TSTP Solution File: SEV100^5 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV100^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 04:11:59 EDT 2024
% Result : Theorem 0.23s 0.46s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEV100^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36 % Computer : n004.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun May 19 19:14:38 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a TH0_THM_NEQ_NAR problem
% 0.15/0.37 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.39 % (1535)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.40 % (1536)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)
% 0.15/0.40 % (1537)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)
% 0.15/0.40 % (1538)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.40 % (1539)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)
% 0.15/0.40 % (1540)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)
% 0.15/0.40 % (1541)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.40 % (1538)Instruction limit reached!
% 0.15/0.40 % (1538)------------------------------
% 0.15/0.40 % (1538)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (1538)Termination reason: Unknown
% 0.15/0.40 % (1538)Termination phase: Preprocessing 3
% 0.15/0.40 % (1539)Instruction limit reached!
% 0.15/0.40 % (1539)------------------------------
% 0.15/0.40 % (1539)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (1539)Termination reason: Unknown
% 0.15/0.40 % (1539)Termination phase: Property scanning
% 0.15/0.40
% 0.15/0.40 % (1539)Memory used [KB]: 895
% 0.15/0.40 % (1539)Time elapsed: 0.004 s
% 0.15/0.40 % (1539)Instructions burned: 2 (million)
% 0.15/0.40 % (1539)------------------------------
% 0.15/0.40 % (1539)------------------------------
% 0.15/0.40
% 0.15/0.40 % (1538)Memory used [KB]: 895
% 0.15/0.40 % (1538)Time elapsed: 0.004 s
% 0.15/0.40 % (1538)Instructions burned: 2 (million)
% 0.15/0.40 % (1538)------------------------------
% 0.15/0.40 % (1538)------------------------------
% 0.15/0.40 % (1543)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)
% 0.15/0.40 % (1536)Instruction limit reached!
% 0.15/0.40 % (1536)------------------------------
% 0.15/0.40 % (1536)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (1536)Termination reason: Unknown
% 0.15/0.40 % (1536)Termination phase: Saturation
% 0.15/0.40
% 0.15/0.40 % (1536)Memory used [KB]: 1023
% 0.15/0.40 % (1536)Time elapsed: 0.006 s
% 0.15/0.40 % (1536)Instructions burned: 4 (million)
% 0.15/0.40 % (1536)------------------------------
% 0.15/0.40 % (1536)------------------------------
% 0.15/0.40 % (1543)Instruction limit reached!
% 0.15/0.40 % (1543)------------------------------
% 0.15/0.40 % (1543)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (1543)Termination reason: Unknown
% 0.15/0.40 % (1543)Termination phase: Property scanning
% 0.15/0.40
% 0.15/0.40 % (1543)Memory used [KB]: 1023
% 0.15/0.40 % (1543)Time elapsed: 0.005 s
% 0.15/0.40 % (1543)Instructions burned: 3 (million)
% 0.15/0.40 % (1543)------------------------------
% 0.15/0.40 % (1543)------------------------------
% 0.15/0.41 % (1537)Refutation not found, incomplete strategy
% 0.15/0.41 % (1537)------------------------------
% 0.15/0.41 % (1537)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.41 % (1537)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.41
% 0.15/0.41
% 0.15/0.41 % (1537)Memory used [KB]: 5500
% 0.15/0.41 % (1537)Time elapsed: 0.011 s
% 0.15/0.41 % (1537)Instructions burned: 9 (million)
% 0.15/0.41 % (1537)------------------------------
% 0.15/0.41 % (1537)------------------------------
% 0.23/0.41 % (1541)Instruction limit reached!
% 0.23/0.41 % (1541)------------------------------
% 0.23/0.41 % (1541)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.41 % (1541)Termination reason: Unknown
% 0.23/0.41 % (1541)Termination phase: Saturation
% 0.23/0.41
% 0.23/0.41 % (1541)Memory used [KB]: 5628
% 0.23/0.41 % (1541)Time elapsed: 0.019 s
% 0.23/0.41 % (1541)Instructions burned: 18 (million)
% 0.23/0.41 % (1541)------------------------------
% 0.23/0.41 % (1541)------------------------------
% 0.23/0.42 % (1545)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)
% 0.23/0.42 % (1544)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)
% 0.23/0.43 % (1546)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)
% 0.23/0.43 % (1547)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)
% 0.23/0.43 % (1546)Instruction limit reached!
% 0.23/0.43 % (1546)------------------------------
% 0.23/0.43 % (1546)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.43 % (1546)Termination reason: Unknown
% 0.23/0.43 % (1546)Termination phase: Property scanning
% 0.23/0.43
% 0.23/0.43 % (1546)Memory used [KB]: 1023
% 0.23/0.43 % (1546)Time elapsed: 0.005 s
% 0.23/0.43 % (1546)Instructions burned: 3 (million)
% 0.23/0.43 % (1546)------------------------------
% 0.23/0.43 % (1546)------------------------------
% 0.23/0.43 % (1545)Instruction limit reached!
% 0.23/0.43 % (1545)------------------------------
% 0.23/0.43 % (1545)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.43 % (1545)Termination reason: Unknown
% 0.23/0.43 % (1545)Termination phase: Saturation
% 0.23/0.43
% 0.23/0.43 % (1545)Memory used [KB]: 5628
% 0.23/0.43 % (1545)Time elapsed: 0.012 s
% 0.23/0.43 % (1545)Instructions burned: 15 (million)
% 0.23/0.43 % (1545)------------------------------
% 0.23/0.43 % (1545)------------------------------
% 0.23/0.43 % (1548)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.23/0.44 % (1549)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.23/0.44 % (1548)Instruction limit reached!
% 0.23/0.44 % (1548)------------------------------
% 0.23/0.44 % (1548)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.44 % (1548)Termination reason: Unknown
% 0.23/0.44 % (1548)Termination phase: Saturation
% 0.23/0.44
% 0.23/0.44 % (1548)Memory used [KB]: 1023
% 0.23/0.44 % (1548)Time elapsed: 0.009 s
% 0.23/0.44 % (1548)Instructions burned: 7 (million)
% 0.23/0.44 % (1548)------------------------------
% 0.23/0.44 % (1548)------------------------------
% 0.23/0.45 % (1551)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)
% 0.23/0.45 % (1549)Instruction limit reached!
% 0.23/0.45 % (1549)------------------------------
% 0.23/0.45 % (1549)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.45 % (1549)Termination reason: Unknown
% 0.23/0.45 % (1549)Termination phase: Saturation
% 0.23/0.45
% 0.23/0.45 % (1549)Memory used [KB]: 5628
% 0.23/0.45 % (1549)Time elapsed: 0.012 s
% 0.23/0.45 % (1549)Instructions burned: 17 (million)
% 0.23/0.45 % (1549)------------------------------
% 0.23/0.45 % (1549)------------------------------
% 0.23/0.45 % (1540)First to succeed.
% 0.23/0.45 % (1551)Instruction limit reached!
% 0.23/0.45 % (1551)------------------------------
% 0.23/0.45 % (1551)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.45 % (1551)Termination reason: Unknown
% 0.23/0.45 % (1551)Termination phase: Property scanning
% 0.23/0.45
% 0.23/0.45 % (1551)Memory used [KB]: 1023
% 0.23/0.45 % (1551)Time elapsed: 0.004 s
% 0.23/0.45 % (1551)Instructions burned: 4 (million)
% 0.23/0.45 % (1551)------------------------------
% 0.23/0.45 % (1551)------------------------------
% 0.23/0.45 % (1544)Instruction limit reached!
% 0.23/0.45 % (1544)------------------------------
% 0.23/0.45 % (1544)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.45 % (1544)Termination reason: Unknown
% 0.23/0.45 % (1544)Termination phase: Saturation
% 0.23/0.45
% 0.23/0.45 % (1544)Memory used [KB]: 5884
% 0.23/0.45 % (1544)Time elapsed: 0.030 s
% 0.23/0.45 % (1544)Instructions burned: 38 (million)
% 0.23/0.45 % (1544)------------------------------
% 0.23/0.45 % (1544)------------------------------
% 0.23/0.45 % (1550)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)
% 0.23/0.45 % (1550)Instruction limit reached!
% 0.23/0.45 % (1550)------------------------------
% 0.23/0.45 % (1550)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.45 % (1550)Termination reason: Unknown
% 0.23/0.45 % (1550)Termination phase: Property scanning
% 0.23/0.45
% 0.23/0.45 % (1550)Memory used [KB]: 1023
% 0.23/0.46 % (1550)Time elapsed: 0.004 s
% 0.23/0.46 % (1550)Instructions burned: 4 (million)
% 0.23/0.46 % (1550)------------------------------
% 0.23/0.46 % (1550)------------------------------
% 0.23/0.46 % (1540)Refutation found. Thanks to Tanya!
% 0.23/0.46 % SZS status Theorem for theBenchmark
% 0.23/0.46 % SZS output start Proof for theBenchmark
% 0.23/0.46 thf(func_def_8, type, sK0: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 0.23/0.46 thf(func_def_9, type, sK1: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 0.23/0.46 thf(func_def_10, type, sK2: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 0.23/0.46 thf(func_def_11, type, sK3: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i).
% 0.23/0.46 thf(func_def_12, type, sK4: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 0.23/0.46 thf(func_def_13, type, sK5: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i).
% 0.23/0.46 thf(func_def_15, type, ph7: !>[X0: $tType]:(X0)).
% 0.23/0.46 thf(func_def_21, type, sK9: (($i > $o) > ($i > $o) > $i > $o) > $i).
% 0.23/0.46 thf(func_def_22, type, sK10: (($i > $o) > ($i > $o) > $i > $o) > $i).
% 0.23/0.46 thf(f452,plain,(
% 0.23/0.46 $false),
% 0.23/0.46 inference(avatar_sat_refutation,[],[f85,f139,f448])).
% 0.23/0.46 thf(f448,plain,(
% 0.23/0.46 ~spl6_1 | spl6_2),
% 0.23/0.46 inference(avatar_contradiction_clause,[],[f447])).
% 0.23/0.46 thf(f447,plain,(
% 0.23/0.46 $false | (~spl6_1 | spl6_2)),
% 0.23/0.46 inference(trivial_inequality_removal,[],[f446])).
% 0.23/0.46 thf(f446,plain,(
% 0.23/0.46 ($true = $false) | (~spl6_1 | spl6_2)),
% 0.23/0.46 inference(beta_eta_normalization,[],[f445])).
% 0.23/0.46 thf(f445,plain,(
% 0.23/0.46 ( ! [X0 : $i] : (($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X0))) ) | (~spl6_1 | spl6_2)),
% 0.23/0.46 inference(trivial_inequality_removal,[],[f439])).
% 0.23/0.46 thf(f439,plain,(
% 0.23/0.46 ( ! [X0 : $i] : (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) != (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X0))) ) | (~spl6_1 | spl6_2)),
% 0.23/0.46 inference(superposition,[],[f80,f437])).
% 0.23/0.46 thf(f437,plain,(
% 0.23/0.46 ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_2),
% 0.23/0.46 inference(forward_demodulation,[],[f432,f371])).
% 0.23/0.46 thf(f371,plain,(
% 0.23/0.46 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_2),
% 0.23/0.46 inference(trivial_inequality_removal,[],[f370])).
% 0.23/0.46 thf(f370,plain,(
% 0.23/0.46 ($true = $false) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_2),
% 0.23/0.46 inference(duplicate_literal_removal,[],[f369])).
% 0.23/0.46 thf(f369,plain,(
% 0.23/0.46 ($true = $false) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ($true = $false) | spl6_2),
% 0.23/0.46 inference(beta_eta_normalization,[],[f354])).
% 0.23/0.46 thf(f354,plain,(
% 0.23/0.46 ( ! [X10 : $i,X6 : $i] : ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X6)) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) ) | spl6_2),
% 0.23/0.46 inference(primitive_instantiation,[],[f224])).
% 0.23/0.46 thf(f224,plain,(
% 0.23/0.46 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (((X1 @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X6) = $true) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) ) | spl6_2),
% 0.23/0.46 inference(subsumption_resolution,[],[f208,f83])).
% 0.23/0.46 thf(f83,plain,(
% 0.23/0.46 ((^[Y0 : $i]: ($true)) != (^[Y0 : $i]: ($false))) | spl6_2),
% 0.23/0.46 inference(avatar_component_clause,[],[f82])).
% 0.23/0.46 thf(f82,plain,(
% 0.23/0.46 spl6_2 <=> ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 0.23/0.46 introduced(avatar_definition,[new_symbols(naming,[spl6_2])])).
% 0.23/0.46 thf(f208,plain,(
% 0.23/0.46 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ((X1 @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X6) = $true) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) )),
% 0.23/0.46 inference(equality_proxy_clausification,[],[f207])).
% 0.23/0.46 thf(f207,plain,(
% 0.23/0.46 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ((X1 @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X6) = $true) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))))) )),
% 0.23/0.46 inference(equality_proxy_clausification,[],[f206])).
% 0.23/0.46 thf(f206,plain,(
% 0.23/0.46 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (((X1 @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X6) = $true) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | (((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) = $true) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))))) )),
% 0.23/0.46 inference(trivial_inequality_removal,[],[f205])).
% 0.23/0.46 thf(f205,plain,(
% 0.23/0.46 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (($true != $true) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | (((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) = $true) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ((X1 @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X6) = $true)) )),
% 0.23/0.46 inference(boolean_simplification,[],[f204])).
% 0.23/0.46 thf(f204,plain,(
% 0.23/0.46 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (((X1 @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X6) = $true) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | (((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) = $true) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ($true != ((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))))) )),
% 0.23/0.46 inference(beta_eta_normalization,[],[f199])).
% 0.23/0.46 thf(f199,plain,(
% 0.23/0.46 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (((X1 @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X6) = $true) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X6) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))))) )),
% 0.23/0.46 inference(primitive_instantiation,[],[f44])).
% 0.23/0.46 thf(f44,plain,(
% 0.23/0.46 ( ! [X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (($true != (X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) | ($true = (X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | ((X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6) = $true) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) )),
% 0.23/0.46 inference(boolean_simplification,[],[f43])).
% 0.23/0.46 thf(f43,plain,(
% 0.23/0.46 ( ! [X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (($true = (X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6)) | ($true = (X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X10)) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ($true != (X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) | ((X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6) = $true)) )),
% 0.23/0.46 inference(boolean_simplification,[],[f42])).
% 0.23/0.46 thf(f42,plain,(
% 0.23/0.46 ( ! [X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10) = $true) | ($true = (X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6)) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ((X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6) = $true) | ($true != (X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) )),
% 0.23/0.46 inference(boolean_simplification,[],[f41])).
% 0.23/0.46 thf(f41,plain,(
% 0.23/0.46 ( ! [X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (($true = (X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6)) | ($true = (X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X10)) | ((X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6) = $true) | ($true != (X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) | ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10) = $true)) )),
% 0.23/0.46 inference(boolean_simplification,[],[f16])).
% 0.23/0.46 thf(f16,plain,(
% 0.23/0.46 ( ! [X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X6 : $i] : (((X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6) = $true) | ($true != (X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) | ($true = (X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10)) | ($true = (X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6)) | ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10) = $true)) )),
% 0.23/0.46 inference(cnf_transformation,[],[f12])).
% 0.23/0.46 thf(f12,plain,(
% 0.23/0.46 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (((((X1 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0)) != $true) & ($true != (X0 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0)))) & ! [X6] : (($true = (X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6)) | ((X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6) = $true)) & ! [X7] : (($true = (X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7)) | ($true = (X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7)))) | (($true != (X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) & ($true != (X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | ! [X10] : (((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10) = $true) | ($true = (X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10))))),
% 0.23/0.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f11,f10,f9])).
% 0.23/0.46 thf(f9,plain,(
% 0.23/0.46 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X2 : $i > $o,X3 : $i > $o,X4 : $i > $o] : (? [X5] : (((X1 @ X2 @ X3 @ X5) != $true) & ((X0 @ X2 @ X3 @ X5) != $true)) & ! [X6] : (($true = (X1 @ X2 @ X4 @ X6)) | ($true = (X0 @ X2 @ X4 @ X6))) & ! [X7] : (($true = (X1 @ X4 @ X3 @ X7)) | ((X0 @ X4 @ X3 @ X7) = $true))) => (? [X5] : (($true != (X1 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X5)) & ($true != (X0 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X5))) & ! [X6] : (($true = (X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6)) | ((X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6) = $true)) & ! [X7] : (($true = (X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7)) | ($true = (X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7)))))),
% 0.23/0.46 introduced(choice_axiom,[])).
% 0.23/0.46 thf(f10,plain,(
% 0.23/0.46 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X5] : (($true != (X1 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X5)) & ($true != (X0 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X5))) => (((X1 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0)) != $true) & ($true != (X0 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0)))))),
% 0.23/0.46 introduced(choice_axiom,[])).
% 0.23/0.46 thf(f11,plain,(
% 0.23/0.46 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X8 : $i > $o,X9] : (($true != (X0 @ X8 @ X8 @ X9)) & ($true != (X1 @ X8 @ X8 @ X9))) => (($true != (X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) & ($true != (X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))))),
% 0.23/0.46 introduced(choice_axiom,[])).
% 0.23/0.46 thf(f8,plain,(
% 0.23/0.46 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X2 : $i > $o,X3 : $i > $o,X4 : $i > $o] : (? [X5] : (((X1 @ X2 @ X3 @ X5) != $true) & ((X0 @ X2 @ X3 @ X5) != $true)) & ! [X6] : (($true = (X1 @ X2 @ X4 @ X6)) | ($true = (X0 @ X2 @ X4 @ X6))) & ! [X7] : (($true = (X1 @ X4 @ X3 @ X7)) | ((X0 @ X4 @ X3 @ X7) = $true))) | ? [X8 : $i > $o,X9] : (($true != (X0 @ X8 @ X8 @ X9)) & ($true != (X1 @ X8 @ X8 @ X9))) | ! [X10] : (((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10) = $true) | ($true = (X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10))))),
% 0.23/0.46 inference(rectify,[],[f7])).
% 0.23/0.46 thf(f7,plain,(
% 0.23/0.46 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X4 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (? [X7] : (($true != (X1 @ X4 @ X2 @ X7)) & ($true != (X0 @ X4 @ X2 @ X7))) & ! [X5] : (($true = (X1 @ X4 @ X3 @ X5)) | ($true = (X0 @ X4 @ X3 @ X5))) & ! [X6] : (($true = (X1 @ X3 @ X2 @ X6)) | ((X0 @ X3 @ X2 @ X6) = $true))) | ? [X8 : $i > $o,X9] : (($true != (X0 @ X8 @ X8 @ X9)) & ($true != (X1 @ X8 @ X8 @ X9))) | ! [X10] : (((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10) = $true) | ($true = (X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10))))),
% 0.23/0.46 inference(flattening,[],[f6])).
% 0.23/0.46 thf(f6,plain,(
% 0.23/0.46 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X8 : $i > $o,X9] : (($true != (X0 @ X8 @ X8 @ X9)) & ($true != (X1 @ X8 @ X8 @ X9))) | ! [X10] : (((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10) = $true) | ($true = (X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10))) | ? [X4 : $i > $o,X3 : $i > $o,X2 : $i > $o] : (? [X7] : (($true != (X1 @ X4 @ X2 @ X7)) & ($true != (X0 @ X4 @ X2 @ X7))) & (! [X6] : (($true = (X1 @ X3 @ X2 @ X6)) | ((X0 @ X3 @ X2 @ X6) = $true)) & ! [X5] : (($true = (X1 @ X4 @ X3 @ X5)) | ($true = (X0 @ X4 @ X3 @ X5))))))),
% 0.23/0.46 inference(ennf_transformation,[],[f5])).
% 0.23/0.46 thf(f5,plain,(
% 0.23/0.46 ~? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X9,X8 : $i > $o] : (($true = (X0 @ X8 @ X8 @ X9)) | ($true = (X1 @ X8 @ X8 @ X9))) & ~! [X10] : (((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10) = $true) | ($true = (X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10))) & ! [X4 : $i > $o,X3 : $i > $o,X2 : $i > $o] : ((! [X6] : (($true = (X1 @ X3 @ X2 @ X6)) | ((X0 @ X3 @ X2 @ X6) = $true)) & ! [X5] : (($true = (X1 @ X4 @ X3 @ X5)) | ($true = (X0 @ X4 @ X3 @ X5)))) => ! [X7] : (($true = (X1 @ X4 @ X2 @ X7)) | ($true = (X0 @ X4 @ X2 @ X7)))))),
% 0.23/0.46 inference(fool_elimination,[],[f4])).
% 0.23/0.46 thf(f4,plain,(
% 0.23/0.46 ~? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X2 : $i > $o,X3 : $i > $o,X4 : $i > $o] : ((! [X5] : ((X1 @ X4 @ X3 @ X5) | (X0 @ X4 @ X3 @ X5)) & ! [X6] : ((X0 @ X3 @ X2 @ X6) | (X1 @ X3 @ X2 @ X6))) => ! [X7] : ((X0 @ X4 @ X2 @ X7) | (X1 @ X4 @ X2 @ X7))) & ! [X8 : $i > $o,X9] : ((X0 @ X8 @ X8 @ X9) | (X1 @ X8 @ X8 @ X9)) & ~! [X10] : ((X1 @ (^[X11 : $i] : (~p | p)) @ (^[X12 : $i] : (~p & p)) @ X10) | (X0 @ (^[X13 : $i] : (~p | p)) @ (^[X14 : $i] : (~p & p)) @ X10)))),
% 0.23/0.46 inference(rectify,[],[f2])).
% 0.23/0.46 thf(f2,negated_conjecture,(
% 0.23/0.46 ~? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X4 : $i > $o,X3 : $i > $o,X2 : $i > $o] : ((! [X5] : ((X1 @ X2 @ X3 @ X5) | (X0 @ X2 @ X3 @ X5)) & ! [X5] : ((X0 @ X3 @ X4 @ X5) | (X1 @ X3 @ X4 @ X5))) => ! [X5] : ((X0 @ X2 @ X4 @ X5) | (X1 @ X2 @ X4 @ X5))) & ! [X2 : $i > $o,X5] : ((X0 @ X2 @ X2 @ X5) | (X1 @ X2 @ X2 @ X5)) & ~! [X5] : ((X1 @ (^[X2 : $i] : (~p | p)) @ (^[X2 : $i] : (~p & p)) @ X5) | (X0 @ (^[X2 : $i] : (~p | p)) @ (^[X2 : $i] : (~p & p)) @ X5)))),
% 0.23/0.46 inference(negated_conjecture,[],[f1])).
% 0.23/0.46 thf(f1,conjecture,(
% 0.23/0.46 ? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X4 : $i > $o,X3 : $i > $o,X2 : $i > $o] : ((! [X5] : ((X1 @ X2 @ X3 @ X5) | (X0 @ X2 @ X3 @ X5)) & ! [X5] : ((X0 @ X3 @ X4 @ X5) | (X1 @ X3 @ X4 @ X5))) => ! [X5] : ((X0 @ X2 @ X4 @ X5) | (X1 @ X2 @ X4 @ X5))) & ! [X2 : $i > $o,X5] : ((X0 @ X2 @ X2 @ X5) | (X1 @ X2 @ X2 @ X5)) & ~! [X5] : ((X1 @ (^[X2 : $i] : (~p | p)) @ (^[X2 : $i] : (~p & p)) @ X5) | (X0 @ (^[X2 : $i] : (~p | p)) @ (^[X2 : $i] : (~p & p)) @ X5)))),
% 0.23/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM120F_pme)).
% 0.23/0.46 thf(f432,plain,(
% 0.23/0.46 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_2),
% 0.23/0.46 inference(trivial_inequality_removal,[],[f431])).
% 0.23/0.46 thf(f431,plain,(
% 0.23/0.46 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ($true = $false) | spl6_2),
% 0.23/0.46 inference(duplicate_literal_removal,[],[f430])).
% 0.23/0.46 thf(f430,plain,(
% 0.23/0.46 ($true = $false) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ($true = $false) | spl6_2),
% 0.23/0.46 inference(beta_eta_normalization,[],[f414])).
% 0.23/0.46 thf(f414,plain,(
% 0.23/0.46 ( ! [X10 : $i,X7 : $i] : ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X7) = $true) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) ) | spl6_2),
% 0.23/0.46 inference(primitive_instantiation,[],[f279])).
% 0.23/0.46 thf(f279,plain,(
% 0.23/0.46 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : (($true = (X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X7)) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) ) | spl6_2),
% 0.23/0.46 inference(subsumption_resolution,[],[f267,f83])).
% 0.23/0.46 thf(f267,plain,(
% 0.23/0.46 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : (($true = (X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X7)) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) )),
% 0.23/0.46 inference(equality_proxy_clausification,[],[f266])).
% 0.23/0.46 thf(f266,plain,(
% 0.23/0.46 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ($true = (X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X7)) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ($true = ((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))))) )),
% 0.23/0.46 inference(equality_proxy_clausification,[],[f265])).
% 0.23/0.46 thf(f265,plain,(
% 0.23/0.46 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : (($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ($true = ((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ($true = (X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X7))) )),
% 0.23/0.46 inference(trivial_inequality_removal,[],[f264])).
% 0.23/0.46 thf(f264,plain,(
% 0.23/0.46 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : (($true = (X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X7)) | ($true != $true) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ($true = ((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))))) )),
% 0.23/0.46 inference(boolean_simplification,[],[f263])).
% 0.23/0.46 thf(f263,plain,(
% 0.23/0.46 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : (($true = (X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X7)) | ($true = ((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ($true != ((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))))) )),
% 0.23/0.46 inference(beta_eta_normalization,[],[f254])).
% 0.23/0.46 thf(f254,plain,(
% 0.23/0.46 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : (($true = (X1 @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X7)) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X7)) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))))) )),
% 0.23/0.46 inference(primitive_instantiation,[],[f52])).
% 0.23/0.46 thf(f52,plain,(
% 0.23/0.46 ( ! [X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : (($true != (X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) | ($true = (X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7)) | ($true = (X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7)) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true)) )),
% 0.23/0.46 inference(boolean_simplification,[],[f51])).
% 0.23/0.46 thf(f51,plain,(
% 0.23/0.46 ( ! [X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : (($true = (X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7)) | ($true = (X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7)) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ($true != (X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) | ($true = (X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X10))) )),
% 0.23/0.46 inference(boolean_simplification,[],[f50])).
% 0.23/0.46 thf(f50,plain,(
% 0.23/0.46 ( ! [X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : (($true = (X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7)) | ($true = (X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7)) | ($true != (X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) | ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10) = $true) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) )),
% 0.23/0.46 inference(boolean_simplification,[],[f49])).
% 0.23/0.46 thf(f49,plain,(
% 0.23/0.46 ( ! [X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : (($true != (X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) | ($true = (X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7)) | ($true = (X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X10)) | ($true = (X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7)) | ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10) = $true)) )),
% 0.23/0.46 inference(boolean_simplification,[],[f14])).
% 0.23/0.46 thf(f14,plain,(
% 0.23/0.46 ( ! [X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : (($true = (X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10)) | ($true = (X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7)) | ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10) = $true) | ($true = (X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7)) | ($true != (X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) )),
% 0.23/0.46 inference(cnf_transformation,[],[f12])).
% 0.23/0.46 thf(f80,plain,(
% 0.23/0.46 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o] : (((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) != (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) ) | ~spl6_1),
% 0.23/0.46 inference(avatar_component_clause,[],[f79])).
% 0.23/0.46 thf(f79,plain,(
% 0.23/0.46 spl6_1 <=> ! [X1 : ($i > $o) > ($i > $o) > $i > $o,X10] : (($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) != (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))))),
% 0.23/0.46 introduced(avatar_definition,[new_symbols(naming,[spl6_1])])).
% 0.23/0.46 thf(f139,plain,(
% 0.23/0.46 ~spl6_2),
% 0.23/0.46 inference(avatar_contradiction_clause,[],[f138])).
% 0.23/0.46 thf(f138,plain,(
% 0.23/0.46 $false | ~spl6_2),
% 0.23/0.46 inference(trivial_inequality_removal,[],[f137])).
% 0.23/0.46 thf(f137,plain,(
% 0.23/0.46 ($true = $false) | ~spl6_2),
% 0.23/0.46 inference(beta_eta_normalization,[],[f136])).
% 0.23/0.46 thf(f136,plain,(
% 0.23/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: ($false)) @ X1) = ((^[Y0 : $i]: ($true)) @ X1))) ) | ~spl6_2),
% 0.23/0.46 inference(argument_congruence,[],[f84])).
% 0.23/0.46 thf(f84,plain,(
% 0.23/0.46 ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ~spl6_2),
% 0.23/0.46 inference(avatar_component_clause,[],[f82])).
% 0.23/0.46 thf(f85,plain,(
% 0.23/0.46 spl6_1 | spl6_2),
% 0.23/0.46 inference(avatar_split_clause,[],[f77,f82,f79])).
% 0.23/0.46 thf(f77,plain,(
% 0.23/0.46 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ((sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) != (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) )),
% 0.23/0.46 inference(equality_proxy_clausification,[],[f76])).
% 0.23/0.46 thf(f76,plain,(
% 0.23/0.46 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true != ((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) )),
% 0.23/0.46 inference(equality_proxy_clausification,[],[f75])).
% 0.23/0.46 thf(f75,plain,(
% 0.23/0.46 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ($true != ((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))))) )),
% 0.23/0.46 inference(trivial_inequality_removal,[],[f74])).
% 0.23/0.46 thf(f74,plain,(
% 0.23/0.46 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ($true != $true) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ($true != ((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))))) )),
% 0.23/0.46 inference(boolean_simplification,[],[f73])).
% 0.23/0.46 thf(f73,plain,(
% 0.23/0.46 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true != ((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ($true != ((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))))) )),
% 0.23/0.46 inference(beta_eta_normalization,[],[f53])).
% 0.23/0.46 thf(f53,plain,(
% 0.23/0.46 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o] : ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) != $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK5 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))))) )),
% 0.23/0.46 inference(primitive_instantiation,[],[f24])).
% 0.23/0.46 thf(f24,plain,(
% 0.23/0.46 ( ! [X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true != (X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) | ($true != (X0 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0))) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true)) )),
% 0.23/0.46 inference(boolean_simplification,[],[f23])).
% 0.23/0.46 thf(f23,plain,(
% 0.23/0.46 ( ! [X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true != (X0 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0))) | ($true != (X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | ($true = (X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X10))) )),
% 0.23/0.46 inference(boolean_simplification,[],[f22])).
% 0.23/0.46 thf(f22,plain,(
% 0.23/0.46 ( ! [X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true = (X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10)) | ($true != (X0 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0))) | ($true != (X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true)) )),
% 0.23/0.46 inference(boolean_simplification,[],[f21])).
% 0.23/0.46 thf(f21,plain,(
% 0.23/0.46 ( ! [X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true = (X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X10)) | ($true != (X0 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0))) | ($true != (X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) | ($true = (X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10))) )),
% 0.23/0.46 inference(boolean_simplification,[],[f18])).
% 0.23/0.46 thf(f18,plain,(
% 0.23/0.46 ( ! [X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true != (X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) | ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10) = $true) | ($true != (X0 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0))) | ($true = (X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X10))) )),
% 0.23/0.46 inference(cnf_transformation,[],[f12])).
% 0.23/0.46 % SZS output end Proof for theBenchmark
% 0.23/0.46 % (1540)------------------------------
% 0.23/0.46 % (1540)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.46 % (1540)Termination reason: Refutation
% 0.23/0.46
% 0.23/0.46 % (1540)Memory used [KB]: 5884
% 0.23/0.46 % (1540)Time elapsed: 0.059 s
% 0.23/0.46 % (1540)Instructions burned: 75 (million)
% 0.23/0.46 % (1540)------------------------------
% 0.23/0.46 % (1540)------------------------------
% 0.23/0.46 % (1534)Success in time 0.074 s
% 0.23/0.46 % Vampire---4.8 exiting
%------------------------------------------------------------------------------