0.00/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.10 % Command : run_vampire %s %d THM 0.10/0.30 % Computer : n001.cluster.edu 0.10/0.30 % Model : x86_64 x86_64 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.30 % Memory : 8042.1875MB 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.30 % CPULimit : 1440 0.10/0.30 % WCLimit : 180 0.10/0.30 % DateTime : Thu Jul 4 09:42:09 EDT 2024 0.10/0.30 % CPUTime : 0.10/0.31 This is a THF_ problem 0.15/0.31 Running higher-order theorem proving 0.15/0.34 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/tmp/tmp.AEOGvNUPJb/E---3.1_16218.p -m 16384 -t 180 0.15/0.37 % (16332)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_16218 for (1799ds/18Mi) 0.15/0.37 % (16331)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on E---3.1_16218 for (1799ds/275Mi) 0.15/0.37 % (16329)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_16218 for (1799ds/2Mi) 0.15/0.37 % (16327)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 E---3.1_16218 for (1799ds/4Mi) 0.15/0.37 % (16328)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 E---3.1_16218 for (1799ds/27Mi) 0.15/0.37 % (16330)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on E---3.1_16218 for (1799ds/2Mi) 0.15/0.37 % (16326)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_16218 for (1799ds/183Mi) 0.15/0.37 % (16329)Instruction limit reached! 0.15/0.37 % (16329)------------------------------ 0.15/0.37 % (16329)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.15/0.37 % (16329)Termination reason: Unknown 0.15/0.37 % (16330)Instruction limit reached! 0.15/0.37 % (16330)------------------------------ 0.15/0.37 % (16330)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.15/0.37 % (16329)Termination phase: shuffling 0.15/0.37 0.15/0.37 % (16329)Memory used [KB]: 1279 0.15/0.37 % (16329)Time elapsed: 0.003 s 0.15/0.37 % (16329)Instructions burned: 2 (million) 0.15/0.37 % (16329)------------------------------ 0.15/0.37 % (16329)------------------------------ 0.15/0.37 % (16330)Termination reason: Unknown 0.15/0.37 % (16330)Termination phase: shuffling 0.15/0.37 0.15/0.37 % (16330)Memory used [KB]: 1279 0.15/0.37 % (16330)Time elapsed: 0.004 s 0.15/0.37 % (16330)Instructions burned: 2 (million) 0.15/0.37 % (16330)------------------------------ 0.15/0.37 % (16330)------------------------------ 0.15/0.37 % (16327)Instruction limit reached! 0.15/0.37 % (16327)------------------------------ 0.15/0.37 % (16327)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.15/0.37 % (16327)Termination reason: Unknown 0.15/0.37 % (16327)Termination phase: shuffling 0.15/0.37 0.15/0.37 % (16327)Memory used [KB]: 1279 0.15/0.37 % (16327)Time elapsed: 0.004 s 0.15/0.37 % (16327)Instructions burned: 4 (million) 0.15/0.37 % (16327)------------------------------ 0.15/0.37 % (16327)------------------------------ 0.15/0.38 % (16332)Instruction limit reached! 0.15/0.38 % (16332)------------------------------ 0.15/0.38 % (16332)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.15/0.38 % (16332)Termination reason: Unknown 0.15/0.38 % (16332)Termination phase: shuffling 0.15/0.38 0.15/0.38 % (16332)Memory used [KB]: 1535 0.15/0.38 % (16332)Time elapsed: 0.011 s 0.15/0.38 % (16332)Instructions burned: 18 (million) 0.15/0.38 % (16332)------------------------------ 0.15/0.38 % (16332)------------------------------ 0.15/0.38 % (16328)Instruction limit reached! 0.15/0.38 % (16328)------------------------------ 0.15/0.38 % (16328)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.15/0.38 % (16328)Termination reason: Unknown 0.15/0.38 % (16328)Termination phase: Preprocessing 1 0.15/0.38 0.15/0.38 % (16328)Memory used [KB]: 1535 0.15/0.38 % (16328)Time elapsed: 0.014 s 0.15/0.38 % (16328)Instructions burned: 27 (million) 0.15/0.38 % (16328)------------------------------ 0.15/0.38 % (16328)------------------------------ 0.15/0.38 % (16333)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on E---3.1_16218 for (1799ds/3Mi) 0.15/0.38 % (16334)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 E---3.1_16218 for (1799ds/37Mi) 0.15/0.38 % (16335)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 E---3.1_16218 for (1799ds/15Mi) 0.15/0.38 % (16333)Instruction limit reached! 0.15/0.38 % (16333)------------------------------ 0.15/0.38 % (16333)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.15/0.38 % (16333)Termination reason: Unknown 0.15/0.38 % (16333)Termination phase: shuffling 0.15/0.38 0.15/0.38 % (16333)Memory used [KB]: 1279 0.15/0.38 % (16333)Time elapsed: 0.003 s 0.15/0.38 % (16333)Instructions burned: 3 (million) 0.15/0.38 % (16333)------------------------------ 0.15/0.38 % (16333)------------------------------ 0.15/0.39 % (16335)Instruction limit reached! 0.15/0.39 % (16335)------------------------------ 0.15/0.39 % (16335)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.15/0.39 % (16335)Termination reason: Unknown 0.15/0.39 % (16335)Termination phase: shuffling 0.15/0.39 0.15/0.39 % (16335)Memory used [KB]: 1535 0.15/0.39 % (16335)Time elapsed: 0.009 s 0.15/0.39 % (16335)Instructions burned: 15 (million) 0.15/0.39 % (16335)------------------------------ 0.15/0.39 % (16335)------------------------------ 0.15/0.39 % (16336)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on E---3.1_16218 for (1799ds/3Mi) 0.15/0.39 % (16337)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 E---3.1_16218 for (1799ds/1041Mi) 0.15/0.40 % (16336)Instruction limit reached! 0.15/0.40 % (16336)------------------------------ 0.15/0.40 % (16336)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.15/0.40 % (16336)Termination reason: Unknown 0.15/0.40 % (16336)Termination phase: shuffling 0.15/0.40 0.15/0.40 % (16336)Memory used [KB]: 1279 0.15/0.40 % (16336)Time elapsed: 0.004 s 0.15/0.40 % (16336)Instructions burned: 3 (million) 0.15/0.40 % (16336)------------------------------ 0.15/0.40 % (16336)------------------------------ 0.15/0.40 % (16334)Instruction limit reached! 0.15/0.40 % (16334)------------------------------ 0.15/0.40 % (16334)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.15/0.40 % (16334)Termination reason: Unknown 0.15/0.40 % (16334)Termination phase: Function definition elimination 0.15/0.40 0.15/0.40 % (16334)Memory used [KB]: 1535 0.15/0.40 % (16334)Time elapsed: 0.017 s 0.15/0.40 % (16334)Instructions burned: 38 (million) 0.15/0.40 % (16334)------------------------------ 0.15/0.40 % (16334)------------------------------ 0.15/0.40 % (16338)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on E---3.1_16218 for (1799ds/7Mi) 0.15/0.40 % (16338)Instruction limit reached! 0.15/0.40 % (16338)------------------------------ 0.15/0.40 % (16338)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.15/0.40 % (16338)Termination reason: Unknown 0.15/0.40 % (16338)Termination phase: shuffling 0.15/0.40 0.15/0.40 % (16338)Memory used [KB]: 1279 0.15/0.40 % (16338)Time elapsed: 0.006 s 0.15/0.40 % (16338)Instructions burned: 8 (million) 0.15/0.40 % (16338)------------------------------ 0.15/0.40 % (16338)------------------------------ 0.15/0.40 % (16339)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on E---3.1_16218 for (1799ds/16Mi) 0.18/0.41 % (16340)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 E---3.1_16218 for (1799ds/3Mi) 0.18/0.41 % (16341)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 E---3.1_16218 for (1799ds/3Mi) 0.18/0.41 % (16339)Instruction limit reached! 0.18/0.41 % (16339)------------------------------ 0.18/0.41 % (16339)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.41 % (16339)Termination reason: Unknown 0.18/0.41 % (16339)Termination phase: shuffling 0.18/0.41 0.18/0.41 % (16339)Memory used [KB]: 1535 0.18/0.41 % (16339)Time elapsed: 0.010 s 0.18/0.41 % (16339)Instructions burned: 17 (million) 0.18/0.41 % (16339)------------------------------ 0.18/0.41 % (16339)------------------------------ 0.18/0.41 % (16340)Instruction limit reached! 0.18/0.41 % (16340)------------------------------ 0.18/0.41 % (16340)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.41 % (16340)Termination reason: Unknown 0.18/0.41 % (16340)Termination phase: shuffling 0.18/0.41 0.18/0.41 % (16340)Memory used [KB]: 1279 0.18/0.41 % (16340)Time elapsed: 0.004 s 0.18/0.41 % (16340)Instructions burned: 3 (million) 0.18/0.41 % (16340)------------------------------ 0.18/0.41 % (16340)------------------------------ 0.18/0.41 % (16341)Instruction limit reached! 0.18/0.41 % (16341)------------------------------ 0.18/0.41 % (16341)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.41 % (16341)Termination reason: Unknown 0.18/0.41 % (16341)Termination phase: shuffling 0.18/0.41 0.18/0.41 % (16341)Memory used [KB]: 1279 0.18/0.41 % (16341)Time elapsed: 0.004 s 0.18/0.41 % (16341)Instructions burned: 4 (million) 0.18/0.41 % (16341)------------------------------ 0.18/0.41 % (16341)------------------------------ 0.18/0.42 % (16342)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on E---3.1_16218 for (1799ds/7Mi) 0.18/0.42 % (16342)Instruction limit reached! 0.18/0.42 % (16342)------------------------------ 0.18/0.42 % (16342)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.42 % (16342)Termination reason: Unknown 0.18/0.42 % (16342)Termination phase: shuffling 0.18/0.42 0.18/0.42 % (16342)Memory used [KB]: 1279 0.18/0.42 % (16342)Time elapsed: 0.006 s 0.18/0.42 % (16342)Instructions burned: 7 (million) 0.18/0.42 % (16342)------------------------------ 0.18/0.42 % (16342)------------------------------ 0.18/0.43 % (16345)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on E---3.1_16218 for (1799ds/18Mi) 0.18/0.43 % (16344)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on E---3.1_16218 for (1799ds/4Mi) 0.18/0.43 % (16343)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on E---3.1_16218 for (1799ds/3Mi) 0.18/0.43 % (16343)Instruction limit reached! 0.18/0.43 % (16343)------------------------------ 0.18/0.43 % (16343)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.43 % (16343)Termination reason: Unknown 0.18/0.43 % (16344)Instruction limit reached! 0.18/0.43 % (16344)------------------------------ 0.18/0.43 % (16344)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.43 % (16343)Termination phase: shuffling 0.18/0.43 0.18/0.43 % (16343)Memory used [KB]: 1279 0.18/0.43 % (16343)Time elapsed: 0.004 s 0.18/0.43 % (16343)Instructions burned: 3 (million) 0.18/0.43 % (16343)------------------------------ 0.18/0.43 % (16343)------------------------------ 0.18/0.43 % (16344)Termination reason: Unknown 0.18/0.43 % (16344)Termination phase: shuffling 0.18/0.43 0.18/0.43 % (16344)Memory used [KB]: 1279 0.18/0.43 % (16344)Time elapsed: 0.004 s 0.18/0.43 % (16344)Instructions burned: 4 (million) 0.18/0.43 % (16344)------------------------------ 0.18/0.43 % (16344)------------------------------ 0.18/0.44 % (16326)Instruction limit reached! 0.18/0.44 % (16326)------------------------------ 0.18/0.44 % (16326)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.44 % (16326)Termination reason: Unknown 0.18/0.44 % (16326)Termination phase: Saturation 0.18/0.44 0.18/0.44 % (16326)Memory used [KB]: 6524 0.18/0.44 % (16326)Time elapsed: 0.071 s 0.18/0.44 % (16326)Instructions burned: 183 (million) 0.18/0.44 % (16326)------------------------------ 0.18/0.44 % (16326)------------------------------ 0.18/0.44 % (16345)Instruction limit reached! 0.18/0.44 % (16345)------------------------------ 0.18/0.44 % (16345)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.44 % (16345)Termination reason: Unknown 0.18/0.44 % (16345)Termination phase: Property scanning 0.18/0.44 0.18/0.44 % (16345)Memory used [KB]: 1535 0.18/0.44 % (16345)Time elapsed: 0.011 s 0.18/0.44 % (16345)Instructions burned: 19 (million) 0.18/0.44 % (16345)------------------------------ 0.18/0.44 % (16345)------------------------------ 0.18/0.44 % (16346)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on E---3.1_16218 for (1799ds/710Mi) 0.18/0.44 % (16347)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on E---3.1_16218 for (1799ds/6Mi) 0.18/0.44 % (16348)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 E---3.1_16218 for (1799ds/902Mi) 0.18/0.45 % (16347)Instruction limit reached! 0.18/0.45 % (16347)------------------------------ 0.18/0.45 % (16347)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.45 % (16347)Termination reason: Unknown 0.18/0.45 % (16347)Termination phase: shuffling 0.18/0.45 0.18/0.45 % (16347)Memory used [KB]: 1279 0.18/0.45 % (16347)Time elapsed: 0.005 s 0.18/0.45 % (16347)Instructions burned: 7 (million) 0.18/0.45 % (16347)------------------------------ 0.18/0.45 % (16347)------------------------------ 0.18/0.45 % (16349)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 E---3.1_16218 for (1799ds/21Mi) 0.18/0.45 % (16350)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on E---3.1_16218 for (1799ds/5Mi) 0.18/0.45 % (16350)Instruction limit reached! 0.18/0.45 % (16350)------------------------------ 0.18/0.45 % (16350)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.45 % (16350)Termination reason: Unknown 0.18/0.45 % (16350)Termination phase: shuffling 0.18/0.45 0.18/0.45 % (16350)Memory used [KB]: 1279 0.18/0.45 % (16350)Time elapsed: 0.005 s 0.18/0.45 % (16350)Instructions burned: 6 (million) 0.18/0.45 % (16350)------------------------------ 0.18/0.45 % (16350)------------------------------ 0.18/0.46 % (16349)Instruction limit reached! 0.18/0.46 % (16349)------------------------------ 0.18/0.46 % (16349)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.46 % (16349)Termination reason: Unknown 0.18/0.46 % (16349)Termination phase: Property scanning 0.18/0.46 0.18/0.46 % (16349)Memory used [KB]: 1535 0.18/0.46 % (16349)Time elapsed: 0.012 s 0.18/0.46 % (16349)Instructions burned: 23 (million) 0.18/0.46 % (16349)------------------------------ 0.18/0.46 % (16349)------------------------------ 0.18/0.46 % (16351)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 E---3.1_16218 for (1798ds/6Mi) 0.18/0.46 % (16351)Instruction limit reached! 0.18/0.46 % (16351)------------------------------ 0.18/0.46 % (16351)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.46 % (16351)Termination reason: Unknown 0.18/0.46 % (16351)Termination phase: shuffling 0.18/0.46 0.18/0.46 % (16351)Memory used [KB]: 1279 0.18/0.46 % (16351)Time elapsed: 0.005 s 0.18/0.46 % (16351)Instructions burned: 7 (million) 0.18/0.46 % (16351)------------------------------ 0.18/0.46 % (16351)------------------------------ 0.18/0.47 % (16352)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on E---3.1_16218 for (1798ds/377Mi) 0.18/0.48 % (16353)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on E---3.1_16218 for (1798ds/779Mi) 0.18/0.48 % (16354)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on E---3.1_16218 for (1798ds/19Mi) 0.18/0.49 % (16354)Instruction limit reached! 0.18/0.49 % (16354)------------------------------ 0.18/0.49 % (16354)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.49 % (16354)Termination reason: Unknown 0.18/0.49 % (16354)Termination phase: Property scanning 0.18/0.49 0.18/0.49 % (16354)Memory used [KB]: 1535 0.18/0.49 % (16354)Time elapsed: 0.011 s 0.18/0.49 % (16354)Instructions burned: 19 (million) 0.18/0.49 % (16354)------------------------------ 0.18/0.49 % (16354)------------------------------ 0.18/0.50 % (16331)Instruction limit reached! 0.18/0.50 % (16331)------------------------------ 0.18/0.50 % (16331)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.50 % (16331)Termination reason: Unknown 0.18/0.50 % (16331)Termination phase: Saturation 0.18/0.50 0.18/0.50 % (16331)Memory used [KB]: 6524 0.18/0.50 % (16331)Time elapsed: 0.132 s 0.18/0.50 % (16331)Instructions burned: 275 (million) 0.18/0.50 % (16331)------------------------------ 0.18/0.50 % (16331)------------------------------ 0.18/0.50 % (16355)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on E---3.1_16218 for (1798ds/879Mi) 0.18/0.51 % (16356)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on E---3.1_16218 for (1798ds/17Mi) 0.18/0.52 % (16356)Instruction limit reached! 0.18/0.52 % (16356)------------------------------ 0.18/0.52 % (16356)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.52 % (16356)Termination reason: Unknown 0.18/0.52 % (16356)Termination phase: shuffling 0.18/0.52 0.18/0.52 % (16356)Memory used [KB]: 1535 0.18/0.52 % (16356)Time elapsed: 0.011 s 0.18/0.52 % (16356)Instructions burned: 18 (million) 0.18/0.52 % (16356)------------------------------ 0.18/0.52 % (16356)------------------------------ 0.18/0.54 % (16357)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on E---3.1_16218 for (1798ds/3Mi) 0.18/0.54 % (16357)Instruction limit reached! 0.18/0.54 % (16357)------------------------------ 0.18/0.54 % (16357)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.54 % (16357)Termination reason: Unknown 0.18/0.54 % (16357)Termination phase: shuffling 0.18/0.54 0.18/0.54 % (16357)Memory used [KB]: 1279 0.18/0.54 % (16357)Time elapsed: 0.004 s 0.18/0.54 % (16357)Instructions burned: 4 (million) 0.18/0.54 % (16357)------------------------------ 0.18/0.54 % (16357)------------------------------ 0.18/0.55 % (16358)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on E---3.1_16218 for (1798ds/30Mi) 0.18/0.57 % (16358)Instruction limit reached! 0.18/0.57 % (16358)------------------------------ 0.18/0.57 % (16358)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.57 % (16358)Termination reason: Unknown 0.18/0.57 % (16358)Termination phase: Property scanning 0.18/0.57 0.18/0.57 % (16358)Memory used [KB]: 1663 0.18/0.57 % (16358)Time elapsed: 0.017 s 0.18/0.57 % (16358)Instructions burned: 31 (million) 0.18/0.57 % (16358)------------------------------ 0.18/0.57 % (16358)------------------------------ 1.67/0.59 % (16359)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on E---3.1_16218 for (1797ds/127Mi) 1.80/0.63 % (16352)Instruction limit reached! 1.80/0.63 % (16352)------------------------------ 1.80/0.63 % (16352)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.80/0.63 % (16352)Termination reason: Unknown 1.80/0.63 % (16352)Termination phase: Saturation 1.80/0.63 1.80/0.63 % (16352)Memory used [KB]: 6908 1.80/0.63 % (16352)Time elapsed: 0.160 s 1.80/0.63 % (16352)Instructions burned: 377 (million) 1.80/0.63 % (16352)------------------------------ 1.80/0.63 % (16352)------------------------------ 2.04/0.64 % (16359)Instruction limit reached! 2.04/0.64 % (16359)------------------------------ 2.04/0.64 % (16359)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.04/0.64 % (16359)Termination reason: Unknown 2.04/0.64 % (16359)Termination phase: Saturation 2.04/0.64 2.04/0.64 % (16359)Memory used [KB]: 6396 2.04/0.64 % (16359)Time elapsed: 0.053 s 2.04/0.64 % (16359)Instructions burned: 128 (million) 2.04/0.64 % (16359)------------------------------ 2.04/0.64 % (16359)------------------------------ 2.04/0.64 % (16360)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on E---3.1_16218 for (1797ds/100Mi) 2.04/0.65 % (16361)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on E---3.1_16218 for (1797ds/3Mi) 2.04/0.65 % (16361)Instruction limit reached! 2.04/0.65 % (16361)------------------------------ 2.04/0.65 % (16361)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.04/0.65 % (16361)Termination reason: Unknown 2.04/0.65 % (16361)Termination phase: shuffling 2.04/0.65 2.04/0.65 % (16361)Memory used [KB]: 1279 2.04/0.65 % (16361)Time elapsed: 0.004 s 2.04/0.65 % (16361)Instructions burned: 3 (million) 2.04/0.65 % (16361)------------------------------ 2.04/0.65 % (16361)------------------------------ 2.04/0.67 % (16362)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on E---3.1_16218 for (1796ds/20Mi) 2.04/0.68 % (16362)Instruction limit reached! 2.04/0.68 % (16362)------------------------------ 2.04/0.68 % (16362)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.04/0.68 % (16362)Termination reason: Unknown 2.04/0.68 % (16362)Termination phase: Property scanning 2.04/0.68 2.04/0.68 % (16362)Memory used [KB]: 1535 2.04/0.68 % (16362)Time elapsed: 0.012 s 2.04/0.68 % (16362)Instructions burned: 21 (million) 2.04/0.68 % (16362)------------------------------ 2.04/0.68 % (16362)------------------------------ 2.04/0.68 % (16360)Instruction limit reached! 2.04/0.68 % (16360)------------------------------ 2.04/0.68 % (16360)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.04/0.68 % (16360)Termination reason: Unknown 2.04/0.68 % (16360)Termination phase: Property scanning 2.04/0.68 2.04/0.68 % (16360)Memory used [KB]: 1918 2.04/0.68 % (16360)Time elapsed: 0.041 s 2.04/0.68 % (16360)Instructions burned: 100 (million) 2.04/0.68 % (16360)------------------------------ 2.04/0.68 % (16360)------------------------------ 2.04/0.69 % (16363)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on E---3.1_16218 for (1796ds/86Mi) 2.04/0.70 % (16364)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on E---3.1_16218 for (1796ds/107Mi) 2.04/0.73 % (16363)Instruction limit reached! 2.04/0.73 % (16363)------------------------------ 2.04/0.73 % (16363)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.04/0.73 % (16363)Termination reason: Unknown 2.04/0.73 % (16363)Termination phase: Property scanning 2.04/0.73 2.04/0.73 % (16363)Memory used [KB]: 1918 2.04/0.73 % (16363)Time elapsed: 0.036 s 2.04/0.73 % (16363)Instructions burned: 88 (million) 2.04/0.73 % (16363)------------------------------ 2.04/0.73 % (16363)------------------------------ 2.70/0.74 % (16364)Instruction limit reached! 2.70/0.74 % (16364)------------------------------ 2.70/0.74 % (16364)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.70/0.74 % (16364)Termination reason: Unknown 2.70/0.74 % (16364)Termination phase: Saturation 2.70/0.74 2.70/0.74 % (16364)Memory used [KB]: 6396 2.70/0.74 % (16364)Time elapsed: 0.046 s 2.70/0.74 % (16364)Instructions burned: 109 (million) 2.70/0.74 % (16364)------------------------------ 2.70/0.74 % (16364)------------------------------ 2.70/0.75 % (16365)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on E---3.1_16218 for (1796ds/39Mi) 2.70/0.76 % (16366)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on E---3.1_16218 for (1796ds/448Mi) 2.70/0.76 % (16365)Instruction limit reached! 2.70/0.76 % (16365)------------------------------ 2.70/0.76 % (16365)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.70/0.76 % (16365)Termination reason: Unknown 2.70/0.76 % (16365)Termination phase: Function definition elimination 2.70/0.76 2.70/0.76 % (16365)Memory used [KB]: 1663 2.70/0.76 % (16365)Time elapsed: 0.020 s 2.70/0.76 % (16365)Instructions burned: 40 (million) 2.70/0.76 % (16365)------------------------------ 2.70/0.76 % (16365)------------------------------ 2.70/0.76 % (16346)Instruction limit reached! 2.70/0.76 % (16346)------------------------------ 2.70/0.76 % (16346)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.70/0.76 % (16346)Termination reason: Unknown 2.70/0.76 % (16346)Termination phase: Saturation 2.70/0.76 2.70/0.76 % (16346)Memory used [KB]: 7291 2.70/0.76 % (16346)Time elapsed: 0.350 s 2.70/0.76 % (16346)Instructions burned: 711 (million) 2.70/0.76 % (16346)------------------------------ 2.70/0.76 % (16346)------------------------------ 2.70/0.78 % (16367)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on E---3.1_16218 for (1795ds/46Mi) 2.70/0.78 % (16368)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on E---3.1_16218 for (1795ds/98Mi) 2.70/0.79 % (16337)Instruction limit reached! 2.70/0.79 % (16337)------------------------------ 2.70/0.79 % (16337)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.70/0.79 % (16337)Termination reason: Unknown 2.70/0.79 % (16337)Termination phase: Saturation 2.70/0.79 2.70/0.79 % (16337)Memory used [KB]: 7291 2.70/0.79 % (16337)Time elapsed: 0.398 s 2.70/0.79 % (16337)Instructions burned: 1041 (million) 2.70/0.79 % (16337)------------------------------ 2.70/0.79 % (16337)------------------------------ 3.10/0.80 % (16367)Instruction limit reached! 3.10/0.80 % (16367)------------------------------ 3.10/0.80 % (16367)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.10/0.80 % (16367)Termination reason: Unknown 3.10/0.80 % (16367)Termination phase: Twee Goal Transformation 3.10/0.80 3.10/0.80 % (16367)Memory used [KB]: 1663 3.10/0.80 % (16367)Time elapsed: 0.023 s 3.10/0.80 % (16367)Instructions burned: 47 (million) 3.10/0.80 % (16367)------------------------------ 3.10/0.80 % (16367)------------------------------ 3.10/0.81 % (16369)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on E---3.1_16218 for (1795ds/507Mi) 3.10/0.82 % (16370)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on E---3.1_16218 for (1795ds/149Mi) 3.10/0.82 % (16368)Instruction limit reached! 3.10/0.82 % (16368)------------------------------ 3.10/0.82 % (16368)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.10/0.82 % (16368)Termination reason: Unknown 3.10/0.82 % (16368)Termination phase: Property scanning 3.10/0.82 3.10/0.82 % (16368)Memory used [KB]: 1791 3.10/0.82 % (16368)Time elapsed: 0.040 s 3.10/0.82 % (16368)Instructions burned: 99 (million) 3.10/0.82 % (16368)------------------------------ 3.10/0.82 % (16368)------------------------------ 3.10/0.83 % (16371)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on E---3.1_16218 for (1795ds/39Mi) 3.10/0.84 % (16353)Instruction limit reached! 3.10/0.84 % (16353)------------------------------ 3.10/0.84 % (16353)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.10/0.84 % (16353)Termination reason: Unknown 3.10/0.84 % (16353)Termination phase: Saturation 3.10/0.84 3.10/0.84 % (16353)Memory used [KB]: 8571 3.10/0.84 % (16353)Time elapsed: 0.363 s 3.10/0.84 % (16353)Instructions burned: 780 (million) 3.10/0.84 % (16353)------------------------------ 3.10/0.84 % (16353)------------------------------ 3.10/0.85 % (16371)Instruction limit reached! 3.10/0.85 % (16371)------------------------------ 3.10/0.85 % (16371)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.10/0.85 % (16371)Termination reason: Unknown 3.10/0.85 % (16371)Termination phase: Function definition elimination 3.10/0.85 3.10/0.85 % (16371)Memory used [KB]: 1663 3.10/0.85 % (16371)Time elapsed: 0.020 s 3.10/0.85 % (16371)Instructions burned: 40 (million) 3.10/0.85 % (16371)------------------------------ 3.10/0.85 % (16371)------------------------------ 3.10/0.85 % (16372)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on E---3.1_16218 for (1795ds/6Mi) 3.10/0.86 % (16372)Instruction limit reached! 3.10/0.86 % (16372)------------------------------ 3.10/0.86 % (16372)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.10/0.86 % (16372)Termination reason: Unknown 3.10/0.86 % (16372)Termination phase: shuffling 3.10/0.86 3.10/0.86 % (16372)Memory used [KB]: 1279 3.10/0.86 % (16372)Time elapsed: 0.005 s 3.10/0.86 % (16372)Instructions burned: 6 (million) 3.10/0.86 % (16372)------------------------------ 3.10/0.86 % (16372)------------------------------ 3.10/0.86 % (16348)Instruction limit reached! 3.10/0.86 % (16348)------------------------------ 3.10/0.86 % (16348)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.10/0.86 % (16348)Termination reason: Unknown 3.10/0.86 % (16348)Termination phase: Saturation 3.10/0.86 3.10/0.86 % (16348)Memory used [KB]: 6780 3.10/0.86 % (16348)Time elapsed: 0.437 s 3.10/0.86 % (16348)Instructions burned: 903 (million) 3.10/0.86 % (16348)------------------------------ 3.10/0.86 % (16348)------------------------------ 3.44/0.87 % (16373)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on E---3.1_16218 for (1794ds/1087Mi) 3.44/0.87 % (16374)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on E---3.1_16218 for (1794ds/47Mi) 3.44/0.87 % (16375)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on E---3.1_16218 for (1794ds/44Mi) 3.44/0.88 % (16370)Instruction limit reached! 3.44/0.88 % (16370)------------------------------ 3.44/0.88 % (16370)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.44/0.88 % (16370)Termination reason: Unknown 3.44/0.88 % (16370)Termination phase: Saturation 3.44/0.88 3.44/0.88 % (16370)Memory used [KB]: 6652 3.44/0.88 % (16370)Time elapsed: 0.070 s 3.44/0.88 % (16370)Instructions burned: 149 (million) 3.44/0.88 % (16370)------------------------------ 3.44/0.88 % (16370)------------------------------ 3.44/0.89 % (16374)Instruction limit reached! 3.44/0.89 % (16374)------------------------------ 3.44/0.89 % (16374)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.44/0.89 % (16374)Termination reason: Unknown 3.44/0.89 % (16374)Termination phase: Function definition elimination 3.44/0.89 3.44/0.89 % (16374)Memory used [KB]: 1663 3.44/0.89 % (16374)Time elapsed: 0.023 s 3.44/0.89 % (16374)Instructions burned: 50 (million) 3.44/0.89 % (16374)------------------------------ 3.44/0.89 % (16374)------------------------------ 3.44/0.89 % (16375)Instruction limit reached! 3.44/0.89 % (16375)------------------------------ 3.44/0.89 % (16375)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.44/0.89 % (16375)Termination reason: Unknown 3.44/0.89 % (16375)Termination phase: Saturation 3.44/0.89 3.44/0.89 % (16375)Memory used [KB]: 1663 3.44/0.89 % (16375)Time elapsed: 0.021 s 3.44/0.89 % (16375)Instructions burned: 44 (million) 3.44/0.89 % (16375)------------------------------ 3.44/0.89 % (16375)------------------------------ 3.44/0.90 % (16355)Instruction limit reached! 3.44/0.90 % (16355)------------------------------ 3.44/0.90 % (16355)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.63/0.90 % (16355)Termination reason: Unknown 3.63/0.90 % (16355)Termination phase: Saturation 3.63/0.90 3.63/0.90 % (16355)Memory used [KB]: 7164 3.63/0.90 % (16355)Time elapsed: 0.398 s 3.63/0.90 % (16355)Instructions burned: 880 (million) 3.63/0.90 % (16355)------------------------------ 3.63/0.90 % (16355)------------------------------ 3.63/0.90 % (16376)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on E---3.1_16218 for (1794ds/432Mi) 3.63/0.91 % (16377)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on E---3.1_16218 for (1794ds/62Mi) 3.63/0.91 % (16378)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on E---3.1_16218 for (1794ds/31Mi) 3.63/0.92 % (16378)Instruction limit reached! 3.63/0.92 % (16378)------------------------------ 3.63/0.92 % (16378)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.63/0.92 % (16378)Termination reason: Unknown 3.63/0.92 % (16378)Termination phase: Property scanning 3.63/0.92 3.63/0.92 % (16378)Memory used [KB]: 1663 3.63/0.92 % (16378)Time elapsed: 0.017 s 3.63/0.92 % (16378)Instructions burned: 33 (million) 3.63/0.92 % (16378)------------------------------ 3.63/0.92 % (16378)------------------------------ 3.63/0.93 % (16379)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on E---3.1_16218 for (1794ds/96Mi) 3.63/0.93 % (16377)Instruction limit reached! 3.63/0.93 % (16377)------------------------------ 3.63/0.93 % (16377)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.63/0.93 % (16377)Termination reason: Unknown 3.63/0.93 % (16377)Termination phase: Function definition elimination 3.63/0.93 3.63/0.93 % (16377)Memory used [KB]: 1791 3.63/0.93 % (16377)Time elapsed: 0.027 s 3.63/0.93 % (16377)Instructions burned: 64 (million) 3.63/0.93 % (16377)------------------------------ 3.63/0.93 % (16377)------------------------------ 3.71/0.94 % (16380)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on E---3.1_16218 for (1794ds/453Mi) 3.71/0.95 % (16381)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on E---3.1_16218 for (1794ds/71Mi) 3.71/0.95 % (16379)Instruction limit reached! 3.71/0.95 % (16379)------------------------------ 3.71/0.95 % (16379)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.71/0.95 % (16379)Termination reason: Unknown 3.71/0.95 % (16379)Termination phase: Property scanning 3.71/0.95 3.71/0.95 % (16379)Memory used [KB]: 1918 3.71/0.95 % (16379)Time elapsed: 0.026 s 3.71/0.95 % (16379)Instructions burned: 96 (million) 3.71/0.95 % (16379)------------------------------ 3.71/0.95 % (16379)------------------------------ 3.71/0.96 % (16382)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on E---3.1_16218 for (1793ds/83Mi) 3.71/0.97 % (16381)Instruction limit reached! 3.71/0.97 % (16381)------------------------------ 3.71/0.97 % (16381)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.71/0.97 % (16381)Termination reason: Unknown 3.71/0.97 % (16381)Termination phase: Property scanning 3.71/0.97 3.71/0.97 % (16381)Memory used [KB]: 1918 3.71/0.97 % (16381)Time elapsed: 0.027 s 3.71/0.97 % (16381)Instructions burned: 73 (million) 3.71/0.97 % (16381)------------------------------ 3.71/0.97 % (16381)------------------------------ 3.71/0.98 % (16366)Instruction limit reached! 3.71/0.98 % (16366)------------------------------ 3.71/0.98 % (16366)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.71/0.98 % (16366)Termination reason: Unknown 3.71/0.98 % (16366)Termination phase: Saturation 3.71/0.98 3.71/0.98 % (16366)Memory used [KB]: 7547 3.71/0.98 % (16366)Time elapsed: 0.245 s 3.71/0.98 % (16366)Instructions burned: 449 (million) 3.71/0.98 % (16366)------------------------------ 3.71/0.98 % (16366)------------------------------ 3.71/0.98 % (16383)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on E---3.1_16218 for (1793ds/11Mi) 3.71/0.98 % (16369)Instruction limit reached! 3.71/0.98 % (16369)------------------------------ 3.71/0.98 % (16369)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.71/0.98 % (16369)Termination reason: Unknown 3.71/0.98 % (16369)Termination phase: Saturation 3.71/0.98 3.71/0.98 % (16369)Memory used [KB]: 6908 3.71/0.98 % (16369)Time elapsed: 0.175 s 3.71/0.98 % (16369)Instructions burned: 509 (million) 3.71/0.98 % (16369)------------------------------ 3.71/0.98 % (16369)------------------------------ 3.71/0.99 % (16383)Instruction limit reached! 3.71/0.99 % (16383)------------------------------ 3.71/0.99 % (16383)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.71/0.99 % (16383)Termination reason: Unknown 3.71/0.99 % (16383)Termination phase: shuffling 3.71/0.99 3.71/0.99 % (16383)Memory used [KB]: 1535 3.71/0.99 % (16383)Time elapsed: 0.006 s 3.71/0.99 % (16383)Instructions burned: 13 (million) 3.71/0.99 % (16383)------------------------------ 3.71/0.99 % (16383)------------------------------ 3.71/0.99 % (16382)Instruction limit reached! 3.71/0.99 % (16382)------------------------------ 3.71/0.99 % (16382)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.71/0.99 % (16382)Termination reason: Unknown 3.71/0.99 % (16382)Termination phase: Saturation 3.71/0.99 3.71/0.99 % (16382)Memory used [KB]: 6396 3.71/0.99 % (16382)Time elapsed: 0.029 s 3.71/0.99 % (16382)Instructions burned: 85 (million) 3.71/0.99 % (16382)------------------------------ 3.71/0.99 % (16382)------------------------------ 3.71/0.99 % (16384)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on E---3.1_16218 for (1793ds/41Mi) 3.71/0.99 % (16385)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on E---3.1_16218 for (1793ds/6Mi) 3.71/0.99 % (16386)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on E---3.1_16218 for (1793ds/150Mi) 3.71/1.00 % (16385)Instruction limit reached! 3.71/1.00 % (16385)------------------------------ 3.71/1.00 % (16385)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.71/1.00 % (16385)Termination reason: Unknown 3.71/1.00 % (16385)Termination phase: shuffling 3.71/1.00 3.71/1.00 % (16385)Memory used [KB]: 1279 3.71/1.00 % (16385)Time elapsed: 0.004 s 3.71/1.00 % (16385)Instructions burned: 7 (million) 3.71/1.00 % (16385)------------------------------ 3.71/1.00 % (16385)------------------------------ 3.71/1.01 % (16387)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on E---3.1_16218 for (1793ds/343Mi) 3.71/1.01 % (16384)Instruction limit reached! 3.71/1.01 % (16384)------------------------------ 3.71/1.01 % (16384)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.71/1.01 % (16384)Termination reason: Unknown 3.71/1.01 % (16384)Termination phase: Function definition elimination 3.71/1.01 3.71/1.01 % (16384)Memory used [KB]: 1663 3.71/1.01 % (16384)Time elapsed: 0.019 s 3.71/1.01 % (16384)Instructions burned: 41 (million) 3.71/1.01 % (16384)------------------------------ 3.71/1.01 % (16384)------------------------------ 3.71/1.02 % (16388)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on E---3.1_16218 for (1793ds/109Mi) 3.71/1.03 % (16389)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on E---3.1_16218 for (1793ds/253Mi) 4.31/1.04 % (16386)Instruction limit reached! 4.31/1.04 % (16386)------------------------------ 4.31/1.04 % (16386)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 4.31/1.04 % (16386)Termination reason: Unknown 4.31/1.04 % (16386)Termination phase: Saturation 4.31/1.04 4.31/1.04 % (16386)Memory used [KB]: 6524 4.31/1.04 % (16386)Time elapsed: 0.046 s 4.31/1.04 % (16386)Instructions burned: 152 (million) 4.31/1.04 % (16386)------------------------------ 4.31/1.04 % (16386)------------------------------ 4.31/1.05 % (16390)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on E---3.1_16218 for (1793ds/140Mi) 4.31/1.06 % (16388)Instruction limit reached! 4.31/1.06 % (16388)------------------------------ 4.31/1.06 % (16388)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 4.31/1.06 % (16388)Termination reason: Unknown 4.31/1.06 % (16388)Termination phase: Saturation 4.31/1.06 4.31/1.06 % (16388)Memory used [KB]: 6396 4.31/1.06 % (16388)Time elapsed: 0.045 s 4.31/1.06 % (16388)Instructions burned: 110 (million) 4.31/1.06 % (16388)------------------------------ 4.31/1.06 % (16388)------------------------------ 4.31/1.07 % (16376)Instruction limit reached! 4.31/1.07 % (16376)------------------------------ 4.31/1.07 % (16376)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 4.31/1.07 % (16376)Termination reason: Unknown 4.31/1.07 % (16376)Termination phase: Saturation 4.31/1.07 4.31/1.07 % (16376)Memory used [KB]: 3709 4.31/1.07 % (16376)Time elapsed: 0.178 s 4.31/1.07 % (16376)Instructions burned: 433 (million) 4.31/1.07 % (16376)------------------------------ 4.31/1.07 % (16376)------------------------------ 4.31/1.07 % (16391)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on E---3.1_16218 for (1792ds/614Mi) 4.61/1.09 % (16390)Instruction limit reached! 4.61/1.09 % (16390)------------------------------ 4.61/1.09 % (16390)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 4.61/1.09 % (16390)Termination reason: Unknown 4.61/1.09 % (16390)Termination phase: Saturation 4.61/1.09 4.61/1.09 % (16390)Memory used [KB]: 6652 4.61/1.09 % (16390)Time elapsed: 0.047 s 4.61/1.09 % (16390)Instructions burned: 141 (million) 4.61/1.09 % (16390)------------------------------ 4.61/1.09 % (16390)------------------------------ 4.61/1.10 % (16392)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on E---3.1_16218 for (1792ds/202Mi) 4.61/1.10 % (16393)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on E---3.1_16218 for (1792ds/339Mi) 4.61/1.11 % (16380)Instruction limit reached! 4.61/1.11 % (16380)------------------------------ 4.61/1.11 % (16380)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 4.61/1.11 % (16380)Termination reason: Unknown 4.61/1.11 % (16380)Termination phase: Saturation 4.61/1.11 4.61/1.11 % (16380)Memory used [KB]: 6524 4.61/1.11 % (16380)Time elapsed: 0.173 s 4.61/1.11 % (16380)Instructions burned: 454 (million) 4.61/1.11 % (16380)------------------------------ 4.61/1.11 % (16380)------------------------------ 4.61/1.13 % (16394)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on E---3.1_16218 for (1792ds/283Mi) 4.61/1.15 % (16389)Instruction limit reached! 4.61/1.15 % (16389)------------------------------ 4.61/1.15 % (16389)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 4.61/1.15 % (16389)Termination reason: Unknown 4.61/1.15 % (16389)Termination phase: Saturation 4.61/1.15 4.61/1.15 % (16389)Memory used [KB]: 6652 4.61/1.15 % (16389)Time elapsed: 0.123 s 4.61/1.15 % (16389)Instructions burned: 254 (million) 4.61/1.15 % (16389)------------------------------ 4.61/1.15 % (16389)------------------------------ 4.61/1.17 % (16387)Instruction limit reached! 4.61/1.17 % (16387)------------------------------ 4.61/1.17 % (16387)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 4.61/1.17 % (16395)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on E---3.1_16218 for (1792ds/134Mi) 4.61/1.17 % (16387)Termination reason: Unknown 4.61/1.17 % (16387)Termination phase: Saturation 4.61/1.17 4.61/1.17 % (16387)Memory used [KB]: 6652 4.61/1.17 % (16387)Time elapsed: 0.163 s 4.61/1.17 % (16387)Instructions burned: 344 (million) 4.61/1.17 % (16387)------------------------------ 4.61/1.17 % (16387)------------------------------ 4.61/1.17 % (16392)Instruction limit reached! 4.61/1.17 % (16392)------------------------------ 4.61/1.17 % (16392)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 4.61/1.17 % (16392)Termination reason: Unknown 4.61/1.17 % (16392)Termination phase: Saturation 4.61/1.17 4.61/1.17 % (16392)Memory used [KB]: 6652 4.61/1.17 % (16392)Time elapsed: 0.098 s 4.61/1.17 % (16392)Instructions burned: 203 (million) 4.61/1.17 % (16392)------------------------------ 4.61/1.17 % (16392)------------------------------ 5.83/1.18 % (16397)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on E---3.1_16218 for (1791ds/192Mi) 5.83/1.18 % (16396)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on E---3.1_16218 for (1791ds/298Mi) 6.02/1.22 % (16395)Instruction limit reached! 6.02/1.22 % (16395)------------------------------ 6.02/1.22 % (16395)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.02/1.22 % (16395)Termination reason: Unknown 6.02/1.22 % (16395)Termination phase: Saturation 6.02/1.22 6.02/1.22 % (16395)Memory used [KB]: 6396 6.02/1.22 % (16395)Time elapsed: 0.054 s 6.02/1.22 % (16395)Instructions burned: 135 (million) 6.02/1.22 % (16395)------------------------------ 6.02/1.22 % (16395)------------------------------ 6.02/1.23 % (16398)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on E---3.1_16218 for (1791ds/258Mi) 6.02/1.23 % (16394)Instruction limit reached! 6.02/1.23 % (16394)------------------------------ 6.02/1.23 % (16394)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.02/1.23 % (16394)Termination reason: Unknown 6.02/1.23 % (16394)Termination phase: Saturation 6.02/1.23 6.02/1.23 % (16394)Memory used [KB]: 6908 6.02/1.23 % (16394)Time elapsed: 0.110 s 6.02/1.23 % (16394)Instructions burned: 285 (million) 6.02/1.23 % (16394)------------------------------ 6.02/1.23 % (16394)------------------------------ 6.09/1.24 % (16397)Instruction limit reached! 6.09/1.24 % (16397)------------------------------ 6.09/1.24 % (16397)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.09/1.24 % (16397)Termination reason: Unknown 6.09/1.24 % (16397)Termination phase: Saturation 6.09/1.24 6.09/1.24 % (16397)Memory used [KB]: 6524 6.09/1.24 % (16397)Time elapsed: 0.058 s 6.09/1.24 % (16397)Instructions burned: 194 (million) 6.09/1.24 % (16397)------------------------------ 6.09/1.24 % (16397)------------------------------ 6.09/1.25 % (16399)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on E---3.1_16218 for (1791ds/90Mi) 6.09/1.25 % (16393)Instruction limit reached! 6.09/1.25 % (16393)------------------------------ 6.09/1.25 % (16393)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.09/1.25 % (16393)Termination reason: Unknown 6.09/1.25 % (16393)Termination phase: Saturation 6.09/1.25 6.09/1.25 % (16393)Memory used [KB]: 7547 6.09/1.25 % (16393)Time elapsed: 0.147 s 6.09/1.25 % (16393)Instructions burned: 340 (million) 6.09/1.25 % (16393)------------------------------ 6.09/1.25 % (16393)------------------------------ 6.09/1.25 % (16400)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on E---3.1_16218 for (1791ds/231Mi) 6.09/1.27 % (16401)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on E---3.1_16218 for (1791ds/458Mi) 6.09/1.28 % (16399)Instruction limit reached! 6.09/1.28 % (16399)------------------------------ 6.09/1.28 % (16399)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.09/1.28 % (16399)Termination reason: Unknown 6.09/1.28 % (16399)Termination phase: Property scanning 6.09/1.28 6.09/1.28 % (16399)Memory used [KB]: 2046 6.09/1.28 % (16399)Time elapsed: 0.038 s 6.09/1.28 % (16399)Instructions burned: 92 (million) 6.09/1.28 % (16399)------------------------------ 6.09/1.28 % (16399)------------------------------ 6.09/1.29 % (16396)Instruction limit reached! 6.09/1.29 % (16396)------------------------------ 6.09/1.29 % (16396)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.09/1.29 % (16396)Termination reason: Unknown 6.09/1.29 % (16396)Termination phase: Saturation 6.09/1.29 6.09/1.29 % (16396)Memory used [KB]: 6524 6.09/1.29 % (16396)Time elapsed: 0.112 s 6.09/1.29 % (16396)Instructions burned: 300 (million) 6.09/1.29 % (16396)------------------------------ 6.09/1.29 % (16396)------------------------------ 6.09/1.29 % (16402)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on E---3.1_16218 for (1790ds/31Mi) 6.09/1.30 % (16398)Instruction limit reached! 6.09/1.30 % (16398)------------------------------ 6.09/1.30 % (16398)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.09/1.30 % (16398)Termination reason: Unknown 6.09/1.30 % (16398)Termination phase: Saturation 6.09/1.30 6.09/1.30 % (16398)Memory used [KB]: 6652 6.09/1.30 % (16398)Time elapsed: 0.074 s 6.09/1.30 % (16398)Instructions burned: 259 (million) 6.09/1.30 % (16398)------------------------------ 6.09/1.30 % (16398)------------------------------ 6.09/1.31 % (16402)Instruction limit reached! 6.09/1.31 % (16402)------------------------------ 6.09/1.31 % (16402)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.09/1.31 % (16402)Termination reason: Unknown 6.09/1.31 % (16402)Termination phase: Property scanning 6.09/1.31 6.09/1.31 % (16402)Memory used [KB]: 1663 6.09/1.31 % (16402)Time elapsed: 0.013 s 6.09/1.31 % (16402)Instructions burned: 31 (million) 6.09/1.31 % (16402)------------------------------ 6.09/1.31 % (16402)------------------------------ 6.09/1.31 % (16403)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on E---3.1_16218 for (1790ds/297Mi) 6.09/1.31 % (16404)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on E---3.1_16218 for (1790ds/987Mi) 6.63/1.32 % (16405)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on E---3.1_16218 for (1790ds/182Mi) 6.63/1.33 % (16391)Instruction limit reached! 6.63/1.33 % (16391)------------------------------ 6.63/1.33 % (16391)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.63/1.33 % (16391)Termination reason: Unknown 6.63/1.33 % (16391)Termination phase: Saturation 6.63/1.33 6.63/1.33 % (16391)Memory used [KB]: 7547 6.63/1.33 % (16391)Time elapsed: 0.259 s 6.63/1.33 % (16391)Instructions burned: 614 (million) 6.63/1.33 % (16391)------------------------------ 6.63/1.33 % (16391)------------------------------ 6.63/1.35 % (16408)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on E---3.1_16218 for (1790ds/182Mi) 6.63/1.36 % (16400)Instruction limit reached! 6.63/1.36 % (16400)------------------------------ 6.63/1.36 % (16400)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.63/1.36 % (16400)Termination reason: Unknown 6.63/1.36 % (16400)Termination phase: Saturation 6.63/1.36 6.63/1.36 % (16400)Memory used [KB]: 7419 6.63/1.36 % (16400)Time elapsed: 0.129 s 6.63/1.36 % (16400)Instructions burned: 231 (million) 6.63/1.36 % (16400)------------------------------ 6.63/1.36 % (16400)------------------------------ 6.63/1.37 % (16411)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on E---3.1_16218 for (1789ds/154Mi) 6.86/1.38 % (16373)Instruction limit reached! 6.86/1.38 % (16373)------------------------------ 6.86/1.38 % (16373)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.86/1.38 % (16373)Termination reason: Unknown 6.86/1.38 % (16373)Termination phase: Saturation 6.86/1.38 6.86/1.38 % (16373)Memory used [KB]: 7547 6.86/1.38 % (16373)Time elapsed: 0.522 s 6.86/1.38 % (16373)Instructions burned: 1087 (million) 6.86/1.38 % (16373)------------------------------ 6.86/1.38 % (16373)------------------------------ 6.86/1.40 % (16405)Instruction limit reached! 6.86/1.40 % (16405)------------------------------ 6.86/1.40 % (16405)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.86/1.40 % (16405)Termination reason: Unknown 6.86/1.40 % (16405)Termination phase: Saturation 6.86/1.40 6.86/1.40 % (16405)Memory used [KB]: 6396 6.86/1.40 % (16405)Time elapsed: 0.075 s 6.86/1.40 % (16405)Instructions burned: 184 (million) 6.86/1.40 % (16405)------------------------------ 6.86/1.40 % (16405)------------------------------ 6.86/1.40 % (16414)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on E---3.1_16218 for (1789ds/79Mi) 6.86/1.41 % (16417)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on E---3.1_16218 for (1789ds/216Mi) 6.86/1.43 % (16411)Instruction limit reached! 6.86/1.43 % (16411)------------------------------ 6.86/1.43 % (16411)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.86/1.43 % (16411)Termination reason: Unknown 6.86/1.43 % (16411)Termination phase: Saturation 6.86/1.43 6.86/1.43 % (16411)Memory used [KB]: 6396 6.86/1.43 % (16411)Time elapsed: 0.062 s 6.86/1.43 % (16411)Instructions burned: 154 (million) 6.86/1.43 % (16411)------------------------------ 6.86/1.43 % (16411)------------------------------ 6.86/1.43 % (16414)Instruction limit reached! 6.86/1.43 % (16414)------------------------------ 6.86/1.43 % (16414)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.86/1.43 % (16414)Termination reason: Unknown 6.86/1.43 % (16414)Termination phase: Property scanning 6.86/1.43 6.86/1.43 % (16414)Memory used [KB]: 1918 6.86/1.43 % (16414)Time elapsed: 0.032 s 6.86/1.43 % (16414)Instructions burned: 79 (million) 6.86/1.43 % (16414)------------------------------ 6.86/1.43 % (16414)------------------------------ 6.86/1.43 % (16408)Instruction limit reached! 6.86/1.43 % (16408)------------------------------ 6.86/1.43 % (16408)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.86/1.43 % (16408)Termination reason: Unknown 6.86/1.43 % (16408)Termination phase: Saturation 6.86/1.43 6.86/1.43 % (16408)Memory used [KB]: 6524 6.86/1.43 % (16408)Time elapsed: 0.087 s 6.86/1.43 % (16408)Instructions burned: 182 (million) 6.86/1.43 % (16408)------------------------------ 6.86/1.43 % (16408)------------------------------ 6.86/1.44 % (16403)Instruction limit reached! 6.86/1.44 % (16403)------------------------------ 6.86/1.44 % (16403)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.86/1.44 % (16403)Termination reason: Unknown 6.86/1.44 % (16403)Termination phase: Saturation 6.86/1.44 6.86/1.44 % (16403)Memory used [KB]: 6652 6.86/1.44 % (16403)Time elapsed: 0.138 s 6.86/1.44 % (16403)Instructions burned: 298 (million) 6.86/1.44 % (16403)------------------------------ 6.86/1.44 % (16403)------------------------------ 6.86/1.45 % (16422)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on E---3.1_16218 for (1789ds/182Mi) 6.86/1.45 % (16420)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on E---3.1_16218 for (1789ds/114Mi) 6.86/1.45 % (16421)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on E---3.1_16218 for (1789ds/922Mi) 6.86/1.45 % (16401)Instruction limit reached! 6.86/1.45 % (16401)------------------------------ 6.86/1.45 % (16401)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.86/1.45 % (16401)Termination reason: Unknown 6.86/1.45 % (16401)Termination phase: Saturation 6.86/1.45 6.86/1.45 % (16401)Memory used [KB]: 6780 6.86/1.45 % (16401)Time elapsed: 0.204 s 6.86/1.45 % (16401)Instructions burned: 460 (million) 6.86/1.45 % (16401)------------------------------ 6.86/1.45 % (16401)------------------------------ 6.86/1.46 % (16423)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on E---3.1_16218 for (1788ds/164Mi) 7.53/1.46 % (16424)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on E---3.1_16218 for (1788ds/50Mi) 7.53/1.48 % (16424)Instruction limit reached! 7.53/1.48 % (16424)------------------------------ 7.53/1.48 % (16424)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 7.53/1.48 % (16424)Termination reason: Unknown 7.53/1.48 % (16424)Termination phase: Function definition elimination 7.53/1.48 7.53/1.48 % (16424)Memory used [KB]: 1663 7.53/1.48 % (16424)Time elapsed: 0.023 s 7.53/1.48 % (16424)Instructions burned: 50 (million) 7.53/1.48 % (16424)------------------------------ 7.53/1.48 % (16424)------------------------------ 7.53/1.49 % (16420)Instruction limit reached! 7.53/1.49 % (16420)------------------------------ 7.53/1.49 % (16420)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 7.53/1.49 % (16420)Termination reason: Unknown 7.53/1.49 % (16420)Termination phase: Saturation 7.53/1.49 7.53/1.49 % (16420)Memory used [KB]: 6396 7.53/1.49 % (16420)Time elapsed: 0.047 s 7.53/1.49 % (16420)Instructions burned: 116 (million) 7.53/1.49 % (16420)------------------------------ 7.53/1.49 % (16420)------------------------------ 7.53/1.50 % (16425)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on E---3.1_16218 for (1788ds/368Mi) 7.53/1.51 % (16426)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on E---3.1_16218 for (1788ds/1021Mi) 7.53/1.51 % (16417)Instruction limit reached! 7.53/1.51 % (16417)------------------------------ 7.53/1.51 % (16417)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 7.53/1.51 % (16417)Termination reason: Unknown 7.53/1.51 % (16417)Termination phase: Saturation 7.53/1.51 7.53/1.51 % (16417)Memory used [KB]: 6524 7.53/1.51 % (16417)Time elapsed: 0.097 s 7.53/1.51 % (16417)Instructions burned: 218 (million) 7.53/1.51 % (16417)------------------------------ 7.53/1.51 % (16417)------------------------------ 7.53/1.51 % (16422)Instruction limit reached! 7.53/1.51 % (16422)------------------------------ 7.53/1.51 % (16422)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 7.53/1.51 % (16422)Termination reason: Unknown 7.53/1.51 % (16422)Termination phase: Saturation 7.53/1.51 7.53/1.51 % (16422)Memory used [KB]: 6396 7.53/1.51 % (16422)Time elapsed: 0.071 s 7.53/1.51 % (16422)Instructions burned: 183 (million) 7.53/1.51 % (16422)------------------------------ 7.53/1.51 % (16422)------------------------------ 7.74/1.52 % (16427)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on E---3.1_16218 for (1788ds/267Mi) 7.74/1.53 % (16428)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on E---3.1_16218 for (1788ds/204Mi) 7.82/1.54 % (16423)Instruction limit reached! 7.82/1.54 % (16423)------------------------------ 7.82/1.54 % (16423)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 7.82/1.54 % (16423)Termination reason: Unknown 7.82/1.54 % (16423)Termination phase: Saturation 7.82/1.54 7.82/1.54 % (16423)Memory used [KB]: 2046 7.82/1.54 % (16423)Time elapsed: 0.082 s 7.82/1.54 % (16423)Instructions burned: 165 (million) 7.82/1.54 % (16423)------------------------------ 7.82/1.54 % (16423)------------------------------ 7.82/1.55 % (16429)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on E---3.1_16218 for (1788ds/26Mi) 7.82/1.56 % (16429)Instruction limit reached! 7.82/1.56 % (16429)------------------------------ 7.82/1.56 % (16429)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 7.82/1.56 % (16429)Termination reason: Unknown 7.82/1.56 % (16429)Termination phase: Property scanning 7.82/1.56 7.82/1.56 % (16429)Memory used [KB]: 1535 7.82/1.56 % (16429)Time elapsed: 0.014 s 7.82/1.56 % (16429)Instructions burned: 26 (million) 7.82/1.56 % (16429)------------------------------ 7.82/1.56 % (16429)------------------------------ 7.82/1.58 % (16430)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on E---3.1_16218 for (1787ds/53Mi) 7.82/1.60 % (16430)Instruction limit reached! 7.82/1.60 % (16430)------------------------------ 7.82/1.60 % (16430)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 7.82/1.60 % (16430)Termination reason: Unknown 7.82/1.60 % (16430)Termination phase: Function definition elimination 7.82/1.60 7.82/1.60 % (16430)Memory used [KB]: 1663 7.82/1.60 % (16430)Time elapsed: 0.024 s 7.82/1.60 % (16430)Instructions burned: 55 (million) 7.82/1.60 % (16430)------------------------------ 7.82/1.60 % (16430)------------------------------ 7.82/1.61 % (16428)Instruction limit reached! 7.82/1.61 % (16428)------------------------------ 7.82/1.61 % (16428)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 7.82/1.61 % (16428)Termination reason: Unknown 7.82/1.61 % (16428)Termination phase: Saturation 7.82/1.61 7.82/1.61 % (16428)Memory used [KB]: 6524 7.82/1.61 % (16428)Time elapsed: 0.081 s 7.82/1.61 % (16428)Instructions burned: 206 (million) 7.82/1.61 % (16428)------------------------------ 7.82/1.61 % (16428)------------------------------ 8.07/1.62 % (16431)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on E---3.1_16218 for (1787ds/4436Mi) 8.07/1.63 % (16432)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on E---3.1_16218 for (1787ds/1539Mi) 8.07/1.63 % (16427)Instruction limit reached! 8.07/1.63 % (16427)------------------------------ 8.07/1.63 % (16427)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 8.07/1.63 % (16427)Termination reason: Unknown 8.07/1.63 % (16427)Termination phase: Saturation 8.07/1.63 8.07/1.63 % (16427)Memory used [KB]: 6908 8.07/1.63 % (16427)Time elapsed: 0.107 s 8.07/1.63 % (16427)Instructions burned: 267 (million) 8.07/1.63 % (16427)------------------------------ 8.07/1.63 % (16427)------------------------------ 8.07/1.64 % (16433)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on E---3.1_16218 for (1787ds/408Mi) 8.07/1.66 % (16425)Instruction limit reached! 8.07/1.66 % (16425)------------------------------ 8.07/1.66 % (16425)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 8.07/1.66 % (16425)Termination reason: Unknown 8.07/1.66 % (16425)Termination phase: Saturation 8.07/1.66 8.07/1.66 % (16425)Memory used [KB]: 7547 8.07/1.66 % (16425)Time elapsed: 0.162 s 8.07/1.66 % (16425)Instructions burned: 368 (million) 8.07/1.66 % (16425)------------------------------ 8.07/1.66 % (16425)------------------------------ 8.07/1.67 % (16434)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on E---3.1_16218 for (1786ds/5205Mi) 8.07/1.69 % (16404)Instruction limit reached! 8.07/1.69 % (16404)------------------------------ 8.07/1.69 % (16404)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 8.07/1.69 % (16404)Termination reason: Unknown 8.07/1.69 % (16404)Termination phase: Saturation 8.07/1.69 8.07/1.69 % (16404)Memory used [KB]: 7675 8.07/1.69 % (16404)Time elapsed: 0.378 s 8.07/1.69 % (16404)Instructions burned: 989 (million) 8.07/1.69 % (16404)------------------------------ 8.07/1.69 % (16404)------------------------------ 9.41/1.70 % (16435)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on E---3.1_16218 for (1786ds/1913Mi) 10.17/1.83 % (16421)Instruction limit reached! 10.17/1.83 % (16421)------------------------------ 10.17/1.83 % (16421)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 10.17/1.83 % (16421)Termination reason: Unknown 10.17/1.83 % (16421)Termination phase: Saturation 10.17/1.83 10.17/1.83 % (16421)Memory used [KB]: 7419 10.17/1.83 % (16421)Time elapsed: 0.391 s 10.17/1.83 % (16421)Instructions burned: 922 (million) 10.17/1.83 % (16421)------------------------------ 10.17/1.83 % (16421)------------------------------ 10.17/1.85 % (16436)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on E---3.1_16218 for (1785ds/4350Mi) 10.17/1.85 % (16433)Instruction limit reached! 10.17/1.85 % (16433)------------------------------ 10.17/1.85 % (16433)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 10.17/1.85 % (16433)Termination reason: Unknown 10.17/1.85 % (16433)Termination phase: Saturation 10.17/1.85 10.17/1.85 % (16433)Memory used [KB]: 7803 10.17/1.85 % (16433)Time elapsed: 0.205 s 10.17/1.85 % (16433)Instructions burned: 408 (million) 10.17/1.85 % (16433)------------------------------ 10.17/1.85 % (16433)------------------------------ 10.17/1.87 % (16437)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on E---3.1_16218 for (1784ds/68Mi) 10.17/1.90 % (16437)Instruction limit reached! 10.17/1.90 % (16437)------------------------------ 10.17/1.90 % (16437)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 10.17/1.90 % (16437)Termination reason: Unknown 10.17/1.90 % (16437)Termination phase: Function definition elimination 10.17/1.90 10.17/1.90 % (16437)Memory used [KB]: 1791 10.17/1.90 % (16437)Time elapsed: 0.029 s 10.17/1.90 % (16437)Instructions burned: 68 (million) 10.17/1.90 % (16437)------------------------------ 10.17/1.90 % (16437)------------------------------ 10.17/1.91 % (16438)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on E---3.1_16218 for (1784ds/358Mi) 10.68/1.92 % (16426)Instruction limit reached! 10.68/1.92 % (16426)------------------------------ 10.68/1.92 % (16426)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 10.68/1.92 % (16426)Termination reason: Unknown 10.68/1.92 % (16426)Termination phase: Saturation 10.68/1.92 10.68/1.92 % (16426)Memory used [KB]: 7036 10.68/1.92 % (16426)Time elapsed: 0.419 s 10.68/1.92 % (16426)Instructions burned: 1021 (million) 10.68/1.92 % (16426)------------------------------ 10.68/1.92 % (16426)------------------------------ 10.68/1.94 % (16439)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on E---3.1_16218 for (1784ds/31Mi) 10.68/1.96 % (16439)Instruction limit reached! 10.68/1.96 % (16439)------------------------------ 10.68/1.96 % (16439)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 10.68/1.96 % (16439)Termination reason: Unknown 10.68/1.96 % (16439)Termination phase: Property scanning 10.68/1.96 10.68/1.96 % (16439)Memory used [KB]: 1663 10.68/1.96 % (16439)Time elapsed: 0.017 s 10.68/1.96 % (16439)Instructions burned: 31 (million) 10.68/1.96 % (16439)------------------------------ 10.68/1.96 % (16439)------------------------------ 10.68/1.97 % (16440)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on E---3.1_16218 for (1783ds/279Mi) 10.97/2.06 % (16438)Instruction limit reached! 10.97/2.06 % (16438)------------------------------ 10.97/2.06 % (16438)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 10.97/2.06 % (16438)Termination reason: Unknown 10.97/2.06 % (16438)Termination phase: Saturation 10.97/2.06 10.97/2.06 % (16438)Memory used [KB]: 6524 10.97/2.06 % (16438)Time elapsed: 0.149 s 10.97/2.06 % (16438)Instructions burned: 358 (million) 10.97/2.06 % (16438)------------------------------ 10.97/2.06 % (16438)------------------------------ 11.37/2.08 % (16441)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on E---3.1_16218 for (1782ds/258Mi) 11.43/2.10 % (16440)Instruction limit reached! 11.43/2.10 % (16440)------------------------------ 11.43/2.10 % (16440)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 11.43/2.10 % (16440)Termination reason: Unknown 11.43/2.10 % (16440)Termination phase: Saturation 11.43/2.10 11.43/2.10 % (16440)Memory used [KB]: 7164 11.43/2.10 % (16440)Time elapsed: 0.134 s 11.43/2.10 % (16440)Instructions burned: 279 (million) 11.43/2.10 % (16440)------------------------------ 11.43/2.10 % (16440)------------------------------ 11.64/2.12 % (16442)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on E---3.1_16218 for (1782ds/26Mi) 11.64/2.13 % (16442)Instruction limit reached! 11.64/2.13 % (16442)------------------------------ 11.64/2.13 % (16442)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 11.64/2.13 % (16442)Termination reason: Unknown 11.64/2.13 % (16442)Termination phase: Property scanning 11.64/2.13 11.64/2.13 % (16442)Memory used [KB]: 1535 11.64/2.13 % (16442)Time elapsed: 0.014 s 11.64/2.13 % (16442)Instructions burned: 27 (million) 11.64/2.13 % (16442)------------------------------ 11.64/2.13 % (16442)------------------------------ 11.64/2.15 % (16443)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on E---3.1_16218 for (1782ds/995Mi) 11.64/2.20 % (16441)Instruction limit reached! 11.64/2.20 % (16441)------------------------------ 11.64/2.20 % (16441)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 11.64/2.20 % (16441)Termination reason: Unknown 11.64/2.20 % (16441)Termination phase: Saturation 11.64/2.20 11.64/2.20 % (16441)Memory used [KB]: 6780 11.64/2.20 % (16441)Time elapsed: 0.128 s 11.64/2.20 % (16441)Instructions burned: 258 (million) 11.64/2.20 % (16441)------------------------------ 11.64/2.20 % (16441)------------------------------ 12.12/2.22 % (16444)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on E---3.1_16218 for (1781ds/373Mi) 12.12/2.23 % (16432)Instruction limit reached! 12.12/2.23 % (16432)------------------------------ 12.12/2.23 % (16432)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 12.12/2.23 % (16432)Termination reason: Unknown 12.12/2.23 % (16432)Termination phase: Saturation 12.12/2.23 12.12/2.23 % (16432)Memory used [KB]: 7547 12.12/2.23 % (16432)Time elapsed: 0.609 s 12.12/2.23 % (16432)Instructions burned: 1539 (million) 12.12/2.23 % (16432)------------------------------ 12.12/2.23 % (16432)------------------------------ 12.12/2.25 % (16445)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on E---3.1_16218 for (1781ds/253Mi) 12.12/2.28 % (16435)First to succeed. 12.12/2.30 % (16435)Refutation found. Thanks to Tanya! 12.12/2.30 % SZS status Theorem for E---3.1_16218 12.12/2.30 % SZS output start Proof for E---3.1_16218 12.12/2.30 thf(func_def_0, type, c_Eps_i: ($i > $o) > $i). 12.12/2.30 thf(func_def_3, type, c_not: $o > $o). 12.12/2.30 thf(func_def_4, type, c_and: $o > $o > $o). 12.12/2.30 thf(func_def_5, type, c_or: $o > $o > $o). 12.12/2.30 thf(func_def_6, type, c_iff: $o > $o > $o). 12.12/2.30 thf(func_def_7, type, c_In: $i > $i > $o). 12.12/2.30 thf(func_def_8, type, c_Subq: $i > $i > $o). 12.12/2.30 thf(func_def_10, type, c_Union: $i > $i). 12.12/2.30 thf(func_def_11, type, c_Power: $i > $i). 12.12/2.30 thf(func_def_12, type, c_Repl: $i > ($i > $i) > $i). 12.12/2.30 thf(func_def_13, type, c_TransSet: $i > $o). 12.12/2.30 thf(func_def_14, type, c_atleast2: $i > $o). 12.12/2.30 thf(func_def_15, type, c_atleast3: $i > $o). 12.12/2.30 thf(func_def_16, type, c_atleast4: $i > $o). 12.12/2.30 thf(func_def_17, type, c_atleast5: $i > $o). 12.12/2.30 thf(func_def_18, type, c_atleast6: $i > $o). 12.12/2.30 thf(func_def_19, type, c_exactly2: $i > $o). 12.12/2.30 thf(func_def_20, type, c_exactly3: $i > $o). 12.12/2.30 thf(func_def_21, type, c_exactly4: $i > $o). 12.12/2.30 thf(func_def_22, type, c_exactly5: $i > $o). 12.12/2.30 thf(func_def_23, type, c_exu_i: ($i > $o) > $o). 12.12/2.30 thf(func_def_24, type, c_reflexive_i: ($i > $i > $o) > $o). 12.12/2.30 thf(func_def_25, type, c_irreflexive_i: ($i > $i > $o) > $o). 12.12/2.30 thf(func_def_26, type, c_symmetric_i: ($i > $i > $o) > $o). 12.12/2.30 thf(func_def_27, type, c_antisymmetric_i: ($i > $i > $o) > $o). 12.12/2.30 thf(func_def_28, type, c_transitive_i: ($i > $i > $o) > $o). 12.12/2.30 thf(func_def_29, type, c_eqreln_i: ($i > $i > $o) > $o). 12.12/2.30 thf(func_def_30, type, c_per_i: ($i > $i > $o) > $o). 12.12/2.30 thf(func_def_31, type, c_linear_i: ($i > $i > $o) > $o). 12.12/2.30 thf(func_def_32, type, c_trichotomous_or_i: ($i > $i > $o) > $o). 12.12/2.30 thf(func_def_33, type, c_partialorder_i: ($i > $i > $o) > $o). 12.12/2.30 thf(func_def_34, type, c_totalorder_i: ($i > $i > $o) > $o). 12.12/2.30 thf(func_def_35, type, c_strictpartialorder_i: ($i > $i > $o) > $o). 12.12/2.30 thf(func_def_36, type, c_stricttotalorder_i: ($i > $i > $o) > $o). 12.12/2.30 thf(func_def_37, type, c_If_i: $o > $i > $i > $i). 12.12/2.30 thf(func_def_38, type, c_exactly1of2: $o > $o > $o). 12.12/2.30 thf(func_def_39, type, c_exactly1of3: $o > $o > $o > $o). 12.12/2.30 thf(func_def_40, type, c_nIn: $i > $i > $o). 12.12/2.30 thf(func_def_41, type, c_nSubq: $i > $i > $o). 12.12/2.30 thf(func_def_42, type, c_UPair: $i > $i > $i). 12.12/2.30 thf(func_def_43, type, c_Sing: $i > $i). 12.12/2.30 thf(func_def_44, type, c_binunion: $i > $i > $i). 12.12/2.30 thf(func_def_45, type, c_SetAdjoin: $i > $i > $i). 12.12/2.30 thf(func_def_46, type, c_famunion: $i > ($i > $i) > $i). 12.12/2.30 thf(func_def_47, type, c_Sep: $i > ($i > $o) > $i). 12.12/2.30 thf(func_def_48, type, c_ReplSep: $i > ($i > $o) > ($i > $i) > $i). 12.12/2.30 thf(func_def_49, type, c_binintersect: $i > $i > $i). 12.12/2.30 thf(func_def_50, type, c_setminus: $i > $i > $i). 12.12/2.30 thf(func_def_51, type, c_inj: $i > $i > ($i > $i) > $o). 12.12/2.30 thf(func_def_52, type, c_bij: $i > $i > ($i > $i) > $o). 12.12/2.30 thf(func_def_53, type, c_atleastp: $i > $i > $o). 12.12/2.30 thf(func_def_54, type, c_equip: $i > $i > $o). 12.12/2.30 thf(func_def_55, type, c_In_rec_poly_G_i: ($i > ($i > $i) > $i) > $i > $i > $o). 12.12/2.30 thf(func_def_56, type, c_In_rec_poly_i: ($i > ($i > $i) > $i) > $i > $i). 12.12/2.30 thf(func_def_57, type, c_ordsucc: $i > $i). 12.12/2.30 thf(func_def_58, type, c_nat_p: $i > $o). 12.12/2.30 thf(func_def_59, type, c_nat_primrec: $i > ($i > $i > $i) > $i > $i). 12.12/2.30 thf(func_def_60, type, c_add_nat: $i > $i > $i). 12.12/2.30 thf(func_def_61, type, c_mul_nat: $i > $i > $i). 12.12/2.30 thf(func_def_62, type, c_ordinal: $i > $o). 12.12/2.30 thf(func_def_63, type, c_V_: $i > $i). 12.12/2.30 thf(func_def_64, type, c_Inj1: $i > $i). 12.12/2.30 thf(func_def_65, type, c_Inj0: $i > $i). 12.12/2.30 thf(func_def_66, type, c_Unj: $i > $i). 12.12/2.30 thf(func_def_67, type, c_combine_funcs: $i > $i > ($i > $i) > ($i > $i) > $i > $i). 12.12/2.30 thf(func_def_68, type, c_setsum: $i > $i > $i). 12.12/2.30 thf(func_def_69, type, c_proj0: $i > $i). 12.12/2.30 thf(func_def_70, type, c_proj1: $i > $i). 12.12/2.30 thf(func_def_71, type, c_binrep: $i > $i > $i). 12.12/2.30 thf(func_def_72, type, c_lam: $i > ($i > $i) > $i). 12.12/2.30 thf(func_def_73, type, c_setprod: $i > $i > $i). 12.12/2.30 thf(func_def_74, type, c_ap: $i > $i > $i). 12.12/2.30 thf(func_def_75, type, c_setsum_p: $i > $o). 12.12/2.30 thf(func_def_76, type, c_tuple_p: $i > $i > $o). 12.12/2.30 thf(func_def_77, type, c_Pi: $i > ($i > $i) > $i). 12.12/2.30 thf(func_def_78, type, c_setexp: $i > $i > $i). 12.12/2.30 thf(func_def_79, type, c_Sep2: $i > ($i > $i) > ($i > $i > $o) > $i). 12.12/2.30 thf(func_def_80, type, c_set_of_pairs: $i > $o). 12.12/2.30 thf(func_def_81, type, c_lam2: $i > ($i > $i) > ($i > $i > $i) > $i). 12.12/2.30 thf(func_def_82, type, c_PNoEq_: $i > ($i > $o) > ($i > $o) > $o). 12.12/2.30 thf(func_def_83, type, c_PNoLt_: $i > ($i > $o) > ($i > $o) > $o). 12.12/2.30 thf(func_def_84, type, c_PNoLt: $i > ($i > $o) > $i > ($i > $o) > $o). 12.12/2.30 thf(func_def_85, type, c_PNoLe: $i > ($i > $o) > $i > ($i > $o) > $o). 12.12/2.30 thf(func_def_86, type, c_PNo_downc: ($i > ($i > $o) > $o) > $i > ($i > $o) > $o). 12.12/2.30 thf(func_def_87, type, c_PNo_upc: ($i > ($i > $o) > $o) > $i > ($i > $o) > $o). 12.12/2.30 thf(func_def_88, type, c_SNoElts_: $i > $i). 12.12/2.30 thf(func_def_89, type, c_SNo_: $i > $i > $o). 12.12/2.30 thf(func_def_90, type, c_PSNo: $i > ($i > $o) > $i). 12.12/2.30 thf(func_def_91, type, c_SNo: $i > $o). 12.12/2.30 thf(func_def_92, type, c_SNoLev: $i > $i). 12.12/2.30 thf(func_def_93, type, c_SNoEq_: $i > $i > $i > $o). 12.12/2.30 thf(func_def_94, type, c_SNoLt: $i > $i > $o). 12.12/2.30 thf(func_def_95, type, c_SNoLe: $i > $i > $o). 12.12/2.30 thf(func_def_96, type, c_binop_on: $i > ($i > $i > $i) > $o). 12.12/2.30 thf(func_def_97, type, c_Loop: $i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > $o). 12.12/2.30 thf(func_def_98, type, c_Loop_with_defs: $i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $o). 12.12/2.30 thf(func_def_99, type, c_Loop_with_defs_cex1: $i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $o). 12.12/2.30 thf(func_def_100, type, c_Loop_with_defs_cex2: $i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $o). 12.12/2.30 thf(func_def_101, type, c_combinator: $i > $o). 12.12/2.30 thf(func_def_102, type, c_combinator_equiv: $i > $i > $o). 12.12/2.30 thf(func_def_103, type, c_equip_mod: $i > $i > $i > $o). 12.12/2.30 thf(func_def_131, type, sP0: ($i > $o) > $o). 12.12/2.30 thf(func_def_132, type, sP1: ($i > $o) > $o). 12.12/2.30 thf(func_def_133, type, sK2: ($i > $i) > $i > $i). 12.12/2.30 thf(func_def_134, type, sK3: ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i). 12.12/2.30 thf(func_def_135, type, sK4: ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i). 12.12/2.30 thf(func_def_136, type, sK5: ($i > $i) > ($i > $i) > $i). 12.12/2.30 thf(func_def_137, type, sK6: ($i > $o) > $i). 12.12/2.30 thf(func_def_138, type, sK7: ($i > $o) > $i). 12.12/2.30 thf(func_def_139, type, sK8: ($i > $o) > $i). 12.12/2.30 thf(func_def_140, type, sK9: ($i > $o) > $i). 12.12/2.30 thf(func_def_141, type, sK10: ($i > $o) > $i > $i). 12.12/2.30 thf(func_def_142, type, sK11: ($i > $o) > $i). 12.12/2.30 thf(func_def_143, type, sK12: ($i > $o) > $i). 12.12/2.30 thf(func_def_145, type, sK14: $i > $i > $i). 12.12/2.30 thf(func_def_146, type, sK15: $i > $i > $i). 12.12/2.30 thf(func_def_147, type, sK16: $i > $i > $i > $o). 12.12/2.30 thf(func_def_148, type, sK17: $o > $o > $o). 12.12/2.30 thf(func_def_149, type, sK18: $o > $o > $o). 12.12/2.30 thf(func_def_150, type, sK19: ($i > $i) > $i > $i > $i). 12.12/2.31 thf(func_def_151, type, sK20: $i > ($i > $i) > $i > $i > $o). 12.12/2.31 thf(func_def_152, type, sK21: $i > $i > $i). 12.12/2.31 thf(func_def_153, type, sK22: $i > $i > $i). 12.12/2.31 thf(func_def_155, type, ph24: !>[X0: $tType]:(X0)). 12.12/2.31 thf(f1543,plain,( 12.12/2.31 $false), 12.12/2.31 inference(trivial_inequality_removal,[],[f1505])). 12.12/2.31 thf(f1505,plain,( 12.12/2.31 ($false = $true)), 12.12/2.31 inference(superposition,[],[f1283,f1418])). 12.12/2.31 thf(f1418,plain,( 12.12/2.31 ( ! [X0 : $o] : (($true = X0)) )), 12.12/2.31 inference(trivial_inequality_removal,[],[f1414])). 12.12/2.31 thf(f1414,plain,( 12.12/2.31 ( ! [X0 : $o] : (($true = X0) | ($true != $true)) )), 12.12/2.31 inference(equality_factoring,[],[f1373])). 12.12/2.31 thf(f1373,plain,( 12.12/2.31 ( ! [X0 : $o,X1 : $o] : (($true = X1) | ($true = X0)) )), 12.12/2.31 inference(trivial_inequality_removal,[],[f1363])). 12.12/2.31 thf(f1363,plain,( 12.12/2.31 ( ! [X0 : $o,X1 : $o] : (($false = $true) | ($true = X1) | ($true = X0)) )), 12.12/2.31 inference(superposition,[],[f1355,f563])). 12.12/2.31 thf(f563,plain,( 12.12/2.31 ( ! [X2 : $i,X1 : $o] : (((c_In @ X2 @ c_Empty) = $false) | ($true = X1)) )), 12.12/2.31 inference(beta_eta_normalization,[],[f562])). 12.12/2.31 thf(f562,plain,( 12.12/2.31 ( ! [X2 : $i,X1 : $o] : (($true = X1) | (((^[Y0 : $i]: (c_In @ Y0 @ c_Empty)) @ X2) = $false)) )), 12.12/2.31 inference(pi_clausification,[],[f561])). 12.12/2.31 thf(f561,plain,( 12.12/2.31 ( ! [X1 : $o] : (((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))) = $false) | ($true = X1)) )), 12.12/2.31 inference(beta_eta_normalization,[],[f560])). 12.12/2.31 thf(f560,plain,( 12.12/2.31 ( ! [X1 : $o] : ((((^[Y0 : $o]: (Y0)) @ X1) = $true) | ((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))) = $false)) )), 12.12/2.31 inference(pi_clausification,[],[f559])). 12.12/2.31 thf(f559,plain,( 12.12/2.31 ((!! @ $o @ (^[Y0 : $o]: (Y0))) = $true) | ((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))) = $false)), 12.12/2.31 inference(binary_proxy_clausification,[],[f558])). 12.12/2.31 thf(f558,plain,( 12.12/2.31 (((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))) => (!! @ $o @ (^[Y0 : $o]: (Y0)))) = $true)), 12.12/2.31 inference(beta_eta_normalization,[],[f468])). 12.12/2.31 thf(f468,plain,( 12.12/2.31 (((^[Y0 : $o]: (Y0 => (!! @ $o @ (^[Y1 : $o]: (Y1))))) @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty)))) = $true)), 12.12/2.31 inference(definition_unfolding,[],[f357,f408])). 12.12/2.31 thf(f408,plain,( 12.12/2.31 (c_not = (^[Y0 : $o]: (Y0 => (!! @ $o @ (^[Y1 : $o]: (Y1))))))), 12.12/2.31 inference(definition_unfolding,[],[f365,f352])). 12.12/2.31 thf(f352,plain,( 12.12/2.31 (c_False = (!! @ $o @ (^[Y0 : $o]: (Y0))))), 12.12/2.31 inference(cnf_transformation,[],[f251])). 12.12/2.31 thf(f251,plain,( 12.12/2.31 (c_False = (!! @ $o @ (^[Y0 : $o]: (Y0))))), 12.12/2.31 inference(fool_elimination,[],[f250])). 12.12/2.31 thf(f250,plain,( 12.12/2.31 (! [X0 : $o] : X0 = c_False)), 12.12/2.31 inference(rectify,[],[f59])). 12.12/2.31 thf(f59,axiom,( 12.12/2.31 (! [X0 : $o] : X0 = c_False)), 12.12/2.31 file('/export/starexec/sandbox2/tmp/tmp.AEOGvNUPJb/E---3.1_16218.p',ax11)). 12.12/2.31 thf(f365,plain,( 12.12/2.31 (c_not = (^[Y0 : $o]: (Y0 => c_False)))), 12.12/2.31 inference(cnf_transformation,[],[f207])). 12.12/2.31 thf(f207,plain,( 12.12/2.31 (c_not = (^[Y0 : $o]: (Y0 => c_False)))), 12.12/2.31 inference(fool_elimination,[],[f206])). 12.12/2.31 thf(f206,plain,( 12.12/2.31 ((^[X0 : $o] : (X0 => c_False)) = c_not)), 12.12/2.31 inference(rectify,[],[f85])). 12.12/2.31 thf(f85,axiom,( 12.12/2.31 ((^[X0 : $o] : (X0 => c_False)) = c_not)), 12.12/2.31 file('/export/starexec/sandbox2/tmp/tmp.AEOGvNUPJb/E---3.1_16218.p',ax13)). 12.12/2.31 thf(f357,plain,( 12.12/2.31 ((c_not @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty)))) = $true)), 12.12/2.31 inference(cnf_transformation,[],[f244])). 12.12/2.31 thf(f244,plain,( 12.12/2.31 ((c_not @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty)))) = $true)), 12.12/2.31 inference(fool_elimination,[],[f243])). 12.12/2.31 thf(f243,plain,( 12.12/2.31 (c_not @ ? [X0] : (c_In @ X0 @ c_Empty))), 12.12/2.31 inference(rectify,[],[f77])). 12.12/2.31 thf(f77,axiom,( 12.12/2.31 (c_not @ ? [X0] : (c_In @ X0 @ c_Empty))), 12.12/2.31 file('/export/starexec/sandbox2/tmp/tmp.AEOGvNUPJb/E---3.1_16218.p',ax5)). 12.12/2.31 thf(f1355,plain,( 12.12/2.31 ( ! [X2 : $o,X0 : $i] : (((c_In @ (c_Union @ c_Empty) @ X0) = $true) | ($true = X2)) )), 12.12/2.31 inference(forward_demodulation,[],[f1354,f1072])). 12.12/2.31 thf(f1072,plain,( 12.12/2.31 ( ! [X0 : $i] : (((c_Union @ c_Empty) = X0)) )), 12.12/2.31 inference(superposition,[],[f1034,f648])). 12.12/2.31 thf(f648,plain,( 12.12/2.31 ( ! [X0 : $i,X1 : $i] : (((sK4 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X0)))) @ X1) = X0)) )), 12.12/2.31 inference(superposition,[],[f643,f338])). 12.12/2.31 thf(f338,plain,( 12.12/2.31 ( ! [X10 : $i] : (((sK4 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X10)))) @ c_Empty) = X10)) )), 12.12/2.31 inference(cnf_transformation,[],[f305])). 12.12/2.31 thf(f305,plain,( 12.12/2.31 ! [X4,X5] : ((sK5 @ (^[Y0 : $i]: (X5)) @ (^[Y0 : $i]: (X4))) = (c_setsum @ (sK4 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (c_Empty)))) @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK5 @ (^[Y3 : $i]: (Y2)) @ (^[Y3 : $i]: (c_Empty)))))))) @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) @ c_Empty)) & ! [X6,X7] : ((sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X6)))))) @ (^[Y0 : $i]: (X7)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = X7) & ! [X8,X9] : ((sK2 @ (^[Y0 : $i]: (c_Inj1 @ (sK2 @ (^[Y1 : $i]: (c_Inj0 @ (sK3 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))) @ (c_Inj1 @ X9)))) @ (c_Inj0 @ (sK4 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (Y1)))) @ X8))) = (c_Inj0 @ (sK4 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X9)))) @ (c_setsum @ c_Empty @ c_Empty)))) & ! [X10] : ((sK4 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X10)))) @ c_Empty) = X10) & ((c_Inj1 @ c_Empty) = (sK5 @ (^[Y0 : $i]: (c_Inj1 @ c_Empty)) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ c_Empty)))) & (c_False != $true) & ! [X11 : $i > $i,X12] : ((X11 @ X12) = (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK2 @ (^[Y3 : $i]: (sK4 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (sK4 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ Y3))) @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : $i]: (X11 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) & ! [X13 : ($i > $i) > ($i > $i) > $i,X14] : ((X13 @ (^[Y0 : $i]: (c_setsum @ (sK4 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (sK5 @ (^[Y1 : $i]: (sK4 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (c_Empty)))) @ c_Empty)) @ (^[Y1 : $i]: (sK2 @ (^[Y2 : $i]: (c_Empty)) @ c_Empty)))) @ (sK4 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (sK4 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ (sK4 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ c_Empty))))) @ (^[Y0 : $i]: (c_Inj1 @ (sK2 @ (^[Y1 : $i]: (X13 @ (^[Y2 : $i]: (sK2 @ (^[Y3 : $i]: (c_Empty)) @ c_Empty)) @ (^[Y2 : $i]: (c_Inj1 @ c_Empty)))) @ X14)))) = (sK2 @ (^[Y0 : $i]: (X13 @ (^[Y1 : $i]: (c_setsum @ Y1 @ Y0)) @ (^[Y1 : $i]: (c_Empty)))) @ c_Empty)) & ! [X15 : $i > ($i > $i > $i) > $i,X16 : $i > $i,X17 : $i > $i] : ((c_setsum @ (X16 @ (X17 @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y0 : $i]: (sK3 @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Empty)))))) @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i > $i > $i]: (c_Empty)))) @ (^[Y0 : $i > $i > $i]: (c_setsum @ c_Empty @ c_Empty))))) @ (sK2 @ (^[Y0 : $i]: (X16 @ c_Empty)) @ (X17 @ (X15 @ (sK2 @ (^[Y0 : $i]: (c_Empty)) @ c_Empty) @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_Empty)))))))) = (sK4 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X16 @ (sK4 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (sK3 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y4 : $i]: (c_Inj0 @ c_Empty)) @ (^[Y4 : $i > $i > $i]: (sK5 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ (c_Inj0 @ (sK3 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))))))) @ (sK5 @ (^[Y0 : $i]: (c_setsum @ Y0 @ c_Empty)) @ (^[Y0 : $i]: (c_Empty)))))), 12.12/2.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f303,f304])). 12.12/2.31 thf(f304,plain,( 12.12/2.31 ? [X0 : ($i > $i) > $i > $i,X1 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X2 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i,X3 : ($i > $i) > ($i > $i) > $i] : (! [X4,X5] : ((X3 @ (^[Y0 : $i]: (X5)) @ (^[Y0 : $i]: (X4))) = (c_setsum @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (c_Empty)))) @ (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X3 @ (^[Y3 : $i]: (Y2)) @ (^[Y3 : $i]: (c_Empty)))))))) @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) @ c_Empty)) & ! [X6,X7] : ((X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X6)))))) @ (^[Y0 : $i]: (X7)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = X7) & ! [X8,X9] : ((c_Inj0 @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X9)))) @ (c_setsum @ c_Empty @ c_Empty))) = (X0 @ (^[Y0 : $i]: (c_Inj1 @ (X0 @ (^[Y1 : $i]: (c_Inj0 @ (X1 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))) @ (c_Inj1 @ X9)))) @ (c_Inj0 @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (Y1)))) @ X8)))) & ! [X10] : ((X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X10)))) @ c_Empty) = X10) & ((c_Inj1 @ c_Empty) = (X3 @ (^[Y0 : $i]: (c_Inj1 @ c_Empty)) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ c_Empty)))) & (c_False != $true) & ! [X11 : $i > $i,X12] : ((X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X0 @ (^[Y3 : $i]: (X2 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (X2 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ Y3))) @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : $i]: (X11 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = (X11 @ X12)) & ! [X13 : ($i > $i) > ($i > $i) > $i,X14] : ((X0 @ (^[Y0 : $i]: (X13 @ (^[Y1 : $i]: (c_setsum @ Y1 @ Y0)) @ (^[Y1 : $i]: (c_Empty)))) @ c_Empty) = (X13 @ (^[Y0 : $i]: (c_setsum @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X3 @ (^[Y1 : $i]: (X2 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (c_Empty)))) @ c_Empty)) @ (^[Y1 : $i]: (X0 @ (^[Y2 : $i]: (c_Empty)) @ c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ c_Empty))))) @ (^[Y0 : $i]: (c_Inj1 @ (X0 @ (^[Y1 : $i]: (X13 @ (^[Y2 : $i]: (X0 @ (^[Y3 : $i]: (c_Empty)) @ c_Empty)) @ (^[Y2 : $i]: (c_Inj1 @ c_Empty)))) @ X14))))) & ! [X15 : $i > ($i > $i > $i) > $i,X16 : $i > $i,X17 : $i > $i] : ((c_setsum @ (X16 @ (X17 @ (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y0 : $i]: (X1 @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Empty)))))) @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i > $i > $i]: (c_Empty)))) @ (^[Y0 : $i > $i > $i]: (c_setsum @ c_Empty @ c_Empty))))) @ (X0 @ (^[Y0 : $i]: (X16 @ c_Empty)) @ (X17 @ (X15 @ (X0 @ (^[Y0 : $i]: (c_Empty)) @ c_Empty) @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_Empty)))))))) = (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X16 @ (X2 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (X1 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y4 : $i]: (c_Inj0 @ c_Empty)) @ (^[Y4 : $i > $i > $i]: (X3 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ (c_Inj0 @ (X1 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))))))) @ (X3 @ (^[Y0 : $i]: (c_setsum @ Y0 @ c_Empty)) @ (^[Y0 : $i]: (c_Empty)))))) => (! [X5,X4] : ((sK5 @ (^[Y0 : $i]: (X5)) @ (^[Y0 : $i]: (X4))) = (c_setsum @ (sK4 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (c_Empty)))) @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK5 @ (^[Y3 : $i]: (Y2)) @ (^[Y3 : $i]: (c_Empty)))))))) @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) @ c_Empty)) & ! [X7,X6] : ((sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X6)))))) @ (^[Y0 : $i]: (X7)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = X7) & ! [X9,X8] : ((sK2 @ (^[Y0 : $i]: (c_Inj1 @ (sK2 @ (^[Y1 : $i]: (c_Inj0 @ (sK3 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))) @ (c_Inj1 @ X9)))) @ (c_Inj0 @ (sK4 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (Y1)))) @ X8))) = (c_Inj0 @ (sK4 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X9)))) @ (c_setsum @ c_Empty @ c_Empty)))) & ! [X10] : ((sK4 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X10)))) @ c_Empty) = X10) & ((c_Inj1 @ c_Empty) = (sK5 @ (^[Y0 : $i]: (c_Inj1 @ c_Empty)) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ c_Empty)))) & (c_False != $true) & ! [X12,X11 : $i > $i] : ((X11 @ X12) = (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK2 @ (^[Y3 : $i]: (sK4 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (sK4 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ Y3))) @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : $i]: (X11 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) & ! [X14,X13 : ($i > $i) > ($i > $i) > $i] : ((X13 @ (^[Y0 : $i]: (c_setsum @ (sK4 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (sK5 @ (^[Y1 : $i]: (sK4 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (c_Empty)))) @ c_Empty)) @ (^[Y1 : $i]: (sK2 @ (^[Y2 : $i]: (c_Empty)) @ c_Empty)))) @ (sK4 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (sK4 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ (sK4 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ c_Empty))))) @ (^[Y0 : $i]: (c_Inj1 @ (sK2 @ (^[Y1 : $i]: (X13 @ (^[Y2 : $i]: (sK2 @ (^[Y3 : $i]: (c_Empty)) @ c_Empty)) @ (^[Y2 : $i]: (c_Inj1 @ c_Empty)))) @ X14)))) = (sK2 @ (^[Y0 : $i]: (X13 @ (^[Y1 : $i]: (c_setsum @ Y1 @ Y0)) @ (^[Y1 : $i]: (c_Empty)))) @ c_Empty)) & ! [X17 : $i > $i,X16 : $i > $i,X15 : $i > ($i > $i > $i) > $i] : ((c_setsum @ (X16 @ (X17 @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y0 : $i]: (sK3 @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Empty)))))) @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i > $i > $i]: (c_Empty)))) @ (^[Y0 : $i > $i > $i]: (c_setsum @ c_Empty @ c_Empty))))) @ (sK2 @ (^[Y0 : $i]: (X16 @ c_Empty)) @ (X17 @ (X15 @ (sK2 @ (^[Y0 : $i]: (c_Empty)) @ c_Empty) @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_Empty)))))))) = (sK4 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X16 @ (sK4 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (sK3 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y4 : $i]: (c_Inj0 @ c_Empty)) @ (^[Y4 : $i > $i > $i]: (sK5 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ (c_Inj0 @ (sK3 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))))))) @ (sK5 @ (^[Y0 : $i]: (c_setsum @ Y0 @ c_Empty)) @ (^[Y0 : $i]: (c_Empty))))))), 12.12/2.31 introduced(choice_axiom,[])). 12.12/2.31 thf(f303,plain,( 12.12/2.31 ? [X0 : ($i > $i) > $i > $i,X1 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X2 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i,X3 : ($i > $i) > ($i > $i) > $i] : (! [X4,X5] : ((X3 @ (^[Y0 : $i]: (X5)) @ (^[Y0 : $i]: (X4))) = (c_setsum @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (c_Empty)))) @ (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X3 @ (^[Y3 : $i]: (Y2)) @ (^[Y3 : $i]: (c_Empty)))))))) @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) @ c_Empty)) & ! [X6,X7] : ((X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X6)))))) @ (^[Y0 : $i]: (X7)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = X7) & ! [X8,X9] : ((c_Inj0 @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X9)))) @ (c_setsum @ c_Empty @ c_Empty))) = (X0 @ (^[Y0 : $i]: (c_Inj1 @ (X0 @ (^[Y1 : $i]: (c_Inj0 @ (X1 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))) @ (c_Inj1 @ X9)))) @ (c_Inj0 @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (Y1)))) @ X8)))) & ! [X10] : ((X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X10)))) @ c_Empty) = X10) & ((c_Inj1 @ c_Empty) = (X3 @ (^[Y0 : $i]: (c_Inj1 @ c_Empty)) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ c_Empty)))) & (c_False != $true) & ! [X11 : $i > $i,X12] : ((X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X0 @ (^[Y3 : $i]: (X2 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (X2 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ Y3))) @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : $i]: (X11 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = (X11 @ X12)) & ! [X13 : ($i > $i) > ($i > $i) > $i,X14] : ((X0 @ (^[Y0 : $i]: (X13 @ (^[Y1 : $i]: (c_setsum @ Y1 @ Y0)) @ (^[Y1 : $i]: (c_Empty)))) @ c_Empty) = (X13 @ (^[Y0 : $i]: (c_setsum @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X3 @ (^[Y1 : $i]: (X2 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (c_Empty)))) @ c_Empty)) @ (^[Y1 : $i]: (X0 @ (^[Y2 : $i]: (c_Empty)) @ c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ c_Empty))))) @ (^[Y0 : $i]: (c_Inj1 @ (X0 @ (^[Y1 : $i]: (X13 @ (^[Y2 : $i]: (X0 @ (^[Y3 : $i]: (c_Empty)) @ c_Empty)) @ (^[Y2 : $i]: (c_Inj1 @ c_Empty)))) @ X14))))) & ! [X15 : $i > ($i > $i > $i) > $i,X16 : $i > $i,X17 : $i > $i] : ((c_setsum @ (X16 @ (X17 @ (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y0 : $i]: (X1 @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Empty)))))) @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i > $i > $i]: (c_Empty)))) @ (^[Y0 : $i > $i > $i]: (c_setsum @ c_Empty @ c_Empty))))) @ (X0 @ (^[Y0 : $i]: (X16 @ c_Empty)) @ (X17 @ (X15 @ (X0 @ (^[Y0 : $i]: (c_Empty)) @ c_Empty) @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_Empty)))))))) = (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X16 @ (X2 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (X1 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y4 : $i]: (c_Inj0 @ c_Empty)) @ (^[Y4 : $i > $i > $i]: (X3 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ (c_Inj0 @ (X1 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))))))) @ (X3 @ (^[Y0 : $i]: (c_setsum @ Y0 @ c_Empty)) @ (^[Y0 : $i]: (c_Empty))))))), 12.12/2.31 inference(rectify,[],[f293])). 12.12/2.31 thf(f293,plain,( 12.12/2.31 ? [X0 : ($i > $i) > $i > $i,X1 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X2 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i,X3 : ($i > $i) > ($i > $i) > $i] : (! [X4,X5] : ((X3 @ (^[Y0 : $i]: (X5)) @ (^[Y0 : $i]: (X4))) = (c_setsum @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (c_Empty)))) @ (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X3 @ (^[Y3 : $i]: (Y2)) @ (^[Y3 : $i]: (c_Empty)))))))) @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) @ c_Empty)) & ! [X14,X15] : ((X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X14)))))) @ (^[Y0 : $i]: (X15)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = X15) & ! [X10,X11] : ((c_Inj0 @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X11)))) @ (c_setsum @ c_Empty @ c_Empty))) = (X0 @ (^[Y0 : $i]: (c_Inj1 @ (X0 @ (^[Y1 : $i]: (c_Inj0 @ (X1 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))) @ (c_Inj1 @ X11)))) @ (c_Inj0 @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (Y1)))) @ X10)))) & ! [X6] : ((X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X6)))) @ c_Empty) = X6) & ((c_Inj1 @ c_Empty) = (X3 @ (^[Y0 : $i]: (c_Inj1 @ c_Empty)) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ c_Empty)))) & (c_False != $true) & ! [X16 : $i > $i,X17] : ((X16 @ X17) = (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X0 @ (^[Y3 : $i]: (X2 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (X2 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ Y3))) @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : $i]: (X16 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) & ! [X12 : ($i > $i) > ($i > $i) > $i,X13] : ((X0 @ (^[Y0 : $i]: (X12 @ (^[Y1 : $i]: (c_setsum @ Y1 @ Y0)) @ (^[Y1 : $i]: (c_Empty)))) @ c_Empty) = (X12 @ (^[Y0 : $i]: (c_setsum @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X3 @ (^[Y1 : $i]: (X2 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (c_Empty)))) @ c_Empty)) @ (^[Y1 : $i]: (X0 @ (^[Y2 : $i]: (c_Empty)) @ c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ c_Empty))))) @ (^[Y0 : $i]: (c_Inj1 @ (X0 @ (^[Y1 : $i]: (X12 @ (^[Y2 : $i]: (X0 @ (^[Y3 : $i]: (c_Empty)) @ c_Empty)) @ (^[Y2 : $i]: (c_Inj1 @ c_Empty)))) @ X13))))) & ! [X7 : $i > ($i > $i > $i) > $i,X8 : $i > $i,X9 : $i > $i] : ((c_setsum @ (X8 @ (X9 @ (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y0 : $i]: (X1 @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Empty)))))) @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i > $i > $i]: (c_Empty)))) @ (^[Y0 : $i > $i > $i]: (c_setsum @ c_Empty @ c_Empty))))) @ (X0 @ (^[Y0 : $i]: (X8 @ c_Empty)) @ (X9 @ (X7 @ (X0 @ (^[Y0 : $i]: (c_Empty)) @ c_Empty) @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_Empty)))))))) = (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X8 @ (X2 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (X1 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y4 : $i]: (c_Inj0 @ c_Empty)) @ (^[Y4 : $i > $i > $i]: (X3 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ (c_Inj0 @ (X1 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))))))) @ (X3 @ (^[Y0 : $i]: (c_setsum @ Y0 @ c_Empty)) @ (^[Y0 : $i]: (c_Empty))))))), 12.12/2.31 inference(flattening,[],[f292])). 12.12/2.31 thf(f292,plain,( 12.12/2.31 ? [X0 : ($i > $i) > $i > $i,X1 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X2 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i,X3 : ($i > $i) > ($i > $i) > $i] : (((((((((c_False != $true) & ! [X16 : $i > $i,X17] : ((X16 @ X17) = (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X0 @ (^[Y3 : $i]: (X2 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (X2 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ Y3))) @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : $i]: (X16 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty))))) & ! [X14,X15] : ((X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X14)))))) @ (^[Y0 : $i]: (X15)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = X15)) & ! [X12 : ($i > $i) > ($i > $i) > $i,X13] : ((X0 @ (^[Y0 : $i]: (X12 @ (^[Y1 : $i]: (c_setsum @ Y1 @ Y0)) @ (^[Y1 : $i]: (c_Empty)))) @ c_Empty) = (X12 @ (^[Y0 : $i]: (c_setsum @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X3 @ (^[Y1 : $i]: (X2 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (c_Empty)))) @ c_Empty)) @ (^[Y1 : $i]: (X0 @ (^[Y2 : $i]: (c_Empty)) @ c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ c_Empty))))) @ (^[Y0 : $i]: (c_Inj1 @ (X0 @ (^[Y1 : $i]: (X12 @ (^[Y2 : $i]: (X0 @ (^[Y3 : $i]: (c_Empty)) @ c_Empty)) @ (^[Y2 : $i]: (c_Inj1 @ c_Empty)))) @ X13)))))) & ! [X10,X11] : ((c_Inj0 @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X11)))) @ (c_setsum @ c_Empty @ c_Empty))) = (X0 @ (^[Y0 : $i]: (c_Inj1 @ (X0 @ (^[Y1 : $i]: (c_Inj0 @ (X1 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))) @ (c_Inj1 @ X11)))) @ (c_Inj0 @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (Y1)))) @ X10))))) & ! [X7 : $i > ($i > $i > $i) > $i,X8 : $i > $i,X9 : $i > $i] : ((c_setsum @ (X8 @ (X9 @ (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y0 : $i]: (X1 @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Empty)))))) @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i > $i > $i]: (c_Empty)))) @ (^[Y0 : $i > $i > $i]: (c_setsum @ c_Empty @ c_Empty))))) @ (X0 @ (^[Y0 : $i]: (X8 @ c_Empty)) @ (X9 @ (X7 @ (X0 @ (^[Y0 : $i]: (c_Empty)) @ c_Empty) @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_Empty)))))))) = (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X8 @ (X2 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (X1 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y4 : $i]: (c_Inj0 @ c_Empty)) @ (^[Y4 : $i > $i > $i]: (X3 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ (c_Inj0 @ (X1 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))))))) @ (X3 @ (^[Y0 : $i]: (c_setsum @ Y0 @ c_Empty)) @ (^[Y0 : $i]: (c_Empty)))))) & ! [X6] : ((X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X6)))) @ c_Empty) = X6)) & ! [X4,X5] : ((X3 @ (^[Y0 : $i]: (X5)) @ (^[Y0 : $i]: (X4))) = (c_setsum @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (c_Empty)))) @ (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X3 @ (^[Y3 : $i]: (Y2)) @ (^[Y3 : $i]: (c_Empty)))))))) @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) @ c_Empty))) & ((c_Inj1 @ c_Empty) = (X3 @ (^[Y0 : $i]: (c_Inj1 @ c_Empty)) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ c_Empty)))))), 12.12/2.31 inference(ennf_transformation,[],[f288])). 12.12/2.31 thf(f288,plain,( 12.12/2.31 ~! [X0 : ($i > $i) > $i > $i,X1 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X2 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i,X3 : ($i > $i) > ($i > $i) > $i] : (((c_Inj1 @ c_Empty) = (X3 @ (^[Y0 : $i]: (c_Inj1 @ c_Empty)) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ c_Empty)))) => (! [X4,X5] : ((X3 @ (^[Y0 : $i]: (X5)) @ (^[Y0 : $i]: (X4))) = (c_setsum @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (c_Empty)))) @ (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X3 @ (^[Y3 : $i]: (Y2)) @ (^[Y3 : $i]: (c_Empty)))))))) @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) @ c_Empty)) => (! [X6] : ((X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X6)))) @ c_Empty) = X6) => (! [X7 : $i > ($i > $i > $i) > $i,X8 : $i > $i,X9 : $i > $i] : ((c_setsum @ (X8 @ (X9 @ (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y0 : $i]: (X1 @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Empty)))))) @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i > $i > $i]: (c_Empty)))) @ (^[Y0 : $i > $i > $i]: (c_setsum @ c_Empty @ c_Empty))))) @ (X0 @ (^[Y0 : $i]: (X8 @ c_Empty)) @ (X9 @ (X7 @ (X0 @ (^[Y0 : $i]: (c_Empty)) @ c_Empty) @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_Empty)))))))) = (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X8 @ (X2 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (X1 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y4 : $i]: (c_Inj0 @ c_Empty)) @ (^[Y4 : $i > $i > $i]: (X3 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ (c_Inj0 @ (X1 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))))))) @ (X3 @ (^[Y0 : $i]: (c_setsum @ Y0 @ c_Empty)) @ (^[Y0 : $i]: (c_Empty))))) => (! [X10,X11] : ((c_Inj0 @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X11)))) @ (c_setsum @ c_Empty @ c_Empty))) = (X0 @ (^[Y0 : $i]: (c_Inj1 @ (X0 @ (^[Y1 : $i]: (c_Inj0 @ (X1 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))) @ (c_Inj1 @ X11)))) @ (c_Inj0 @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (Y1)))) @ X10)))) => (! [X12 : ($i > $i) > ($i > $i) > $i,X13] : ((X0 @ (^[Y0 : $i]: (X12 @ (^[Y1 : $i]: (c_setsum @ Y1 @ Y0)) @ (^[Y1 : $i]: (c_Empty)))) @ c_Empty) = (X12 @ (^[Y0 : $i]: (c_setsum @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X3 @ (^[Y1 : $i]: (X2 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (c_Empty)))) @ c_Empty)) @ (^[Y1 : $i]: (X0 @ (^[Y2 : $i]: (c_Empty)) @ c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ c_Empty))))) @ (^[Y0 : $i]: (c_Inj1 @ (X0 @ (^[Y1 : $i]: (X12 @ (^[Y2 : $i]: (X0 @ (^[Y3 : $i]: (c_Empty)) @ c_Empty)) @ (^[Y2 : $i]: (c_Inj1 @ c_Empty)))) @ X13))))) => (! [X14,X15] : ((X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X14)))))) @ (^[Y0 : $i]: (X15)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = X15) => (! [X16 : $i > $i,X17] : ((X16 @ X17) = (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X0 @ (^[Y3 : $i]: (X2 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (X2 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ Y3))) @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : $i]: (X16 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) => (c_False = $true)))))))))), 12.12/2.31 inference(rectify,[],[f221])). 12.12/2.31 thf(f221,plain,( 12.12/2.31 ~! [X0 : ($i > $i) > $i > $i,X1 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X2 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i,X3 : ($i > $i) > ($i > $i) > $i] : (((c_Inj1 @ c_Empty) = (X3 @ (^[Y0 : $i]: (c_Inj1 @ c_Empty)) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ c_Empty)))) => (! [X10,X13] : ((X3 @ (^[Y0 : $i]: (X13)) @ (^[Y0 : $i]: (X10))) = (c_setsum @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (c_Empty)))) @ (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X3 @ (^[Y3 : $i]: (Y2)) @ (^[Y3 : $i]: (c_Empty)))))))) @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) @ c_Empty)) => (! [X28] : ((X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X28)))) @ c_Empty) = X28) => (! [X32 : $i > ($i > $i > $i) > $i,X33 : $i > $i,X34 : $i > $i] : ((X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X33 @ (X2 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (X1 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y4 : $i]: (c_Inj0 @ c_Empty)) @ (^[Y4 : $i > $i > $i]: (X3 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ (c_Inj0 @ (X1 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))))))) @ (X3 @ (^[Y0 : $i]: (c_setsum @ Y0 @ c_Empty)) @ (^[Y0 : $i]: (c_Empty)))) = (c_setsum @ (X33 @ (X34 @ (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y0 : $i]: (X1 @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Empty)))))) @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i > $i > $i]: (c_Empty)))) @ (^[Y0 : $i > $i > $i]: (c_setsum @ c_Empty @ c_Empty))))) @ (X0 @ (^[Y0 : $i]: (X33 @ c_Empty)) @ (X34 @ (X32 @ (X0 @ (^[Y0 : $i]: (c_Empty)) @ c_Empty) @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_Empty))))))))) => (! [X67,X70] : ((X0 @ (^[Y0 : $i]: (c_Inj1 @ (X0 @ (^[Y1 : $i]: (c_Inj0 @ (X1 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))) @ (c_Inj1 @ X70)))) @ (c_Inj0 @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (Y1)))) @ X67))) = (c_Inj0 @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X70)))) @ (c_setsum @ c_Empty @ c_Empty)))) => (! [X82 : ($i > $i) > ($i > $i) > $i,X84] : ((X0 @ (^[Y0 : $i]: (X82 @ (^[Y1 : $i]: (c_setsum @ Y1 @ Y0)) @ (^[Y1 : $i]: (c_Empty)))) @ c_Empty) = (X82 @ (^[Y0 : $i]: (c_setsum @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X3 @ (^[Y1 : $i]: (X2 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (c_Empty)))) @ c_Empty)) @ (^[Y1 : $i]: (X0 @ (^[Y2 : $i]: (c_Empty)) @ c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ c_Empty))))) @ (^[Y0 : $i]: (c_Inj1 @ (X0 @ (^[Y1 : $i]: (X82 @ (^[Y2 : $i]: (X0 @ (^[Y3 : $i]: (c_Empty)) @ c_Empty)) @ (^[Y2 : $i]: (c_Inj1 @ c_Empty)))) @ X84))))) => (! [X108,X111] : ((X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X108)))))) @ (^[Y0 : $i]: (X111)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = X111) => (! [X117 : $i > $i,X118] : ((X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X0 @ (^[Y3 : $i]: (X2 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (X2 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ Y3))) @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : $i]: (X117 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = (X117 @ X118)) => (c_False = $true)))))))))), 12.12/2.31 inference(fool_elimination,[],[f220])). 12.12/2.31 thf(f220,plain,( 12.12/2.31 ~! [X0 : ($i > $i) > $i > $i,X1 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X2 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i,X3 : ($i > $i) > ($i > $i) > $i] : (((c_Inj1 @ c_Empty) = (X3 @ (^[X8 : $i] : (c_Inj1 @ c_Empty)) @ (^[X9 : $i] : (c_setsum @ c_Empty @ c_Empty)))) => (! [X10,X13] : ((X3 @ (^[X14 : $i] : (X13)) @ (^[X15 : $i] : (X10))) = (c_setsum @ (X2 @ (^[X16 : ($i > $i > $i > $i) > $i, X17 : $i] : (c_Empty)) @ (X1 @ (^[X18 : $i, X19 : $i, X20 : $i] : (X3 @ (^[X21 : $i] : (X20)) @ (^[X22 : $i] : (c_Empty)))) @ (^[X23 : $i] : (c_Empty)) @ (^[X24 : $i > $i > $i] : (c_Empty)))) @ c_Empty)) => (! [X28] : ((X2 @ (^[X29 : ($i > $i > $i > $i) > $i, X30 : $i] : (X28)) @ c_Empty) = X28) => (! [X32 : $i > ($i > $i > $i) > $i,X33 : $i > $i,X34 : $i > $i] : ((X2 @ (^[X35 : ($i > $i > $i > $i) > $i, X36 : $i] : (X33 @ (X2 @ (^[X37 : ($i > $i > $i > $i) > $i, X38 : $i] : (X1 @ (^[X39 : $i, X40 : $i, X41 : $i] : (c_Inj1 @ c_Empty)) @ (^[X42 : $i] : (c_Inj0 @ c_Empty)) @ (^[X43 : $i > $i > $i] : (X3 @ (^[X44 : $i] : (c_Empty)) @ (^[X45 : $i] : (c_Empty)))))) @ (c_Inj0 @ (X1 @ (^[X46 : $i, X47 : $i, X48 : $i] : (c_Empty)) @ (^[X49 : $i] : (c_Empty)) @ (^[X50 : $i > $i > $i] : (c_Empty))))))) @ (X3 @ (^[X51 : $i] : (c_setsum @ X51 @ c_Empty)) @ (^[X52 : $i] : (c_Empty)))) = (c_setsum @ (X33 @ (X34 @ (X1 @ (^[X53 : $i, X54 : $i, X55 : $i] : (c_Inj1 @ c_Empty)) @ (^[X56 : $i] : (X1 @ (^[X57 : $i, X58 : $i, X59 : $i] : (c_Empty)) @ (^[X60 : $i] : (c_Empty)) @ (^[X61 : $i > $i > $i] : (c_Empty)))) @ (^[X62 : $i > $i > $i] : (c_setsum @ c_Empty @ c_Empty))))) @ (X0 @ (^[X63 : $i] : (X33 @ c_Empty)) @ (X34 @ (X32 @ (X0 @ (^[X64 : $i] : (c_Empty)) @ c_Empty) @ (^[X65 : $i, X66 : $i] : (c_Empty))))))) => (! [X67,X70] : ((c_Inj0 @ (X2 @ (^[X71 : ($i > $i > $i > $i) > $i, X72 : $i] : (X70)) @ (c_setsum @ c_Empty @ c_Empty))) = (X0 @ (^[X73 : $i] : (c_Inj1 @ (X0 @ (^[X74 : $i] : (c_Inj0 @ (X1 @ (^[X75 : $i, X76 : $i, X77 : $i] : (c_Empty)) @ (^[X78 : $i] : (c_Empty)) @ (^[X79 : $i > $i > $i] : (c_Empty))))) @ (c_Inj1 @ X70)))) @ (c_Inj0 @ (X2 @ (^[X80 : ($i > $i > $i > $i) > $i, X81 : $i] : (X81)) @ X67)))) => (! [X82 : ($i > $i) > ($i > $i) > $i,X84] : ((X0 @ (^[X86 : $i] : (X82 @ (^[X87 : $i] : (c_setsum @ X87 @ X86)) @ (^[X88 : $i] : (c_Empty)))) @ c_Empty) = (X82 @ (^[X89 : $i] : (c_setsum @ (X2 @ (^[X90 : ($i > $i > $i > $i) > $i, X91 : $i] : (c_Empty)) @ (X3 @ (^[X92 : $i] : (X2 @ (^[X93 : ($i > $i > $i > $i) > $i, X94 : $i] : (c_Empty)) @ c_Empty)) @ (^[X95 : $i] : (X0 @ (^[X96 : $i] : (c_Empty)) @ c_Empty)))) @ (X2 @ (^[X97 : ($i > $i > $i > $i) > $i, X98 : $i] : (c_Empty)) @ (X2 @ (^[X99 : ($i > $i > $i > $i) > $i, X100 : $i] : (c_setsum @ c_Empty @ c_Empty)) @ (X2 @ (^[X101 : ($i > $i > $i > $i) > $i, X102 : $i] : (c_Empty)) @ c_Empty))))) @ (^[X103 : $i] : (c_Inj1 @ (X0 @ (^[X104 : $i] : (X82 @ (^[X105 : $i] : (X0 @ (^[X106 : $i] : (c_Empty)) @ c_Empty)) @ (^[X107 : $i] : (c_Inj1 @ c_Empty)))) @ X84))))) => (! [X108,X111] : (X111 = (X1 @ (^[X112 : $i, X113 : $i, X114 : $i] : (X108)) @ (^[X115 : $i] : (X111)) @ (^[X116 : $i > $i > $i] : (c_Empty)))) => (! [X117 : $i > $i,X118] : ((X1 @ (^[X121 : $i, X122 : $i, X123 : $i] : (X0 @ (^[X124 : $i] : (X2 @ (^[X125 : ($i > $i > $i > $i) > $i, X126 : $i] : (X123)) @ (X2 @ (^[X127 : ($i > $i > $i > $i) > $i, X128 : $i] : (c_setsum @ c_Empty @ c_Empty)) @ X124))) @ (c_Inj1 @ c_Empty))) @ (^[X129 : $i] : (X117 @ c_Empty)) @ (^[X130 : $i > $i > $i] : (c_Empty))) = (X117 @ X118)) => c_False))))))))), 12.12/2.31 inference(rectify,[],[f72])). 12.12/2.31 thf(f72,negated_conjecture,( 12.12/2.31 ~! [X1 : ($i > $i) > $i > $i,X0 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X2 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i,X3 : ($i > $i) > ($i > $i) > $i] : (! [X6 : (($i > $i > $i) > ($i > $i) > $i) > $i,X4 : $i > (($i > $i) > $i) > $i,X5 : ($i > $i) > $i,X7] : ((c_Inj1 @ c_Empty) = (X3 @ (^[X8 : $i] : (c_Inj1 @ c_Empty)) @ (^[X8 : $i] : (c_setsum @ c_Empty @ c_Empty)))) => (! [X7,X5,X4,X6] : ((X3 @ (^[X8 : $i] : (X6)) @ (^[X8 : $i] : (X7))) = (c_setsum @ (X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (c_Empty)) @ (X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : (X3 @ (^[X11 : $i] : (X10)) @ (^[X11 : $i] : (c_Empty)))) @ (^[X8 : $i] : (c_Empty)) @ (^[X8 : $i > $i > $i] : (c_Empty)))) @ c_Empty)) => (! [X4 : $i > $i,X6 : $i > $i,X5 : $i > $i > $i,X7] : ((X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (X7)) @ c_Empty) = X7) => (! [X6 : ((($i > $i) > $i) > $i) > $i,X4 : $i > ($i > $i > $i) > $i,X7 : $i > $i,X5 : $i > $i] : ((X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (X7 @ (X2 @ (^[X10 : ($i > $i > $i > $i) > $i, X11 : $i] : (X0 @ (^[X12 : $i, X13 : $i, X14 : $i] : (c_Inj1 @ c_Empty)) @ (^[X12 : $i] : (c_Inj0 @ c_Empty)) @ (^[X12 : $i > $i > $i] : (X3 @ (^[X13 : $i] : (c_Empty)) @ (^[X13 : $i] : (c_Empty)))))) @ (c_Inj0 @ (X0 @ (^[X10 : $i, X11 : $i, X12 : $i] : (c_Empty)) @ (^[X10 : $i] : (c_Empty)) @ (^[X10 : $i > $i > $i] : (c_Empty))))))) @ (X3 @ (^[X8 : $i] : (c_setsum @ X8 @ c_Empty)) @ (^[X8 : $i] : (c_Empty)))) = (c_setsum @ (X7 @ (X5 @ (X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : (c_Inj1 @ c_Empty)) @ (^[X8 : $i] : (X0 @ (^[X9 : $i, X10 : $i, X11 : $i] : (c_Empty)) @ (^[X9 : $i] : (c_Empty)) @ (^[X9 : $i > $i > $i] : (c_Empty)))) @ (^[X8 : $i > $i > $i] : (c_setsum @ c_Empty @ c_Empty))))) @ (X1 @ (^[X8 : $i] : (X7 @ c_Empty)) @ (X5 @ (X4 @ (X1 @ (^[X8 : $i] : (c_Empty)) @ c_Empty) @ (^[X8 : $i, X9 : $i] : (c_Empty))))))) => (! [X5,X6,X4 : (($i > $i) > $i > $i) > $i,X7] : ((c_Inj0 @ (X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (X7)) @ (c_setsum @ c_Empty @ c_Empty))) = (X1 @ (^[X8 : $i] : (c_Inj1 @ (X1 @ (^[X9 : $i] : (c_Inj0 @ (X0 @ (^[X10 : $i, X11 : $i, X12 : $i] : (c_Empty)) @ (^[X10 : $i] : (c_Empty)) @ (^[X10 : $i > $i > $i] : (c_Empty))))) @ (c_Inj1 @ X7)))) @ (c_Inj0 @ (X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (X9)) @ X5)))) => (! [X7 : ($i > $i) > ($i > $i) > $i,X5 : $i > $i > ($i > $i) > $i,X6,X4 : (($i > $i) > $i) > $i] : ((X1 @ (^[X8 : $i] : (X7 @ (^[X9 : $i] : (c_setsum @ X9 @ X8)) @ (^[X9 : $i] : (c_Empty)))) @ c_Empty) = (X7 @ (^[X8 : $i] : (c_setsum @ (X2 @ (^[X9 : ($i > $i > $i > $i) > $i, X10 : $i] : (c_Empty)) @ (X3 @ (^[X9 : $i] : (X2 @ (^[X10 : ($i > $i > $i > $i) > $i, X11 : $i] : (c_Empty)) @ c_Empty)) @ (^[X9 : $i] : (X1 @ (^[X10 : $i] : (c_Empty)) @ c_Empty)))) @ (X2 @ (^[X9 : ($i > $i > $i > $i) > $i, X10 : $i] : (c_Empty)) @ (X2 @ (^[X9 : ($i > $i > $i > $i) > $i, X10 : $i] : (c_setsum @ c_Empty @ c_Empty)) @ (X2 @ (^[X9 : ($i > $i > $i > $i) > $i, X10 : $i] : (c_Empty)) @ c_Empty))))) @ (^[X8 : $i] : (c_Inj1 @ (X1 @ (^[X9 : $i] : (X7 @ (^[X10 : $i] : (X1 @ (^[X11 : $i] : (c_Empty)) @ c_Empty)) @ (^[X10 : $i] : (c_Inj1 @ c_Empty)))) @ X6))))) => (! [X7,X5,X4 : $i > (($i > $i) > $i > $i) > $i,X6] : (X6 = (X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : (X7)) @ (^[X8 : $i] : (X6)) @ (^[X8 : $i > $i > $i] : (c_Empty)))) => (! [X7 : $i > $i,X4,X5,X6 : $i > ($i > $i) > $i] : ((X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : (X1 @ (^[X11 : $i] : (X2 @ (^[X12 : ($i > $i > $i > $i) > $i, X13 : $i] : (X10)) @ (X2 @ (^[X12 : ($i > $i > $i > $i) > $i, X13 : $i] : (c_setsum @ c_Empty @ c_Empty)) @ X11))) @ (c_Inj1 @ c_Empty))) @ (^[X8 : $i] : (X7 @ c_Empty)) @ (^[X8 : $i > $i > $i] : (c_Empty))) = (X7 @ X4)) => c_False))))))))), 12.12/2.31 inference(negated_conjecture,[],[f71])). 12.12/2.31 thf(f71,conjecture,( 12.12/2.31 ! [X1 : ($i > $i) > $i > $i,X0 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X2 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i,X3 : ($i > $i) > ($i > $i) > $i] : (! [X6 : (($i > $i > $i) > ($i > $i) > $i) > $i,X4 : $i > (($i > $i) > $i) > $i,X5 : ($i > $i) > $i,X7] : ((c_Inj1 @ c_Empty) = (X3 @ (^[X8 : $i] : (c_Inj1 @ c_Empty)) @ (^[X8 : $i] : (c_setsum @ c_Empty @ c_Empty)))) => (! [X7,X5,X4,X6] : ((X3 @ (^[X8 : $i] : (X6)) @ (^[X8 : $i] : (X7))) = (c_setsum @ (X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (c_Empty)) @ (X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : (X3 @ (^[X11 : $i] : (X10)) @ (^[X11 : $i] : (c_Empty)))) @ (^[X8 : $i] : (c_Empty)) @ (^[X8 : $i > $i > $i] : (c_Empty)))) @ c_Empty)) => (! [X4 : $i > $i,X6 : $i > $i,X5 : $i > $i > $i,X7] : ((X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (X7)) @ c_Empty) = X7) => (! [X6 : ((($i > $i) > $i) > $i) > $i,X4 : $i > ($i > $i > $i) > $i,X7 : $i > $i,X5 : $i > $i] : ((X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (X7 @ (X2 @ (^[X10 : ($i > $i > $i > $i) > $i, X11 : $i] : (X0 @ (^[X12 : $i, X13 : $i, X14 : $i] : (c_Inj1 @ c_Empty)) @ (^[X12 : $i] : (c_Inj0 @ c_Empty)) @ (^[X12 : $i > $i > $i] : (X3 @ (^[X13 : $i] : (c_Empty)) @ (^[X13 : $i] : (c_Empty)))))) @ (c_Inj0 @ (X0 @ (^[X10 : $i, X11 : $i, X12 : $i] : (c_Empty)) @ (^[X10 : $i] : (c_Empty)) @ (^[X10 : $i > $i > $i] : (c_Empty))))))) @ (X3 @ (^[X8 : $i] : (c_setsum @ X8 @ c_Empty)) @ (^[X8 : $i] : (c_Empty)))) = (c_setsum @ (X7 @ (X5 @ (X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : (c_Inj1 @ c_Empty)) @ (^[X8 : $i] : (X0 @ (^[X9 : $i, X10 : $i, X11 : $i] : (c_Empty)) @ (^[X9 : $i] : (c_Empty)) @ (^[X9 : $i > $i > $i] : (c_Empty)))) @ (^[X8 : $i > $i > $i] : (c_setsum @ c_Empty @ c_Empty))))) @ (X1 @ (^[X8 : $i] : (X7 @ c_Empty)) @ (X5 @ (X4 @ (X1 @ (^[X8 : $i] : (c_Empty)) @ c_Empty) @ (^[X8 : $i, X9 : $i] : (c_Empty))))))) => (! [X5,X6,X4 : (($i > $i) > $i > $i) > $i,X7] : ((c_Inj0 @ (X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (X7)) @ (c_setsum @ c_Empty @ c_Empty))) = (X1 @ (^[X8 : $i] : (c_Inj1 @ (X1 @ (^[X9 : $i] : (c_Inj0 @ (X0 @ (^[X10 : $i, X11 : $i, X12 : $i] : (c_Empty)) @ (^[X10 : $i] : (c_Empty)) @ (^[X10 : $i > $i > $i] : (c_Empty))))) @ (c_Inj1 @ X7)))) @ (c_Inj0 @ (X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (X9)) @ X5)))) => (! [X7 : ($i > $i) > ($i > $i) > $i,X5 : $i > $i > ($i > $i) > $i,X6,X4 : (($i > $i) > $i) > $i] : ((X1 @ (^[X8 : $i] : (X7 @ (^[X9 : $i] : (c_setsum @ X9 @ X8)) @ (^[X9 : $i] : (c_Empty)))) @ c_Empty) = (X7 @ (^[X8 : $i] : (c_setsum @ (X2 @ (^[X9 : ($i > $i > $i > $i) > $i, X10 : $i] : (c_Empty)) @ (X3 @ (^[X9 : $i] : (X2 @ (^[X10 : ($i > $i > $i > $i) > $i, X11 : $i] : (c_Empty)) @ c_Empty)) @ (^[X9 : $i] : (X1 @ (^[X10 : $i] : (c_Empty)) @ c_Empty)))) @ (X2 @ (^[X9 : ($i > $i > $i > $i) > $i, X10 : $i] : (c_Empty)) @ (X2 @ (^[X9 : ($i > $i > $i > $i) > $i, X10 : $i] : (c_setsum @ c_Empty @ c_Empty)) @ (X2 @ (^[X9 : ($i > $i > $i > $i) > $i, X10 : $i] : (c_Empty)) @ c_Empty))))) @ (^[X8 : $i] : (c_Inj1 @ (X1 @ (^[X9 : $i] : (X7 @ (^[X10 : $i] : (X1 @ (^[X11 : $i] : (c_Empty)) @ c_Empty)) @ (^[X10 : $i] : (c_Inj1 @ c_Empty)))) @ X6))))) => (! [X7,X5,X4 : $i > (($i > $i) > $i > $i) > $i,X6] : (X6 = (X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : (X7)) @ (^[X8 : $i] : (X6)) @ (^[X8 : $i > $i > $i] : (c_Empty)))) => (! [X7 : $i > $i,X4,X5,X6 : $i > ($i > $i) > $i] : ((X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : (X1 @ (^[X11 : $i] : (X2 @ (^[X12 : ($i > $i > $i > $i) > $i, X13 : $i] : (X10)) @ (X2 @ (^[X12 : ($i > $i > $i > $i) > $i, X13 : $i] : (c_setsum @ c_Empty @ c_Empty)) @ X11))) @ (c_Inj1 @ c_Empty))) @ (^[X8 : $i] : (X7 @ c_Empty)) @ (^[X8 : $i > $i > $i] : (c_Empty))) = (X7 @ X4)) => c_False))))))))), 12.12/2.31 file('/export/starexec/sandbox2/tmp/tmp.AEOGvNUPJb/E---3.1_16218.p',conj)). 12.12/2.31 thf(f643,plain,( 12.12/2.31 ( ! [X2 : $i,X0 : $i > $i,X1 : $i] : (((X0 @ X2) = (X0 @ X1))) )), 12.12/2.31 inference(superposition,[],[f564,f564])). 12.12/2.31 thf(f564,plain,( 12.12/2.31 ( ! [X11 : $i > $i,X12 : $i] : (((sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK2 @ (^[Y3 : $i]: (sK4 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (sK4 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((c_Repl @ c_Empty @ (^[Y10 : $i]: (c_Repl @ Y10 @ (^[Y11 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y12 : $i]: ((^[Y13 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((c_Empty = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: ((((c_In @ c_Empty @ Y18) => (!! @ $o @ (^[Y22 : $o]: (Y22)))) => ((c_Empty = Y19) => Y21)) => Y21))) => Y20) => Y20)))))))) = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => (!! @ $o @ (^[Y18 : $o]: (Y18)))) => (((c_Repl @ Y12 @ Y13) = Y15) => Y17)) => Y17))) => Y16) => Y16)))))))))))) @ Y11)))))) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ c_Empty @ Y6) => (!! @ $o @ (^[Y10 : $o]: (Y10)))) => (((c_Repl @ c_Empty @ (^[Y10 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y11 : $i]: ((^[Y12 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((c_Empty = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: ((((c_In @ c_Empty @ Y17) => (!! @ $o @ (^[Y21 : $o]: (Y21)))) => ((c_Empty = Y18) => Y20)) => Y20))) => Y19) => Y19)))))))) = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => (!! @ $o @ (^[Y17 : $o]: (Y17)))) => (((c_Repl @ Y11 @ Y12) = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))))))) @ Y10)))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))))) @ Y3))) @ (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y3 : $i]: ((^[Y4 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $o @ (^[Y8 : $o]: (((c_In @ c_Empty @ Y5) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => (!! @ $o @ (^[Y13 : $o]: (Y13)))) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))) = Y6) => Y8)) => Y8))) => Y7) => (((!! @ $o @ (^[Y8 : $o]: ((((c_In @ c_Empty @ Y5) => (!! @ $o @ (^[Y9 : $o]: (Y9)))) => (((c_Repl @ Y3 @ Y4) = Y6) => Y8)) => Y8))) => Y7) => Y7)))))))))))) @ c_Empty)))))))) @ (^[Y0 : $i]: (X11 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = (X11 @ X12))) )), 12.12/2.31 inference(beta_eta_normalization,[],[f464])). 12.12/2.31 thf(f464,plain,( 12.12/2.31 ( ! [X11 : $i > $i,X12 : $i] : (((sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK2 @ (^[Y3 : $i]: (sK4 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (sK4 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Union @ ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $i]: ((^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => Y19) => ((Y18 => Y19) => Y19))))))) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ Y13 @ (Y14 = Y16)) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ ((^[Y17 : $o]: (Y17 => (!! @ $o @ (^[Y18 : $o]: (Y18))))) @ Y13) @ (Y15 = Y16)))))))))) @ (c_In @ c_Empty @ Y12) @ Y10 @ Y11)))))) @ Y8 @ Y9))))) @ (c_Repl @ Y6 @ (^[Y8 : $i]: ((^[Y9 : $i]: (c_Repl @ Y9 @ (^[Y10 : $i]: ((^[Y11 : $i > ($i > $i) > $i]: ((^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (c_In_rec_poly_G_i @ Y11 @ Y12 @ Y13)))))) @ (^[Y11 : $i]: ((^[Y12 : $i > $i]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Union @ ((^[Y15 : $i]: ((^[Y16 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y17 : $i]: ((^[Y18 : $o]: ((^[Y19 : $i]: ((^[Y20 : $i]: (c_Eps_i @ (^[Y21 : $i]: ((^[Y22 : $o]: ((^[Y23 : $o]: (!! @ $o @ (^[Y24 : $o]: ((Y22 => Y24) => ((Y23 => Y24) => Y24))))))) @ ((^[Y22 : $o]: ((^[Y23 : $o]: (!! @ $o @ (^[Y24 : $o]: ((Y22 => (Y23 => Y24)) => Y24)))))) @ Y18 @ (Y19 = Y21)) @ ((^[Y22 : $o]: ((^[Y23 : $o]: (!! @ $o @ (^[Y24 : $o]: ((Y22 => (Y23 => Y24)) => Y24)))))) @ ((^[Y22 : $o]: (Y22 => (!! @ $o @ (^[Y23 : $o]: (Y23))))) @ Y18) @ (Y20 = Y21)))))))))) @ (c_In @ c_Empty @ Y17) @ Y15 @ Y16)))))) @ Y13 @ Y14))))) @ ((^[Y13 : $i]: ((^[Y14 : $i]: ((^[Y15 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y16 : $i]: ((^[Y17 : $o]: ((^[Y18 : $i]: ((^[Y19 : $i]: (c_Eps_i @ (^[Y20 : $i]: ((^[Y21 : $o]: ((^[Y22 : $o]: (!! @ $o @ (^[Y23 : $o]: ((Y21 => Y23) => ((Y22 => Y23) => Y23))))))) @ ((^[Y21 : $o]: ((^[Y22 : $o]: (!! @ $o @ (^[Y23 : $o]: ((Y21 => (Y22 => Y23)) => Y23)))))) @ Y17 @ (Y18 = Y20)) @ ((^[Y21 : $o]: ((^[Y22 : $o]: (!! @ $o @ (^[Y23 : $o]: ((Y21 => (Y22 => Y23)) => Y23)))))) @ ((^[Y21 : $o]: (Y21 => (!! @ $o @ (^[Y22 : $o]: (Y22))))) @ Y17) @ (Y19 = Y20)))))))))) @ (c_In @ c_Empty @ Y16) @ Y14 @ Y15)))))) @ Y13 @ Y13)) @ c_Empty) @ (c_Repl @ Y11 @ (^[Y13 : $i]: (Y12 @ Y13))))))) @ Y10)))) @ Y8))) @ (c_Repl @ Y7 @ (^[Y8 : $i]: ((^[Y9 : $i > ($i > $i) > $i]: ((^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (c_In_rec_poly_G_i @ Y9 @ Y10 @ Y11)))))) @ (^[Y9 : $i]: ((^[Y10 : $i > $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Union @ ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $i]: ((^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: ((^[Y20 : $o]: ((^[Y21 : $o]: (!! @ $o @ (^[Y22 : $o]: ((Y20 => Y22) => ((Y21 => Y22) => Y22))))))) @ ((^[Y20 : $o]: ((^[Y21 : $o]: (!! @ $o @ (^[Y22 : $o]: ((Y20 => (Y21 => Y22)) => Y22)))))) @ Y16 @ (Y17 = Y19)) @ ((^[Y20 : $o]: ((^[Y21 : $o]: (!! @ $o @ (^[Y22 : $o]: ((Y20 => (Y21 => Y22)) => Y22)))))) @ ((^[Y20 : $o]: (Y20 => (!! @ $o @ (^[Y21 : $o]: (Y21))))) @ Y16) @ (Y18 = Y19)))))))))) @ (c_In @ c_Empty @ Y15) @ Y13 @ Y14)))))) @ Y11 @ Y12))))) @ ((^[Y11 : $i]: ((^[Y12 : $i]: ((^[Y13 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y14 : $i]: ((^[Y15 : $o]: ((^[Y16 : $i]: ((^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: ((^[Y19 : $o]: ((^[Y20 : $o]: (!! @ $o @ (^[Y21 : $o]: ((Y19 => Y21) => ((Y20 => Y21) => Y21))))))) @ ((^[Y19 : $o]: ((^[Y20 : $o]: (!! @ $o @ (^[Y21 : $o]: ((Y19 => (Y20 => Y21)) => Y21)))))) @ Y15 @ (Y16 = Y18)) @ ((^[Y19 : $o]: ((^[Y20 : $o]: (!! @ $o @ (^[Y21 : $o]: ((Y19 => (Y20 => Y21)) => Y21)))))) @ ((^[Y19 : $o]: (Y19 => (!! @ $o @ (^[Y20 : $o]: (Y20))))) @ Y15) @ (Y17 = Y18)))))))))) @ (c_In @ c_Empty @ Y14) @ Y12 @ Y13)))))) @ Y11 @ Y11)) @ c_Empty) @ (c_Repl @ Y9 @ (^[Y11 : $i]: (Y10 @ Y11))))))) @ Y8))))))) @ c_Empty @ c_Empty)))) @ Y3))) @ ((^[Y3 : $i > ($i > $i) > $i]: ((^[Y4 : $i]: (c_Eps_i @ (^[Y5 : $i]: (c_In_rec_poly_G_i @ Y3 @ Y4 @ Y5)))))) @ (^[Y3 : $i]: ((^[Y4 : $i > $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Union @ ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => Y16) => ((Y15 => Y16) => Y16))))))) @ ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => (Y15 => Y16)) => Y16)))))) @ Y10 @ (Y11 = Y13)) @ ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => (Y15 => Y16)) => Y16)))))) @ ((^[Y14 : $o]: (Y14 => (!! @ $o @ (^[Y15 : $o]: (Y15))))) @ Y10) @ (Y12 = Y13)))))))))) @ (c_In @ c_Empty @ Y9) @ Y7 @ Y8)))))) @ Y5 @ Y6))))) @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => (!! @ $o @ (^[Y14 : $o]: (Y14))))) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y5 @ Y5)) @ c_Empty) @ (c_Repl @ Y3 @ (^[Y5 : $i]: (Y4 @ Y5))))))) @ c_Empty))))))) @ (^[Y0 : $i]: (X11 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = (X11 @ X12))) )), 12.12/2.31 inference(definition_unfolding,[],[f335,f438,f434])). 12.12/2.31 thf(f434,plain,( 12.12/2.31 (c_Inj1 = ((^[Y0 : $i > ($i > $i) > $i]: ((^[Y1 : $i]: (c_Eps_i @ (^[Y2 : $i]: (c_In_rec_poly_G_i @ Y0 @ Y1 @ Y2)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Union @ ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => Y13) => ((Y12 => Y13) => Y13))))))) @ ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => (Y12 => Y13)) => Y13)))))) @ Y7 @ (Y8 = Y10)) @ ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => (Y12 => Y13)) => Y13)))))) @ ((^[Y11 : $o]: (Y11 => (!! @ $o @ (^[Y12 : $o]: (Y12))))) @ Y7) @ (Y9 = Y10)))))))))) @ (c_In @ c_Empty @ Y6) @ Y4 @ Y5)))))) @ Y2 @ Y3))))) @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: ((^[Y6 : $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => Y12) => ((Y11 => Y12) => Y12))))))) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ Y6 @ (Y7 = Y9)) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ ((^[Y10 : $o]: (Y10 => (!! @ $o @ (^[Y11 : $o]: (Y11))))) @ Y6) @ (Y8 = Y9)))))))))) @ (c_In @ c_Empty @ Y5) @ Y3 @ Y4)))))) @ Y2 @ Y2)) @ c_Empty) @ (c_Repl @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2)))))))))), 12.12/2.31 inference(definition_unfolding,[],[f342,f349,f424,f423])). 12.12/2.31 thf(f423,plain,( 12.12/2.31 (c_Sing = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => Y10) => ((Y9 => Y10) => Y10))))))) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ Y4 @ (Y5 = Y7)) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ ((^[Y8 : $o]: (Y8 => (!! @ $o @ (^[Y9 : $o]: (Y9))))) @ Y4) @ (Y6 = Y7)))))))))) @ (c_In @ c_Empty @ Y3) @ Y1 @ Y2)))))) @ Y0 @ Y0)))), 12.12/2.31 inference(definition_unfolding,[],[f346,f422])). 12.12/2.31 thf(f422,plain,( 12.12/2.31 (c_UPair = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => Y9) => ((Y8 => Y9) => Y9))))))) @ ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => (Y8 => Y9)) => Y9)))))) @ Y3 @ (Y4 = Y6)) @ ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => (Y8 => Y9)) => Y9)))))) @ ((^[Y7 : $o]: (Y7 => (!! @ $o @ (^[Y8 : $o]: (Y8))))) @ Y3) @ (Y5 = Y6)))))))))) @ (c_In @ c_Empty @ Y2) @ Y0 @ Y1)))))))), 12.12/2.31 inference(definition_unfolding,[],[f375,f420])). 12.12/2.31 thf(f420,plain,( 12.12/2.31 (c_If_i = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Eps_i @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $o]: (!! @ $o @ (^[Y6 : $o]: ((Y4 => Y6) => ((Y5 => Y6) => Y6))))))) @ ((^[Y4 : $o]: ((^[Y5 : $o]: (!! @ $o @ (^[Y6 : $o]: ((Y4 => (Y5 => Y6)) => Y6)))))) @ Y0 @ (Y1 = Y3)) @ ((^[Y4 : $o]: ((^[Y5 : $o]: (!! @ $o @ (^[Y6 : $o]: ((Y4 => (Y5 => Y6)) => Y6)))))) @ ((^[Y4 : $o]: (Y4 => (!! @ $o @ (^[Y5 : $o]: (Y5))))) @ Y0) @ (Y2 = Y3)))))))))))), 12.12/2.31 inference(definition_unfolding,[],[f331,f329,f382,f382,f408])). 12.12/2.31 thf(f382,plain,( 12.12/2.31 (c_and = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => (Y1 => Y2)) => Y2)))))))), 12.12/2.31 inference(cnf_transformation,[],[f150])). 12.12/2.31 thf(f150,plain,( 12.12/2.31 (c_and = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => (Y1 => Y2)) => Y2)))))))), 12.12/2.31 inference(fool_elimination,[],[f149])). 12.12/2.31 thf(f149,plain,( 12.12/2.31 ((^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => (X1 => X2)) => X2))) = c_and)), 12.12/2.31 inference(rectify,[],[f107])). 12.12/2.31 thf(f107,axiom,( 12.12/2.31 ((^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => (X1 => X2)) => X2))) = c_and)), 12.12/2.31 file('/export/starexec/sandbox2/tmp/tmp.AEOGvNUPJb/E---3.1_16218.p',ax14)). 12.12/2.31 thf(f329,plain,( 12.12/2.31 (c_or = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => Y2) => ((Y1 => Y2) => Y2))))))))), 12.12/2.31 inference(cnf_transformation,[],[f269])). 12.12/2.31 thf(f269,plain,( 12.12/2.31 (c_or = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => Y2) => ((Y1 => Y2) => Y2))))))))), 12.12/2.31 inference(fool_elimination,[],[f268])). 12.12/2.31 thf(f268,plain,( 12.12/2.31 ((^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => X2) => ((X1 => X2) => X2)))) = c_or)), 12.12/2.31 inference(rectify,[],[f25])). 12.12/2.31 thf(f25,axiom,( 12.12/2.31 ((^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => X2) => ((X1 => X2) => X2)))) = c_or)), 12.12/2.31 file('/export/starexec/sandbox2/tmp/tmp.AEOGvNUPJb/E---3.1_16218.p',ax15)). 12.12/2.31 thf(f331,plain,( 12.12/2.31 (c_If_i = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Eps_i @ (^[Y3 : $i]: (c_or @ (c_and @ Y0 @ (Y1 = Y3)) @ (c_and @ (c_not @ Y0) @ (Y2 = Y3)))))))))))), 12.12/2.31 inference(cnf_transformation,[],[f236])). 12.12/2.31 thf(f236,plain,( 12.12/2.31 (c_If_i = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Eps_i @ (^[Y3 : $i]: (c_or @ (c_and @ Y0 @ (Y1 = Y3)) @ (c_and @ (c_not @ Y0) @ (Y2 = Y3)))))))))))), 12.12/2.31 inference(fool_elimination,[],[f9])). 12.12/2.31 thf(f9,axiom,( 12.12/2.31 (c_If_i = (^[X0 : $o, X1 : $i, X2 : $i] : (c_Eps_i @ (^[X3 : $i] : (c_or @ (c_and @ X0 @ (X1 = X3)) @ (c_and @ (c_not @ X0) @ (X2 = X3)))))))), 12.12/2.31 file('/export/starexec/sandbox2/tmp/tmp.AEOGvNUPJb/E---3.1_16218.p',ax42)). 12.12/2.31 thf(f375,plain,( 12.12/2.31 (c_UPair = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y2 : $i]: (c_If_i @ (c_In @ c_Empty @ Y2) @ Y0 @ Y1)))))))), 12.12/2.31 inference(cnf_transformation,[],[f190])). 12.12/2.31 thf(f190,plain,( 12.12/2.31 (c_UPair = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y2 : $i]: (c_If_i @ (c_In @ c_Empty @ Y2) @ Y0 @ Y1)))))))), 12.12/2.31 inference(fool_elimination,[],[f90])). 12.12/2.31 thf(f90,axiom,( 12.12/2.31 ((^[X0 : $i, X1 : $i] : (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[X2 : $i] : (c_If_i @ (c_In @ c_Empty @ X2) @ X0 @ X1)))) = c_UPair)), 12.12/2.31 file('/export/starexec/sandbox2/tmp/tmp.AEOGvNUPJb/E---3.1_16218.p',ax47)). 12.12/2.31 thf(f346,plain,( 12.12/2.31 (c_Sing = (^[Y0 : $i]: (c_UPair @ Y0 @ Y0)))), 12.12/2.31 inference(cnf_transformation,[],[f223])). 12.12/2.31 thf(f223,plain,( 12.12/2.31 (c_Sing = (^[Y0 : $i]: (c_UPair @ Y0 @ Y0)))), 12.12/2.31 inference(fool_elimination,[],[f28])). 12.12/2.31 thf(f28,axiom,( 12.12/2.31 ((^[X0 : $i] : (c_UPair @ X0 @ X0)) = c_Sing)), 12.12/2.31 file('/export/starexec/sandbox2/tmp/tmp.AEOGvNUPJb/E---3.1_16218.p',ax48)). 12.12/2.31 thf(f424,plain,( 12.12/2.31 (c_binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Union @ ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => Y11) => ((Y10 => Y11) => Y11))))))) @ ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => (Y10 => Y11)) => Y11)))))) @ Y5 @ (Y6 = Y8)) @ ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => (Y10 => Y11)) => Y11)))))) @ ((^[Y9 : $o]: (Y9 => (!! @ $o @ (^[Y10 : $o]: (Y10))))) @ Y5) @ (Y7 = Y8)))))))))) @ (c_In @ c_Empty @ Y4) @ Y2 @ Y3)))))) @ Y0 @ Y1))))))), 12.12/2.31 inference(definition_unfolding,[],[f385,f422])). 12.12/2.31 thf(f385,plain,( 12.12/2.31 (c_binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Union @ (c_UPair @ Y0 @ Y1))))))), 12.12/2.31 inference(cnf_transformation,[],[f157])). 12.12/2.31 thf(f157,plain,( 12.12/2.31 (c_binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Union @ (c_UPair @ Y0 @ Y1))))))), 12.12/2.31 inference(fool_elimination,[],[f73])). 12.12/2.31 thf(f73,axiom,( 12.12/2.31 ((^[X0 : $i, X1 : $i] : (c_Union @ (c_UPair @ X0 @ X1))) = c_binunion)), 12.12/2.31 file('/export/starexec/sandbox2/tmp/tmp.AEOGvNUPJb/E---3.1_16218.p',ax49)). 12.12/2.31 thf(f349,plain,( 12.12/2.31 (c_In_rec_poly_i = (^[Y0 : $i > ($i > $i) > $i]: ((^[Y1 : $i]: (c_Eps_i @ (^[Y2 : $i]: (c_In_rec_poly_G_i @ Y0 @ Y1 @ Y2)))))))), 12.12/2.31 inference(cnf_transformation,[],[f277])). 12.12/2.31 thf(f277,plain,( 12.12/2.31 (c_In_rec_poly_i = (^[Y0 : $i > ($i > $i) > $i]: ((^[Y1 : $i]: (c_Eps_i @ (^[Y2 : $i]: (c_In_rec_poly_G_i @ Y0 @ Y1 @ Y2)))))))), 12.12/2.31 inference(fool_elimination,[],[f82])). 12.12/2.31 thf(f82,axiom,( 12.12/2.31 ((^[X0 : $i > ($i > $i) > $i, X1 : $i] : (c_Eps_i @ (^[X2 : $i] : (c_In_rec_poly_G_i @ X0 @ X1 @ X2)))) = c_In_rec_poly_i)), 12.12/2.31 file('/export/starexec/sandbox2/tmp/tmp.AEOGvNUPJb/E---3.1_16218.p',ax61)). 12.12/2.31 thf(f342,plain,( 12.12/2.31 (c_Inj1 = (c_In_rec_poly_i @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: (c_binunion @ (c_Sing @ c_Empty) @ (c_Repl @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2)))))))))), 12.12/2.31 inference(cnf_transformation,[],[f202])). 12.12/2.31 thf(f202,plain,( 12.12/2.31 (c_Inj1 = (c_In_rec_poly_i @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: (c_binunion @ (c_Sing @ c_Empty) @ (c_Repl @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2)))))))))), 12.12/2.31 inference(fool_elimination,[],[f95])). 12.12/2.31 thf(f95,axiom,( 12.12/2.31 ((c_In_rec_poly_i @ (^[X0 : $i, X1 : $i > $i] : (c_binunion @ (c_Sing @ c_Empty) @ (c_Repl @ X0 @ (^[X2 : $i] : (X1 @ X2)))))) = c_Inj1)), 12.12/2.31 file('/export/starexec/sandbox2/tmp/tmp.AEOGvNUPJb/E---3.1_16218.p',ax69)). 12.12/2.31 thf(f438,plain,( 12.12/2.31 (c_setsum = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Union @ ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => Y13) => ((Y12 => Y13) => Y13))))))) @ ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => (Y12 => Y13)) => Y13)))))) @ Y7 @ (Y8 = Y10)) @ ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => (Y12 => Y13)) => Y13)))))) @ ((^[Y11 : $o]: (Y11 => (!! @ $o @ (^[Y12 : $o]: (Y12))))) @ Y7) @ (Y9 = Y10)))))))))) @ (c_In @ c_Empty @ Y6) @ Y4 @ Y5)))))) @ Y2 @ Y3))))) @ (c_Repl @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (c_Repl @ Y3 @ (^[Y4 : $i]: ((^[Y5 : $i > ($i > $i) > $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (c_In_rec_poly_G_i @ Y5 @ Y6 @ Y7)))))) @ (^[Y5 : $i]: ((^[Y6 : $i > $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Union @ ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => Y18) => ((Y17 => Y18) => Y18))))))) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ Y12 @ (Y13 = Y15)) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ ((^[Y16 : $o]: (Y16 => (!! @ $o @ (^[Y17 : $o]: (Y17))))) @ Y12) @ (Y14 = Y15)))))))))) @ (c_In @ c_Empty @ Y11) @ Y9 @ Y10)))))) @ Y7 @ Y8))))) @ ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $i]: ((^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => Y17) => ((Y16 => Y17) => Y17))))))) @ ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => (Y16 => Y17)) => Y17)))))) @ Y11 @ (Y12 = Y14)) @ ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => (Y16 => Y17)) => Y17)))))) @ ((^[Y15 : $o]: (Y15 => (!! @ $o @ (^[Y16 : $o]: (Y16))))) @ Y11) @ (Y13 = Y14)))))))))) @ (c_In @ c_Empty @ Y10) @ Y8 @ Y9)))))) @ Y7 @ Y7)) @ c_Empty) @ (c_Repl @ Y5 @ (^[Y7 : $i]: (Y6 @ Y7))))))) @ Y4)))) @ Y2))) @ (c_Repl @ Y1 @ (^[Y2 : $i]: ((^[Y3 : $i > ($i > $i) > $i]: ((^[Y4 : $i]: (c_Eps_i @ (^[Y5 : $i]: (c_In_rec_poly_G_i @ Y3 @ Y4 @ Y5)))))) @ (^[Y3 : $i]: ((^[Y4 : $i > $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Union @ ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => Y16) => ((Y15 => Y16) => Y16))))))) @ ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => (Y15 => Y16)) => Y16)))))) @ Y10 @ (Y11 = Y13)) @ ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => (Y15 => Y16)) => Y16)))))) @ ((^[Y14 : $o]: (Y14 => (!! @ $o @ (^[Y15 : $o]: (Y15))))) @ Y10) @ (Y12 = Y13)))))))))) @ (c_In @ c_Empty @ Y9) @ Y7 @ Y8)))))) @ Y5 @ Y6))))) @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => (!! @ $o @ (^[Y14 : $o]: (Y14))))) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y5 @ Y5)) @ c_Empty) @ (c_Repl @ Y3 @ (^[Y5 : $i]: (Y4 @ Y5))))))) @ Y2))))))))), 12.12/2.31 inference(definition_unfolding,[],[f350,f424,f435,f434])). 12.12/2.31 thf(f435,plain,( 12.12/2.31 (c_Inj0 = (^[Y0 : $i]: (c_Repl @ Y0 @ (^[Y1 : $i]: ((^[Y2 : $i > ($i > $i) > $i]: ((^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: (c_In_rec_poly_G_i @ Y2 @ Y3 @ Y4)))))) @ (^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Union @ ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => (!! @ $o @ (^[Y14 : $o]: (Y14))))) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y4 @ Y5))))) @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => Y14) => ((Y13 => Y14) => Y14))))))) @ ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => (Y13 => Y14)) => Y14)))))) @ Y8 @ (Y9 = Y11)) @ ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => (Y13 => Y14)) => Y14)))))) @ ((^[Y12 : $o]: (Y12 => (!! @ $o @ (^[Y13 : $o]: (Y13))))) @ Y8) @ (Y10 = Y11)))))))))) @ (c_In @ c_Empty @ Y7) @ Y5 @ Y6)))))) @ Y4 @ Y4)) @ c_Empty) @ (c_Repl @ Y2 @ (^[Y4 : $i]: (Y3 @ Y4))))))) @ Y1)))))), 12.12/2.31 inference(definition_unfolding,[],[f379,f434])). 12.12/2.31 thf(f379,plain,( 12.12/2.31 (c_Inj0 = (^[Y0 : $i]: (c_Repl @ Y0 @ (^[Y1 : $i]: (c_Inj1 @ Y1)))))), 12.12/2.31 inference(cnf_transformation,[],[f198])). 12.12/2.31 thf(f198,plain,( 12.12/2.31 (c_Inj0 = (^[Y0 : $i]: (c_Repl @ Y0 @ (^[Y1 : $i]: (c_Inj1 @ Y1)))))), 12.12/2.31 inference(fool_elimination,[],[f60])). 12.12/2.31 thf(f60,axiom,( 12.12/2.31 (c_Inj0 = (^[X0 : $i] : (c_Repl @ X0 @ (^[X1 : $i] : (c_Inj1 @ X1)))))), 12.12/2.31 file('/export/starexec/sandbox2/tmp/tmp.AEOGvNUPJb/E---3.1_16218.p',ax70)). 12.12/2.31 thf(f350,plain,( 12.12/2.31 (c_setsum = (^[Y0 : $i]: ((^[Y1 : $i]: (c_binunion @ (c_Repl @ Y0 @ (^[Y2 : $i]: (c_Inj0 @ Y2))) @ (c_Repl @ Y1 @ (^[Y2 : $i]: (c_Inj1 @ Y2))))))))), 12.12/2.31 inference(cnf_transformation,[],[f265])). 12.12/2.31 thf(f265,plain,( 12.12/2.31 (c_setsum = (^[Y0 : $i]: ((^[Y1 : $i]: (c_binunion @ (c_Repl @ Y0 @ (^[Y2 : $i]: (c_Inj0 @ Y2))) @ (c_Repl @ Y1 @ (^[Y2 : $i]: (c_Inj1 @ Y2))))))))), 12.12/2.31 inference(fool_elimination,[],[f264])). 12.12/2.31 thf(f264,plain,( 12.12/2.31 ((^[X0 : $i, X1 : $i] : (c_binunion @ (c_Repl @ X0 @ (^[X2 : $i] : (c_Inj0 @ X2))) @ (c_Repl @ X1 @ (^[X3 : $i] : (c_Inj1 @ X3))))) = c_setsum)), 12.12/2.31 inference(rectify,[],[f79])). 12.12/2.31 thf(f79,axiom,( 12.12/2.31 ((^[X0 : $i, X1 : $i] : (c_binunion @ (c_Repl @ X0 @ (^[X2 : $i] : (c_Inj0 @ X2))) @ (c_Repl @ X1 @ (^[X2 : $i] : (c_Inj1 @ X2))))) = c_setsum)), 12.12/2.31 file('/export/starexec/sandbox2/tmp/tmp.AEOGvNUPJb/E---3.1_16218.p',ax73)). 12.12/2.31 thf(f335,plain,( 12.12/2.31 ( ! [X11 : $i > $i,X12 : $i] : (((X11 @ X12) = (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK2 @ (^[Y3 : $i]: (sK4 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (sK4 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ Y3))) @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : $i]: (X11 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty))))) )), 12.12/2.31 inference(cnf_transformation,[],[f305])). 12.12/2.31 thf(f1034,plain,( 12.12/2.31 ( ! [X0 : $i > $i] : (((c_Union @ c_Empty) = (X0 @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y3 : $i]: ((^[Y4 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $o @ (^[Y8 : $o]: (((c_In @ c_Empty @ Y5) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => (!! @ $o @ (^[Y13 : $o]: (Y13)))) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))) = Y6) => Y8)) => Y8))) => Y7) => (((!! @ $o @ (^[Y8 : $o]: ((((c_In @ c_Empty @ Y5) => (!! @ $o @ (^[Y9 : $o]: (Y9)))) => (((c_Repl @ Y3 @ Y4) = Y6) => Y8)) => Y8))) => Y7) => Y7)))))))))))) @ c_Empty))))))) @ (^[Y0 : $i]: (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y2 : $i]: ((^[Y3 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y4 : $i]: (c_Eps_i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((c_In @ c_Empty @ Y4) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((c_Empty = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => (!! @ $o @ (^[Y12 : $o]: (Y12)))) => ((c_Empty = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))) = Y5) => Y7)) => Y7))) => Y6) => (((!! @ $o @ (^[Y7 : $o]: ((((c_In @ c_Empty @ Y4) => (!! @ $o @ (^[Y8 : $o]: (Y8)))) => (((c_Repl @ Y2 @ Y3) = Y5) => Y7)) => Y7))) => Y6) => Y6)))))))))))) @ Y1))))) @ (^[Y0 : $i > $i > $i]: (sK5 @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i]: (c_Empty)))))))) )), 12.12/2.31 inference(forward_demodulation,[],[f739,f644])). 12.12/2.31 thf(f644,plain,( 12.12/2.31 ( ! [X0 : $i] : (((sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK2 @ (^[Y3 : $i]: (sK4 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (sK4 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((c_Repl @ c_Empty @ (^[Y10 : $i]: (c_Repl @ Y10 @ (^[Y11 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y12 : $i]: ((^[Y13 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((c_Empty = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: ((((c_In @ c_Empty @ Y18) => (!! @ $o @ (^[Y22 : $o]: (Y22)))) => ((c_Empty = Y19) => Y21)) => Y21))) => Y20) => Y20)))))))) = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => (!! @ $o @ (^[Y18 : $o]: (Y18)))) => (((c_Repl @ Y12 @ Y13) = Y15) => Y17)) => Y17))) => Y16) => Y16)))))))))))) @ Y11)))))) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ c_Empty @ Y6) => (!! @ $o @ (^[Y10 : $o]: (Y10)))) => (((c_Repl @ c_Empty @ (^[Y10 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y11 : $i]: ((^[Y12 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((c_Empty = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: ((((c_In @ c_Empty @ Y17) => (!! @ $o @ (^[Y21 : $o]: (Y21)))) => ((c_Empty = Y18) => Y20)) => Y20))) => Y19) => Y19)))))))) = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => (!! @ $o @ (^[Y17 : $o]: (Y17)))) => (((c_Repl @ Y11 @ Y12) = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))))))) @ Y10)))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))))) @ Y3))) @ (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y3 : $i]: ((^[Y4 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $o @ (^[Y8 : $o]: (((c_In @ c_Empty @ Y5) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => (!! @ $o @ (^[Y13 : $o]: (Y13)))) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))) = Y6) => Y8)) => Y8))) => Y7) => (((!! @ $o @ (^[Y8 : $o]: ((((c_In @ c_Empty @ Y5) => (!! @ $o @ (^[Y9 : $o]: (Y9)))) => (((c_Repl @ Y3 @ Y4) = Y6) => Y8)) => Y8))) => Y7) => Y7)))))))))))) @ c_Empty)))))))) @ (^[Y0 : $i]: (X0)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = X0)) )), 12.12/2.31 inference(superposition,[],[f564,f338])). 12.12/2.31 thf(f739,plain,( 12.12/2.31 ( ! [X0 : $i > $i] : (((sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK2 @ (^[Y3 : $i]: (sK4 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (sK4 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((c_Repl @ c_Empty @ (^[Y10 : $i]: (c_Repl @ Y10 @ (^[Y11 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y12 : $i]: ((^[Y13 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((c_Empty = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: ((((c_In @ c_Empty @ Y18) => (!! @ $o @ (^[Y22 : $o]: (Y22)))) => ((c_Empty = Y19) => Y21)) => Y21))) => Y20) => Y20)))))))) = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => (!! @ $o @ (^[Y18 : $o]: (Y18)))) => (((c_Repl @ Y12 @ Y13) = Y15) => Y17)) => Y17))) => Y16) => Y16)))))))))))) @ Y11)))))) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ c_Empty @ Y6) => (!! @ $o @ (^[Y10 : $o]: (Y10)))) => (((c_Repl @ c_Empty @ (^[Y10 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y11 : $i]: ((^[Y12 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((c_Empty = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: ((((c_In @ c_Empty @ Y17) => (!! @ $o @ (^[Y21 : $o]: (Y21)))) => ((c_Empty = Y18) => Y20)) => Y20))) => Y19) => Y19)))))))) = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => (!! @ $o @ (^[Y17 : $o]: (Y17)))) => (((c_Repl @ Y11 @ Y12) = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))))))) @ Y10)))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))))) @ Y3))) @ (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y3 : $i]: ((^[Y4 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $o @ (^[Y8 : $o]: (((c_In @ c_Empty @ Y5) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => (!! @ $o @ (^[Y13 : $o]: (Y13)))) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))) = Y6) => Y8)) => Y8))) => Y7) => (((!! @ $o @ (^[Y8 : $o]: ((((c_In @ c_Empty @ Y5) => (!! @ $o @ (^[Y9 : $o]: (Y9)))) => (((c_Repl @ Y3 @ Y4) = Y6) => Y8)) => Y8))) => Y7) => Y7)))))))))))) @ c_Empty)))))))) @ (^[Y0 : $i]: (c_Union @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = (X0 @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y3 : $i]: ((^[Y4 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $o @ (^[Y8 : $o]: (((c_In @ c_Empty @ Y5) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => (!! @ $o @ (^[Y13 : $o]: (Y13)))) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))) = Y6) => Y8)) => Y8))) => Y7) => (((!! @ $o @ (^[Y8 : $o]: ((((c_In @ c_Empty @ Y5) => (!! @ $o @ (^[Y9 : $o]: (Y9)))) => (((c_Repl @ Y3 @ Y4) = Y6) => Y8)) => Y8))) => Y7) => Y7)))))))))))) @ c_Empty))))))) @ (^[Y0 : $i]: (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y2 : $i]: ((^[Y3 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y4 : $i]: (c_Eps_i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((c_In @ c_Empty @ Y4) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((c_Empty = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => (!! @ $o @ (^[Y12 : $o]: (Y12)))) => ((c_Empty = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))) = Y5) => Y7)) => Y7))) => Y6) => (((!! @ $o @ (^[Y7 : $o]: ((((c_In @ c_Empty @ Y4) => (!! @ $o @ (^[Y8 : $o]: (Y8)))) => (((c_Repl @ Y2 @ Y3) = Y5) => Y7)) => Y7))) => Y6) => Y6)))))))))))) @ Y1))))) @ (^[Y0 : $i > $i > $i]: (sK5 @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i]: (c_Empty)))))))) )), 12.12/2.31 inference(superposition,[],[f731,f564])). 12.12/2.31 thf(f731,plain,( 12.12/2.31 ( ! [X16 : $i > $i,X17 : $i > $i,X15 : $i > ($i > $i > $i) > $i] : (((c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y0 : $i]: (c_Eps_i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $o @ (^[Y3 : $o]: (((c_In @ c_Empty @ Y0) => (((c_Repl @ (X16 @ (X17 @ (sK3 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => ((c_Empty = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => (!! @ $o @ (^[Y17 : $o]: (Y17)))) => ((c_Empty = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))) = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => (!! @ $o @ (^[Y13 : $o]: (Y13)))) => (((c_Repl @ Y7 @ Y8) = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))))))) @ c_Empty))))))) @ (^[Y4 : $i]: (sK3 @ (^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Empty)))))) @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i > $i > $i]: (c_Empty)))) @ (^[Y4 : $i > $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $o @ (^[Y8 : $o]: (((c_In @ c_Empty @ Y5) => (((c_Repl @ c_Empty @ (^[Y9 : $i]: (c_Repl @ Y9 @ (^[Y10 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y11 : $i]: ((^[Y12 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((c_Empty = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: ((((c_In @ c_Empty @ Y17) => (!! @ $o @ (^[Y21 : $o]: (Y21)))) => ((c_Empty = Y18) => Y20)) => Y20))) => Y19) => Y19)))))))) = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => (!! @ $o @ (^[Y17 : $o]: (Y17)))) => (((c_Repl @ Y11 @ Y12) = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))))))) @ Y10)))))) = Y6) => Y8)) => Y8))) => Y7) => (((!! @ $o @ (^[Y8 : $o]: ((((c_In @ c_Empty @ Y5) => (!! @ $o @ (^[Y9 : $o]: (Y9)))) => (((c_Repl @ c_Empty @ (^[Y9 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y10 : $i]: ((^[Y11 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: (!! @ $o @ (^[Y18 : $o]: (((!! @ $o @ (^[Y19 : $o]: (((c_In @ c_Empty @ Y16) => ((c_Empty = Y17) => Y19)) => Y19))) => Y18) => (((!! @ $o @ (^[Y19 : $o]: ((((c_In @ c_Empty @ Y16) => (!! @ $o @ (^[Y20 : $o]: (Y20)))) => ((c_Empty = Y17) => Y19)) => Y19))) => Y18) => Y18)))))))) = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => (!! @ $o @ (^[Y16 : $o]: (Y16)))) => (((c_Repl @ Y10 @ Y11) = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))))))) @ Y9)))) = Y6) => Y8)) => Y8))) => Y7) => Y7))))))))))))) @ (^[Y4 : $i]: (c_Repl @ Y4 @ (^[Y5 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y6 : $i]: ((^[Y7 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((c_Empty = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => (!! @ $o @ (^[Y16 : $o]: (Y16)))) => ((c_Empty = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => (!! @ $o @ (^[Y12 : $o]: (Y12)))) => (((c_Repl @ Y6 @ Y7) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))))) @ Y5)))))) = Y1) => Y3)) => Y3))) => Y2) => (((!! @ $o @ (^[Y3 : $o]: ((((c_In @ c_Empty @ Y0) => (!! @ $o @ (^[Y4 : $o]: (Y4)))) => (((c_Repl @ (sK2 @ (^[Y4 : $i]: (X16 @ c_Empty)) @ (X17 @ (X15 @ (sK2 @ (^[Y4 : $i]: (c_Empty)) @ c_Empty) @ (^[Y4 : $i]: ((^[Y5 : $i]: (c_Empty))))))) @ (^[Y4 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y5 : $i]: ((^[Y6 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((c_Empty = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => (!! @ $o @ (^[Y15 : $o]: (Y15)))) => ((c_Empty = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ c_Empty @ Y7) => (!! @ $o @ (^[Y11 : $o]: (Y11)))) => (((c_Repl @ Y5 @ Y6) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))))) @ Y4)))) = Y1) => Y3)) => Y3))) => Y2) => Y2))))))))) = (X16 @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y3 : $i]: ((^[Y4 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $o @ (^[Y8 : $o]: (((c_In @ c_Empty @ Y5) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => (!! @ $o @ (^[Y13 : $o]: (Y13)))) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))) = Y6) => Y8)) => Y8))) => Y7) => (((!! @ $o @ (^[Y8 : $o]: ((((c_In @ c_Empty @ Y5) => (!! @ $o @ (^[Y9 : $o]: (Y9)))) => (((c_Repl @ Y3 @ Y4) = Y6) => Y8)) => Y8))) => Y7) => Y7)))))))))))) @ c_Empty))))))) @ (^[Y0 : $i]: (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y2 : $i]: ((^[Y3 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y4 : $i]: (c_Eps_i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((c_In @ c_Empty @ Y4) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((c_Empty = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => (!! @ $o @ (^[Y12 : $o]: (Y12)))) => ((c_Empty = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))) = Y5) => Y7)) => Y7))) => Y6) => (((!! @ $o @ (^[Y7 : $o]: ((((c_In @ c_Empty @ Y4) => (!! @ $o @ (^[Y8 : $o]: (Y8)))) => (((c_Repl @ Y2 @ Y3) = Y5) => Y7)) => Y7))) => Y6) => Y6)))))))))))) @ Y1))))) @ (^[Y0 : $i > $i > $i]: (sK5 @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i]: (c_Empty)))))))) )), 12.12/2.31 inference(forward_demodulation,[],[f730,f648])). 12.12/2.31 thf(f730,plain,( 12.12/2.31 ( ! [X16 : $i > $i,X17 : $i > $i,X15 : $i > ($i > $i > $i) > $i] : (((X16 @ (sK4 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (sK3 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y5 : $i]: ((^[Y6 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((c_Empty = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => (!! @ $o @ (^[Y15 : $o]: (Y15)))) => ((c_Empty = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ c_Empty @ Y7) => (!! @ $o @ (^[Y11 : $o]: (Y11)))) => (((c_Repl @ Y5 @ Y6) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))))) @ c_Empty))))))) @ (^[Y2 : $i]: (c_Repl @ c_Empty @ (^[Y3 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y4 : $i]: ((^[Y5 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => ((c_Empty = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: ((((c_In @ c_Empty @ Y10) => (!! @ $o @ (^[Y14 : $o]: (Y14)))) => ((c_Empty = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ c_Empty @ Y6) => (!! @ $o @ (^[Y10 : $o]: (Y10)))) => (((c_Repl @ Y4 @ Y5) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))))) @ Y3))))) @ (^[Y2 : $i > $i > $i]: (sK5 @ (^[Y3 : $i]: (c_Empty)) @ (^[Y3 : $i]: (c_Empty)))))))) @ (c_Repl @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Empty)))))) @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) @ (^[Y0 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y1 : $i]: ((^[Y2 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $o @ (^[Y6 : $o]: (((c_In @ c_Empty @ Y3) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => ((c_Empty = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ c_Empty @ Y7) => (!! @ $o @ (^[Y11 : $o]: (Y11)))) => ((c_Empty = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))) = Y4) => Y6)) => Y6))) => Y5) => (((!! @ $o @ (^[Y6 : $o]: ((((c_In @ c_Empty @ Y3) => (!! @ $o @ (^[Y7 : $o]: (Y7)))) => (((c_Repl @ Y1 @ Y2) = Y4) => Y6)) => Y6))) => Y5) => Y5)))))))))))) @ Y0)))))) = (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y0 : $i]: (c_Eps_i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $o @ (^[Y3 : $o]: (((c_In @ c_Empty @ Y0) => (((c_Repl @ (X16 @ (X17 @ (sK3 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => ((c_Empty = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => (!! @ $o @ (^[Y17 : $o]: (Y17)))) => ((c_Empty = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))) = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => (!! @ $o @ (^[Y13 : $o]: (Y13)))) => (((c_Repl @ Y7 @ Y8) = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))))))) @ c_Empty))))))) @ (^[Y4 : $i]: (sK3 @ (^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Empty)))))) @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i > $i > $i]: (c_Empty)))) @ (^[Y4 : $i > $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $o @ (^[Y8 : $o]: (((c_In @ c_Empty @ Y5) => (((c_Repl @ c_Empty @ (^[Y9 : $i]: (c_Repl @ Y9 @ (^[Y10 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y11 : $i]: ((^[Y12 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((c_Empty = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: ((((c_In @ c_Empty @ Y17) => (!! @ $o @ (^[Y21 : $o]: (Y21)))) => ((c_Empty = Y18) => Y20)) => Y20))) => Y19) => Y19)))))))) = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => (!! @ $o @ (^[Y17 : $o]: (Y17)))) => (((c_Repl @ Y11 @ Y12) = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))))))) @ Y10)))))) = Y6) => Y8)) => Y8))) => Y7) => (((!! @ $o @ (^[Y8 : $o]: ((((c_In @ c_Empty @ Y5) => (!! @ $o @ (^[Y9 : $o]: (Y9)))) => (((c_Repl @ c_Empty @ (^[Y9 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y10 : $i]: ((^[Y11 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: (!! @ $o @ (^[Y18 : $o]: (((!! @ $o @ (^[Y19 : $o]: (((c_In @ c_Empty @ Y16) => ((c_Empty = Y17) => Y19)) => Y19))) => Y18) => (((!! @ $o @ (^[Y19 : $o]: ((((c_In @ c_Empty @ Y16) => (!! @ $o @ (^[Y20 : $o]: (Y20)))) => ((c_Empty = Y17) => Y19)) => Y19))) => Y18) => Y18)))))))) = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => (!! @ $o @ (^[Y16 : $o]: (Y16)))) => (((c_Repl @ Y10 @ Y11) = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))))))) @ Y9)))) = Y6) => Y8)) => Y8))) => Y7) => Y7))))))))))))) @ (^[Y4 : $i]: (c_Repl @ Y4 @ (^[Y5 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y6 : $i]: ((^[Y7 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((c_Empty = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => (!! @ $o @ (^[Y16 : $o]: (Y16)))) => ((c_Empty = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => (!! @ $o @ (^[Y12 : $o]: (Y12)))) => (((c_Repl @ Y6 @ Y7) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))))) @ Y5)))))) = Y1) => Y3)) => Y3))) => Y2) => (((!! @ $o @ (^[Y3 : $o]: ((((c_In @ c_Empty @ Y0) => (!! @ $o @ (^[Y4 : $o]: (Y4)))) => (((c_Repl @ (sK2 @ (^[Y4 : $i]: (X16 @ c_Empty)) @ (X17 @ (X15 @ (sK2 @ (^[Y4 : $i]: (c_Empty)) @ c_Empty) @ (^[Y4 : $i]: ((^[Y5 : $i]: (c_Empty))))))) @ (^[Y4 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y5 : $i]: ((^[Y6 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((c_Empty = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => (!! @ $o @ (^[Y15 : $o]: (Y15)))) => ((c_Empty = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ c_Empty @ Y7) => (!! @ $o @ (^[Y11 : $o]: (Y11)))) => (((c_Repl @ Y5 @ Y6) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))))) @ Y4)))) = Y1) => Y3)) => Y3))) => Y2) => Y2))))))))))) )), 12.12/2.31 inference(forward_demodulation,[],[f521,f648])). 12.12/2.31 thf(f521,plain,( 12.12/2.31 ( ! [X16 : $i > $i,X17 : $i > $i,X15 : $i > ($i > $i > $i) > $i] : (((c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y0 : $i]: (c_Eps_i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $o @ (^[Y3 : $o]: (((c_In @ c_Empty @ Y0) => (((c_Repl @ (X16 @ (X17 @ (sK3 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => ((c_Empty = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => (!! @ $o @ (^[Y17 : $o]: (Y17)))) => ((c_Empty = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))) = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => (!! @ $o @ (^[Y13 : $o]: (Y13)))) => (((c_Repl @ Y7 @ Y8) = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))))))) @ c_Empty))))))) @ (^[Y4 : $i]: (sK3 @ (^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Empty)))))) @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i > $i > $i]: (c_Empty)))) @ (^[Y4 : $i > $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $o @ (^[Y8 : $o]: (((c_In @ c_Empty @ Y5) => (((c_Repl @ c_Empty @ (^[Y9 : $i]: (c_Repl @ Y9 @ (^[Y10 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y11 : $i]: ((^[Y12 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((c_Empty = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: ((((c_In @ c_Empty @ Y17) => (!! @ $o @ (^[Y21 : $o]: (Y21)))) => ((c_Empty = Y18) => Y20)) => Y20))) => Y19) => Y19)))))))) = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => (!! @ $o @ (^[Y17 : $o]: (Y17)))) => (((c_Repl @ Y11 @ Y12) = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))))))) @ Y10)))))) = Y6) => Y8)) => Y8))) => Y7) => (((!! @ $o @ (^[Y8 : $o]: ((((c_In @ c_Empty @ Y5) => (!! @ $o @ (^[Y9 : $o]: (Y9)))) => (((c_Repl @ c_Empty @ (^[Y9 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y10 : $i]: ((^[Y11 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: (!! @ $o @ (^[Y18 : $o]: (((!! @ $o @ (^[Y19 : $o]: (((c_In @ c_Empty @ Y16) => ((c_Empty = Y17) => Y19)) => Y19))) => Y18) => (((!! @ $o @ (^[Y19 : $o]: ((((c_In @ c_Empty @ Y16) => (!! @ $o @ (^[Y20 : $o]: (Y20)))) => ((c_Empty = Y17) => Y19)) => Y19))) => Y18) => Y18)))))))) = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => (!! @ $o @ (^[Y16 : $o]: (Y16)))) => (((c_Repl @ Y10 @ Y11) = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))))))) @ Y9)))) = Y6) => Y8)) => Y8))) => Y7) => Y7))))))))))))) @ (^[Y4 : $i]: (c_Repl @ Y4 @ (^[Y5 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y6 : $i]: ((^[Y7 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((c_Empty = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => (!! @ $o @ (^[Y16 : $o]: (Y16)))) => ((c_Empty = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => (!! @ $o @ (^[Y12 : $o]: (Y12)))) => (((c_Repl @ Y6 @ Y7) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))))) @ Y5)))))) = Y1) => Y3)) => Y3))) => Y2) => (((!! @ $o @ (^[Y3 : $o]: ((((c_In @ c_Empty @ Y0) => (!! @ $o @ (^[Y4 : $o]: (Y4)))) => (((c_Repl @ (sK2 @ (^[Y4 : $i]: (X16 @ c_Empty)) @ (X17 @ (X15 @ (sK2 @ (^[Y4 : $i]: (c_Empty)) @ c_Empty) @ (^[Y4 : $i]: ((^[Y5 : $i]: (c_Empty))))))) @ (^[Y4 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y5 : $i]: ((^[Y6 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((c_Empty = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => (!! @ $o @ (^[Y15 : $o]: (Y15)))) => ((c_Empty = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ c_Empty @ Y7) => (!! @ $o @ (^[Y11 : $o]: (Y11)))) => (((c_Repl @ Y5 @ Y6) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))))) @ Y4)))) = Y1) => Y3)) => Y3))) => Y2) => Y2))))))))) = (sK4 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X16 @ (sK4 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (sK3 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => ((c_Empty = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => (!! @ $o @ (^[Y17 : $o]: (Y17)))) => ((c_Empty = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))) = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => (!! @ $o @ (^[Y13 : $o]: (Y13)))) => (((c_Repl @ Y7 @ Y8) = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))))))) @ c_Empty))))))) @ (^[Y4 : $i]: (c_Repl @ c_Empty @ (^[Y5 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y6 : $i]: ((^[Y7 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((c_Empty = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => (!! @ $o @ (^[Y16 : $o]: (Y16)))) => ((c_Empty = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => (!! @ $o @ (^[Y12 : $o]: (Y12)))) => (((c_Repl @ Y6 @ Y7) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))))) @ Y5))))) @ (^[Y4 : $i > $i > $i]: (sK5 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ (c_Repl @ (sK3 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))) @ (^[Y2 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y3 : $i]: ((^[Y4 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $o @ (^[Y8 : $o]: (((c_In @ c_Empty @ Y5) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => (!! @ $o @ (^[Y13 : $o]: (Y13)))) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))) = Y6) => Y8)) => Y8))) => Y7) => (((!! @ $o @ (^[Y8 : $o]: ((((c_In @ c_Empty @ Y5) => (!! @ $o @ (^[Y9 : $o]: (Y9)))) => (((c_Repl @ Y3 @ Y4) = Y6) => Y8)) => Y8))) => Y7) => Y7)))))))))))) @ Y2))))))))) @ (sK5 @ (^[Y0 : $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y1 : $i]: (c_Eps_i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $o @ (^[Y4 : $o]: (((c_In @ c_Empty @ Y1) => (((c_Repl @ Y0 @ (^[Y5 : $i]: (c_Repl @ Y5 @ (^[Y6 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => ((c_Empty = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => (!! @ $o @ (^[Y17 : $o]: (Y17)))) => ((c_Empty = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))) = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => (!! @ $o @ (^[Y13 : $o]: (Y13)))) => (((c_Repl @ Y7 @ Y8) = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))))))) @ Y6)))))) = Y2) => Y4)) => Y4))) => Y3) => (((!! @ $o @ (^[Y4 : $o]: ((((c_In @ c_Empty @ Y1) => (!! @ $o @ (^[Y5 : $o]: (Y5)))) => (((c_Repl @ c_Empty @ (^[Y5 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y6 : $i]: ((^[Y7 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((c_Empty = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => (!! @ $o @ (^[Y16 : $o]: (Y16)))) => ((c_Empty = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => (!! @ $o @ (^[Y12 : $o]: (Y12)))) => (((c_Repl @ Y6 @ Y7) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))))) @ Y5)))) = Y2) => Y4)) => Y4))) => Y3) => Y3)))))))))) @ (^[Y0 : $i]: (c_Empty)))))) )), 12.12/2.31 inference(beta_eta_normalization,[],[f466])). 12.12/2.31 thf(f466,plain,( 12.12/2.31 ( ! 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@ $o @ (^[Y17 : $o]: ((Y15 => Y17) => ((Y16 => Y17) => Y17))))))) @ ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => (Y16 => Y17)) => Y17)))))) @ Y11 @ (Y12 = Y14)) @ ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => (Y16 => Y17)) => Y17)))))) @ ((^[Y15 : $o]: (Y15 => (!! @ $o @ (^[Y16 : $o]: (Y16))))) @ Y11) @ (Y13 = Y14)))))))))) @ (c_In @ c_Empty @ Y10) @ Y8 @ Y9)))))) @ Y6 @ Y7))))) @ ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => Y16) => ((Y15 => Y16) => Y16))))))) @ ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => (Y15 => Y16)) => Y16)))))) @ Y10 @ (Y11 = Y13)) @ ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => (Y15 => Y16)) => Y16)))))) @ ((^[Y14 : $o]: (Y14 => (!! @ $o @ (^[Y15 : $o]: (Y15))))) @ Y10) @ (Y12 = Y13)))))))))) @ (c_In @ c_Empty @ Y9) @ Y7 @ Y8)))))) @ Y6 @ Y6)) @ c_Empty) @ (c_Repl @ Y4 @ (^[Y6 : $i]: (Y5 @ Y6))))))) @ Y3)))) @ (sK3 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))))))) @ (sK5 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Union @ ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => Y14) => ((Y13 => Y14) => Y14))))))) @ ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => (Y13 => Y14)) => Y14)))))) @ Y8 @ (Y9 = Y11)) @ ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => (Y13 => Y14)) => Y14)))))) @ ((^[Y12 : $o]: (Y12 => (!! @ $o @ (^[Y13 : $o]: (Y13))))) @ Y8) @ (Y10 = Y11)))))))))) @ (c_In @ c_Empty @ Y7) @ Y5 @ Y6)))))) @ Y3 @ Y4))))) @ (c_Repl @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: (c_Repl @ Y4 @ (^[Y5 : $i]: ((^[Y6 : $i > ($i > $i) > $i]: ((^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (c_In_rec_poly_G_i @ Y6 @ Y7 @ Y8)))))) @ (^[Y6 : $i]: ((^[Y7 : $i > $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Union @ ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $i]: ((^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => Y19) => ((Y18 => Y19) => Y19))))))) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ Y13 @ (Y14 = Y16)) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ ((^[Y17 : $o]: (Y17 => (!! @ $o @ (^[Y18 : $o]: (Y18))))) @ Y13) @ (Y15 = Y16)))))))))) @ (c_In @ c_Empty @ Y12) @ Y10 @ Y11)))))) @ Y8 @ Y9))))) @ ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => Y18) => ((Y17 => Y18) => Y18))))))) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ Y12 @ (Y13 = Y15)) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ ((^[Y16 : $o]: (Y16 => (!! @ $o @ (^[Y17 : $o]: (Y17))))) @ Y12) @ (Y14 = Y15)))))))))) @ (c_In @ c_Empty @ Y11) @ Y9 @ Y10)))))) @ Y8 @ Y8)) @ c_Empty) @ (c_Repl @ Y6 @ (^[Y8 : $i]: (Y7 @ Y8))))))) @ Y5)))) @ Y3))) @ (c_Repl @ Y2 @ (^[Y3 : $i]: ((^[Y4 : $i > ($i > $i) > $i]: ((^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (c_In_rec_poly_G_i @ Y4 @ Y5 @ Y6)))))) @ (^[Y4 : $i]: ((^[Y5 : $i > $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Union @ ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $i]: ((^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => Y17) => ((Y16 => Y17) => Y17))))))) @ ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => (Y16 => Y17)) => Y17)))))) @ Y11 @ (Y12 = Y14)) @ ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => (Y16 => Y17)) => Y17)))))) @ ((^[Y15 : $o]: (Y15 => (!! @ $o @ (^[Y16 : $o]: (Y16))))) @ Y11) @ (Y13 = Y14)))))))))) @ (c_In @ c_Empty @ Y10) @ Y8 @ Y9)))))) @ Y6 @ Y7))))) @ ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => Y16) => ((Y15 => Y16) => Y16))))))) @ ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => (Y15 => Y16)) => Y16)))))) @ Y10 @ (Y11 = Y13)) @ ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => (Y15 => Y16)) => Y16)))))) @ ((^[Y14 : $o]: (Y14 => (!! @ $o @ (^[Y15 : $o]: (Y15))))) @ Y10) @ (Y12 = Y13)))))))))) @ (c_In @ c_Empty @ Y9) @ Y7 @ Y8)))))) @ Y6 @ Y6)) @ c_Empty) @ (c_Repl @ Y4 @ (^[Y6 : $i]: (Y5 @ Y6))))))) @ Y3))))))) @ Y0 @ c_Empty)) @ (^[Y0 : $i]: (c_Empty)))))) )), 12.12/2.31 inference(definition_unfolding,[],[f333,f438,f434,f438,f434,f435,f435,f438])). 12.12/2.31 thf(f333,plain,( 12.12/2.31 ( ! [X16 : $i > $i,X17 : $i > $i,X15 : $i > ($i > $i > $i) > $i] : (((c_setsum @ (X16 @ (X17 @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y0 : $i]: (sK3 @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Empty)))))) @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i > $i > $i]: (c_Empty)))) @ (^[Y0 : $i > $i > $i]: (c_setsum @ c_Empty @ c_Empty))))) @ (sK2 @ (^[Y0 : $i]: (X16 @ c_Empty)) @ (X17 @ (X15 @ (sK2 @ (^[Y0 : $i]: (c_Empty)) @ c_Empty) @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_Empty)))))))) = (sK4 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X16 @ (sK4 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (sK3 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y4 : $i]: (c_Inj0 @ c_Empty)) @ (^[Y4 : $i > $i > $i]: (sK5 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ (c_Inj0 @ (sK3 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))))))) @ (sK5 @ (^[Y0 : $i]: (c_setsum @ Y0 @ c_Empty)) @ (^[Y0 : $i]: (c_Empty)))))) )), 12.12/2.31 inference(cnf_transformation,[],[f305])). 12.12/2.31 thf(f1354,plain,( 12.12/2.31 ( ! [X2 : $o,X0 : $i,X1 : $i] : (((c_In @ (sK14 @ X1 @ X0) @ X0) = $true) | ($true = X2)) )), 12.12/2.31 inference(subsumption_resolution,[],[f490,f1261])). 12.12/2.31 thf(f1261,plain,( 12.12/2.31 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (((c_In @ X1 @ X0) != $true) | ((X2 @ X1) = $true)) )), 12.12/2.31 inference(superposition,[],[f1233,f1072])). 12.12/2.31 thf(f1233,plain,( 12.12/2.31 ( ! [X3 : $i,X0 : $i > $o] : (((c_In @ X3 @ (c_Union @ c_Empty)) != $true) | ((X0 @ X3) = $true)) )), 12.12/2.31 inference(subsumption_resolution,[],[f1129,f1220])). 12.12/2.31 thf(f1220,plain,( 12.12/2.31 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((X1 @ X0) != $true) | ((X1 @ X2) = $true)) )), 12.12/2.31 inference(superposition,[],[f1132,f1072])). 12.12/2.31 thf(f1132,plain,( 12.12/2.31 ( ! [X0 : $i > $o,X1 : $i] : (((X0 @ (c_Union @ c_Empty)) != $true) | ((X0 @ X1) = $true)) )), 12.12/2.31 inference(backward_demodulation,[],[f368,f1072])). 12.12/2.31 thf(f368,plain,( 12.12/2.31 ( ! [X0 : $i > $o,X1 : $i] : (($true != (X0 @ (sK6 @ X0))) | ((X0 @ X1) = $true)) )), 12.12/2.31 inference(cnf_transformation,[],[f308])). 12.12/2.31 thf(f308,plain,( 12.12/2.31 ! [X0 : $i > $o] : (! [X1] : ((X0 @ X1) = $true) | (! [X3] : (((c_In @ X3 @ (sK6 @ X0)) != $true) | ((X0 @ X3) = $true)) & ($true != (X0 @ (sK6 @ X0)))))), 12.12/2.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f306,f307])). 12.12/2.31 thf(f307,plain,( 12.12/2.31 ! [X0 : $i > $o] : (? [X2] : (! [X3] : (((c_In @ X3 @ X2) != $true) | ((X0 @ X3) = $true)) & ((X0 @ X2) != $true)) => (! [X3] : (((c_In @ X3 @ (sK6 @ X0)) != $true) | ((X0 @ X3) = $true)) & ($true != (X0 @ (sK6 @ X0)))))), 12.12/2.31 introduced(choice_axiom,[])). 12.12/2.31 thf(f306,plain,( 12.12/2.31 ! [X0 : $i > $o] : (! [X1] : ((X0 @ X1) = $true) | ? [X2] : (! [X3] : (((c_In @ X3 @ X2) != $true) | ((X0 @ X3) = $true)) & ((X0 @ X2) != $true)))), 12.12/2.31 inference(rectify,[],[f291])). 12.12/2.31 thf(f291,plain,( 12.12/2.31 ! [X0 : $i > $o] : (! [X3] : ((X0 @ X3) = $true) | ? [X1] : (! [X2] : (((c_In @ X2 @ X1) != $true) | ((X0 @ X2) = $true)) & ((X0 @ X1) != $true)))), 12.12/2.31 inference(ennf_transformation,[],[f125])). 12.12/2.31 thf(f125,plain,( 12.12/2.31 ! [X0 : $i > $o] : (! [X1] : (! [X2] : (((c_In @ X2 @ X1) = $true) => ((X0 @ X2) = $true)) => ((X0 @ X1) = $true)) => ! [X3] : ((X0 @ X3) = $true))), 12.12/2.31 inference(fool_elimination,[],[f124])). 12.12/2.31 thf(f124,plain,( 12.12/2.31 ! [X0 : $i > $o] : (! [X1] : (! [X2] : ((c_In @ X2 @ X1) => (X0 @ X2)) => (X0 @ X1)) => ! [X3] : (X0 @ X3))), 12.12/2.31 inference(rectify,[],[f39])). 12.12/2.31 thf(f39,axiom,( 12.12/2.31 ! [X0 : $i > $o] : (! [X1] : (! [X2] : ((c_In @ X2 @ X1) => (X0 @ X2)) => (X0 @ X1)) => ! [X1] : (X0 @ X1))), 12.12/2.31 file('/export/starexec/sandbox2/tmp/tmp.AEOGvNUPJb/E---3.1_16218.p',ax10)). 12.12/2.31 thf(f1129,plain,( 12.12/2.31 ( ! [X3 : $i,X0 : $i > $o,X1 : $i] : (((c_In @ X3 @ (c_Union @ c_Empty)) != $true) | ((X0 @ X1) = $true) | ((X0 @ X3) = $true)) )), 12.12/2.31 inference(backward_demodulation,[],[f369,f1072])). 12.12/2.31 thf(f369,plain,( 12.12/2.31 ( ! [X3 : $i,X0 : $i > $o,X1 : $i] : (((c_In @ X3 @ (sK6 @ X0)) != $true) | ((X0 @ X1) = $true) | ((X0 @ X3) = $true)) )), 12.12/2.31 inference(cnf_transformation,[],[f308])). 12.12/2.31 thf(f490,plain,( 12.12/2.31 ( ! [X2 : $o,X0 : $i,X1 : $i] : (((c_In @ X0 @ (c_Power @ X1)) = $true) | ((c_In @ (sK14 @ X1 @ X0) @ X0) = $true) | ($true = X2)) )), 12.12/2.31 inference(binary_proxy_clausification,[],[f488])). 12.12/2.31 thf(f488,plain,( 12.12/2.31 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($false = ((c_In @ (sK14 @ X1 @ X0) @ X0) => (c_In @ (sK14 @ X1 @ X0) @ X1))) | ($true = X2) | ((c_In @ X0 @ (c_Power @ X1)) = $true)) )), 12.12/2.31 inference(beta_eta_normalization,[],[f487])). 12.12/2.31 thf(f487,plain,( 12.12/2.31 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = X2) | (((^[Y0 : $i]: ((c_In @ Y0 @ X0) => (c_In @ Y0 @ X1))) @ (sK14 @ X1 @ X0)) = $false) | ((c_In @ X0 @ (c_Power @ X1)) = $true)) )), 12.12/2.31 inference(sigma_clausification,[],[f486])). 12.12/2.31 thf(f486,plain,( 12.12/2.31 ( ! [X2 : $o,X0 : $i,X1 : $i] : (((c_In @ X0 @ (c_Power @ X1)) = $true) | ($true = X2) | ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X0) => (c_In @ Y0 @ X1)))) = $false)) )), 12.12/2.31 inference(binary_proxy_clausification,[],[f485])). 12.12/2.31 thf(f485,plain,( 12.12/2.31 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = X2) | (((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X0) => (c_In @ Y0 @ X1)))) => (c_In @ X0 @ (c_Power @ X1))) = $true)) )), 12.12/2.31 inference(binary_proxy_clausification,[],[f478])). 12.12/2.31 thf(f478,plain,( 12.12/2.31 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($false = (((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X0) => (c_In @ Y0 @ X1)))) => (c_In @ X0 @ (c_Power @ X1))) => X2)) | ($true = X2)) )), 12.12/2.31 inference(binary_proxy_clausification,[],[f477])). 12.12/2.31 thf(f477,plain,( 12.12/2.31 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = X2) | ((((c_In @ X0 @ (c_Power @ X1)) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X0) => (c_In @ Y0 @ X1))))) => (((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X0) => (c_In @ Y0 @ X1)))) => (c_In @ X0 @ (c_Power @ X1))) => X2)) = $false)) )), 12.12/2.31 inference(binary_proxy_clausification,[],[f476])). 12.12/2.31 thf(f476,plain,( 12.12/2.31 ( ! [X2 : $o,X0 : $i,X1 : $i] : ((((((c_In @ X0 @ (c_Power @ X1)) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X0) => (c_In @ Y0 @ X1))))) => (((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X0) => (c_In @ Y0 @ X1)))) => (c_In @ X0 @ (c_Power @ X1))) => X2)) => X2) = $true)) )), 12.12/2.31 inference(beta_eta_normalization,[],[f475])). 12.12/2.31 thf(f475,plain,( 12.12/2.31 ( ! [X2 : $o,X0 : $i,X1 : $i] : ((((^[Y0 : $o]: ((((c_In @ X0 @ (c_Power @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ X0) => (c_In @ Y1 @ X1))))) => (((!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ X0) => (c_In @ Y1 @ X1)))) => (c_In @ X0 @ (c_Power @ X1))) => Y0)) => Y0)) @ X2) = $true)) )), 12.12/2.31 inference(pi_clausification,[],[f474])). 12.12/2.31 thf(f474,plain,( 12.12/2.31 ( ! [X0 : $i,X1 : $i] : (((!! @ $o @ (^[Y0 : $o]: ((((c_In @ X0 @ (c_Power @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ X0) => (c_In @ Y1 @ X1))))) => (((!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ X0) => (c_In @ Y1 @ X1)))) => (c_In @ X0 @ (c_Power @ X1))) => Y0)) => Y0))) = $true)) )), 12.12/2.31 inference(beta_eta_normalization,[],[f467])). 12.12/2.31 thf(f467,plain,( 12.12/2.31 ( ! [X0 : $i,X1 : $i] : ((((^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ (Y0 => Y1) @ (Y1 => Y0))))) @ (c_In @ X0 @ (c_Power @ X1)) @ ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ Y1))))))) @ X0 @ X1)) = $true)) )), 12.12/2.31 inference(definition_unfolding,[],[f343,f409,f390])). 12.12/2.31 thf(f390,plain,( 12.12/2.31 (c_Subq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ Y1))))))))), 12.12/2.31 inference(cnf_transformation,[],[f195])). 12.12/2.31 thf(f195,plain,( 12.12/2.31 (c_Subq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ Y1))))))))), 12.12/2.31 inference(fool_elimination,[],[f194])). 12.12/2.31 thf(f194,plain,( 12.12/2.31 ((^[X0 : $i, X1 : $i] : (! [X2] : ((c_In @ X2 @ X0) => (c_In @ X2 @ X1)))) = c_Subq)), 12.12/2.31 inference(rectify,[],[f19])). 12.12/2.31 thf(f19,axiom,( 12.12/2.31 ((^[X0 : $i, X1 : $i] : (! [X2] : ((c_In @ X2 @ X0) => (c_In @ X2 @ X1)))) = c_Subq)), 12.12/2.31 file('/export/starexec/sandbox2/tmp/tmp.AEOGvNUPJb/E---3.1_16218.p',ax17)). 12.12/2.31 thf(f409,plain,( 12.12/2.31 (c_iff = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ (Y0 => Y1) @ (Y1 => Y0))))))), 12.12/2.31 inference(definition_unfolding,[],[f355,f382])). 12.12/2.31 thf(f355,plain,( 12.12/2.31 (c_iff = (^[Y0 : $o]: ((^[Y1 : $o]: (c_and @ (Y0 => Y1) @ (Y1 => Y0))))))), 12.12/2.31 inference(cnf_transformation,[],[f241])). 12.12/2.31 thf(f241,plain,( 12.12/2.31 (c_iff = (^[Y0 : $o]: ((^[Y1 : $o]: (c_and @ (Y0 => Y1) @ (Y1 => Y0))))))), 12.12/2.31 inference(fool_elimination,[],[f240])). 12.12/2.31 thf(f240,plain,( 12.12/2.31 ((^[X0 : $o, X1 : $o] : (c_and @ X0 => X1 @ X1 => X0)) = c_iff)), 12.12/2.31 inference(rectify,[],[f62])). 12.12/2.31 thf(f62,axiom,( 12.12/2.31 ((^[X0 : $o, X1 : $o] : (c_and @ X0 => X1 @ X1 => X0)) = c_iff)), 12.12/2.31 file('/export/starexec/sandbox2/tmp/tmp.AEOGvNUPJb/E---3.1_16218.p',ax16)). 12.12/2.31 thf(f343,plain,( 12.12/2.31 ( ! [X0 : $i,X1 : $i] : (((c_iff @ (c_In @ X0 @ (c_Power @ X1)) @ (c_Subq @ X0 @ X1)) = $true)) )), 12.12/2.31 inference(cnf_transformation,[],[f142])). 12.12/2.31 thf(f142,plain,( 12.12/2.31 ! [X0,X1] : ((c_iff @ (c_In @ X0 @ (c_Power @ X1)) @ (c_Subq @ X0 @ X1)) = $true)), 12.12/2.31 inference(fool_elimination,[],[f141])). 12.12/2.31 thf(f141,plain,( 12.12/2.31 ! [X0,X1] : (c_iff @ (c_In @ X0 @ (c_Power @ X1)) @ (c_Subq @ X0 @ X1))), 12.12/2.31 inference(rectify,[],[f61])). 12.12/2.31 thf(f61,axiom,( 12.12/2.31 ! [X1,X0] : (c_iff @ (c_In @ X1 @ (c_Power @ X0)) @ (c_Subq @ X1 @ X0))), 12.12/2.31 file('/export/starexec/sandbox2/tmp/tmp.AEOGvNUPJb/E---3.1_16218.p',ax7)). 12.12/2.31 thf(f1283,plain,( 12.12/2.31 ( ! [X0 : $i > $o] : (((sP1 @ X0) = $false)) )), 12.12/2.31 inference(trivial_inequality_removal,[],[f1282])). 12.12/2.31 thf(f1282,plain,( 12.12/2.31 ( ! [X0 : $i > $o] : (((sP1 @ X0) = $false) | ($true != $true)) )), 12.12/2.31 inference(superposition,[],[f1281,f484])). 12.12/2.31 thf(f484,plain,( 12.12/2.31 ( ! [X2 : $o] : (($true = X2) | ($false = X2)) )), 12.12/2.31 inference(binary_proxy_clausification,[],[f478])). 12.12/2.31 thf(f1281,plain,( 12.12/2.31 ( ! [X0 : $i > $o] : (((sP1 @ X0) != $true)) )), 12.12/2.31 inference(subsumption_resolution,[],[f1139,f1136])). 12.12/2.31 thf(f1136,plain,( 12.12/2.31 ( ! [X0 : $i > $o] : (((sP1 @ X0) != $true) | ((X0 @ (c_Union @ c_Empty)) = $true)) )), 12.12/2.31 inference(backward_demodulation,[],[f393,f1072])). 12.12/2.31 thf(f393,plain,( 12.12/2.31 ( ! [X0 : $i > $o] : (((sP1 @ X0) != $true) | ((X0 @ (sK7 @ X0)) = $true)) )), 12.12/2.31 inference(cnf_transformation,[],[f312])). 12.12/2.31 thf(f312,plain,( 12.12/2.31 ! [X0 : $i > $o] : (((((c_In @ (sK8 @ X0) @ (sK7 @ X0)) = $true) & ((X0 @ (sK8 @ X0)) != $true)) & ((X0 @ (sK7 @ X0)) = $true)) | ((sP1 @ X0) != $true))), 12.12/2.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f309,f311,f310])). 12.12/2.31 thf(f310,plain,( 12.12/2.31 ! [X0 : $i > $o] : (? [X1] : (? [X2] : (((c_In @ X2 @ X1) = $true) & ((X0 @ X2) != $true)) & ((X0 @ X1) = $true)) => (? [X2] : (((c_In @ X2 @ (sK7 @ X0)) = $true) & ((X0 @ X2) != $true)) & ((X0 @ (sK7 @ X0)) = $true)))), 12.12/2.31 introduced(choice_axiom,[])). 12.12/2.31 thf(f311,plain,( 12.12/2.31 ! [X0 : $i > $o] : (? [X2] : (((c_In @ X2 @ (sK7 @ X0)) = $true) & ((X0 @ X2) != $true)) => (((c_In @ (sK8 @ X0) @ (sK7 @ X0)) = $true) & ((X0 @ (sK8 @ X0)) != $true)))), 12.12/2.31 introduced(choice_axiom,[])). 12.12/2.31 thf(f309,plain,( 12.12/2.31 ! [X0 : $i > $o] : (? [X1] : (? [X2] : (((c_In @ X2 @ X1) = $true) & ((X0 @ X2) != $true)) & ((X0 @ X1) = $true)) | ((sP1 @ X0) != $true))), 12.12/2.31 inference(nnf_transformation,[],[f301])). 12.12/2.31 thf(f301,plain,( 12.12/2.31 ! [X0 : $i > $o] : (? [X1] : (? [X2] : (((c_In @ X2 @ X1) = $true) & ((X0 @ X2) != $true)) & ((X0 @ X1) = $true)) | ~((sP1 @ X0) = $true))), 12.12/2.31 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])). 12.12/2.31 thf(f1139,plain,( 12.12/2.31 ( ! [X0 : $i > $o] : (((sP1 @ X0) != $true) | ((X0 @ (c_Union @ c_Empty)) != $true)) )), 12.12/2.31 inference(backward_demodulation,[],[f394,f1072])). 12.12/2.31 thf(f394,plain,( 12.12/2.31 ( ! [X0 : $i > $o] : (((X0 @ (sK8 @ X0)) != $true) | ((sP1 @ X0) != $true)) )), 12.12/2.31 inference(cnf_transformation,[],[f312])). 12.12/2.31 % SZS output end Proof for E---3.1_16218 12.12/2.31 % (16435)------------------------------ 12.12/2.31 % (16435)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 12.12/2.31 % (16435)Termination reason: Refutation 12.12/2.31 12.12/2.31 % (16435)Memory used [KB]: 4477 12.12/2.31 % (16435)Time elapsed: 0.602 s 12.12/2.31 % (16435)Instructions burned: 1344 (million) 12.12/2.31 % (16435)------------------------------ 12.12/2.31 % (16435)------------------------------ 12.12/2.31 % (16325)Success in time 1.951 s 12.12/2.31 EOF