TSTP Solution File: SEV302^5 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV302^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n017.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 : Mon Jun 24 16:02:42 EDT 2024
% Result : Theorem 0.16s 0.39s
% Output : Refutation 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : SEV302^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% 0.09/0.12 % Command : run_vampire %s %d THM
% 0.12/0.31 % Computer : n017.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Fri Jun 21 19:16:39 EDT 2024
% 0.16/0.32 % CPUTime :
% 0.16/0.33 This is a TH0_THM_EQU_NAR problem
% 0.16/0.33 Running higher-order theorem proving
% 0.16/0.33 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.16/0.35 % (1469)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.16/0.35 % (1465)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.16/0.35 % (1466)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.16/0.35 % (1466)Instruction limit reached!
% 0.16/0.35 % (1466)------------------------------
% 0.16/0.35 % (1466)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.35 % (1466)Termination reason: Unknown
% 0.16/0.35 % (1466)Termination phase: Property scanning
% 0.16/0.35
% 0.16/0.35 % (1466)Memory used [KB]: 1023
% 0.16/0.35 % (1466)Time elapsed: 0.003 s
% 0.16/0.35 % (1466)Instructions burned: 5 (million)
% 0.16/0.35 % (1466)------------------------------
% 0.16/0.35 % (1466)------------------------------
% 0.16/0.35 % (1469)Instruction limit reached!
% 0.16/0.35 % (1469)------------------------------
% 0.16/0.35 % (1469)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.35 % (1469)Termination reason: Unknown
% 0.16/0.35 % (1469)Termination phase: Saturation
% 0.16/0.35
% 0.16/0.35 % (1469)Memory used [KB]: 5500
% 0.16/0.35 % (1469)Time elapsed: 0.008 s
% 0.16/0.35 % (1469)Instructions burned: 20 (million)
% 0.16/0.35 % (1469)------------------------------
% 0.16/0.35 % (1469)------------------------------
% 0.16/0.35 % (1463)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.16/0.35 % (1464)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.16/0.35 % (1467)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.16/0.36 % (1468)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.16/0.36 % (1467)Instruction limit reached!
% 0.16/0.36 % (1467)------------------------------
% 0.16/0.36 % (1467)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.36 % (1467)Termination reason: Unknown
% 0.16/0.36 % (1467)Termination phase: Property scanning
% 0.16/0.36
% 0.16/0.36 % (1467)Memory used [KB]: 1023
% 0.16/0.36 % (1467)Time elapsed: 0.003 s
% 0.16/0.36 % (1467)Instructions burned: 2 (million)
% 0.16/0.36 % (1467)------------------------------
% 0.16/0.36 % (1467)------------------------------
% 0.16/0.36 % (1464)Instruction limit reached!
% 0.16/0.36 % (1464)------------------------------
% 0.16/0.36 % (1464)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.36 % (1464)Termination reason: Unknown
% 0.16/0.36 % (1464)Termination phase: Property scanning
% 0.16/0.36
% 0.16/0.36 % (1464)Memory used [KB]: 1023
% 0.16/0.36 % (1464)Time elapsed: 0.004 s
% 0.16/0.36 % (1464)Instructions burned: 4 (million)
% 0.16/0.36 % (1464)------------------------------
% 0.16/0.36 % (1464)------------------------------
% 0.16/0.36 % (1465)Instruction limit reached!
% 0.16/0.36 % (1465)------------------------------
% 0.16/0.36 % (1465)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.36 % (1465)Termination reason: Unknown
% 0.16/0.36 % (1465)Termination phase: Saturation
% 0.16/0.36
% 0.16/0.36 % (1465)Memory used [KB]: 5500
% 0.16/0.36 % (1465)Time elapsed: 0.010 s
% 0.16/0.36 % (1465)Instructions burned: 29 (million)
% 0.16/0.36 % (1465)------------------------------
% 0.16/0.36 % (1465)------------------------------
% 0.16/0.36 % (1468)Refutation not found, incomplete strategy
% 0.16/0.36 % (1468)------------------------------
% 0.16/0.36 % (1468)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.36 % (1468)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.36
% 0.16/0.36
% 0.16/0.36 % (1468)Memory used [KB]: 5500
% 0.16/0.36 % (1468)Time elapsed: 0.005 s
% 0.16/0.36 % (1468)Instructions burned: 4 (million)
% 0.16/0.36 % (1468)------------------------------
% 0.16/0.36 % (1468)------------------------------
% 0.16/0.36 % (1470)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.16/0.36 % (1470)Instruction limit reached!
% 0.16/0.36 % (1470)------------------------------
% 0.16/0.36 % (1470)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.36 % (1470)Termination reason: Unknown
% 0.16/0.36 % (1470)Termination phase: Function definition elimination
% 0.16/0.36
% 0.16/0.36 % (1470)Memory used [KB]: 1023
% 0.16/0.36 % (1470)Time elapsed: 0.003 s
% 0.16/0.36 % (1470)Instructions burned: 3 (million)
% 0.16/0.36 % (1470)------------------------------
% 0.16/0.36 % (1470)------------------------------
% 0.16/0.36 % (1471)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.16/0.37 % (1474)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.16/0.37 % (1476)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.16/0.37 % (1472)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.16/0.37 % (1473)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.16/0.37 % (1473)Instruction limit reached!
% 0.16/0.37 % (1473)------------------------------
% 0.16/0.37 % (1473)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.37 % (1473)Termination reason: Unknown
% 0.16/0.37 % (1473)Termination phase: Function definition elimination
% 0.16/0.37
% 0.16/0.37 % (1473)Memory used [KB]: 1023
% 0.16/0.37 % (1473)Time elapsed: 0.004 s
% 0.16/0.37 % (1473)Instructions burned: 3 (million)
% 0.16/0.37 % (1473)------------------------------
% 0.16/0.37 % (1473)------------------------------
% 0.16/0.37 % (1475)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.16/0.37 % (1471)Instruction limit reached!
% 0.16/0.37 % (1471)------------------------------
% 0.16/0.37 % (1471)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.37 % (1471)Termination reason: Unknown
% 0.16/0.37 % (1471)Termination phase: Saturation
% 0.16/0.37
% 0.16/0.37 % (1471)Memory used [KB]: 5628
% 0.16/0.37 % (1471)Time elapsed: 0.013 s
% 0.16/0.37 % (1471)Instructions burned: 38 (million)
% 0.16/0.37 % (1471)------------------------------
% 0.16/0.37 % (1471)------------------------------
% 0.16/0.38 % (1476)Instruction limit reached!
% 0.16/0.38 % (1476)------------------------------
% 0.16/0.38 % (1476)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.38 % (1476)Termination reason: Unknown
% 0.16/0.38 % (1476)Termination phase: Saturation
% 0.16/0.38
% 0.16/0.38 % (1476)Memory used [KB]: 5884
% 0.16/0.38 % (1476)Time elapsed: 0.009 s
% 0.16/0.38 % (1476)Instructions burned: 16 (million)
% 0.16/0.38 % (1476)------------------------------
% 0.16/0.38 % (1476)------------------------------
% 0.16/0.38 % (1475)Instruction limit reached!
% 0.16/0.38 % (1475)------------------------------
% 0.16/0.38 % (1475)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.38 % (1475)Termination reason: Unknown
% 0.16/0.38 % (1475)Termination phase: Saturation
% 0.16/0.38
% 0.16/0.38 % (1475)Memory used [KB]: 1023
% 0.16/0.38 % (1475)Time elapsed: 0.006 s
% 0.16/0.38 % (1475)Instructions burned: 7 (million)
% 0.16/0.38 % (1475)------------------------------
% 0.16/0.38 % (1475)------------------------------
% 0.16/0.38 % (1478)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)
% 0.16/0.38 % (1472)Instruction limit reached!
% 0.16/0.38 % (1472)------------------------------
% 0.16/0.38 % (1472)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.38 % (1472)Termination reason: Unknown
% 0.16/0.38 % (1472)Termination phase: Saturation
% 0.16/0.38
% 0.16/0.38 % (1472)Memory used [KB]: 5628
% 0.16/0.38 % (1472)Time elapsed: 0.013 s
% 0.16/0.38 % (1472)Instructions burned: 15 (million)
% 0.16/0.38 % (1472)------------------------------
% 0.16/0.38 % (1472)------------------------------
% 0.16/0.38 % (1474)First to succeed.
% 0.16/0.39 % (1478)Instruction limit reached!
% 0.16/0.39 % (1478)------------------------------
% 0.16/0.39 % (1478)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.39 % (1478)Termination reason: Unknown
% 0.16/0.39 % (1478)Termination phase: Property scanning
% 0.16/0.39
% 0.16/0.39 % (1478)Memory used [KB]: 1023
% 0.16/0.39 % (1478)Time elapsed: 0.003 s
% 0.16/0.39 % (1478)Instructions burned: 6 (million)
% 0.16/0.39 % (1478)------------------------------
% 0.16/0.39 % (1478)------------------------------
% 0.16/0.39 % (1479)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)
% 0.16/0.39 % (1479)Instruction limit reached!
% 0.16/0.39 % (1479)------------------------------
% 0.16/0.39 % (1479)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.39 % (1479)Termination reason: Unknown
% 0.16/0.39 % (1479)Termination phase: Saturation
% 0.16/0.39
% 0.16/0.39 % (1479)Memory used [KB]: 5500
% 0.16/0.39 % (1479)Time elapsed: 0.004 s
% 0.16/0.39 % (1479)Instructions burned: 7 (million)
% 0.16/0.39 % (1479)------------------------------
% 0.16/0.39 % (1479)------------------------------
% 0.16/0.39 % (1477)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)
% 0.16/0.39 % (1474)Refutation found. Thanks to Tanya!
% 0.16/0.39 % SZS status Theorem for theBenchmark
% 0.16/0.39 % SZS output start Proof for theBenchmark
% 0.16/0.39 thf(func_def_0, type, cNAT: (($i > $o) > $o) > $o).
% 0.16/0.39 thf(func_def_1, type, cSUCC: (($i > $o) > $o) > ($i > $o) > $o).
% 0.16/0.39 thf(func_def_2, type, cZERO: ($i > $o) > $o).
% 0.16/0.39 thf(func_def_18, type, ph1: !>[X0: $tType]:(X0)).
% 0.16/0.39 thf(func_def_19, type, sK2: (($i > $o) > $o) > $o).
% 0.16/0.39 thf(func_def_20, type, sK3: ($i > $o) > $o).
% 0.16/0.39 thf(func_def_21, type, sK4: (($i > $o) > $o) > $o).
% 0.16/0.39 thf(func_def_22, type, sK5: ($i > $o) > $o).
% 0.16/0.39 thf(func_def_24, type, sK6: (($i > $o) > $o) > $o).
% 0.16/0.39 thf(f187,plain,(
% 0.16/0.39 $false),
% 0.16/0.39 inference(avatar_sat_refutation,[],[f66,f88,f111,f120,f186])).
% 0.16/0.39 thf(f186,plain,(
% 0.16/0.39 ~spl0_2 | ~spl0_4),
% 0.16/0.39 inference(avatar_contradiction_clause,[],[f185])).
% 0.16/0.39 thf(f185,plain,(
% 0.16/0.39 $false | (~spl0_2 | ~spl0_4)),
% 0.16/0.39 inference(trivial_inequality_removal,[],[f184])).
% 0.16/0.39 thf(f184,plain,(
% 0.16/0.39 ($true = $false) | (~spl0_2 | ~spl0_4)),
% 0.16/0.39 inference(boolean_simplification,[],[f183])).
% 0.16/0.39 thf(f183,plain,(
% 0.16/0.39 ($true = (~ $true)) | (~spl0_2 | ~spl0_4)),
% 0.16/0.39 inference(forward_demodulation,[],[f174,f162])).
% 0.16/0.39 thf(f162,plain,(
% 0.16/0.39 ($true = (sK6 @ sK5)) | (~spl0_2 | ~spl0_4)),
% 0.16/0.39 inference(boolean_simplification,[],[f161])).
% 0.16/0.39 thf(f161,plain,(
% 0.16/0.39 (($true => (sK6 @ sK5)) = $true) | (~spl0_2 | ~spl0_4)),
% 0.16/0.39 inference(forward_demodulation,[],[f160,f141])).
% 0.16/0.39 thf(f141,plain,(
% 0.16/0.39 ($true = (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK6 @ Y0) => (sK6 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2)))))))))) | ~spl0_4),
% 0.16/0.39 inference(binary_proxy_clausification,[],[f137])).
% 0.16/0.39 thf(f137,plain,(
% 0.16/0.39 (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK6 @ Y0) => (sK6 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))) & (sK6 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) = $true) | ~spl0_4),
% 0.16/0.39 inference(binary_proxy_clausification,[],[f125])).
% 0.16/0.39 thf(f125,plain,(
% 0.16/0.39 ((((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK6 @ Y0) => (sK6 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))) & (sK6 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) => (sK6 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK5 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))) & (Y0 @ Y1))))))) = $false) | ~spl0_4),
% 0.16/0.39 inference(beta_eta_normalization,[],[f123])).
% 0.16/0.39 thf(f123,plain,(
% 0.16/0.39 ($false = ((^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((sK5 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2)))))))) @ sK6)) | ~spl0_4),
% 0.16/0.39 inference(sigma_clausification,[],[f107])).
% 0.16/0.39 thf(f107,plain,(
% 0.16/0.39 ((!! @ ((($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((sK5 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))) = $false) | ~spl0_4),
% 0.16/0.39 inference(avatar_component_clause,[],[f106])).
% 0.16/0.39 thf(f106,plain,(
% 0.16/0.39 spl0_4 <=> ((!! @ ((($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((sK5 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))) = $false)),
% 0.16/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.16/0.39 thf(f160,plain,(
% 0.16/0.39 ($true = ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK6 @ Y0) => (sK6 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))) => (sK6 @ sK5))) | (~spl0_2 | ~spl0_4)),
% 0.16/0.39 inference(boolean_simplification,[],[f155])).
% 0.16/0.39 thf(f155,plain,(
% 0.16/0.39 ((((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK6 @ Y0) => (sK6 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))) & $true) => (sK6 @ sK5)) = $true) | (~spl0_2 | ~spl0_4)),
% 0.16/0.39 inference(superposition,[],[f147,f143])).
% 0.16/0.39 thf(f143,plain,(
% 0.16/0.39 ((sK6 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $true) | ~spl0_4),
% 0.16/0.39 inference(boolean_simplification,[],[f142])).
% 0.16/0.39 thf(f142,plain,(
% 0.16/0.39 ($true = ($true & (sK6 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))) | ~spl0_4),
% 0.16/0.39 inference(backward_demodulation,[],[f137,f141])).
% 0.16/0.39 thf(f147,plain,(
% 0.16/0.39 ( ! [X1 : (($i > $o) > $o) > $o] : (((((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((X1 @ Y0) => (X1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))) & (X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) => (X1 @ sK5)) = $true)) ) | ~spl0_2),
% 0.16/0.39 inference(beta_eta_normalization,[],[f144])).
% 0.16/0.39 thf(f144,plain,(
% 0.16/0.39 ( ! [X1 : (($i > $o) > $o) > $o] : (($true = ((^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK5))) @ X1))) ) | ~spl0_2),
% 0.16/0.39 inference(pi_clausification,[],[f103])).
% 0.16/0.39 thf(f103,plain,(
% 0.16/0.39 ((!! @ ((($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK5)))) = $true) | ~spl0_2),
% 0.16/0.39 inference(boolean_simplification,[],[f102])).
% 0.16/0.39 thf(f102,plain,(
% 0.16/0.39 ($true = ($true & (!! @ ((($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK5)))))) | ~spl0_2),
% 0.16/0.39 inference(backward_demodulation,[],[f97,f101])).
% 0.16/0.39 thf(f101,plain,(
% 0.16/0.39 ($true = (sK2 @ sK5)) | ~spl0_2),
% 0.16/0.39 inference(binary_proxy_clausification,[],[f97])).
% 0.16/0.39 thf(f97,plain,(
% 0.16/0.39 ($true = ((sK2 @ sK5) & (!! @ ((($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK5)))))) | ~spl0_2),
% 0.16/0.39 inference(binary_proxy_clausification,[],[f92])).
% 0.16/0.39 thf(f92,plain,(
% 0.16/0.39 ((((sK2 @ sK5) & (!! @ ((($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK5))))) => ((!! @ ((($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((sK5 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))) & (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK5 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))) & (Y0 @ Y1)))))))) = $false) | ~spl0_2),
% 0.16/0.39 inference(beta_eta_normalization,[],[f91])).
% 0.16/0.39 thf(f91,plain,(
% 0.16/0.39 (((^[Y0 : ($i > $o) > $o]: (((sK2 @ Y0) & (!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))) => ((!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))) @ sK5) = $false) | ~spl0_2),
% 0.16/0.39 inference(sigma_clausification,[],[f65])).
% 0.16/0.39 thf(f65,plain,(
% 0.16/0.39 ($false = (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((sK2 @ Y0) & (!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))) => ((!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))))) | ~spl0_2),
% 0.16/0.39 inference(avatar_component_clause,[],[f64])).
% 0.16/0.39 thf(f64,plain,(
% 0.16/0.39 spl0_2 <=> ($false = (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((sK2 @ Y0) & (!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))) => ((!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2)))))))))))),
% 0.16/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.16/0.39 thf(f174,plain,(
% 0.16/0.39 ($true = (~ (sK6 @ sK5))) | ~spl0_4),
% 0.16/0.39 inference(boolean_simplification,[],[f170])).
% 0.16/0.39 thf(f170,plain,(
% 0.16/0.39 ($true = ((sK6 @ sK5) => $false)) | ~spl0_4),
% 0.16/0.39 inference(superposition,[],[f151,f139])).
% 0.16/0.39 thf(f139,plain,(
% 0.16/0.39 ((sK6 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK5 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))) & (Y0 @ Y1)))))) = $false) | ~spl0_4),
% 0.16/0.39 inference(boolean_simplification,[],[f138])).
% 0.16/0.39 thf(f138,plain,(
% 0.16/0.39 (($true => (sK6 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK5 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))) & (Y0 @ Y1))))))) = $false) | ~spl0_4),
% 0.16/0.39 inference(backward_demodulation,[],[f125,f137])).
% 0.16/0.39 thf(f151,plain,(
% 0.16/0.39 ( ! [X1 : ($i > $o) > $o] : (($true = ((sK6 @ X1) => (sK6 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))) & (Y0 @ Y1))))))))) ) | ~spl0_4),
% 0.16/0.39 inference(beta_eta_normalization,[],[f150])).
% 0.16/0.39 thf(f150,plain,(
% 0.16/0.39 ( ! [X1 : ($i > $o) > $o] : (($true = ((^[Y0 : ($i > $o) > $o]: ((sK6 @ Y0) => (sK6 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2)))))))) @ X1))) ) | ~spl0_4),
% 0.16/0.39 inference(pi_clausification,[],[f141])).
% 0.16/0.39 thf(f120,plain,(
% 0.16/0.39 ~spl0_2 | ~spl0_5),
% 0.16/0.39 inference(avatar_contradiction_clause,[],[f119])).
% 0.16/0.39 thf(f119,plain,(
% 0.16/0.39 $false | (~spl0_2 | ~spl0_5)),
% 0.16/0.39 inference(trivial_inequality_removal,[],[f118])).
% 0.16/0.39 thf(f118,plain,(
% 0.16/0.39 ($true = $false) | (~spl0_2 | ~spl0_5)),
% 0.16/0.39 inference(forward_demodulation,[],[f117,f110])).
% 0.16/0.39 thf(f110,plain,(
% 0.16/0.39 ((sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK5 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))) & (Y0 @ Y1)))))) = $false) | ~spl0_5),
% 0.16/0.39 inference(avatar_component_clause,[],[f109])).
% 0.16/0.39 thf(f109,plain,(
% 0.16/0.39 spl0_5 <=> ((sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK5 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))) & (Y0 @ Y1)))))) = $false)),
% 0.16/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])).
% 0.16/0.39 thf(f117,plain,(
% 0.16/0.39 ((sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK5 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))) & (Y0 @ Y1)))))) = $true) | ~spl0_2),
% 0.16/0.39 inference(boolean_simplification,[],[f116])).
% 0.16/0.39 thf(f116,plain,(
% 0.16/0.39 ($true = ($true => (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK5 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))) & (Y0 @ Y1)))))))) | ~spl0_2),
% 0.16/0.39 inference(forward_demodulation,[],[f115,f103])).
% 0.16/0.39 thf(f115,plain,(
% 0.16/0.39 (((!! @ ((($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK5)))) => (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK5 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))) & (Y0 @ Y1))))))) = $true) | ~spl0_2),
% 0.16/0.39 inference(boolean_simplification,[],[f114])).
% 0.16/0.39 thf(f114,plain,(
% 0.16/0.39 ($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK5)))) => ($true => (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK5 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))) & (Y0 @ Y1))))))))) | ~spl0_2),
% 0.16/0.39 inference(superposition,[],[f38,f101])).
% 0.16/0.39 thf(f38,plain,(
% 0.16/0.39 ( ! [X1 : ($i > $o) > $o] : (($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ X1)))) => ((sK2 @ X1) => (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))) & (Y0 @ Y1)))))))))) )),
% 0.16/0.39 inference(beta_eta_normalization,[],[f37])).
% 0.16/0.39 thf(f37,plain,(
% 0.16/0.39 ( ! [X1 : ($i > $o) > $o] : (($true = ((^[Y0 : ($i > $o) > $o]: ((!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) => ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))) @ X1))) )),
% 0.16/0.39 inference(pi_clausification,[],[f33])).
% 0.16/0.39 thf(f33,plain,(
% 0.16/0.39 ($true = (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) => ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2)))))))))))),
% 0.16/0.39 inference(binary_proxy_clausification,[],[f28])).
% 0.16/0.39 thf(f28,plain,(
% 0.16/0.39 ($true = ((sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) => ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))))))),
% 0.16/0.39 inference(binary_proxy_clausification,[],[f26])).
% 0.16/0.39 thf(f26,plain,(
% 0.16/0.39 ((((sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) => ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))))) => (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((sK2 @ Y1) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y1 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (sK2 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3)))))))))) & (sK2 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) & (!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2)))))))) => ((sK2 @ Y0) & (!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))))) => (sK2 @ Y0))))) = $false)),
% 0.16/0.39 inference(beta_eta_normalization,[],[f25])).
% 0.16/0.39 thf(f25,plain,(
% 0.16/0.39 ($false = ((^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($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]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1)))) => ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))))) => (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: (((Y0 @ Y2) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ (^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y4 @ (^[Y7 : $i]: ((~ (Y6 = Y7)) & (Y5 @ Y7)))) & (Y5 @ Y6))))))))) & (Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ Y4))))) => (Y3 @ Y2))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ (^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y4 @ (^[Y7 : $i]: ((~ (Y6 = Y7)) & (Y5 @ Y7)))) & (Y5 @ Y6))))))))) & (Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ Y4))))) => (Y3 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y2 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))) & (Y4 @ Y5))))))))) & (Y0 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4)))))))))) & (Y0 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3)))))))) => ((Y0 @ Y1) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1)))))) => (Y0 @ Y1)))))) @ sK2))),
% 0.16/0.39 inference(sigma_clausification,[],[f22])).
% 0.16/0.39 thf(f22,plain,(
% 0.16/0.39 ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($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]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1)))) => ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))))) => (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: (((Y0 @ Y2) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ (^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y4 @ (^[Y7 : $i]: ((~ (Y6 = Y7)) & (Y5 @ Y7)))) & (Y5 @ Y6))))))))) & (Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ Y4))))) => (Y3 @ Y2))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ (^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y4 @ (^[Y7 : $i]: ((~ (Y6 = Y7)) & (Y5 @ Y7)))) & (Y5 @ Y6))))))))) & (Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ Y4))))) => (Y3 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y2 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))) & (Y4 @ Y5))))))))) & (Y0 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4)))))))))) & (Y0 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3)))))))) => ((Y0 @ Y1) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1)))))) => (Y0 @ Y1))))))) = $false)),
% 0.16/0.39 inference(not_proxy_clausification,[],[f21])).
% 0.16/0.39 thf(f21,plain,(
% 0.16/0.39 ($true = (~ (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($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]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1)))) => ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))))) => (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: (((Y0 @ Y2) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ (^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y4 @ (^[Y7 : $i]: ((~ (Y6 = Y7)) & (Y5 @ Y7)))) & (Y5 @ Y6))))))))) & (Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ Y4))))) => (Y3 @ Y2))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ (^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y4 @ (^[Y7 : $i]: ((~ (Y6 = Y7)) & (Y5 @ Y7)))) & (Y5 @ Y6))))))))) & (Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ Y4))))) => (Y3 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y2 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))) & (Y4 @ Y5))))))))) & (Y0 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4)))))))))) & (Y0 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3)))))))) => ((Y0 @ Y1) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1)))))) => (Y0 @ Y1)))))))))),
% 0.16/0.39 inference(beta_eta_normalization,[],[f20])).
% 0.16/0.39 thf(f20,plain,(
% 0.16/0.39 ((~ (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ (^[Y2 : $i]: (Y1 @ Y2)))))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($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]: ((Y5 @ (^[Y8 : $i]: ((~ (Y7 = Y8)) & (Y6 @ Y8)))) & (Y6 @ Y7))))))) @ Y4))))) & (Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ (^[Y5 : $i]: (Y4 @ Y5))))))) => (Y3 @ Y2))))) @ Y1) => ((Y0 @ Y1) => (Y0 @ ((^[Y2 : ($i > $o) > $o]: ((^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))) @ Y1))))))) => (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: (((Y0 @ Y2) & ((^[Y3 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y4 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y5 : ($i > $o) > $o]: ((Y4 @ Y5) => (Y4 @ ((^[Y6 : ($i > $o) > $o]: ((^[Y7 : $i > $o]: (?? @ $i @ (^[Y8 : $i]: ((Y6 @ (^[Y9 : $i]: ((~ (Y8 = Y9)) & (Y7 @ Y9)))) & (Y7 @ Y8))))))) @ Y5))))) & (Y4 @ (^[Y5 : $i > $o]: (~ (?? @ $i @ (^[Y6 : $i]: (Y5 @ Y6))))))) => (Y4 @ Y3))))) @ Y2)) => (((^[Y3 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y4 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y5 : ($i > $o) > $o]: ((Y4 @ Y5) => (Y4 @ ((^[Y6 : ($i > $o) > $o]: ((^[Y7 : $i > $o]: (?? @ $i @ (^[Y8 : $i]: ((Y6 @ (^[Y9 : $i]: ((~ (Y8 = Y9)) & (Y7 @ Y9)))) & (Y7 @ Y8))))))) @ Y5))))) & (Y4 @ (^[Y5 : $i > $o]: (~ (?? @ $i @ (^[Y6 : $i]: (Y5 @ Y6))))))) => (Y4 @ Y3))))) @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))) & (Y4 @ Y5))))))) @ Y2)) & (Y0 @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))) & (Y4 @ Y5))))))) @ Y2)))))) & (Y0 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ (^[Y3 : $i]: (Y2 @ Y3))))))) & ((^[Y2 : ($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]: ((Y5 @ (^[Y8 : $i]: ((~ (Y7 = Y8)) & (Y6 @ Y8)))) & (Y6 @ Y7))))))) @ Y4))))) & (Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ (^[Y5 : $i]: (Y4 @ Y5))))))) => (Y3 @ Y2))))) @ (^[Y2 : $i > $o]: (~ (?? @ $i @ (^[Y3 : $i]: (Y2 @ Y3))))))) => ((Y0 @ Y1) & ((^[Y2 : ($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]: ((Y5 @ (^[Y8 : $i]: ((~ (Y7 = Y8)) & (Y6 @ Y8)))) & (Y6 @ Y7))))))) @ Y4))))) & (Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ (^[Y5 : $i]: (Y4 @ Y5))))))) => (Y3 @ Y2))))) @ Y1))) => (Y0 @ Y1)))))))) = $true)),
% 0.16/0.39 inference(definition_unfolding,[],[f15,f18,f19,f16,f19,f19,f16,f16,f18,f19,f18,f19])).
% 0.16/0.39 thf(f16,plain,(
% 0.16/0.39 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))),
% 0.16/0.39 inference(cnf_transformation,[],[f8])).
% 0.16/0.39 thf(f8,plain,(
% 0.16/0.39 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))),
% 0.16/0.39 inference(fool_elimination,[],[f7])).
% 0.16/0.39 thf(f7,plain,(
% 0.16/0.39 (cSUCC = (^[X0 : ($i > $o) > $o, X1 : $i > $o] : (? [X2] : ((X1 @ X2) & (X0 @ (^[X3 : $i] : ((X1 @ X3) & (X2 != X3))))))))),
% 0.16/0.39 inference(rectify,[],[f2])).
% 0.16/0.39 thf(f2,axiom,(
% 0.16/0.39 (cSUCC = (^[X2 : ($i > $o) > $o, X0 : $i > $o] : (? [X1] : ((X0 @ X1) & (X2 @ (^[X3 : $i] : ((X0 @ X3) & (X1 != X3))))))))),
% 0.16/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cSUCC_def)).
% 0.16/0.39 thf(f19,plain,(
% 0.16/0.39 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))) & (Y4 @ Y5))))))) @ Y2))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ (^[Y3 : $i]: (Y2 @ Y3))))))) => (Y1 @ Y0))))))),
% 0.16/0.39 inference(definition_unfolding,[],[f17,f16,f18])).
% 0.16/0.39 thf(f17,plain,(
% 0.16/0.39 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (cSUCC @ Y2))))) & (Y1 @ cZERO)) => (Y1 @ Y0))))))),
% 0.16/0.39 inference(cnf_transformation,[],[f14])).
% 0.16/0.39 thf(f14,plain,(
% 0.16/0.39 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (cSUCC @ Y2))))) & (Y1 @ cZERO)) => (Y1 @ Y0))))))),
% 0.16/0.39 inference(fool_elimination,[],[f13])).
% 0.16/0.39 thf(f13,plain,(
% 0.16/0.39 ((^[X0 : ($i > $o) > $o] : (! [X1 : (($i > $o) > $o) > $o] : (((X1 @ cZERO) & ! [X2 : ($i > $o) > $o] : ((X1 @ X2) => (X1 @ (cSUCC @ X2)))) => (X1 @ X0)))) = cNAT)),
% 0.16/0.39 inference(rectify,[],[f3])).
% 0.16/0.39 thf(f3,axiom,(
% 0.16/0.39 ((^[X2 : ($i > $o) > $o] : (! [X0 : (($i > $o) > $o) > $o] : (((X0 @ cZERO) & ! [X1 : ($i > $o) > $o] : ((X0 @ X1) => (X0 @ (cSUCC @ X1)))) => (X0 @ X2)))) = cNAT)),
% 0.16/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cNAT_def)).
% 0.16/0.39 thf(f18,plain,(
% 0.16/0.39 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 0.16/0.39 inference(cnf_transformation,[],[f10])).
% 0.16/0.39 thf(f10,plain,(
% 0.16/0.39 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 0.16/0.39 inference(fool_elimination,[],[f9])).
% 0.16/0.39 thf(f9,plain,(
% 0.16/0.39 (cZERO = (^[X0 : $i > $o] : (~? [X1] : (X0 @ X1))))),
% 0.16/0.39 inference(rectify,[],[f1])).
% 0.16/0.39 thf(f1,axiom,(
% 0.16/0.39 (cZERO = (^[X0 : $i > $o] : (~? [X1] : (X0 @ X1))))),
% 0.16/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cZERO_def)).
% 0.16/0.39 thf(f15,plain,(
% 0.16/0.39 ($true = (~ (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ cZERO) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((cNAT @ Y1) => ((Y0 @ Y1) => (Y0 @ (cSUCC @ Y1))))))) => (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: (((Y0 @ Y2) & (cNAT @ Y2)) => ((cNAT @ (cSUCC @ Y2)) & (Y0 @ (cSUCC @ Y2)))))) & (Y0 @ cZERO)) & (cNAT @ cZERO)) => ((Y0 @ Y1) & (cNAT @ Y1))) => (Y0 @ Y1)))))))))),
% 0.16/0.39 inference(cnf_transformation,[],[f12])).
% 0.16/0.39 thf(f12,plain,(
% 0.16/0.39 ($true = (~ (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ cZERO) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((cNAT @ Y1) => ((Y0 @ Y1) => (Y0 @ (cSUCC @ Y1))))))) => (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: (((Y0 @ Y2) & (cNAT @ Y2)) => ((cNAT @ (cSUCC @ Y2)) & (Y0 @ (cSUCC @ Y2)))))) & (Y0 @ cZERO)) & (cNAT @ cZERO)) => ((Y0 @ Y1) & (cNAT @ Y1))) => (Y0 @ Y1)))))))))),
% 0.16/0.39 inference(fool_elimination,[],[f11])).
% 0.16/0.39 thf(f11,plain,(
% 0.16/0.39 ~! [X0 : (($i > $o) > $o) > $o] : ((! [X1 : ($i > $o) > $o] : ((cNAT @ X1) => ((X0 @ X1) => (X0 @ (cSUCC @ X1)))) & (X0 @ cZERO)) => ! [X2 : ($i > $o) > $o] : ((((cNAT @ cZERO) & (X0 @ cZERO) & ! [X3 : ($i > $o) > $o] : (((cNAT @ X3) & (X0 @ X3)) => ((X0 @ (cSUCC @ X3)) & (cNAT @ (cSUCC @ X3))))) => ((cNAT @ X2) & (X0 @ X2))) => (X0 @ X2)))),
% 0.16/0.39 inference(rectify,[],[f5])).
% 0.16/0.39 thf(f5,negated_conjecture,(
% 0.16/0.39 ~! [X0 : (($i > $o) > $o) > $o] : ((! [X1 : ($i > $o) > $o] : ((cNAT @ X1) => ((X0 @ X1) => (X0 @ (cSUCC @ X1)))) & (X0 @ cZERO)) => ! [X4 : ($i > $o) > $o] : ((((cNAT @ cZERO) & (X0 @ cZERO) & ! [X1 : ($i > $o) > $o] : (((cNAT @ X1) & (X0 @ X1)) => ((X0 @ (cSUCC @ X1)) & (cNAT @ (cSUCC @ X1))))) => ((cNAT @ X4) & (X0 @ X4))) => (X0 @ X4)))),
% 0.16/0.39 inference(negated_conjecture,[],[f4])).
% 0.16/0.39 thf(f4,conjecture,(
% 0.16/0.39 ! [X0 : (($i > $o) > $o) > $o] : ((! [X1 : ($i > $o) > $o] : ((cNAT @ X1) => ((X0 @ X1) => (X0 @ (cSUCC @ X1)))) & (X0 @ cZERO)) => ! [X4 : ($i > $o) > $o] : ((((cNAT @ cZERO) & (X0 @ cZERO) & ! [X1 : ($i > $o) > $o] : (((cNAT @ X1) & (X0 @ X1)) => ((X0 @ (cSUCC @ X1)) & (cNAT @ (cSUCC @ X1))))) => ((cNAT @ X4) & (X0 @ X4))) => (X0 @ X4)))),
% 0.16/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX6102_B)).
% 0.16/0.39 thf(f111,plain,(
% 0.16/0.39 spl0_4 | spl0_5 | ~spl0_2),
% 0.16/0.39 inference(avatar_split_clause,[],[f104,f64,f109,f106])).
% 0.16/0.39 thf(f104,plain,(
% 0.16/0.39 ((!! @ ((($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((sK5 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))) = $false) | ((sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK5 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))) & (Y0 @ Y1)))))) = $false) | ~spl0_2),
% 0.16/0.39 inference(binary_proxy_clausification,[],[f99])).
% 0.16/0.39 thf(f99,plain,(
% 0.16/0.39 ($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((sK5 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))) & (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK5 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))) & (Y0 @ Y1)))))))) | ~spl0_2),
% 0.16/0.39 inference(boolean_simplification,[],[f98])).
% 0.16/0.39 thf(f98,plain,(
% 0.16/0.39 (($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((sK5 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))) & (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK5 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))) & (Y0 @ Y1)))))))) = $false) | ~spl0_2),
% 0.16/0.39 inference(backward_demodulation,[],[f92,f97])).
% 0.16/0.39 thf(f88,plain,(
% 0.16/0.39 ~spl0_1),
% 0.16/0.39 inference(avatar_contradiction_clause,[],[f87])).
% 0.16/0.39 thf(f87,plain,(
% 0.16/0.39 $false | ~spl0_1),
% 0.16/0.39 inference(trivial_inequality_removal,[],[f86])).
% 0.16/0.39 thf(f86,plain,(
% 0.16/0.39 ($true = $false) | ~spl0_1),
% 0.16/0.39 inference(boolean_simplification,[],[f85])).
% 0.16/0.39 thf(f85,plain,(
% 0.16/0.39 ($true = ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK4 @ Y0) => (sK4 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))) & $false)) | ~spl0_1),
% 0.16/0.39 inference(backward_demodulation,[],[f82,f84])).
% 0.16/0.39 thf(f84,plain,(
% 0.16/0.39 ($false = (sK4 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) | ~spl0_1),
% 0.16/0.39 inference(boolean_simplification,[],[f83])).
% 0.16/0.39 thf(f83,plain,(
% 0.16/0.39 (($true => (sK4 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) = $false) | ~spl0_1),
% 0.16/0.39 inference(backward_demodulation,[],[f80,f82])).
% 0.16/0.39 thf(f80,plain,(
% 0.16/0.39 ((((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK4 @ Y0) => (sK4 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))) & (sK4 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) => (sK4 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) = $false) | ~spl0_1),
% 0.16/0.39 inference(beta_eta_normalization,[],[f76])).
% 0.16/0.39 thf(f76,plain,(
% 0.16/0.39 ($false = ((^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))))) @ sK4)) | ~spl0_1),
% 0.16/0.39 inference(sigma_clausification,[],[f62])).
% 0.16/0.39 thf(f62,plain,(
% 0.16/0.39 ((!! @ ((($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))))) = $false) | ~spl0_1),
% 0.16/0.39 inference(avatar_component_clause,[],[f61])).
% 0.16/0.39 thf(f61,plain,(
% 0.16/0.39 spl0_1 <=> ((!! @ ((($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))))) = $false)),
% 0.16/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.16/0.39 thf(f82,plain,(
% 0.16/0.39 (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK4 @ Y0) => (sK4 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))) & (sK4 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) = $true) | ~spl0_1),
% 0.16/0.39 inference(binary_proxy_clausification,[],[f80])).
% 0.16/0.39 thf(f66,plain,(
% 0.16/0.39 spl0_1 | spl0_2),
% 0.16/0.39 inference(avatar_split_clause,[],[f59,f64,f61])).
% 0.16/0.39 thf(f59,plain,(
% 0.16/0.39 ((!! @ ((($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))))) = $false) | ($false = (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((sK2 @ Y0) & (!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))) => ((!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2)))))))))))),
% 0.16/0.39 inference(binary_proxy_clausification,[],[f53])).
% 0.16/0.39 thf(f53,plain,(
% 0.16/0.39 (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((sK2 @ Y0) & (!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))) => ((!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2)))))))))) & (!! @ ((($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))))))) = $false)),
% 0.16/0.39 inference(boolean_simplification,[],[f52])).
% 0.16/0.39 thf(f52,plain,(
% 0.16/0.39 ((~ (~ ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((sK2 @ Y0) & (!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))) => ((!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2)))))))))) & (!! @ ((($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))))))))) = $false)),
% 0.16/0.39 inference(boolean_simplification,[],[f51])).
% 0.16/0.39 thf(f51,plain,(
% 0.16/0.39 ((~ (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((sK2 @ Y0) & (!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))) => ((!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2)))))))))) & (!! @ ((($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))))))) => $false)) = $false)),
% 0.16/0.39 inference(boolean_simplification,[],[f50])).
% 0.16/0.39 thf(f50,plain,(
% 0.16/0.39 ((~ (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((sK2 @ Y0) & (!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))) => ((!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2)))))))))) & (!! @ ((($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))))))) => ($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK3))))))) = $false)),
% 0.16/0.39 inference(boolean_simplification,[],[f49])).
% 0.16/0.39 thf(f49,plain,(
% 0.16/0.39 ($false = ((((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((sK2 @ Y0) & (!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))) => ((!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2)))))))))) & (!! @ ((($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))))))) => ($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK3)))))) => $false))),
% 0.16/0.39 inference(backward_demodulation,[],[f42,f47])).
% 0.16/0.39 thf(f47,plain,(
% 0.16/0.39 ((sK2 @ sK3) = $false)),
% 0.16/0.39 inference(binary_proxy_clausification,[],[f42])).
% 0.16/0.39 thf(f42,plain,(
% 0.16/0.39 ($false = ((((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((sK2 @ Y0) & (!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))) => ((!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2)))))))))) & (!! @ ((($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))))))) => ((sK2 @ sK3) & (!! @ ((($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK3)))))) => (sK2 @ sK3)))),
% 0.16/0.39 inference(boolean_simplification,[],[f41])).
% 0.16/0.39 thf(f41,plain,(
% 0.16/0.39 ((((((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((sK2 @ Y0) & (!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))) => ((!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2)))))))))) & $true) & (!! @ ((($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))))))) => ((sK2 @ sK3) & (!! @ ((($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK3)))))) => (sK2 @ sK3)) = $false)),
% 0.16/0.39 inference(forward_demodulation,[],[f40,f36])).
% 0.16/0.39 thf(f36,plain,(
% 0.16/0.39 ($true = (sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))),
% 0.16/0.39 inference(boolean_simplification,[],[f35])).
% 0.16/0.39 thf(f35,plain,(
% 0.16/0.39 ($true = ((sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & $true))),
% 0.16/0.39 inference(backward_demodulation,[],[f28,f33])).
% 0.16/0.39 thf(f40,plain,(
% 0.16/0.39 ((((((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((sK2 @ Y0) & (!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))) => ((!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2)))))))))) & (sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) & (!! @ ((($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))))))) => ((sK2 @ sK3) & (!! @ ((($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]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK3)))))) => (sK2 @ sK3)) = $false)),
% 0.16/0.39 inference(beta_eta_normalization,[],[f39])).
% 0.16/0.39 thf(f39,plain,(
% 0.16/0.39 (((^[Y0 : ($i > $o) > $o]: (((((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((sK2 @ Y1) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y1 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (sK2 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3)))))))))) & (sK2 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) & (!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2)))))))) => ((sK2 @ Y0) & (!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))))) => (sK2 @ Y0))) @ sK3) = $false)),
% 0.16/0.39 inference(sigma_clausification,[],[f27])).
% 0.16/0.39 thf(f27,plain,(
% 0.16/0.39 ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((sK2 @ Y1) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y1 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (sK2 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3)))))))))) & (sK2 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) & (!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2)))))))) => ((sK2 @ Y0) & (!! @ ((($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]: ((Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))))) => (sK2 @ Y0)))) = $false)),
% 0.16/0.39 inference(binary_proxy_clausification,[],[f26])).
% 0.16/0.39 % SZS output end Proof for theBenchmark
% 0.16/0.39 % (1474)------------------------------
% 0.16/0.39 % (1474)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.39 % (1474)Termination reason: Refutation
% 0.16/0.39
% 0.16/0.39 % (1474)Memory used [KB]: 6140
% 0.16/0.39 % (1474)Time elapsed: 0.025 s
% 0.16/0.39 % (1474)Instructions burned: 55 (million)
% 0.16/0.39 % (1474)------------------------------
% 0.16/0.39 % (1474)------------------------------
% 0.16/0.39 % (1461)Success in time 0.046 s
%------------------------------------------------------------------------------