TSTP Solution File: SEU649^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU649^2 : TPTP v8.2.0. Released v3.7.0.
% 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 : n003.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 03:50:19 EDT 2024
% Result : Theorem 0.24s 0.45s
% Output : Refutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU649^2 : TPTP v8.2.0. Released v3.7.0.
% 0.08/0.15 % 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
% 0.15/0.37 % Computer : n003.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sun May 19 18:17:08 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.15/0.37 This is a TH0_THM_EQU_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/sandbox2/benchmark/theBenchmark.p
% 0.15/0.39 % (26050)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.39 % (26057)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)
% 0.15/0.39 % (26056)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.39 % (26055)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)
% 0.15/0.39 % (26057)Instruction limit reached!
% 0.15/0.39 % (26057)------------------------------
% 0.15/0.39 % (26057)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (26057)Termination reason: Unknown
% 0.15/0.39 % (26057)Termination phase: Saturation
% 0.15/0.39
% 0.15/0.39 % (26057)Memory used [KB]: 1023
% 0.15/0.39 % (26057)Time elapsed: 0.004 s
% 0.15/0.39 % (26057)Instructions burned: 4 (million)
% 0.15/0.39 % (26057)------------------------------
% 0.15/0.39 % (26057)------------------------------
% 0.15/0.40 % (26052)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 % (26051)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 % (26051)Instruction limit reached!
% 0.15/0.40 % (26051)------------------------------
% 0.15/0.40 % (26051)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (26051)Termination reason: Unknown
% 0.15/0.40 % (26051)Termination phase: Saturation
% 0.15/0.40
% 0.15/0.40 % (26051)Memory used [KB]: 5500
% 0.15/0.40 % (26051)Time elapsed: 0.005 s
% 0.15/0.40 % (26051)Instructions burned: 4 (million)
% 0.15/0.40 % (26051)------------------------------
% 0.15/0.40 % (26051)------------------------------
% 0.15/0.40 % (26056)Instruction limit reached!
% 0.15/0.40 % (26056)------------------------------
% 0.15/0.40 % (26056)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (26056)Termination reason: Unknown
% 0.15/0.40 % (26056)Termination phase: Saturation
% 0.15/0.40
% 0.15/0.40 % (26056)Memory used [KB]: 5628
% 0.15/0.40 % (26056)Time elapsed: 0.013 s
% 0.15/0.40 % (26056)Instructions burned: 18 (million)
% 0.15/0.40 % (26056)------------------------------
% 0.15/0.40 % (26056)------------------------------
% 0.15/0.40 % (26054)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)
% 0.15/0.41 % (26054)Instruction limit reached!
% 0.15/0.41 % (26054)------------------------------
% 0.15/0.41 % (26054)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.41 % (26054)Termination reason: Unknown
% 0.15/0.41 % (26054)Termination phase: Property scanning
% 0.15/0.41
% 0.15/0.41 % (26054)Memory used [KB]: 895
% 0.15/0.41 % (26054)Time elapsed: 0.003 s
% 0.15/0.41 % (26054)Instructions burned: 2 (million)
% 0.15/0.41 % (26054)------------------------------
% 0.15/0.41 % (26054)------------------------------
% 0.15/0.41 % (26053)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.41 % (26058)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)
% 0.15/0.41 % (26053)Instruction limit reached!
% 0.15/0.41 % (26053)------------------------------
% 0.15/0.41 % (26053)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.41 % (26053)Termination reason: Unknown
% 0.15/0.41 % (26053)Termination phase: Preprocessing 1
% 0.15/0.41
% 0.15/0.41 % (26053)Memory used [KB]: 895
% 0.15/0.41 % (26053)Time elapsed: 0.003 s
% 0.15/0.41 % (26053)Instructions burned: 2 (million)
% 0.15/0.41 % (26053)------------------------------
% 0.15/0.41 % (26053)------------------------------
% 0.15/0.41 % (26052)Instruction limit reached!
% 0.15/0.41 % (26052)------------------------------
% 0.15/0.41 % (26052)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.41 % (26052)Termination reason: Unknown
% 0.15/0.41 % (26052)Termination phase: Saturation
% 0.15/0.41
% 0.15/0.41 % (26052)Memory used [KB]: 5628
% 0.15/0.41 % (26052)Time elapsed: 0.016 s
% 0.15/0.41 % (26052)Instructions burned: 27 (million)
% 0.15/0.41 % (26052)------------------------------
% 0.15/0.41 % (26052)------------------------------
% 0.15/0.42 % (26059)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)
% 0.24/0.42 % (26061)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)
% 0.24/0.42 % (26060)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)
% 0.24/0.42 % (26060)Instruction limit reached!
% 0.24/0.42 % (26060)------------------------------
% 0.24/0.42 % (26060)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.42 % (26060)Termination reason: Unknown
% 0.24/0.42 % (26060)Termination phase: Saturation
% 0.24/0.42
% 0.24/0.42 % (26060)Memory used [KB]: 5500
% 0.24/0.42 % (26060)Time elapsed: 0.004 s
% 0.24/0.42 % (26060)Instructions burned: 4 (million)
% 0.24/0.42 % (26060)------------------------------
% 0.24/0.42 % (26060)------------------------------
% 0.24/0.42 % (26062)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.24/0.43 % (26059)Instruction limit reached!
% 0.24/0.43 % (26059)------------------------------
% 0.24/0.43 % (26059)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.43 % (26059)Termination reason: Unknown
% 0.24/0.43 % (26059)Termination phase: Saturation
% 0.24/0.43
% 0.24/0.43 % (26059)Memory used [KB]: 5628
% 0.24/0.43 % (26059)Time elapsed: 0.012 s
% 0.24/0.43 % (26059)Instructions burned: 15 (million)
% 0.24/0.43 % (26059)------------------------------
% 0.24/0.43 % (26059)------------------------------
% 0.24/0.43 % (26062)Instruction limit reached!
% 0.24/0.43 % (26062)------------------------------
% 0.24/0.43 % (26062)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.43 % (26062)Termination reason: Unknown
% 0.24/0.43 % (26062)Termination phase: Saturation
% 0.24/0.43
% 0.24/0.43 % (26062)Memory used [KB]: 1023
% 0.24/0.43 % (26063)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.24/0.43 % (26062)Time elapsed: 0.006 s
% 0.24/0.43 % (26062)Instructions burned: 7 (million)
% 0.24/0.43 % (26062)------------------------------
% 0.24/0.43 % (26062)------------------------------
% 0.24/0.43 % (26058)Instruction limit reached!
% 0.24/0.43 % (26058)------------------------------
% 0.24/0.43 % (26058)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.43 % (26058)Termination reason: Unknown
% 0.24/0.43 % (26058)Termination phase: Saturation
% 0.24/0.43
% 0.24/0.43 % (26058)Memory used [KB]: 5756
% 0.24/0.43 % (26058)Time elapsed: 0.025 s
% 0.24/0.43 % (26058)Instructions burned: 38 (million)
% 0.24/0.43 % (26058)------------------------------
% 0.24/0.43 % (26058)------------------------------
% 0.24/0.44 % (26064)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)
% 0.24/0.44 % (26064)Instruction limit reached!
% 0.24/0.44 % (26064)------------------------------
% 0.24/0.44 % (26064)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.44 % (26064)Termination reason: Unknown
% 0.24/0.44 % (26064)Termination phase: Function definition elimination
% 0.24/0.44
% 0.24/0.44 % (26064)Memory used [KB]: 1023
% 0.24/0.44 % (26064)Time elapsed: 0.004 s
% 0.24/0.44 % (26064)Instructions burned: 3 (million)
% 0.24/0.44 % (26064)------------------------------
% 0.24/0.44 % (26064)------------------------------
% 0.24/0.44 % (26063)Instruction limit reached!
% 0.24/0.44 % (26063)------------------------------
% 0.24/0.44 % (26063)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.44 % (26063)Termination reason: Unknown
% 0.24/0.44 % (26063)Termination phase: Saturation
% 0.24/0.44
% 0.24/0.44 % (26063)Memory used [KB]: 5756
% 0.24/0.44 % (26063)Time elapsed: 0.011 s
% 0.24/0.44 % (26063)Instructions burned: 17 (million)
% 0.24/0.44 % (26063)------------------------------
% 0.24/0.44 % (26063)------------------------------
% 0.24/0.44 % (26065)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)
% 0.24/0.44 % (26065)Instruction limit reached!
% 0.24/0.44 % (26065)------------------------------
% 0.24/0.44 % (26065)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.44 % (26065)Termination reason: Unknown
% 0.24/0.44 % (26065)Termination phase: Property scanning
% 0.24/0.44
% 0.24/0.44 % (26065)Memory used [KB]: 1023
% 0.24/0.44 % (26065)Time elapsed: 0.004 s
% 0.24/0.44 % (26065)Instructions burned: 4 (million)
% 0.24/0.44 % (26065)------------------------------
% 0.24/0.44 % (26065)------------------------------
% 0.24/0.44 % (26066)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.24/0.45 % (26066)Refutation not found, incomplete strategy
% 0.24/0.45 % (26066)------------------------------
% 0.24/0.45 % (26066)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.45 % (26066)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.45
% 0.24/0.45
% 0.24/0.45 % (26066)Memory used [KB]: 5500
% 0.24/0.45 % (26066)Time elapsed: 0.004 s
% 0.24/0.45 % (26066)Instructions burned: 4 (million)
% 0.24/0.45 % (26066)------------------------------
% 0.24/0.45 % (26066)------------------------------
% 0.24/0.45 % (26061)First to succeed.
% 0.24/0.45 % (26067)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.24/0.45 % (26067)Instruction limit reached!
% 0.24/0.45 % (26067)------------------------------
% 0.24/0.45 % (26067)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.45 % (26067)Termination reason: Unknown
% 0.24/0.45 % (26067)Termination phase: Saturation
% 0.24/0.45
% 0.24/0.45 % (26067)Memory used [KB]: 5500
% 0.24/0.45 % (26067)Time elapsed: 0.004 s
% 0.24/0.45 % (26067)Instructions burned: 4 (million)
% 0.24/0.45 % (26067)------------------------------
% 0.24/0.45 % (26067)------------------------------
% 0.24/0.45 % (26061)Refutation found. Thanks to Tanya!
% 0.24/0.45 % SZS status Theorem for theBenchmark
% 0.24/0.45 % SZS output start Proof for theBenchmark
% 0.24/0.45 thf(func_def_0, type, in: $i > $i > $o).
% 0.24/0.45 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 0.24/0.45 thf(func_def_21, type, ph1: !>[X0: $tType]:(X0)).
% 0.24/0.45 thf(f287,plain,(
% 0.24/0.45 $false),
% 0.24/0.45 inference(avatar_sat_refutation,[],[f167,f225,f286])).
% 0.24/0.45 thf(f286,plain,(
% 0.24/0.45 ~spl0_1),
% 0.24/0.45 inference(avatar_contradiction_clause,[],[f285])).
% 0.24/0.45 thf(f285,plain,(
% 0.24/0.45 $false | ~spl0_1),
% 0.24/0.45 inference(trivial_inequality_removal,[],[f284])).
% 0.24/0.45 thf(f284,plain,(
% 0.24/0.45 ($false = $true) | ~spl0_1),
% 0.24/0.45 inference(boolean_simplification,[],[f283])).
% 0.24/0.45 thf(f283,plain,(
% 0.24/0.45 ((~ $true) = $true) | ~spl0_1),
% 0.24/0.45 inference(backward_demodulation,[],[f263,f276])).
% 0.24/0.45 thf(f276,plain,(
% 0.24/0.45 ((in @ sK2 @ (setadjoin @ sK5 @ emptyset)) = $true) | ~spl0_1),
% 0.24/0.45 inference(boolean_simplification,[],[f270])).
% 0.24/0.45 thf(f270,plain,(
% 0.24/0.45 (($true => (in @ sK2 @ (setadjoin @ sK5 @ emptyset))) = $true) | ~spl0_1),
% 0.24/0.45 inference(superposition,[],[f73,f254])).
% 0.24/0.45 thf(f254,plain,(
% 0.24/0.45 ((sK5 = sK2) = $true) | ~spl0_1),
% 0.24/0.45 inference(boolean_simplification,[],[f252])).
% 0.24/0.45 thf(f252,plain,(
% 0.24/0.45 (((sK5 = sK2) | $false) = $true) | ~spl0_1),
% 0.24/0.45 inference(backward_demodulation,[],[f250,f251])).
% 0.24/0.45 thf(f251,plain,(
% 0.24/0.45 ($false = (sK2 = sK5)) | ~spl0_1),
% 0.24/0.45 inference(not_proxy_clausification,[],[f248])).
% 0.24/0.45 thf(f248,plain,(
% 0.24/0.45 ((~ (sK2 = sK5)) = $true) | ~spl0_1),
% 0.24/0.45 inference(boolean_simplification,[],[f245])).
% 0.24/0.45 thf(f245,plain,(
% 0.24/0.45 (((sK2 = sK5) => $false) = $true) | ~spl0_1),
% 0.24/0.45 inference(superposition,[],[f73,f239])).
% 0.24/0.45 thf(f239,plain,(
% 0.24/0.45 ($false = (in @ sK5 @ (setadjoin @ sK2 @ emptyset))) | ~spl0_1),
% 0.24/0.45 inference(binary_proxy_clausification,[],[f238])).
% 0.24/0.45 thf(f238,plain,(
% 0.24/0.45 ($false = ((in @ sK5 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset))) => (in @ sK5 @ (setadjoin @ sK2 @ emptyset)))) | ~spl0_1),
% 0.24/0.45 inference(beta_eta_normalization,[],[f232])).
% 0.24/0.45 thf(f232,plain,(
% 0.24/0.45 ($false = ((^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset))) => (in @ Y0 @ (setadjoin @ sK2 @ emptyset)))) @ sK5)) | ~spl0_1),
% 0.24/0.45 inference(sigma_clausification,[],[f163])).
% 0.24/0.45 thf(f163,plain,(
% 0.24/0.45 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset))) => (in @ Y0 @ (setadjoin @ sK2 @ emptyset)))))) | ~spl0_1),
% 0.24/0.45 inference(avatar_component_clause,[],[f162])).
% 0.24/0.45 thf(f162,plain,(
% 0.24/0.45 spl0_1 <=> ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset))) => (in @ Y0 @ (setadjoin @ sK2 @ emptyset))))))),
% 0.24/0.45 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.24/0.45 thf(f250,plain,(
% 0.24/0.45 (((sK5 = sK2) | (sK2 = sK5)) = $true) | ~spl0_1),
% 0.24/0.45 inference(boolean_simplification,[],[f249])).
% 0.24/0.45 thf(f249,plain,(
% 0.24/0.45 (($true => ((sK5 = sK2) | (sK2 = sK5))) = $true) | ~spl0_1),
% 0.24/0.45 inference(superposition,[],[f117,f240])).
% 0.24/0.45 thf(f240,plain,(
% 0.24/0.45 ((in @ sK5 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset))) = $true) | ~spl0_1),
% 0.24/0.45 inference(binary_proxy_clausification,[],[f238])).
% 0.24/0.45 thf(f117,plain,(
% 0.24/0.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X2 @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset))) => ((X2 = X1) | (X3 = X2))) = $true)) )),
% 0.24/0.45 inference(beta_eta_normalization,[],[f116])).
% 0.24/0.45 thf(f116,plain,(
% 0.24/0.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X2 @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset))) => ((X2 = X1) | (Y0 = X2)))) @ X3) = $true)) )),
% 0.24/0.45 inference(pi_clausification,[],[f108])).
% 0.24/0.45 thf(f108,plain,(
% 0.24/0.45 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset))) => ((X2 = X1) | (Y0 = X2))))) = $true)) )),
% 0.24/0.45 inference(beta_eta_normalization,[],[f107])).
% 0.24/0.45 thf(f107,plain,(
% 0.24/0.45 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ X1 @ (setadjoin @ Y1 @ emptyset))) => ((Y0 = X1) | (Y1 = Y0)))))) @ X2) = $true)) )),
% 0.24/0.45 inference(pi_clausification,[],[f106])).
% 0.24/0.45 thf(f106,plain,(
% 0.24/0.45 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ X1 @ (setadjoin @ Y1 @ emptyset))) => ((Y0 = X1) | (Y1 = Y0))))))) = $true)) )),
% 0.24/0.45 inference(beta_eta_normalization,[],[f105])).
% 0.24/0.45 thf(f105,plain,(
% 0.24/0.45 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1)))))))) @ X1) = $true)) )),
% 0.24/0.45 inference(pi_clausification,[],[f78])).
% 0.24/0.45 thf(f78,plain,(
% 0.24/0.45 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) = $true)),
% 0.24/0.45 inference(binary_proxy_clausification,[],[f64])).
% 0.24/0.45 thf(f64,plain,(
% 0.24/0.45 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))))),
% 0.24/0.45 inference(binary_proxy_clausification,[],[f50])).
% 0.24/0.45 thf(f50,plain,(
% 0.24/0.45 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))))),
% 0.24/0.45 inference(binary_proxy_clausification,[],[f35])).
% 0.24/0.45 thf(f35,plain,(
% 0.24/0.45 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))))))),
% 0.24/0.45 inference(binary_proxy_clausification,[],[f34])).
% 0.24/0.45 thf(f34,plain,(
% 0.24/0.45 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))))))),
% 0.24/0.45 inference(boolean_simplification,[],[f33])).
% 0.24/0.45 thf(f33,plain,(
% 0.24/0.45 ($false = ($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))))))))),
% 0.24/0.45 inference(backward_demodulation,[],[f28,f32])).
% 0.24/0.45 thf(f32,plain,(
% 0.24/0.45 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) = $true)),
% 0.24/0.45 inference(binary_proxy_clausification,[],[f28])).
% 0.24/0.45 thf(f28,plain,(
% 0.24/0.45 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))))))))),
% 0.24/0.45 inference(not_proxy_clausification,[],[f27])).
% 0.24/0.45 thf(f27,plain,(
% 0.24/0.45 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))))))) = $true)),
% 0.24/0.45 inference(definition_unfolding,[],[f24,f23,f21,f25,f26,f22])).
% 0.24/0.45 thf(f22,plain,(
% 0.24/0.45 (upairset2E = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))))),
% 0.24/0.45 inference(cnf_transformation,[],[f18])).
% 0.24/0.45 thf(f18,plain,(
% 0.24/0.45 (upairset2E = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))))),
% 0.24/0.45 inference(fool_elimination,[],[f17])).
% 0.24/0.45 thf(f17,plain,(
% 0.24/0.45 (! [X0,X1,X2] : ((in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset))) => ((X0 = X1) | (X1 = X2))) = upairset2E)),
% 0.24/0.45 inference(rectify,[],[f5])).
% 0.24/0.45 thf(f5,axiom,(
% 0.24/0.45 (! [X3,X4,X2] : ((in @ X4 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))) => ((X3 = X4) | (X2 = X4))) = upairset2E)),
% 0.24/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2E)).
% 0.24/0.45 thf(f26,plain,(
% 0.24/0.45 (eqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))),
% 0.24/0.45 inference(cnf_transformation,[],[f20])).
% 0.24/0.45 thf(f20,plain,(
% 0.24/0.45 (eqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))),
% 0.24/0.45 inference(fool_elimination,[],[f19])).
% 0.24/0.45 thf(f19,plain,(
% 0.24/0.45 (eqinunit = ! [X0,X1] : ((X0 = X1) => (in @ X1 @ (setadjoin @ X0 @ emptyset))))),
% 0.24/0.45 inference(rectify,[],[f4])).
% 0.24/0.45 thf(f4,axiom,(
% 0.24/0.45 (eqinunit = ! [X3,X2] : ((X2 = X3) => (in @ X2 @ (setadjoin @ X3 @ emptyset))))),
% 0.24/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit)).
% 0.24/0.45 thf(f25,plain,(
% 0.24/0.45 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))))),
% 0.24/0.45 inference(cnf_transformation,[],[f10])).
% 0.24/0.45 thf(f10,plain,(
% 0.24/0.45 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))))),
% 0.24/0.45 inference(fool_elimination,[],[f9])).
% 0.24/0.45 thf(f9,plain,(
% 0.24/0.45 (uniqinunit = ! [X0,X1] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 0.24/0.45 inference(rectify,[],[f3])).
% 0.24/0.45 thf(f3,axiom,(
% 0.24/0.45 (uniqinunit = ! [X2,X3] : ((in @ X2 @ (setadjoin @ X3 @ emptyset)) => (X2 = X3)))),
% 0.24/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit)).
% 0.24/0.45 thf(f21,plain,(
% 0.24/0.45 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))))),
% 0.24/0.45 inference(cnf_transformation,[],[f16])).
% 0.24/0.45 thf(f16,plain,(
% 0.24/0.45 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))))),
% 0.24/0.45 inference(fool_elimination,[],[f15])).
% 0.24/0.45 thf(f15,plain,(
% 0.24/0.45 (setadjoinIL = ! [X0,X1] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 0.24/0.45 inference(rectify,[],[f2])).
% 0.24/0.45 thf(f2,axiom,(
% 0.24/0.45 (setadjoinIL = ! [X2,X3] : (in @ X2 @ (setadjoin @ X2 @ X3)))),
% 0.24/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL)).
% 0.24/0.45 thf(f23,plain,(
% 0.24/0.45 (setext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))))),
% 0.24/0.45 inference(cnf_transformation,[],[f14])).
% 0.24/0.45 thf(f14,plain,(
% 0.24/0.45 (setext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))))),
% 0.24/0.45 inference(fool_elimination,[],[f13])).
% 0.24/0.45 thf(f13,plain,(
% 0.24/0.45 (! [X0,X1] : (! [X2] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (! [X3] : ((in @ X3 @ X0) => (in @ X3 @ X1)) => (X0 = X1))) = setext)),
% 0.24/0.45 inference(rectify,[],[f1])).
% 0.24/0.45 thf(f1,axiom,(
% 0.24/0.45 (! [X1,X0] : (! [X2] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X2] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (X0 = X1))) = setext)),
% 0.24/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext)).
% 0.24/0.45 thf(f24,plain,(
% 0.24/0.45 ((~ (setext => (setadjoinIL => (uniqinunit => (eqinunit => (upairset2E => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))))))) = $true)),
% 0.24/0.45 inference(cnf_transformation,[],[f12])).
% 0.24/0.45 thf(f12,plain,(
% 0.24/0.45 ((~ (setext => (setadjoinIL => (uniqinunit => (eqinunit => (upairset2E => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))))))) = $true)),
% 0.24/0.45 inference(fool_elimination,[],[f11])).
% 0.24/0.45 thf(f11,plain,(
% 0.24/0.45 ~(setext => (setadjoinIL => (uniqinunit => (eqinunit => (upairset2E => ! [X0,X1] : ((X0 = X1) => ((setadjoin @ X1 @ emptyset) = (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)))))))))),
% 0.24/0.45 inference(rectify,[],[f7])).
% 0.24/0.45 thf(f7,negated_conjecture,(
% 0.24/0.45 ~(setext => (setadjoinIL => (uniqinunit => (eqinunit => (upairset2E => ! [X3,X2] : ((X2 = X3) => ((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) = (setadjoin @ X2 @ emptyset))))))))),
% 0.24/0.45 inference(negated_conjecture,[],[f6])).
% 0.24/0.45 thf(f6,conjecture,(
% 0.24/0.45 setext => (setadjoinIL => (uniqinunit => (eqinunit => (upairset2E => ! [X3,X2] : ((X2 = X3) => ((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) = (setadjoin @ X2 @ emptyset)))))))),
% 0.24/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR11)).
% 0.24/0.45 thf(f73,plain,(
% 0.24/0.45 ( ! [X2 : $i,X1 : $i] : ((((X2 = X1) => (in @ X1 @ (setadjoin @ X2 @ emptyset))) = $true)) )),
% 0.24/0.45 inference(beta_eta_normalization,[],[f72])).
% 0.24/0.45 thf(f72,plain,(
% 0.24/0.45 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((Y0 = X1) => (in @ X1 @ (setadjoin @ Y0 @ emptyset)))) @ X2) = $true)) )),
% 0.24/0.45 inference(pi_clausification,[],[f71])).
% 0.24/0.45 thf(f71,plain,(
% 0.24/0.45 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((Y0 = X1) => (in @ X1 @ (setadjoin @ Y0 @ emptyset))))) = $true)) )),
% 0.24/0.45 inference(beta_eta_normalization,[],[f70])).
% 0.24/0.45 thf(f70,plain,(
% 0.24/0.45 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))) @ X1) = $true)) )),
% 0.24/0.45 inference(pi_clausification,[],[f65])).
% 0.24/0.45 thf(f65,plain,(
% 0.24/0.45 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))),
% 0.24/0.45 inference(binary_proxy_clausification,[],[f50])).
% 0.24/0.45 thf(f263,plain,(
% 0.24/0.45 ((~ (in @ sK2 @ (setadjoin @ sK5 @ emptyset))) = $true) | ~spl0_1),
% 0.24/0.45 inference(boolean_simplification,[],[f260])).
% 0.24/0.45 thf(f260,plain,(
% 0.24/0.45 (((in @ sK2 @ (setadjoin @ sK5 @ emptyset)) => $false) = $true) | ~spl0_1),
% 0.24/0.45 inference(superposition,[],[f59,f251])).
% 0.24/0.45 thf(f59,plain,(
% 0.24/0.45 ( ! [X2 : $i,X1 : $i] : ((((in @ X2 @ (setadjoin @ X1 @ emptyset)) => (X2 = X1)) = $true)) )),
% 0.24/0.45 inference(beta_eta_normalization,[],[f58])).
% 0.24/0.45 thf(f58,plain,(
% 0.24/0.45 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ X1 @ emptyset)) => (Y0 = X1))) @ X2))) )),
% 0.24/0.45 inference(pi_clausification,[],[f57])).
% 0.24/0.45 thf(f57,plain,(
% 0.24/0.45 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ X1 @ emptyset)) => (Y0 = X1)))) = $true)) )),
% 0.24/0.45 inference(beta_eta_normalization,[],[f56])).
% 0.24/0.45 thf(f56,plain,(
% 0.24/0.45 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0))))) @ X1))) )),
% 0.24/0.45 inference(pi_clausification,[],[f51])).
% 0.24/0.45 thf(f51,plain,(
% 0.24/0.45 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) = $true)),
% 0.24/0.45 inference(binary_proxy_clausification,[],[f35])).
% 0.24/0.45 thf(f225,plain,(
% 0.24/0.45 ~spl0_2),
% 0.24/0.45 inference(avatar_contradiction_clause,[],[f224])).
% 0.24/0.45 thf(f224,plain,(
% 0.24/0.45 $false | ~spl0_2),
% 0.24/0.45 inference(trivial_inequality_removal,[],[f219])).
% 0.24/0.45 thf(f219,plain,(
% 0.24/0.45 ($false = $true) | ~spl0_2),
% 0.24/0.45 inference(superposition,[],[f216,f44])).
% 0.24/0.45 thf(f44,plain,(
% 0.24/0.45 ( ! [X2 : $i,X1 : $i] : (((in @ X2 @ (setadjoin @ X2 @ X1)) = $true)) )),
% 0.24/0.45 inference(beta_eta_normalization,[],[f43])).
% 0.24/0.45 thf(f43,plain,(
% 0.24/0.45 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ X1))) @ X2) = $true)) )),
% 0.24/0.45 inference(pi_clausification,[],[f42])).
% 0.24/0.45 thf(f42,plain,(
% 0.24/0.45 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ X1)))))) )),
% 0.24/0.45 inference(beta_eta_normalization,[],[f41])).
% 0.24/0.45 thf(f41,plain,(
% 0.24/0.45 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0))))) @ X1) = $true)) )),
% 0.24/0.45 inference(pi_clausification,[],[f36])).
% 0.24/0.45 thf(f36,plain,(
% 0.24/0.45 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) = $true)),
% 0.24/0.45 inference(binary_proxy_clausification,[],[f34])).
% 0.24/0.45 thf(f216,plain,(
% 0.24/0.45 ($false = (in @ sK2 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset)))) | ~spl0_2),
% 0.24/0.45 inference(backward_demodulation,[],[f188,f200])).
% 0.24/0.45 thf(f200,plain,(
% 0.24/0.45 (sK4 = sK2) | ~spl0_2),
% 0.24/0.45 inference(equality_proxy_clausification,[],[f196])).
% 0.24/0.45 thf(f196,plain,(
% 0.24/0.45 ((sK4 = sK2) = $true) | ~spl0_2),
% 0.24/0.45 inference(boolean_simplification,[],[f195])).
% 0.24/0.45 thf(f195,plain,(
% 0.24/0.45 ($true = ($true => (sK4 = sK2))) | ~spl0_2),
% 0.24/0.45 inference(superposition,[],[f59,f189])).
% 0.24/0.45 thf(f189,plain,(
% 0.24/0.45 ((in @ sK4 @ (setadjoin @ sK2 @ emptyset)) = $true) | ~spl0_2),
% 0.24/0.45 inference(binary_proxy_clausification,[],[f187])).
% 0.24/0.45 thf(f187,plain,(
% 0.24/0.45 ($false = ((in @ sK4 @ (setadjoin @ sK2 @ emptyset)) => (in @ sK4 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset))))) | ~spl0_2),
% 0.24/0.45 inference(beta_eta_normalization,[],[f181])).
% 0.24/0.45 thf(f181,plain,(
% 0.24/0.45 ($false = ((^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK2 @ emptyset)) => (in @ Y0 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset))))) @ sK4)) | ~spl0_2),
% 0.24/0.45 inference(sigma_clausification,[],[f176])).
% 0.24/0.45 thf(f176,plain,(
% 0.24/0.45 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK2 @ emptyset)) => (in @ Y0 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset))))))) | ~spl0_2),
% 0.24/0.45 inference(not_proxy_clausification,[],[f166])).
% 0.24/0.45 thf(f166,plain,(
% 0.24/0.45 ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK2 @ emptyset)) => (in @ Y0 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset))))))) = $true) | ~spl0_2),
% 0.24/0.45 inference(avatar_component_clause,[],[f165])).
% 0.24/0.45 thf(f165,plain,(
% 0.24/0.45 spl0_2 <=> ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK2 @ emptyset)) => (in @ Y0 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset))))))) = $true)),
% 0.24/0.45 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.24/0.45 thf(f188,plain,(
% 0.24/0.45 ($false = (in @ sK4 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset)))) | ~spl0_2),
% 0.24/0.45 inference(binary_proxy_clausification,[],[f187])).
% 0.24/0.45 thf(f167,plain,(
% 0.24/0.45 spl0_1 | spl0_2),
% 0.24/0.45 inference(avatar_split_clause,[],[f160,f165,f162])).
% 0.24/0.45 thf(f160,plain,(
% 0.24/0.45 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset))) => (in @ Y0 @ (setadjoin @ sK2 @ emptyset)))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK2 @ emptyset)) => (in @ Y0 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset))))))) = $true)),
% 0.24/0.45 inference(binary_proxy_clausification,[],[f114])).
% 0.24/0.45 thf(f114,plain,(
% 0.24/0.45 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset))) => (in @ Y0 @ (setadjoin @ sK2 @ emptyset))))) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK2 @ emptyset)) => (in @ Y0 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset)))))))) = $true)),
% 0.24/0.45 inference(boolean_simplification,[],[f112])).
% 0.24/0.45 thf(f112,plain,(
% 0.24/0.45 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset))) => (in @ Y0 @ (setadjoin @ sK2 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK2 @ emptyset)) => (in @ Y0 @ (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset)))))) => $false)) = $true)),
% 0.24/0.45 inference(superposition,[],[f48,f103])).
% 0.24/0.45 thf(f103,plain,(
% 0.24/0.45 ($false = ((setadjoin @ sK2 @ emptyset) = (setadjoin @ sK2 @ (setadjoin @ sK2 @ emptyset))))),
% 0.24/0.45 inference(backward_demodulation,[],[f87,f93])).
% 0.24/0.45 thf(f93,plain,(
% 0.24/0.45 (sK3 = sK2)),
% 0.24/0.45 inference(equality_proxy_clausification,[],[f88])).
% 0.24/0.45 thf(f88,plain,(
% 0.24/0.45 ((sK3 = sK2) = $true)),
% 0.24/0.45 inference(binary_proxy_clausification,[],[f86])).
% 0.24/0.45 thf(f86,plain,(
% 0.24/0.45 ($false = ((sK3 = sK2) => ((setadjoin @ sK2 @ emptyset) = (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)))))),
% 0.24/0.45 inference(beta_eta_normalization,[],[f85])).
% 0.24/0.45 thf(f85,plain,(
% 0.24/0.45 ($false = ((^[Y0 : $i]: ((Y0 = sK2) => ((setadjoin @ sK2 @ emptyset) = (setadjoin @ sK2 @ (setadjoin @ Y0 @ emptyset))))) @ sK3))),
% 0.24/0.45 inference(sigma_clausification,[],[f84])).
% 0.24/0.45 thf(f84,plain,(
% 0.24/0.45 ($false = (!! @ $i @ (^[Y0 : $i]: ((Y0 = sK2) => ((setadjoin @ sK2 @ emptyset) = (setadjoin @ sK2 @ (setadjoin @ Y0 @ emptyset)))))))),
% 0.24/0.45 inference(beta_eta_normalization,[],[f83])).
% 0.24/0.45 thf(f83,plain,(
% 0.24/0.45 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) @ sK2))),
% 0.24/0.45 inference(sigma_clausification,[],[f77])).
% 0.24/0.45 thf(f77,plain,(
% 0.24/0.45 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 0.24/0.45 inference(binary_proxy_clausification,[],[f64])).
% 0.24/0.45 thf(f87,plain,(
% 0.24/0.45 ($false = ((setadjoin @ sK2 @ emptyset) = (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset))))),
% 0.24/0.45 inference(binary_proxy_clausification,[],[f86])).
% 0.24/0.45 thf(f48,plain,(
% 0.24/0.45 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) => (X2 = X1))) = $true)) )),
% 0.24/0.45 inference(beta_eta_normalization,[],[f47])).
% 0.24/0.45 thf(f47,plain,(
% 0.24/0.45 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => (Y0 = X1)))) @ X2))) )),
% 0.24/0.45 inference(pi_clausification,[],[f46])).
% 0.24/0.45 thf(f46,plain,(
% 0.24/0.45 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => (Y0 = X1))))) = $true)) )),
% 0.24/0.45 inference(beta_eta_normalization,[],[f45])).
% 0.24/0.45 thf(f45,plain,(
% 0.24/0.45 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) @ X1) = $true)) )),
% 0.24/0.45 inference(pi_clausification,[],[f32])).
% 0.24/0.45 % SZS output end Proof for theBenchmark
% 0.24/0.45 % (26061)------------------------------
% 0.24/0.45 % (26061)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.45 % (26061)Termination reason: Refutation
% 0.24/0.45
% 0.24/0.45 % (26061)Memory used [KB]: 5884
% 0.24/0.45 % (26061)Time elapsed: 0.032 s
% 0.24/0.45 % (26061)Instructions burned: 53 (million)
% 0.24/0.45 % (26061)------------------------------
% 0.24/0.45 % (26061)------------------------------
% 0.24/0.45 % (26049)Success in time 0.064 s
% 0.24/0.45 % Vampire---4.8 exiting
%------------------------------------------------------------------------------