) | ~spl0_2),
% 0.18/0.40 inference(binary_proxy_clausification,[],[f52])).
% 0.18/0.40 thf(f52,plain,(
% 0.18/0.40 ((((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) & (sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) => (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))) = $false) | ~spl0_2),
% 0.18/0.40 inference(beta_eta_normalization,[],[f50])).
% 0.18/0.40 thf(f50,plain,(
% 0.18/0.40 (((^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) @ sK2) = $false) | ~spl0_2),
% 0.18/0.40 inference(sigma_clausification,[],[f46])).
% 0.18/0.40 thf(f46,plain,(
% 0.18/0.40 ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))))) = $false) | ~spl0_2),
% 0.18/0.40 inference(avatar_component_clause,[],[f45])).
% 0.18/0.40 thf(f45,plain,(
% 0.18/0.40 spl0_2 <=> ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))))) = $false)),
% 0.18/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.18/0.40 thf(f70,plain,(
% 0.18/0.40 ((sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))) = $true) | ~spl0_2),
% 0.18/0.40 inference(boolean_simplification,[],[f69])).
% 0.18/0.40 thf(f69,plain,(
% 0.18/0.40 (($true => (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))) = $true) | ~spl0_2),
% 0.18/0.40 inference(beta_eta_normalization,[],[f67])).
% 0.18/0.40 thf(f67,plain,(
% 0.18/0.40 ($true = ($true => (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & ((^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))) @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))) | ~spl0_2),
% 0.18/0.40 inference(superposition,[],[f65,f63])).
% 0.18/0.40 thf(f63,plain,(
% 0.18/0.40 ((sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $true) | ~spl0_2),
% 0.18/0.40 inference(boolean_simplification,[],[f62])).
% 0.18/0.40 thf(f62,plain,(
% 0.18/0.40 (($true & (sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) = $true) | ~spl0_2),
% 0.18/0.40 inference(backward_demodulation,[],[f55,f61])).
% 0.18/0.40 thf(f61,plain,(
% 0.18/0.40 ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) = $true) | ~spl0_2),
% 0.18/0.40 inference(binary_proxy_clausification,[],[f55])).
% 0.18/0.40 thf(f55,plain,(
% 0.18/0.40 ($true = ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) & (sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))) | ~spl0_2),
% 0.18/0.40 inference(binary_proxy_clausification,[],[f52])).
% 0.18/0.40 thf(f65,plain,(
% 0.18/0.40 ( ! [X1 : ($i > $o) > $o] : ((((sK2 @ X1) => (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))) = $true)) ) | ~spl0_2),
% 0.18/0.40 inference(beta_eta_normalization,[],[f64])).
% 0.18/0.40 thf(f64,plain,(
% 0.18/0.40 ( ! [X1 : ($i > $o) > $o] : ((((^[Y0 : ($i > $o) > $o]: ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) @ X1) = $true)) ) | ~spl0_2),
% 0.18/0.40 inference(pi_clausification,[],[f61])).
% 0.18/0.40 thf(f47,plain,(
% 0.18/0.40 spl0_1 | spl0_2),
% 0.18/0.40 inference(avatar_split_clause,[],[f40,f45,f42])).
% 0.18/0.40 thf(f40,plain,(
% 0.18/0.40 ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (?? @ $i @ (^[Y3 : $i]: (((~ (Y2 = Y3)) & (Y1 @ Y3)) & (~ (?? @ $i @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & ((~ (Y2 = Y4)) & (Y1 @ Y4))))))))))))))))) = $false) | ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))))) = $false)),
% 0.18/0.40 inference(binary_proxy_clausification,[],[f39])).
% 0.18/0.40 thf(f39,plain,(
% 0.18/0.40 (((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (?? @ $i @ (^[Y3 : $i]: (((~ (Y2 = Y3)) & (Y1 @ Y3)) & (~ (?? @ $i @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & ((~ (Y2 = Y4)) & (Y1 @ Y4))))))))))))))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))))) = $false)),
% 0.18/0.40 inference(boolean_simplification,[],[f38])).
% 0.18/0.40 thf(f38,plain,(
% 0.18/0.40 ((($true & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (?? @ $i @ (^[Y3 : $i]: (((~ (Y2 = Y3)) & (Y1 @ Y3)) & (~ (?? @ $i @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & ((~ (Y2 = Y4)) & (Y1 @ Y4)))))))))))))))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))))) = $false)),
% 0.18/0.40 inference(superposition,[],[f36,f30])).
% 0.18/0.40 thf(f30,plain,(
% 0.18/0.40 ((cP @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))) = $true)),
% 0.18/0.40 inference(binary_proxy_clausification,[],[f26])).
% 0.18/0.40 thf(f26,plain,(
% 0.18/0.40 (((cP @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))) => (?? @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((cP @ Y0) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))))))))))) & (Y1 @ Y0)) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (?? @ $i @ (^[Y4 : $i]: (((~ (Y3 = Y4)) & (Y2 @ Y4)) & (~ (?? @ $i @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & ((~ (Y3 = Y5)) & (Y2 @ Y5)))))))))))))))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))))))) = $false)),
% 0.18/0.40 inference(not_proxy_clausification,[],[f25])).
% 0.18/0.40 thf(f25,plain,(
% 0.18/0.40 ($true = (~ ((cP @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))) => (?? @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((cP @ Y0) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))))))))))) & (Y1 @ Y0)) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (?? @ $i @ (^[Y4 : $i]: (((~ (Y3 = Y4)) & (Y2 @ Y4)) & (~ (?? @ $i @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & ((~ (Y3 = Y5)) & (Y2 @ Y5)))))))))))))))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))))))))),
% 0.18/0.40 inference(beta_eta_normalization,[],[f24])).
% 0.18/0.40 thf(f24,plain,(
% 0.18/0.40 ($true = (~ ((cP @ ((^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))) => (?? @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((cP @ Y0) & ((^[Y1 : ($i > $o) > $o]: ((^[Y2 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ ((^[Y5 : ($i > $o) > $o]: ((^[Y6 : $i > $o]: (?? @ $i @ (^[Y7 : $i]: ((Y6 @ Y7) & (Y5 @ (^[Y8 : $i]: ((~ (Y7 = Y8)) & (Y6 @ Y8)))))))))) @ Y4))))) & (Y3 @ Y1)) => (Y3 @ Y2))))))) @ Y0 @ ((^[Y1 : ($i > $o) > $o]: ((^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))) @ ((^[Y1 : ($i > $o) > $o]: ((^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))) @ (^[Y1 : $i > $o]: (~ (?? @ $i @ (^[Y2 : $i]: (Y1 @ Y2))))))))) & ((^[Y1 : ($i > $o) > $o]: ((^[Y2 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ ((^[Y5 : ($i > $o) > $o]: ((^[Y6 : $i > $o]: (?? @ $i @ (^[Y7 : $i]: ((Y6 @ Y7) & (Y5 @ (^[Y8 : $i]: ((~ (Y7 = Y8)) & (Y6 @ Y8)))))))))) @ Y4))))) & (Y3 @ Y1)) => (Y3 @ Y2))))))) @ (^[Y1 : $i > $o]: (~ (?? @ $i @ (^[Y2 : $i]: (Y1 @ Y2))))) @ Y0)))))))),
% 0.18/0.40 inference(definition_unfolding,[],[f19,f22,f23,f21,f22,f23,f20])).
% 0.18/0.40 thf(f20,plain,(
% 0.18/0.40 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 0.18/0.40 inference(cnf_transformation,[],[f12])).
% 0.18/0.40 thf(f12,plain,(
% 0.18/0.40 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 0.18/0.40 inference(fool_elimination,[],[f11])).
% 0.18/0.40 thf(f11,plain,(
% 0.18/0.40 ((^[X0 : $i > $o] : (~? [X1] : (X0 @ X1))) = cZERO)),
% 0.18/0.40 inference(rectify,[],[f1])).
% 0.18/0.40 thf(f1,axiom,(
% 0.18/0.40 ((^[X0 : $i > $o] : (~? [X1] : (X0 @ X1))) = cZERO)),
% 0.18/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cZERO_def)).
% 0.18/0.40 thf(f21,plain,(
% 0.18/0.40 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))),
% 0.18/0.40 inference(cnf_transformation,[],[f16])).
% 0.18/0.40 thf(f16,plain,(
% 0.18/0.40 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))),
% 0.18/0.40 inference(fool_elimination,[],[f15])).
% 0.18/0.40 thf(f15,plain,(
% 0.18/0.40 ((^[X0 : ($i > $o) > $o, X1 : $i > $o] : (? [X2] : ((X0 @ (^[X3 : $i] : ((X1 @ X3) & (X2 != X3)))) & (X1 @ X2)))) = cSUCC)),
% 0.18/0.40 inference(rectify,[],[f2])).
% 0.18/0.40 thf(f2,axiom,(
% 0.18/0.40 ((^[X2 : ($i > $o) > $o, X0 : $i > $o] : (? [X1] : ((X2 @ (^[X3 : $i] : ((X0 @ X3) & (X1 != X3)))) & (X0 @ X1)))) = cSUCC)),
% 0.18/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cSUCC_def)).
% 0.18/0.40 thf(f23,plain,(
% 0.18/0.40 (c_less__eq_ = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ ((^[Y4 : ($i > $o) > $o]: ((^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ (^[Y7 : $i]: ((~ (Y6 = Y7)) & (Y5 @ Y7)))))))))) @ Y3))))) & (Y2 @ Y0)) => (Y2 @ Y1))))))))),
% 0.18/0.40 inference(definition_unfolding,[],[f17,f21])).
% 0.18/0.40 thf(f17,plain,(
% 0.18/0.40 (c_less__eq_ = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (cSUCC @ Y3))))) & (Y2 @ Y0)) => (Y2 @ Y1))))))))),
% 0.18/0.40 inference(cnf_transformation,[],[f14])).
% 0.18/0.40 thf(f14,plain,(
% 0.18/0.40 (c_less__eq_ = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (cSUCC @ Y3))))) & (Y2 @ Y0)) => (Y2 @ Y1))))))))),
% 0.18/0.40 inference(fool_elimination,[],[f13])).
% 0.18/0.40 thf(f13,plain,(
% 0.18/0.40 (c_less__eq_ = (^[X0 : ($i > $o) > $o, X1 : ($i > $o) > $o] : (! [X2 : (($i > $o) > $o) > $o] : (((X2 @ X0) & ! [X3 : ($i > $o) > $o] : ((X2 @ X3) => (X2 @ (cSUCC @ X3)))) => (X2 @ X1)))))),
% 0.18/0.40 inference(rectify,[],[f4])).
% 0.18/0.40 thf(f4,axiom,(
% 0.18/0.40 (c_less__eq_ = (^[X1 : ($i > $o) > $o, X4 : ($i > $o) > $o] : (! [X0 : (($i > $o) > $o) > $o] : (((X0 @ X1) & ! [X5 : ($i > $o) > $o] : ((X0 @ X5) => (X0 @ (cSUCC @ X5)))) => (X0 @ X4)))))),
% 0.18/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_less__eq__def)).
% 0.18/0.40 thf(f22,plain,(
% 0.18/0.40 (cONE = ((^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 0.18/0.40 inference(definition_unfolding,[],[f18,f21,f20])).
% 0.18/0.40 thf(f18,plain,(
% 0.18/0.40 (cONE = (cSUCC @ cZERO))),
% 0.18/0.40 inference(cnf_transformation,[],[f8])).
% 0.18/0.40 thf(f8,plain,(
% 0.18/0.40 (cONE = (cSUCC @ cZERO))),
% 0.18/0.40 inference(fool_elimination,[],[f3])).
% 0.18/0.40 thf(f3,axiom,(
% 0.18/0.40 (cONE = (cSUCC @ cZERO))),
% 0.18/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cONE_def)).
% 0.18/0.40 thf(f19,plain,(
% 0.18/0.40 ((~ ((cP @ cONE) => (?? @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((cP @ Y0) & (c_less__eq_ @ Y0 @ (cSUCC @ cONE))) & (c_less__eq_ @ cZERO @ Y0)))))) = $true)),
% 0.18/0.40 inference(cnf_transformation,[],[f10])).
% 0.18/0.40 thf(f10,plain,(
% 0.18/0.40 ((~ ((cP @ cONE) => (?? @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((cP @ Y0) & (c_less__eq_ @ Y0 @ (cSUCC @ cONE))) & (c_less__eq_ @ cZERO @ Y0)))))) = $true)),
% 0.18/0.40 inference(fool_elimination,[],[f9])).
% 0.18/0.40 thf(f9,plain,(
% 0.18/0.40 ~((cP @ cONE) => ? [X0 : ($i > $o) > $o] : ((c_less__eq_ @ cZERO @ X0) & (c_less__eq_ @ X0 @ (cSUCC @ cONE)) & (cP @ X0)))),
% 0.18/0.40 inference(rectify,[],[f6])).
% 0.18/0.40 thf(f6,negated_conjecture,(
% 0.18/0.40 ~((cP @ cONE) => ? [X1 : ($i > $o) > $o] : ((c_less__eq_ @ cZERO @ X1) & (c_less__eq_ @ X1 @ (cSUCC @ cONE)) & (cP @ X1)))),
% 0.18/0.40 inference(negated_conjecture,[],[f5])).
% 0.18/0.40 thf(f5,conjecture,(
% 0.18/0.40 (cP @ cONE) => ? [X1 : ($i > $o) > $o] : ((c_less__eq_ @ cZERO @ X1) & (c_less__eq_ @ X1 @ (cSUCC @ cONE)) & (cP @ X1))),
% 0.18/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBLEDSOE7A)).
% 0.18/0.40 thf(f36,plain,(
% 0.18/0.40 ( ! [X1 : ($i > $o) > $o] : (((((cP @ X1) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ X1)) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (?? @ $i @ (^[Y3 : $i]: (((~ (Y2 = Y3)) & (Y1 @ Y3)) & (~ (?? @ $i @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & ((~ (Y2 = Y4)) & (Y1 @ Y4)))))))))))))))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ X1))))) = $false)) )),
% 0.18/0.40 inference(beta_eta_normalization,[],[f35])).
% 0.18/0.40 thf(f35,plain,(
% 0.18/0.40 ( ! [X1 : ($i > $o) > $o] : ((((^[Y0 : ($i > $o) > $o]: (((cP @ Y0) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))))))))))) & (Y1 @ Y0)) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (?? @ $i @ (^[Y4 : $i]: (((~ (Y3 = Y4)) & (Y2 @ Y4)) & (~ (?? @ $i @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & ((~ (Y3 = Y5)) & (Y2 @ Y5)))))))))))))))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))))) @ X1) = $false)) )),
% 0.18/0.40 inference(pi_clausification,[],[f29])).
% 0.18/0.40 thf(f29,plain,(
% 0.18/0.40 ((?? @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((cP @ Y0) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))))))))))) & (Y1 @ Y0)) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (?? @ $i @ (^[Y4 : $i]: (((~ (Y3 = Y4)) & (Y2 @ Y4)) & (~ (?? @ $i @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & ((~ (Y3 = Y5)) & (Y2 @ Y5)))))))))))))))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))))) = $false)),
% 0.18/0.40 inference(binary_proxy_clausification,[],[f26])).
% 0.18/0.40 % SZS output end Proof for theBenchmark
% 0.18/0.40 % (11238)------------------------------
% 0.18/0.40 % (11238)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.40 % (11238)Termination reason: Refutation
% 0.18/0.40
% 0.18/0.40 % (11238)Memory used [KB]: 5756
% 0.18/0.40 % (11238)Time elapsed: 0.026 s
% 0.18/0.40 % (11238)Instructions burned: 30 (million)
% 0.18/0.40 % (11238)------------------------------
% 0.18/0.40 % (11238)------------------------------
% 0.18/0.40 % (11220)Success in time 0.051 s
% 0.18/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------