TSTP Solution File: SEU637^2 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEU637^2 : 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 15:41:54 EDT 2024
% Result : Theorem 0.20s 0.53s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU637^2 : TPTP v8.2.0. Released v3.7.0.
% 0.12/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 14:26:24 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.35 This is a TH0_THM_EQU_NAR problem
% 0.12/0.36 Running higher-order theorem proving
% 0.12/0.36 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.12/0.38 % (1852)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.12/0.39 % (1853)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)
% 0.12/0.39 % (1854)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)
% 0.12/0.39 % (1856)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)
% 0.12/0.39 % (1858)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.12/0.39 % (1855)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.39 % (1857)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)
% 0.12/0.39 % (1856)Instruction limit reached!
% 0.12/0.39 % (1856)------------------------------
% 0.12/0.39 % (1856)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.39 % (1856)Termination reason: Unknown
% 0.12/0.39 % (1856)Termination phase: shuffling
% 0.12/0.39
% 0.12/0.39 % (1856)Memory used [KB]: 1023
% 0.12/0.39 % (1856)Time elapsed: 0.004 s
% 0.12/0.39 % (1856)Instructions burned: 2 (million)
% 0.12/0.39 % (1856)------------------------------
% 0.12/0.39 % (1856)------------------------------
% 0.12/0.39 % (1855)Instruction limit reached!
% 0.12/0.39 % (1855)------------------------------
% 0.12/0.39 % (1855)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.39 % (1855)Termination reason: Unknown
% 0.12/0.39 % (1855)Termination phase: Property scanning
% 0.12/0.39
% 0.12/0.39 % (1855)Memory used [KB]: 1023
% 0.12/0.39 % (1855)Time elapsed: 0.005 s
% 0.12/0.39 % (1855)Instructions burned: 2 (million)
% 0.12/0.39 % (1855)------------------------------
% 0.12/0.39 % (1855)------------------------------
% 0.12/0.39 % (1853)Instruction limit reached!
% 0.12/0.39 % (1853)------------------------------
% 0.12/0.39 % (1853)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.39 % (1853)Termination reason: Unknown
% 0.12/0.39 % (1853)Termination phase: Function definition elimination
% 0.12/0.39
% 0.12/0.39 % (1853)Memory used [KB]: 1023
% 0.12/0.39 % (1853)Time elapsed: 0.006 s
% 0.12/0.39 % (1853)Instructions burned: 4 (million)
% 0.12/0.39 % (1853)------------------------------
% 0.12/0.39 % (1853)------------------------------
% 0.12/0.41 % (1858)Instruction limit reached!
% 0.12/0.41 % (1858)------------------------------
% 0.12/0.41 % (1858)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.41 % (1858)Termination reason: Unknown
% 0.12/0.41 % (1858)Termination phase: Saturation
% 0.12/0.41
% 0.12/0.41 % (1858)Memory used [KB]: 5628
% 0.12/0.41 % (1858)Time elapsed: 0.023 s
% 0.12/0.41 % (1858)Instructions burned: 18 (million)
% 0.12/0.41 % (1858)------------------------------
% 0.12/0.41 % (1858)------------------------------
% 0.20/0.42 % (1861)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)
% 0.20/0.42 % (1854)Instruction limit reached!
% 0.20/0.42 % (1854)------------------------------
% 0.20/0.42 % (1854)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.42 % (1854)Termination reason: Unknown
% 0.20/0.42 % (1854)Termination phase: Saturation
% 0.20/0.42
% 0.20/0.42 % (1854)Memory used [KB]: 5628
% 0.20/0.42 % (1854)Time elapsed: 0.031 s
% 0.20/0.42 % (1854)Instructions burned: 27 (million)
% 0.20/0.42 % (1854)------------------------------
% 0.20/0.42 % (1854)------------------------------
% 0.20/0.42 % (1859)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)
% 0.20/0.42 % (1860)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)
% 0.20/0.42 % (1859)Instruction limit reached!
% 0.20/0.42 % (1859)------------------------------
% 0.20/0.42 % (1859)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.42 % (1859)Termination reason: Unknown
% 0.20/0.42 % (1859)Termination phase: Preprocessing 3
% 0.20/0.42
% 0.20/0.42 % (1859)Memory used [KB]: 1023
% 0.20/0.42 % (1859)Time elapsed: 0.005 s
% 0.20/0.42 % (1859)Instructions burned: 3 (million)
% 0.20/0.42 % (1859)------------------------------
% 0.20/0.42 % (1859)------------------------------
% 0.20/0.43 % (1861)Instruction limit reached!
% 0.20/0.43 % (1861)------------------------------
% 0.20/0.43 % (1861)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.43 % (1861)Termination reason: Unknown
% 0.20/0.43 % (1861)Termination phase: Saturation
% 0.20/0.43
% 0.20/0.43 % (1861)Memory used [KB]: 5628
% 0.20/0.43 % (1861)Time elapsed: 0.014 s
% 0.20/0.43 % (1861)Instructions burned: 16 (million)
% 0.20/0.43 % (1861)------------------------------
% 0.20/0.43 % (1861)------------------------------
% 0.20/0.44 % (1862)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)
% 0.20/0.45 % (1863)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)
% 0.20/0.45 % (1862)Instruction limit reached!
% 0.20/0.45 % (1862)------------------------------
% 0.20/0.45 % (1862)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.45 % (1862)Termination reason: Unknown
% 0.20/0.45 % (1862)Termination phase: Property scanning
% 0.20/0.45
% 0.20/0.45 % (1862)Memory used [KB]: 1023
% 0.20/0.45 % (1862)Time elapsed: 0.004 s
% 0.20/0.45 % (1862)Instructions burned: 3 (million)
% 0.20/0.45 % (1862)------------------------------
% 0.20/0.45 % (1862)------------------------------
% 0.20/0.45 % (1860)Instruction limit reached!
% 0.20/0.45 % (1860)------------------------------
% 0.20/0.45 % (1860)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.45 % (1860)Termination reason: Unknown
% 0.20/0.45 % (1860)Termination phase: Saturation
% 0.20/0.45
% 0.20/0.45 % (1860)Memory used [KB]: 5756
% 0.20/0.45 % (1860)Time elapsed: 0.030 s
% 0.20/0.45 % (1860)Instructions burned: 37 (million)
% 0.20/0.45 % (1860)------------------------------
% 0.20/0.45 % (1860)------------------------------
% 0.20/0.45 % (1865)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.20/0.45 % (1864)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.46 % (1864)Instruction limit reached!
% 0.20/0.46 % (1864)------------------------------
% 0.20/0.46 % (1864)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.46 % (1864)Termination reason: Unknown
% 0.20/0.46 % (1864)Termination phase: Saturation
% 0.20/0.46
% 0.20/0.46 % (1864)Memory used [KB]: 1023
% 0.20/0.46 % (1864)Time elapsed: 0.009 s
% 0.20/0.46 % (1864)Instructions burned: 7 (million)
% 0.20/0.46 % (1864)------------------------------
% 0.20/0.46 % (1864)------------------------------
% 0.20/0.46 % (1867)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)
% 0.20/0.46 % (1867)Instruction limit reached!
% 0.20/0.46 % (1867)------------------------------
% 0.20/0.46 % (1867)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.46 % (1867)Termination reason: Unknown
% 0.20/0.46 % (1867)Termination phase: Preprocessing 3
% 0.20/0.46
% 0.20/0.46 % (1867)Memory used [KB]: 1023
% 0.20/0.46 % (1867)Time elapsed: 0.004 s
% 0.20/0.46 % (1867)Instructions burned: 3 (million)
% 0.20/0.46 % (1867)------------------------------
% 0.20/0.46 % (1867)------------------------------
% 0.20/0.46 % (1865)Instruction limit reached!
% 0.20/0.46 % (1865)------------------------------
% 0.20/0.46 % (1865)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.46 % (1865)Termination reason: Unknown
% 0.20/0.46 % (1865)Termination phase: Saturation
% 0.20/0.46
% 0.20/0.46 % (1865)Memory used [KB]: 5884
% 0.20/0.46 % (1865)Time elapsed: 0.013 s
% 0.20/0.46 % (1865)Instructions burned: 16 (million)
% 0.20/0.46 % (1865)------------------------------
% 0.20/0.46 % (1865)------------------------------
% 0.20/0.47 % (1866)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)
% 0.20/0.47 % (1866)Instruction limit reached!
% 0.20/0.47 % (1866)------------------------------
% 0.20/0.47 % (1866)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.47 % (1866)Termination reason: Unknown
% 0.20/0.47 % (1866)Termination phase: Function definition elimination
% 0.20/0.47
% 0.20/0.47 % (1866)Memory used [KB]: 1023
% 0.20/0.47 % (1866)Time elapsed: 0.004 s
% 0.20/0.47 % (1866)Instructions burned: 4 (million)
% 0.20/0.47 % (1866)------------------------------
% 0.20/0.47 % (1866)------------------------------
% 0.20/0.48 % (1869)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)
% 0.20/0.48 % (1870)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.20/0.48 % (1868)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)
% 0.20/0.48 % (1869)Instruction limit reached!
% 0.20/0.48 % (1869)------------------------------
% 0.20/0.48 % (1869)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.48 % (1869)Termination reason: Unknown
% 0.20/0.48 % (1869)Termination phase: Function definition elimination
% 0.20/0.48
% 0.20/0.48 % (1869)Memory used [KB]: 1023
% 0.20/0.48 % (1869)Time elapsed: 0.004 s
% 0.20/0.48 % (1869)Instructions burned: 4 (million)
% 0.20/0.48 % (1869)------------------------------
% 0.20/0.48 % (1869)------------------------------
% 0.20/0.48 % (1870)Instruction limit reached!
% 0.20/0.48 % (1870)------------------------------
% 0.20/0.48 % (1870)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.48 % (1870)Termination reason: Unknown
% 0.20/0.48 % (1870)Termination phase: Property scanning
% 0.20/0.48
% 0.20/0.48 % (1870)Memory used [KB]: 1023
% 0.20/0.48 % (1870)Time elapsed: 0.004 s
% 0.20/0.48 % (1870)Instructions burned: 4 (million)
% 0.20/0.48 % (1870)------------------------------
% 0.20/0.48 % (1870)------------------------------
% 0.20/0.48 % (1868)Refutation not found, incomplete strategy
% 0.20/0.48 % (1868)------------------------------
% 0.20/0.48 % (1868)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.48 % (1868)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.48
% 0.20/0.48
% 0.20/0.48 % (1868)Memory used [KB]: 5500
% 0.20/0.48 % (1868)Time elapsed: 0.006 s
% 0.20/0.48 % (1868)Instructions burned: 6 (million)
% 0.20/0.48 % (1868)------------------------------
% 0.20/0.48 % (1868)------------------------------
% 0.20/0.48 % (1871)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 (2998ds/18Mi)
% 0.20/0.50 % (1871)Instruction limit reached!
% 0.20/0.50 % (1871)------------------------------
% 0.20/0.50 % (1871)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.50 % (1871)Termination reason: Unknown
% 0.20/0.50 % (1871)Termination phase: Saturation
% 0.20/0.50
% 0.20/0.50 % (1871)Memory used [KB]: 5756
% 0.20/0.50 % (1871)Time elapsed: 0.014 s
% 0.20/0.50 % (1871)Instructions burned: 19 (million)
% 0.20/0.50 % (1871)------------------------------
% 0.20/0.50 % (1871)------------------------------
% 0.20/0.50 % (1872)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2998ds/710Mi)
% 0.20/0.50 % (1873)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2998ds/6Mi)
% 0.20/0.50 % (1874)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 (2998ds/902Mi)
% 0.20/0.50 % (1873)Instruction limit reached!
% 0.20/0.50 % (1873)------------------------------
% 0.20/0.50 % (1873)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.50 % (1873)Termination reason: Unknown
% 0.20/0.50 % (1873)Termination phase: Saturation
% 0.20/0.50
% 0.20/0.50 % (1873)Memory used [KB]: 5500
% 0.20/0.50 % (1873)Time elapsed: 0.006 s
% 0.20/0.50 % (1873)Instructions burned: 7 (million)
% 0.20/0.50 % (1873)------------------------------
% 0.20/0.50 % (1873)------------------------------
% 0.20/0.51 % (1875)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 (2998ds/21Mi)
% 0.20/0.52 % (1876)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2998ds/5Mi)
% 0.20/0.52 % (1876)Instruction limit reached!
% 0.20/0.52 % (1876)------------------------------
% 0.20/0.52 % (1876)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.52 % (1876)Termination reason: Unknown
% 0.20/0.52 % (1876)Termination phase: Saturation
% 0.20/0.52
% 0.20/0.52 % (1876)Memory used [KB]: 5500
% 0.20/0.52 % (1876)Time elapsed: 0.005 s
% 0.20/0.52 % (1876)Instructions burned: 6 (million)
% 0.20/0.52 % (1876)------------------------------
% 0.20/0.52 % (1876)------------------------------
% 0.20/0.52 % (1863)First to succeed.
% 0.20/0.52 % (1852)Instruction limit reached!
% 0.20/0.52 % (1852)------------------------------
% 0.20/0.52 % (1852)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.52 % (1852)Termination reason: Unknown
% 0.20/0.52 % (1852)Termination phase: Saturation
% 0.20/0.52
% 0.20/0.52 % (1852)Memory used [KB]: 6780
% 0.20/0.52 % (1852)Time elapsed: 0.147 s
% 0.20/0.52 % (1852)Instructions burned: 184 (million)
% 0.20/0.52 % (1852)------------------------------
% 0.20/0.52 % (1852)------------------------------
% 0.20/0.53 % (1875)Instruction limit reached!
% 0.20/0.53 % (1875)------------------------------
% 0.20/0.53 % (1875)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.53 % (1875)Termination reason: Unknown
% 0.20/0.53 % (1875)Termination phase: Saturation
% 0.20/0.53
% 0.20/0.53 % (1875)Memory used [KB]: 5628
% 0.20/0.53 % (1875)Time elapsed: 0.016 s
% 0.20/0.53 % (1875)Instructions burned: 21 (million)
% 0.20/0.53 % (1875)------------------------------
% 0.20/0.53 % (1875)------------------------------
% 0.20/0.53 % (1863)Refutation found. Thanks to Tanya!
% 0.20/0.53 % SZS status Theorem for theBenchmark
% 0.20/0.53 % SZS output start Proof for theBenchmark
% 0.20/0.53 thf(func_def_0, type, in: $i > $i > $o).
% 0.20/0.53 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 0.20/0.53 thf(func_def_3, type, dsetconstr: $i > ($i > $o) > $i).
% 0.20/0.53 thf(func_def_11, type, singleton: $i > $o).
% 0.20/0.53 thf(func_def_26, type, ph1: !>[X0: $tType]:(X0)).
% 0.20/0.53 thf(func_def_28, type, sK3: $i > $o).
% 0.20/0.53 thf(f657,plain,(
% 0.20/0.53 $false),
% 0.20/0.53 inference(avatar_sat_refutation,[],[f325,f455,f656])).
% 0.20/0.53 thf(f656,plain,(
% 0.20/0.53 ~spl0_1),
% 0.20/0.53 inference(avatar_contradiction_clause,[],[f655])).
% 0.20/0.53 thf(f655,plain,(
% 0.20/0.53 $false | ~spl0_1),
% 0.20/0.53 inference(subsumption_resolution,[],[f640,f595])).
% 0.20/0.53 thf(f595,plain,(
% 0.20/0.53 (sK4 != sK6) | ~spl0_1),
% 0.20/0.53 inference(equality_proxy_clausification,[],[f550])).
% 0.20/0.53 thf(f550,plain,(
% 0.20/0.53 ($false = (sK6 = sK4)) | ~spl0_1),
% 0.20/0.53 inference(not_proxy_clausification,[],[f543])).
% 0.20/0.53 thf(f543,plain,(
% 0.20/0.53 ((~ (sK6 = sK4)) = $true) | ~spl0_1),
% 0.20/0.53 inference(boolean_simplification,[],[f537])).
% 0.20/0.53 thf(f537,plain,(
% 0.20/0.53 ($true = ((sK6 = sK4) => $false)) | ~spl0_1),
% 0.20/0.53 inference(superposition,[],[f104,f522])).
% 0.20/0.53 thf(f522,plain,(
% 0.20/0.53 ($false = (in @ sK6 @ (setadjoin @ sK4 @ emptyset))) | ~spl0_1),
% 0.20/0.53 inference(binary_proxy_clausification,[],[f520])).
% 0.20/0.53 thf(f520,plain,(
% 0.20/0.53 ($false = ((in @ sK6 @ (dsetconstr @ sK2 @ sK3)) => (in @ sK6 @ (setadjoin @ sK4 @ emptyset)))) | ~spl0_1),
% 0.20/0.53 inference(beta_eta_normalization,[],[f515])).
% 0.20/0.53 thf(f515,plain,(
% 0.20/0.53 ($false = ((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK3)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset)))) @ sK6)) | ~spl0_1),
% 0.20/0.53 inference(sigma_clausification,[],[f512])).
% 0.20/0.53 thf(f512,plain,(
% 0.20/0.53 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK3)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset)))))) | ~spl0_1),
% 0.20/0.53 inference(not_proxy_clausification,[],[f321])).
% 0.20/0.53 thf(f321,plain,(
% 0.20/0.53 ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK3)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset)))))) = $true) | ~spl0_1),
% 0.20/0.53 inference(avatar_component_clause,[],[f320])).
% 0.20/0.53 thf(f320,plain,(
% 0.20/0.53 spl0_1 <=> ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK3)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset)))))) = $true)),
% 0.20/0.53 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.20/0.53 thf(f104,plain,(
% 0.20/0.53 ( ! [X2 : $i,X1 : $i] : (($true = ((X2 = X1) => (in @ X2 @ (setadjoin @ X1 @ emptyset))))) )),
% 0.20/0.53 inference(beta_eta_normalization,[],[f103])).
% 0.20/0.53 thf(f103,plain,(
% 0.20/0.53 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((Y0 = X1) => (in @ Y0 @ (setadjoin @ X1 @ emptyset)))) @ X2) = $true)) )),
% 0.20/0.53 inference(pi_clausification,[],[f100])).
% 0.20/0.53 thf(f100,plain,(
% 0.20/0.53 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((Y0 = X1) => (in @ Y0 @ (setadjoin @ X1 @ emptyset))))) = $true)) )),
% 0.20/0.53 inference(beta_eta_normalization,[],[f99])).
% 0.20/0.53 thf(f99,plain,(
% 0.20/0.53 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))) @ X1))) )),
% 0.20/0.53 inference(pi_clausification,[],[f96])).
% 0.20/0.53 thf(f96,plain,(
% 0.20/0.53 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) = $true)),
% 0.20/0.53 inference(binary_proxy_clausification,[],[f81])).
% 0.20/0.53 thf(f81,plain,(
% 0.20/0.53 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1)))))))))))))),
% 0.20/0.53 inference(binary_proxy_clausification,[],[f78])).
% 0.20/0.53 thf(f78,plain,(
% 0.20/0.53 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))))))),
% 0.20/0.53 inference(boolean_simplification,[],[f77])).
% 0.20/0.53 thf(f77,plain,(
% 0.20/0.53 ($false = ($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1)))))))))))))))),
% 0.20/0.53 inference(backward_demodulation,[],[f50,f76])).
% 0.20/0.53 thf(f76,plain,(
% 0.20/0.53 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))))),
% 0.20/0.53 inference(binary_proxy_clausification,[],[f50])).
% 0.20/0.53 thf(f50,plain,(
% 0.20/0.53 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1)))))))))))))))),
% 0.20/0.53 inference(binary_proxy_clausification,[],[f47])).
% 0.20/0.53 thf(f47,plain,(
% 0.20/0.53 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))))))) = $false)),
% 0.20/0.53 inference(boolean_simplification,[],[f46])).
% 0.20/0.53 thf(f46,plain,(
% 0.20/0.53 ($false = ($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1)))))))))))))))))),
% 0.20/0.53 inference(backward_demodulation,[],[f43,f45])).
% 0.20/0.53 thf(f45,plain,(
% 0.20/0.53 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))))),
% 0.20/0.53 inference(binary_proxy_clausification,[],[f43])).
% 0.20/0.53 thf(f43,plain,(
% 0.20/0.53 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1)))))))))))))))))),
% 0.20/0.53 inference(boolean_simplification,[],[f42])).
% 0.20/0.53 thf(f42,plain,(
% 0.20/0.53 ($false = ($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))))))))))),
% 0.20/0.53 inference(backward_demodulation,[],[f37,f41])).
% 0.20/0.53 thf(f41,plain,(
% 0.20/0.53 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) = $true)),
% 0.20/0.53 inference(binary_proxy_clausification,[],[f37])).
% 0.20/0.53 thf(f37,plain,(
% 0.20/0.53 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))))))))))),
% 0.20/0.53 inference(not_proxy_clausification,[],[f36])).
% 0.20/0.53 thf(f36,plain,(
% 0.20/0.53 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1)))))))))))))))))))),
% 0.20/0.53 inference(beta_eta_normalization,[],[f35])).
% 0.20/0.53 thf(f35,plain,(
% 0.20/0.53 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) & ((setadjoin @ Y3 @ emptyset) = Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))))))))))))),
% 0.20/0.53 inference(definition_unfolding,[],[f32,f29,f30,f34,f31,f27,f33,f28])).
% 0.20/0.53 thf(f28,plain,(
% 0.20/0.53 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))),
% 0.20/0.53 inference(cnf_transformation,[],[f24])).
% 0.20/0.53 thf(f24,plain,(
% 0.20/0.53 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))),
% 0.20/0.53 inference(fool_elimination,[],[f23])).
% 0.20/0.53 thf(f23,plain,(
% 0.20/0.53 (singleton = (^[X0 : $i] : (? [X1] : (((setadjoin @ X1 @ emptyset) = X0) & (in @ X1 @ X0)))))),
% 0.20/0.53 inference(rectify,[],[f7])).
% 0.20/0.53 thf(f7,axiom,(
% 0.20/0.53 (singleton = (^[X0 : $i] : (? [X2] : (((setadjoin @ X2 @ emptyset) = X0) & (in @ X2 @ X0)))))),
% 0.20/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton)).
% 0.20/0.53 thf(f33,plain,(
% 0.20/0.53 (eqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))),
% 0.20/0.53 inference(cnf_transformation,[],[f16])).
% 0.20/0.53 thf(f16,plain,(
% 0.20/0.53 (eqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))),
% 0.20/0.53 inference(fool_elimination,[],[f15])).
% 0.20/0.53 thf(f15,plain,(
% 0.20/0.53 (eqinunit = ! [X0,X1] : ((X0 = X1) => (in @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 0.20/0.53 inference(rectify,[],[f6])).
% 0.20/0.53 thf(f6,axiom,(
% 0.20/0.53 (eqinunit = ! [X2,X3] : ((X2 = X3) => (in @ X2 @ (setadjoin @ X3 @ emptyset))))),
% 0.20/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit)).
% 0.20/0.53 thf(f27,plain,(
% 0.20/0.53 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))))),
% 0.20/0.53 inference(cnf_transformation,[],[f22])).
% 0.20/0.53 thf(f22,plain,(
% 0.20/0.53 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))))),
% 0.20/0.53 inference(fool_elimination,[],[f21])).
% 0.20/0.53 thf(f21,plain,(
% 0.20/0.53 (uniqinunit = ! [X0,X1] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 0.20/0.53 inference(rectify,[],[f5])).
% 0.20/0.53 thf(f5,axiom,(
% 0.20/0.53 (uniqinunit = ! [X2,X3] : ((in @ X2 @ (setadjoin @ X3 @ emptyset)) => (X2 = X3)))),
% 0.20/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit)).
% 0.20/0.53 thf(f31,plain,(
% 0.20/0.53 (setext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))))),
% 0.20/0.53 inference(cnf_transformation,[],[f26])).
% 0.20/0.53 thf(f26,plain,(
% 0.20/0.53 (setext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))))),
% 0.20/0.53 inference(fool_elimination,[],[f25])).
% 0.20/0.53 thf(f25,plain,(
% 0.20/0.53 (! [X0,X1] : (! [X2] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X3] : ((in @ X3 @ X1) => (in @ X3 @ X0)) => (X0 = X1))) = setext)),
% 0.20/0.53 inference(rectify,[],[f4])).
% 0.20/0.53 thf(f4,axiom,(
% 0.20/0.53 (! [X0,X4] : (! [X2] : ((in @ X2 @ X0) => (in @ X2 @ X4)) => (! [X2] : ((in @ X2 @ X4) => (in @ X2 @ X0)) => (X0 = X4))) = setext)),
% 0.20/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext)).
% 0.20/0.53 thf(f34,plain,(
% 0.20/0.53 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y0)))))))))),
% 0.20/0.53 inference(cnf_transformation,[],[f14])).
% 0.20/0.53 thf(f14,plain,(
% 0.20/0.53 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y0)))))))))),
% 0.20/0.53 inference(fool_elimination,[],[f13])).
% 0.20/0.53 thf(f13,plain,(
% 0.20/0.53 (! [X0 : $i > $o,X1,X2] : ((in @ X2 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X0 @ X3)))) => (X0 @ X2)) = dsetconstrER)),
% 0.20/0.53 inference(rectify,[],[f3])).
% 0.20/0.53 thf(f3,axiom,(
% 0.20/0.53 (! [X1 : $i > $o,X0,X2] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)) = dsetconstrER)),
% 0.20/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER)).
% 0.20/0.53 thf(f30,plain,(
% 0.20/0.53 (dsetconstrEL = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (in @ Y0 @ Y2)))))))))),
% 0.20/0.53 inference(cnf_transformation,[],[f12])).
% 0.20/0.53 thf(f12,plain,(
% 0.20/0.53 (dsetconstrEL = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (in @ Y0 @ Y2)))))))))),
% 0.20/0.53 inference(fool_elimination,[],[f11])).
% 0.20/0.53 thf(f11,plain,(
% 0.20/0.53 (! [X0,X1 : $i > $o,X2] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X2 @ X0)) = dsetconstrEL)),
% 0.20/0.53 inference(rectify,[],[f2])).
% 0.20/0.53 thf(f2,axiom,(
% 0.20/0.53 (! [X0,X1 : $i > $o,X2] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X2 @ X0)) = dsetconstrEL)),
% 0.20/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL)).
% 0.20/0.53 thf(f29,plain,(
% 0.20/0.53 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 0.20/0.53 inference(cnf_transformation,[],[f20])).
% 0.20/0.53 thf(f20,plain,(
% 0.20/0.53 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 0.20/0.53 inference(fool_elimination,[],[f19])).
% 0.20/0.53 thf(f19,plain,(
% 0.20/0.53 (dsetconstrI = ! [X0 : $i > $o,X1,X2] : ((in @ X2 @ X1) => ((X0 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X0 @ X3)))))))),
% 0.20/0.53 inference(rectify,[],[f1])).
% 0.20/0.53 thf(f1,axiom,(
% 0.20/0.53 (dsetconstrI = ! [X1 : $i > $o,X0,X2] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))))),
% 0.20/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI)).
% 0.20/0.53 thf(f32,plain,(
% 0.20/0.53 ($true = (~ (dsetconstrI => (dsetconstrEL => (dsetconstrER => (setext => (uniqinunit => (eqinunit => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))))))))))))),
% 0.20/0.53 inference(cnf_transformation,[],[f18])).
% 0.20/0.53 thf(f18,plain,(
% 0.20/0.53 ($true = (~ (dsetconstrI => (dsetconstrEL => (dsetconstrER => (setext => (uniqinunit => (eqinunit => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))))))))))))),
% 0.20/0.53 inference(fool_elimination,[],[f17])).
% 0.20/0.53 thf(f17,plain,(
% 0.20/0.53 ~(dsetconstrI => (dsetconstrEL => (dsetconstrER => (setext => (uniqinunit => (eqinunit => ! [X0 : $i > $o,X1] : (! [X2] : ((in @ X2 @ X1) => ! [X3] : ((in @ X3 @ X1) => ((X0 @ X2) => ((X0 @ X3) => (X2 = X3))))) => (? [X4] : ((in @ X4 @ X1) & (X0 @ X4)) => (singleton @ (dsetconstr @ X1 @ (^[X5 : $i] : (X0 @ X5))))))))))))),
% 0.20/0.53 inference(rectify,[],[f9])).
% 0.20/0.53 thf(f9,negated_conjecture,(
% 0.20/0.53 ~(dsetconstrI => (dsetconstrEL => (dsetconstrER => (setext => (uniqinunit => (eqinunit => ! [X1 : $i > $o,X0] : (! [X2] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (? [X2] : ((in @ X2 @ X0) & (X1 @ X2)) => (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))))))))))),
% 0.20/0.53 inference(negated_conjecture,[],[f8])).
% 0.20/0.53 thf(f8,conjecture,(
% 0.20/0.53 dsetconstrI => (dsetconstrEL => (dsetconstrER => (setext => (uniqinunit => (eqinunit => ! [X1 : $i > $o,X0] : (! [X2] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (? [X2] : ((in @ X2 @ X0) & (X1 @ X2)) => (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2)))))))))))),
% 0.20/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonprop)).
% 0.20/0.53 thf(f640,plain,(
% 0.20/0.53 (sK4 = sK6) | ~spl0_1),
% 0.20/0.53 inference(equality_proxy_clausification,[],[f575])).
% 0.20/0.53 thf(f575,plain,(
% 0.20/0.53 ($true = (sK4 = sK6)) | ~spl0_1),
% 0.20/0.53 inference(boolean_simplification,[],[f574])).
% 0.20/0.53 thf(f574,plain,(
% 0.20/0.53 ($true = ($true => (sK4 = sK6))) | ~spl0_1),
% 0.20/0.53 inference(backward_demodulation,[],[f534,f569])).
% 0.20/0.53 thf(f569,plain,(
% 0.20/0.53 ((in @ sK6 @ sK2) = $true) | ~spl0_1),
% 0.20/0.53 inference(boolean_simplification,[],[f558])).
% 0.20/0.53 thf(f558,plain,(
% 0.20/0.53 ($true = ($true => (in @ sK6 @ sK2))) | ~spl0_1),
% 0.20/0.53 inference(superposition,[],[f59,f523])).
% 0.20/0.53 thf(f523,plain,(
% 0.20/0.53 ($true = (in @ sK6 @ (dsetconstr @ sK2 @ sK3))) | ~spl0_1),
% 0.20/0.53 inference(binary_proxy_clausification,[],[f520])).
% 0.20/0.53 thf(f59,plain,(
% 0.20/0.53 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = ((in @ X1 @ (dsetconstr @ X3 @ X2)) => (in @ X1 @ X3)))) )),
% 0.20/0.53 inference(beta_eta_normalization,[],[f58])).
% 0.20/0.53 thf(f58,plain,(
% 0.20/0.53 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ X1 @ (dsetconstr @ Y0 @ X2)) => (in @ X1 @ Y0))) @ X3))) )),
% 0.20/0.53 inference(pi_clausification,[],[f57])).
% 0.20/0.53 thf(f57,plain,(
% 0.20/0.53 ( ! [X2 : $i > $o,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (dsetconstr @ Y0 @ X2)) => (in @ X1 @ Y0)))))) )),
% 0.20/0.53 inference(beta_eta_normalization,[],[f56])).
% 0.20/0.53 thf(f56,plain,(
% 0.20/0.53 ( ! [X2 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (dsetconstr @ Y1 @ Y0)) => (in @ X1 @ Y1))))) @ X2) = $true)) )),
% 0.20/0.53 inference(pi_clausification,[],[f49])).
% 0.20/0.53 thf(f49,plain,(
% 0.20/0.53 ( ! [X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (dsetconstr @ Y1 @ Y0)) => (in @ X1 @ Y1)))))))) )),
% 0.20/0.53 inference(beta_eta_normalization,[],[f48])).
% 0.20/0.53 thf(f48,plain,(
% 0.20/0.53 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2))))))) @ X1))) )),
% 0.20/0.53 inference(pi_clausification,[],[f45])).
% 0.20/0.53 thf(f534,plain,(
% 0.20/0.53 ($true = ((in @ sK6 @ sK2) => (sK4 = sK6))) | ~spl0_1),
% 0.20/0.53 inference(boolean_simplification,[],[f531])).
% 0.20/0.53 thf(f531,plain,(
% 0.20/0.53 ($true = ((in @ sK6 @ sK2) => ($true => (sK4 = sK6)))) | ~spl0_1),
% 0.20/0.53 inference(superposition,[],[f186,f526])).
% 0.20/0.53 thf(f526,plain,(
% 0.20/0.53 ($true = (sK3 @ sK6)) | ~spl0_1),
% 0.20/0.53 inference(trivial_inequality_removal,[],[f525])).
% 0.20/0.53 thf(f525,plain,(
% 0.20/0.53 ($false = $true) | ($true = (sK3 @ sK6)) | ~spl0_1),
% 0.20/0.53 inference(boolean_simplification,[],[f524])).
% 0.20/0.53 thf(f524,plain,(
% 0.20/0.53 ($false = ($false => (in @ sK6 @ (setadjoin @ sK4 @ emptyset)))) | ($true = (sK3 @ sK6)) | ~spl0_1),
% 0.20/0.53 inference(superposition,[],[f520,f67])).
% 0.20/0.53 thf(f67,plain,(
% 0.20/0.53 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($false = (in @ X1 @ (dsetconstr @ X2 @ X3))) | ((X3 @ X1) = $true)) )),
% 0.20/0.53 inference(binary_proxy_clausification,[],[f66])).
% 0.20/0.53 thf(f66,plain,(
% 0.20/0.53 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = ((in @ X1 @ (dsetconstr @ X2 @ X3)) => (X3 @ X1)))) )),
% 0.20/0.53 inference(beta_eta_normalization,[],[f65])).
% 0.20/0.53 thf(f65,plain,(
% 0.20/0.53 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: ((in @ X1 @ (dsetconstr @ X2 @ Y0)) => (Y0 @ X1))) @ X3) = $true)) )),
% 0.20/0.53 inference(pi_clausification,[],[f64])).
% 0.20/0.53 thf(f64,plain,(
% 0.20/0.53 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X1 @ (dsetconstr @ X2 @ Y0)) => (Y0 @ X1)))))) )),
% 0.20/0.53 inference(beta_eta_normalization,[],[f63])).
% 0.20/0.53 thf(f63,plain,(
% 0.20/0.53 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ X1 @ (dsetconstr @ Y0 @ Y1)) => (Y1 @ X1))))) @ X2))) )),
% 0.20/0.53 inference(pi_clausification,[],[f62])).
% 0.20/0.53 thf(f62,plain,(
% 0.20/0.53 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ X1 @ (dsetconstr @ Y0 @ Y1)) => (Y1 @ X1)))))) = $true)) )),
% 0.20/0.53 inference(beta_eta_normalization,[],[f61])).
% 0.20/0.53 thf(f61,plain,(
% 0.20/0.53 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (Y2 @ Y0))))))) @ X1))) )),
% 0.20/0.53 inference(pi_clausification,[],[f51])).
% 0.20/0.53 thf(f51,plain,(
% 0.20/0.53 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (Y2 @ Y0)))))))))),
% 0.20/0.53 inference(binary_proxy_clausification,[],[f47])).
% 0.20/0.53 thf(f186,plain,(
% 0.20/0.53 ( ! [X1 : $i] : ((((in @ X1 @ sK2) => ((sK3 @ X1) => (sK4 = X1))) = $true)) )),
% 0.20/0.53 inference(boolean_simplification,[],[f185])).
% 0.20/0.53 thf(f185,plain,(
% 0.20/0.53 ( ! [X1 : $i] : ((((in @ X1 @ sK2) => ($true => ((sK3 @ X1) => (sK4 = X1)))) = $true)) )),
% 0.20/0.53 inference(forward_demodulation,[],[f183,f123])).
% 0.20/0.53 thf(f123,plain,(
% 0.20/0.53 ($true = (sK3 @ sK4))),
% 0.20/0.53 inference(binary_proxy_clausification,[],[f119])).
% 0.20/0.53 thf(f119,plain,(
% 0.20/0.53 ($true = ((sK3 @ sK4) & (in @ sK4 @ sK2)))),
% 0.20/0.53 inference(beta_eta_normalization,[],[f118])).
% 0.20/0.53 thf(f118,plain,(
% 0.20/0.53 ($true = ((^[Y0 : $i]: ((sK3 @ Y0) & (in @ Y0 @ sK2))) @ sK4))),
% 0.20/0.53 inference(sigma_clausification,[],[f115])).
% 0.20/0.53 thf(f115,plain,(
% 0.20/0.53 ($true = (?? @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) & (in @ Y0 @ sK2)))))),
% 0.20/0.53 inference(binary_proxy_clausification,[],[f111])).
% 0.20/0.53 thf(f111,plain,(
% 0.20/0.53 ($false = ((?? @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) & (in @ Y0 @ sK2)))) => (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK3)) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK2 @ sK3)))))))),
% 0.20/0.53 inference(boolean_simplification,[],[f110])).
% 0.20/0.53 thf(f110,plain,(
% 0.20/0.53 ($false = ($true => ((?? @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) & (in @ Y0 @ sK2)))) => (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK3)) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK2 @ sK3))))))))),
% 0.20/0.53 inference(backward_demodulation,[],[f106,f109])).
% 0.20/0.53 thf(f109,plain,(
% 0.20/0.53 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((sK3 @ Y0) => ((sK3 @ Y1) => (Y0 = Y1))))))))))),
% 0.20/0.53 inference(binary_proxy_clausification,[],[f106])).
% 0.20/0.53 thf(f106,plain,(
% 0.20/0.53 ($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((sK3 @ Y0) => ((sK3 @ Y1) => (Y0 = Y1))))))))) => ((?? @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) & (in @ Y0 @ sK2)))) => (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK3)) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK2 @ sK3))))))))),
% 0.20/0.53 inference(beta_eta_normalization,[],[f105])).
% 0.20/0.53 thf(f105,plain,(
% 0.20/0.53 ($false = ((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK2) => ((Y0 @ Y1) => ((Y0 @ Y2) => (Y1 = Y2))))))))) => ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (in @ Y1 @ sK2)))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ sK2 @ Y0)) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK2 @ Y0)))))))) @ sK3))),
% 0.20/0.53 inference(sigma_clausification,[],[f102])).
% 0.20/0.53 thf(f102,plain,(
% 0.20/0.53 ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK2) => ((Y0 @ Y1) => ((Y0 @ Y2) => (Y1 = Y2))))))))) => ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (in @ Y1 @ sK2)))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ sK2 @ Y0)) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK2 @ Y0))))))))))),
% 0.20/0.53 inference(beta_eta_normalization,[],[f101])).
% 0.20/0.53 thf(f101,plain,(
% 0.20/0.53 ($false = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1)))))))))) @ sK2))),
% 0.20/0.53 inference(sigma_clausification,[],[f98])).
% 0.20/0.53 thf(f98,plain,(
% 0.20/0.53 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))))),
% 0.20/0.53 inference(boolean_simplification,[],[f97])).
% 0.20/0.53 thf(f97,plain,(
% 0.20/0.53 ($false = ($true => (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1)))))))))))))),
% 0.20/0.53 inference(backward_demodulation,[],[f81,f96])).
% 0.20/0.53 thf(f183,plain,(
% 0.20/0.53 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK2) => ((sK3 @ sK4) => ((sK3 @ X1) => (sK4 = X1)))))) )),
% 0.20/0.53 inference(beta_eta_normalization,[],[f181])).
% 0.20/0.53 thf(f181,plain,(
% 0.20/0.53 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ sK2) => ((sK3 @ sK4) => ((sK3 @ Y0) => (sK4 = Y0))))) @ X1))) )),
% 0.20/0.53 inference(pi_clausification,[],[f146])).
% 0.20/0.53 thf(f146,plain,(
% 0.20/0.53 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((sK3 @ sK4) => ((sK3 @ Y0) => (sK4 = Y0)))))) = $true)),
% 0.20/0.53 inference(boolean_simplification,[],[f145])).
% 0.20/0.53 thf(f145,plain,(
% 0.20/0.53 ($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((sK3 @ sK4) => ((sK3 @ Y0) => (sK4 = Y0))))))))),
% 0.20/0.53 inference(superposition,[],[f113,f125])).
% 0.20/0.53 thf(f125,plain,(
% 0.20/0.53 ($true = (in @ sK4 @ sK2))),
% 0.20/0.53 inference(boolean_simplification,[],[f124])).
% 0.20/0.53 thf(f124,plain,(
% 0.20/0.53 ($true = ($true & (in @ sK4 @ sK2)))),
% 0.20/0.53 inference(backward_demodulation,[],[f119,f123])).
% 0.20/0.53 thf(f113,plain,(
% 0.20/0.53 ( ! [X1 : $i] : ((((in @ X1 @ sK2) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((sK3 @ X1) => ((sK3 @ Y0) => (X1 = Y0))))))) = $true)) )),
% 0.20/0.53 inference(beta_eta_normalization,[],[f112])).
% 0.20/0.53 thf(f112,plain,(
% 0.20/0.53 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((sK3 @ Y0) => ((sK3 @ Y1) => (Y0 = Y1)))))))) @ X1))) )),
% 0.20/0.53 inference(pi_clausification,[],[f109])).
% 0.20/0.53 thf(f455,plain,(
% 0.20/0.53 ~spl0_2),
% 0.20/0.53 inference(avatar_contradiction_clause,[],[f454])).
% 0.20/0.53 thf(f454,plain,(
% 0.20/0.53 $false | ~spl0_2),
% 0.20/0.53 inference(trivial_inequality_removal,[],[f453])).
% 0.20/0.53 thf(f453,plain,(
% 0.20/0.53 ($false = $true) | ~spl0_2),
% 0.20/0.53 inference(boolean_simplification,[],[f452])).
% 0.20/0.53 thf(f452,plain,(
% 0.20/0.53 ($true = (~ $true)) | ~spl0_2),
% 0.20/0.53 inference(forward_demodulation,[],[f451,f123])).
% 0.20/0.53 thf(f451,plain,(
% 0.20/0.53 ($true = (~ (sK3 @ sK4))) | ~spl0_2),
% 0.20/0.53 inference(boolean_simplification,[],[f450])).
% 0.20/0.53 thf(f450,plain,(
% 0.20/0.53 ($true = ($true => (~ (sK3 @ sK4)))) | ~spl0_2),
% 0.20/0.53 inference(forward_demodulation,[],[f442,f125])).
% 0.20/0.53 thf(f442,plain,(
% 0.20/0.53 (((in @ sK4 @ sK2) => (~ (sK3 @ sK4))) = $true) | ~spl0_2),
% 0.20/0.53 inference(backward_demodulation,[],[f360,f419])).
% 0.20/0.53 thf(f419,plain,(
% 0.20/0.53 (sK4 = sK5) | ~spl0_2),
% 0.20/0.53 inference(equality_proxy_clausification,[],[f347])).
% 0.20/0.53 thf(f347,plain,(
% 0.20/0.53 ($true = (sK5 = sK4)) | ~spl0_2),
% 0.20/0.53 inference(boolean_simplification,[],[f340])).
% 0.20/0.53 thf(f340,plain,(
% 0.20/0.53 ($true = ($true => (sK5 = sK4))) | ~spl0_2),
% 0.20/0.53 inference(superposition,[],[f90,f336])).
% 0.20/0.53 thf(f336,plain,(
% 0.20/0.53 ($true = (in @ sK5 @ (setadjoin @ sK4 @ emptyset))) | ~spl0_2),
% 0.20/0.53 inference(binary_proxy_clausification,[],[f331])).
% 0.20/0.53 thf(f331,plain,(
% 0.20/0.53 ($false = ((in @ sK5 @ (setadjoin @ sK4 @ emptyset)) => (in @ sK5 @ (dsetconstr @ sK2 @ sK3)))) | ~spl0_2),
% 0.20/0.53 inference(beta_eta_normalization,[],[f328])).
% 0.20/0.53 thf(f328,plain,(
% 0.20/0.53 ($false = ((^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK4 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK2 @ sK3)))) @ sK5)) | ~spl0_2),
% 0.20/0.53 inference(sigma_clausification,[],[f324])).
% 0.20/0.53 thf(f324,plain,(
% 0.20/0.53 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK4 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK2 @ sK3)))))) | ~spl0_2),
% 0.20/0.53 inference(avatar_component_clause,[],[f323])).
% 0.20/0.53 thf(f323,plain,(
% 0.20/0.53 spl0_2 <=> ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK4 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK2 @ sK3))))))),
% 0.20/0.53 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.20/0.53 thf(f90,plain,(
% 0.20/0.53 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ X2 @ (setadjoin @ X1 @ emptyset)) => (X2 = X1)))) )),
% 0.20/0.53 inference(beta_eta_normalization,[],[f89])).
% 0.20/0.53 thf(f89,plain,(
% 0.20/0.53 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ X1 @ emptyset)) => (Y0 = X1))) @ X2))) )),
% 0.20/0.53 inference(pi_clausification,[],[f88])).
% 0.20/0.53 thf(f88,plain,(
% 0.20/0.53 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ X1 @ emptyset)) => (Y0 = X1)))))) )),
% 0.20/0.53 inference(beta_eta_normalization,[],[f87])).
% 0.20/0.53 thf(f87,plain,(
% 0.20/0.53 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0))))) @ X1))) )),
% 0.20/0.53 inference(pi_clausification,[],[f82])).
% 0.20/0.53 thf(f82,plain,(
% 0.20/0.53 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))))),
% 0.20/0.53 inference(binary_proxy_clausification,[],[f78])).
% 0.20/0.53 thf(f360,plain,(
% 0.20/0.53 ($true = ((in @ sK5 @ sK2) => (~ (sK3 @ sK5)))) | ~spl0_2),
% 0.20/0.53 inference(boolean_simplification,[],[f352])).
% 0.20/0.53 thf(f352,plain,(
% 0.20/0.53 (((in @ sK5 @ sK2) => ((sK3 @ sK5) => $false)) = $true) | ~spl0_2),
% 0.20/0.53 inference(superposition,[],[f73,f338])).
% 0.20/0.53 thf(f338,plain,(
% 0.20/0.53 ($false = (in @ sK5 @ (dsetconstr @ sK2 @ sK3))) | ~spl0_2),
% 0.20/0.53 inference(boolean_simplification,[],[f337])).
% 0.20/0.53 thf(f337,plain,(
% 0.20/0.53 ($false = ($true => (in @ sK5 @ (dsetconstr @ sK2 @ sK3)))) | ~spl0_2),
% 0.20/0.53 inference(backward_demodulation,[],[f331,f336])).
% 0.20/0.53 thf(f73,plain,(
% 0.20/0.53 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = ((in @ X1 @ X2) => ((X3 @ X1) => (in @ X1 @ (dsetconstr @ X2 @ X3)))))) )),
% 0.20/0.53 inference(beta_eta_normalization,[],[f72])).
% 0.20/0.53 thf(f72,plain,(
% 0.20/0.53 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: ((in @ X1 @ X2) => ((Y0 @ X1) => (in @ X1 @ (dsetconstr @ X2 @ Y0))))) @ X3) = $true)) )),
% 0.20/0.53 inference(pi_clausification,[],[f71])).
% 0.20/0.53 thf(f71,plain,(
% 0.20/0.53 ( ! [X2 : $i,X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X1 @ X2) => ((Y0 @ X1) => (in @ X1 @ (dsetconstr @ X2 @ Y0)))))) = $true)) )),
% 0.20/0.53 inference(beta_eta_normalization,[],[f70])).
% 0.20/0.53 thf(f70,plain,(
% 0.20/0.53 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ X1 @ Y0) => ((Y1 @ X1) => (in @ X1 @ (dsetconstr @ Y0 @ Y1))))))) @ X2) = $true)) )),
% 0.20/0.53 inference(pi_clausification,[],[f69])).
% 0.20/0.53 thf(f69,plain,(
% 0.20/0.53 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ X1 @ Y0) => ((Y1 @ X1) => (in @ X1 @ (dsetconstr @ Y0 @ Y1)))))))))) )),
% 0.20/0.53 inference(beta_eta_normalization,[],[f68])).
% 0.20/0.53 thf(f68,plain,(
% 0.20/0.53 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2))))))))) @ X1))) )),
% 0.20/0.53 inference(pi_clausification,[],[f41])).
% 0.20/0.53 thf(f325,plain,(
% 0.20/0.53 spl0_1 | spl0_2),
% 0.20/0.53 inference(avatar_split_clause,[],[f318,f323,f320])).
% 0.20/0.53 thf(f318,plain,(
% 0.20/0.53 ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK3)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset)))))) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK4 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK2 @ sK3))))))),
% 0.20/0.53 inference(binary_proxy_clausification,[],[f180])).
% 0.20/0.53 thf(f180,plain,(
% 0.20/0.53 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK4 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK2 @ sK3))))) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK3)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset))))))) = $true)),
% 0.20/0.53 inference(boolean_simplification,[],[f170])).
% 0.20/0.53 thf(f170,plain,(
% 0.20/0.53 ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK4 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK2 @ sK3))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK3)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset))))) => $false)))),
% 0.20/0.53 inference(superposition,[],[f93,f156])).
% 0.20/0.53 thf(f156,plain,(
% 0.20/0.53 ($false = ((setadjoin @ sK4 @ emptyset) = (dsetconstr @ sK2 @ sK3)))),
% 0.20/0.53 inference(boolean_simplification,[],[f148])).
% 0.20/0.53 thf(f148,plain,(
% 0.20/0.53 ($false = ($true & ((setadjoin @ sK4 @ emptyset) = (dsetconstr @ sK2 @ sK3))))),
% 0.20/0.53 inference(superposition,[],[f121,f143])).
% 0.20/0.53 thf(f143,plain,(
% 0.20/0.53 ($true = (in @ sK4 @ (dsetconstr @ sK2 @ sK3)))),
% 0.20/0.53 inference(boolean_simplification,[],[f140])).
% 0.20/0.53 thf(f140,plain,(
% 0.20/0.53 ($true = ($true => (in @ sK4 @ (dsetconstr @ sK2 @ sK3))))),
% 0.20/0.53 inference(superposition,[],[f138,f123])).
% 0.20/0.53 thf(f138,plain,(
% 0.20/0.53 ( ! [X0 : $i > $o] : ((((X0 @ sK4) => (in @ sK4 @ (dsetconstr @ sK2 @ X0))) = $true)) )),
% 0.20/0.53 inference(boolean_simplification,[],[f131])).
% 0.20/0.53 thf(f131,plain,(
% 0.20/0.53 ( ! [X0 : $i > $o] : ((($true => ((X0 @ sK4) => (in @ sK4 @ (dsetconstr @ sK2 @ X0)))) = $true)) )),
% 0.20/0.53 inference(superposition,[],[f73,f125])).
% 0.20/0.53 thf(f121,plain,(
% 0.20/0.53 ( ! [X1 : $i] : (($false = ((in @ X1 @ (dsetconstr @ sK2 @ sK3)) & ((setadjoin @ X1 @ emptyset) = (dsetconstr @ sK2 @ sK3))))) )),
% 0.20/0.53 inference(beta_eta_normalization,[],[f120])).
% 0.20/0.53 thf(f120,plain,(
% 0.20/0.53 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK3)) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK2 @ sK3)))) @ X1))) )),
% 0.20/0.53 inference(pi_clausification,[],[f117])).
% 0.20/0.53 thf(f117,plain,(
% 0.20/0.53 ($false = (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK3)) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK2 @ sK3))))))),
% 0.20/0.53 inference(boolean_simplification,[],[f116])).
% 0.20/0.53 thf(f116,plain,(
% 0.20/0.53 ($false = ($true => (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK2 @ sK3)) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK2 @ sK3)))))))),
% 0.20/0.53 inference(backward_demodulation,[],[f111,f115])).
% 0.20/0.53 thf(f93,plain,(
% 0.20/0.53 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => (X2 = X1))))) )),
% 0.20/0.53 inference(beta_eta_normalization,[],[f92])).
% 0.20/0.53 thf(f92,plain,(
% 0.20/0.53 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (Y0 = X1)))) @ X2) = $true)) )),
% 0.20/0.53 inference(pi_clausification,[],[f80])).
% 0.20/0.53 thf(f80,plain,(
% 0.20/0.53 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (Y0 = X1))))))) )),
% 0.20/0.53 inference(beta_eta_normalization,[],[f79])).
% 0.20/0.53 thf(f79,plain,(
% 0.20/0.53 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) @ X1))) )),
% 0.20/0.53 inference(pi_clausification,[],[f76])).
% 0.20/0.53 % SZS output end Proof for theBenchmark
% 0.20/0.53 % (1863)------------------------------
% 0.20/0.53 % (1863)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.53 % (1863)Termination reason: Refutation
% 0.20/0.53
% 0.20/0.53 % (1863)Memory used [KB]: 6268
% 0.20/0.53 % (1863)Time elapsed: 0.088 s
% 0.20/0.53 % (1863)Instructions burned: 123 (million)
% 0.20/0.53 % (1863)------------------------------
% 0.20/0.53 % (1863)------------------------------
% 0.20/0.53 % (1851)Success in time 0.159 s
%------------------------------------------------------------------------------