TSTP Solution File: SEV101^5 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV101^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n023.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 16:01:48 EDT 2024
% Result : Theorem 0.41s 0.62s
% Output : Refutation 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : SEV101^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.14 % Command : run_vampire %s %d THM
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 21 19:30:09 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.23/0.37 This is a TH0_THM_NEQ_NAR problem
% 0.23/0.38 Running higher-order theorem proving
% 0.23/0.38 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
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% 0.24/0.51 ipcrm: permission denied for id (1675624545)
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% 0.24/0.53 ipcrm: permission denied for id (1675952240)
% 0.24/0.53 ipcrm: permission denied for id (1675985009)
% 0.24/0.54 ipcrm: permission denied for id (1676083316)
% 0.24/0.54 ipcrm: permission denied for id (1676214393)
% 0.24/0.54 ipcrm: permission denied for id (1676247162)
% 0.24/0.55 ipcrm: permission denied for id (1676279931)
% 0.38/0.55 ipcrm: permission denied for id (1676378237)
% 0.38/0.55 ipcrm: permission denied for id (1676443775)
% 0.38/0.57 % (19133)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2998ds/18Mi)
% 0.38/0.57 % (19127)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2998ds/183Mi)
% 0.38/0.57 % (19129)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 (2998ds/27Mi)
% 0.41/0.57 % (19133)Instruction limit reached!
% 0.41/0.57 % (19133)------------------------------
% 0.41/0.57 % (19133)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.41/0.57 % (19133)Termination reason: Unknown
% 0.41/0.57 % (19133)Termination phase: Saturation
% 0.41/0.57
% 0.41/0.57 % (19133)Memory used [KB]: 5628
% 0.41/0.57 % (19133)Time elapsed: 0.009 s
% 0.41/0.57 % (19133)Instructions burned: 19 (million)
% 0.41/0.57 % (19133)------------------------------
% 0.41/0.57 % (19133)------------------------------
% 0.41/0.58 % (19129)Refutation not found, incomplete strategy
% 0.41/0.58 % (19129)------------------------------
% 0.41/0.58 % (19129)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.41/0.58 % (19129)Termination reason: Refutation not found, incomplete strategy
% 0.41/0.58
% 0.41/0.58
% 0.41/0.58 % (19129)Memory used [KB]: 5500
% 0.41/0.58 % (19129)Time elapsed: 0.007 s
% 0.41/0.58 % (19129)Instructions burned: 8 (million)
% 0.41/0.58 % (19129)------------------------------
% 0.41/0.58 % (19129)------------------------------
% 0.41/0.58 % (19128)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 (2998ds/4Mi)
% 0.41/0.58 % (19132)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 (2998ds/275Mi)
% 0.41/0.58 % (19130)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2998ds/2Mi)
% 0.41/0.58 % (19130)Instruction limit reached!
% 0.41/0.58 % (19130)------------------------------
% 0.41/0.58 % (19130)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.41/0.58 % (19130)Termination reason: Unknown
% 0.41/0.58 % (19130)Termination phase: Preprocessing 3
% 0.41/0.58
% 0.41/0.58 % (19130)Memory used [KB]: 1023
% 0.41/0.58 % (19130)Time elapsed: 0.003 s
% 0.41/0.58 % (19130)Instructions burned: 2 (million)
% 0.41/0.58 % (19130)------------------------------
% 0.41/0.58 % (19130)------------------------------
% 0.41/0.58 % (19134)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.41/0.58 % (19131)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 (2998ds/2Mi)
% 0.41/0.58 % (19134)Instruction limit reached!
% 0.41/0.58 % (19134)------------------------------
% 0.41/0.58 % (19134)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.41/0.58 % (19134)Termination reason: Unknown
% 0.41/0.58 % (19134)Termination phase: Saturation
% 0.41/0.58
% 0.41/0.58 % (19134)Memory used [KB]: 1023
% 0.41/0.58 % (19134)Time elapsed: 0.003 s
% 0.41/0.58 % (19134)Instructions burned: 4 (million)
% 0.41/0.58 % (19134)------------------------------
% 0.41/0.58 % (19134)------------------------------
% 0.41/0.58 % (19131)Instruction limit reached!
% 0.41/0.58 % (19131)------------------------------
% 0.41/0.58 % (19131)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.41/0.58 % (19131)Termination reason: Unknown
% 0.41/0.58 % (19131)Termination phase: Property scanning
% 0.41/0.58
% 0.41/0.58 % (19131)Memory used [KB]: 1023
% 0.41/0.58 % (19131)Time elapsed: 0.003 s
% 0.41/0.58 % (19131)Instructions burned: 2 (million)
% 0.41/0.58 % (19131)------------------------------
% 0.41/0.58 % (19131)------------------------------
% 0.41/0.59 % (19128)Instruction limit reached!
% 0.41/0.59 % (19128)------------------------------
% 0.41/0.59 % (19128)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.41/0.59 % (19128)Termination reason: Unknown
% 0.41/0.59 % (19128)Termination phase: Saturation
% 0.41/0.59
% 0.41/0.59 % (19128)Memory used [KB]: 5500
% 0.41/0.59 % (19128)Time elapsed: 0.006 s
% 0.41/0.59 % (19128)Instructions burned: 4 (million)
% 0.41/0.59 % (19128)------------------------------
% 0.41/0.59 % (19128)------------------------------
% 0.41/0.59 % (19135)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 (2998ds/37Mi)
% 0.41/0.59 % (19137)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 (2998ds/3Mi)
% 0.41/0.59 % (19137)Instruction limit reached!
% 0.41/0.59 % (19137)------------------------------
% 0.41/0.59 % (19137)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.41/0.60 % (19137)Termination reason: Unknown
% 0.41/0.60 % (19137)Termination phase: Saturation
% 0.41/0.60
% 0.41/0.60 % (19137)Memory used [KB]: 1023
% 0.41/0.60 % (19137)Time elapsed: 0.003 s
% 0.41/0.60 % (19137)Instructions burned: 4 (million)
% 0.41/0.60 % (19137)------------------------------
% 0.41/0.60 % (19137)------------------------------
% 0.41/0.60 % (19136)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 (2998ds/15Mi)
% 0.41/0.60 % (19138)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 (2998ds/1041Mi)
% 0.41/0.60 % (19139)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2998ds/7Mi)
% 0.41/0.60 % (19140)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2997ds/16Mi)
% 0.41/0.61 % (19139)Instruction limit reached!
% 0.41/0.61 % (19139)------------------------------
% 0.41/0.61 % (19139)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.41/0.61 % (19139)Termination reason: Unknown
% 0.41/0.61 % (19139)Termination phase: Saturation
% 0.41/0.61
% 0.41/0.61 % (19139)Memory used [KB]: 1023
% 0.41/0.61 % (19139)Time elapsed: 0.007 s
% 0.41/0.61 % (19139)Instructions burned: 8 (million)
% 0.41/0.61 % (19139)------------------------------
% 0.41/0.61 % (19139)------------------------------
% 0.41/0.61 % (19136)Instruction limit reached!
% 0.41/0.61 % (19136)------------------------------
% 0.41/0.61 % (19136)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.41/0.61 % (19136)Termination reason: Unknown
% 0.41/0.61 % (19136)Termination phase: Saturation
% 0.41/0.61
% 0.41/0.61 % (19136)Memory used [KB]: 5628
% 0.41/0.61 % (19136)Time elapsed: 0.012 s
% 0.41/0.61 % (19136)Instructions burned: 15 (million)
% 0.41/0.61 % (19136)------------------------------
% 0.41/0.61 % (19136)------------------------------
% 0.41/0.61 % (19140)Instruction limit reached!
% 0.41/0.61 % (19140)------------------------------
% 0.41/0.61 % (19140)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.41/0.61 % (19140)Termination reason: Unknown
% 0.41/0.61 % (19140)Termination phase: Saturation
% 0.41/0.61
% 0.41/0.61 % (19140)Memory used [KB]: 5628
% 0.41/0.61 % (19140)Time elapsed: 0.010 s
% 0.41/0.61 % (19140)Instructions burned: 16 (million)
% 0.41/0.61 % (19140)------------------------------
% 0.41/0.61 % (19140)------------------------------
% 0.41/0.61 % (19135)Instruction limit reached!
% 0.41/0.61 % (19135)------------------------------
% 0.41/0.61 % (19135)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.41/0.61 % (19135)Termination reason: Unknown
% 0.41/0.61 % (19135)Termination phase: Saturation
% 0.41/0.61
% 0.41/0.61 % (19135)Memory used [KB]: 5884
% 0.41/0.61 % (19135)Time elapsed: 0.024 s
% 0.41/0.61 % (19135)Instructions burned: 38 (million)
% 0.41/0.61 % (19135)------------------------------
% 0.41/0.61 % (19135)------------------------------
% 0.41/0.62 % (19132)First to succeed.
% 0.41/0.62 % (19132)Refutation found. Thanks to Tanya!
% 0.41/0.62 % SZS status Theorem for theBenchmark
% 0.41/0.62 % SZS output start Proof for theBenchmark
% 0.41/0.62 thf(func_def_8, type, sK0: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 0.41/0.62 thf(func_def_9, type, sK1: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 0.41/0.62 thf(func_def_10, type, sK2: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 0.41/0.62 thf(func_def_11, type, sK3: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i).
% 0.41/0.62 thf(func_def_12, type, sK4: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 0.41/0.62 thf(func_def_13, type, sK5: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i).
% 0.41/0.62 thf(func_def_15, type, ph7: !>[X0: $tType]:(X0)).
% 0.41/0.62 thf(func_def_21, type, sK9: (($i > $o) > ($i > $o) > $i > $o) > $i).
% 0.41/0.62 thf(func_def_22, type, sK10: (($i > $o) > ($i > $o) > $i > $o) > $i).
% 0.41/0.62 thf(func_def_25, type, sK13: (($i > $o) > ($i > $o) > $i > $o) > $i).
% 0.41/0.62 thf(f502,plain,(
% 0.41/0.62 $false),
% 0.41/0.62 inference(avatar_sat_refutation,[],[f86,f351,f363,f367,f500])).
% 0.41/0.62 thf(f500,plain,(
% 0.41/0.62 ~spl6_2 | ~spl6_11 | ~spl6_14),
% 0.41/0.62 inference(avatar_contradiction_clause,[],[f499])).
% 0.41/0.62 thf(f499,plain,(
% 0.41/0.62 $false | (~spl6_2 | ~spl6_11 | ~spl6_14)),
% 0.41/0.62 inference(subsumption_resolution,[],[f498,f476])).
% 0.41/0.62 thf(f476,plain,(
% 0.41/0.62 ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) != (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | (~spl6_2 | ~spl6_11)),
% 0.41/0.62 inference(trivial_inequality_removal,[],[f475])).
% 0.41/0.62 thf(f475,plain,(
% 0.41/0.62 ($false = $true) | ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) != (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | (~spl6_2 | ~spl6_11)),
% 0.41/0.62 inference(beta_eta_normalization,[],[f469])).
% 0.41/0.62 thf(f469,plain,(
% 0.41/0.62 ( ! [X0 : $i] : (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) != (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X0) = $true)) ) | (~spl6_2 | ~spl6_11)),
% 0.41/0.62 inference(superposition,[],[f85,f458])).
% 0.41/0.62 thf(f458,plain,(
% 0.41/0.62 ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ~spl6_11),
% 0.41/0.62 inference(trivial_inequality_removal,[],[f457])).
% 0.41/0.62 thf(f457,plain,(
% 0.41/0.62 ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ($false = $true) | ~spl6_11),
% 0.41/0.62 inference(duplicate_literal_removal,[],[f456])).
% 0.41/0.62 thf(f456,plain,(
% 0.41/0.62 ($false = $true) | ($false = $true) | ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ~spl6_11),
% 0.41/0.62 inference(beta_eta_normalization,[],[f450])).
% 0.41/0.62 thf(f450,plain,(
% 0.41/0.62 ( ! [X8 : $i,X7 : $i] : ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ X7) = $true) | ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) ) | ~spl6_11),
% 0.41/0.62 inference(primitive_instantiation,[],[f350])).
% 0.41/0.62 thf(f350,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X7 : $i] : (($true = (X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X7)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) ) | ~spl6_11),
% 0.41/0.62 inference(avatar_component_clause,[],[f349])).
% 0.41/0.62 thf(f349,plain,(
% 0.41/0.62 spl6_11 <=> ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8,X7] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ($true = (X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X7)) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)))),
% 0.41/0.62 introduced(avatar_definition,[new_symbols(naming,[spl6_11])])).
% 0.41/0.62 thf(f85,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) != (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) ) | ~spl6_2),
% 0.41/0.62 inference(avatar_component_clause,[],[f84])).
% 0.41/0.62 thf(f84,plain,(
% 0.41/0.62 spl6_2 <=> ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8] : (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) != (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true))),
% 0.41/0.62 introduced(avatar_definition,[new_symbols(naming,[spl6_2])])).
% 0.41/0.62 thf(f498,plain,(
% 0.41/0.62 ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ~spl6_14),
% 0.41/0.62 inference(trivial_inequality_removal,[],[f497])).
% 0.41/0.62 thf(f497,plain,(
% 0.41/0.62 ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ($false = $true) | ~spl6_14),
% 0.41/0.62 inference(duplicate_literal_removal,[],[f496])).
% 0.41/0.62 thf(f496,plain,(
% 0.41/0.62 ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ($false = $true) | ($false = $true) | ~spl6_14),
% 0.41/0.62 inference(beta_eta_normalization,[],[f480])).
% 0.41/0.62 thf(f480,plain,(
% 0.41/0.62 ( ! [X8 : $i,X6 : $i] : (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ X6)) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) ) | ~spl6_14),
% 0.41/0.62 inference(primitive_instantiation,[],[f362])).
% 0.41/0.62 thf(f362,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X6 : $i] : (((X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X6) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) ) | ~spl6_14),
% 0.41/0.62 inference(avatar_component_clause,[],[f361])).
% 0.41/0.62 thf(f361,plain,(
% 0.41/0.62 spl6_14 <=> ! [X6,X0 : ($i > $o) > ($i > $o) > $i > $o,X8] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X6) = $true) | ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)))),
% 0.41/0.62 introduced(avatar_definition,[new_symbols(naming,[spl6_14])])).
% 0.41/0.62 thf(f367,plain,(
% 0.41/0.62 ~spl6_1),
% 0.41/0.62 inference(avatar_contradiction_clause,[],[f366])).
% 0.41/0.62 thf(f366,plain,(
% 0.41/0.62 $false | ~spl6_1),
% 0.41/0.62 inference(trivial_inequality_removal,[],[f365])).
% 0.41/0.62 thf(f365,plain,(
% 0.41/0.62 ($false = $true) | ~spl6_1),
% 0.41/0.62 inference(beta_eta_normalization,[],[f364])).
% 0.41/0.62 thf(f364,plain,(
% 0.41/0.62 ( ! [X1 : $i] : ((((^[Y0 : $i]: ($false)) @ X1) = ((^[Y0 : $i]: ($true)) @ X1))) ) | ~spl6_1),
% 0.41/0.62 inference(argument_congruence,[],[f82])).
% 0.41/0.62 thf(f82,plain,(
% 0.41/0.62 ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ~spl6_1),
% 0.41/0.62 inference(avatar_component_clause,[],[f80])).
% 0.41/0.62 thf(f80,plain,(
% 0.41/0.62 spl6_1 <=> ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 0.41/0.62 introduced(avatar_definition,[new_symbols(naming,[spl6_1])])).
% 0.41/0.62 thf(f363,plain,(
% 0.41/0.62 spl6_14 | spl6_1),
% 0.41/0.62 inference(avatar_split_clause,[],[f274,f80,f361])).
% 0.41/0.62 thf(f274,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X6 : $i] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) | ((X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X6) = $true) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) )),
% 0.41/0.62 inference(equality_proxy_clausification,[],[f273])).
% 0.41/0.62 thf(f273,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X6 : $i] : (((X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X6) = $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) )),
% 0.41/0.62 inference(equality_proxy_clausification,[],[f272])).
% 0.41/0.62 thf(f272,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X6 : $i] : (((X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X6) = $true) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) = $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) )),
% 0.41/0.62 inference(trivial_inequality_removal,[],[f271])).
% 0.41/0.62 thf(f271,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X6 : $i] : (((X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X6) = $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ($true != $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) = $true)) )),
% 0.41/0.62 inference(boolean_simplification,[],[f270])).
% 0.41/0.62 thf(f270,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X6 : $i] : (((X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X6) = $true) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) != $true)) )),
% 0.41/0.62 inference(beta_eta_normalization,[],[f252])).
% 0.41/0.62 thf(f252,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X6 : $i] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X6) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) != $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X6) = $true)) )),
% 0.41/0.62 inference(primitive_instantiation,[],[f49])).
% 0.41/0.62 thf(f49,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X6 : $i] : (((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) | ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6) = $true) | ((X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) )),
% 0.41/0.62 inference(boolean_simplification,[],[f48])).
% 0.41/0.62 thf(f48,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X6 : $i] : (((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6) = $true) | ((X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6) = $true) | ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) | ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) )),
% 0.41/0.62 inference(boolean_simplification,[],[f47])).
% 0.41/0.62 thf(f47,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X6 : $i] : (((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) | ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6) = $true) | ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6) = $true) | ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) )),
% 0.41/0.62 inference(boolean_simplification,[],[f46])).
% 0.41/0.62 thf(f46,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X6 : $i] : (((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X8) = $true) | ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) | ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6) = $true) | ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6) = $true)) )),
% 0.41/0.62 inference(boolean_simplification,[],[f16])).
% 0.41/0.62 thf(f16,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X6 : $i] : (((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) | ((X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6) = $true) | ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X8) = $true) | ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X8) = $true) | ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6) = $true)) )),
% 0.41/0.62 inference(cnf_transformation,[],[f13])).
% 0.41/0.62 thf(f13,plain,(
% 0.41/0.62 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (((((X0 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)) != $true) & ((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)) != $true)) & ! [X6] : (((X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6) = $true) | ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6) = $true)) & ! [X7] : (($true = (X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7)) | ((X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7) = $true))) | ! [X8] : (((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X8) = $true) | ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X8) = $true)) | (($true != (X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) & ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true)))),
% 0.41/0.62 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f9,f12,f11,f10])).
% 0.41/0.62 thf(f10,plain,(
% 0.41/0.62 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X2 : $i > $o,X3 : $i > $o,X4 : $i > $o] : (? [X5] : (((X0 @ X3 @ X4 @ X5) != $true) & ((X1 @ X3 @ X4 @ X5) != $true)) & ! [X6] : (((X1 @ X3 @ X2 @ X6) = $true) | ($true = (X0 @ X3 @ X2 @ X6))) & ! [X7] : (((X1 @ X2 @ X4 @ X7) = $true) | ((X0 @ X2 @ X4 @ X7) = $true))) => (? [X5] : (((X0 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X5) != $true) & ((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X5) != $true)) & ! [X6] : (((X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6) = $true) | ((X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6) = $true)) & ! [X7] : (($true = (X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7)) | ((X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7) = $true))))),
% 0.41/0.62 introduced(choice_axiom,[])).
% 0.41/0.62 thf(f11,plain,(
% 0.41/0.62 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X5] : (((X0 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X5) != $true) & ((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X5) != $true)) => (((X0 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)) != $true) & ((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)) != $true)))),
% 0.41/0.62 introduced(choice_axiom,[])).
% 0.41/0.62 thf(f12,plain,(
% 0.41/0.62 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X9 : $i > $o,X10] : (((X0 @ X9 @ X9 @ X10) != $true) & ((X1 @ X9 @ X9 @ X10) != $true)) => (($true != (X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) & ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true)))),
% 0.41/0.62 introduced(choice_axiom,[])).
% 0.41/0.62 thf(f9,plain,(
% 0.41/0.62 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X2 : $i > $o,X3 : $i > $o,X4 : $i > $o] : (? [X5] : (((X0 @ X3 @ X4 @ X5) != $true) & ((X1 @ X3 @ X4 @ X5) != $true)) & ! [X6] : (((X1 @ X3 @ X2 @ X6) = $true) | ($true = (X0 @ X3 @ X2 @ X6))) & ! [X7] : (((X1 @ X2 @ X4 @ X7) = $true) | ((X0 @ X2 @ X4 @ X7) = $true))) | ! [X8] : (((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X8) = $true) | ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X8) = $true)) | ? [X9 : $i > $o,X10] : (((X0 @ X9 @ X9 @ X10) != $true) & ((X1 @ X9 @ X9 @ X10) != $true)))),
% 0.41/0.62 inference(rectify,[],[f8])).
% 0.41/0.62 thf(f8,plain,(
% 0.41/0.62 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X3 : $i > $o,X5 : $i > $o,X4 : $i > $o] : (? [X8] : (((X0 @ X5 @ X4 @ X8) != $true) & ((X1 @ X5 @ X4 @ X8) != $true)) & ! [X7] : (((X1 @ X5 @ X3 @ X7) = $true) | ((X0 @ X5 @ X3 @ X7) = $true)) & ! [X6] : (((X1 @ X3 @ X4 @ X6) = $true) | ((X0 @ X3 @ X4 @ X6) = $true))) | ! [X2] : (((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2) = $true) | ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2) = $true)) | ? [X9 : $i > $o,X10] : (((X0 @ X9 @ X9 @ X10) != $true) & ((X1 @ X9 @ X9 @ X10) != $true)))),
% 0.41/0.62 inference(flattening,[],[f7])).
% 0.41/0.62 thf(f7,plain,(
% 0.41/0.62 ! [X1 : ($i > $o) > ($i > $o) > $i > $o,X0 : ($i > $o) > ($i > $o) > $i > $o] : (? [X9 : $i > $o,X10] : (((X0 @ X9 @ X9 @ X10) != $true) & ((X1 @ X9 @ X9 @ X10) != $true)) | ? [X3 : $i > $o,X4 : $i > $o,X5 : $i > $o] : (? [X8] : (((X0 @ X5 @ X4 @ X8) != $true) & ((X1 @ X5 @ X4 @ X8) != $true)) & (! [X7] : (((X1 @ X5 @ X3 @ X7) = $true) | ((X0 @ X5 @ X3 @ X7) = $true)) & ! [X6] : (((X1 @ X3 @ X4 @ X6) = $true) | ((X0 @ X3 @ X4 @ X6) = $true)))) | ! [X2] : (((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2) = $true) | ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2) = $true)))),
% 0.41/0.62 inference(ennf_transformation,[],[f6])).
% 0.41/0.62 thf(f6,plain,(
% 0.41/0.62 ~? [X1 : ($i > $o) > ($i > $o) > $i > $o,X0 : ($i > $o) > ($i > $o) > $i > $o] : (! [X9 : $i > $o,X10] : (((X0 @ X9 @ X9 @ X10) = $true) | ((X1 @ X9 @ X9 @ X10) = $true)) & ! [X3 : $i > $o,X4 : $i > $o,X5 : $i > $o] : ((! [X7] : (((X1 @ X5 @ X3 @ X7) = $true) | ((X0 @ X5 @ X3 @ X7) = $true)) & ! [X6] : (((X1 @ X3 @ X4 @ X6) = $true) | ((X0 @ X3 @ X4 @ X6) = $true))) => ! [X8] : (((X1 @ X5 @ X4 @ X8) = $true) | ((X0 @ X5 @ X4 @ X8) = $true))) & ~! [X2] : (((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2) = $true) | ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2) = $true)))),
% 0.41/0.62 inference(rectify,[],[f5])).
% 0.41/0.62 thf(f5,plain,(
% 0.41/0.62 ~? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (~! [X2] : (((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2) = $true) | ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2) = $true)) & ! [X7 : $i > $o,X8 : $i > $o,X9 : $i > $o] : ((! [X10] : (((X1 @ X7 @ X8 @ X10) = $true) | ((X0 @ X7 @ X8 @ X10) = $true)) & ! [X11] : (((X0 @ X9 @ X7 @ X11) = $true) | ((X1 @ X9 @ X7 @ X11) = $true))) => ! [X12] : (((X1 @ X9 @ X8 @ X12) = $true) | ((X0 @ X9 @ X8 @ X12) = $true))) & ! [X13 : $i > $o,X14] : (((X1 @ X13 @ X13 @ X14) = $true) | ((X0 @ X13 @ X13 @ X14) = $true)))),
% 0.41/0.62 inference(fool_elimination,[],[f4])).
% 0.41/0.62 thf(f4,plain,(
% 0.41/0.62 ~? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (~! [X2] : ((X1 @ (^[X3 : $i] : (~p | p)) @ (^[X4 : $i] : (~p & p)) @ X2) | (X0 @ (^[X5 : $i] : (p | ~p)) @ (^[X6 : $i] : (~p & p)) @ X2)) & ! [X7 : $i > $o,X8 : $i > $o,X9 : $i > $o] : ((! [X10] : ((X1 @ X7 @ X8 @ X10) | (X0 @ X7 @ X8 @ X10)) & ! [X11] : ((X0 @ X9 @ X7 @ X11) | (X1 @ X9 @ X7 @ X11))) => ! [X12] : ((X1 @ X9 @ X8 @ X12) | (X0 @ X9 @ X8 @ X12))) & ! [X13 : $i > $o,X14] : ((X1 @ X13 @ X13 @ X14) | (X0 @ X13 @ X13 @ X14)))),
% 0.41/0.62 inference(rectify,[],[f2])).
% 0.41/0.62 thf(f2,negated_conjecture,(
% 0.41/0.62 ~? [X1 : ($i > $o) > ($i > $o) > $i > $o,X0 : ($i > $o) > ($i > $o) > $i > $o] : (~! [X3] : ((X0 @ (^[X2 : $i] : (~p | p)) @ (^[X2 : $i] : (~p & p)) @ X3) | (X1 @ (^[X2 : $i] : (p | ~p)) @ (^[X2 : $i] : (~p & p)) @ X3)) & ! [X4 : $i > $o,X5 : $i > $o,X2 : $i > $o] : ((! [X3] : ((X0 @ X4 @ X5 @ X3) | (X1 @ X4 @ X5 @ X3)) & ! [X3] : ((X1 @ X2 @ X4 @ X3) | (X0 @ X2 @ X4 @ X3))) => ! [X3] : ((X0 @ X2 @ X5 @ X3) | (X1 @ X2 @ X5 @ X3))) & ! [X2 : $i > $o,X3] : ((X0 @ X2 @ X2 @ X3) | (X1 @ X2 @ X2 @ X3)))),
% 0.41/0.62 inference(negated_conjecture,[],[f1])).
% 0.41/0.62 thf(f1,conjecture,(
% 0.41/0.62 ? [X1 : ($i > $o) > ($i > $o) > $i > $o,X0 : ($i > $o) > ($i > $o) > $i > $o] : (~! [X3] : ((X0 @ (^[X2 : $i] : (~p | p)) @ (^[X2 : $i] : (~p & p)) @ X3) | (X1 @ (^[X2 : $i] : (p | ~p)) @ (^[X2 : $i] : (~p & p)) @ X3)) & ! [X4 : $i > $o,X5 : $i > $o,X2 : $i > $o] : ((! [X3] : ((X0 @ X4 @ X5 @ X3) | (X1 @ X4 @ X5 @ X3)) & ! [X3] : ((X1 @ X2 @ X4 @ X3) | (X0 @ X2 @ X4 @ X3))) => ! [X3] : ((X0 @ X2 @ X5 @ X3) | (X1 @ X2 @ X5 @ X3))) & ! [X2 : $i > $o,X3] : ((X0 @ X2 @ X2 @ X3) | (X1 @ X2 @ X2 @ X3)))),
% 0.41/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM120E_pme)).
% 0.41/0.62 thf(f351,plain,(
% 0.41/0.62 spl6_1 | spl6_11),
% 0.41/0.62 inference(avatar_split_clause,[],[f218,f349,f80])).
% 0.41/0.62 thf(f218,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X7 : $i] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ($true = (X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X7))) )),
% 0.41/0.62 inference(equality_proxy_clausification,[],[f217])).
% 0.41/0.62 thf(f217,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X7 : $i] : (($true = (X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X7)) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) )),
% 0.41/0.62 inference(equality_proxy_clausification,[],[f216])).
% 0.41/0.62 thf(f216,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X7 : $i] : ((((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) = $true) | ($true = (X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X7)) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) )),
% 0.41/0.62 inference(trivial_inequality_removal,[],[f215])).
% 0.41/0.62 thf(f215,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X7 : $i] : (($true != $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) = $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ($true = (X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X7))) )),
% 0.41/0.62 inference(boolean_simplification,[],[f214])).
% 0.41/0.62 thf(f214,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X7 : $i] : ((((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) != $true) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) = $true) | ($true = (X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X7)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true)) )),
% 0.41/0.62 inference(beta_eta_normalization,[],[f196])).
% 0.41/0.62 thf(f196,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X7 : $i] : ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) != $true) | ($true = (X0 @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X7)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X7) = $true)) )),
% 0.41/0.62 inference(primitive_instantiation,[],[f29])).
% 0.41/0.62 thf(f29,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X7 : $i] : (((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) | ($true = (X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7)) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) )),
% 0.41/0.62 inference(boolean_simplification,[],[f28])).
% 0.41/0.62 thf(f28,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X7 : $i] : (((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) | ($true = (X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7)) | ((X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7) = $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) )),
% 0.41/0.62 inference(boolean_simplification,[],[f27])).
% 0.41/0.62 thf(f27,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X7 : $i] : (((X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7) = $true) | ($true = (X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7)) | ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) | ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) )),
% 0.41/0.62 inference(boolean_simplification,[],[f26])).
% 0.41/0.62 thf(f26,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X7 : $i] : (((X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7) = $true) | ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X8) = $true) | ($true = (X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7)) | ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) | ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) )),
% 0.41/0.62 inference(boolean_simplification,[],[f14])).
% 0.41/0.62 thf(f14,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X7 : $i] : (((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) | ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X8) = $true) | ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X8) = $true) | ((X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7) = $true) | ($true = (X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7))) )),
% 0.41/0.62 inference(cnf_transformation,[],[f13])).
% 0.41/0.62 thf(f86,plain,(
% 0.41/0.62 spl6_1 | spl6_2),
% 0.41/0.62 inference(avatar_split_clause,[],[f76,f84,f80])).
% 0.41/0.62 thf(f76,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) != (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) )),
% 0.41/0.62 inference(equality_proxy_clausification,[],[f75])).
% 0.41/0.62 thf(f75,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (($true != ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) )),
% 0.41/0.62 inference(equality_proxy_clausification,[],[f74])).
% 0.41/0.62 thf(f74,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ($true != ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)))) )),
% 0.41/0.62 inference(trivial_inequality_removal,[],[f73])).
% 0.41/0.62 thf(f73,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ($true != ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) | ($true != $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true)) )),
% 0.41/0.62 inference(boolean_simplification,[],[f72])).
% 0.41/0.62 thf(f72,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : ((((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ($true != ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) | (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) != $true)) )),
% 0.41/0.62 inference(beta_eta_normalization,[],[f54])).
% 0.41/0.62 thf(f54,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) != $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) != $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) )),
% 0.41/0.62 inference(primitive_instantiation,[],[f37])).
% 0.41/0.62 thf(f37,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)) != $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) )),
% 0.41/0.62 inference(boolean_simplification,[],[f36])).
% 0.41/0.62 thf(f36,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)) != $true) | ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true)) )),
% 0.41/0.62 inference(boolean_simplification,[],[f35])).
% 0.41/0.62 thf(f35,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X8) = $true) | ((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)) != $true)) )),
% 0.41/0.62 inference(boolean_simplification,[],[f34])).
% 0.41/0.62 thf(f34,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) | ((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)) != $true) | ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X8) = $true)) )),
% 0.41/0.62 inference(boolean_simplification,[],[f18])).
% 0.41/0.62 thf(f18,plain,(
% 0.41/0.62 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)) != $true) | ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X8) = $true) | ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X8) = $true) | ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true)) )),
% 0.41/0.62 inference(cnf_transformation,[],[f13])).
% 0.41/0.62 % SZS output end Proof for theBenchmark
% 0.41/0.62 % (19132)------------------------------
% 0.41/0.62 % (19132)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.41/0.62 % (19132)Termination reason: Refutation
% 0.41/0.62
% 0.41/0.62 % (19132)Memory used [KB]: 5884
% 0.41/0.62 % (19132)Time elapsed: 0.040 s
% 0.41/0.62 % (19132)Instructions burned: 70 (million)
% 0.41/0.62 % (19132)------------------------------
% 0.41/0.62 % (19132)------------------------------
% 0.41/0.62 % (18992)Success in time 0.228 s
%------------------------------------------------------------------------------