TSTP Solution File: SYN044^4 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYN044^4 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n027.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 08:20:32 EDT 2024
% Result : Theorem 0.14s 0.36s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SYN044^4 : TPTP v8.2.0. Released v4.0.0.
% 0.02/0.10 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.09/0.30 % Computer : n027.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon May 20 14:36:07 EDT 2024
% 0.09/0.30 % CPUTime :
% 0.09/0.30 This is a TH0_THM_EQU_NAR problem
% 0.09/0.30 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.32 % (3010)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)
% 0.14/0.32 % (3008)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.32 % (3012)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)
% 0.14/0.32 % (3011)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.32 % (3013)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)
% 0.14/0.32 % (3009)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)
% 0.14/0.32 % (3014)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.32 % (3015)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)
% 0.14/0.32 % (3011)Instruction limit reached!
% 0.14/0.32 % (3011)------------------------------
% 0.14/0.32 % (3011)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.32 % (3011)Termination reason: Unknown
% 0.14/0.32 % (3011)Termination phase: Property scanning
% 0.14/0.32 % (3012)Instruction limit reached!
% 0.14/0.32 % (3012)------------------------------
% 0.14/0.32 % (3012)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.32 % (3012)Termination reason: Unknown
% 0.14/0.32 % (3012)Termination phase: Property scanning
% 0.14/0.32
% 0.14/0.32 % (3012)Memory used [KB]: 1023
% 0.14/0.32 % (3012)Time elapsed: 0.003 s
% 0.14/0.32 % (3012)Instructions burned: 3 (million)
% 0.14/0.32 % (3012)------------------------------
% 0.14/0.32 % (3012)------------------------------
% 0.14/0.32
% 0.14/0.32 % (3011)Memory used [KB]: 1023
% 0.14/0.32 % (3011)Time elapsed: 0.003 s
% 0.14/0.32 % (3011)Instructions burned: 3 (million)
% 0.14/0.32 % (3011)------------------------------
% 0.14/0.32 % (3011)------------------------------
% 0.14/0.32 % (3015)Instruction limit reached!
% 0.14/0.32 % (3015)------------------------------
% 0.14/0.32 % (3015)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.32 % (3015)Termination reason: Unknown
% 0.14/0.32 % (3015)Termination phase: Property scanning
% 0.14/0.32
% 0.14/0.32 % (3015)Memory used [KB]: 1023
% 0.14/0.32 % (3015)Time elapsed: 0.003 s
% 0.14/0.32 % (3015)Instructions burned: 3 (million)
% 0.14/0.32 % (3015)------------------------------
% 0.14/0.32 % (3015)------------------------------
% 0.14/0.32 % (3009)Instruction limit reached!
% 0.14/0.32 % (3009)------------------------------
% 0.14/0.32 % (3009)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.32 % (3009)Termination reason: Unknown
% 0.14/0.32 % (3009)Termination phase: Property scanning
% 0.14/0.32
% 0.14/0.32 % (3009)Memory used [KB]: 1023
% 0.14/0.32 % (3009)Time elapsed: 0.004 s
% 0.14/0.32 % (3009)Instructions burned: 5 (million)
% 0.14/0.32 % (3009)------------------------------
% 0.14/0.32 % (3009)------------------------------
% 0.14/0.32 % (3013)Refutation not found, incomplete strategy
% 0.14/0.32 % (3013)------------------------------
% 0.14/0.32 % (3013)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.32 % (3013)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.32
% 0.14/0.32
% 0.14/0.32 % (3013)Memory used [KB]: 5500
% 0.14/0.32 % (3013)Time elapsed: 0.004 s
% 0.14/0.32 % (3013)Instructions burned: 4 (million)
% 0.14/0.32 % (3013)------------------------------
% 0.14/0.32 % (3013)------------------------------
% 0.14/0.32 % (3014)Instruction limit reached!
% 0.14/0.32 % (3014)------------------------------
% 0.14/0.32 % (3014)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.32 % (3014)Termination reason: Unknown
% 0.14/0.32 % (3014)Termination phase: Saturation
% 0.14/0.32
% 0.14/0.32 % (3014)Memory used [KB]: 5756
% 0.14/0.32 % (3014)Time elapsed: 0.011 s
% 0.14/0.32 % (3014)Instructions burned: 19 (million)
% 0.14/0.32 % (3014)------------------------------
% 0.14/0.32 % (3014)------------------------------
% 0.14/0.33 % (3010)Instruction limit reached!
% 0.14/0.33 % (3010)------------------------------
% 0.14/0.33 % (3010)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.33 % (3010)Termination reason: Unknown
% 0.14/0.33 % (3010)Termination phase: Saturation
% 0.14/0.33
% 0.14/0.33 % (3010)Memory used [KB]: 5756
% 0.14/0.33 % (3010)Time elapsed: 0.016 s
% 0.14/0.33 % (3010)Instructions burned: 28 (million)
% 0.14/0.33 % (3010)------------------------------
% 0.14/0.33 % (3010)------------------------------
% 0.14/0.33 % (3016)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)
% 0.14/0.33 % (3017)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)
% 0.14/0.33 % (3018)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)
% 0.14/0.33 % (3019)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)
% 0.14/0.33 % (3018)Instruction limit reached!
% 0.14/0.33 % (3018)------------------------------
% 0.14/0.33 % (3018)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.33 % (3018)Termination reason: Unknown
% 0.14/0.33 % (3018)Termination phase: Clausification
% 0.14/0.33
% 0.14/0.33 % (3018)Memory used [KB]: 1023
% 0.14/0.33 % (3018)Time elapsed: 0.003 s
% 0.14/0.33 % (3018)Instructions burned: 3 (million)
% 0.14/0.33 % (3018)------------------------------
% 0.14/0.33 % (3018)------------------------------
% 0.14/0.33 % (3020)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.33 % (3020)Instruction limit reached!
% 0.14/0.33 % (3020)------------------------------
% 0.14/0.33 % (3020)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.33 % (3020)Termination reason: Unknown
% 0.14/0.33 % (3020)Termination phase: Saturation
% 0.14/0.33
% 0.14/0.33 % (3020)Memory used [KB]: 1023
% 0.14/0.33 % (3020)Time elapsed: 0.005 s
% 0.14/0.33 % (3020)Instructions burned: 8 (million)
% 0.14/0.33 % (3020)------------------------------
% 0.14/0.33 % (3020)------------------------------
% 0.14/0.34 % (3017)Instruction limit reached!
% 0.14/0.34 % (3017)------------------------------
% 0.14/0.34 % (3017)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.34 % (3017)Termination reason: Unknown
% 0.14/0.34 % (3017)Termination phase: Saturation
% 0.14/0.34
% 0.14/0.34 % (3017)Memory used [KB]: 5628
% 0.14/0.34 % (3017)Time elapsed: 0.009 s
% 0.14/0.34 % (3017)Instructions burned: 15 (million)
% 0.14/0.34 % (3017)------------------------------
% 0.14/0.34 % (3017)------------------------------
% 0.14/0.34 % (3021)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.14/0.34 % (3022)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)
% 0.14/0.34 % (3022)Instruction limit reached!
% 0.14/0.34 % (3022)------------------------------
% 0.14/0.34 % (3022)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.34 % (3022)Termination reason: Unknown
% 0.14/0.34 % (3022)Termination phase: SInE selection
% 0.14/0.34
% 0.14/0.34 % (3022)Memory used [KB]: 1023
% 0.14/0.34 % (3022)Time elapsed: 0.003 s
% 0.14/0.34 % (3022)Instructions burned: 3 (million)
% 0.14/0.34 % (3022)------------------------------
% 0.14/0.34 % (3022)------------------------------
% 0.14/0.34 % (3023)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)
% 0.14/0.35 % (3021)Instruction limit reached!
% 0.14/0.35 % (3021)------------------------------
% 0.14/0.35 % (3021)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.35 % (3021)Termination reason: Unknown
% 0.14/0.35 % (3021)Termination phase: Saturation
% 0.14/0.35
% 0.14/0.35 % (3021)Memory used [KB]: 5628
% 0.14/0.35 % (3021)Time elapsed: 0.009 s
% 0.14/0.35 % (3021)Instructions burned: 16 (million)
% 0.14/0.35 % (3021)------------------------------
% 0.14/0.35 % (3021)------------------------------
% 0.14/0.35 % (3023)Instruction limit reached!
% 0.14/0.35 % (3023)------------------------------
% 0.14/0.35 % (3023)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.35 % (3023)Termination reason: Unknown
% 0.14/0.35 % (3023)Termination phase: shuffling
% 0.14/0.35
% 0.14/0.35 % (3023)Memory used [KB]: 1023
% 0.14/0.35 % (3023)Time elapsed: 0.003 s
% 0.14/0.35 % (3023)Instructions burned: 3 (million)
% 0.14/0.35 % (3023)------------------------------
% 0.14/0.35 % (3023)------------------------------
% 0.14/0.35 % (3024)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)
% 0.14/0.35 % (3016)Instruction limit reached!
% 0.14/0.35 % (3016)------------------------------
% 0.14/0.35 % (3016)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.35 % (3016)Termination reason: Unknown
% 0.14/0.35 % (3016)Termination phase: Saturation
% 0.14/0.35
% 0.14/0.35 % (3016)Memory used [KB]: 5756
% 0.14/0.35 % (3016)Time elapsed: 0.020 s
% 0.14/0.35 % (3016)Instructions burned: 38 (million)
% 0.14/0.35 % (3016)------------------------------
% 0.14/0.35 % (3016)------------------------------
% 0.14/0.35 % (3025)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)
% 0.14/0.35 % (3024)Instruction limit reached!
% 0.14/0.35 % (3024)------------------------------
% 0.14/0.35 % (3024)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.35 % (3024)Termination reason: Unknown
% 0.14/0.35 % (3024)Termination phase: Saturation
% 0.14/0.35
% 0.14/0.35 % (3024)Memory used [KB]: 5500
% 0.14/0.35 % (3024)Time elapsed: 0.005 s
% 0.14/0.35 % (3024)Instructions burned: 8 (million)
% 0.14/0.35 % (3024)------------------------------
% 0.14/0.35 % (3024)------------------------------
% 0.14/0.35 % (3025)Instruction limit reached!
% 0.14/0.35 % (3025)------------------------------
% 0.14/0.35 % (3025)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.35 % (3025)Termination reason: Unknown
% 0.14/0.35 % (3025)Termination phase: Property scanning
% 0.14/0.35
% 0.14/0.35 % (3025)Memory used [KB]: 1023
% 0.14/0.35 % (3025)Time elapsed: 0.003 s
% 0.14/0.35 % (3025)Instructions burned: 3 (million)
% 0.14/0.35 % (3025)------------------------------
% 0.14/0.35 % (3025)------------------------------
% 0.14/0.36 % (3019)First to succeed.
% 0.14/0.36 % (3026)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.14/0.36 % (3027)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)
% 0.14/0.36 % (3028)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.14/0.36 % (3026)Instruction limit reached!
% 0.14/0.36 % (3026)------------------------------
% 0.14/0.36 % (3026)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.36 % (3026)Termination reason: Unknown
% 0.14/0.36 % (3026)Termination phase: Property scanning
% 0.14/0.36
% 0.14/0.36 % (3026)Memory used [KB]: 1023
% 0.14/0.36 % (3026)Time elapsed: 0.004 s
% 0.14/0.36 % (3026)Instructions burned: 6 (million)
% 0.14/0.36 % (3026)------------------------------
% 0.14/0.36 % (3026)------------------------------
% 0.14/0.36 % (3029)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.14/0.36 % (3019)Refutation found. Thanks to Tanya!
% 0.14/0.36 % SZS status Theorem for theBenchmark
% 0.14/0.36 % SZS output start Proof for theBenchmark
% 0.14/0.36 thf(func_def_0, type, irel: $i > $i > $o).
% 0.14/0.36 thf(func_def_2, type, mnot: ($i > $o) > $i > $o).
% 0.14/0.36 thf(func_def_3, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.36 thf(func_def_4, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.36 thf(func_def_5, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.36 thf(func_def_6, type, mbox_s4: ($i > $o) > $i > $o).
% 0.14/0.36 thf(func_def_7, type, iatom: ($i > $o) > $i > $o).
% 0.14/0.36 thf(func_def_8, type, inot: ($i > $o) > $i > $o).
% 0.14/0.36 thf(func_def_9, type, itrue: $i > $o).
% 0.14/0.36 thf(func_def_10, type, ifalse: $i > $o).
% 0.14/0.36 thf(func_def_11, type, iand: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.36 thf(func_def_12, type, ior: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.36 thf(func_def_13, type, iimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.36 thf(func_def_14, type, iimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.36 thf(func_def_15, type, iequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.36 thf(func_def_16, type, ixor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.36 thf(func_def_17, type, ivalid: ($i > $o) > $o).
% 0.14/0.36 thf(func_def_18, type, isatisfiable: ($i > $o) > $o).
% 0.14/0.36 thf(func_def_19, type, icountersatisfiable: ($i > $o) > $o).
% 0.14/0.36 thf(func_def_20, type, iinvalid: ($i > $o) > $o).
% 0.14/0.36 thf(func_def_21, type, p: $i > $o).
% 0.14/0.36 thf(func_def_22, type, q: $i > $o).
% 0.14/0.36 thf(func_def_23, type, r: $i > $o).
% 0.14/0.36 thf(func_def_37, type, ph1: !>[X0: $tType]:(X0)).
% 0.14/0.36 thf(f402,plain,(
% 0.14/0.36 $false),
% 0.14/0.36 inference(avatar_sat_refutation,[],[f157,f249,f401])).
% 0.14/0.36 thf(f401,plain,(
% 0.14/0.36 ~spl0_1),
% 0.14/0.36 inference(avatar_contradiction_clause,[],[f400])).
% 0.14/0.36 thf(f400,plain,(
% 0.14/0.36 $false | ~spl0_1),
% 0.14/0.36 inference(trivial_inequality_removal,[],[f399])).
% 0.14/0.36 thf(f399,plain,(
% 0.14/0.36 ($false = $true) | ~spl0_1),
% 0.14/0.36 inference(boolean_simplification,[],[f398])).
% 0.14/0.36 thf(f398,plain,(
% 0.14/0.36 ((~ $true) = $true) | ~spl0_1),
% 0.14/0.36 inference(forward_demodulation,[],[f380,f262])).
% 0.14/0.36 thf(f262,plain,(
% 0.14/0.36 ($true = (irel @ sK2 @ sK4)) | ~spl0_1),
% 0.14/0.36 inference(binary_proxy_clausification,[],[f258])).
% 0.14/0.36 thf(f258,plain,(
% 0.14/0.36 ($false = ((irel @ sK2 @ sK4) => (q @ sK4))) | ~spl0_1),
% 0.14/0.36 inference(beta_eta_normalization,[],[f256])).
% 0.14/0.36 thf(f256,plain,(
% 0.14/0.36 ($false = ((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0))) @ sK4)) | ~spl0_1),
% 0.14/0.36 inference(sigma_clausification,[],[f255])).
% 0.14/0.36 thf(f255,plain,(
% 0.14/0.36 ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0))))) | ~spl0_1),
% 0.14/0.36 inference(boolean_simplification,[],[f254])).
% 0.14/0.36 thf(f254,plain,(
% 0.14/0.36 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0)))) | $false) = $false) | ~spl0_1),
% 0.14/0.36 inference(backward_demodulation,[],[f153,f252])).
% 0.14/0.36 thf(f252,plain,(
% 0.14/0.36 ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0))))) = $false) | ~spl0_1),
% 0.14/0.36 inference(binary_proxy_clausification,[],[f153])).
% 0.14/0.36 thf(f153,plain,(
% 0.14/0.36 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0))))))) | ~spl0_1),
% 0.14/0.36 inference(avatar_component_clause,[],[f152])).
% 0.14/0.36 thf(f152,plain,(
% 0.14/0.36 spl0_1 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0)))))))),
% 0.14/0.36 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.14/0.36 thf(f380,plain,(
% 0.14/0.36 ((~ (irel @ sK2 @ sK4)) = $true) | ~spl0_1),
% 0.14/0.36 inference(boolean_simplification,[],[f379])).
% 0.14/0.36 thf(f379,plain,(
% 0.14/0.36 ($true = ((irel @ sK2 @ sK4) => $false)) | ~spl0_1),
% 0.14/0.36 inference(boolean_simplification,[],[f376])).
% 0.14/0.36 thf(f376,plain,(
% 0.14/0.36 (((irel @ sK2 @ sK4) => ($false & (p @ sK4))) = $true) | ~spl0_1),
% 0.14/0.36 inference(superposition,[],[f372,f261])).
% 0.14/0.36 thf(f261,plain,(
% 0.14/0.36 ((q @ sK4) = $false) | ~spl0_1),
% 0.14/0.36 inference(binary_proxy_clausification,[],[f258])).
% 0.14/0.36 thf(f372,plain,(
% 0.14/0.36 ( ! [X1 : $i] : (($true = ((irel @ sK2 @ X1) => ((q @ X1) & (p @ X1))))) ) | ~spl0_1),
% 0.14/0.36 inference(beta_eta_normalization,[],[f369])).
% 0.14/0.36 thf(f369,plain,(
% 0.14/0.36 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((q @ Y0) & (p @ Y0)))) @ X1))) ) | ~spl0_1),
% 0.14/0.36 inference(pi_clausification,[],[f329])).
% 0.14/0.36 thf(f329,plain,(
% 0.14/0.36 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((q @ Y0) & (p @ Y0))))) = $true) | ~spl0_1),
% 0.14/0.36 inference(boolean_simplification,[],[f328])).
% 0.14/0.36 thf(f328,plain,(
% 0.14/0.36 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((q @ Y0) & (p @ Y0))))) | $false) = $true) | ~spl0_1),
% 0.14/0.36 inference(boolean_simplification,[],[f323])).
% 0.14/0.36 thf(f323,plain,(
% 0.14/0.36 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((q @ Y0) & (p @ Y0))))) | (~ $true)) = $true) | ~spl0_1),
% 0.14/0.36 inference(superposition,[],[f140,f318])).
% 0.14/0.36 thf(f318,plain,(
% 0.14/0.36 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (r @ Y0))))) | ~spl0_1),
% 0.14/0.36 inference(boolean_simplification,[],[f317])).
% 0.14/0.36 thf(f317,plain,(
% 0.14/0.36 (($true => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (r @ Y0))))) = $true) | ~spl0_1),
% 0.14/0.36 inference(forward_demodulation,[],[f316,f120])).
% 0.14/0.36 thf(f120,plain,(
% 0.14/0.36 ( ! [X1 : $i] : (($true = (irel @ X1 @ X1))) )),
% 0.14/0.36 inference(beta_eta_normalization,[],[f119])).
% 0.14/0.36 thf(f119,plain,(
% 0.14/0.36 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (irel @ Y0 @ Y0)) @ X1))) )),
% 0.14/0.36 inference(pi_clausification,[],[f92])).
% 0.14/0.36 thf(f92,plain,(
% 0.14/0.36 ((!! @ $i @ (^[Y0 : $i]: (irel @ Y0 @ Y0))) = $true)),
% 0.14/0.36 inference(cnf_transformation,[],[f31])).
% 0.14/0.36 thf(f31,plain,(
% 0.14/0.36 ((!! @ $i @ (^[Y0 : $i]: (irel @ Y0 @ Y0))) = $true)),
% 0.14/0.36 inference(fool_elimination,[],[f30])).
% 0.14/0.36 thf(f30,plain,(
% 0.14/0.36 ! [X0] : (irel @ X0 @ X0)),
% 0.14/0.36 inference(rectify,[],[f1])).
% 0.14/0.36 thf(f1,axiom,(
% 0.14/0.36 ! [X0] : (irel @ X0 @ X0)),
% 0.14/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_axiom)).
% 0.14/0.36 thf(f316,plain,(
% 0.14/0.36 (((irel @ sK2 @ sK2) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (r @ Y0))))) = $true) | ~spl0_1),
% 0.14/0.36 inference(boolean_simplification,[],[f311])).
% 0.14/0.36 thf(f311,plain,(
% 0.14/0.36 ($true = ((irel @ sK2 @ sK2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (r @ Y0)))) | $false))) | ~spl0_1),
% 0.14/0.36 inference(superposition,[],[f308,f255])).
% 0.14/0.36 thf(f308,plain,(
% 0.14/0.36 ( ! [X1 : $i] : (($true = ((irel @ sK2 @ X1) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (r @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (q @ Y0)))))))) ) | ~spl0_1),
% 0.14/0.36 inference(beta_eta_normalization,[],[f306])).
% 0.14/0.36 thf(f306,plain,(
% 0.14/0.36 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))))) @ X1))) ) | ~spl0_1),
% 0.14/0.36 inference(pi_clausification,[],[f275])).
% 0.14/0.36 thf(f275,plain,(
% 0.14/0.36 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1)))))))) = $true) | ~spl0_1),
% 0.14/0.36 inference(boolean_simplification,[],[f274])).
% 0.14/0.36 thf(f274,plain,(
% 0.14/0.36 ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1)))))))) | $false)) | ~spl0_1),
% 0.14/0.36 inference(superposition,[],[f143,f252])).
% 0.14/0.36 thf(f143,plain,(
% 0.14/0.36 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p @ Y0)))))))) )),
% 0.14/0.36 inference(beta_eta_normalization,[],[f142])).
% 0.14/0.36 thf(f142,plain,(
% 0.14/0.36 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (r @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (q @ Y2)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1))))))) @ X1) = $true)) )),
% 0.14/0.36 inference(pi_clausification,[],[f116])).
% 0.14/0.36 thf(f116,plain,(
% 0.14/0.36 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (r @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (q @ Y2)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))))))) = $true)),
% 0.14/0.36 inference(beta_eta_normalization,[],[f114])).
% 0.14/0.36 thf(f114,plain,(
% 0.14/0.36 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ q) @ ((^[Y0 : $i > $o]: (Y0)) @ r)))) = $true)),
% 0.14/0.36 inference(definition_unfolding,[],[f100,f87,f107,f79,f106,f79,f79])).
% 0.14/0.36 thf(f106,plain,(
% 0.14/0.36 (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))))),
% 0.14/0.36 inference(definition_unfolding,[],[f93,f97,f81,f81])).
% 0.14/0.36 thf(f81,plain,(
% 0.14/0.36 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.14/0.36 inference(cnf_transformation,[],[f39])).
% 0.14/0.36 thf(f39,plain,(
% 0.14/0.36 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.14/0.36 inference(fool_elimination,[],[f38])).
% 0.14/0.36 thf(f38,plain,(
% 0.14/0.36 (mbox_s4 = (^[X0 : $i > $o, X1 : $i] : (! [X2] : ((irel @ X1 @ X2) => (X0 @ X2)))))),
% 0.14/0.36 inference(rectify,[],[f7])).
% 0.14/0.36 thf(f7,axiom,(
% 0.14/0.36 (mbox_s4 = (^[X5 : $i > $o, X0 : $i] : (! [X1] : ((irel @ X0 @ X1) => (X5 @ X1)))))),
% 0.14/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s4)).
% 0.14/0.36 thf(f97,plain,(
% 0.14/0.36 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.14/0.36 inference(cnf_transformation,[],[f74])).
% 0.14/0.36 thf(f74,plain,(
% 0.14/0.36 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.14/0.36 inference(fool_elimination,[],[f73])).
% 0.14/0.36 thf(f73,plain,(
% 0.14/0.36 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.14/0.36 inference(rectify,[],[f4])).
% 0.14/0.36 thf(f4,axiom,(
% 0.14/0.36 (mor = (^[X0 : $i > $o, X1 : $i > $o, X3 : $i] : ((X0 @ X3) | (X1 @ X3))))),
% 0.14/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.14/0.36 thf(f93,plain,(
% 0.14/0.36 (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.14/0.36 inference(cnf_transformation,[],[f53])).
% 0.14/0.36 thf(f53,plain,(
% 0.14/0.36 (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.14/0.36 inference(fool_elimination,[],[f52])).
% 0.14/0.36 thf(f52,plain,(
% 0.14/0.36 (ior = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mbox_s4 @ X0) @ (mbox_s4 @ X1))))),
% 0.14/0.36 inference(rectify,[],[f13])).
% 0.14/0.36 thf(f13,axiom,(
% 0.14/0.36 (ior = (^[X5 : $i > $o, X7 : $i > $o] : (mor @ (mbox_s4 @ X5) @ (mbox_s4 @ X7))))),
% 0.14/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ior)).
% 0.14/0.36 thf(f79,plain,(
% 0.14/0.36 (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 0.14/0.36 inference(cnf_transformation,[],[f76])).
% 0.14/0.36 thf(f76,plain,(
% 0.14/0.36 (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 0.14/0.36 inference(fool_elimination,[],[f75])).
% 0.14/0.36 thf(f75,plain,(
% 0.14/0.36 ((^[X0 : $i > $o] : (X0)) = iatom)),
% 0.14/0.36 inference(rectify,[],[f8])).
% 0.14/0.36 thf(f8,axiom,(
% 0.14/0.36 ((^[X5 : $i > $o] : (X5)) = iatom)),
% 0.14/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',iatom)).
% 0.14/0.36 thf(f107,plain,(
% 0.14/0.36 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))))),
% 0.14/0.36 inference(definition_unfolding,[],[f94,f102,f81,f81])).
% 0.14/0.36 thf(f102,plain,(
% 0.14/0.36 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.14/0.36 inference(definition_unfolding,[],[f90,f97,f84])).
% 0.14/0.36 thf(f84,plain,(
% 0.14/0.36 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.36 inference(cnf_transformation,[],[f68])).
% 0.14/0.36 thf(f68,plain,(
% 0.14/0.36 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.36 inference(fool_elimination,[],[f67])).
% 0.14/0.36 thf(f67,plain,(
% 0.14/0.36 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.14/0.36 inference(rectify,[],[f3])).
% 0.14/0.36 thf(f3,axiom,(
% 0.14/0.36 ((^[X0 : $i > $o, X3 : $i] : (~(X0 @ X3))) = mnot)),
% 0.14/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.14/0.36 thf(f90,plain,(
% 0.14/0.36 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.36 inference(cnf_transformation,[],[f60])).
% 0.14/0.36 thf(f60,plain,(
% 0.14/0.36 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.36 inference(fool_elimination,[],[f59])).
% 0.14/0.36 thf(f59,plain,(
% 0.14/0.36 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.14/0.36 inference(rectify,[],[f6])).
% 0.14/0.36 thf(f6,axiom,(
% 0.14/0.36 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.14/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.14/0.36 thf(f94,plain,(
% 0.14/0.36 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.14/0.36 inference(cnf_transformation,[],[f45])).
% 0.14/0.36 thf(f45,plain,(
% 0.14/0.36 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.14/0.36 inference(fool_elimination,[],[f44])).
% 0.14/0.36 thf(f44,plain,(
% 0.14/0.36 ((^[X0 : $i > $o, X1 : $i > $o] : (mimplies @ (mbox_s4 @ X0) @ (mbox_s4 @ X1))) = iimplies)),
% 0.14/0.36 inference(rectify,[],[f14])).
% 0.14/0.36 thf(f14,axiom,(
% 0.14/0.36 ((^[X5 : $i > $o, X7 : $i > $o] : (mimplies @ (mbox_s4 @ X5) @ (mbox_s4 @ X7))) = iimplies)),
% 0.14/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',iimplies)).
% 0.14/0.36 thf(f87,plain,(
% 0.14/0.36 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.36 inference(cnf_transformation,[],[f51])).
% 0.14/0.36 thf(f51,plain,(
% 0.14/0.36 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.36 inference(fool_elimination,[],[f50])).
% 0.14/0.36 thf(f50,plain,(
% 0.14/0.36 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = ivalid)),
% 0.14/0.36 inference(rectify,[],[f18])).
% 0.14/0.36 thf(f18,axiom,(
% 0.14/0.36 ((^[X8 : $i > $o] : (! [X6] : (X8 @ X6))) = ivalid)),
% 0.14/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ivalid)).
% 0.14/0.36 thf(f100,plain,(
% 0.14/0.36 ((ivalid @ (iimplies @ (iatom @ p) @ (ior @ (iatom @ q) @ (iatom @ r)))) = $true)),
% 0.14/0.36 inference(cnf_transformation,[],[f43])).
% 0.14/0.36 thf(f43,plain,(
% 0.14/0.36 ((ivalid @ (iimplies @ (iatom @ p) @ (ior @ (iatom @ q) @ (iatom @ r)))) = $true)),
% 0.14/0.36 inference(fool_elimination,[],[f42])).
% 0.14/0.36 thf(f42,plain,(
% 0.14/0.36 (ivalid @ (iimplies @ (iatom @ p) @ (ior @ (iatom @ q) @ (iatom @ r))))),
% 0.14/0.36 inference(rectify,[],[f24])).
% 0.14/0.36 thf(f24,axiom,(
% 0.14/0.36 (ivalid @ (iimplies @ (iatom @ p) @ (ior @ (iatom @ q) @ (iatom @ r))))),
% 0.14/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel10_3)).
% 0.14/0.36 thf(f140,plain,(
% 0.14/0.36 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((q @ Y0) & (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (r @ Y0)))))) = $true)) )),
% 0.14/0.36 inference(beta_eta_normalization,[],[f139])).
% 0.14/0.36 thf(f139,plain,(
% 0.14/0.36 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((q @ Y1) & (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1))))))) @ X1))) )),
% 0.14/0.36 inference(pi_clausification,[],[f118])).
% 0.14/0.36 thf(f118,plain,(
% 0.14/0.36 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((q @ Y1) & (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1)))))))))),
% 0.14/0.36 inference(beta_eta_normalization,[],[f111])).
% 0.14/0.36 thf(f111,plain,(
% 0.14/0.36 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ r) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ Y4))))))) @ Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: (Y0)) @ p) @ ((^[Y0 : $i > $o]: (Y0)) @ q)))) = $true)),
% 0.14/0.36 inference(definition_unfolding,[],[f85,f87,f107,f79,f105,f79,f79])).
% 0.14/0.36 thf(f105,plain,(
% 0.14/0.36 (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ Y4))))))) @ Y0 @ Y1)))))),
% 0.14/0.36 inference(definition_unfolding,[],[f77,f89])).
% 0.14/0.36 thf(f89,plain,(
% 0.14/0.36 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 0.14/0.36 inference(cnf_transformation,[],[f66])).
% 0.14/0.36 thf(f66,plain,(
% 0.14/0.36 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 0.14/0.36 inference(fool_elimination,[],[f65])).
% 0.14/0.36 thf(f65,plain,(
% 0.14/0.36 (mand = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) & (X1 @ X2))))),
% 0.14/0.36 inference(rectify,[],[f5])).
% 0.14/0.36 thf(f5,axiom,(
% 0.14/0.36 (mand = (^[X0 : $i > $o, X1 : $i > $o, X3 : $i] : ((X0 @ X3) & (X1 @ X3))))),
% 0.14/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.14/0.36 thf(f77,plain,(
% 0.14/0.36 (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ Y0 @ Y1)))))),
% 0.14/0.36 inference(cnf_transformation,[],[f37])).
% 0.14/0.36 thf(f37,plain,(
% 0.14/0.36 (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ Y0 @ Y1)))))),
% 0.14/0.36 inference(fool_elimination,[],[f36])).
% 0.14/0.36 thf(f36,plain,(
% 0.14/0.36 (iand = (^[X0 : $i > $o, X1 : $i > $o] : (mand @ X0 @ X1)))),
% 0.14/0.36 inference(rectify,[],[f12])).
% 0.14/0.36 thf(f12,axiom,(
% 0.14/0.36 (iand = (^[X5 : $i > $o, X7 : $i > $o] : (mand @ X5 @ X7)))),
% 0.14/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',iand)).
% 0.14/0.36 thf(f85,plain,(
% 0.14/0.36 ((ivalid @ (iimplies @ (iatom @ r) @ (iand @ (iatom @ p) @ (iatom @ q)))) = $true)),
% 0.14/0.36 inference(cnf_transformation,[],[f64])).
% 0.14/0.36 thf(f64,plain,(
% 0.14/0.36 ((ivalid @ (iimplies @ (iatom @ r) @ (iand @ (iatom @ p) @ (iatom @ q)))) = $true)),
% 0.14/0.36 inference(fool_elimination,[],[f63])).
% 0.14/0.36 thf(f63,plain,(
% 0.14/0.36 (ivalid @ (iimplies @ (iatom @ r) @ (iand @ (iatom @ p) @ (iatom @ q))))),
% 0.14/0.36 inference(rectify,[],[f23])).
% 0.14/0.36 thf(f23,axiom,(
% 0.14/0.36 (ivalid @ (iimplies @ (iatom @ r) @ (iand @ (iatom @ p) @ (iatom @ q))))),
% 0.14/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel10_2)).
% 0.14/0.36 thf(f249,plain,(
% 0.14/0.36 ~spl0_2),
% 0.14/0.36 inference(avatar_contradiction_clause,[],[f248])).
% 0.14/0.36 thf(f248,plain,(
% 0.14/0.36 $false | ~spl0_2),
% 0.14/0.36 inference(trivial_inequality_removal,[],[f247])).
% 0.14/0.36 thf(f247,plain,(
% 0.14/0.36 ($false = $true) | ~spl0_2),
% 0.14/0.36 inference(forward_demodulation,[],[f246,f184])).
% 0.14/0.36 thf(f184,plain,(
% 0.14/0.36 ($false = (p @ sK3)) | ~spl0_2),
% 0.14/0.36 inference(binary_proxy_clausification,[],[f183])).
% 0.14/0.36 thf(f183,plain,(
% 0.14/0.36 ($false = ((irel @ sK2 @ sK3) => (p @ sK3))) | ~spl0_2),
% 0.14/0.36 inference(beta_eta_normalization,[],[f179])).
% 0.14/0.36 thf(f179,plain,(
% 0.14/0.36 ($false = ((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0))) @ sK3)) | ~spl0_2),
% 0.14/0.36 inference(sigma_clausification,[],[f161])).
% 0.14/0.36 thf(f161,plain,(
% 0.14/0.36 ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0))))) | ~spl0_2),
% 0.14/0.36 inference(binary_proxy_clausification,[],[f156])).
% 0.14/0.36 thf(f156,plain,(
% 0.14/0.36 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0))))))) | ~spl0_2),
% 0.14/0.36 inference(avatar_component_clause,[],[f155])).
% 0.14/0.36 thf(f155,plain,(
% 0.14/0.36 spl0_2 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0)))))))),
% 0.14/0.36 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.14/0.36 thf(f246,plain,(
% 0.14/0.36 ((p @ sK3) = $true) | ~spl0_2),
% 0.14/0.36 inference(boolean_simplification,[],[f245])).
% 0.14/0.36 thf(f245,plain,(
% 0.14/0.36 ($true = ($true & (p @ sK3))) | ~spl0_2),
% 0.14/0.36 inference(forward_demodulation,[],[f226,f211])).
% 0.14/0.36 thf(f211,plain,(
% 0.14/0.36 ($true = (q @ sK3)) | ~spl0_2),
% 0.14/0.36 inference(boolean_simplification,[],[f203])).
% 0.14/0.36 thf(f203,plain,(
% 0.14/0.36 (($true => (q @ sK3)) = $true) | ~spl0_2),
% 0.14/0.36 inference(superposition,[],[f171,f185])).
% 0.14/0.36 thf(f185,plain,(
% 0.14/0.36 ((irel @ sK2 @ sK3) = $true) | ~spl0_2),
% 0.14/0.36 inference(binary_proxy_clausification,[],[f183])).
% 0.14/0.36 thf(f171,plain,(
% 0.14/0.36 ( ! [X1 : $i] : ((((irel @ sK2 @ X1) => (q @ X1)) = $true)) ) | ~spl0_2),
% 0.14/0.36 inference(beta_eta_normalization,[],[f169])).
% 0.14/0.36 thf(f169,plain,(
% 0.14/0.36 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0))) @ X1) = $true)) ) | ~spl0_2),
% 0.14/0.36 inference(pi_clausification,[],[f164])).
% 0.14/0.36 thf(f164,plain,(
% 0.14/0.36 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0))))) | ~spl0_2),
% 0.14/0.36 inference(not_proxy_clausification,[],[f163])).
% 0.14/0.36 thf(f163,plain,(
% 0.14/0.36 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0)))))) | ~spl0_2),
% 0.14/0.36 inference(boolean_simplification,[],[f162])).
% 0.14/0.36 thf(f162,plain,(
% 0.14/0.36 (($false | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0)))))) = $false) | ~spl0_2),
% 0.14/0.36 inference(backward_demodulation,[],[f156,f161])).
% 0.14/0.36 thf(f226,plain,(
% 0.14/0.36 (((q @ sK3) & (p @ sK3)) = $true) | ~spl0_2),
% 0.14/0.36 inference(boolean_simplification,[],[f225])).
% 0.14/0.36 thf(f225,plain,(
% 0.14/0.36 ($true = ($true => ((q @ sK3) & (p @ sK3)))) | ~spl0_2),
% 0.14/0.36 inference(superposition,[],[f217,f185])).
% 0.14/0.36 thf(f217,plain,(
% 0.14/0.36 ( ! [X1 : $i] : (($true = ((irel @ sK2 @ X1) => ((q @ X1) & (p @ X1))))) ) | ~spl0_2),
% 0.14/0.36 inference(beta_eta_normalization,[],[f214])).
% 0.14/0.36 thf(f214,plain,(
% 0.14/0.36 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((q @ Y0) & (p @ Y0)))) @ X1))) ) | ~spl0_2),
% 0.14/0.36 inference(pi_clausification,[],[f196])).
% 0.14/0.36 thf(f196,plain,(
% 0.14/0.36 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((q @ Y0) & (p @ Y0))))) = $true) | ~spl0_2),
% 0.14/0.36 inference(boolean_simplification,[],[f195])).
% 0.14/0.36 thf(f195,plain,(
% 0.14/0.36 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((q @ Y0) & (p @ Y0))))) | $false) = $true) | ~spl0_2),
% 0.14/0.36 inference(boolean_simplification,[],[f192])).
% 0.14/0.36 thf(f192,plain,(
% 0.14/0.36 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((q @ Y0) & (p @ Y0))))) | (~ $true)) = $true) | ~spl0_2),
% 0.14/0.36 inference(superposition,[],[f140,f166])).
% 0.14/0.36 thf(f166,plain,(
% 0.14/0.36 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (r @ Y0))))) | ~spl0_2),
% 0.14/0.36 inference(boolean_simplification,[],[f165])).
% 0.14/0.36 thf(f165,plain,(
% 0.14/0.36 ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (r @ Y0)))) | $false)) | ~spl0_2),
% 0.14/0.36 inference(superposition,[],[f137,f163])).
% 0.14/0.36 thf(f137,plain,(
% 0.14/0.36 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (r @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (q @ Y0)))))) = $true)) )),
% 0.14/0.36 inference(beta_eta_normalization,[],[f136])).
% 0.14/0.36 thf(f136,plain,(
% 0.14/0.36 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))))) @ X1) = $true)) )),
% 0.14/0.36 inference(pi_clausification,[],[f117])).
% 0.14/0.36 thf(f117,plain,(
% 0.14/0.36 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1)))))))))),
% 0.14/0.36 inference(beta_eta_normalization,[],[f113])).
% 0.14/0.36 thf(f113,plain,(
% 0.14/0.36 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ q) @ ((^[Y0 : $i > $o]: (Y0)) @ r))))),
% 0.14/0.36 inference(definition_unfolding,[],[f98,f87,f107,f79,f79])).
% 0.14/0.36 thf(f98,plain,(
% 0.14/0.36 ((ivalid @ (iimplies @ (iatom @ q) @ (iatom @ r))) = $true)),
% 0.14/0.36 inference(cnf_transformation,[],[f47])).
% 0.14/0.36 thf(f47,plain,(
% 0.14/0.36 ((ivalid @ (iimplies @ (iatom @ q) @ (iatom @ r))) = $true)),
% 0.14/0.36 inference(fool_elimination,[],[f46])).
% 0.14/0.36 thf(f46,plain,(
% 0.14/0.36 (ivalid @ (iimplies @ (iatom @ q) @ (iatom @ r)))),
% 0.14/0.36 inference(rectify,[],[f22])).
% 0.14/0.36 thf(f22,axiom,(
% 0.14/0.36 (ivalid @ (iimplies @ (iatom @ q) @ (iatom @ r)))),
% 0.14/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel10_1)).
% 0.14/0.36 thf(f157,plain,(
% 0.14/0.36 spl0_1 | spl0_2),
% 0.14/0.36 inference(avatar_split_clause,[],[f150,f155,f152])).
% 0.14/0.36 thf(f150,plain,(
% 0.14/0.36 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0)))))))),
% 0.14/0.36 inference(binary_proxy_clausification,[],[f149])).
% 0.14/0.36 thf(f149,plain,(
% 0.14/0.36 ((((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0)))))) & ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0))))))) = $false)),
% 0.14/0.36 inference(beta_eta_normalization,[],[f148])).
% 0.14/0.36 thf(f148,plain,(
% 0.14/0.36 (((^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1)))))) & ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))))))) @ sK2) = $false)),
% 0.14/0.36 inference(sigma_clausification,[],[f145])).
% 0.14/0.36 thf(f145,plain,(
% 0.14/0.36 ($false = (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1)))))) & ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1))))))))))),
% 0.14/0.36 inference(not_proxy_clausification,[],[f115])).
% 0.14/0.36 thf(f115,plain,(
% 0.14/0.36 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1)))))) & ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))))))))))),
% 0.14/0.36 inference(beta_eta_normalization,[],[f112])).
% 0.14/0.36 thf(f112,plain,(
% 0.14/0.36 ((~ ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ Y2 @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y7 @ Y8) | (Y6 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y7 @ Y8) | (Y6 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p) @ ((^[Y0 : $i > $o]: (Y0)) @ q)))) = $true)),
% 0.14/0.36 inference(definition_unfolding,[],[f96,f87,f109,f79,f79])).
% 0.14/0.36 thf(f109,plain,(
% 0.14/0.36 (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ Y2 @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y7 @ Y8) | (Y6 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y7 @ Y8) | (Y6 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y1 @ Y0))))))),
% 0.14/0.36 inference(definition_unfolding,[],[f95,f105,f107,f107])).
% 0.14/0.36 thf(f95,plain,(
% 0.14/0.36 (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (iand @ (iimplies @ Y0 @ Y1) @ (iimplies @ Y1 @ Y0))))))),
% 0.14/0.36 inference(cnf_transformation,[],[f49])).
% 0.14/0.36 thf(f49,plain,(
% 0.14/0.36 (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (iand @ (iimplies @ Y0 @ Y1) @ (iimplies @ Y1 @ Y0))))))),
% 0.14/0.36 inference(fool_elimination,[],[f48])).
% 0.14/0.36 thf(f48,plain,(
% 0.14/0.36 ((^[X0 : $i > $o, X1 : $i > $o] : (iand @ (iimplies @ X0 @ X1) @ (iimplies @ X1 @ X0))) = iequiv)),
% 0.14/0.36 inference(rectify,[],[f16])).
% 0.14/0.36 thf(f16,axiom,(
% 0.14/0.36 ((^[X5 : $i > $o, X7 : $i > $o] : (iand @ (iimplies @ X5 @ X7) @ (iimplies @ X7 @ X5))) = iequiv)),
% 0.14/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',iequiv)).
% 0.14/0.36 thf(f96,plain,(
% 0.14/0.36 ($true = (~ (ivalid @ (iequiv @ (iatom @ p) @ (iatom @ q)))))),
% 0.14/0.36 inference(cnf_transformation,[],[f33])).
% 0.14/0.36 thf(f33,plain,(
% 0.14/0.36 ($true = (~ (ivalid @ (iequiv @ (iatom @ p) @ (iatom @ q)))))),
% 0.14/0.36 inference(fool_elimination,[],[f32])).
% 0.14/0.36 thf(f32,plain,(
% 0.14/0.36 ~(ivalid @ (iequiv @ (iatom @ p) @ (iatom @ q)))),
% 0.14/0.36 inference(rectify,[],[f26])).
% 0.14/0.36 thf(f26,negated_conjecture,(
% 0.14/0.36 ~(ivalid @ (iequiv @ (iatom @ p) @ (iatom @ q)))),
% 0.14/0.36 inference(negated_conjecture,[],[f25])).
% 0.14/0.36 thf(f25,conjecture,(
% 0.14/0.36 (ivalid @ (iequiv @ (iatom @ p) @ (iatom @ q)))),
% 0.14/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel10)).
% 0.14/0.36 % SZS output end Proof for theBenchmark
% 0.14/0.36 % (3019)------------------------------
% 0.14/0.36 % (3019)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.36 % (3019)Termination reason: Refutation
% 0.14/0.36
% 0.14/0.36 % (3019)Memory used [KB]: 5884
% 0.14/0.36 % (3019)Time elapsed: 0.053 s
% 0.14/0.36 % (3019)Instructions burned: 50 (million)
% 0.14/0.36 % (3019)------------------------------
% 0.14/0.36 % (3019)------------------------------
% 0.14/0.36 % (3007)Success in time 0.063 s
% 0.14/0.36 % Vampire---4.8 exiting
%------------------------------------------------------------------------------