TSTP Solution File: SEV158^5 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV158^5 : TPTP v8.1.2. 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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:41:34 EDT 2024
% Result : Theorem 0.15s 0.40s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEV158^5 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.35 % Computer : n027.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 12:34:51 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 This is a TH0_THM_EQU_NAR problem
% 0.15/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.VFKsIW4N4G/Vampire---4.8_22953
% 0.15/0.37 % (23064)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 Vampire---4 for (3000ds/27Mi)
% 0.15/0.37 % (23062)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (3000ds/183Mi)
% 0.15/0.37 % (23065)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (3000ds/2Mi)
% 0.15/0.37 % (23063)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 Vampire---4 for (3000ds/4Mi)
% 0.15/0.37 % (23067)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (3000ds/275Mi)
% 0.15/0.37 % (23068)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (3000ds/18Mi)
% 0.15/0.37 % (23065)Instruction limit reached!
% 0.15/0.37 % (23065)------------------------------
% 0.15/0.37 % (23065)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (23066)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (3000ds/2Mi)
% 0.15/0.37 % (23065)Termination reason: Unknown
% 0.15/0.37 % (23065)Termination phase: Saturation
% 0.15/0.37
% 0.15/0.37 % (23065)Memory used [KB]: 895
% 0.15/0.37 % (23065)Time elapsed: 0.003 s
% 0.15/0.37 % (23065)Instructions burned: 2 (million)
% 0.15/0.37 % (23065)------------------------------
% 0.15/0.37 % (23065)------------------------------
% 0.15/0.38 % (23066)Instruction limit reached!
% 0.15/0.38 % (23066)------------------------------
% 0.15/0.38 % (23066)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (23066)Termination reason: Unknown
% 0.15/0.38 % (23066)Termination phase: Saturation
% 0.15/0.38
% 0.15/0.38 % (23066)Memory used [KB]: 5500
% 0.15/0.38 % (23066)Time elapsed: 0.003 s
% 0.15/0.38 % (23066)Instructions burned: 2 (million)
% 0.15/0.38 % (23066)------------------------------
% 0.15/0.38 % (23066)------------------------------
% 0.15/0.38 % (23063)Instruction limit reached!
% 0.15/0.38 % (23063)------------------------------
% 0.15/0.38 % (23063)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (23063)Termination reason: Unknown
% 0.15/0.38 % (23063)Termination phase: Saturation
% 0.15/0.38
% 0.15/0.38 % (23063)Memory used [KB]: 5500
% 0.15/0.38 % (23063)Time elapsed: 0.005 s
% 0.15/0.38 % (23063)Instructions burned: 4 (million)
% 0.15/0.38 % (23063)------------------------------
% 0.15/0.38 % (23063)------------------------------
% 0.15/0.38 % (23064)Refutation not found, incomplete strategy
% 0.15/0.38 % (23064)------------------------------
% 0.15/0.38 % (23064)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (23064)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.38
% 0.15/0.38
% 0.15/0.38 % (23064)Memory used [KB]: 5500
% 0.15/0.38 % (23064)Time elapsed: 0.005 s
% 0.15/0.38 % (23064)Instructions burned: 5 (million)
% 0.15/0.38 % (23064)------------------------------
% 0.15/0.38 % (23064)------------------------------
% 0.15/0.39 % (23068)Instruction limit reached!
% 0.15/0.39 % (23068)------------------------------
% 0.15/0.39 % (23068)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (23068)Termination reason: Unknown
% 0.15/0.39 % (23068)Termination phase: Saturation
% 0.15/0.39
% 0.15/0.39 % (23068)Memory used [KB]: 5628
% 0.15/0.39 % (23068)Time elapsed: 0.013 s
% 0.15/0.39 % (23068)Instructions burned: 18 (million)
% 0.15/0.39 % (23068)------------------------------
% 0.15/0.39 % (23068)------------------------------
% 0.15/0.39 % (23069)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (3000ds/3Mi)
% 0.15/0.39 % (23071)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 Vampire---4 for (2999ds/15Mi)
% 0.15/0.39 % (23069)Instruction limit reached!
% 0.15/0.39 % (23069)------------------------------
% 0.15/0.39 % (23069)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (23069)Termination reason: Unknown
% 0.15/0.39 % (23069)Termination phase: Saturation
% 0.15/0.39
% 0.15/0.39 % (23069)Memory used [KB]: 5500
% 0.15/0.39 % (23069)Time elapsed: 0.004 s
% 0.15/0.39 % (23069)Instructions burned: 3 (million)
% 0.15/0.39 % (23069)------------------------------
% 0.15/0.39 % (23069)------------------------------
% 0.15/0.39 % (23070)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 Vampire---4 for (2999ds/37Mi)
% 0.15/0.39 % (23072)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.15/0.39 % (23067)Refutation not found, incomplete strategy
% 0.15/0.39 % (23067)------------------------------
% 0.15/0.39 % (23067)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (23067)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.39
% 0.15/0.39
% 0.15/0.39 % (23067)Memory used [KB]: 5628
% 0.15/0.39 % (23067)Time elapsed: 0.019 s
% 0.15/0.39 % (23067)Instructions burned: 28 (million)
% 0.15/0.39 % (23067)------------------------------
% 0.15/0.39 % (23067)------------------------------
% 0.15/0.39 % (23073)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 Vampire---4 for (2999ds/1041Mi)
% 0.15/0.39 % (23072)Instruction limit reached!
% 0.15/0.39 % (23072)------------------------------
% 0.15/0.39 % (23072)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (23072)Termination reason: Unknown
% 0.15/0.39 % (23072)Termination phase: Saturation
% 0.15/0.39
% 0.15/0.39 % (23072)Memory used [KB]: 5500
% 0.15/0.39 % (23072)Time elapsed: 0.025 s
% 0.15/0.39 % (23072)Instructions burned: 3 (million)
% 0.15/0.39 % (23072)------------------------------
% 0.15/0.39 % (23072)------------------------------
% 0.15/0.40 % (23071)First to succeed.
% 0.15/0.40 % (23074)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.15/0.40 % (23071)Refutation found. Thanks to Tanya!
% 0.15/0.40 % SZS status Theorem for Vampire---4
% 0.15/0.40 % SZS output start Proof for Vampire---4
% 0.15/0.40 thf(func_def_3, type, sP0: (($i > $o) > ($i > $o) > $o) > $o).
% 0.15/0.40 thf(func_def_4, type, sP1: (($i > $o) > ($i > $o) > $o) > $o).
% 0.15/0.40 thf(func_def_5, type, sK2: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 0.15/0.40 thf(func_def_6, type, sK3: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 0.15/0.40 thf(func_def_7, type, sK4: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 0.15/0.40 thf(func_def_8, type, sK5: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 0.15/0.40 thf(func_def_9, type, sK6: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 0.15/0.40 thf(func_def_10, type, sK7: (($i > $o) > ($i > $o) > $o) > $i).
% 0.15/0.40 thf(func_def_11, type, sK8: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 0.15/0.40 thf(func_def_13, type, ph10: !>[X0: $tType]:(X0)).
% 0.15/0.40 thf(f243,plain,(
% 0.15/0.40 $false),
% 0.15/0.40 inference(avatar_sat_refutation,[],[f55,f135,f144,f150,f157,f159,f179,f201,f219,f224,f229,f230,f232,f242])).
% 0.15/0.40 thf(f242,plain,(
% 0.15/0.40 ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))) != $false) | ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $false) | ($true != (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))) = $true)),
% 0.15/0.40 introduced(theory_tautology_sat_conflict,[])).
% 0.15/0.40 thf(f232,plain,(
% 0.15/0.40 ((sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ($false != (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $false)),
% 0.15/0.40 introduced(theory_tautology_sat_conflict,[])).
% 0.15/0.40 thf(f230,plain,(
% 0.15/0.40 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 0.15/0.40 introduced(theory_tautology_sat_conflict,[])).
% 0.15/0.40 thf(f229,plain,(
% 0.15/0.40 spl9_23 | ~spl9_1),
% 0.15/0.40 inference(avatar_split_clause,[],[f208,f48,f226])).
% 0.15/0.40 thf(f226,plain,(
% 0.15/0.40 spl9_23 <=> ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 0.15/0.40 introduced(avatar_definition,[new_symbols(naming,[spl9_23])])).
% 0.15/0.40 thf(f48,plain,(
% 0.15/0.40 spl9_1 <=> ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true)),
% 0.15/0.40 introduced(avatar_definition,[new_symbols(naming,[spl9_1])])).
% 0.15/0.40 thf(f208,plain,(
% 0.15/0.40 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_1),
% 0.15/0.40 inference(equality_proxy_clausification,[],[f207])).
% 0.15/0.40 thf(f207,plain,(
% 0.15/0.40 ($true = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_1),
% 0.15/0.40 inference(beta_eta_normalization,[],[f206])).
% 0.15/0.40 thf(f206,plain,(
% 0.15/0.40 ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_1),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f203])).
% 0.15/0.40 thf(f203,plain,(
% 0.15/0.40 ($true != $true) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_1),
% 0.15/0.40 inference(superposition,[],[f23,f50])).
% 0.15/0.40 thf(f50,plain,(
% 0.15/0.40 ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true) | ~spl9_1),
% 0.15/0.40 inference(avatar_component_clause,[],[f48])).
% 0.15/0.40 thf(f23,plain,(
% 0.15/0.40 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true != (sP1 @ X0)) | ($true = (X0 @ (sK3 @ X0) @ (sK2 @ X0)))) )),
% 0.15/0.40 inference(cnf_transformation,[],[f14])).
% 0.15/0.40 thf(f14,plain,(
% 0.15/0.40 ! [X0 : ($i > $o) > ($i > $o) > $o] : ((($true != (X0 @ (sK3 @ X0) @ (sK4 @ X0))) & ($true = (X0 @ (sK3 @ X0) @ (sK2 @ X0))) & ($true = (X0 @ (sK2 @ X0) @ (sK4 @ X0)))) | ($true != (sP1 @ X0)))),
% 0.15/0.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f12,f13])).
% 0.15/0.40 thf(f13,plain,(
% 0.15/0.40 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X2 @ X3) != $true) & ($true = (X0 @ X2 @ X1)) & ((X0 @ X1 @ X3) = $true)) => (($true != (X0 @ (sK3 @ X0) @ (sK4 @ X0))) & ($true = (X0 @ (sK3 @ X0) @ (sK2 @ X0))) & ($true = (X0 @ (sK2 @ X0) @ (sK4 @ X0)))))),
% 0.15/0.40 introduced(choice_axiom,[])).
% 0.15/0.40 thf(f12,plain,(
% 0.15/0.40 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X2 @ X3) != $true) & ($true = (X0 @ X2 @ X1)) & ((X0 @ X1 @ X3) = $true)) | ($true != (sP1 @ X0)))),
% 0.15/0.40 inference(rectify,[],[f11])).
% 0.15/0.40 thf(f11,plain,(
% 0.15/0.40 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X5 : $i > $o,X6 : $i > $o,X7 : $i > $o] : (($true != (X0 @ X6 @ X7)) & ($true = (X0 @ X6 @ X5)) & ($true = (X0 @ X5 @ X7))) | ($true != (sP1 @ X0)))),
% 0.15/0.40 inference(nnf_transformation,[],[f9])).
% 0.15/0.40 thf(f9,plain,(
% 0.15/0.40 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X5 : $i > $o,X6 : $i > $o,X7 : $i > $o] : (($true != (X0 @ X6 @ X7)) & ($true = (X0 @ X6 @ X5)) & ($true = (X0 @ X5 @ X7))) | ~($true = (sP1 @ X0)))),
% 0.15/0.40 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 0.15/0.40 thf(f224,plain,(
% 0.15/0.40 spl9_22 | ~spl9_1),
% 0.15/0.40 inference(avatar_split_clause,[],[f211,f48,f221])).
% 0.15/0.40 thf(f221,plain,(
% 0.15/0.40 spl9_22 <=> ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 0.15/0.40 introduced(avatar_definition,[new_symbols(naming,[spl9_22])])).
% 0.15/0.40 thf(f211,plain,(
% 0.15/0.40 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_1),
% 0.15/0.40 inference(equality_proxy_clausification,[],[f210])).
% 0.15/0.40 thf(f210,plain,(
% 0.15/0.40 ($true = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_1),
% 0.15/0.40 inference(beta_eta_normalization,[],[f209])).
% 0.15/0.40 thf(f209,plain,(
% 0.15/0.40 ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_1),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f204])).
% 0.15/0.40 thf(f204,plain,(
% 0.15/0.40 ($true != $true) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_1),
% 0.15/0.40 inference(superposition,[],[f22,f50])).
% 0.15/0.40 thf(f22,plain,(
% 0.15/0.40 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true != (sP1 @ X0)) | ($true = (X0 @ (sK2 @ X0) @ (sK4 @ X0)))) )),
% 0.15/0.40 inference(cnf_transformation,[],[f14])).
% 0.15/0.40 thf(f219,plain,(
% 0.15/0.40 ~spl9_21 | ~spl9_1),
% 0.15/0.40 inference(avatar_split_clause,[],[f214,f48,f216])).
% 0.15/0.40 thf(f216,plain,(
% 0.15/0.40 spl9_21 <=> ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 0.15/0.40 introduced(avatar_definition,[new_symbols(naming,[spl9_21])])).
% 0.15/0.40 thf(f214,plain,(
% 0.15/0.40 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_1),
% 0.15/0.40 inference(equality_proxy_clausification,[],[f213])).
% 0.15/0.40 thf(f213,plain,(
% 0.15/0.40 ($true != ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_1),
% 0.15/0.40 inference(beta_eta_normalization,[],[f212])).
% 0.15/0.40 thf(f212,plain,(
% 0.15/0.40 ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_1),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f205])).
% 0.15/0.40 thf(f205,plain,(
% 0.15/0.40 ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true != $true) | ~spl9_1),
% 0.15/0.40 inference(superposition,[],[f24,f50])).
% 0.15/0.40 thf(f24,plain,(
% 0.15/0.40 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true != (X0 @ (sK3 @ X0) @ (sK4 @ X0))) | ($true != (sP1 @ X0))) )),
% 0.15/0.40 inference(cnf_transformation,[],[f14])).
% 0.15/0.40 thf(f201,plain,(
% 0.15/0.40 spl9_20 | spl9_4),
% 0.15/0.40 inference(avatar_split_clause,[],[f196,f61,f198])).
% 0.15/0.40 thf(f198,plain,(
% 0.15/0.40 spl9_20 <=> ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))) = $false)),
% 0.15/0.40 introduced(avatar_definition,[new_symbols(naming,[spl9_20])])).
% 0.15/0.40 thf(f61,plain,(
% 0.15/0.40 spl9_4 <=> ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))) = $true)),
% 0.15/0.40 introduced(avatar_definition,[new_symbols(naming,[spl9_4])])).
% 0.15/0.40 thf(f196,plain,(
% 0.15/0.40 ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))) = $false) | spl9_4),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f195])).
% 0.15/0.40 thf(f195,plain,(
% 0.15/0.40 ($true != $true) | ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))) = $false) | spl9_4),
% 0.15/0.40 inference(fool_paramodulation,[],[f62])).
% 0.15/0.40 thf(f62,plain,(
% 0.15/0.40 ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))) != $true) | spl9_4),
% 0.15/0.40 inference(avatar_component_clause,[],[f61])).
% 0.15/0.40 thf(f179,plain,(
% 0.15/0.40 ~spl9_4),
% 0.15/0.40 inference(avatar_contradiction_clause,[],[f178])).
% 0.15/0.40 thf(f178,plain,(
% 0.15/0.40 $false | ~spl9_4),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f177])).
% 0.15/0.40 thf(f177,plain,(
% 0.15/0.40 ($true != $true) | ~spl9_4),
% 0.15/0.40 inference(beta_eta_normalization,[],[f176])).
% 0.15/0.40 thf(f176,plain,(
% 0.15/0.40 ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))))) | ~spl9_4),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f171])).
% 0.15/0.40 thf(f171,plain,(
% 0.15/0.40 ($true != $true) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))))) | ~spl9_4),
% 0.15/0.40 inference(superposition,[],[f24,f63])).
% 0.15/0.40 thf(f63,plain,(
% 0.15/0.40 ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))) = $true) | ~spl9_4),
% 0.15/0.40 inference(avatar_component_clause,[],[f61])).
% 0.15/0.40 thf(f159,plain,(
% 0.15/0.40 ((sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $false) | ($true != (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true = $false)),
% 0.15/0.40 introduced(theory_tautology_sat_conflict,[])).
% 0.15/0.40 thf(f157,plain,(
% 0.15/0.40 ~spl9_9),
% 0.15/0.40 inference(avatar_contradiction_clause,[],[f156])).
% 0.15/0.40 thf(f156,plain,(
% 0.15/0.40 $false | ~spl9_9),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f97])).
% 0.15/0.40 thf(f97,plain,(
% 0.15/0.40 ($true = $false) | ~spl9_9),
% 0.15/0.40 inference(avatar_component_clause,[],[f95])).
% 0.15/0.40 thf(f95,plain,(
% 0.15/0.40 spl9_9 <=> ($true = $false)),
% 0.15/0.40 introduced(avatar_definition,[new_symbols(naming,[spl9_9])])).
% 0.15/0.40 thf(f150,plain,(
% 0.15/0.40 spl9_17 | ~spl9_2),
% 0.15/0.40 inference(avatar_split_clause,[],[f120,f52,f146])).
% 0.15/0.40 thf(f146,plain,(
% 0.15/0.40 spl9_17 <=> ((sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 0.15/0.40 introduced(avatar_definition,[new_symbols(naming,[spl9_17])])).
% 0.15/0.40 thf(f52,plain,(
% 0.15/0.40 spl9_2 <=> ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 0.15/0.40 introduced(avatar_definition,[new_symbols(naming,[spl9_2])])).
% 0.15/0.40 thf(f120,plain,(
% 0.15/0.40 ((sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_2),
% 0.15/0.40 inference(equality_proxy_clausification,[],[f119])).
% 0.15/0.40 thf(f119,plain,(
% 0.15/0.40 ($true = ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_2),
% 0.15/0.40 inference(beta_eta_normalization,[],[f118])).
% 0.15/0.40 thf(f118,plain,(
% 0.15/0.40 ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_2),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f116])).
% 0.15/0.40 thf(f116,plain,(
% 0.15/0.40 ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true != $true) | ~spl9_2),
% 0.15/0.40 inference(superposition,[],[f25,f54])).
% 0.15/0.40 thf(f54,plain,(
% 0.15/0.40 ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_2),
% 0.15/0.40 inference(avatar_component_clause,[],[f52])).
% 0.15/0.40 thf(f25,plain,(
% 0.15/0.40 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true = (X0 @ (sK6 @ X0) @ (sK5 @ X0))) | ($true != (sP0 @ X0))) )),
% 0.15/0.40 inference(cnf_transformation,[],[f18])).
% 0.15/0.40 thf(f18,plain,(
% 0.15/0.40 ! [X0 : ($i > $o) > ($i > $o) > $o] : ((((sK5 @ X0 @ (sK7 @ X0)) != (sK6 @ X0 @ (sK7 @ X0))) & ($true = (X0 @ (sK5 @ X0) @ (sK6 @ X0))) & ($true = (X0 @ (sK6 @ X0) @ (sK5 @ X0)))) | ($true != (sP0 @ X0)))),
% 0.15/0.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f15,f17,f16])).
% 0.15/0.40 thf(f16,plain,(
% 0.15/0.40 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o] : (? [X3] : ((X2 @ X3) != (X1 @ X3)) & ((X0 @ X1 @ X2) = $true) & ($true = (X0 @ X2 @ X1))) => (? [X3] : ((sK6 @ X0 @ X3) != (sK5 @ X0 @ X3)) & ($true = (X0 @ (sK5 @ X0) @ (sK6 @ X0))) & ($true = (X0 @ (sK6 @ X0) @ (sK5 @ X0)))))),
% 0.15/0.40 introduced(choice_axiom,[])).
% 0.15/0.40 thf(f17,plain,(
% 0.15/0.40 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X3] : ((sK6 @ X0 @ X3) != (sK5 @ X0 @ X3)) => ((sK5 @ X0 @ (sK7 @ X0)) != (sK6 @ X0 @ (sK7 @ X0))))),
% 0.15/0.40 introduced(choice_axiom,[])).
% 0.15/0.40 thf(f15,plain,(
% 0.15/0.40 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o] : (? [X3] : ((X2 @ X3) != (X1 @ X3)) & ((X0 @ X1 @ X2) = $true) & ($true = (X0 @ X2 @ X1))) | ($true != (sP0 @ X0)))),
% 0.15/0.40 inference(nnf_transformation,[],[f8])).
% 0.15/0.40 thf(f8,plain,(
% 0.15/0.40 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o] : (? [X3] : ((X2 @ X3) != (X1 @ X3)) & ((X0 @ X1 @ X2) = $true) & ($true = (X0 @ X2 @ X1))) | ~($true = (sP0 @ X0)))),
% 0.15/0.40 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 0.15/0.40 thf(f144,plain,(
% 0.15/0.40 spl9_15 | spl9_16 | ~spl9_2),
% 0.15/0.40 inference(avatar_split_clause,[],[f126,f52,f141,f137])).
% 0.15/0.40 thf(f137,plain,(
% 0.15/0.40 spl9_15 <=> ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $false)),
% 0.15/0.40 introduced(avatar_definition,[new_symbols(naming,[spl9_15])])).
% 0.15/0.40 thf(f141,plain,(
% 0.15/0.40 spl9_16 <=> ($false = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 0.15/0.40 introduced(avatar_definition,[new_symbols(naming,[spl9_16])])).
% 0.15/0.40 thf(f126,plain,(
% 0.15/0.40 ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $false) | ($false = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_2),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f124])).
% 0.15/0.40 thf(f124,plain,(
% 0.15/0.40 ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_2),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f115])).
% 0.15/0.40 thf(f115,plain,(
% 0.15/0.40 ($true != $true) | ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_2),
% 0.15/0.40 inference(superposition,[],[f27,f54])).
% 0.15/0.40 thf(f27,plain,(
% 0.15/0.40 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((sK5 @ X0 @ (sK7 @ X0)) != (sK6 @ X0 @ (sK7 @ X0))) | ($true != (sP0 @ X0))) )),
% 0.15/0.40 inference(cnf_transformation,[],[f18])).
% 0.15/0.40 thf(f135,plain,(
% 0.15/0.40 spl9_13 | spl9_14 | ~spl9_2),
% 0.15/0.40 inference(avatar_split_clause,[],[f125,f52,f132,f128])).
% 0.15/0.40 thf(f128,plain,(
% 0.15/0.40 spl9_13 <=> ($true = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 0.15/0.40 introduced(avatar_definition,[new_symbols(naming,[spl9_13])])).
% 0.15/0.40 thf(f132,plain,(
% 0.15/0.40 spl9_14 <=> ($true = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 0.15/0.40 introduced(avatar_definition,[new_symbols(naming,[spl9_14])])).
% 0.15/0.40 thf(f125,plain,(
% 0.15/0.40 ($true = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_2),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f124])).
% 0.15/0.40 thf(f55,plain,(
% 0.15/0.40 spl9_1 | spl9_2),
% 0.15/0.40 inference(avatar_split_clause,[],[f46,f52,f48])).
% 0.15/0.40 thf(f46,plain,(
% 0.15/0.40 ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true)),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f45])).
% 0.15/0.40 thf(f45,plain,(
% 0.15/0.40 ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true) | ($true != $true) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 0.15/0.40 inference(boolean_simplification,[],[f44])).
% 0.15/0.40 thf(f44,plain,(
% 0.15/0.40 ($true != ((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true)),
% 0.15/0.40 inference(beta_eta_normalization,[],[f30])).
% 0.15/0.40 thf(f30,plain,(
% 0.15/0.40 ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 0.15/0.40 inference(primitive_instantiation,[],[f28])).
% 0.15/0.40 thf(f28,plain,(
% 0.15/0.40 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true != (X0 @ (sK8 @ X0) @ (sK8 @ X0))) | ($true = (sP1 @ X0)) | ($true = (sP0 @ X0))) )),
% 0.15/0.40 inference(cnf_transformation,[],[f21])).
% 0.15/0.40 thf(f21,plain,(
% 0.15/0.40 ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true = (sP1 @ X0)) | ($true != (X0 @ (sK8 @ X0) @ (sK8 @ X0))) | ($true = (sP0 @ X0)))),
% 0.15/0.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f19,f20])).
% 0.15/0.40 thf(f20,plain,(
% 0.15/0.40 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o] : ((X0 @ X1 @ X1) != $true) => ($true != (X0 @ (sK8 @ X0) @ (sK8 @ X0))))),
% 0.15/0.40 introduced(choice_axiom,[])).
% 0.15/0.40 thf(f19,plain,(
% 0.15/0.40 ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true = (sP1 @ X0)) | ? [X1 : $i > $o] : ((X0 @ X1 @ X1) != $true) | ($true = (sP0 @ X0)))),
% 0.15/0.40 inference(rectify,[],[f10])).
% 0.15/0.40 thf(f10,plain,(
% 0.15/0.40 ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true = (sP1 @ X0)) | ? [X4 : $i > $o] : ($true != (X0 @ X4 @ X4)) | ($true = (sP0 @ X0)))),
% 0.15/0.40 inference(definition_folding,[],[f7,f9,f8])).
% 0.15/0.40 thf(f7,plain,(
% 0.15/0.40 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X5 : $i > $o,X6 : $i > $o,X7 : $i > $o] : (($true != (X0 @ X6 @ X7)) & ($true = (X0 @ X6 @ X5)) & ($true = (X0 @ X5 @ X7))) | ? [X4 : $i > $o] : ($true != (X0 @ X4 @ X4)) | ? [X1 : $i > $o,X2 : $i > $o] : (? [X3] : ((X2 @ X3) != (X1 @ X3)) & ((X0 @ X1 @ X2) = $true) & ($true = (X0 @ X2 @ X1))))),
% 0.15/0.40 inference(flattening,[],[f6])).
% 0.15/0.40 thf(f6,plain,(
% 0.15/0.40 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X2 : $i > $o,X1 : $i > $o] : (? [X3] : ((X2 @ X3) != (X1 @ X3)) & (($true = (X0 @ X2 @ X1)) & ((X0 @ X1 @ X2) = $true))) | ? [X7 : $i > $o,X5 : $i > $o,X6 : $i > $o] : (($true != (X0 @ X6 @ X7)) & (($true = (X0 @ X6 @ X5)) & ($true = (X0 @ X5 @ X7)))) | ? [X4 : $i > $o] : ($true != (X0 @ X4 @ X4)))),
% 0.15/0.40 inference(ennf_transformation,[],[f5])).
% 0.15/0.40 thf(f5,plain,(
% 0.15/0.40 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X2 : $i > $o,X1 : $i > $o] : ((($true = (X0 @ X2 @ X1)) & ((X0 @ X1 @ X2) = $true)) => ! [X3] : ((X2 @ X3) = (X1 @ X3))) & ! [X7 : $i > $o,X5 : $i > $o,X6 : $i > $o] : ((($true = (X0 @ X6 @ X5)) & ($true = (X0 @ X5 @ X7))) => ($true = (X0 @ X6 @ X7))) & ! [X4 : $i > $o] : ($true = (X0 @ X4 @ X4)))),
% 0.15/0.40 inference(fool_elimination,[],[f4])).
% 0.15/0.40 thf(f4,plain,(
% 0.15/0.40 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X1 : $i > $o,X2 : $i > $o] : (((X0 @ X2 @ X1) & (X0 @ X1 @ X2)) => ! [X3] : ((X2 @ X3) = (X1 @ X3))) & ! [X4 : $i > $o] : (X0 @ X4 @ X4) & ! [X5 : $i > $o,X6 : $i > $o,X7 : $i > $o] : (((X0 @ X6 @ X5) & (X0 @ X5 @ X7)) => (X0 @ X6 @ X7)))),
% 0.15/0.40 inference(rectify,[],[f2])).
% 0.15/0.40 thf(f2,negated_conjecture,(
% 0.15/0.40 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X5 : $i > $o,X4 : $i > $o] : (((X0 @ X4 @ X5) & (X0 @ X5 @ X4)) => ! [X1] : ((X4 @ X1) = (X5 @ X1))) & ! [X1 : $i > $o] : (X0 @ X1 @ X1) & ! [X2 : $i > $o,X1 : $i > $o,X3 : $i > $o] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3)))),
% 0.15/0.40 inference(negated_conjecture,[],[f1])).
% 0.15/0.40 thf(f1,conjecture,(
% 0.15/0.40 ? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X5 : $i > $o,X4 : $i > $o] : (((X0 @ X4 @ X5) & (X0 @ X5 @ X4)) => ! [X1] : ((X4 @ X1) = (X5 @ X1))) & ! [X1 : $i > $o] : (X0 @ X1 @ X1) & ! [X2 : $i > $o,X1 : $i > $o,X3 : $i > $o] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3)))),
% 0.15/0.40 file('/export/starexec/sandbox2/tmp/tmp.VFKsIW4N4G/Vampire---4.8_22953',cTHM120I_1_pme)).
% 0.15/0.40 % SZS output end Proof for Vampire---4
% 0.15/0.40 % (23071)------------------------------
% 0.15/0.40 % (23071)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (23071)Termination reason: Refutation
% 0.15/0.40
% 0.15/0.40 % (23071)Memory used [KB]: 5756
% 0.15/0.40 % (23071)Time elapsed: 0.034 s
% 0.15/0.40 % (23071)Instructions burned: 14 (million)
% 0.15/0.40 % (23071)------------------------------
% 0.15/0.40 % (23071)------------------------------
% 0.15/0.40 % (23061)Success in time 0.05 s
% 0.15/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------