TSTP Solution File: SEU655^2 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEU655^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 15:42:05 EDT 2024
% Result : Theorem 0.22s 0.49s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU655^2 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.13 % Command : run_vampire %s %d THM
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 : Fri Jun 21 16:38:38 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.21/0.37 This is a TH0_THM_EQU_NAR problem
% 0.21/0.37 Running higher-order theorem proving
% 0.21/0.37 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/benchmark/theBenchmark.p -m 16384 -t 300
% 0.21/0.39 % (19150)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.39 % (19144)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.21/0.39 % (19146)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)
% 0.21/0.39 % (19147)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.39 % (19147)Instruction limit reached!
% 0.21/0.39 % (19147)------------------------------
% 0.21/0.39 % (19147)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.39 % (19147)Termination reason: Unknown
% 0.21/0.39 % (19147)Termination phase: shuffling
% 0.21/0.39
% 0.21/0.39 % (19147)Memory used [KB]: 1023
% 0.21/0.39 % (19147)Time elapsed: 0.003 s
% 0.21/0.39 % (19147)Instructions burned: 2 (million)
% 0.21/0.39 % (19147)------------------------------
% 0.21/0.39 % (19147)------------------------------
% 0.21/0.39 % (19148)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)
% 0.21/0.39 % (19148)Instruction limit reached!
% 0.21/0.39 % (19148)------------------------------
% 0.21/0.39 % (19148)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.39 % (19148)Termination reason: Unknown
% 0.21/0.39 % (19148)Termination phase: shuffling
% 0.21/0.39
% 0.21/0.39 % (19148)Memory used [KB]: 1023
% 0.21/0.39 % (19148)Time elapsed: 0.003 s
% 0.21/0.39 % (19148)Instructions burned: 2 (million)
% 0.21/0.39 % (19148)------------------------------
% 0.21/0.39 % (19148)------------------------------
% 0.21/0.39 % (19145)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)
% 0.21/0.40 % (19145)Instruction limit reached!
% 0.21/0.40 % (19145)------------------------------
% 0.21/0.40 % (19145)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.40 % (19145)Termination reason: Unknown
% 0.21/0.40 % (19145)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (19145)Memory used [KB]: 5500
% 0.21/0.40 % (19145)Time elapsed: 0.005 s
% 0.21/0.40 % (19145)Instructions burned: 5 (million)
% 0.21/0.40 % (19145)------------------------------
% 0.21/0.40 % (19145)------------------------------
% 0.21/0.40 % (19150)Instruction limit reached!
% 0.21/0.40 % (19150)------------------------------
% 0.21/0.40 % (19150)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.40 % (19150)Termination reason: Unknown
% 0.21/0.40 % (19150)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (19150)Memory used [KB]: 5628
% 0.21/0.40 % (19150)Time elapsed: 0.012 s
% 0.21/0.40 % (19150)Instructions burned: 18 (million)
% 0.21/0.40 % (19150)------------------------------
% 0.21/0.40 % (19150)------------------------------
% 0.21/0.40 % (19149)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)
% 0.21/0.41 % (19146)Instruction limit reached!
% 0.21/0.41 % (19146)------------------------------
% 0.21/0.41 % (19146)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.41 % (19146)Termination reason: Unknown
% 0.21/0.41 % (19146)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (19146)Memory used [KB]: 5628
% 0.21/0.41 % (19146)Time elapsed: 0.020 s
% 0.21/0.41 % (19146)Instructions burned: 28 (million)
% 0.21/0.41 % (19146)------------------------------
% 0.21/0.41 % (19146)------------------------------
% 0.21/0.41 % (19151)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)
% 0.21/0.41 % (19149)Refutation not found, incomplete strategy
% 0.21/0.41 % (19149)------------------------------
% 0.21/0.41 % (19149)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.41 % (19149)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.41
% 0.21/0.41
% 0.21/0.41 % (19149)Memory used [KB]: 5628
% 0.21/0.41 % (19149)Time elapsed: 0.010 s
% 0.21/0.41 % (19149)Instructions burned: 10 (million)
% 0.21/0.41 % (19149)------------------------------
% 0.21/0.41 % (19149)------------------------------
% 0.21/0.41 % (19151)Instruction limit reached!
% 0.21/0.41 % (19151)------------------------------
% 0.21/0.41 % (19151)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.41 % (19151)Termination reason: Unknown
% 0.21/0.41 % (19151)Termination phase: Property scanning
% 0.21/0.41
% 0.21/0.41 % (19151)Memory used [KB]: 1023
% 0.21/0.41 % (19151)Time elapsed: 0.004 s
% 0.21/0.41 % (19151)Instructions burned: 3 (million)
% 0.21/0.41 % (19151)------------------------------
% 0.21/0.41 % (19151)------------------------------
% 0.21/0.41 % (19154)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)
% 0.21/0.41 % (19153)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)
% 0.21/0.41 % (19154)Instruction limit reached!
% 0.21/0.41 % (19154)------------------------------
% 0.21/0.41 % (19154)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.41 % (19154)Termination reason: Unknown
% 0.21/0.41 % (19154)Termination phase: Property scanning
% 0.21/0.41
% 0.21/0.41 % (19154)Memory used [KB]: 1023
% 0.21/0.41 % (19154)Time elapsed: 0.003 s
% 0.21/0.41 % (19154)Instructions burned: 3 (million)
% 0.21/0.41 % (19154)------------------------------
% 0.21/0.41 % (19154)------------------------------
% 0.21/0.41 % (19152)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)
% 0.21/0.42 % (19155)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)
% 0.21/0.42 % (19153)Instruction limit reached!
% 0.21/0.42 % (19153)------------------------------
% 0.21/0.42 % (19153)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.42 % (19153)Termination reason: Unknown
% 0.21/0.42 % (19153)Termination phase: Saturation
% 0.21/0.42
% 0.21/0.42 % (19153)Memory used [KB]: 5628
% 0.21/0.42 % (19153)Time elapsed: 0.012 s
% 0.21/0.42 % (19153)Instructions burned: 15 (million)
% 0.21/0.42 % (19153)------------------------------
% 0.21/0.42 % (19153)------------------------------
% 0.21/0.42 % (19156)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.42 % (19157)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.21/0.43 % (19156)Instruction limit reached!
% 0.21/0.43 % (19156)------------------------------
% 0.21/0.43 % (19156)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.43 % (19156)Termination reason: Unknown
% 0.21/0.43 % (19156)Termination phase: Saturation
% 0.21/0.43
% 0.21/0.43 % (19156)Memory used [KB]: 1023
% 0.21/0.43 % (19156)Time elapsed: 0.006 s
% 0.21/0.43 % (19156)Instructions burned: 7 (million)
% 0.21/0.43 % (19156)------------------------------
% 0.21/0.43 % (19156)------------------------------
% 0.21/0.43 % (19158)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)
% 0.21/0.43 % (19158)Instruction limit reached!
% 0.21/0.43 % (19158)------------------------------
% 0.21/0.43 % (19158)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.43 % (19158)Termination reason: Unknown
% 0.21/0.43 % (19158)Termination phase: Unused predicate definition removal
% 0.21/0.43
% 0.21/0.43 % (19158)Memory used [KB]: 1023
% 0.21/0.43 % (19158)Time elapsed: 0.003 s
% 0.21/0.43 % (19158)Instructions burned: 3 (million)
% 0.21/0.43 % (19158)------------------------------
% 0.21/0.43 % (19158)------------------------------
% 0.21/0.43 % (19152)Instruction limit reached!
% 0.21/0.43 % (19152)------------------------------
% 0.21/0.43 % (19152)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.43 % (19152)Termination reason: Unknown
% 0.21/0.43 % (19152)Termination phase: Saturation
% 0.21/0.43
% 0.21/0.43 % (19152)Memory used [KB]: 5884
% 0.21/0.43 % (19152)Time elapsed: 0.042 s
% 0.21/0.43 % (19152)Instructions burned: 37 (million)
% 0.21/0.43 % (19152)------------------------------
% 0.21/0.43 % (19152)------------------------------
% 0.21/0.44 % (19157)Instruction limit reached!
% 0.21/0.44 % (19157)------------------------------
% 0.21/0.44 % (19157)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.44 % (19157)Termination reason: Unknown
% 0.21/0.44 % (19157)Termination phase: Saturation
% 0.21/0.44
% 0.21/0.44 % (19157)Memory used [KB]: 5884
% 0.21/0.44 % (19157)Time elapsed: 0.014 s
% 0.21/0.44 % (19157)Instructions burned: 17 (million)
% 0.21/0.44 % (19157)------------------------------
% 0.21/0.44 % (19157)------------------------------
% 0.21/0.44 % (19159)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)
% 0.21/0.44 % (19159)Instruction limit reached!
% 0.21/0.44 % (19159)------------------------------
% 0.21/0.44 % (19159)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.44 % (19159)Termination reason: Unknown
% 0.21/0.44 % (19159)Termination phase: Function definition elimination
% 0.21/0.44
% 0.21/0.44 % (19159)Memory used [KB]: 1023
% 0.21/0.44 % (19159)Time elapsed: 0.004 s
% 0.21/0.44 % (19159)Instructions burned: 4 (million)
% 0.21/0.44 % (19159)------------------------------
% 0.21/0.44 % (19159)------------------------------
% 0.22/0.44 % (19160)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)
% 0.22/0.45 % (19162)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.22/0.45 % (19160)Refutation not found, incomplete strategy
% 0.22/0.45 % (19160)------------------------------
% 0.22/0.45 % (19160)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.45 % (19160)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.45
% 0.22/0.45
% 0.22/0.45 % (19160)Memory used [KB]: 5500
% 0.22/0.45 % (19160)Time elapsed: 0.006 s
% 0.22/0.45 % (19160)Instructions burned: 6 (million)
% 0.22/0.45 % (19160)------------------------------
% 0.22/0.45 % (19160)------------------------------
% 0.22/0.45 % (19162)Instruction limit reached!
% 0.22/0.45 % (19162)------------------------------
% 0.22/0.45 % (19162)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.45 % (19162)Termination reason: Unknown
% 0.22/0.45 % (19162)Termination phase: Saturation
% 0.22/0.45
% 0.22/0.45 % (19162)Memory used [KB]: 5500
% 0.22/0.45 % (19162)Time elapsed: 0.004 s
% 0.22/0.45 % (19162)Instructions burned: 5 (million)
% 0.22/0.45 % (19162)------------------------------
% 0.22/0.45 % (19162)------------------------------
% 0.22/0.45 % (19164)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.22/0.45 % (19163)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.45 % (19161)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)
% 0.22/0.45 % (19161)Instruction limit reached!
% 0.22/0.45 % (19161)------------------------------
% 0.22/0.45 % (19161)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.45 % (19161)Termination reason: Unknown
% 0.22/0.45 % (19161)Termination phase: Property scanning
% 0.22/0.45
% 0.22/0.45 % (19161)Memory used [KB]: 1023
% 0.22/0.45 % (19161)Time elapsed: 0.003 s
% 0.22/0.45 % (19161)Instructions burned: 3 (million)
% 0.22/0.45 % (19161)------------------------------
% 0.22/0.45 % (19161)------------------------------
% 0.22/0.46 % (19163)Instruction limit reached!
% 0.22/0.46 % (19163)------------------------------
% 0.22/0.46 % (19163)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.46 % (19163)Termination reason: Unknown
% 0.22/0.46 % (19163)Termination phase: Saturation
% 0.22/0.46
% 0.22/0.46 % (19163)Memory used [KB]: 5628
% 0.22/0.46 % (19163)Time elapsed: 0.037 s
% 0.22/0.46 % (19163)Instructions burned: 19 (million)
% 0.22/0.46 % (19163)------------------------------
% 0.22/0.46 % (19163)------------------------------
% 0.22/0.47 % (19167)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.22/0.47 % (19165)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.22/0.47 % (19166)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.22/0.47 % (19166)Refutation not found, incomplete strategy
% 0.22/0.47 % (19166)------------------------------
% 0.22/0.47 % (19166)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.47 % (19166)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.47
% 0.22/0.47
% 0.22/0.47 % (19166)Memory used [KB]: 5500
% 0.22/0.47 % (19166)Time elapsed: 0.004 s
% 0.22/0.47 % (19166)Instructions burned: 4 (million)
% 0.22/0.47 % (19166)------------------------------
% 0.22/0.47 % (19166)------------------------------
% 0.22/0.47 % (19165)Instruction limit reached!
% 0.22/0.47 % (19165)------------------------------
% 0.22/0.47 % (19165)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.47 % (19165)Termination reason: Unknown
% 0.22/0.47 % (19165)Termination phase: Saturation
% 0.22/0.47
% 0.22/0.47 % (19165)Memory used [KB]: 5500
% 0.22/0.47 % (19165)Time elapsed: 0.008 s
% 0.22/0.47 % (19165)Instructions burned: 6 (million)
% 0.22/0.47 % (19165)------------------------------
% 0.22/0.47 % (19165)------------------------------
% 0.22/0.47 % (19167)Instruction limit reached!
% 0.22/0.47 % (19167)------------------------------
% 0.22/0.47 % (19167)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.47 % (19167)Termination reason: Unknown
% 0.22/0.47 % (19167)Termination phase: Saturation
% 0.22/0.47
% 0.22/0.47 % (19167)Memory used [KB]: 5628
% 0.22/0.47 % (19167)Time elapsed: 0.009 s
% 0.22/0.47 % (19167)Instructions burned: 23 (million)
% 0.22/0.47 % (19167)------------------------------
% 0.22/0.47 % (19167)------------------------------
% 0.22/0.48 % (19168)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.22/0.48 % (19168)Instruction limit reached!
% 0.22/0.48 % (19168)------------------------------
% 0.22/0.48 % (19168)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.48 % (19168)Termination reason: Unknown
% 0.22/0.48 % (19168)Termination phase: Saturation
% 0.22/0.48
% 0.22/0.48 % (19168)Memory used [KB]: 5500
% 0.22/0.48 % (19168)Time elapsed: 0.004 s
% 0.22/0.48 % (19168)Instructions burned: 6 (million)
% 0.22/0.48 % (19168)------------------------------
% 0.22/0.48 % (19168)------------------------------
% 0.22/0.48 % (19155)First to succeed.
% 0.22/0.48 % (19169)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.22/0.49 % (19155)Refutation found. Thanks to Tanya!
% 0.22/0.49 % SZS status Theorem for theBenchmark
% 0.22/0.49 % SZS output start Proof for theBenchmark
% 0.22/0.49 thf(func_def_0, type, in: $i > $i > $o).
% 0.22/0.49 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 0.22/0.49 thf(func_def_3, type, setunion: $i > $i).
% 0.22/0.49 thf(func_def_4, type, dsetconstr: $i > ($i > $o) > $i).
% 0.22/0.49 thf(func_def_5, type, iskpair: $i > $o).
% 0.22/0.49 thf(func_def_7, type, kpair: $i > $i > $i).
% 0.22/0.49 thf(func_def_8, type, singleton: $i > $o).
% 0.22/0.49 thf(func_def_9, type, ex1: $i > ($i > $o) > $o).
% 0.22/0.49 thf(func_def_11, type, kfst: $i > $i).
% 0.22/0.49 thf(func_def_28, type, ph1: !>[X0: $tType]:(X0)).
% 0.22/0.49 thf(f255,plain,(
% 0.22/0.49 $false),
% 0.22/0.49 inference(subsumption_resolution,[],[f246,f204])).
% 0.22/0.49 thf(f204,plain,(
% 0.22/0.49 (sK4 != sK5)),
% 0.22/0.49 inference(equality_proxy_clausification,[],[f196])).
% 0.22/0.49 thf(f196,plain,(
% 0.22/0.49 ($false = (sK4 = sK5))),
% 0.22/0.49 inference(binary_proxy_clausification,[],[f187])).
% 0.22/0.49 thf(f187,plain,(
% 0.22/0.49 ((((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK5 @ emptyset)) @ emptyset)) = sK2) => (sK4 = sK5)) = $false)),
% 0.22/0.49 inference(boolean_simplification,[],[f186])).
% 0.22/0.49 thf(f186,plain,(
% 0.22/0.49 ($false = ($true => (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK5 @ emptyset)) @ emptyset)) = sK2) => (sK4 = sK5))))),
% 0.22/0.49 inference(backward_demodulation,[],[f175,f185])).
% 0.22/0.49 thf(f185,plain,(
% 0.22/0.49 ((in @ sK5 @ (setunion @ sK2)) = $true)),
% 0.22/0.49 inference(binary_proxy_clausification,[],[f175])).
% 0.22/0.49 thf(f175,plain,(
% 0.22/0.49 (((in @ sK5 @ (setunion @ sK2)) => (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK5 @ emptyset)) @ emptyset)) = sK2) => (sK4 = sK5))) = $false)),
% 0.22/0.49 inference(beta_eta_normalization,[],[f173])).
% 0.22/0.49 thf(f173,plain,(
% 0.22/0.49 (((^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2) => (sK4 = Y0)))) @ sK5) = $false)),
% 0.22/0.49 inference(sigma_clausification,[],[f162])).
% 0.22/0.49 thf(f162,plain,(
% 0.22/0.49 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2) => (sK4 = Y0))))) = $false)),
% 0.22/0.49 inference(not_proxy_clausification,[],[f148])).
% 0.22/0.49 thf(f148,plain,(
% 0.22/0.49 ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2) => (sK4 = Y0)))))) = $true)),
% 0.22/0.49 inference(boolean_simplification,[],[f147])).
% 0.22/0.49 thf(f147,plain,(
% 0.22/0.49 (($true => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2) => (sK4 = Y0))))))) = $true)),
% 0.22/0.49 inference(boolean_simplification,[],[f146])).
% 0.22/0.49 thf(f146,plain,(
% 0.22/0.49 (((sK2 = sK2) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2) => (sK4 = Y0))))))) = $true)),
% 0.22/0.49 inference(forward_demodulation,[],[f142,f129])).
% 0.22/0.49 thf(f129,plain,(
% 0.22/0.49 ((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK4 @ emptyset)) @ emptyset)) = sK2)),
% 0.22/0.49 inference(equality_proxy_clausification,[],[f115])).
% 0.22/0.49 thf(f115,plain,(
% 0.22/0.49 (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK4 @ emptyset)) @ emptyset)) = sK2) = $true)),
% 0.22/0.49 inference(binary_proxy_clausification,[],[f107])).
% 0.22/0.49 thf(f107,plain,(
% 0.22/0.49 ($true = (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK4 @ emptyset)) @ emptyset)) = sK2) & (in @ sK4 @ (setunion @ sK2))))),
% 0.22/0.49 inference(beta_eta_normalization,[],[f106])).
% 0.22/0.49 thf(f106,plain,(
% 0.22/0.49 (((^[Y0 : $i]: (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2) & (in @ Y0 @ (setunion @ sK2)))) @ sK4) = $true)),
% 0.22/0.49 inference(sigma_clausification,[],[f105])).
% 0.22/0.49 thf(f105,plain,(
% 0.22/0.49 ((?? @ $i @ (^[Y0 : $i]: (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2) & (in @ Y0 @ (setunion @ sK2))))) = $true)),
% 0.22/0.49 inference(boolean_simplification,[],[f104])).
% 0.22/0.49 thf(f104,plain,(
% 0.22/0.49 (($true & (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2) & (in @ Y0 @ (setunion @ sK2)))))) = $true)),
% 0.22/0.49 inference(backward_demodulation,[],[f100,f103])).
% 0.22/0.49 thf(f103,plain,(
% 0.22/0.49 ((in @ sK3 @ (setunion @ sK2)) = $true)),
% 0.22/0.49 inference(binary_proxy_clausification,[],[f100])).
% 0.22/0.49 thf(f100,plain,(
% 0.22/0.49 (((in @ sK3 @ (setunion @ sK2)) & (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2) & (in @ Y0 @ (setunion @ sK2)))))) = $true)),
% 0.22/0.49 inference(beta_eta_normalization,[],[f99])).
% 0.22/0.49 thf(f99,plain,(
% 0.22/0.49 ($true = ((^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) & (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK2) & (in @ Y1 @ (setunion @ sK2))))))) @ sK3))),
% 0.22/0.49 inference(sigma_clausification,[],[f91])).
% 0.22/0.49 thf(f91,plain,(
% 0.22/0.49 ($true = (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) & (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK2) & (in @ Y1 @ (setunion @ sK2)))))))))),
% 0.22/0.49 inference(binary_proxy_clausification,[],[f89])).
% 0.22/0.49 thf(f89,plain,(
% 0.22/0.49 ($false = ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) & (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK2) & (in @ Y1 @ (setunion @ sK2)))))))) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ (setunion @ sK2) @ (^[Y1 : $i]: ((setadjoin @ (setadjoin @ (kfst @ sK2) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK2) @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK2)))) & (in @ Y0 @ (dsetconstr @ (setunion @ sK2) @ (^[Y1 : $i]: ((setadjoin @ (setadjoin @ (kfst @ sK2) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK2) @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK2)))))))))),
% 0.22/0.49 inference(beta_eta_normalization,[],[f88])).
% 0.22/0.49 thf(f88,plain,(
% 0.22/0.49 ($false = ((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ (setunion @ Y0)))))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((setadjoin @ (setadjoin @ (kfst @ Y0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ Y0) @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((setadjoin @ (setadjoin @ (kfst @ Y0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ Y0) @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0))))))))) @ sK2))),
% 0.22/0.49 inference(sigma_clausification,[],[f73])).
% 0.22/0.49 thf(f73,plain,(
% 0.22/0.49 ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ (setunion @ Y0)))))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((setadjoin @ (setadjoin @ (kfst @ Y0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ Y0) @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((setadjoin @ (setadjoin @ (kfst @ Y0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ Y0) @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))))))))) = $false)),
% 0.22/0.49 inference(binary_proxy_clausification,[],[f57])).
% 0.22/0.49 thf(f57,plain,(
% 0.22/0.49 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y3 = Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ (setunion @ Y0)))))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((setadjoin @ (setadjoin @ (kfst @ Y0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ Y0) @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((setadjoin @ (setadjoin @ (kfst @ Y0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ Y0) @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0))))))))))))),
% 0.22/0.49 inference(binary_proxy_clausification,[],[f44])).
% 0.22/0.49 thf(f44,plain,(
% 0.22/0.49 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) = Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y3 = Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ (setunion @ Y0)))))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((setadjoin @ (setadjoin @ (kfst @ Y0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ Y0) @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((setadjoin @ (setadjoin @ (kfst @ Y0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ Y0) @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))))))))))) = $false)),
% 0.22/0.49 inference(binary_proxy_clausification,[],[f41])).
% 0.22/0.49 thf(f41,plain,(
% 0.22/0.49 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) => (Y1 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ Y2)) & (in @ Y3 @ (dsetconstr @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) = Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y3 = Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ (setunion @ Y0)))))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((setadjoin @ (setadjoin @ (kfst @ Y0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ Y0) @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((setadjoin @ (setadjoin @ (kfst @ Y0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ Y0) @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0))))))))))))) = $false)),
% 0.22/0.49 inference(not_proxy_clausification,[],[f40])).
% 0.22/0.49 thf(f40,plain,(
% 0.22/0.49 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) => (Y1 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ Y2)) & (in @ Y3 @ (dsetconstr @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) = Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y3 = Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ (setunion @ Y0)))))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((setadjoin @ (setadjoin @ (kfst @ Y0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ Y0) @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((setadjoin @ (setadjoin @ (kfst @ Y0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ Y0) @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))))))))))))) = $true)),
% 0.22/0.49 inference(beta_eta_normalization,[],[f39])).
% 0.22/0.49 thf(f39,plain,(
% 0.22/0.49 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) => (Y1 = Y3))))) => ((^[Y3 : $i]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (((setadjoin @ Y6 @ emptyset) = Y5) & (in @ Y6 @ Y5))))) @ (dsetconstr @ Y3 @ (^[Y5 : $i]: (Y4 @ Y5))))))) @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ ((^[Y2 : $i]: ((^[Y3 : $i]: (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))))) @ Y1 @ Y0)) = Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((^[Y4 : $i]: ((^[Y5 : $i]: (setadjoin @ (setadjoin @ Y4 @ emptyset) @ (setadjoin @ (setadjoin @ Y4 @ (setadjoin @ Y5 @ emptyset)) @ emptyset))))) @ Y1 @ Y3) = ((^[Y4 : $i]: ((^[Y5 : $i]: (setadjoin @ (setadjoin @ Y4 @ emptyset) @ (setadjoin @ (setadjoin @ Y4 @ (setadjoin @ Y5 @ emptyset)) @ emptyset))))) @ Y2 @ Y0)) => (Y3 = Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y1)) & (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = Y1) & (in @ Y3 @ (setunion @ Y1))))))))) @ Y0) => ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = Y1) & (in @ Y2 @ Y1))))) @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))))) @ (kfst @ Y0) @ Y1) = Y0))))))))))) = $true)),
% 0.22/0.49 inference(definition_unfolding,[],[f29,f37,f38,f35,f27,f33,f32])).
% 0.22/0.49 thf(f32,plain,(
% 0.22/0.49 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
% 0.22/0.49 inference(cnf_transformation,[],[f24])).
% 0.22/0.49 thf(f24,plain,(
% 0.22/0.49 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
% 0.22/0.49 inference(fool_elimination,[],[f23])).
% 0.22/0.49 thf(f23,plain,(
% 0.22/0.49 ((^[X0 : $i, X1 : $i] : (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = kpair)),
% 0.22/0.49 inference(rectify,[],[f2])).
% 0.22/0.49 thf(f2,axiom,(
% 0.22/0.49 ((^[X1 : $i, X2 : $i] : (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) = kpair)),
% 0.22/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpair)).
% 0.22/0.49 thf(f33,plain,(
% 0.22/0.49 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 0.22/0.49 inference(cnf_transformation,[],[f18])).
% 0.22/0.49 thf(f18,plain,(
% 0.22/0.49 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 0.22/0.49 inference(fool_elimination,[],[f17])).
% 0.22/0.49 thf(f17,plain,(
% 0.22/0.49 ((^[X0 : $i] : (? [X1] : ((in @ X1 @ X0) & ((setadjoin @ X1 @ emptyset) = X0)))) = singleton)),
% 0.22/0.49 inference(rectify,[],[f3])).
% 0.22/0.49 thf(f3,axiom,(
% 0.22/0.49 ((^[X0 : $i] : (? [X1] : ((in @ X1 @ X0) & ((setadjoin @ X1 @ emptyset) = X0)))) = singleton)),
% 0.22/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton)).
% 0.22/0.49 thf(f27,plain,(
% 0.22/0.49 (iskpair = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ (setunion @ Y0))))))))))),
% 0.22/0.49 inference(cnf_transformation,[],[f26])).
% 0.22/0.49 thf(f26,plain,(
% 0.22/0.49 (iskpair = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ (setunion @ Y0))))))))))),
% 0.22/0.49 inference(fool_elimination,[],[f25])).
% 0.22/0.49 thf(f25,plain,(
% 0.22/0.49 ((^[X0 : $i] : (? [X1] : (? [X2] : ((in @ X2 @ (setunion @ X0)) & ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = X0)) & (in @ X1 @ (setunion @ X0))))) = iskpair)),
% 0.22/0.49 inference(rectify,[],[f1])).
% 0.22/0.49 thf(f1,axiom,(
% 0.22/0.49 ((^[X0 : $i] : (? [X1] : (? [X2] : ((in @ X2 @ (setunion @ X0)) & ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = X0)) & (in @ X1 @ (setunion @ X0))))) = iskpair)),
% 0.22/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',iskpair)).
% 0.22/0.49 thf(f35,plain,(
% 0.22/0.49 (setukpairinjR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((^[Y4 : $i]: ((^[Y5 : $i]: (setadjoin @ (setadjoin @ Y4 @ emptyset) @ (setadjoin @ (setadjoin @ Y4 @ (setadjoin @ Y5 @ emptyset)) @ emptyset))))) @ Y1 @ Y3) = ((^[Y4 : $i]: ((^[Y5 : $i]: (setadjoin @ (setadjoin @ Y4 @ emptyset) @ (setadjoin @ (setadjoin @ Y4 @ (setadjoin @ Y5 @ emptyset)) @ emptyset))))) @ Y2 @ Y0)) => (Y3 = Y0)))))))))))),
% 0.22/0.49 inference(definition_unfolding,[],[f30,f32,f32])).
% 0.22/0.49 thf(f30,plain,(
% 0.22/0.49 (setukpairinjR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y2 @ Y0)) => (Y3 = Y0)))))))))))),
% 0.22/0.49 inference(cnf_transformation,[],[f12])).
% 0.22/0.49 thf(f12,plain,(
% 0.22/0.49 (setukpairinjR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y2 @ Y0)) => (Y3 = Y0)))))))))))),
% 0.22/0.49 inference(fool_elimination,[],[f11])).
% 0.22/0.49 thf(f11,plain,(
% 0.22/0.49 (! [X0,X1,X2,X3] : (((kpair @ X2 @ X0) = (kpair @ X1 @ X3)) => (X0 = X3)) = setukpairinjR)),
% 0.22/0.49 inference(rectify,[],[f7])).
% 0.22/0.49 thf(f7,axiom,(
% 0.22/0.49 (! [X5,X1,X4,X2] : (((kpair @ X1 @ X2) = (kpair @ X4 @ X5)) => (X2 = X5)) = setukpairinjR)),
% 0.22/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR)).
% 0.22/0.49 thf(f38,plain,(
% 0.22/0.49 (kfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ ((^[Y2 : $i]: ((^[Y3 : $i]: (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))))) @ Y1 @ Y0)) = Y1))))))),
% 0.22/0.49 inference(definition_unfolding,[],[f28,f32])).
% 0.22/0.49 thf(f28,plain,(
% 0.22/0.49 (kfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y1 @ Y0)) = Y1))))))),
% 0.22/0.49 inference(cnf_transformation,[],[f14])).
% 0.22/0.49 thf(f14,plain,(
% 0.22/0.49 (kfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y1 @ Y0)) = Y1))))))),
% 0.22/0.49 inference(fool_elimination,[],[f13])).
% 0.22/0.49 thf(f13,plain,(
% 0.22/0.49 (kfstpairEq = ! [X0,X1] : ((kfst @ (kpair @ X0 @ X1)) = X0))),
% 0.22/0.49 inference(rectify,[],[f6])).
% 0.22/0.49 thf(f6,axiom,(
% 0.22/0.49 (kfstpairEq = ! [X1,X2] : ((kfst @ (kpair @ X1 @ X2)) = X1))),
% 0.22/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstpairEq)).
% 0.22/0.49 thf(f37,plain,(
% 0.22/0.49 (ex1I = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) => (Y1 = Y3))))) => ((^[Y3 : $i]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (((setadjoin @ Y6 @ emptyset) = Y5) & (in @ Y6 @ Y5))))) @ (dsetconstr @ Y3 @ (^[Y5 : $i]: (Y4 @ Y5))))))) @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 0.22/0.49 inference(definition_unfolding,[],[f34,f36])).
% 0.22/0.49 thf(f36,plain,(
% 0.22/0.49 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = Y2) & (in @ Y3 @ Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 0.22/0.49 inference(definition_unfolding,[],[f31,f33])).
% 0.22/0.49 thf(f31,plain,(
% 0.22/0.49 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 0.22/0.49 inference(cnf_transformation,[],[f20])).
% 0.22/0.49 thf(f20,plain,(
% 0.22/0.49 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 0.22/0.49 inference(fool_elimination,[],[f19])).
% 0.22/0.49 thf(f19,plain,(
% 0.22/0.49 ((^[X0 : $i, X1 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))) = ex1)),
% 0.22/0.49 inference(rectify,[],[f4])).
% 0.22/0.49 thf(f4,axiom,(
% 0.22/0.49 ((^[X0 : $i, X3 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X1 : $i] : (X3 @ X1))))) = ex1)),
% 0.22/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1)).
% 0.22/0.49 thf(f34,plain,(
% 0.22/0.49 (ex1I = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) => (Y1 = Y3))))) => (ex1 @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 0.22/0.49 inference(cnf_transformation,[],[f22])).
% 0.22/0.49 thf(f22,plain,(
% 0.22/0.49 (ex1I = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) => (Y1 = Y3))))) => (ex1 @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 0.22/0.49 inference(fool_elimination,[],[f21])).
% 0.22/0.49 thf(f21,plain,(
% 0.22/0.49 (ex1I = ! [X0 : $i > $o,X1,X2] : ((in @ X1 @ X2) => ((X0 @ X1) => (! [X3] : ((in @ X3 @ X2) => ((X0 @ X3) => (X1 = X3))) => (ex1 @ X2 @ (^[X4 : $i] : (X0 @ X4)))))))),
% 0.22/0.49 inference(rectify,[],[f5])).
% 0.22/0.49 thf(f5,axiom,(
% 0.22/0.49 (ex1I = ! [X3 : $i > $o,X1,X0] : ((in @ X1 @ X0) => ((X3 @ X1) => (! [X2] : ((in @ X2 @ X0) => ((X3 @ X2) => (X1 = X2))) => (ex1 @ X0 @ (^[X2 : $i] : (X3 @ X2)))))))),
% 0.22/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I)).
% 0.22/0.49 thf(f29,plain,(
% 0.22/0.49 ((~ (ex1I => (kfstpairEq => (setukpairinjR => (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0))))))))))) = $true)),
% 0.22/0.49 inference(cnf_transformation,[],[f16])).
% 0.22/0.49 thf(f16,plain,(
% 0.22/0.49 ((~ (ex1I => (kfstpairEq => (setukpairinjR => (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0))))))))))) = $true)),
% 0.22/0.49 inference(fool_elimination,[],[f15])).
% 0.22/0.49 thf(f15,plain,(
% 0.22/0.49 ~(ex1I => (kfstpairEq => (setukpairinjR => ! [X0] : ((iskpair @ X0) => (singleton @ (dsetconstr @ (setunion @ X0) @ (^[X1 : $i] : (((kpair @ (kfst @ X0) @ X1) = X0)))))))))),
% 0.22/0.49 inference(rectify,[],[f9])).
% 0.22/0.49 thf(f9,negated_conjecture,(
% 0.22/0.49 ~(ex1I => (kfstpairEq => (setukpairinjR => ! [X5] : ((iskpair @ X5) => (singleton @ (dsetconstr @ (setunion @ X5) @ (^[X1 : $i] : (((kpair @ (kfst @ X5) @ X1) = X5)))))))))),
% 0.22/0.49 inference(negated_conjecture,[],[f8])).
% 0.22/0.49 thf(f8,conjecture,(
% 0.22/0.49 ex1I => (kfstpairEq => (setukpairinjR => ! [X5] : ((iskpair @ X5) => (singleton @ (dsetconstr @ (setunion @ X5) @ (^[X1 : $i] : (((kpair @ (kfst @ X5) @ X1) = X5))))))))),
% 0.22/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndsingleton)).
% 0.22/0.49 thf(f142,plain,(
% 0.22/0.49 ((((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK4 @ emptyset)) @ emptyset)) = sK2) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => (((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2) => (sK4 = Y0))))))) = $true)),
% 0.22/0.49 inference(backward_demodulation,[],[f127,f138])).
% 0.22/0.49 thf(f138,plain,(
% 0.22/0.49 ((kfst @ sK2) = sK3)),
% 0.22/0.49 inference(superposition,[],[f67,f129])).
% 0.22/0.49 thf(f67,plain,(
% 0.22/0.49 ( ! [X2 : $i,X1 : $i] : (((kfst @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = X2)) )),
% 0.22/0.49 inference(equality_proxy_clausification,[],[f66])).
% 0.22/0.49 thf(f66,plain,(
% 0.22/0.49 ( ! [X2 : $i,X1 : $i] : ((((kfst @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = X2) = $true)) )),
% 0.22/0.49 inference(beta_eta_normalization,[],[f65])).
% 0.22/0.49 thf(f65,plain,(
% 0.22/0.49 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((kfst @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = Y0)) @ X2) = $true)) )),
% 0.22/0.49 inference(pi_clausification,[],[f64])).
% 0.22/0.49 thf(f64,plain,(
% 0.22/0.49 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((kfst @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = Y0))))) )),
% 0.22/0.49 inference(beta_eta_normalization,[],[f63])).
% 0.22/0.49 thf(f63,plain,(
% 0.22/0.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) = Y1)))) @ X1) = $true)) )),
% 0.22/0.49 inference(pi_clausification,[],[f58])).
% 0.22/0.49 thf(f58,plain,(
% 0.22/0.49 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) = Y1))))) = $true)),
% 0.22/0.49 inference(binary_proxy_clausification,[],[f44])).
% 0.22/0.49 thf(f127,plain,(
% 0.22/0.49 ((((setadjoin @ (setadjoin @ (kfst @ sK2) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK2) @ (setadjoin @ sK4 @ emptyset)) @ emptyset)) = sK2) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => (((setadjoin @ (setadjoin @ (kfst @ sK2) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK2) @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2) => (sK4 = Y0))))))) = $true)),
% 0.22/0.49 inference(boolean_simplification,[],[f126])).
% 0.22/0.49 thf(f126,plain,(
% 0.22/0.49 (($true => (((setadjoin @ (setadjoin @ (kfst @ sK2) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK2) @ (setadjoin @ sK4 @ emptyset)) @ emptyset)) = sK2) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => (((setadjoin @ (setadjoin @ (kfst @ sK2) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK2) @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2) => (sK4 = Y0)))))))) = $true)),
% 0.22/0.49 inference(superposition,[],[f98,f117])).
% 0.22/0.49 thf(f117,plain,(
% 0.22/0.49 ((in @ sK4 @ (setunion @ sK2)) = $true)),
% 0.22/0.49 inference(boolean_simplification,[],[f116])).
% 0.22/0.49 thf(f116,plain,(
% 0.22/0.49 (($true & (in @ sK4 @ (setunion @ sK2))) = $true)),
% 0.22/0.49 inference(backward_demodulation,[],[f107,f115])).
% 0.22/0.49 thf(f98,plain,(
% 0.22/0.49 ( ! [X0 : $i] : ((((in @ X0 @ (setunion @ sK2)) => (((setadjoin @ (setadjoin @ (kfst @ sK2) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK2) @ (setadjoin @ X0 @ emptyset)) @ emptyset)) = sK2) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => (((setadjoin @ (setadjoin @ (kfst @ sK2) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK2) @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2) => (X0 = Y0)))))))) = $true)) )),
% 0.22/0.49 inference(boolean_simplification,[],[f97])).
% 0.22/0.49 thf(f97,plain,(
% 0.22/0.49 ( ! [X0 : $i] : ((((in @ X0 @ (setunion @ sK2)) => (((setadjoin @ (setadjoin @ (kfst @ sK2) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK2) @ (setadjoin @ X0 @ emptyset)) @ emptyset)) = sK2) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => (((setadjoin @ (setadjoin @ (kfst @ sK2) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK2) @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2) => (X0 = Y0))))) => $false))) = $true)) )),
% 0.22/0.49 inference(beta_eta_normalization,[],[f95])).
% 0.22/0.49 thf(f95,plain,(
% 0.22/0.49 ( ! [X0 : $i] : (($true = ((in @ X0 @ (setunion @ sK2)) => (((^[Y0 : $i]: ((setadjoin @ (setadjoin @ (kfst @ sK2) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK2) @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2)) @ X0) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => (((^[Y1 : $i]: ((setadjoin @ (setadjoin @ (kfst @ sK2) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK2) @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK2)) @ Y0) => (X0 = Y0))))) => $false))))) )),
% 0.22/0.49 inference(superposition,[],[f55,f93])).
% 0.22/0.49 thf(f93,plain,(
% 0.22/0.49 ((?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ (setunion @ sK2) @ (^[Y1 : $i]: ((setadjoin @ (setadjoin @ (kfst @ sK2) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK2) @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK2)))) & (in @ Y0 @ (dsetconstr @ (setunion @ sK2) @ (^[Y1 : $i]: ((setadjoin @ (setadjoin @ (kfst @ sK2) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK2) @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK2))))))) = $false)),
% 0.22/0.49 inference(boolean_simplification,[],[f92])).
% 0.22/0.49 thf(f92,plain,(
% 0.22/0.49 ($false = ($true => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ (setunion @ sK2) @ (^[Y1 : $i]: ((setadjoin @ (setadjoin @ (kfst @ sK2) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK2) @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK2)))) & (in @ Y0 @ (dsetconstr @ (setunion @ sK2) @ (^[Y1 : $i]: ((setadjoin @ (setadjoin @ (kfst @ sK2) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK2) @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK2)))))))))),
% 0.22/0.49 inference(backward_demodulation,[],[f89,f91])).
% 0.22/0.49 thf(f55,plain,(
% 0.22/0.49 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = ((in @ X2 @ X1) => ((X3 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((X3 @ Y0) => (X2 = Y0))))) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X1 @ X3)) & (in @ Y0 @ (dsetconstr @ X1 @ X3)))))))))) )),
% 0.22/0.49 inference(beta_eta_normalization,[],[f54])).
% 0.22/0.49 thf(f54,plain,(
% 0.22/0.49 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: ((in @ X2 @ X1) => ((Y0 @ X2) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((Y0 @ Y1) => (X2 = Y1))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X1 @ Y0)) & (in @ Y1 @ (dsetconstr @ X1 @ Y0))))))))) @ X3) = $true)) )),
% 0.22/0.49 inference(pi_clausification,[],[f53])).
% 0.22/0.49 thf(f53,plain,(
% 0.22/0.49 ( ! [X2 : $i,X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X2 @ X1) => ((Y0 @ X2) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((Y0 @ Y1) => (X2 = Y1))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X1 @ Y0)) & (in @ Y1 @ (dsetconstr @ X1 @ Y0)))))))))) = $true)) )),
% 0.22/0.49 inference(beta_eta_normalization,[],[f52])).
% 0.22/0.49 thf(f52,plain,(
% 0.22/0.49 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ X1) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((Y1 @ Y2) => (Y0 = Y2))))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ X1 @ Y1)) & (in @ Y2 @ (dsetconstr @ X1 @ Y1))))))))))) @ X2) = $true)) )),
% 0.22/0.49 inference(pi_clausification,[],[f51])).
% 0.22/0.49 thf(f51,plain,(
% 0.22/0.49 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ X1) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((Y1 @ Y2) => (Y0 = Y2))))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ X1 @ Y1)) & (in @ Y2 @ (dsetconstr @ X1 @ Y1)))))))))))) = $true)) )),
% 0.22/0.49 inference(beta_eta_normalization,[],[f50])).
% 0.22/0.49 thf(f50,plain,(
% 0.22/0.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) => (Y1 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ Y2)) & (in @ Y3 @ (dsetconstr @ Y0 @ Y2))))))))))))) @ X1) = $true)) )),
% 0.22/0.49 inference(pi_clausification,[],[f45])).
% 0.22/0.49 thf(f45,plain,(
% 0.22/0.49 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) => (Y1 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ Y2)) & (in @ Y3 @ (dsetconstr @ Y0 @ Y2)))))))))))))) = $true)),
% 0.22/0.49 inference(binary_proxy_clausification,[],[f41])).
% 0.22/0.49 thf(f246,plain,(
% 0.22/0.49 (sK4 = sK5)),
% 0.22/0.49 inference(equality_proxy_clausification,[],[f231])).
% 0.22/0.49 thf(f231,plain,(
% 0.22/0.49 ((sK5 = sK4) = $true)),
% 0.22/0.49 inference(boolean_simplification,[],[f227])).
% 0.22/0.49 thf(f227,plain,(
% 0.22/0.49 (($true => (sK5 = sK4)) = $true)),
% 0.22/0.49 inference(superposition,[],[f137,f197])).
% 0.22/0.49 thf(f197,plain,(
% 0.22/0.49 ($true = ((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK5 @ emptyset)) @ emptyset)) = sK2))),
% 0.22/0.49 inference(binary_proxy_clausification,[],[f187])).
% 0.22/0.49 thf(f137,plain,(
% 0.22/0.49 ( ! [X0 : $i,X1 : $i] : (((((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = sK2) => (X1 = sK4)) = $true)) )),
% 0.22/0.49 inference(superposition,[],[f86,f129])).
% 0.22/0.49 thf(f86,plain,(
% 0.22/0.49 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X4 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (X4 = X1)) = $true)) )),
% 0.22/0.49 inference(beta_eta_normalization,[],[f85])).
% 0.22/0.49 thf(f85,plain,(
% 0.22/0.49 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((^[Y0 : $i]: (((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (Y0 = X1))) @ X4) = $true)) )),
% 0.22/0.49 inference(pi_clausification,[],[f84])).
% 0.22/0.49 thf(f84,plain,(
% 0.22/0.49 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (Y0 = X1)))) = $true)) )),
% 0.22/0.49 inference(beta_eta_normalization,[],[f83])).
% 0.22/0.49 thf(f83,plain,(
% 0.22/0.49 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (Y1 = X1))))) @ X3) = $true)) )),
% 0.22/0.49 inference(pi_clausification,[],[f82])).
% 0.22/0.49 thf(f82,plain,(
% 0.22/0.49 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (Y1 = X1)))))) = $true)) )),
% 0.22/0.49 inference(beta_eta_normalization,[],[f81])).
% 0.22/0.49 thf(f81,plain,(
% 0.22/0.49 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (Y2 = X1))))))) @ X2) = $true)) )),
% 0.22/0.49 inference(pi_clausification,[],[f80])).
% 0.22/0.49 thf(f80,plain,(
% 0.22/0.49 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (Y2 = X1)))))))) = $true)) )),
% 0.22/0.49 inference(beta_eta_normalization,[],[f79])).
% 0.22/0.49 thf(f79,plain,(
% 0.22/0.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y3 = Y0))))))))) @ X1) = $true)) )),
% 0.22/0.49 inference(pi_clausification,[],[f74])).
% 0.22/0.49 thf(f74,plain,(
% 0.22/0.49 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y3 = Y0)))))))))) = $true)),
% 0.22/0.49 inference(binary_proxy_clausification,[],[f57])).
% 0.22/0.49 % SZS output end Proof for theBenchmark
% 0.22/0.49 % (19155)------------------------------
% 0.22/0.49 % (19155)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.49 % (19155)Termination reason: Refutation
% 0.22/0.49
% 0.22/0.49 % (19155)Memory used [KB]: 6268
% 0.22/0.49 % (19155)Time elapsed: 0.064 s
% 0.22/0.49 % (19155)Instructions burned: 98 (million)
% 0.22/0.49 % (19155)------------------------------
% 0.22/0.49 % (19155)------------------------------
% 0.22/0.49 % (19143)Success in time 0.109 s
%------------------------------------------------------------------------------