TSTP Solution File: SEU731^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU731^2 : 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 : n028.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 03:51:06 EDT 2024
% Result : Theorem 0.21s 0.44s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU731^2 : TPTP v8.2.0. Released v3.7.0.
% 0.12/0.14 % 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
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun May 19 17:43:07 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 This is a TH0_THM_EQU_NAR problem
% 0.13/0.35 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
% 0.13/0.37 % (21697)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)
% 0.13/0.37 % (21702)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.38 % (21697)Instruction limit reached!
% 0.13/0.38 % (21697)------------------------------
% 0.13/0.38 % (21697)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (21697)Termination reason: Unknown
% 0.13/0.38 % (21697)Termination phase: Saturation
% 0.13/0.38
% 0.13/0.38 % (21697)Memory used [KB]: 5500
% 0.13/0.38 % (21697)Time elapsed: 0.005 s
% 0.13/0.38 % (21697)Instructions burned: 5 (million)
% 0.13/0.38 % (21697)------------------------------
% 0.13/0.38 % (21697)------------------------------
% 0.13/0.38 % (21696)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.39 % (21701)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)
% 0.13/0.39 % (21699)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.39 % (21699)Instruction limit reached!
% 0.13/0.39 % (21699)------------------------------
% 0.13/0.39 % (21699)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (21699)Termination reason: Unknown
% 0.13/0.39 % (21699)Termination phase: shuffling
% 0.13/0.39
% 0.13/0.39 % (21700)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)
% 0.13/0.39 % (21699)Memory used [KB]: 895
% 0.13/0.39 % (21699)Time elapsed: 0.003 s
% 0.13/0.39 % (21699)Instructions burned: 2 (million)
% 0.13/0.39 % (21699)------------------------------
% 0.13/0.39 % (21699)------------------------------
% 0.13/0.39 % (21702)Instruction limit reached!
% 0.13/0.39 % (21702)------------------------------
% 0.13/0.39 % (21702)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (21702)Termination reason: Unknown
% 0.13/0.39 % (21702)Termination phase: Saturation
% 0.13/0.39
% 0.13/0.39 % (21702)Memory used [KB]: 5628
% 0.13/0.39 % (21702)Time elapsed: 0.014 s
% 0.13/0.39 % (21702)Instructions burned: 19 (million)
% 0.13/0.39 % (21702)------------------------------
% 0.13/0.39 % (21702)------------------------------
% 0.13/0.39 % (21700)Instruction limit reached!
% 0.13/0.39 % (21700)------------------------------
% 0.13/0.39 % (21700)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (21700)Termination reason: Unknown
% 0.13/0.39 % (21700)Termination phase: shuffling
% 0.13/0.39
% 0.13/0.39 % (21700)Memory used [KB]: 895
% 0.13/0.39 % (21700)Time elapsed: 0.004 s
% 0.13/0.39 % (21700)Instructions burned: 2 (million)
% 0.13/0.39 % (21700)------------------------------
% 0.13/0.39 % (21700)------------------------------
% 0.13/0.39 % (21703)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)
% 0.13/0.39 % (21698)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)
% 0.13/0.39 % (21703)Instruction limit reached!
% 0.13/0.39 % (21703)------------------------------
% 0.13/0.39 % (21703)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (21703)Termination reason: Unknown
% 0.13/0.39 % (21703)Termination phase: Property scanning
% 0.13/0.39
% 0.13/0.39 % (21703)Memory used [KB]: 1023
% 0.13/0.39 % (21703)Time elapsed: 0.006 s
% 0.13/0.39 % (21703)Instructions burned: 4 (million)
% 0.13/0.39 % (21703)------------------------------
% 0.13/0.39 % (21703)------------------------------
% 0.13/0.39 % (21705)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)
% 0.13/0.40 % (21708)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)
% 0.13/0.40 % (21706)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)
% 0.13/0.40 % (21707)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)
% 0.13/0.40 % (21707)Instruction limit reached!
% 0.13/0.40 % (21707)------------------------------
% 0.13/0.40 % (21707)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.40 % (21707)Termination reason: Unknown
% 0.13/0.40 % (21707)Termination phase: Function definition elimination
% 0.13/0.40
% 0.13/0.40 % (21707)Memory used [KB]: 1023
% 0.13/0.40 % (21707)Time elapsed: 0.003 s
% 0.13/0.40 % (21707)Instructions burned: 3 (million)
% 0.13/0.40 % (21707)------------------------------
% 0.13/0.40 % (21707)------------------------------
% 0.13/0.41 % (21698)Instruction limit reached!
% 0.13/0.41 % (21698)------------------------------
% 0.13/0.41 % (21698)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.41 % (21698)Termination reason: Unknown
% 0.13/0.41 % (21698)Termination phase: Saturation
% 0.13/0.41
% 0.13/0.41 % (21698)Memory used [KB]: 5628
% 0.13/0.41 % (21698)Time elapsed: 0.044 s
% 0.13/0.41 % (21698)Instructions burned: 27 (million)
% 0.13/0.41 % (21698)------------------------------
% 0.13/0.41 % (21698)------------------------------
% 0.13/0.41 % (21705)Instruction limit reached!
% 0.13/0.41 % (21705)------------------------------
% 0.13/0.41 % (21705)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.41 % (21705)Termination reason: Unknown
% 0.13/0.41 % (21705)Termination phase: Saturation
% 0.13/0.41
% 0.13/0.41 % (21705)Memory used [KB]: 5628
% 0.13/0.41 % (21705)Time elapsed: 0.025 s
% 0.13/0.41 % (21705)Instructions burned: 37 (million)
% 0.13/0.41 % (21705)------------------------------
% 0.13/0.41 % (21705)------------------------------
% 0.13/0.41 % (21706)Instruction limit reached!
% 0.13/0.41 % (21706)------------------------------
% 0.13/0.41 % (21706)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.41 % (21706)Termination reason: Unknown
% 0.13/0.41 % (21706)Termination phase: Saturation
% 0.13/0.41
% 0.13/0.41 % (21706)Memory used [KB]: 5628
% 0.13/0.41 % (21706)Time elapsed: 0.014 s
% 0.13/0.41 % (21706)Instructions burned: 15 (million)
% 0.13/0.41 % (21706)------------------------------
% 0.13/0.41 % (21706)------------------------------
% 0.13/0.41 % (21709)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.13/0.42 % (21709)Instruction limit reached!
% 0.13/0.42 % (21709)------------------------------
% 0.13/0.42 % (21709)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.42 % (21709)Termination reason: Unknown
% 0.13/0.42 % (21709)Termination phase: Saturation
% 0.13/0.42
% 0.13/0.42 % (21709)Memory used [KB]: 1023
% 0.13/0.42 % (21709)Time elapsed: 0.007 s
% 0.13/0.42 % (21709)Instructions burned: 8 (million)
% 0.13/0.42 % (21709)------------------------------
% 0.13/0.42 % (21709)------------------------------
% 0.13/0.42 % (21711)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)
% 0.13/0.42 % (21711)Instruction limit reached!
% 0.13/0.42 % (21711)------------------------------
% 0.13/0.42 % (21711)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.42 % (21711)Termination reason: Unknown
% 0.13/0.42 % (21711)Termination phase: Twee Goal Transformation
% 0.13/0.42
% 0.13/0.42 % (21711)Memory used [KB]: 1023
% 0.13/0.42 % (21711)Time elapsed: 0.004 s
% 0.13/0.42 % (21711)Instructions burned: 4 (million)
% 0.13/0.42 % (21711)------------------------------
% 0.13/0.42 % (21711)------------------------------
% 0.13/0.43 % (21712)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)
% 0.13/0.43 % (21713)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)
% 0.21/0.43 % (21712)Instruction limit reached!
% 0.21/0.43 % (21712)------------------------------
% 0.21/0.43 % (21712)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (21712)Termination reason: Unknown
% 0.21/0.43 % (21712)Termination phase: Function definition elimination
% 0.21/0.43
% 0.21/0.43 % (21712)Memory used [KB]: 1023
% 0.21/0.43 % (21712)Time elapsed: 0.004 s
% 0.21/0.43 % (21712)Instructions burned: 4 (million)
% 0.21/0.43 % (21712)------------------------------
% 0.21/0.43 % (21712)------------------------------
% 0.21/0.43 % (21713)Refutation not found, incomplete strategy
% 0.21/0.43 % (21713)------------------------------
% 0.21/0.43 % (21713)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (21713)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.43
% 0.21/0.43
% 0.21/0.43 % (21713)Memory used [KB]: 5500
% 0.21/0.43 % (21713)Time elapsed: 0.005 s
% 0.21/0.43 % (21713)Instructions burned: 4 (million)
% 0.21/0.43 % (21713)------------------------------
% 0.21/0.43 % (21713)------------------------------
% 0.21/0.43 % (21708)First to succeed.
% 0.21/0.43 % (21714)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)
% 0.21/0.44 % (21714)Instruction limit reached!
% 0.21/0.44 % (21714)------------------------------
% 0.21/0.44 % (21714)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (21714)Termination reason: Unknown
% 0.21/0.44 % (21714)Termination phase: Saturation
% 0.21/0.44
% 0.21/0.44 % (21714)Memory used [KB]: 1023
% 0.21/0.44 % (21714)Time elapsed: 0.003 s
% 0.21/0.44 % (21714)Instructions burned: 4 (million)
% 0.21/0.44 % (21714)------------------------------
% 0.21/0.44 % (21714)------------------------------
% 0.21/0.44 % (21715)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.44 % (21708)Refutation found. Thanks to Tanya!
% 0.21/0.44 % SZS status Theorem for theBenchmark
% 0.21/0.44 % SZS output start Proof for theBenchmark
% 0.21/0.44 thf(func_def_0, type, in: $i > $i > $o).
% 0.21/0.44 thf(func_def_1, type, powerset: $i > $i).
% 0.21/0.44 thf(func_def_2, type, setminus: $i > $i > $i).
% 0.21/0.44 thf(func_def_20, type, ph1: !>[X0: $tType]:(X0)).
% 0.21/0.44 thf(f221,plain,(
% 0.21/0.44 $false),
% 0.21/0.44 inference(subsumption_resolution,[],[f216,f65])).
% 0.21/0.44 thf(f65,plain,(
% 0.21/0.44 (sK3 != (setminus @ sK2 @ (setminus @ sK2 @ sK3)))),
% 0.21/0.44 inference(equality_proxy_clausification,[],[f64])).
% 0.21/0.44 thf(f64,plain,(
% 0.21/0.44 (((setminus @ sK2 @ (setminus @ sK2 @ sK3)) = sK3) = $false)),
% 0.21/0.44 inference(boolean_simplification,[],[f63])).
% 0.21/0.44 thf(f63,plain,(
% 0.21/0.44 (($true => ((setminus @ sK2 @ (setminus @ sK2 @ sK3)) = sK3)) = $false)),
% 0.21/0.44 inference(backward_demodulation,[],[f60,f62])).
% 0.21/0.44 thf(f62,plain,(
% 0.21/0.44 ((in @ sK3 @ (powerset @ sK2)) = $true)),
% 0.21/0.44 inference(binary_proxy_clausification,[],[f60])).
% 0.21/0.44 thf(f60,plain,(
% 0.21/0.44 (((in @ sK3 @ (powerset @ sK2)) => ((setminus @ sK2 @ (setminus @ sK2 @ sK3)) = sK3)) = $false)),
% 0.21/0.44 inference(beta_eta_normalization,[],[f59])).
% 0.21/0.44 thf(f59,plain,(
% 0.21/0.44 (((^[Y0 : $i]: ((in @ Y0 @ (powerset @ sK2)) => ((setminus @ sK2 @ (setminus @ sK2 @ Y0)) = Y0))) @ sK3) = $false)),
% 0.21/0.44 inference(sigma_clausification,[],[f58])).
% 0.21/0.44 thf(f58,plain,(
% 0.21/0.44 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ sK2)) => ((setminus @ sK2 @ (setminus @ sK2 @ Y0)) = Y0)))) = $false)),
% 0.21/0.44 inference(beta_eta_normalization,[],[f57])).
% 0.21/0.44 thf(f57,plain,(
% 0.21/0.44 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1))))) @ sK2) = $false)),
% 0.21/0.44 inference(sigma_clausification,[],[f51])).
% 0.21/0.44 thf(f51,plain,(
% 0.21/0.44 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1)))))) = $false)),
% 0.21/0.44 inference(binary_proxy_clausification,[],[f50])).
% 0.21/0.44 thf(f50,plain,(
% 0.21/0.44 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0))) => (in @ Y2 @ Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1))))))) = $false)),
% 0.21/0.44 inference(boolean_simplification,[],[f49])).
% 0.21/0.44 thf(f49,plain,(
% 0.21/0.44 (($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0))) => (in @ Y2 @ Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1)))))))) = $false)),
% 0.21/0.44 inference(backward_demodulation,[],[f31,f48])).
% 0.21/0.44 thf(f48,plain,(
% 0.21/0.44 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0)))))))))))) = $true)),
% 0.21/0.44 inference(binary_proxy_clausification,[],[f31])).
% 0.21/0.44 thf(f31,plain,(
% 0.21/0.44 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0))) => (in @ Y2 @ Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1)))))))) = $false)),
% 0.21/0.44 inference(binary_proxy_clausification,[],[f30])).
% 0.21/0.44 thf(f30,plain,(
% 0.21/0.44 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y1) => (in @ Y3 @ Y2))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y2) => (in @ Y3 @ Y1))))) => (Y1 = Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0))) => (in @ Y2 @ Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1))))))))) = $false)),
% 0.21/0.44 inference(boolean_simplification,[],[f29])).
% 0.21/0.44 thf(f29,plain,(
% 0.21/0.44 (($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y1) => (in @ Y3 @ Y2))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y2) => (in @ Y3 @ Y1))))) => (Y1 = Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0))) => (in @ Y2 @ Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1)))))))))) = $false)),
% 0.21/0.44 inference(backward_demodulation,[],[f24,f28])).
% 0.21/0.44 thf(f28,plain,(
% 0.21/0.44 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ Y1))))))))),
% 0.21/0.44 inference(binary_proxy_clausification,[],[f24])).
% 0.21/0.44 thf(f24,plain,(
% 0.21/0.44 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y1) => (in @ Y3 @ Y2))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y2) => (in @ Y3 @ Y1))))) => (Y1 = Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0))) => (in @ Y2 @ Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1)))))))))) = $false)),
% 0.21/0.44 inference(not_proxy_clausification,[],[f23])).
% 0.21/0.44 thf(f23,plain,(
% 0.21/0.44 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y1) => (in @ Y3 @ Y2))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y2) => (in @ Y3 @ Y1))))) => (Y1 = Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0))) => (in @ Y2 @ Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1))))))))))) = $true)),
% 0.21/0.44 inference(definition_unfolding,[],[f18,f19,f21,f20,f22])).
% 0.21/0.44 thf(f22,plain,(
% 0.21/0.44 (doubleComplementE1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0))) => (in @ Y2 @ Y0)))))))))))),
% 0.21/0.44 inference(cnf_transformation,[],[f11])).
% 0.21/0.44 thf(f11,plain,(
% 0.21/0.44 (doubleComplementE1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0))) => (in @ Y2 @ Y0)))))))))))),
% 0.21/0.44 inference(fool_elimination,[],[f10])).
% 0.21/0.44 thf(f10,plain,(
% 0.21/0.44 (doubleComplementE1 = ! [X0,X1] : ((in @ X1 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ X0) => ((in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1))) => (in @ X2 @ X1)))))),
% 0.21/0.44 inference(rectify,[],[f4])).
% 0.21/0.44 thf(f4,axiom,(
% 0.21/0.44 (doubleComplementE1 = ! [X0,X1] : ((in @ X1 @ (powerset @ X0)) => ! [X3] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ (setminus @ X0 @ X1))) => (in @ X3 @ X1)))))),
% 0.21/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementE1)).
% 0.21/0.44 thf(f20,plain,(
% 0.21/0.44 (doubleComplementI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0)))))))))))))),
% 0.21/0.44 inference(cnf_transformation,[],[f17])).
% 0.21/0.44 thf(f17,plain,(
% 0.21/0.44 (doubleComplementI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0)))))))))))))),
% 0.21/0.44 inference(fool_elimination,[],[f16])).
% 0.21/0.44 thf(f16,plain,(
% 0.21/0.44 (! [X0,X1] : ((in @ X1 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1)))))) = doubleComplementI1)),
% 0.21/0.44 inference(rectify,[],[f3])).
% 0.21/0.44 thf(f3,axiom,(
% 0.21/0.44 (! [X0,X1] : ((in @ X1 @ (powerset @ X0)) => ! [X3] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ (setminus @ X0 @ (setminus @ X0 @ X1)))))) = doubleComplementI1)),
% 0.21/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementI1)).
% 0.21/0.44 thf(f21,plain,(
% 0.21/0.44 (setextT = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y1) => (in @ Y3 @ Y2))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y2) => (in @ Y3 @ Y1))))) => (Y1 = Y2))))))))))))),
% 0.21/0.44 inference(cnf_transformation,[],[f9])).
% 0.21/0.44 thf(f9,plain,(
% 0.21/0.44 (setextT = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y1) => (in @ Y3 @ Y2))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y2) => (in @ Y3 @ Y1))))) => (Y1 = Y2))))))))))))),
% 0.21/0.44 inference(fool_elimination,[],[f8])).
% 0.21/0.44 thf(f8,plain,(
% 0.21/0.44 (! [X0,X1] : ((in @ X0 @ (powerset @ X1)) => ! [X2] : ((in @ X2 @ (powerset @ X1)) => (! [X3] : ((in @ X3 @ X1) => ((in @ X3 @ X0) => (in @ X3 @ X2))) => (! [X4] : ((in @ X4 @ X1) => ((in @ X4 @ X2) => (in @ X4 @ X0))) => (X0 = X2))))) = setextT)),
% 0.21/0.44 inference(rectify,[],[f2])).
% 0.21/0.44 thf(f2,axiom,(
% 0.21/0.44 (! [X1,X0] : ((in @ X1 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ (powerset @ X0)) => (! [X3] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (! [X3] : ((in @ X3 @ X0) => ((in @ X3 @ X2) => (in @ X3 @ X1))) => (X1 = X2))))) = setextT)),
% 0.21/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextT)).
% 0.21/0.44 thf(f19,plain,(
% 0.21/0.44 (complementT_lem = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ Y1))))))))),
% 0.21/0.44 inference(cnf_transformation,[],[f13])).
% 0.21/0.44 thf(f13,plain,(
% 0.21/0.44 (complementT_lem = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ Y1))))))))),
% 0.21/0.44 inference(fool_elimination,[],[f12])).
% 0.21/0.44 thf(f12,plain,(
% 0.21/0.44 (complementT_lem = ! [X0,X1] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))))),
% 0.21/0.44 inference(rectify,[],[f1])).
% 0.21/0.44 thf(f1,axiom,(
% 0.21/0.44 (complementT_lem = ! [X0,X1] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))))),
% 0.21/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementT_lem)).
% 0.21/0.44 thf(f18,plain,(
% 0.21/0.44 ((~ (complementT_lem => (setextT => (doubleComplementI1 => (doubleComplementE1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1))))))))))) = $true)),
% 0.21/0.44 inference(cnf_transformation,[],[f15])).
% 0.21/0.44 thf(f15,plain,(
% 0.21/0.44 ((~ (complementT_lem => (setextT => (doubleComplementI1 => (doubleComplementE1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1))))))))))) = $true)),
% 0.21/0.44 inference(fool_elimination,[],[f14])).
% 0.21/0.44 thf(f14,plain,(
% 0.21/0.44 ~(complementT_lem => (setextT => (doubleComplementI1 => (doubleComplementE1 => ! [X0,X1] : ((in @ X0 @ (powerset @ X1)) => ((setminus @ X1 @ (setminus @ X1 @ X0)) = X0))))))),
% 0.21/0.44 inference(rectify,[],[f6])).
% 0.21/0.44 thf(f6,negated_conjecture,(
% 0.21/0.44 ~(complementT_lem => (setextT => (doubleComplementI1 => (doubleComplementE1 => ! [X1,X0] : ((in @ X1 @ (powerset @ X0)) => ((setminus @ X0 @ (setminus @ X0 @ X1)) = X1))))))),
% 0.21/0.44 inference(negated_conjecture,[],[f5])).
% 0.21/0.44 thf(f5,conjecture,(
% 0.21/0.44 complementT_lem => (setextT => (doubleComplementI1 => (doubleComplementE1 => ! [X1,X0] : ((in @ X1 @ (powerset @ X0)) => ((setminus @ X0 @ (setminus @ X0 @ X1)) = X1)))))),
% 0.21/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementEq)).
% 0.21/0.44 thf(f216,plain,(
% 0.21/0.44 (sK3 = (setminus @ sK2 @ (setminus @ sK2 @ sK3)))),
% 0.21/0.44 inference(equality_proxy_clausification,[],[f207])).
% 0.21/0.44 thf(f207,plain,(
% 0.21/0.44 ((sK3 = (setminus @ sK2 @ (setminus @ sK2 @ sK3))) = $true)),
% 0.21/0.44 inference(boolean_simplification,[],[f206])).
% 0.21/0.44 thf(f206,plain,(
% 0.21/0.44 (($true => (sK3 = (setminus @ sK2 @ (setminus @ sK2 @ sK3)))) = $true)),
% 0.21/0.44 inference(forward_demodulation,[],[f205,f142])).
% 0.21/0.44 thf(f142,plain,(
% 0.21/0.44 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ Y0 @ (setminus @ sK2 @ (setminus @ sK2 @ sK3))) => (in @ Y0 @ sK3))))) = $true)),
% 0.21/0.44 inference(boolean_simplification,[],[f130])).
% 0.21/0.44 thf(f130,plain,(
% 0.21/0.44 (($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ Y0 @ (setminus @ sK2 @ (setminus @ sK2 @ sK3))) => (in @ Y0 @ sK3)))))) = $true)),
% 0.21/0.44 inference(superposition,[],[f120,f62])).
% 0.21/0.44 thf(f120,plain,(
% 0.21/0.44 ( ! [X2 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ Y0 @ (setminus @ X2 @ (setminus @ X2 @ X1))) => (in @ Y0 @ X1)))))) = $true)) )),
% 0.21/0.44 inference(beta_eta_normalization,[],[f119])).
% 0.21/0.44 thf(f119,plain,(
% 0.21/0.44 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ (setminus @ Y0 @ (setminus @ Y0 @ X1))) => (in @ Y1 @ X1))))))) @ X2) = $true)) )),
% 0.21/0.44 inference(pi_clausification,[],[f110])).
% 0.21/0.44 thf(f110,plain,(
% 0.21/0.44 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ (setminus @ Y0 @ (setminus @ Y0 @ X1))) => (in @ Y1 @ X1)))))))) = $true)) )),
% 0.21/0.44 inference(beta_eta_normalization,[],[f109])).
% 0.21/0.44 thf(f109,plain,(
% 0.21/0.44 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0))) => (in @ Y2 @ Y0))))))))) @ X1) = $true)) )),
% 0.21/0.44 inference(pi_clausification,[],[f52])).
% 0.21/0.44 thf(f52,plain,(
% 0.21/0.44 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0))) => (in @ Y2 @ Y0)))))))))) = $true)),
% 0.21/0.44 inference(binary_proxy_clausification,[],[f50])).
% 0.21/0.44 thf(f205,plain,(
% 0.21/0.44 ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ Y0 @ (setminus @ sK2 @ (setminus @ sK2 @ sK3))) => (in @ Y0 @ sK3))))) => (sK3 = (setminus @ sK2 @ (setminus @ sK2 @ sK3)))))),
% 0.21/0.44 inference(boolean_simplification,[],[f204])).
% 0.21/0.44 thf(f204,plain,(
% 0.21/0.44 (($true => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ Y0 @ (setminus @ sK2 @ (setminus @ sK2 @ sK3))) => (in @ Y0 @ sK3))))) => (sK3 = (setminus @ sK2 @ (setminus @ sK2 @ sK3))))) = $true)),
% 0.21/0.44 inference(forward_demodulation,[],[f196,f99])).
% 0.21/0.44 thf(f99,plain,(
% 0.21/0.44 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ Y0 @ sK3) => (in @ Y0 @ (setminus @ sK2 @ (setminus @ sK2 @ sK3))))))))),
% 0.21/0.44 inference(boolean_simplification,[],[f93])).
% 0.21/0.44 thf(f93,plain,(
% 0.21/0.44 (($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ Y0 @ sK3) => (in @ Y0 @ (setminus @ sK2 @ (setminus @ sK2 @ sK3)))))))) = $true)),
% 0.21/0.44 inference(superposition,[],[f85,f62])).
% 0.21/0.44 thf(f85,plain,(
% 0.21/0.44 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ X1 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ Y0 @ X1) => (in @ Y0 @ (setminus @ X2 @ (setminus @ X2 @ X1)))))))))) )),
% 0.21/0.44 inference(beta_eta_normalization,[],[f84])).
% 0.21/0.44 thf(f84,plain,(
% 0.21/0.44 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ X1) => (in @ Y1 @ (setminus @ Y0 @ (setminus @ Y0 @ X1))))))))) @ X2))) )),
% 0.21/0.44 inference(pi_clausification,[],[f77])).
% 0.21/0.44 thf(f77,plain,(
% 0.21/0.44 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ X1) => (in @ Y1 @ (setminus @ Y0 @ (setminus @ Y0 @ X1)))))))))) = $true)) )),
% 0.21/0.44 inference(beta_eta_normalization,[],[f76])).
% 0.21/0.44 thf(f76,plain,(
% 0.21/0.44 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0))))))))))) @ X1) = $true)) )),
% 0.21/0.44 inference(pi_clausification,[],[f48])).
% 0.21/0.44 thf(f196,plain,(
% 0.21/0.44 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ Y0 @ sK3) => (in @ Y0 @ (setminus @ sK2 @ (setminus @ sK2 @ sK3))))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ Y0 @ (setminus @ sK2 @ (setminus @ sK2 @ sK3))) => (in @ Y0 @ sK3))))) => (sK3 = (setminus @ sK2 @ (setminus @ sK2 @ sK3))))) = $true)),
% 0.21/0.44 inference(boolean_simplification,[],[f183])).
% 0.21/0.44 thf(f183,plain,(
% 0.21/0.44 (($true => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ Y0 @ sK3) => (in @ Y0 @ (setminus @ sK2 @ (setminus @ sK2 @ sK3))))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ Y0 @ (setminus @ sK2 @ (setminus @ sK2 @ sK3))) => (in @ Y0 @ sK3))))) => (sK3 = (setminus @ sK2 @ (setminus @ sK2 @ sK3)))))) = $true)),
% 0.21/0.44 inference(superposition,[],[f167,f74])).
% 0.21/0.44 thf(f74,plain,(
% 0.21/0.44 ((in @ (setminus @ sK2 @ (setminus @ sK2 @ sK3)) @ (powerset @ sK2)) = $true)),
% 0.21/0.44 inference(boolean_simplification,[],[f72])).
% 0.21/0.44 thf(f72,plain,(
% 0.21/0.44 (($true => (in @ (setminus @ sK2 @ (setminus @ sK2 @ sK3)) @ (powerset @ sK2))) = $true)),
% 0.21/0.44 inference(superposition,[],[f40,f68])).
% 0.21/0.44 thf(f68,plain,(
% 0.21/0.44 ((in @ (setminus @ sK2 @ sK3) @ (powerset @ sK2)) = $true)),
% 0.21/0.44 inference(boolean_simplification,[],[f67])).
% 0.21/0.44 thf(f67,plain,(
% 0.21/0.44 (($true => (in @ (setminus @ sK2 @ sK3) @ (powerset @ sK2))) = $true)),
% 0.21/0.44 inference(superposition,[],[f40,f62])).
% 0.21/0.44 thf(f40,plain,(
% 0.21/0.44 ( ! [X2 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2)) => (in @ (setminus @ X2 @ X1) @ (powerset @ X2))) = $true)) )),
% 0.21/0.44 inference(beta_eta_normalization,[],[f39])).
% 0.21/0.44 thf(f39,plain,(
% 0.21/0.44 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ X1) @ (powerset @ Y0)))) @ X2) = $true)) )),
% 0.21/0.44 inference(pi_clausification,[],[f38])).
% 0.21/0.44 thf(f38,plain,(
% 0.21/0.44 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ X1) @ (powerset @ Y0))))) = $true)) )),
% 0.21/0.44 inference(beta_eta_normalization,[],[f37])).
% 0.21/0.44 thf(f37,plain,(
% 0.21/0.44 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ Y1)))))) @ X1) = $true)) )),
% 0.21/0.44 inference(pi_clausification,[],[f28])).
% 0.21/0.44 thf(f167,plain,(
% 0.21/0.44 ( ! [X1 : $i] : ((((in @ X1 @ (powerset @ sK2)) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ Y0 @ sK3) => (in @ Y0 @ X1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ Y0 @ X1) => (in @ Y0 @ sK3))))) => (sK3 = X1)))) = $true)) )),
% 0.21/0.44 inference(beta_eta_normalization,[],[f164])).
% 0.21/0.44 thf(f164,plain,(
% 0.21/0.44 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ (powerset @ sK2)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ Y1 @ sK3) => (in @ Y1 @ Y0))))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ Y1 @ Y0) => (in @ Y1 @ sK3))))) => (sK3 = Y0))))) @ X1) = $true)) )),
% 0.21/0.44 inference(pi_clausification,[],[f69])).
% 0.21/0.44 thf(f69,plain,(
% 0.21/0.44 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ sK2)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ Y1 @ sK3) => (in @ Y1 @ Y0))))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ Y1 @ Y0) => (in @ Y1 @ sK3))))) => (sK3 = Y0)))))) = $true)),
% 0.21/0.44 inference(boolean_simplification,[],[f66])).
% 0.21/0.44 thf(f66,plain,(
% 0.21/0.44 (($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ sK2)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ Y1 @ sK3) => (in @ Y1 @ Y0))))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ Y1 @ Y0) => (in @ Y1 @ sK3))))) => (sK3 = Y0))))))) = $true)),
% 0.21/0.44 inference(superposition,[],[f45,f62])).
% 0.21/0.44 thf(f45,plain,(
% 0.21/0.44 ( ! [X2 : $i,X1 : $i] : ((((in @ X2 @ (powerset @ X1)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((in @ Y1 @ X2) => (in @ Y1 @ Y0))))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((in @ Y1 @ Y0) => (in @ Y1 @ X2))))) => (X2 = Y0))))))) = $true)) )),
% 0.21/0.44 inference(beta_eta_normalization,[],[f44])).
% 0.21/0.44 thf(f44,plain,(
% 0.21/0.44 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X1)) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))) => (Y0 = Y1)))))))) @ X2))) )),
% 0.21/0.44 inference(pi_clausification,[],[f43])).
% 0.21/0.44 thf(f43,plain,(
% 0.21/0.44 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X1)) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))) => (Y0 = Y1))))))))) = $true)) )),
% 0.21/0.44 inference(beta_eta_normalization,[],[f42])).
% 0.21/0.44 thf(f42,plain,(
% 0.21/0.44 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y1) => (in @ Y3 @ Y2))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y2) => (in @ Y3 @ Y1))))) => (Y1 = Y2)))))))))) @ X1) = $true)) )),
% 0.21/0.44 inference(pi_clausification,[],[f32])).
% 0.21/0.44 thf(f32,plain,(
% 0.21/0.44 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y1) => (in @ Y3 @ Y2))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y2) => (in @ Y3 @ Y1))))) => (Y1 = Y2))))))))))) = $true)),
% 0.21/0.44 inference(binary_proxy_clausification,[],[f30])).
% 0.21/0.44 % SZS output end Proof for theBenchmark
% 0.21/0.44 % (21708)------------------------------
% 0.21/0.44 % (21708)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (21708)Termination reason: Refutation
% 0.21/0.44
% 0.21/0.44 % (21708)Memory used [KB]: 5884
% 0.21/0.44 % (21708)Time elapsed: 0.037 s
% 0.21/0.44 % (21708)Instructions burned: 67 (million)
% 0.21/0.44 % (21708)------------------------------
% 0.21/0.44 % (21708)------------------------------
% 0.21/0.44 % (21695)Success in time 0.073 s
% 0.21/0.44 % Vampire---4.8 exiting
%------------------------------------------------------------------------------