0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.03 % Command : run_vampire %s %d THM 0.08/0.34 % Computer : n006.cluster.edu 0.08/0.34 % Model : x86_64 x86_64 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.08/0.34 % Memory : 8046.5625MB 0.08/0.34 % OS : Linux 6.8.0-71-generic 0.08/0.34 % CPULimit : 1440 0.08/0.34 % WCLimit : 180 0.08/0.34 % DateTime : Mon Jul 27 12:40:19 UTC 2026 0.08/0.35 % CPUTime : 0.13/0.38 This is a THF_ problem 0.13/0.38 Running higher-order theorem proving 0.13/0.39 Running /export/starexec/sandbox2/solver/bin/vampire-hol --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --print_def_sorts on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/tmp/tmp.ChJweH4qDA/E---3.1_2816099.p -m 16384 -t 180 0.13/0.42 % (2816145)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_2816099 for (1799ds/27Mi) 0.13/0.43 % (2816143)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_2816099 for (1799ds/183Mi) 0.13/0.43 % (2816144)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_2816099 for (1799ds/4Mi) 0.13/0.43 % (2816146)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_2816099 for (1799ds/2Mi) 0.13/0.43 % (2816145)Instruction limit reached! 0.13/0.43 % (2816145)------------------------------ 0.13/0.43 % (2816145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.13/0.43 % (2816145)Termination reason: Unknown 0.13/0.43 % (2816145)Termination phase: Saturation 0.13/0.43 0.13/0.43 % (2816145)Memory used [KB]: 5756 0.13/0.43 % (2816145)Time elapsed: 0.010 s 0.13/0.43 % (2816145)Instructions burned: 27 (million) 0.13/0.43 % (2816145)------------------------------ 0.13/0.43 % (2816145)------------------------------ 0.13/0.43 % (2816147)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_2816099 for (1799ds/2Mi) 0.13/0.43 % (2816149)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_2816099 for (1799ds/18Mi) 0.13/0.43 % (2816146)Instruction limit reached! 0.13/0.43 % (2816146)------------------------------ 0.13/0.43 % (2816146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.13/0.43 % (2816146)Termination reason: Unknown 0.13/0.43 % (2816146)Termination phase: shuffling 0.13/0.43 0.13/0.43 % (2816146)Memory used [KB]: 1023 0.13/0.43 % (2816146)Time elapsed: 0.004 s 0.13/0.43 % (2816146)Instructions burned: 3 (million) 0.13/0.43 % (2816146)------------------------------ 0.13/0.43 % (2816146)------------------------------ 0.13/0.43 % (2816147)Instruction limit reached! 0.13/0.43 % (2816147)------------------------------ 0.13/0.43 % (2816147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.13/0.43 % (2816147)Termination reason: Unknown 0.13/0.43 % (2816147)Termination phase: shuffling 0.13/0.43 0.13/0.43 % (2816147)Memory used [KB]: 1023 0.13/0.43 % (2816147)Time elapsed: 0.004 s 0.13/0.43 % (2816147)Instructions burned: 3 (million) 0.13/0.43 % (2816147)------------------------------ 0.13/0.43 % (2816147)------------------------------ 0.13/0.43 % (2816144)Instruction limit reached! 0.13/0.43 % (2816144)------------------------------ 0.13/0.43 % (2816144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.13/0.43 % (2816144)Termination reason: Unknown 0.13/0.43 % (2816144)Termination phase: shuffling 0.13/0.43 0.13/0.43 % (2816144)Memory used [KB]: 1023 0.13/0.43 % (2816144)Time elapsed: 0.004 s 0.13/0.43 % (2816144)Instructions burned: 4 (million) 0.13/0.43 % (2816144)------------------------------ 0.13/0.43 % (2816144)------------------------------ 0.13/0.43 % (2816148)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_2816099 for (1799ds/275Mi) 0.13/0.44 % (2816149)Instruction limit reached! 0.13/0.44 % (2816149)------------------------------ 0.13/0.44 % (2816149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.13/0.44 % (2816149)Termination reason: Unknown 0.13/0.44 % (2816149)Termination phase: Saturation 0.13/0.44 0.13/0.44 % (2816149)Memory used [KB]: 5628 0.13/0.44 % (2816149)Time elapsed: 0.012 s 0.13/0.44 % (2816149)Instructions burned: 18 (million) 0.13/0.44 % (2816149)------------------------------ 0.13/0.44 % (2816149)------------------------------ 0.13/0.44 % (2816150)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_2816099 for (1799ds/3Mi) 0.13/0.44 % (2816150)Instruction limit reached! 0.13/0.44 % (2816150)------------------------------ 0.13/0.44 % (2816150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.13/0.44 % (2816150)Termination reason: Unknown 0.13/0.44 % (2816150)Termination phase: Property scanning 0.13/0.44 0.13/0.44 % (2816150)Memory used [KB]: 1023 0.13/0.44 % (2816150)Time elapsed: 0.003 s 0.13/0.44 % (2816150)Instructions burned: 6 (million) 0.13/0.44 % (2816150)------------------------------ 0.13/0.44 % (2816150)------------------------------ 0.13/0.45 % (2816151)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_2816099 for (1799ds/37Mi) 0.13/0.45 % (2816152)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_2816099 for (1799ds/15Mi) 0.13/0.45 % (2816153)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_2816099 for (1799ds/3Mi) 0.13/0.45 % (2816153)Instruction limit reached! 0.13/0.45 % (2816153)------------------------------ 0.13/0.45 % (2816153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.13/0.45 % (2816153)Termination reason: Unknown 0.13/0.45 % (2816153)Termination phase: shuffling 0.13/0.45 0.13/0.45 % (2816153)Memory used [KB]: 1023 0.13/0.45 % (2816153)Time elapsed: 0.004 s 0.13/0.45 % (2816153)Instructions burned: 3 (million) 0.13/0.45 % (2816153)------------------------------ 0.13/0.45 % (2816153)------------------------------ 0.13/0.45 % (2816155)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on E---3.1_2816099 for (1799ds/7Mi) 0.13/0.45 % (2816148)Refutation not found, incomplete strategy 0.13/0.45 % (2816148)------------------------------ 0.13/0.45 % (2816148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.13/0.45 % (2816148)Termination reason: Refutation not found, incomplete strategy 0.13/0.45 0.13/0.45 0.13/0.45 % (2816148)Memory used [KB]: 5756 0.13/0.45 % (2816148)Time elapsed: 0.015 s 0.13/0.45 % (2816148)Instructions burned: 17 (million) 0.13/0.45 % (2816148)------------------------------ 0.13/0.45 % (2816148)------------------------------ 0.13/0.45 % (2816155)Instruction limit reached! 0.13/0.45 % (2816155)------------------------------ 0.13/0.45 % (2816155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.13/0.45 % (2816155)Termination reason: Unknown 0.13/0.45 % (2816155)Termination phase: Property scanning 0.13/0.45 0.13/0.45 % (2816155)Memory used [KB]: 1151 0.13/0.45 % (2816155)Time elapsed: 0.004 s 0.13/0.45 % (2816155)Instructions burned: 10 (million) 0.13/0.45 % (2816155)------------------------------ 0.13/0.45 % (2816155)------------------------------ 0.13/0.46 % (2816152)Instruction limit reached! 0.13/0.46 % (2816152)------------------------------ 0.13/0.46 % (2816152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.13/0.46 % (2816152)Termination reason: Unknown 0.13/0.46 % (2816152)Termination phase: Saturation 0.13/0.46 0.13/0.46 % (2816152)Memory used [KB]: 5628 0.13/0.46 % (2816152)Time elapsed: 0.011 s 0.13/0.46 % (2816152)Instructions burned: 16 (million) 0.13/0.46 % (2816152)------------------------------ 0.13/0.46 % (2816152)------------------------------ 0.13/0.46 % (2816154)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_2816099 for (1799ds/1041Mi) 0.13/0.46 % (2816157)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_2816099 for (1799ds/3Mi) 0.13/0.46 % (2816157)Instruction limit reached! 0.13/0.46 % (2816157)------------------------------ 0.13/0.46 % (2816157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.13/0.46 % (2816157)Termination reason: Unknown 0.13/0.46 % (2816157)Termination phase: Property scanning 0.13/0.46 0.13/0.46 % (2816157)Memory used [KB]: 1023 0.13/0.46 % (2816157)Time elapsed: 0.003 s 0.13/0.46 % (2816157)Instructions burned: 6 (million) 0.13/0.46 % (2816157)------------------------------ 0.13/0.46 % (2816157)------------------------------ 0.13/0.47 % (2816156)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on E---3.1_2816099 for (1799ds/16Mi) 0.13/0.47 % (2816151)Instruction limit reached! 0.13/0.47 % (2816151)------------------------------ 0.13/0.47 % (2816151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.13/0.47 % (2816151)Termination reason: Unknown 0.13/0.47 % (2816151)Termination phase: Saturation 0.13/0.47 0.13/0.47 % (2816151)Memory used [KB]: 5756 0.13/0.47 % (2816151)Time elapsed: 0.024 s 0.13/0.47 % (2816151)Instructions burned: 38 (million) 0.13/0.47 % (2816151)------------------------------ 0.13/0.47 % (2816151)------------------------------ 0.46/0.47 % (2816158)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_2816099 for (1799ds/3Mi) 0.46/0.47 % (2816164)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_2816099 for (1799ds/3Mi) 0.46/0.47 % (2816164)Instruction limit reached! 0.46/0.47 % (2816164)------------------------------ 0.46/0.47 % (2816164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.46/0.47 % (2816164)Termination reason: Unknown 0.46/0.47 % (2816164)Termination phase: shuffling 0.46/0.47 0.46/0.47 % (2816164)Memory used [KB]: 1023 0.46/0.47 % (2816164)Time elapsed: 0.002 s 0.46/0.47 % (2816164)Instructions burned: 3 (million) 0.46/0.47 % (2816164)------------------------------ 0.46/0.47 % (2816164)------------------------------ 0.46/0.48 % (2816158)Instruction limit reached! 0.46/0.48 % (2816158)------------------------------ 0.46/0.48 % (2816158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.46/0.48 % (2816158)Termination reason: Unknown 0.46/0.48 % (2816158)Termination phase: shuffling 0.46/0.48 0.46/0.48 % (2816158)Memory used [KB]: 1023 0.46/0.48 % (2816158)Time elapsed: 0.004 s 0.46/0.48 % (2816158)Instructions burned: 3 (million) 0.46/0.48 % (2816158)------------------------------ 0.46/0.48 % (2816158)------------------------------ 0.46/0.48 % (2816160)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_2816099 for (1799ds/7Mi) 0.46/0.48 % (2816156)Instruction limit reached! 0.46/0.48 % (2816156)------------------------------ 0.46/0.48 % (2816156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.46/0.48 % (2816156)Termination reason: Unknown 0.46/0.48 % (2816156)Termination phase: Saturation 0.46/0.48 0.46/0.48 % (2816156)Memory used [KB]: 5884 0.46/0.48 % (2816156)Time elapsed: 0.012 s 0.46/0.48 % (2816156)Instructions burned: 16 (million) 0.46/0.48 % (2816156)------------------------------ 0.46/0.48 % (2816156)------------------------------ 0.46/0.48 % (2816160)Instruction limit reached! 0.46/0.48 % (2816160)------------------------------ 0.46/0.48 % (2816160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.46/0.48 % (2816160)Termination reason: Unknown 0.46/0.48 % (2816160)Termination phase: Function definition elimination 0.46/0.48 0.46/0.48 % (2816160)Memory used [KB]: 1023 0.46/0.48 % (2816160)Time elapsed: 0.006 s 0.46/0.48 % (2816160)Instructions burned: 8 (million) 0.46/0.48 % (2816160)------------------------------ 0.46/0.48 % (2816160)------------------------------ 0.46/0.48 % (2816170)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_2816099 for (1799ds/18Mi) 0.46/0.49 % (2816167)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on E---3.1_2816099 for (1799ds/4Mi) 0.46/0.49 % (2816167)Instruction limit reached! 0.46/0.49 % (2816167)------------------------------ 0.46/0.49 % (2816167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.46/0.49 % (2816167)Termination reason: Unknown 0.46/0.49 % (2816167)Termination phase: Property scanning 0.46/0.49 0.46/0.49 % (2816167)Memory used [KB]: 1023 0.46/0.49 % (2816167)Time elapsed: 0.005 s 0.46/0.49 % (2816167)Instructions burned: 5 (million) 0.46/0.49 % (2816167)------------------------------ 0.46/0.49 % (2816167)------------------------------ 0.46/0.49 % (2816170)Instruction limit reached! 0.46/0.49 % (2816170)------------------------------ 0.46/0.49 % (2816170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.46/0.49 % (2816170)Termination reason: Unknown 0.46/0.49 % (2816170)Termination phase: Saturation 0.46/0.49 0.46/0.49 % (2816170)Memory used [KB]: 5628 0.46/0.49 % (2816170)Time elapsed: 0.008 s 0.46/0.49 % (2816170)Instructions burned: 19 (million) 0.46/0.49 % (2816170)------------------------------ 0.46/0.49 % (2816170)------------------------------ 0.46/0.49 % (2816171)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on E---3.1_2816099 for (1799ds/710Mi) 0.46/0.50 % (2816173)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on E---3.1_2816099 for (1799ds/6Mi) 0.46/0.50 % (2816175)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_2816099 for (1799ds/902Mi) 0.46/0.50 % (2816173)Instruction limit reached! 0.46/0.50 % (2816173)------------------------------ 0.46/0.50 % (2816173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.46/0.50 % (2816173)Termination reason: Unknown 0.46/0.50 % (2816173)Termination phase: Property scanning 0.46/0.50 0.46/0.50 % (2816173)Memory used [KB]: 1023 0.46/0.50 % (2816173)Time elapsed: 0.005 s 0.46/0.50 % (2816173)Instructions burned: 6 (million) 0.46/0.50 % (2816173)------------------------------ 0.46/0.50 % (2816173)------------------------------ 0.46/0.50 % (2816175)Refutation not found, incomplete strategy 0.46/0.50 % (2816175)------------------------------ 0.46/0.50 % (2816175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.46/0.50 % (2816175)Termination reason: Refutation not found, incomplete strategy 0.46/0.50 0.46/0.50 0.46/0.50 % (2816175)Memory used [KB]: 5628 0.46/0.50 % (2816175)Time elapsed: 0.008 s 0.46/0.50 % (2816175)Instructions burned: 11 (million) 0.46/0.50 % (2816175)------------------------------ 0.46/0.50 % (2816175)------------------------------ 0.46/0.51 % (2816171)Refutation not found, incomplete strategy 0.46/0.51 % (2816171)------------------------------ 0.46/0.51 % (2816171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.46/0.51 % (2816171)Termination reason: Refutation not found, incomplete strategy 0.46/0.51 0.46/0.51 0.46/0.51 % (2816171)Memory used [KB]: 5756 0.46/0.51 % (2816171)Time elapsed: 0.015 s 0.46/0.51 % (2816171)Instructions burned: 23 (million) 0.46/0.51 % (2816171)------------------------------ 0.46/0.51 % (2816171)------------------------------ 0.46/0.51 % (2816180)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_2816099 for (1799ds/21Mi) 0.46/0.51 % (2816181)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on E---3.1_2816099 for (1799ds/5Mi) 0.46/0.51 % (2816181)Instruction limit reached! 0.46/0.51 % (2816181)------------------------------ 0.46/0.51 % (2816181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.46/0.51 % (2816181)Termination reason: Unknown 0.46/0.51 % (2816181)Termination phase: Property scanning 0.46/0.51 0.46/0.51 % (2816181)Memory used [KB]: 1023 0.46/0.51 % (2816181)Time elapsed: 0.005 s 0.46/0.51 % (2816181)Instructions burned: 5 (million) 0.46/0.51 % (2816181)------------------------------ 0.46/0.51 % (2816181)------------------------------ 0.46/0.52 % (2816183)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_2816099 for (1799ds/6Mi) 0.46/0.52 % (2816183)Instruction limit reached! 0.46/0.52 % (2816183)------------------------------ 0.46/0.52 % (2816183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.46/0.52 % (2816183)Termination reason: Unknown 0.46/0.52 % (2816183)Termination phase: SInE selection 0.46/0.52 0.46/0.52 % (2816183)Memory used [KB]: 1023 0.46/0.52 % (2816183)Time elapsed: 0.005 s 0.46/0.52 % (2816183)Instructions burned: 6 (million) 0.46/0.52 % (2816183)------------------------------ 0.46/0.52 % (2816183)------------------------------ 0.46/0.52 % (2816180)Instruction limit reached! 0.46/0.52 % (2816180)------------------------------ 0.46/0.52 % (2816180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.46/0.52 % (2816180)Termination reason: Unknown 0.46/0.52 % (2816180)Termination phase: Saturation 0.46/0.52 0.46/0.52 % (2816180)Memory used [KB]: 5756 0.46/0.52 % (2816180)Time elapsed: 0.015 s 0.46/0.52 % (2816180)Instructions burned: 21 (million) 0.46/0.52 % (2816180)------------------------------ 0.46/0.52 % (2816180)------------------------------ 0.46/0.52 % (2816186)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on E---3.1_2816099 for (1798ds/377Mi) 0.46/0.52 % (2816187)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_2816099 for (1798ds/779Mi) 0.46/0.53 % (2816143)Instruction limit reached! 0.46/0.53 % (2816143)------------------------------ 0.46/0.53 % (2816143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.46/0.53 % (2816143)Termination reason: Unknown 0.46/0.53 % (2816143)Termination phase: Saturation 0.46/0.53 0.46/0.53 % (2816143)Memory used [KB]: 6652 0.46/0.53 % (2816143)Time elapsed: 0.100 s 0.46/0.53 % (2816143)Instructions burned: 183 (million) 0.46/0.53 % (2816143)------------------------------ 0.46/0.53 % (2816143)------------------------------ 0.46/0.53 % (2816190)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_2816099 for (1798ds/19Mi) 0.46/0.54 % (2816193)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_2816099 for (1798ds/879Mi) 0.46/0.54 % (2816194)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on E---3.1_2816099 for (1798ds/17Mi) 0.46/0.54 % (2816190)Instruction limit reached! 0.46/0.54 % (2816190)------------------------------ 0.46/0.54 % (2816190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.46/0.54 % (2816190)Termination reason: Unknown 0.46/0.54 % (2816190)Termination phase: Saturation 0.46/0.54 0.46/0.54 % (2816190)Memory used [KB]: 5628 0.46/0.54 % (2816190)Time elapsed: 0.013 s 0.46/0.54 % (2816190)Instructions burned: 19 (million) 0.46/0.54 % (2816190)------------------------------ 0.46/0.54 % (2816190)------------------------------ 0.46/0.54 % (2816197)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on E---3.1_2816099 for (1798ds/3Mi) 0.46/0.55 % (2816197)Instruction limit reached! 0.46/0.55 % (2816197)------------------------------ 0.46/0.55 % (2816197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.46/0.55 % (2816197)Termination reason: Unknown 0.46/0.55 % (2816197)Termination phase: shuffling 0.46/0.55 0.46/0.55 % (2816197)Memory used [KB]: 1023 0.46/0.55 % (2816197)Time elapsed: 0.004 s 0.46/0.55 % (2816197)Instructions burned: 4 (million) 0.46/0.55 % (2816197)------------------------------ 0.46/0.55 % (2816197)------------------------------ 0.46/0.55 % (2816194)Instruction limit reached! 0.46/0.55 % (2816194)------------------------------ 0.46/0.55 % (2816194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.46/0.55 % (2816194)Termination reason: Unknown 0.46/0.55 % (2816194)Termination phase: Saturation 0.46/0.55 0.46/0.55 % (2816194)Memory used [KB]: 5628 0.46/0.55 % (2816194)Time elapsed: 0.011 s 0.46/0.55 % (2816194)Instructions burned: 17 (million) 0.46/0.55 % (2816194)------------------------------ 0.46/0.55 % (2816194)------------------------------ 0.46/0.56 % (2816206)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on E---3.1_2816099 for (1798ds/30Mi) 0.46/0.56 % (2816206)Refutation not found, incomplete strategy 0.46/0.56 % (2816206)------------------------------ 0.46/0.56 % (2816206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.46/0.56 % (2816206)Termination reason: Refutation not found, incomplete strategy 0.46/0.56 0.46/0.56 0.46/0.56 % (2816206)Memory used [KB]: 5628 0.46/0.56 % (2816206)Time elapsed: 0.005 s 0.46/0.56 % (2816206)Instructions burned: 11 (million) 0.46/0.56 % (2816206)------------------------------ 0.46/0.56 % (2816206)------------------------------ 0.46/0.57 % (2816210)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_2816099 for (1798ds/100Mi) 0.46/0.57 % (2816209)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_2816099 for (1798ds/127Mi) 0.46/0.57 % (2816216)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_2816099 for (1798ds/3Mi) 0.46/0.57 % (2816216)Instruction limit reached! 0.46/0.57 % (2816216)------------------------------ 0.46/0.57 % (2816216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.46/0.57 % (2816216)Termination reason: Unknown 0.46/0.57 % (2816216)Termination phase: Property scanning 0.46/0.57 0.46/0.57 % (2816216)Memory used [KB]: 1023 0.46/0.57 % (2816216)Time elapsed: 0.003 s 0.46/0.57 % (2816216)Instructions burned: 6 (million) 0.46/0.57 % (2816216)------------------------------ 0.46/0.57 % (2816216)------------------------------ 1.16/0.58 % (2816222)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_2816099 for (1798ds/20Mi) 1.16/0.58 % (2816222)Refutation not found, incomplete strategy 1.16/0.58 % (2816222)------------------------------ 1.16/0.58 % (2816222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1.16/0.58 % (2816222)Termination reason: Refutation not found, incomplete strategy 1.16/0.58 1.16/0.58 1.16/0.58 % (2816222)Memory used [KB]: 5628 1.16/0.58 % (2816222)Time elapsed: 0.005 s 1.16/0.58 % (2816222)Instructions burned: 12 (million) 1.16/0.58 % (2816222)------------------------------ 1.16/0.58 % (2816222)------------------------------ 1.16/0.59 % (2816230)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_2816099 for (1798ds/86Mi) 1.41/0.63 % (2816210)Instruction limit reached! 1.41/0.63 % (2816210)------------------------------ 1.41/0.63 % (2816210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1.41/0.63 % (2816210)Termination reason: Unknown 1.41/0.63 % (2816210)Termination phase: Saturation 1.41/0.63 1.41/0.63 % (2816210)Memory used [KB]: 6140 1.41/0.63 % (2816210)Time elapsed: 0.062 s 1.41/0.63 % (2816210)Instructions burned: 100 (million) 1.41/0.63 % (2816210)------------------------------ 1.41/0.63 % (2816210)------------------------------ 1.41/0.63 % (2816230)Instruction limit reached! 1.41/0.63 % (2816230)------------------------------ 1.41/0.63 % (2816230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1.41/0.63 % (2816230)Termination reason: Unknown 1.41/0.63 % (2816230)Termination phase: Saturation 1.41/0.63 1.41/0.63 % (2816230)Memory used [KB]: 6268 1.41/0.63 % (2816230)Time elapsed: 0.035 s 1.41/0.63 % (2816230)Instructions burned: 86 (million) 1.41/0.63 % (2816230)------------------------------ 1.41/0.63 % (2816230)------------------------------ 1.41/0.64 % (2816209)Instruction limit reached! 1.41/0.64 % (2816209)------------------------------ 1.41/0.64 % (2816209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1.41/0.64 % (2816209)Termination reason: Unknown 1.41/0.64 % (2816209)Termination phase: Saturation 1.41/0.64 1.41/0.64 % (2816209)Memory used [KB]: 6140 1.41/0.64 % (2816209)Time elapsed: 0.079 s 1.41/0.64 % (2816209)Instructions burned: 128 (million) 1.41/0.64 % (2816209)------------------------------ 1.41/0.64 % (2816209)------------------------------ 1.41/0.64 % (2816247)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_2816099 for (1797ds/107Mi) 1.41/0.65 % (2816248)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_2816099 for (1797ds/39Mi) 1.41/0.65 % (2816186)First to succeed. 1.41/0.67 % (2816257)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_2816099 for (1797ds/448Mi) 1.41/0.67 % (2816248)Instruction limit reached! 1.41/0.67 % (2816248)------------------------------ 1.41/0.67 % (2816248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1.41/0.67 % (2816248)Termination reason: Unknown 1.41/0.67 % (2816248)Termination phase: Saturation 1.41/0.67 1.41/0.67 % (2816248)Memory used [KB]: 5756 1.41/0.67 % (2816248)Time elapsed: 0.026 s 1.41/0.67 % (2816248)Instructions burned: 39 (million) 1.41/0.67 % (2816248)------------------------------ 1.41/0.67 % (2816248)------------------------------ 1.41/0.67 % (2816186)Refutation found. Thanks to Tanya! 1.41/0.67 % SZS status Theorem for E---3.1_2816099 1.41/0.67 % SZS output start Proof for E---3.1_2816099 1.41/0.67 thf(type_def_5, type, mu: $tType). 1.41/0.67 thf(func_def_0, type, mu: $tType). 1.41/0.67 thf(func_def_1, type, meq_ind: mu > mu > $i > $o). 1.41/0.67 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o). 1.41/0.67 thf(func_def_4, type, mnot: ($i > $o) > $i > $o). 1.41/0.67 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o). 1.41/0.67 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o). 1.41/0.67 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o). 1.41/0.67 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o). 1.41/0.67 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o). 1.41/0.67 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o). 1.41/0.67 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o). 1.41/0.67 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o). 1.41/0.67 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o). 1.41/0.67 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o). 1.41/0.67 thf(func_def_15, type, mtrue: $i > $o). 1.41/0.67 thf(func_def_16, type, mfalse: $i > $o). 1.41/0.67 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o). 1.41/0.67 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o). 1.41/0.67 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o). 1.41/0.67 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o). 1.41/0.67 thf(func_def_21, type, mserial: ($i > $i > $o) > $o). 1.41/0.67 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o). 1.41/0.67 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o). 1.41/0.67 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o). 1.41/0.67 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o). 1.41/0.67 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o). 1.41/0.67 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o). 1.41/0.67 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o). 1.41/0.67 thf(func_def_29, type, mvalid: ($i > $o) > $o). 1.41/0.67 thf(func_def_30, type, minvalid: ($i > $o) > $o). 1.41/0.67 thf(func_def_31, type, msatisfiable: ($i > $o) > $o). 1.41/0.67 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o). 1.41/0.67 thf(func_def_33, type, i: $i > $i > $o). 1.41/0.67 thf(func_def_34, type, j: $i > $i > $o). 1.41/0.67 thf(func_def_35, type, k: $i > $i > $o). 1.41/0.67 thf(func_def_36, type, l: $i > $i > $o). 1.41/0.67 thf(func_def_37, type, confluence: ($i > $i > $o) > ($i > $i > $o) > ($i > $i > $o) > ($i > $i > $o) > $o). 1.41/0.67 thf(func_def_59, type, sK5: $i > $o). 1.41/0.67 thf(func_def_64, type, sK10: $i > $o). 1.41/0.67 thf(func_def_67, type, sK13: ($i > $o) > $i > $i). 1.41/0.67 thf(func_def_68, type, sK14: ($i > $o) > $i > $i). 1.41/0.67 thf(func_def_69, type, sK15: $i > $i > $i). 1.41/0.67 thf(func_def_70, type, ph16: !>[X0: $tType]:(X0)). 1.41/0.67 thf(f1581,plain,( 1.41/0.67 $false), 1.41/0.67 inference(avatar_sat_refutation,[status(thm)],[f298,f302,f306,f307,f311,f315,f316,f317,f325,f329,f334,f338,f347,f351,f356,f360,f369,f373,f378,f382,f417,f451,f475,f503,f512,f537,f546,f587,f656,f665,f699,f716,f772,f927,f994,f1011,f1027,f1197,f1221,f1240,f1331,f1361,f1547,f1562,f1578,f1580])). 1.41/0.67 thf(f1580,plain,( 1.41/0.67 spl0_27 | spl0_50 | ~spl0_5 | ~spl0_19 | ~spl0_31), 1.41/0.67 inference(avatar_split_clause,[status(thm)],[f935,f769,f371,f309,f943,f584])). 1.41/0.67 thf(f584,definition,( 1.41/0.67 spl0_27 <=> ! [X0 : $i] : (((k @ X0 @ sK6) = $false) | ((i @ X0 @ sK7) = $false))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_27])],[avatar_definition])). 1.41/0.67 thf(f943,definition,( 1.41/0.67 spl0_50 <=> ! [X0 : $i,X1 : $i] : (((i @ X0 @ sK7) = $false) | ((k @ X0 @ X1) = $false) | ($true = (sK5 @ (sK14 @ sK5 @ X1))))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_50])],[avatar_definition])). 1.41/0.67 thf(f309,definition,( 1.41/0.67 spl0_5 <=> ! [X5 : $i,X3 : $i > $o,X6 : $i,X1 : $i] : (($true = (X3 @ (sK14 @ X3 @ X6))) | ((k @ X1 @ X6) = $false) | ((i @ X1 @ X5) = $false) | ($true = (j @ X5 @ (sK13 @ X3 @ X5))))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])). 1.41/0.67 thf(f371,definition,( 1.41/0.67 spl0_19 <=> ! [X1 : $i] : (($true = (sK5 @ X1)) | ((j @ sK7 @ X1) = $false))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_19])],[avatar_definition])). 1.41/0.67 thf(f769,definition,( 1.41/0.67 spl0_31 <=> ! [X2 : $i,X3 : $i] : (((sK5 @ (sK13 @ sK5 @ X2)) = $false) | ((k @ X3 @ sK6) = $false) | ((i @ X3 @ X2) = $false))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_31])],[avatar_definition])). 1.41/0.67 thf(f935,plain,( 1.41/0.67 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((i @ X1 @ sK7) = $false) | ((i @ X0 @ sK7) = $false) | ((sK5 @ (sK14 @ sK5 @ X2)) = $true) | ((k @ X1 @ X2) = $false) | ((k @ X0 @ sK6) = $false)) ) | (~spl0_5 | ~spl0_19 | ~spl0_31)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f934])). 1.41/0.67 thf(f934,plain,( 1.41/0.67 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((i @ X0 @ sK7) = $false) | ((sK5 @ (sK14 @ sK5 @ X2)) = $true) | ($true = $false) | ((k @ X1 @ X2) = $false) | ((k @ X0 @ sK6) = $false) | ((i @ X1 @ sK7) = $false)) ) | (~spl0_5 | ~spl0_19 | ~spl0_31)), 1.41/0.67 inference(superposition,[status(thm)],[f770,f690])). 1.41/0.67 thf(f690,plain,( 1.41/0.67 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (($true = (sK5 @ (sK13 @ X0 @ sK7))) | ((i @ X1 @ sK7) = $false) | ($true = (X0 @ (sK14 @ X0 @ X2))) | ((k @ X1 @ X2) = $false)) ) | (~spl0_5 | ~spl0_19)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f684])). 1.41/0.67 thf(f684,plain,( 1.41/0.67 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (($true = (sK5 @ (sK13 @ X0 @ sK7))) | ($true = (X0 @ (sK14 @ X0 @ X2))) | ($true = $false) | ((k @ X1 @ X2) = $false) | ((i @ X1 @ sK7) = $false)) ) | (~spl0_5 | ~spl0_19)), 1.41/0.67 inference(superposition,[status(thm)],[f310,f372])). 1.41/0.67 thf(f372,plain,( 1.41/0.67 ( ! [X1 : $i] : (((j @ sK7 @ X1) = $false) | ($true = (sK5 @ X1))) ) | ~spl0_19), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f371])). 1.41/0.67 thf(f310,plain,( 1.41/0.67 ( ! [X3 : $i > $o,X1 : $i,X6 : $i,X5 : $i] : (($true = (j @ X5 @ (sK13 @ X3 @ X5))) | ((i @ X1 @ X5) = $false) | ($true = (X3 @ (sK14 @ X3 @ X6))) | ((k @ X1 @ X6) = $false)) ) | ~spl0_5), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f309])). 1.41/0.67 thf(f770,plain,( 1.41/0.67 ( ! [X2 : $i,X3 : $i] : (((sK5 @ (sK13 @ sK5 @ X2)) = $false) | ((k @ X3 @ sK6) = $false) | ((i @ X3 @ X2) = $false)) ) | ~spl0_31), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f769])). 1.41/0.67 thf(f1578,plain,( 1.41/0.67 spl0_27 | ~spl0_50 | ~spl0_85), 1.41/0.67 inference(avatar_split_clause,[status(thm)],[f1575,f1558,f943,f584])). 1.41/0.67 thf(f1558,definition,( 1.41/0.67 spl0_85 <=> ((sK5 @ (sK14 @ sK5 @ sK6)) = $false)), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_85])],[avatar_definition])). 1.41/0.67 thf(f1575,plain,( 1.41/0.67 ( ! [X0 : $i] : (((k @ X0 @ sK6) = $false) | ((i @ X0 @ sK7) = $false)) ) | (~spl0_50 | ~spl0_85)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f1564])). 1.41/0.67 thf(f1564,plain,( 1.41/0.67 ( ! [X0 : $i] : (((k @ X0 @ sK6) = $false) | ((i @ X0 @ sK7) = $false) | ($true = $false)) ) | (~spl0_50 | ~spl0_85)), 1.41/0.67 inference(superposition,[status(thm)],[f1560,f944])). 1.41/0.67 thf(f944,plain,( 1.41/0.67 ( ! [X0 : $i,X1 : $i] : (($true = (sK5 @ (sK14 @ sK5 @ X1))) | ((i @ X0 @ sK7) = $false) | ((k @ X0 @ X1) = $false)) ) | ~spl0_50), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f943])). 1.41/0.67 thf(f1560,plain,( 1.41/0.67 ((sK5 @ (sK14 @ sK5 @ sK6)) = $false) | ~spl0_85), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f1558])). 1.41/0.67 thf(f1562,plain,( 1.41/0.67 spl0_27 | spl0_85 | ~spl0_31 | ~spl0_84), 1.41/0.67 inference(avatar_split_clause,[status(thm)],[f1553,f1544,f769,f1558,f584])). 1.41/0.67 thf(f1544,definition,( 1.41/0.67 spl0_84 <=> ! [X0 : $i > $o] : (($true = (sK5 @ (sK13 @ X0 @ sK7))) | ((sK5 @ (sK14 @ X0 @ sK6)) = $false))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_84])],[avatar_definition])). 1.41/0.67 thf(f1553,plain,( 1.41/0.67 ( ! [X0 : $i] : (((i @ X0 @ sK7) = $false) | ((k @ X0 @ sK6) = $false) | ((sK5 @ (sK14 @ sK5 @ sK6)) = $false)) ) | (~spl0_31 | ~spl0_84)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f1550])). 1.41/0.67 thf(f1550,plain,( 1.41/0.67 ( ! [X0 : $i] : (($true = $false) | ((i @ X0 @ sK7) = $false) | ((sK5 @ (sK14 @ sK5 @ sK6)) = $false) | ((k @ X0 @ sK6) = $false)) ) | (~spl0_31 | ~spl0_84)), 1.41/0.67 inference(superposition,[status(thm)],[f1545,f770])). 1.41/0.67 thf(f1545,plain,( 1.41/0.67 ( ! [X0 : $i > $o] : (($true = (sK5 @ (sK13 @ X0 @ sK7))) | ((sK5 @ (sK14 @ X0 @ sK6)) = $false)) ) | ~spl0_84), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f1544])). 1.41/0.67 thf(f1547,plain,( 1.41/0.67 spl0_27 | spl0_84 | ~spl0_2 | ~spl0_19 | ~spl0_21), 1.41/0.67 inference(avatar_split_clause,[status(thm)],[f1541,f380,f371,f296,f1544,f584])). 1.41/0.67 thf(f296,definition,( 1.41/0.67 spl0_2 <=> ! [X5 : $i,X3 : $i > $o,X6 : $i,X1 : $i] : (($true = (l @ X6 @ (sK14 @ X3 @ X6))) | ((k @ X1 @ X6) = $false) | ((i @ X1 @ X5) = $false) | ($true = (j @ X5 @ (sK13 @ X3 @ X5))))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])). 1.41/0.67 thf(f380,definition,( 1.41/0.67 spl0_21 <=> ! [X1 : $i] : (((l @ sK6 @ X1) = $false) | ((sK5 @ X1) = $false))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_21])],[avatar_definition])). 1.41/0.67 thf(f1541,plain,( 1.41/0.67 ( ! [X0 : $i > $o,X1 : $i] : (((sK5 @ (sK14 @ X0 @ sK6)) = $false) | ((k @ X1 @ sK6) = $false) | ((i @ X1 @ sK7) = $false) | ($true = (sK5 @ (sK13 @ X0 @ sK7)))) ) | (~spl0_2 | ~spl0_19 | ~spl0_21)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f1532])). 1.41/0.67 thf(f1532,plain,( 1.41/0.67 ( ! [X0 : $i > $o,X1 : $i] : (($true = (sK5 @ (sK13 @ X0 @ sK7))) | ((i @ X1 @ sK7) = $false) | ($true = $false) | ((sK5 @ (sK14 @ X0 @ sK6)) = $false) | ((k @ X1 @ sK6) = $false)) ) | (~spl0_2 | ~spl0_19 | ~spl0_21)), 1.41/0.67 inference(superposition,[status(thm)],[f1403,f372])). 1.41/0.67 thf(f1403,plain,( 1.41/0.67 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (($true = (j @ X1 @ (sK13 @ X0 @ X1))) | ((sK5 @ (sK14 @ X0 @ sK6)) = $false) | ((k @ X2 @ sK6) = $false) | ((i @ X2 @ X1) = $false)) ) | (~spl0_2 | ~spl0_21)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f1394])). 1.41/0.67 thf(f1394,plain,( 1.41/0.67 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (($true = $false) | ((k @ X2 @ sK6) = $false) | ((i @ X2 @ X1) = $false) | ($true = (j @ X1 @ (sK13 @ X0 @ X1))) | ((sK5 @ (sK14 @ X0 @ sK6)) = $false)) ) | (~spl0_2 | ~spl0_21)), 1.41/0.67 inference(superposition,[status(thm)],[f381,f297])). 1.41/0.67 thf(f297,plain,( 1.41/0.67 ( ! [X3 : $i > $o,X1 : $i,X6 : $i,X5 : $i] : (($true = (l @ X6 @ (sK14 @ X3 @ X6))) | ($true = (j @ X5 @ (sK13 @ X3 @ X5))) | ((i @ X1 @ X5) = $false) | ((k @ X1 @ X6) = $false)) ) | ~spl0_2), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f296])). 1.41/0.67 thf(f381,plain,( 1.41/0.67 ( ! [X1 : $i] : (((l @ sK6 @ X1) = $false) | ((sK5 @ X1) = $false)) ) | ~spl0_21), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f380])). 1.41/0.67 thf(f1361,plain,( 1.41/0.67 spl0_29 | ~spl0_5 | ~spl0_14 | ~spl0_72 | spl0_75), 1.41/0.67 inference(avatar_split_clause,[status(thm)],[f1360,f1315,f1237,f349,f309,f653])). 1.41/0.67 thf(f653,definition,( 1.41/0.67 spl0_29 <=> ! [X0 : $i] : (((k @ X0 @ sK8) = $false) | ((i @ X0 @ sK9) = $false))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_29])],[avatar_definition])). 1.41/0.67 thf(f349,definition,( 1.41/0.67 spl0_14 <=> ! [X1 : $i] : (($true = (sK5 @ X1)) | ((j @ sK9 @ X1) = $false))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition])). 1.41/0.67 thf(f1237,definition,( 1.41/0.67 spl0_72 <=> ! [X0 : $i > $o] : (((sK5 @ (sK14 @ X0 @ sK8)) = $false) | ((sK5 @ (sK13 @ X0 @ sK9)) = $true))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_72])],[avatar_definition])). 1.41/0.67 thf(f1315,definition,( 1.41/0.67 spl0_75 <=> ((sK5 @ (sK13 @ sK5 @ sK9)) = $true)), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_75])],[avatar_definition])). 1.41/0.67 thf(f1360,plain,( 1.41/0.67 ( ! [X0 : $i] : (((i @ X0 @ sK9) = $false) | ((k @ X0 @ sK8) = $false)) ) | (~spl0_5 | ~spl0_14 | ~spl0_72 | spl0_75)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f1359])). 1.41/0.67 thf(f1359,plain,( 1.41/0.67 ( ! [X0 : $i] : (($true = $false) | ((k @ X0 @ sK8) = $false) | ((i @ X0 @ sK9) = $false)) ) | (~spl0_5 | ~spl0_14 | ~spl0_72 | spl0_75)), 1.41/0.67 inference(forward_demodulation,[status(thm)],[f1348,f1336])). 1.41/0.67 thf(f1336,plain,( 1.41/0.67 ((sK5 @ (sK13 @ sK5 @ sK9)) = $false) | spl0_75), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f1333])). 1.41/0.67 thf(f1333,plain,( 1.41/0.67 ((sK5 @ (sK13 @ sK5 @ sK9)) = $false) | ($true != $true) | spl0_75), 1.41/0.67 inference(fool_paramodulation,[status(thm)],[f1316])). 1.41/0.67 thf(f1316,plain,( 1.41/0.67 ((sK5 @ (sK13 @ sK5 @ sK9)) != $true) | spl0_75), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f1315])). 1.41/0.67 thf(f1348,plain,( 1.41/0.67 ( ! [X0 : $i] : (((k @ X0 @ sK8) = $false) | ((sK5 @ (sK13 @ sK5 @ sK9)) = $true) | ((i @ X0 @ sK9) = $false)) ) | (~spl0_5 | ~spl0_14 | ~spl0_72)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f1347])). 1.41/0.67 thf(f1347,plain,( 1.41/0.67 ( ! [X0 : $i] : (((sK5 @ (sK13 @ sK5 @ sK9)) = $true) | ((i @ X0 @ sK9) = $false) | ($true = $false) | ((k @ X0 @ sK8) = $false)) ) | (~spl0_5 | ~spl0_14 | ~spl0_72)), 1.41/0.67 inference(duplicate_literal_removal,[status(thm)],[f1342])). 1.41/0.67 thf(f1342,plain,( 1.41/0.67 ( ! [X0 : $i] : (($true = $false) | ((sK5 @ (sK13 @ sK5 @ sK9)) = $true) | ((sK5 @ (sK13 @ sK5 @ sK9)) = $true) | ((i @ X0 @ sK9) = $false) | ((k @ X0 @ sK8) = $false)) ) | (~spl0_5 | ~spl0_14 | ~spl0_72)), 1.41/0.67 inference(superposition,[status(thm)],[f1238,f608])). 1.41/0.67 thf(f608,plain,( 1.41/0.67 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (($true = (X0 @ (sK14 @ X0 @ X2))) | ((i @ X1 @ sK9) = $false) | ((sK5 @ (sK13 @ X0 @ sK9)) = $true) | ((k @ X1 @ X2) = $false)) ) | (~spl0_5 | ~spl0_14)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f601])). 1.41/0.67 thf(f601,plain,( 1.41/0.67 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((k @ X1 @ X2) = $false) | ((sK5 @ (sK13 @ X0 @ sK9)) = $true) | ((i @ X1 @ sK9) = $false) | ($true = $false) | ($true = (X0 @ (sK14 @ X0 @ X2)))) ) | (~spl0_5 | ~spl0_14)), 1.41/0.67 inference(superposition,[status(thm)],[f350,f310])). 1.41/0.67 thf(f350,plain,( 1.41/0.67 ( ! [X1 : $i] : (((j @ sK9 @ X1) = $false) | ($true = (sK5 @ X1))) ) | ~spl0_14), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f349])). 1.41/0.67 thf(f1238,plain,( 1.41/0.67 ( ! [X0 : $i > $o] : (((sK5 @ (sK14 @ X0 @ sK8)) = $false) | ((sK5 @ (sK13 @ X0 @ sK9)) = $true)) ) | ~spl0_72), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f1237])). 1.41/0.67 thf(f1331,plain,( 1.41/0.67 spl0_29 | ~spl0_48 | ~spl0_75), 1.41/0.67 inference(avatar_split_clause,[status(thm)],[f1326,f1315,f924,f653])). 1.41/0.67 thf(f924,definition,( 1.41/0.67 spl0_48 <=> ! [X0 : $i,X1 : $i] : (((sK5 @ (sK13 @ sK5 @ X1)) = $false) | ((k @ X0 @ sK8) = $false) | ((i @ X0 @ X1) = $false))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_48])],[avatar_definition])). 1.41/0.67 thf(f1326,plain,( 1.41/0.67 ( ! [X0 : $i] : (((k @ X0 @ sK8) = $false) | ((i @ X0 @ sK9) = $false)) ) | (~spl0_48 | ~spl0_75)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f1323])). 1.41/0.67 thf(f1323,plain,( 1.41/0.67 ( ! [X0 : $i] : (((i @ X0 @ sK9) = $false) | ((k @ X0 @ sK8) = $false) | ($true = $false)) ) | (~spl0_48 | ~spl0_75)), 1.41/0.67 inference(superposition,[status(thm)],[f925,f1317])). 1.41/0.67 thf(f1317,plain,( 1.41/0.67 ((sK5 @ (sK13 @ sK5 @ sK9)) = $true) | ~spl0_75), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f1315])). 1.41/0.67 thf(f925,plain,( 1.41/0.67 ( ! [X0 : $i,X1 : $i] : (((sK5 @ (sK13 @ sK5 @ X1)) = $false) | ((i @ X0 @ X1) = $false) | ((k @ X0 @ sK8) = $false)) ) | ~spl0_48), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f924])). 1.41/0.67 thf(f1240,plain,( 1.41/0.67 spl0_72 | spl0_29 | ~spl0_2 | ~spl0_14 | ~spl0_16), 1.41/0.67 inference(avatar_split_clause,[status(thm)],[f1109,f358,f349,f296,f653,f1237])). 1.41/0.67 thf(f358,definition,( 1.41/0.67 spl0_16 <=> ! [X1 : $i] : (((sK5 @ X1) = $false) | ((l @ sK8 @ X1) = $false))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition])). 1.41/0.67 thf(f1109,plain,( 1.41/0.67 ( ! [X0 : $i > $o,X1 : $i] : (((k @ X1 @ sK8) = $false) | ((sK5 @ (sK13 @ X0 @ sK9)) = $true) | ((sK5 @ (sK14 @ X0 @ sK8)) = $false) | ((i @ X1 @ sK9) = $false)) ) | (~spl0_2 | ~spl0_14 | ~spl0_16)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f1101])). 1.41/0.67 thf(f1101,plain,( 1.41/0.67 ( ! [X0 : $i > $o,X1 : $i] : (((sK5 @ (sK14 @ X0 @ sK8)) = $false) | ($true = $false) | ((k @ X1 @ sK8) = $false) | ((sK5 @ (sK13 @ X0 @ sK9)) = $true) | ((i @ X1 @ sK9) = $false)) ) | (~spl0_2 | ~spl0_14 | ~spl0_16)), 1.41/0.67 inference(superposition,[status(thm)],[f967,f350])). 1.41/0.67 thf(f967,plain,( 1.41/0.67 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (($true = (j @ X1 @ (sK13 @ X0 @ X1))) | ((sK5 @ (sK14 @ X0 @ sK8)) = $false) | ((k @ X2 @ sK8) = $false) | ((i @ X2 @ X1) = $false)) ) | (~spl0_2 | ~spl0_16)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f958])). 1.41/0.67 thf(f958,plain,( 1.41/0.67 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((i @ X2 @ X1) = $false) | ((sK5 @ (sK14 @ X0 @ sK8)) = $false) | ($true = (j @ X1 @ (sK13 @ X0 @ X1))) | ((k @ X2 @ sK8) = $false) | ($true = $false)) ) | (~spl0_2 | ~spl0_16)), 1.41/0.67 inference(superposition,[status(thm)],[f297,f359])). 1.41/0.67 thf(f359,plain,( 1.41/0.67 ( ! [X1 : $i] : (((l @ sK8 @ X1) = $false) | ((sK5 @ X1) = $false)) ) | ~spl0_16), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f358])). 1.41/0.67 thf(f1221,plain,( 1.41/0.67 spl0_25 | ~spl0_24 | ~spl0_64), 1.41/0.67 inference(avatar_split_clause,[status(thm)],[f1214,f1177,f469,f472])). 1.41/0.67 thf(f472,definition,( 1.41/0.67 spl0_25 <=> ! [X0 : $i] : (((k @ X0 @ sK4) = $false) | ((i @ X0 @ sK1) = $false))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_25])],[avatar_definition])). 1.41/0.67 thf(f469,definition,( 1.41/0.67 spl0_24 <=> ! [X2 : $i,X1 : $i] : (((k @ X1 @ X2) = $false) | ($true = (j @ sK1 @ (sK14 @ (j @ sK1) @ X2))) | ((i @ X1 @ sK1) = $false))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_24])],[avatar_definition])). 1.41/0.67 thf(f1177,definition,( 1.41/0.67 spl0_64 <=> ((j @ sK1 @ (sK14 @ (j @ sK1) @ sK4)) = $false)), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_64])],[avatar_definition])). 1.41/0.67 thf(f1214,plain,( 1.41/0.67 ( ! [X0 : $i] : (((i @ X0 @ sK1) = $false) | ((k @ X0 @ sK4) = $false)) ) | (~spl0_24 | ~spl0_64)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f1210])). 1.41/0.67 thf(f1210,plain,( 1.41/0.67 ( ! [X0 : $i] : (((k @ X0 @ sK4) = $false) | ($true = $false) | ((i @ X0 @ sK1) = $false)) ) | (~spl0_24 | ~spl0_64)), 1.41/0.67 inference(superposition,[status(thm)],[f470,f1179])). 1.41/0.67 thf(f1179,plain,( 1.41/0.67 ((j @ sK1 @ (sK14 @ (j @ sK1) @ sK4)) = $false) | ~spl0_64), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f1177])). 1.41/0.67 thf(f470,plain,( 1.41/0.67 ( ! [X2 : $i,X1 : $i] : (($true = (j @ sK1 @ (sK14 @ (j @ sK1) @ X2))) | ((i @ X1 @ sK1) = $false) | ((k @ X1 @ X2) = $false)) ) | ~spl0_24), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f469])). 1.41/0.67 thf(f1197,plain,( 1.41/0.67 spl0_25 | spl0_25 | spl0_64 | ~spl0_2 | ~spl0_8 | ~spl0_22), 1.41/0.67 inference(avatar_split_clause,[status(thm)],[f1170,f414,f323,f296,f1177,f472,f472])). 1.41/0.67 thf(f323,definition,( 1.41/0.67 spl0_8 <=> ! [X1 : $i] : (((j @ sK1 @ X1) = $false) | ((l @ sK4 @ X1) = $false))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])). 1.41/0.67 thf(f414,definition,( 1.41/0.67 spl0_22 <=> ! [X0 : $i,X1 : $i] : (((j @ sK1 @ (sK13 @ (j @ sK1) @ X1)) = $false) | ((k @ X0 @ sK4) = $false) | ((i @ X0 @ X1) = $false))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_22])],[avatar_definition])). 1.41/0.67 thf(f1170,plain,( 1.41/0.67 ( ! [X0 : $i,X1 : $i] : (((i @ X1 @ sK1) = $false) | ((k @ X1 @ sK4) = $false) | ((i @ X0 @ sK1) = $false) | ((k @ X0 @ sK4) = $false) | ((j @ sK1 @ (sK14 @ (j @ sK1) @ sK4)) = $false)) ) | (~spl0_2 | ~spl0_8 | ~spl0_22)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f1167])). 1.41/0.67 thf(f1167,plain,( 1.41/0.67 ( ! [X0 : $i,X1 : $i] : (((i @ X1 @ sK1) = $false) | ((j @ sK1 @ (sK14 @ (j @ sK1) @ sK4)) = $false) | ((i @ X0 @ sK1) = $false) | ((k @ X1 @ sK4) = $false) | ($true = $false) | ((k @ X0 @ sK4) = $false)) ) | (~spl0_2 | ~spl0_8 | ~spl0_22)), 1.41/0.67 inference(superposition,[status(thm)],[f415,f1049])). 1.41/0.67 thf(f1049,plain,( 1.41/0.67 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (($true = (j @ X1 @ (sK13 @ X0 @ X1))) | ((k @ X2 @ sK4) = $false) | ((i @ X2 @ X1) = $false) | ((j @ sK1 @ (sK14 @ X0 @ sK4)) = $false)) ) | (~spl0_2 | ~spl0_8)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f1039])). 1.41/0.67 thf(f1039,plain,( 1.41/0.67 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((i @ X2 @ X1) = $false) | ((j @ sK1 @ (sK14 @ X0 @ sK4)) = $false) | ($true = $false) | ((k @ X2 @ sK4) = $false) | ($true = (j @ X1 @ (sK13 @ X0 @ X1)))) ) | (~spl0_2 | ~spl0_8)), 1.41/0.67 inference(superposition,[status(thm)],[f297,f324])). 1.41/0.67 thf(f324,plain,( 1.41/0.67 ( ! [X1 : $i] : (((l @ sK4 @ X1) = $false) | ((j @ sK1 @ X1) = $false)) ) | ~spl0_8), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f323])). 1.41/0.67 thf(f415,plain,( 1.41/0.67 ( ! [X0 : $i,X1 : $i] : (((j @ sK1 @ (sK13 @ (j @ sK1) @ X1)) = $false) | ((k @ X0 @ sK4) = $false) | ((i @ X0 @ X1) = $false)) ) | ~spl0_22), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f414])). 1.41/0.67 thf(f1027,plain,( 1.41/0.67 spl0_26 | ~spl0_30 | ~spl0_54), 1.41/0.67 inference(avatar_split_clause,[status(thm)],[f1020,f1007,f713,f500])). 1.41/0.67 thf(f500,definition,( 1.41/0.67 spl0_26 <=> ! [X0 : $i] : (((i @ X0 @ sK12) = $false) | ((k @ X0 @ sK11) = $false))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_26])],[avatar_definition])). 1.41/0.67 thf(f713,definition,( 1.41/0.67 spl0_30 <=> ! [X0 : $i,X1 : $i] : (((k @ X0 @ X1) = $false) | ($true = (sK10 @ (sK14 @ sK10 @ X1))) | ((i @ X0 @ sK12) = $false))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_30])],[avatar_definition])). 1.41/0.67 thf(f1007,definition,( 1.41/0.67 spl0_54 <=> ((sK10 @ (sK14 @ sK10 @ sK11)) = $false)), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_54])],[avatar_definition])). 1.41/0.67 thf(f1020,plain,( 1.41/0.67 ( ! [X0 : $i] : (((i @ X0 @ sK12) = $false) | ((k @ X0 @ sK11) = $false)) ) | (~spl0_30 | ~spl0_54)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f1016])). 1.41/0.67 thf(f1016,plain,( 1.41/0.67 ( ! [X0 : $i] : (($true = $false) | ((k @ X0 @ sK11) = $false) | ((i @ X0 @ sK12) = $false)) ) | (~spl0_30 | ~spl0_54)), 1.41/0.67 inference(superposition,[status(thm)],[f714,f1009])). 1.41/0.67 thf(f1009,plain,( 1.41/0.67 ((sK10 @ (sK14 @ sK10 @ sK11)) = $false) | ~spl0_54), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f1007])). 1.41/0.67 thf(f714,plain,( 1.41/0.67 ( ! [X0 : $i,X1 : $i] : (($true = (sK10 @ (sK14 @ sK10 @ X1))) | ((k @ X0 @ X1) = $false) | ((i @ X0 @ sK12) = $false)) ) | ~spl0_30), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f713])). 1.41/0.67 thf(f1011,plain,( 1.41/0.67 spl0_26 | spl0_54 | ~spl0_23 | ~spl0_53), 1.41/0.67 inference(avatar_split_clause,[status(thm)],[f1004,f991,f448,f1007,f500])). 1.41/0.67 thf(f448,definition,( 1.41/0.67 spl0_23 <=> ! [X0 : $i,X1 : $i] : (((k @ X1 @ sK11) = $false) | ((sK10 @ (sK13 @ sK10 @ X0)) = $false) | ((i @ X1 @ X0) = $false))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_23])],[avatar_definition])). 1.41/0.67 thf(f991,definition,( 1.41/0.67 spl0_53 <=> ! [X0 : $i > $o] : (((sK10 @ (sK14 @ X0 @ sK11)) = $false) | ($true = (sK10 @ (sK13 @ X0 @ sK12))))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_53])],[avatar_definition])). 1.41/0.67 thf(f1004,plain,( 1.41/0.67 ( ! [X0 : $i] : (((k @ X0 @ sK11) = $false) | ((sK10 @ (sK14 @ sK10 @ sK11)) = $false) | ((i @ X0 @ sK12) = $false)) ) | (~spl0_23 | ~spl0_53)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f1002])). 1.41/0.67 thf(f1002,plain,( 1.41/0.67 ( ! [X0 : $i] : (((sK10 @ (sK14 @ sK10 @ sK11)) = $false) | ($true = $false) | ((k @ X0 @ sK11) = $false) | ((i @ X0 @ sK12) = $false)) ) | (~spl0_23 | ~spl0_53)), 1.41/0.67 inference(superposition,[status(thm)],[f992,f449])). 1.41/0.67 thf(f449,plain,( 1.41/0.67 ( ! [X0 : $i,X1 : $i] : (((sK10 @ (sK13 @ sK10 @ X0)) = $false) | ((k @ X1 @ sK11) = $false) | ((i @ X1 @ X0) = $false)) ) | ~spl0_23), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f448])). 1.41/0.67 thf(f992,plain,( 1.41/0.67 ( ! [X0 : $i > $o] : (($true = (sK10 @ (sK13 @ X0 @ sK12))) | ((sK10 @ (sK14 @ X0 @ sK11)) = $false)) ) | ~spl0_53), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f991])). 1.41/0.67 thf(f994,plain,( 1.41/0.67 spl0_53 | spl0_26 | ~spl0_2 | ~spl0_9 | ~spl0_11), 1.41/0.67 inference(avatar_split_clause,[status(thm)],[f976,f336,f327,f296,f500,f991])). 1.41/0.67 thf(f327,definition,( 1.41/0.67 spl0_9 <=> ! [X2 : $i] : (($true = (sK10 @ X2)) | ((j @ sK12 @ X2) = $false))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])). 1.41/0.67 thf(f336,definition,( 1.41/0.67 spl0_11 <=> ! [X2 : $i] : (((l @ sK11 @ X2) = $false) | ((sK10 @ X2) = $false))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])). 1.41/0.67 thf(f976,plain,( 1.41/0.67 ( ! [X0 : $i > $o,X1 : $i] : (((k @ X1 @ sK11) = $false) | ((i @ X1 @ sK12) = $false) | ($true = (sK10 @ (sK13 @ X0 @ sK12))) | ((sK10 @ (sK14 @ X0 @ sK11)) = $false)) ) | (~spl0_2 | ~spl0_9 | ~spl0_11)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f973])). 1.41/0.67 thf(f973,plain,( 1.41/0.67 ( ! [X0 : $i > $o,X1 : $i] : (((k @ X1 @ sK11) = $false) | ((sK10 @ (sK14 @ X0 @ sK11)) = $false) | ($true = $false) | ($true = (sK10 @ (sK13 @ X0 @ sK12))) | ((i @ X1 @ sK12) = $false)) ) | (~spl0_2 | ~spl0_9 | ~spl0_11)), 1.41/0.67 inference(superposition,[status(thm)],[f328,f966])). 1.41/0.67 thf(f966,plain,( 1.41/0.67 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (($true = (j @ X1 @ (sK13 @ X0 @ X1))) | ((k @ X2 @ sK11) = $false) | ((i @ X2 @ X1) = $false) | ((sK10 @ (sK14 @ X0 @ sK11)) = $false)) ) | (~spl0_2 | ~spl0_11)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f959])). 1.41/0.67 thf(f959,plain,( 1.41/0.67 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((i @ X2 @ X1) = $false) | ((sK10 @ (sK14 @ X0 @ sK11)) = $false) | ((k @ X2 @ sK11) = $false) | ($true = (j @ X1 @ (sK13 @ X0 @ X1))) | ($true = $false)) ) | (~spl0_2 | ~spl0_11)), 1.41/0.67 inference(superposition,[status(thm)],[f297,f337])). 1.41/0.67 thf(f337,plain,( 1.41/0.67 ( ! [X2 : $i] : (((l @ sK11 @ X2) = $false) | ((sK10 @ X2) = $false)) ) | ~spl0_11), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f336])). 1.41/0.67 thf(f328,plain,( 1.41/0.67 ( ! [X2 : $i] : (((j @ sK12 @ X2) = $false) | ($true = (sK10 @ X2))) ) | ~spl0_9), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f327])). 1.41/0.67 thf(f927,plain,( 1.41/0.67 spl0_48 | spl0_48 | ~spl0_4 | ~spl0_6 | ~spl0_16), 1.41/0.67 inference(avatar_split_clause,[status(thm)],[f916,f358,f313,f304,f924,f924])). 1.41/0.67 thf(f304,definition,( 1.41/0.67 spl0_4 <=> ! [X5 : $i,X3 : $i > $o,X6 : $i,X1 : $i] : (($true = (l @ X6 @ (sK14 @ X3 @ X6))) | ((X3 @ (sK13 @ X3 @ X5)) = $false) | ((i @ X1 @ X5) = $false) | ((k @ X1 @ X6) = $false))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])). 1.41/0.67 thf(f313,definition,( 1.41/0.67 spl0_6 <=> ! [X5 : $i,X3 : $i > $o,X6 : $i,X1 : $i] : (((X3 @ (sK13 @ X3 @ X5)) = $false) | ((k @ X1 @ X6) = $false) | ((i @ X1 @ X5) = $false) | ($true = (X3 @ (sK14 @ X3 @ X6))))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])). 1.41/0.67 thf(f916,plain,( 1.41/0.67 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((sK5 @ (sK13 @ sK5 @ X0)) = $false) | ((k @ X2 @ sK8) = $false) | ((i @ X2 @ X3) = $false) | ((sK5 @ (sK13 @ sK5 @ X3)) = $false) | ((i @ X1 @ X0) = $false) | ((k @ X1 @ sK8) = $false)) ) | (~spl0_4 | ~spl0_6 | ~spl0_16)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f915])). 1.41/0.67 thf(f915,plain,( 1.41/0.67 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((sK5 @ (sK13 @ sK5 @ X0)) = $false) | ((k @ X2 @ sK8) = $false) | ((sK5 @ (sK13 @ sK5 @ X3)) = $false) | ((i @ X1 @ X0) = $false) | ((i @ X2 @ X3) = $false) | ((k @ X1 @ sK8) = $false) | ($true = $false)) ) | (~spl0_4 | ~spl0_6 | ~spl0_16)), 1.41/0.67 inference(superposition,[status(thm)],[f314,f617])). 1.41/0.67 thf(f617,plain,( 1.41/0.67 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((sK5 @ (sK14 @ X0 @ sK8)) = $false) | ((i @ X2 @ X1) = $false) | ((k @ X2 @ sK8) = $false) | ((X0 @ (sK13 @ X0 @ X1)) = $false)) ) | (~spl0_4 | ~spl0_16)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f613])). 1.41/0.67 thf(f613,plain,( 1.41/0.67 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((X0 @ (sK13 @ X0 @ X1)) = $false) | ((k @ X2 @ sK8) = $false) | ((sK5 @ (sK14 @ X0 @ sK8)) = $false) | ($true = $false) | ((i @ X2 @ X1) = $false)) ) | (~spl0_4 | ~spl0_16)), 1.41/0.67 inference(superposition,[status(thm)],[f305,f359])). 1.41/0.67 thf(f305,plain,( 1.41/0.67 ( ! [X3 : $i > $o,X1 : $i,X6 : $i,X5 : $i] : (($true = (l @ X6 @ (sK14 @ X3 @ X6))) | ((X3 @ (sK13 @ X3 @ X5)) = $false) | ((k @ X1 @ X6) = $false) | ((i @ X1 @ X5) = $false)) ) | ~spl0_4), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f304])). 1.41/0.67 thf(f314,plain,( 1.41/0.67 ( ! [X3 : $i > $o,X1 : $i,X6 : $i,X5 : $i] : (($true = (X3 @ (sK14 @ X3 @ X6))) | ((X3 @ (sK13 @ X3 @ X5)) = $false) | ((k @ X1 @ X6) = $false) | ((i @ X1 @ X5) = $false)) ) | ~spl0_6), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f313])). 1.41/0.67 thf(f772,plain,( 1.41/0.67 spl0_31 | spl0_31 | ~spl0_4 | ~spl0_6 | ~spl0_21), 1.41/0.67 inference(avatar_split_clause,[status(thm)],[f766,f380,f313,f304,f769,f769])). 1.41/0.67 thf(f766,plain,( 1.41/0.67 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((i @ X2 @ X3) = $false) | ((sK5 @ (sK13 @ sK5 @ X3)) = $false) | ((k @ X1 @ sK6) = $false) | ((i @ X1 @ X0) = $false) | ((k @ X2 @ sK6) = $false) | ((sK5 @ (sK13 @ sK5 @ X0)) = $false)) ) | (~spl0_4 | ~spl0_6 | ~spl0_21)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f764])). 1.41/0.67 thf(f764,plain,( 1.41/0.67 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((i @ X2 @ X3) = $false) | ((sK5 @ (sK13 @ sK5 @ X3)) = $false) | ((sK5 @ (sK13 @ sK5 @ X0)) = $false) | ((k @ X2 @ sK6) = $false) | ($true = $false) | ((k @ X1 @ sK6) = $false) | ((i @ X1 @ X0) = $false)) ) | (~spl0_4 | ~spl0_6 | ~spl0_21)), 1.41/0.67 inference(superposition,[status(thm)],[f314,f575])). 1.41/0.67 thf(f575,plain,( 1.41/0.67 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((sK5 @ (sK14 @ X0 @ sK6)) = $false) | ((i @ X2 @ X1) = $false) | ((k @ X2 @ sK6) = $false) | ((X0 @ (sK13 @ X0 @ X1)) = $false)) ) | (~spl0_4 | ~spl0_21)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f569])). 1.41/0.67 thf(f569,plain,( 1.41/0.67 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((X0 @ (sK13 @ X0 @ X1)) = $false) | ((sK5 @ (sK14 @ X0 @ sK6)) = $false) | ((i @ X2 @ X1) = $false) | ((k @ X2 @ sK6) = $false) | ($true = $false)) ) | (~spl0_4 | ~spl0_21)), 1.41/0.67 inference(superposition,[status(thm)],[f305,f381])). 1.41/0.67 thf(f716,plain,( 1.41/0.67 spl0_30 | spl0_26 | ~spl0_5 | ~spl0_9 | ~spl0_23), 1.41/0.67 inference(avatar_split_clause,[status(thm)],[f709,f448,f327,f309,f500,f713])). 1.41/0.67 thf(f709,plain,( 1.41/0.67 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((i @ X0 @ sK12) = $false) | ((k @ X0 @ sK11) = $false) | ((i @ X1 @ sK12) = $false) | ($true = (sK10 @ (sK14 @ sK10 @ X2))) | ((k @ X1 @ X2) = $false)) ) | (~spl0_5 | ~spl0_9 | ~spl0_23)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f707])). 1.41/0.67 thf(f707,plain,( 1.41/0.67 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = $false) | ((i @ X0 @ sK12) = $false) | ($true = (sK10 @ (sK14 @ sK10 @ X2))) | ((k @ X1 @ X2) = $false) | ((k @ X0 @ sK11) = $false) | ((i @ X1 @ sK12) = $false)) ) | (~spl0_5 | ~spl0_9 | ~spl0_23)), 1.41/0.67 inference(superposition,[status(thm)],[f449,f427])). 1.41/0.67 thf(f427,plain,( 1.41/0.67 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (($true = (sK10 @ (sK13 @ X0 @ sK12))) | ((i @ X1 @ sK12) = $false) | ($true = (X0 @ (sK14 @ X0 @ X2))) | ((k @ X1 @ X2) = $false)) ) | (~spl0_5 | ~spl0_9)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f423])). 1.41/0.67 thf(f423,plain,( 1.41/0.67 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((i @ X1 @ sK12) = $false) | ($true = $false) | ($true = (X0 @ (sK14 @ X0 @ X2))) | ($true = (sK10 @ (sK13 @ X0 @ sK12))) | ((k @ X1 @ X2) = $false)) ) | (~spl0_5 | ~spl0_9)), 1.41/0.67 inference(superposition,[status(thm)],[f310,f328])). 1.41/0.67 thf(f699,plain,( 1.41/0.67 ~spl0_18 | ~spl0_20 | ~spl0_27), 1.41/0.67 inference(avatar_contradiction_clause,[status(thm)],[f698])). 1.41/0.67 thf(f698,plain,( 1.41/0.67 $false | (~spl0_18 | ~spl0_20 | ~spl0_27)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f697])). 1.41/0.67 thf(f697,plain,( 1.41/0.67 ($true = $false) | (~spl0_18 | ~spl0_20 | ~spl0_27)), 1.41/0.67 inference(backward_demodulation,[status(thm)],[f368,f695])). 1.41/0.67 thf(f695,plain,( 1.41/0.67 ((i @ sK2 @ sK7) = $false) | (~spl0_20 | ~spl0_27)), 1.41/0.67 inference(trivial_inequality_removal,[status(thm)],[f693])). 1.41/0.67 thf(f693,plain,( 1.41/0.67 ($true = $false) | ((i @ sK2 @ sK7) = $false) | (~spl0_20 | ~spl0_27)), 1.41/0.67 inference(superposition,[status(thm)],[f377,f585])). 1.41/0.67 thf(f585,plain,( 1.41/0.67 ( ! [X0 : $i] : (((k @ X0 @ sK6) = $false) | ((i @ X0 @ sK7) = $false)) ) | ~spl0_27), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f584])). 1.41/0.67 thf(f377,plain,( 1.41/0.67 ($true = (k @ sK2 @ sK6)) | ~spl0_20), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f375])). 1.41/0.67 thf(f375,definition,( 1.41/0.67 spl0_20 <=> ($true = (k @ sK2 @ sK6))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_20])],[avatar_definition])). 1.41/0.67 thf(f368,plain,( 1.41/0.67 ($true = (i @ sK2 @ sK7)) | ~spl0_18), 1.41/0.67 inference(avatar_component_clause,[status(thm)],[f366])). 1.41/0.67 thf(f366,definition,( 1.41/0.67 spl0_18 <=> ($true = (i @ sK2 @ sK7))), 1.41/0.67 introduced(definition,[new_symbols(naming,[spl0_18])],[avatar_definition])). 1.41/0.67 thf(f665,plain,( 1.41/0.67 ~spl0_13 | ~spl0_15 | ~spl0_29), 1.41/0.67 inference(avatar_contradiction_clause,[status(thm)],[f664])). 1.41/0.67 thf(f664,plain,( 1.41/0.67 $false | (~spl0_13 | ~spl0_15 | ~spl0_29)), 1.41/0.68 inference(trivial_inequality_removal,[status(thm)],[f663])). 1.41/0.68 thf(f663,plain,( 1.41/0.68 ($true = $false) | (~spl0_13 | ~spl0_15 | ~spl0_29)), 1.41/0.68 inference(backward_demodulation,[status(thm)],[f346,f661])). 1.41/0.68 thf(f661,plain,( 1.41/0.68 ((i @ sK2 @ sK9) = $false) | (~spl0_15 | ~spl0_29)), 1.41/0.68 inference(trivial_inequality_removal,[status(thm)],[f659])). 1.41/0.68 thf(f659,plain,( 1.41/0.68 ((i @ sK2 @ sK9) = $false) | ($true = $false) | (~spl0_15 | ~spl0_29)), 1.41/0.68 inference(superposition,[status(thm)],[f355,f654])). 1.41/0.68 thf(f654,plain,( 1.41/0.68 ( ! [X0 : $i] : (((k @ X0 @ sK8) = $false) | ((i @ X0 @ sK9) = $false)) ) | ~spl0_29), 1.41/0.68 inference(avatar_component_clause,[status(thm)],[f653])). 1.41/0.68 thf(f355,plain,( 1.41/0.68 ($true = (k @ sK2 @ sK8)) | ~spl0_15), 1.41/0.68 inference(avatar_component_clause,[status(thm)],[f353])). 1.41/0.68 thf(f353,definition,( 1.41/0.68 spl0_15 <=> ($true = (k @ sK2 @ sK8))), 1.41/0.68 introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition])). 1.41/0.68 thf(f346,plain,( 1.41/0.68 ($true = (i @ sK2 @ sK9)) | ~spl0_13), 1.41/0.68 inference(avatar_component_clause,[status(thm)],[f344])). 1.41/0.68 thf(f344,definition,( 1.41/0.68 spl0_13 <=> ($true = (i @ sK2 @ sK9))), 1.41/0.68 introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition])). 1.41/0.68 thf(f656,plain,( 1.41/0.68 spl0_29 | spl0_29 | ~spl0_1 | ~spl0_3 | ~spl0_14 | ~spl0_16), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f649,f358,f349,f300,f293,f653,f653])). 1.41/0.68 thf(f293,definition,( 1.41/0.68 spl0_1 <=> ! [X2 : $i,X7 : $i,X4 : $i] : (($true = (l @ X7 @ (sK15 @ X7 @ X2))) | ((k @ X4 @ X7) = $false) | ((i @ X4 @ X2) = $false))), 1.41/0.68 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])). 1.41/0.68 thf(f300,definition,( 1.41/0.68 spl0_3 <=> ! [X2 : $i,X7 : $i,X4 : $i] : (((j @ X2 @ (sK15 @ X7 @ X2)) = $true) | ((i @ X4 @ X2) = $false) | ((k @ X4 @ X7) = $false))), 1.41/0.68 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])). 1.41/0.68 thf(f649,plain,( 1.41/0.68 ( ! [X0 : $i,X1 : $i] : (((i @ X1 @ sK9) = $false) | ((i @ X0 @ sK9) = $false) | ((k @ X1 @ sK8) = $false) | ((k @ X0 @ sK8) = $false)) ) | (~spl0_1 | ~spl0_3 | ~spl0_14 | ~spl0_16)), 1.41/0.68 inference(trivial_inequality_removal,[status(thm)],[f647])). 1.41/0.68 thf(f647,plain,( 1.41/0.68 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ((k @ X0 @ sK8) = $false) | ((i @ X1 @ sK9) = $false) | ((i @ X0 @ sK9) = $false) | ((k @ X1 @ sK8) = $false)) ) | (~spl0_1 | ~spl0_3 | ~spl0_14 | ~spl0_16)), 1.41/0.68 inference(superposition,[status(thm)],[f619,f607])). 1.41/0.68 thf(f607,plain,( 1.41/0.68 ( ! [X0 : $i,X1 : $i] : (($true = (sK5 @ (sK15 @ X0 @ sK9))) | ((i @ X1 @ sK9) = $false) | ((k @ X1 @ X0) = $false)) ) | (~spl0_3 | ~spl0_14)), 1.41/0.68 inference(trivial_inequality_removal,[status(thm)],[f604])). 1.41/0.68 thf(f604,plain,( 1.41/0.68 ( ! [X0 : $i,X1 : $i] : (((k @ X1 @ X0) = $false) | ((i @ X1 @ sK9) = $false) | ($true = (sK5 @ (sK15 @ X0 @ sK9))) | ($true = $false)) ) | (~spl0_3 | ~spl0_14)), 1.41/0.68 inference(superposition,[status(thm)],[f301,f350])). 1.41/0.68 thf(f301,plain,( 1.41/0.68 ( ! [X2 : $i,X7 : $i,X4 : $i] : (((j @ X2 @ (sK15 @ X7 @ X2)) = $true) | ((k @ X4 @ X7) = $false) | ((i @ X4 @ X2) = $false)) ) | ~spl0_3), 1.41/0.68 inference(avatar_component_clause,[status(thm)],[f300])). 1.41/0.68 thf(f619,plain,( 1.41/0.68 ( ! [X0 : $i,X1 : $i] : (((sK5 @ (sK15 @ sK8 @ X0)) = $false) | ((k @ X1 @ sK8) = $false) | ((i @ X1 @ X0) = $false)) ) | (~spl0_1 | ~spl0_16)), 1.41/0.68 inference(trivial_inequality_removal,[status(thm)],[f612])). 1.41/0.68 thf(f612,plain,( 1.41/0.68 ( ! [X0 : $i,X1 : $i] : (((k @ X1 @ sK8) = $false) | ((sK5 @ (sK15 @ sK8 @ X0)) = $false) | ((i @ X1 @ X0) = $false) | ($true = $false)) ) | (~spl0_1 | ~spl0_16)), 1.41/0.68 inference(superposition,[status(thm)],[f359,f294])). 1.41/0.68 thf(f294,plain,( 1.41/0.68 ( ! [X2 : $i,X7 : $i,X4 : $i] : (($true = (l @ X7 @ (sK15 @ X7 @ X2))) | ((k @ X4 @ X7) = $false) | ((i @ X4 @ X2) = $false)) ) | ~spl0_1), 1.41/0.68 inference(avatar_component_clause,[status(thm)],[f293])). 1.41/0.68 thf(f587,plain,( 1.41/0.68 spl0_27 | spl0_27 | ~spl0_1 | ~spl0_3 | ~spl0_19 | ~spl0_21), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f581,f380,f371,f300,f293,f584,f584])). 1.41/0.68 thf(f581,plain,( 1.41/0.68 ( ! [X0 : $i,X1 : $i] : (((k @ X0 @ sK6) = $false) | ((k @ X1 @ sK6) = $false) | ((i @ X1 @ sK7) = $false) | ((i @ X0 @ sK7) = $false)) ) | (~spl0_1 | ~spl0_3 | ~spl0_19 | ~spl0_21)), 1.41/0.68 inference(trivial_inequality_removal,[status(thm)],[f578])). 1.41/0.68 thf(f578,plain,( 1.41/0.68 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ((k @ X1 @ sK6) = $false) | ((i @ X0 @ sK7) = $false) | ((k @ X0 @ sK6) = $false) | ((i @ X1 @ sK7) = $false)) ) | (~spl0_1 | ~spl0_3 | ~spl0_19 | ~spl0_21)), 1.41/0.68 inference(superposition,[status(thm)],[f574,f565])). 1.41/0.68 thf(f565,plain,( 1.41/0.68 ( ! [X0 : $i,X1 : $i] : (($true = (sK5 @ (sK15 @ X0 @ sK7))) | ((k @ X1 @ X0) = $false) | ((i @ X1 @ sK7) = $false)) ) | (~spl0_3 | ~spl0_19)), 1.41/0.68 inference(trivial_inequality_removal,[status(thm)],[f560])). 1.41/0.68 thf(f560,plain,( 1.41/0.68 ( ! [X0 : $i,X1 : $i] : (($true = (sK5 @ (sK15 @ X0 @ sK7))) | ((k @ X1 @ X0) = $false) | ((i @ X1 @ sK7) = $false) | ($true = $false)) ) | (~spl0_3 | ~spl0_19)), 1.41/0.68 inference(superposition,[status(thm)],[f301,f372])). 1.41/0.68 thf(f574,plain,( 1.41/0.68 ( ! [X0 : $i,X1 : $i] : (((sK5 @ (sK15 @ sK6 @ X0)) = $false) | ((i @ X1 @ X0) = $false) | ((k @ X1 @ sK6) = $false)) ) | (~spl0_1 | ~spl0_21)), 1.41/0.68 inference(trivial_inequality_removal,[status(thm)],[f568])). 1.41/0.68 thf(f568,plain,( 1.41/0.68 ( ! [X0 : $i,X1 : $i] : (((sK5 @ (sK15 @ sK6 @ X0)) = $false) | ((k @ X1 @ sK6) = $false) | ((i @ X1 @ X0) = $false) | ($true = $false)) ) | (~spl0_1 | ~spl0_21)), 1.41/0.68 inference(superposition,[status(thm)],[f381,f294])). 1.41/0.68 thf(f546,plain,( 1.41/0.68 ~spl0_12 | ~spl0_17 | ~spl0_25), 1.41/0.68 inference(avatar_contradiction_clause,[status(thm)],[f545])). 1.41/0.68 thf(f545,plain,( 1.41/0.68 $false | (~spl0_12 | ~spl0_17 | ~spl0_25)), 1.41/0.68 inference(trivial_inequality_removal,[status(thm)],[f544])). 1.41/0.68 thf(f544,plain,( 1.41/0.68 ($true = $false) | (~spl0_12 | ~spl0_17 | ~spl0_25)), 1.41/0.68 inference(backward_demodulation,[status(thm)],[f342,f543])). 1.41/0.68 thf(f543,plain,( 1.41/0.68 ((i @ sK3 @ sK1) = $false) | (~spl0_17 | ~spl0_25)), 1.41/0.68 inference(trivial_inequality_removal,[status(thm)],[f540])). 1.41/0.68 thf(f540,plain,( 1.41/0.68 ($true = $false) | ((i @ sK3 @ sK1) = $false) | (~spl0_17 | ~spl0_25)), 1.41/0.68 inference(superposition,[status(thm)],[f364,f473])). 1.41/0.68 thf(f473,plain,( 1.41/0.68 ( ! [X0 : $i] : (((k @ X0 @ sK4) = $false) | ((i @ X0 @ sK1) = $false)) ) | ~spl0_25), 1.41/0.68 inference(avatar_component_clause,[status(thm)],[f472])). 1.41/0.68 thf(f364,plain,( 1.41/0.68 ($true = (k @ sK3 @ sK4)) | ~spl0_17), 1.41/0.68 inference(avatar_component_clause,[status(thm)],[f362])). 1.41/0.68 thf(f362,definition,( 1.41/0.68 spl0_17 <=> ($true = (k @ sK3 @ sK4))), 1.41/0.68 introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition])). 1.41/0.68 thf(f342,plain,( 1.41/0.68 ($true = (i @ sK3 @ sK1)) | ~spl0_12), 1.41/0.68 inference(avatar_component_clause,[status(thm)],[f340])). 1.41/0.68 thf(f340,definition,( 1.41/0.68 spl0_12 <=> ($true = (i @ sK3 @ sK1))), 1.41/0.68 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])). 1.41/0.68 thf(f537,plain,( 1.41/0.68 spl0_25 | spl0_25 | ~spl0_1 | ~spl0_3 | ~spl0_8), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f533,f323,f300,f293,f472,f472])). 1.41/0.68 thf(f533,plain,( 1.41/0.68 ( ! [X0 : $i,X1 : $i] : (((i @ X0 @ sK1) = $false) | ((k @ X1 @ sK4) = $false) | ((i @ X1 @ sK1) = $false) | ((k @ X0 @ sK4) = $false)) ) | (~spl0_1 | ~spl0_3 | ~spl0_8)), 1.41/0.68 inference(trivial_inequality_removal,[status(thm)],[f531])). 1.41/0.68 thf(f531,plain,( 1.41/0.68 ( ! [X0 : $i,X1 : $i] : (((k @ X0 @ sK4) = $false) | ((i @ X1 @ sK1) = $false) | ((k @ X1 @ sK4) = $false) | ((i @ X0 @ sK1) = $false) | ($true = $false)) ) | (~spl0_1 | ~spl0_3 | ~spl0_8)), 1.41/0.68 inference(superposition,[status(thm)],[f529,f301])). 1.41/0.68 thf(f529,plain,( 1.41/0.68 ( ! [X0 : $i,X1 : $i] : (((j @ sK1 @ (sK15 @ sK4 @ X0)) = $false) | ((k @ X1 @ sK4) = $false) | ((i @ X1 @ X0) = $false)) ) | (~spl0_1 | ~spl0_8)), 1.41/0.68 inference(trivial_inequality_removal,[status(thm)],[f522])). 1.41/0.68 thf(f522,plain,( 1.41/0.68 ( ! [X0 : $i,X1 : $i] : (((i @ X1 @ X0) = $false) | ((k @ X1 @ sK4) = $false) | ($true = $false) | ((j @ sK1 @ (sK15 @ sK4 @ X0)) = $false)) ) | (~spl0_1 | ~spl0_8)), 1.41/0.68 inference(superposition,[status(thm)],[f324,f294])). 1.41/0.68 thf(f512,plain,( 1.41/0.68 ~spl0_7 | ~spl0_10 | ~spl0_26), 1.41/0.68 inference(avatar_contradiction_clause,[status(thm)],[f511])). 1.41/0.68 thf(f511,plain,( 1.41/0.68 $false | (~spl0_7 | ~spl0_10 | ~spl0_26)), 1.41/0.68 inference(trivial_inequality_removal,[status(thm)],[f510])). 1.41/0.68 thf(f510,plain,( 1.41/0.68 ($true = $false) | (~spl0_7 | ~spl0_10 | ~spl0_26)), 1.41/0.68 inference(backward_demodulation,[status(thm)],[f321,f509])). 1.41/0.68 thf(f509,plain,( 1.41/0.68 ((i @ sK2 @ sK12) = $false) | (~spl0_10 | ~spl0_26)), 1.41/0.68 inference(trivial_inequality_removal,[status(thm)],[f506])). 1.41/0.68 thf(f506,plain,( 1.41/0.68 ($true = $false) | ((i @ sK2 @ sK12) = $false) | (~spl0_10 | ~spl0_26)), 1.41/0.68 inference(superposition,[status(thm)],[f333,f501])). 1.41/0.68 thf(f501,plain,( 1.41/0.68 ( ! [X0 : $i] : (((k @ X0 @ sK11) = $false) | ((i @ X0 @ sK12) = $false)) ) | ~spl0_26), 1.41/0.68 inference(avatar_component_clause,[status(thm)],[f500])). 1.41/0.68 thf(f333,plain,( 1.41/0.68 ($true = (k @ sK2 @ sK11)) | ~spl0_10), 1.41/0.68 inference(avatar_component_clause,[status(thm)],[f331])). 1.41/0.68 thf(f331,definition,( 1.41/0.68 spl0_10 <=> ($true = (k @ sK2 @ sK11))), 1.41/0.68 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])). 1.41/0.68 thf(f321,plain,( 1.41/0.68 ($true = (i @ sK2 @ sK12)) | ~spl0_7), 1.41/0.68 inference(avatar_component_clause,[status(thm)],[f319])). 1.41/0.68 thf(f319,definition,( 1.41/0.68 spl0_7 <=> ($true = (i @ sK2 @ sK12))), 1.41/0.68 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])). 1.41/0.68 thf(f503,plain,( 1.41/0.68 spl0_26 | spl0_26 | ~spl0_1 | ~spl0_3 | ~spl0_9 | ~spl0_11), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f497,f336,f327,f300,f293,f500,f500])). 1.41/0.68 thf(f497,plain,( 1.41/0.68 ( ! [X0 : $i,X1 : $i] : (((i @ X1 @ sK12) = $false) | ((k @ X0 @ sK11) = $false) | ((i @ X0 @ sK12) = $false) | ((k @ X1 @ sK11) = $false)) ) | (~spl0_1 | ~spl0_3 | ~spl0_9 | ~spl0_11)), 1.41/0.68 inference(trivial_inequality_removal,[status(thm)],[f495])). 1.41/0.68 thf(f495,plain,( 1.41/0.68 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ((i @ X0 @ sK12) = $false) | ((k @ X1 @ sK11) = $false) | ((k @ X0 @ sK11) = $false) | ((i @ X1 @ sK12) = $false)) ) | (~spl0_1 | ~spl0_3 | ~spl0_9 | ~spl0_11)), 1.41/0.68 inference(superposition,[status(thm)],[f493,f486])). 1.41/0.68 thf(f486,plain,( 1.41/0.68 ( ! [X0 : $i,X1 : $i] : (((sK10 @ (sK15 @ sK11 @ X0)) = $false) | ((i @ X1 @ X0) = $false) | ((k @ X1 @ sK11) = $false)) ) | (~spl0_1 | ~spl0_11)), 1.41/0.68 inference(trivial_inequality_removal,[status(thm)],[f483])). 1.41/0.68 thf(f483,plain,( 1.41/0.68 ( ! [X0 : $i,X1 : $i] : (((i @ X1 @ X0) = $false) | ((sK10 @ (sK15 @ sK11 @ X0)) = $false) | ((k @ X1 @ sK11) = $false) | ($true = $false)) ) | (~spl0_1 | ~spl0_11)), 1.41/0.68 inference(superposition,[status(thm)],[f294,f337])). 1.41/0.68 thf(f493,plain,( 1.41/0.68 ( ! [X0 : $i,X1 : $i] : (((sK10 @ (sK15 @ X0 @ sK12)) = $true) | ((k @ X1 @ X0) = $false) | ((i @ X1 @ sK12) = $false)) ) | (~spl0_3 | ~spl0_9)), 1.41/0.68 inference(trivial_inequality_removal,[status(thm)],[f491])). 1.41/0.68 thf(f491,plain,( 1.41/0.68 ( ! [X0 : $i,X1 : $i] : (((sK10 @ (sK15 @ X0 @ sK12)) = $true) | ($true = $false) | ((k @ X1 @ X0) = $false) | ((i @ X1 @ sK12) = $false)) ) | (~spl0_3 | ~spl0_9)), 1.41/0.68 inference(superposition,[status(thm)],[f328,f301])). 1.41/0.68 thf(f475,plain,( 1.41/0.68 spl0_24 | spl0_25 | ~spl0_5 | ~spl0_22), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f465,f414,f309,f472,f469])). 1.41/0.68 thf(f465,plain,( 1.41/0.68 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((k @ X0 @ X1) = $false) | ((k @ X2 @ sK4) = $false) | ((i @ X2 @ sK1) = $false) | ((i @ X0 @ sK1) = $false) | ($true = (j @ sK1 @ (sK14 @ (j @ sK1) @ X1)))) ) | (~spl0_5 | ~spl0_22)), 1.41/0.68 inference(trivial_inequality_removal,[status(thm)],[f464])). 1.41/0.68 thf(f464,plain,( 1.41/0.68 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (j @ sK1 @ (sK14 @ (j @ sK1) @ X1))) | ((i @ X0 @ sK1) = $false) | ((k @ X2 @ sK4) = $false) | ($true = $false) | ((i @ X2 @ sK1) = $false) | ((k @ X0 @ X1) = $false)) ) | (~spl0_5 | ~spl0_22)), 1.41/0.68 inference(superposition,[status(thm)],[f310,f415])). 1.41/0.68 thf(f451,plain,( 1.41/0.68 spl0_23 | spl0_23 | ~spl0_4 | ~spl0_6 | ~spl0_11), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f444,f336,f313,f304,f448,f448])). 1.41/0.68 thf(f444,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((i @ X0 @ X1) = $false) | ((k @ X3 @ sK11) = $false) | ((sK10 @ (sK13 @ sK10 @ X1)) = $false) | ((sK10 @ (sK13 @ sK10 @ X2)) = $false) | ((k @ X0 @ sK11) = $false) | ((i @ X3 @ X2) = $false)) ) | (~spl0_4 | ~spl0_6 | ~spl0_11)), 1.41/0.68 inference(trivial_inequality_removal,[status(thm)],[f443])). 1.41/0.68 thf(f443,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((sK10 @ (sK13 @ sK10 @ X1)) = $false) | ($true = $false) | ((k @ X0 @ sK11) = $false) | ((k @ X3 @ sK11) = $false) | ((i @ X3 @ X2) = $false) | ((i @ X0 @ X1) = $false) | ((sK10 @ (sK13 @ sK10 @ X2)) = $false)) ) | (~spl0_4 | ~spl0_6 | ~spl0_11)), 1.41/0.68 inference(superposition,[status(thm)],[f314,f438])). 1.41/0.68 thf(f438,plain,( 1.41/0.68 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((sK10 @ (sK14 @ X0 @ sK11)) = $false) | ((X0 @ (sK13 @ X0 @ X1)) = $false) | ((k @ X2 @ sK11) = $false) | ((i @ X2 @ X1) = $false)) ) | (~spl0_4 | ~spl0_11)), 1.41/0.68 inference(trivial_inequality_removal,[status(thm)],[f431])). 1.41/0.68 thf(f431,plain,( 1.41/0.68 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((k @ X2 @ sK11) = $false) | ((X0 @ (sK13 @ X0 @ X1)) = $false) | ((sK10 @ (sK14 @ X0 @ sK11)) = $false) | ($true = $false) | ((i @ X2 @ X1) = $false)) ) | (~spl0_4 | ~spl0_11)), 1.41/0.68 inference(superposition,[status(thm)],[f337,f305])). 1.41/0.68 thf(f417,plain,( 1.41/0.68 spl0_22 | spl0_22 | ~spl0_4 | ~spl0_6 | ~spl0_8), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f411,f323,f313,f304,f414,f414])). 1.41/0.68 thf(f411,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((k @ X0 @ sK4) = $false) | ((j @ sK1 @ (sK13 @ (j @ sK1) @ X3)) = $false) | ((k @ X2 @ sK4) = $false) | ((i @ X2 @ X3) = $false) | ((j @ sK1 @ (sK13 @ (j @ sK1) @ X1)) = $false) | ((i @ X0 @ X1) = $false)) ) | (~spl0_4 | ~spl0_6 | ~spl0_8)), 1.41/0.68 inference(trivial_inequality_removal,[status(thm)],[f409])). 1.41/0.68 thf(f409,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((j @ sK1 @ (sK13 @ (j @ sK1) @ X3)) = $false) | ($true = $false) | ((j @ sK1 @ (sK13 @ (j @ sK1) @ X1)) = $false) | ((i @ X2 @ X3) = $false) | ((k @ X2 @ sK4) = $false) | ((k @ X0 @ sK4) = $false) | ((i @ X0 @ X1) = $false)) ) | (~spl0_4 | ~spl0_6 | ~spl0_8)), 1.41/0.68 inference(superposition,[status(thm)],[f314,f405])). 1.41/0.68 thf(f405,plain,( 1.41/0.68 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((j @ sK1 @ (sK14 @ X0 @ sK4)) = $false) | ((k @ X2 @ sK4) = $false) | ((i @ X2 @ X1) = $false) | ((X0 @ (sK13 @ X0 @ X1)) = $false)) ) | (~spl0_4 | ~spl0_8)), 1.41/0.68 inference(trivial_inequality_removal,[status(thm)],[f402])). 1.41/0.68 thf(f402,plain,( 1.41/0.68 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((j @ sK1 @ (sK14 @ X0 @ sK4)) = $false) | ((k @ X2 @ sK4) = $false) | ($true = $false) | ((X0 @ (sK13 @ X0 @ X1)) = $false) | ((i @ X2 @ X1) = $false)) ) | (~spl0_4 | ~spl0_8)), 1.41/0.68 inference(superposition,[status(thm)],[f305,f324])). 1.41/0.68 thf(f382,plain,( 1.41/0.68 spl0_17 | spl0_21), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f171,f380,f362])). 1.41/0.68 thf(f171,plain,( 1.41/0.68 ( ! [X1 : $i] : (((l @ sK6 @ X1) = $false) | ($true = (k @ sK3 @ sK4)) | ((sK5 @ X1) = $false)) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f170])). 1.41/0.68 thf(f170,plain,( 1.41/0.68 ( ! [X1 : $i] : (($true = (k @ sK3 @ sK4)) | ((l @ sK6 @ X1) = $false) | ($true = (~ (sK5 @ X1)))) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f169])). 1.41/0.68 thf(f169,plain,( 1.41/0.68 ( ! [X1 : $i] : (($true = (~ (l @ sK6 @ X1))) | ($true = (~ (sK5 @ X1))) | ($true = (k @ sK3 @ sK4))) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f168])). 1.41/0.68 thf(f168,plain,( 1.41/0.68 ( ! [X1 : $i] : (($true = (k @ sK3 @ sK4)) | ($true = ((~ (sK5 @ X1)) | (~ (l @ sK6 @ X1))))) )), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f167])). 1.41/0.68 thf(f167,plain,( 1.41/0.68 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (sK5 @ Y0)) | (~ (l @ sK6 @ Y0)))) @ X1)) | ($true = (k @ sK3 @ sK4))) )), 1.41/0.68 inference(pi_clausification,[status(thm)],[f166])). 1.41/0.68 thf(f166,plain,( 1.41/0.68 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (sK5 @ Y0)) | (~ (l @ sK6 @ Y0)))))) | ($true = (k @ sK3 @ sK4))), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f165])). 1.41/0.68 thf(f165,plain,( 1.41/0.68 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK5 @ Y0)) | (~ (l @ sK6 @ Y0)))))) = $false) | ($true = (k @ sK3 @ sK4))), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f163])). 1.41/0.68 thf(f163,plain,( 1.41/0.68 ($true = (k @ sK3 @ sK4)) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK5 @ Y0)) | (~ (l @ sK6 @ Y0)))))) | (~ (k @ sK2 @ sK6))) = $false)), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f162])). 1.41/0.68 thf(f162,plain,( 1.41/0.68 ($true = (k @ sK3 @ sK4)) | (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK5 @ Y1)) | (~ (l @ Y0 @ Y1)))))) | (~ (k @ sK2 @ Y0)))) @ sK6) = $false)), 1.41/0.68 inference(sigma_clausification,[status(thm)],[f161])). 1.41/0.68 thf(f161,plain,( 1.41/0.68 ($true = (k @ sK3 @ sK4)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK5 @ Y1)) | (~ (l @ Y0 @ Y1)))))) | (~ (k @ sK2 @ Y0))))) = $false)), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f159])). 1.41/0.68 thf(f159,plain,( 1.41/0.68 ($true = (k @ sK3 @ sK4)) | (((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK5 @ Y1)) | (~ (l @ Y0 @ Y1)))))) | (~ (k @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK5 @ Y1) | (~ (j @ Y0 @ Y1)))))) | (~ (i @ sK2 @ Y0)))))) = $false)), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f157])). 1.41/0.68 thf(f157,plain,( 1.41/0.68 ($true = ((k @ sK3 @ sK4) & (i @ sK3 @ sK1))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK5 @ Y1)) | (~ (l @ Y0 @ Y1)))))) | (~ (k @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK5 @ Y1) | (~ (j @ Y0 @ Y1)))))) | (~ (i @ sK2 @ Y0)))))) = $false)), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f156])). 1.41/0.68 thf(f156,plain,( 1.41/0.68 ($true = ((k @ sK3 @ sK4) & (i @ sK3 @ sK1))) | (((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) | (~ (l @ Y1 @ Y2)))))) | (~ (k @ sK2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (j @ Y1 @ Y2)))))) | (~ (i @ sK2 @ Y1))))))) @ sK5) = $false)), 1.41/0.68 inference(sigma_clausification,[status(thm)],[f155])). 1.41/0.68 thf(f155,plain,( 1.41/0.68 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) | (~ (l @ Y1 @ Y2)))))) | (~ (k @ sK2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (j @ Y1 @ Y2)))))) | (~ (i @ sK2 @ Y1)))))))) = $false) | ($true = ((k @ sK3 @ sK4) & (i @ sK3 @ sK1)))), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f153])). 1.41/0.68 thf(f153,plain,( 1.41/0.68 ((((k @ sK3 @ sK4) & (i @ sK3 @ sK1)) => (?? @ $i @ (^[Y0 : $i]: ((j @ sK1 @ Y0) & (l @ sK4 @ Y0))))) = $false) | ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) | (~ (l @ Y1 @ Y2)))))) | (~ (k @ sK2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (j @ Y1 @ Y2)))))) | (~ (i @ sK2 @ Y1)))))))) = $false)), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f152])). 1.41/0.68 thf(f152,plain,( 1.41/0.68 (((^[Y0 : $i]: (((k @ sK3 @ Y0) & (i @ sK3 @ sK1)) => (?? @ $i @ (^[Y1 : $i]: ((j @ sK1 @ Y1) & (l @ Y0 @ Y1)))))) @ sK4) = $false) | ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) | (~ (l @ Y1 @ Y2)))))) | (~ (k @ sK2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (j @ Y1 @ Y2)))))) | (~ (i @ sK2 @ Y1)))))))) = $false)), 1.41/0.68 inference(sigma_clausification,[status(thm)],[f151])). 1.41/0.68 thf(f151,plain,( 1.41/0.68 ((!! @ $i @ (^[Y0 : $i]: (((k @ sK3 @ Y0) & (i @ sK3 @ sK1)) => (?? @ $i @ (^[Y1 : $i]: ((j @ sK1 @ Y1) & (l @ Y0 @ Y1))))))) = $false) | ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) | (~ (l @ Y1 @ Y2)))))) | (~ (k @ sK2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (j @ Y1 @ Y2)))))) | (~ (i @ sK2 @ Y1)))))))) = $false)), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f150])). 1.41/0.68 thf(f150,plain,( 1.41/0.68 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((k @ Y0 @ Y1) & (i @ Y0 @ sK1)) => (?? @ $i @ (^[Y2 : $i]: ((j @ sK1 @ Y2) & (l @ Y1 @ Y2)))))))) @ sK3) = $false) | ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) | (~ (l @ Y1 @ Y2)))))) | (~ (k @ sK2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (j @ Y1 @ Y2)))))) | (~ (i @ sK2 @ Y1)))))))) = $false)), 1.41/0.68 inference(sigma_clausification,[status(thm)],[f149])). 1.41/0.68 thf(f149,plain,( 1.41/0.68 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((k @ Y0 @ Y1) & (i @ Y0 @ sK1)) => (?? @ $i @ (^[Y2 : $i]: ((j @ sK1 @ Y2) & (l @ Y1 @ Y2))))))))) = $false) | ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) | (~ (l @ Y1 @ Y2)))))) | (~ (k @ sK2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (j @ Y1 @ Y2)))))) | (~ (i @ sK2 @ Y1)))))))) = $false)), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f148])). 1.41/0.68 thf(f148,plain,( 1.41/0.68 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((k @ Y0 @ Y1) & (i @ Y0 @ sK1)) => (?? @ $i @ (^[Y2 : $i]: ((j @ sK1 @ Y2) & (l @ Y1 @ Y2))))))))) = $false) | (((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (l @ Y2 @ Y3)))))) | (~ (k @ Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (j @ Y2 @ Y3)))))) | (~ (i @ Y0 @ Y2))))))))) @ sK2) = $false)), 1.41/0.68 inference(sigma_clausification,[status(thm)],[f147])). 1.41/0.68 thf(f147,plain,( 1.41/0.68 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (l @ Y2 @ Y3)))))) | (~ (k @ Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (j @ Y2 @ Y3)))))) | (~ (i @ Y0 @ Y2)))))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((k @ Y0 @ Y1) & (i @ Y0 @ sK1)) => (?? @ $i @ (^[Y2 : $i]: ((j @ sK1 @ Y2) & (l @ Y1 @ Y2))))))))) = $false)), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f146])). 1.41/0.68 thf(f146,plain,( 1.41/0.68 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((k @ Y1 @ Y2) & (i @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((j @ Y0 @ Y3) & (l @ Y2 @ Y3)))))))))) @ sK1) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (l @ Y2 @ Y3)))))) | (~ (k @ Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (j @ Y2 @ Y3)))))) | (~ (i @ Y0 @ Y2)))))))))) = $false)), 1.41/0.68 inference(sigma_clausification,[status(thm)],[f145])). 1.41/0.68 thf(f145,plain,( 1.41/0.68 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((k @ Y1 @ Y2) & (i @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((j @ Y0 @ Y3) & (l @ Y2 @ Y3))))))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (l @ Y2 @ Y3)))))) | (~ (k @ Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (j @ Y2 @ Y3)))))) | (~ (i @ Y0 @ Y2)))))))))) = $false)), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f143])). 1.41/0.68 thf(f143,plain,( 1.41/0.68 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((k @ Y1 @ Y2) & (i @ Y1 @ Y0)) => (?? 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[X4 : $i,X5 : $i,X6 : $i] : (((X0 @ X5 @ X6) & (X2 @ X5 @ X4)) => ? [X7 : $i] : ((X3 @ X4 @ X7) & (X1 @ X6 @ X7))))) = confluence)), 1.41/0.68 inference(rectify,[status(thm)],[f32])). 1.41/0.68 thf(f32,axiom,( 1.41/0.68 ((^[X11 : $i > $i > $o, X12 : $i > $i > $o, X13 : $i > $i > $o, X14 : $i > $i > $o] : (! [X17 : $i,X15 : $i,X16 : $i] : (((X11 @ X15 @ X16) & (X13 @ X15 @ X17)) => ? [X18 : $i] : ((X14 @ X17 @ X18) & (X12 @ X16 @ X18))))) = confluence)), 1.41/0.68 file('/export/starexec/sandbox2/tmp/tmp.ChJweH4qDA/E---3.1_2816099.p',confluence)). 1.41/0.68 thf(f116,plain,( 1.41/0.68 ((confluence @ i @ j @ k @ l) != (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mdia @ i @ (mbox @ j @ Y0)) @ (mbox @ k @ (mdia @ l @ Y0)))))))), 1.41/0.68 inference(cnf_transformation,[status(thm)],[f98])). 1.41/0.68 thf(f98,plain,( 1.41/0.68 ((confluence @ i @ j @ k @ l) != (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mdia @ i @ (mbox @ j @ Y0)) @ (mbox @ k @ (mdia @ l @ Y0)))))))), 1.41/0.68 inference(flattening,[status(thm)],[f91])). 1.41/0.68 thf(f91,plain,( 1.41/0.68 ~((confluence @ i @ j @ k @ l) = (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mdia @ i @ (mbox @ j @ Y0)) @ (mbox @ k @ (mdia @ l @ Y0)))))))), 1.41/0.68 inference(fool_elimination,[status(thm)],[f90])). 1.41/0.68 thf(f90,plain,( 1.41/0.68 ~((mvalid @ (mforall_prop @ (^[X0 : $i > $o] : (mimplies @ (mdia @ i @ (mbox @ j @ X0)) @ (mbox @ k @ (mdia @ l @ X0)))))) <=> (confluence @ i @ j @ k @ l))), 1.41/0.68 inference(rectify,[status(thm)],[f34])). 1.41/0.68 thf(f34,negated_conjecture,( 1.41/0.68 ~((mvalid @ (mforall_prop @ (^[X5 : $i > $o] : (mimplies @ (mdia @ i @ (mbox @ j @ X5)) @ (mbox @ k @ (mdia @ l @ X5)))))) <=> (confluence @ i @ j @ k @ l))), 1.41/0.68 inference(negated_conjecture,[status(cth)],[f33])). 1.41/0.68 thf(f33,conjecture,( 1.41/0.68 (mvalid @ (mforall_prop @ (^[X5 : $i > $o] : (mimplies @ (mdia @ i @ (mbox @ j @ X5)) @ (mbox @ k @ (mdia @ l @ X5)))))) <=> (confluence @ i @ j @ k @ l)), 1.41/0.68 file('/export/starexec/sandbox2/tmp/tmp.ChJweH4qDA/E---3.1_2816099.p',conj)). 1.41/0.68 thf(f378,plain,( 1.41/0.68 spl0_17 | spl0_20), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f172,f375,f362])). 1.41/0.68 thf(f172,plain,( 1.41/0.68 ($true = (k @ sK3 @ sK4)) | ($true = (k @ sK2 @ sK6))), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f164])). 1.41/0.68 thf(f164,plain,( 1.41/0.68 ((~ (k @ sK2 @ sK6)) = $false) | ($true = (k @ sK3 @ sK4))), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f163])). 1.41/0.68 thf(f373,plain,( 1.41/0.68 spl0_19 | spl0_17), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f181,f362,f371])). 1.41/0.68 thf(f181,plain,( 1.41/0.68 ( ! [X1 : $i] : (($true = (k @ sK3 @ sK4)) | ($true = (sK5 @ X1)) | ((j @ sK7 @ X1) = $false)) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f180])). 1.41/0.68 thf(f180,plain,( 1.41/0.68 ( ! [X1 : $i] : (($true = (sK5 @ X1)) | ($true = (k @ sK3 @ sK4)) | ($true = (~ (j @ sK7 @ X1)))) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f179])). 1.41/0.68 thf(f179,plain,( 1.41/0.68 ( ! [X1 : $i] : (($true = (k @ sK3 @ sK4)) | ($true = ((sK5 @ X1) | (~ (j @ sK7 @ X1))))) )), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f178])). 1.41/0.68 thf(f178,plain,( 1.41/0.68 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((sK5 @ Y0) | (~ (j @ sK7 @ Y0)))) @ X1)) | ($true = (k @ sK3 @ sK4))) )), 1.41/0.68 inference(pi_clausification,[status(thm)],[f177])). 1.41/0.68 thf(f177,plain,( 1.41/0.68 ($true = (k @ sK3 @ sK4)) | ((!! @ $i @ (^[Y0 : $i]: ((sK5 @ Y0) | (~ (j @ sK7 @ Y0))))) = $true)), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f176])). 1.41/0.68 thf(f176,plain,( 1.41/0.68 ($true = (k @ sK3 @ sK4)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK5 @ Y0) | (~ (j @ sK7 @ Y0)))))) = $false)), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f174])). 1.41/0.68 thf(f174,plain,( 1.41/0.68 ($true = (k @ sK3 @ sK4)) | (((~ (!! @ $i @ (^[Y0 : $i]: ((sK5 @ Y0) | (~ (j @ sK7 @ Y0)))))) | (~ (i @ sK2 @ sK7))) = $false)), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f173])). 1.41/0.68 thf(f173,plain,( 1.41/0.68 ($true = (k @ sK3 @ sK4)) | (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK5 @ Y1) | (~ (j @ Y0 @ Y1)))))) | (~ (i @ sK2 @ Y0)))) @ sK7) = $false)), 1.41/0.68 inference(sigma_clausification,[status(thm)],[f160])). 1.41/0.68 thf(f160,plain,( 1.41/0.68 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK5 @ Y1) | (~ (j @ Y0 @ Y1)))))) | (~ (i @ sK2 @ Y0))))) = $false) | ($true = (k @ sK3 @ sK4))), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f159])). 1.41/0.68 thf(f369,plain,( 1.41/0.68 spl0_17 | spl0_18), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f182,f366,f362])). 1.41/0.68 thf(f182,plain,( 1.41/0.68 ($true = (i @ sK2 @ sK7)) | ($true = (k @ sK3 @ sK4))), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f175])). 1.41/0.68 thf(f175,plain,( 1.41/0.68 ($true = (k @ sK3 @ sK4)) | ((~ (i @ sK2 @ sK7)) = $false)), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f174])). 1.41/0.68 thf(f360,plain,( 1.41/0.68 spl0_12 | spl0_16), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f194,f358,f340])). 1.41/0.68 thf(f194,plain,( 1.41/0.68 ( ! [X1 : $i] : (((sK5 @ X1) = $false) | ((l @ sK8 @ X1) = $false) | ($true = (i @ sK3 @ sK1))) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f193])). 1.41/0.68 thf(f193,plain,( 1.41/0.68 ( ! [X1 : $i] : (($true = (~ (l @ sK8 @ X1))) | ($true = (i @ sK3 @ sK1)) | ((sK5 @ X1) = $false)) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f192])). 1.41/0.68 thf(f192,plain,( 1.41/0.68 ( ! [X1 : $i] : (($true = (~ (sK5 @ X1))) | ($true = (~ (l @ sK8 @ X1))) | ($true = (i @ sK3 @ sK1))) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f191])). 1.41/0.68 thf(f191,plain,( 1.41/0.68 ( ! [X1 : $i] : (($true = (i @ sK3 @ sK1)) | ($true = ((~ (sK5 @ X1)) | (~ (l @ sK8 @ X1))))) )), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f190])). 1.41/0.68 thf(f190,plain,( 1.41/0.68 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (sK5 @ Y0)) | (~ (l @ sK8 @ Y0)))) @ X1)) | ($true = (i @ sK3 @ sK1))) )), 1.41/0.68 inference(pi_clausification,[status(thm)],[f189])). 1.41/0.68 thf(f189,plain,( 1.41/0.68 ($true = (i @ sK3 @ sK1)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (sK5 @ Y0)) | (~ (l @ sK8 @ Y0))))))), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f188])). 1.41/0.68 thf(f188,plain,( 1.41/0.68 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK5 @ Y0)) | (~ (l @ sK8 @ Y0)))))) = $false) | ($true = (i @ sK3 @ sK1))), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f186])). 1.41/0.68 thf(f186,plain,( 1.41/0.68 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK5 @ Y0)) | (~ (l @ sK8 @ Y0)))))) | (~ (k @ sK2 @ sK8))) = $false) | ($true = (i @ sK3 @ sK1))), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f185])). 1.41/0.68 thf(f185,plain,( 1.41/0.68 (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK5 @ Y1)) | (~ (l @ Y0 @ Y1)))))) | (~ (k @ sK2 @ Y0)))) @ sK8) = $false) | ($true = (i @ sK3 @ sK1))), 1.41/0.68 inference(sigma_clausification,[status(thm)],[f184])). 1.41/0.68 thf(f184,plain,( 1.41/0.68 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK5 @ Y1)) | (~ (l @ Y0 @ Y1)))))) | (~ (k @ sK2 @ Y0))))) = $false) | ($true = (i @ sK3 @ sK1))), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f158])). 1.41/0.68 thf(f158,plain,( 1.41/0.68 ($true = (i @ sK3 @ sK1)) | (((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK5 @ Y1)) | (~ (l @ Y0 @ Y1)))))) | (~ (k @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK5 @ Y1) | (~ (j @ Y0 @ Y1)))))) | (~ (i @ sK2 @ Y0)))))) = $false)), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f157])). 1.41/0.68 thf(f356,plain,( 1.41/0.68 spl0_15 | spl0_12), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f195,f340,f353])). 1.41/0.68 thf(f195,plain,( 1.41/0.68 ($true = (k @ sK2 @ sK8)) | ($true = (i @ sK3 @ sK1))), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f187])). 1.41/0.68 thf(f187,plain,( 1.41/0.68 ($true = (i @ sK3 @ sK1)) | ((~ (k @ sK2 @ sK8)) = $false)), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f186])). 1.41/0.68 thf(f351,plain,( 1.41/0.68 spl0_12 | spl0_14), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f204,f349,f340])). 1.41/0.68 thf(f204,plain,( 1.41/0.68 ( ! [X1 : $i] : (($true = (sK5 @ X1)) | ((j @ sK9 @ X1) = $false) | ($true = (i @ sK3 @ sK1))) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f203])). 1.41/0.68 thf(f203,plain,( 1.41/0.68 ( ! [X1 : $i] : (($true = (i @ sK3 @ sK1)) | ($true = (~ (j @ sK9 @ X1))) | ($true = (sK5 @ X1))) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f202])). 1.41/0.68 thf(f202,plain,( 1.41/0.68 ( ! [X1 : $i] : (($true = (i @ sK3 @ sK1)) | ($true = ((sK5 @ X1) | (~ (j @ sK9 @ X1))))) )), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f201])). 1.41/0.68 thf(f201,plain,( 1.41/0.68 ( ! [X1 : $i] : (($true = (i @ sK3 @ sK1)) | ($true = ((^[Y0 : $i]: ((sK5 @ Y0) | (~ (j @ sK9 @ Y0)))) @ X1))) )), 1.41/0.68 inference(pi_clausification,[status(thm)],[f200])). 1.41/0.68 thf(f200,plain,( 1.41/0.68 ($true = (!! @ $i @ (^[Y0 : $i]: ((sK5 @ Y0) | (~ (j @ sK9 @ Y0)))))) | ($true = (i @ sK3 @ sK1))), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f199])). 1.41/0.68 thf(f199,plain,( 1.41/0.68 ($true = (i @ sK3 @ sK1)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK5 @ Y0) | (~ (j @ sK9 @ Y0)))))) = $false)), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f197])). 1.41/0.68 thf(f197,plain,( 1.41/0.68 ($true = (i @ sK3 @ sK1)) | (((~ (!! @ $i @ (^[Y0 : $i]: ((sK5 @ Y0) | (~ (j @ sK9 @ Y0)))))) | (~ (i @ sK2 @ sK9))) = $false)), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f196])). 1.41/0.68 thf(f196,plain,( 1.41/0.68 ($true = (i @ sK3 @ sK1)) | (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK5 @ Y1) | (~ (j @ Y0 @ Y1)))))) | (~ (i @ sK2 @ Y0)))) @ sK9) = $false)), 1.41/0.68 inference(sigma_clausification,[status(thm)],[f183])). 1.41/0.68 thf(f183,plain,( 1.41/0.68 ($true = (i @ sK3 @ sK1)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK5 @ Y1) | (~ (j @ Y0 @ Y1)))))) | (~ (i @ sK2 @ Y0))))) = $false)), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f158])). 1.41/0.68 thf(f347,plain,( 1.41/0.68 spl0_12 | spl0_13), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f205,f344,f340])). 1.41/0.68 thf(f205,plain,( 1.41/0.68 ($true = (i @ sK2 @ sK9)) | ($true = (i @ sK3 @ sK1))), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f198])). 1.41/0.68 thf(f198,plain,( 1.41/0.68 ($true = (i @ sK3 @ sK1)) | ((~ (i @ sK2 @ sK9)) = $false)), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f197])). 1.41/0.68 thf(f338,plain,( 1.41/0.68 spl0_11 | spl0_8), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f222,f323,f336])). 1.41/0.68 thf(f222,plain,( 1.41/0.68 ( ! [X2 : $i,X1 : $i] : (((l @ sK4 @ X1) = $false) | ((l @ sK11 @ X2) = $false) | ((sK10 @ X2) = $false) | ((j @ sK1 @ X1) = $false)) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f221])). 1.41/0.68 thf(f221,plain,( 1.41/0.68 ( ! [X2 : $i,X1 : $i] : (($true = (~ (l @ sK11 @ X2))) | ((sK10 @ X2) = $false) | ((l @ sK4 @ X1) = $false) | ((j @ sK1 @ X1) = $false)) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f220])). 1.41/0.68 thf(f220,plain,( 1.41/0.68 ( ! [X2 : $i,X1 : $i] : (((l @ sK4 @ X1) = $false) | ($true = (~ (sK10 @ X2))) | ($true = (~ (l @ sK11 @ X2))) | ((j @ sK1 @ X1) = $false)) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f219])). 1.41/0.68 thf(f219,plain,( 1.41/0.68 ( ! [X2 : $i,X1 : $i] : (((l @ sK4 @ X1) = $false) | ((j @ sK1 @ X1) = $false) | ($true = ((~ (sK10 @ X2)) | (~ (l @ sK11 @ X2))))) )), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f218])). 1.41/0.68 thf(f218,plain,( 1.41/0.68 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (sK10 @ Y0)) | (~ (l @ sK11 @ Y0)))) @ X2)) | ((j @ sK1 @ X1) = $false) | ((l @ sK4 @ X1) = $false)) )), 1.41/0.68 inference(pi_clausification,[status(thm)],[f217])). 1.41/0.68 thf(f217,plain,( 1.41/0.68 ( ! [X1 : $i] : (((l @ sK4 @ X1) = $false) | ((j @ sK1 @ X1) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (sK10 @ Y0)) | (~ (l @ sK11 @ Y0))))))) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f216])). 1.41/0.68 thf(f216,plain,( 1.41/0.68 ( ! [X1 : $i] : (((j @ sK1 @ X1) = $false) | ((l @ sK4 @ X1) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK10 @ Y0)) | (~ (l @ sK11 @ Y0)))))) = $false)) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f214])). 1.41/0.68 thf(f214,plain,( 1.41/0.68 ( ! [X1 : $i] : (((j @ sK1 @ X1) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK10 @ Y0)) | (~ (l @ sK11 @ Y0)))))) | (~ (k @ sK2 @ sK11))) = $false) | ((l @ sK4 @ X1) = $false)) )), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f213])). 1.41/0.68 thf(f213,plain,( 1.41/0.68 ( ! [X1 : $i] : (((l @ sK4 @ X1) = $false) | ((j @ sK1 @ X1) = $false) | (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK10 @ Y1)) | (~ (l @ Y0 @ Y1)))))) | (~ (k @ sK2 @ Y0)))) @ sK11) = $false)) )), 1.41/0.68 inference(sigma_clausification,[status(thm)],[f212])). 1.41/0.68 thf(f212,plain,( 1.41/0.68 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK10 @ Y1)) | (~ (l @ Y0 @ Y1)))))) | (~ (k @ sK2 @ Y0))))) = $false) | ((j @ sK1 @ X1) = $false) | ((l @ sK4 @ X1) = $false)) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f210])). 1.41/0.68 thf(f210,plain,( 1.41/0.68 ( ! [X1 : $i] : (((l @ sK4 @ X1) = $false) | ((j @ sK1 @ X1) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK10 @ Y1)) | (~ (l @ Y0 @ Y1)))))) | (~ (k @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK10 @ Y1) | (~ (j @ Y0 @ Y1)))))) | (~ (i @ sK2 @ Y0)))))) = $false)) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f209])). 1.41/0.68 thf(f209,plain,( 1.41/0.68 ( ! [X1 : $i] : ((((j @ sK1 @ X1) & (l @ sK4 @ X1)) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK10 @ Y1)) | (~ (l @ Y0 @ Y1)))))) | (~ (k @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK10 @ Y1) | (~ (j @ Y0 @ Y1)))))) | (~ (i @ sK2 @ Y0)))))) = $false)) )), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f208])). 1.41/0.68 thf(f208,plain,( 1.41/0.68 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((j @ sK1 @ Y0) & (l @ sK4 @ Y0))) @ X1) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK10 @ Y1)) | (~ (l @ Y0 @ Y1)))))) | (~ (k @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK10 @ Y1) | (~ (j @ Y0 @ Y1)))))) | (~ (i @ sK2 @ Y0)))))) = $false)) )), 1.41/0.68 inference(pi_clausification,[status(thm)],[f207])). 1.41/0.68 thf(f207,plain,( 1.41/0.68 ((?? @ $i @ (^[Y0 : $i]: ((j @ sK1 @ Y0) & (l @ sK4 @ Y0)))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK10 @ Y1)) | (~ (l @ Y0 @ Y1)))))) | (~ (k @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK10 @ Y1) | (~ (j @ Y0 @ Y1)))))) | (~ (i @ sK2 @ Y0)))))) = $false)), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f206])). 1.41/0.68 thf(f206,plain,( 1.41/0.68 (((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) | (~ (l @ Y1 @ Y2)))))) | (~ (k @ sK2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (j @ Y1 @ Y2)))))) | (~ (i @ sK2 @ Y1))))))) @ sK10) = $false) | ((?? @ $i @ (^[Y0 : $i]: ((j @ sK1 @ Y0) & (l @ sK4 @ Y0)))) = $false)), 1.41/0.68 inference(sigma_clausification,[status(thm)],[f154])). 1.41/0.68 thf(f154,plain,( 1.41/0.68 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) | (~ (l @ Y1 @ Y2)))))) | (~ (k @ sK2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (j @ Y1 @ Y2)))))) | (~ (i @ sK2 @ Y1)))))))) = $false) | ((?? @ $i @ (^[Y0 : $i]: ((j @ sK1 @ Y0) & (l @ sK4 @ Y0)))) = $false)), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f153])). 1.41/0.68 thf(f334,plain,( 1.41/0.68 spl0_8 | spl0_10), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f223,f331,f323])). 1.41/0.68 thf(f223,plain,( 1.41/0.68 ( ! [X1 : $i] : (((j @ sK1 @ X1) = $false) | ((l @ sK4 @ X1) = $false) | ($true = (k @ sK2 @ sK11))) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f215])). 1.41/0.68 thf(f215,plain,( 1.41/0.68 ( ! [X1 : $i] : (((j @ sK1 @ X1) = $false) | ((l @ sK4 @ X1) = $false) | ((~ (k @ sK2 @ sK11)) = $false)) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f214])). 1.41/0.68 thf(f329,plain,( 1.41/0.68 spl0_9 | spl0_8), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f232,f323,f327])). 1.41/0.68 thf(f232,plain,( 1.41/0.68 ( ! [X2 : $i,X1 : $i] : (((l @ sK4 @ X1) = $false) | ($true = (sK10 @ X2)) | ((j @ sK12 @ X2) = $false) | ((j @ sK1 @ X1) = $false)) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f231])). 1.41/0.68 thf(f231,plain,( 1.41/0.68 ( ! [X2 : $i,X1 : $i] : (((l @ sK4 @ X1) = $false) | ($true = (~ (j @ sK12 @ X2))) | ((j @ sK1 @ X1) = $false) | ($true = (sK10 @ X2))) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f230])). 1.41/0.68 thf(f230,plain,( 1.41/0.68 ( ! [X2 : $i,X1 : $i] : (((l @ sK4 @ X1) = $false) | ((j @ sK1 @ X1) = $false) | ($true = ((sK10 @ X2) | (~ (j @ sK12 @ X2))))) )), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f229])). 1.41/0.68 thf(f229,plain,( 1.41/0.68 ( ! [X2 : $i,X1 : $i] : (((j @ sK1 @ X1) = $false) | ($true = ((^[Y0 : $i]: ((sK10 @ Y0) | (~ (j @ sK12 @ Y0)))) @ X2)) | ((l @ sK4 @ X1) = $false)) )), 1.41/0.68 inference(pi_clausification,[status(thm)],[f228])). 1.41/0.68 thf(f228,plain,( 1.41/0.68 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((sK10 @ Y0) | (~ (j @ sK12 @ Y0)))))) | ((j @ sK1 @ X1) = $false) | ((l @ sK4 @ X1) = $false)) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f227])). 1.41/0.68 thf(f227,plain,( 1.41/0.68 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((sK10 @ Y0) | (~ (j @ sK12 @ Y0)))))) = $false) | ((j @ sK1 @ X1) = $false) | ((l @ sK4 @ X1) = $false)) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f225])). 1.41/0.68 thf(f225,plain,( 1.41/0.68 ( ! [X1 : $i] : (((l @ sK4 @ X1) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((sK10 @ Y0) | (~ (j @ sK12 @ Y0)))))) | (~ (i @ sK2 @ sK12))) = $false) | ((j @ sK1 @ X1) = $false)) )), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f224])). 1.41/0.68 thf(f224,plain,( 1.41/0.68 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK10 @ Y1) | (~ (j @ Y0 @ Y1)))))) | (~ (i @ sK2 @ Y0)))) @ sK12) = $false) | ((l @ sK4 @ X1) = $false) | ((j @ sK1 @ X1) = $false)) )), 1.41/0.68 inference(sigma_clausification,[status(thm)],[f211])). 1.41/0.68 thf(f211,plain,( 1.41/0.68 ( ! [X1 : $i] : (((l @ sK4 @ X1) = $false) | ((j @ sK1 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK10 @ Y1) | (~ (j @ Y0 @ Y1)))))) | (~ (i @ sK2 @ Y0))))) = $false)) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f210])). 1.41/0.68 thf(f325,plain,( 1.41/0.68 spl0_7 | spl0_8), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f233,f323,f319])). 1.41/0.68 thf(f233,plain,( 1.41/0.68 ( ! [X1 : $i] : (($true = (i @ sK2 @ sK12)) | ((j @ sK1 @ X1) = $false) | ((l @ sK4 @ X1) = $false)) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f226])). 1.41/0.68 thf(f226,plain,( 1.41/0.68 ( ! [X1 : $i] : (((l @ sK4 @ X1) = $false) | ((~ (i @ sK2 @ sK12)) = $false) | ((j @ sK1 @ X1) = $false)) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f225])). 1.41/0.68 thf(f317,plain,( 1.41/0.68 spl0_3 | spl0_6), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f269,f313,f300])). 1.41/0.68 thf(f269,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((i @ X1 @ X5) = $false) | ((i @ X4 @ X2) = $false) | ((k @ X1 @ X6) = $false) | ((j @ X2 @ (sK15 @ X7 @ X2)) = $true) | ($true = (X3 @ (sK14 @ X3 @ X6))) | ((k @ X4 @ X7) = $false) | ((X3 @ (sK13 @ X3 @ X5)) = $false)) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f268])). 1.41/0.68 thf(f268,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((j @ X2 @ (sK15 @ X7 @ X2)) = $true) | ((k @ X4 @ X7) = $false) | ((X3 @ (sK13 @ X3 @ X5)) = $false) | ((i @ X4 @ X2) = $false) | ((i @ X1 @ X5) = $false) | ((~ (X3 @ (sK14 @ X3 @ X6))) = $false) | ((k @ X1 @ X6) = $false)) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f266])). 1.41/0.68 thf(f266,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((k @ X4 @ X7) = $false) | ((i @ X4 @ X2) = $false) | (((X3 @ (sK13 @ X3 @ X5)) | (~ (j @ X5 @ (sK13 @ X3 @ X5)))) = $false) | ((k @ X1 @ X6) = $false) | ((j @ X2 @ (sK15 @ X7 @ X2)) = $true) | ((~ (X3 @ (sK14 @ X3 @ X6))) = $false) | ((i @ X1 @ X5) = $false)) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f265])). 1.41/0.68 thf(f265,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((j @ X2 @ (sK15 @ X7 @ X2)) = $true) | ($true = (~ (k @ X1 @ X6))) | ((i @ X4 @ X2) = $false) | ((i @ X1 @ X5) = $false) | ((k @ X4 @ X7) = $false) | (((X3 @ (sK13 @ X3 @ X5)) | (~ (j @ X5 @ (sK13 @ X3 @ X5)))) = $false) | ((~ (X3 @ (sK14 @ X3 @ X6))) = $false)) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f263])). 1.41/0.68 thf(f263,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((i @ X4 @ X2) = $false) | ($true = ((j @ X2 @ (sK15 @ X7 @ X2)) & (l @ X7 @ (sK15 @ X7 @ X2)))) | ((i @ X1 @ X5) = $false) | (((X3 @ (sK13 @ X3 @ X5)) | (~ (j @ X5 @ (sK13 @ X3 @ X5)))) = $false) | ((~ (X3 @ (sK14 @ X3 @ X6))) = $false) | ($true = (~ (k @ X1 @ X6))) | ((k @ X4 @ X7) = $false)) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f261])). 1.41/0.68 thf(f261,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((~ (X3 @ (sK14 @ X3 @ X6))) | (~ (l @ X6 @ (sK14 @ X3 @ X6)))) = $false) | ($true = (~ (k @ X1 @ X6))) | ((i @ X4 @ X2) = $false) | ((i @ X1 @ X5) = $false) | (((X3 @ (sK13 @ X3 @ X5)) | (~ (j @ X5 @ (sK13 @ X3 @ X5)))) = $false) | ($true = ((j @ X2 @ (sK15 @ X7 @ X2)) & (l @ X7 @ (sK15 @ X7 @ X2)))) | ((k @ X4 @ X7) = $false)) )), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f260])). 1.41/0.68 thf(f260,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((i @ X4 @ X2) = $false) | ($true = ((^[Y0 : $i]: ((j @ X2 @ Y0) & (l @ X7 @ Y0))) @ (sK15 @ X7 @ X2))) | (((X3 @ (sK13 @ X3 @ X5)) | (~ (j @ X5 @ (sK13 @ X3 @ X5)))) = $false) | (((~ (X3 @ (sK14 @ X3 @ X6))) | (~ (l @ X6 @ (sK14 @ X3 @ X6)))) = $false) | ((i @ X1 @ X5) = $false) | ((k @ X4 @ X7) = $false) | ($true = (~ (k @ X1 @ X6)))) )), 1.41/0.68 inference(sigma_clausification,[status(thm)],[f259])). 1.41/0.68 thf(f259,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((i @ X4 @ X2) = $false) | ((k @ X4 @ X7) = $false) | ((i @ X1 @ X5) = $false) | ($true = (?? @ $i @ (^[Y0 : $i]: ((j @ X2 @ Y0) & (l @ X7 @ Y0))))) | ($true = (~ (k @ X1 @ X6))) | (((~ (X3 @ (sK14 @ X3 @ X6))) | (~ (l @ X6 @ (sK14 @ X3 @ X6)))) = $false) | (((X3 @ (sK13 @ X3 @ X5)) | (~ (j @ X5 @ (sK13 @ X3 @ X5)))) = $false)) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f258])). 1.41/0.68 thf(f258,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((i @ X1 @ X5) = $false) | (((k @ X4 @ X7) & (i @ X4 @ X2)) = $false) | ($true = (?? @ $i @ (^[Y0 : $i]: ((j @ X2 @ Y0) & (l @ X7 @ Y0))))) | ($true = (~ (k @ X1 @ X6))) | (((X3 @ (sK13 @ X3 @ X5)) | (~ (j @ X5 @ (sK13 @ X3 @ X5)))) = $false) | (((~ (X3 @ (sK14 @ X3 @ X6))) | (~ (l @ X6 @ (sK14 @ X3 @ X6)))) = $false)) )), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f257])). 1.41/0.68 thf(f257,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (~ (k @ X1 @ X6))) | ((i @ X1 @ X5) = $false) | (((k @ X4 @ X7) & (i @ X4 @ X2)) = $false) | (((X3 @ (sK13 @ X3 @ X5)) | (~ (j @ X5 @ (sK13 @ X3 @ X5)))) = $false) | (((^[Y0 : $i]: ((~ (X3 @ Y0)) | (~ (l @ X6 @ Y0)))) @ (sK14 @ X3 @ X6)) = $false) | ($true = (?? @ $i @ (^[Y0 : $i]: ((j @ X2 @ Y0) & (l @ X7 @ Y0)))))) )), 1.41/0.68 inference(sigma_clausification,[status(thm)],[f256])). 1.41/0.68 thf(f256,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (X3 @ Y0)) | (~ (l @ X6 @ Y0))))) = $false) | (((k @ X4 @ X7) & (i @ X4 @ X2)) = $false) | ($true = (~ (k @ X1 @ X6))) | ($true = (?? @ $i @ (^[Y0 : $i]: ((j @ X2 @ Y0) & (l @ X7 @ Y0))))) | ((i @ X1 @ X5) = $false) | (((X3 @ (sK13 @ X3 @ X5)) | (~ (j @ X5 @ (sK13 @ X3 @ X5)))) = $false)) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f255])). 1.41/0.68 thf(f255,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (X3 @ Y0)) | (~ (l @ X6 @ Y0))))))) | ((i @ X1 @ X5) = $false) | (((k @ X4 @ X7) & (i @ X4 @ X2)) = $false) | ($true = (?? @ $i @ (^[Y0 : $i]: ((j @ X2 @ Y0) & (l @ X7 @ Y0))))) | (((X3 @ (sK13 @ X3 @ X5)) | (~ (j @ X5 @ (sK13 @ X3 @ X5)))) = $false) | ($true = (~ (k @ X1 @ X6)))) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f254])). 1.41/0.68 thf(f254,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (((k @ X4 @ X7) & (i @ X4 @ X2)) => (?? @ $i @ (^[Y0 : $i]: ((j @ X2 @ Y0) & (l @ X7 @ Y0)))))) | ($true = (~ (k @ X1 @ X6))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (X3 @ Y0)) | (~ (l @ X6 @ Y0))))))) | (((X3 @ (sK13 @ X3 @ X5)) | (~ (j @ X5 @ (sK13 @ X3 @ X5)))) = $false) | ((i @ X1 @ X5) = $false)) )), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f253])). 1.41/0.68 thf(f253,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((i @ X1 @ X5) = $false) | (((^[Y0 : $i]: ((X3 @ Y0) | (~ (j @ X5 @ Y0)))) @ (sK13 @ X3 @ X5)) = $false) | ($true = (~ (k @ X1 @ X6))) | ($true = (((k @ X4 @ X7) & (i @ X4 @ X2)) => (?? @ $i @ (^[Y0 : $i]: ((j @ X2 @ Y0) & (l @ X7 @ Y0)))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (X3 @ Y0)) | (~ (l @ X6 @ Y0)))))))) )), 1.41/0.68 inference(sigma_clausification,[status(thm)],[f252])). 1.41/0.68 thf(f252,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (j @ X5 @ Y0))))) = $false) | ($true = (~ (k @ X1 @ X6))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (X3 @ Y0)) | (~ (l @ X6 @ Y0))))))) | ($true = (((k @ X4 @ X7) & (i @ X4 @ X2)) => (?? @ $i @ (^[Y0 : $i]: ((j @ X2 @ Y0) & (l @ X7 @ Y0)))))) | ((i @ X1 @ X5) = $false)) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f251])). 1.41/0.68 thf(f251,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (j @ X5 @ Y0))))))) | ($true = (~ (k @ X1 @ X6))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (X3 @ Y0)) | (~ (l @ X6 @ Y0))))))) | ((i @ X1 @ X5) = $false) | ($true = (((k @ X4 @ X7) & (i @ X4 @ X2)) => (?? @ $i @ (^[Y0 : $i]: ((j @ X2 @ Y0) & (l @ X7 @ Y0))))))) )), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f250])). 1.41/0.68 thf(f250,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (X3 @ Y0)) | (~ (l @ X6 @ Y0))))))) | ((i @ X1 @ X5) = $false) | ($true = (~ (k @ X1 @ X6))) | ($true = ((^[Y0 : $i]: (((k @ X4 @ Y0) & (i @ X4 @ X2)) => (?? @ $i @ (^[Y1 : $i]: ((j @ X2 @ Y1) & (l @ Y0 @ Y1)))))) @ X7)) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (j @ X5 @ Y0)))))))) )), 1.41/0.68 inference(pi_clausification,[status(thm)],[f249])). 1.41/0.68 thf(f249,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((k @ X4 @ Y0) & (i @ X4 @ X2)) => (?? @ $i @ (^[Y1 : $i]: ((j @ X2 @ Y1) & (l @ Y0 @ Y1)))))))) | ($true = (~ (k @ X1 @ X6))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (X3 @ Y0)) | (~ (l @ X6 @ Y0))))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (j @ X5 @ Y0))))))) | ((i @ X1 @ X5) = $false)) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f248])). 1.41/0.68 thf(f248,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (((i @ X1 @ X5) = $false) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (X3 @ Y0)) | (~ (l @ X6 @ Y0)))))) | (~ (k @ X1 @ X6)))) | ($true = (!! @ $i @ (^[Y0 : $i]: (((k @ X4 @ Y0) & (i @ X4 @ X2)) => (?? @ $i @ (^[Y1 : $i]: ((j @ X2 @ Y1) & (l @ Y0 @ Y1)))))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (j @ X5 @ Y0)))))))) )), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f247])). 1.41/0.68 thf(f247,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (((i @ X1 @ X5) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (j @ X5 @ Y0))))))) | ($true = ((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (X3 @ Y1)) | (~ (l @ Y0 @ Y1)))))) | (~ (k @ X1 @ Y0)))) @ X6)) | ($true = (!! @ $i @ (^[Y0 : $i]: (((k @ X4 @ Y0) & (i @ X4 @ X2)) => (?? @ $i @ (^[Y1 : $i]: ((j @ X2 @ Y1) & (l @ Y0 @ Y1))))))))) )), 1.41/0.68 inference(pi_clausification,[status(thm)],[f246])). 1.41/0.68 thf(f246,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X4 : $i,X5 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (X3 @ Y1)) | (~ (l @ Y0 @ Y1)))))) | (~ (k @ X1 @ Y0)))))) | ((i @ X1 @ X5) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: (((k @ X4 @ Y0) & (i @ X4 @ X2)) => (?? @ $i @ (^[Y1 : $i]: ((j @ X2 @ Y1) & (l @ Y0 @ Y1)))))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (j @ X5 @ Y0)))))))) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f245])). 1.41/0.68 thf(f245,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X4 : $i,X5 : $i] : (($true = (~ (i @ X1 @ X5))) | ($true = (!! @ $i @ (^[Y0 : $i]: (((k @ X4 @ Y0) & (i @ X4 @ X2)) => (?? @ $i @ (^[Y1 : $i]: ((j @ X2 @ Y1) & (l @ Y0 @ Y1)))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (X3 @ Y1)) | (~ (l @ Y0 @ Y1)))))) | (~ (k @ X1 @ Y0)))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (j @ X5 @ Y0)))))))) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f244])). 1.41/0.68 thf(f244,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X4 : $i,X5 : $i] : (($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (j @ X5 @ Y0)))))) | (~ (i @ X1 @ X5)))) | ($true = (!! @ $i @ (^[Y0 : $i]: (((k @ X4 @ Y0) & (i @ X4 @ X2)) => (?? @ $i @ (^[Y1 : $i]: ((j @ X2 @ Y1) & (l @ Y0 @ Y1)))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (X3 @ Y1)) | (~ (l @ Y0 @ Y1)))))) | (~ (k @ X1 @ Y0))))))) )), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f243])). 1.41/0.68 thf(f243,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X4 : $i,X5 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (X3 @ Y1)) | (~ (l @ Y0 @ Y1)))))) | (~ (k @ X1 @ Y0)))))) | ($true = ((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((X3 @ Y1) | (~ (j @ Y0 @ Y1)))))) | (~ (i @ X1 @ Y0)))) @ X5)) | ($true = (!! @ $i @ (^[Y0 : $i]: (((k @ X4 @ Y0) & (i @ X4 @ X2)) => (?? @ $i @ (^[Y1 : $i]: ((j @ X2 @ Y1) & (l @ Y0 @ Y1))))))))) )), 1.41/0.68 inference(pi_clausification,[status(thm)],[f242])). 1.41/0.68 thf(f242,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X4 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((X3 @ Y1) | (~ (j @ Y0 @ Y1)))))) | (~ (i @ X1 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: (((k @ X4 @ Y0) & (i @ X4 @ X2)) => (?? @ $i @ (^[Y1 : $i]: ((j @ X2 @ Y1) & (l @ Y0 @ Y1)))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (X3 @ Y1)) | (~ (l @ Y0 @ Y1)))))) | (~ (k @ X1 @ Y0))))))) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f241])). 1.41/0.68 thf(f241,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X4 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (X3 @ Y1)) | (~ (l @ Y0 @ Y1)))))) | (~ (k @ X1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((X3 @ Y1) | (~ (j @ Y0 @ Y1)))))) | (~ (i @ X1 @ Y0))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: (((k @ X4 @ Y0) & (i @ X4 @ X2)) => (?? @ $i @ (^[Y1 : $i]: ((j @ X2 @ Y1) & (l @ Y0 @ Y1))))))))) )), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f240])). 1.41/0.68 thf(f240,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X4 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (X3 @ Y1)) | (~ (l @ Y0 @ Y1)))))) | (~ (k @ X1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((X3 @ Y1) | (~ (j @ Y0 @ Y1)))))) | (~ (i @ X1 @ Y0))))))) | ($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((k @ Y0 @ Y1) & (i @ Y0 @ X2)) => (?? @ $i @ (^[Y2 : $i]: ((j @ X2 @ Y2) & (l @ Y1 @ Y2)))))))) @ X4))) )), 1.41/0.68 inference(pi_clausification,[status(thm)],[f239])). 1.41/0.68 thf(f239,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((k @ Y0 @ Y1) & (i @ Y0 @ X2)) => (?? @ $i @ (^[Y2 : $i]: ((j @ X2 @ Y2) & (l @ Y1 @ Y2)))))))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (X3 @ Y1)) | (~ (l @ Y0 @ Y1)))))) | (~ (k @ X1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((X3 @ Y1) | (~ (j @ Y0 @ Y1)))))) | (~ (i @ X1 @ Y0)))))))) )), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f238])). 1.41/0.68 thf(f238,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) | (~ (l @ Y1 @ Y2)))))) | (~ (k @ X1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (j @ Y1 @ Y2)))))) | (~ (i @ X1 @ Y1))))))) @ X3)) | ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((k @ Y0 @ Y1) & (i @ Y0 @ X2)) => (?? @ $i @ (^[Y2 : $i]: ((j @ X2 @ Y2) & (l @ Y1 @ Y2))))))))))) )), 1.41/0.68 inference(pi_clausification,[status(thm)],[f237])). 1.41/0.68 thf(f237,plain,( 1.41/0.68 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) | (~ (l @ Y1 @ Y2)))))) | (~ (k @ X1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (j @ Y1 @ Y2)))))) | (~ (i @ X1 @ Y1))))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((k @ Y0 @ Y1) & (i @ Y0 @ X2)) => (?? @ $i @ (^[Y2 : $i]: ((j @ X2 @ Y2) & (l @ Y1 @ Y2))))))))))) )), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f236])). 1.41/0.68 thf(f236,plain,( 1.41/0.68 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) | (~ (l @ Y1 @ Y2)))))) | (~ (k @ X1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (j @ Y1 @ Y2)))))) | (~ (i @ X1 @ Y1))))))))) | ($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((k @ Y1 @ Y2) & (i @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((j @ Y0 @ Y3) & (l @ Y2 @ Y3)))))))))) @ X2))) )), 1.41/0.68 inference(pi_clausification,[status(thm)],[f235])). 1.41/0.68 thf(f235,plain,( 1.41/0.68 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((k @ Y1 @ Y2) & (i @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((j @ Y0 @ Y3) & (l @ Y2 @ Y3)))))))))))) | ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) | (~ (l @ Y1 @ Y2)))))) | (~ (k @ X1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (j @ Y1 @ Y2)))))) | (~ (i @ X1 @ Y1)))))))))) )), 1.41/0.68 inference(beta_eta_normalization,[status(thm)],[f234])). 1.41/0.68 thf(f234,plain,( 1.41/0.68 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (l @ Y2 @ Y3)))))) | (~ (k @ Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (j @ Y2 @ Y3)))))) | (~ (i @ Y0 @ Y2))))))))) @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((k @ Y1 @ Y2) & (i @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((j @ Y0 @ Y3) & (l @ Y2 @ Y3))))))))))))) )), 1.41/0.68 inference(pi_clausification,[status(thm)],[f144])). 1.41/0.68 thf(f144,plain,( 1.41/0.68 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (l @ Y2 @ Y3)))))) | (~ (k @ Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (j @ Y2 @ Y3)))))) | (~ (i @ Y0 @ Y2))))))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((k @ Y1 @ Y2) & (i @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((j @ Y0 @ Y3) & (l @ Y2 @ Y3))))))))))))), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f143])). 1.41/0.68 thf(f316,plain,( 1.41/0.68 spl0_3 | spl0_5), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f271,f309,f300])). 1.41/0.68 thf(f271,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (X3 @ (sK14 @ X3 @ X6))) | ($true = (j @ X5 @ (sK13 @ X3 @ X5))) | ((j @ X2 @ (sK15 @ X7 @ X2)) = $true) | ((k @ X1 @ X6) = $false) | ((i @ X4 @ X2) = $false) | ((k @ X4 @ X7) = $false) | ((i @ X1 @ X5) = $false)) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f270])). 1.41/0.68 thf(f270,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((k @ X4 @ X7) = $false) | ((k @ X1 @ X6) = $false) | ((~ (j @ X5 @ (sK13 @ X3 @ X5))) = $false) | ((i @ X4 @ X2) = $false) | ((j @ X2 @ (sK15 @ X7 @ X2)) = $true) | ((i @ X1 @ X5) = $false) | ($true = (X3 @ (sK14 @ X3 @ X6)))) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f267])). 1.41/0.68 thf(f267,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((i @ X1 @ X5) = $false) | ((~ (X3 @ (sK14 @ X3 @ X6))) = $false) | ((i @ X4 @ X2) = $false) | ((j @ X2 @ (sK15 @ X7 @ X2)) = $true) | ((~ (j @ X5 @ (sK13 @ X3 @ X5))) = $false) | ((k @ X4 @ X7) = $false) | ((k @ X1 @ X6) = $false)) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f266])). 1.41/0.68 thf(f315,plain,( 1.41/0.68 spl0_6 | spl0_1), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f275,f293,f313])). 1.41/0.68 thf(f275,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((k @ X4 @ X7) = $false) | ($true = (l @ X7 @ (sK15 @ X7 @ X2))) | ((X3 @ (sK13 @ X3 @ X5)) = $false) | ((i @ X4 @ X2) = $false) | ($true = (X3 @ (sK14 @ X3 @ X6))) | ((i @ X1 @ X5) = $false) | ((k @ X1 @ X6) = $false)) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f274])). 1.41/0.68 thf(f274,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((X3 @ (sK13 @ X3 @ X5)) = $false) | ((i @ X4 @ X2) = $false) | ((i @ X1 @ X5) = $false) | ($true = (~ (k @ X1 @ X6))) | ($true = (X3 @ (sK14 @ X3 @ X6))) | ((k @ X4 @ X7) = $false) | ($true = (l @ X7 @ (sK15 @ X7 @ X2)))) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f273])). 1.41/0.68 thf(f273,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((i @ X1 @ X5) = $false) | ((X3 @ (sK13 @ X3 @ X5)) = $false) | ((~ (X3 @ (sK14 @ X3 @ X6))) = $false) | ((i @ X4 @ X2) = $false) | ($true = (~ (k @ X1 @ X6))) | ((k @ X4 @ X7) = $false) | ($true = (l @ X7 @ (sK15 @ X7 @ X2)))) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f264])). 1.41/0.68 thf(f264,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((X3 @ (sK13 @ X3 @ X5)) | (~ (j @ X5 @ (sK13 @ X3 @ X5)))) = $false) | ((~ (X3 @ (sK14 @ X3 @ X6))) = $false) | ((i @ X1 @ X5) = $false) | ($true = (~ (k @ X1 @ X6))) | ($true = (l @ X7 @ (sK15 @ X7 @ X2))) | ((i @ X4 @ X2) = $false) | ((k @ X4 @ X7) = $false)) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f263])). 1.41/0.68 thf(f311,plain,( 1.41/0.68 spl0_5 | spl0_1), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f278,f293,f309])). 1.41/0.68 thf(f278,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((k @ X4 @ X7) = $false) | ($true = (X3 @ (sK14 @ X3 @ X6))) | ($true = (l @ X7 @ (sK15 @ X7 @ X2))) | ((i @ X4 @ X2) = $false) | ($true = (j @ X5 @ (sK13 @ X3 @ X5))) | ((i @ X1 @ X5) = $false) | ((k @ X1 @ X6) = $false)) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f277])). 1.41/0.68 thf(f277,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (j @ X5 @ (sK13 @ X3 @ X5))) | ($true = (l @ X7 @ (sK15 @ X7 @ X2))) | ((~ (X3 @ (sK14 @ X3 @ X6))) = $false) | ((k @ X1 @ X6) = $false) | ((i @ X1 @ X5) = $false) | ((i @ X4 @ X2) = $false) | ((k @ X4 @ X7) = $false)) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f276])). 1.41/0.68 thf(f276,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((~ (j @ X5 @ (sK13 @ X3 @ X5))) = $false) | ((k @ X4 @ X7) = $false) | ((k @ X1 @ X6) = $false) | ($true = (l @ X7 @ (sK15 @ X7 @ X2))) | ((i @ X4 @ X2) = $false) | ((~ (X3 @ (sK14 @ X3 @ X6))) = $false) | ((i @ X1 @ X5) = $false)) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f272])). 1.41/0.68 thf(f272,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (~ (k @ X1 @ X6))) | ($true = (l @ X7 @ (sK15 @ X7 @ X2))) | ((k @ X4 @ X7) = $false) | ((i @ X1 @ X5) = $false) | ((i @ X4 @ X2) = $false) | ((~ (j @ X5 @ (sK13 @ X3 @ X5))) = $false) | ((~ (X3 @ (sK14 @ X3 @ X6))) = $false)) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f264])). 1.41/0.68 thf(f307,plain,( 1.41/0.68 spl0_4 | spl0_3), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f284,f300,f304])). 1.41/0.68 thf(f284,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((k @ X1 @ X6) = $false) | ((i @ X4 @ X2) = $false) | ($true = (l @ X6 @ (sK14 @ X3 @ X6))) | ((X3 @ (sK13 @ X3 @ X5)) = $false) | ((j @ X2 @ (sK15 @ X7 @ X2)) = $true) | ((k @ X4 @ X7) = $false) | ((i @ X1 @ X5) = $false)) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f283])). 1.41/0.68 thf(f283,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((X3 @ (sK13 @ X3 @ X5)) = $false) | ((j @ X2 @ (sK15 @ X7 @ X2)) = $true) | ((i @ X1 @ X5) = $false) | ((i @ X4 @ X2) = $false) | ((k @ X1 @ X6) = $false) | ((~ (l @ X6 @ (sK14 @ X3 @ X6))) = $false) | ((k @ X4 @ X7) = $false)) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f282])). 1.41/0.68 thf(f282,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (~ (k @ X1 @ X6))) | ((i @ X4 @ X2) = $false) | ((i @ X1 @ X5) = $false) | ((X3 @ (sK13 @ X3 @ X5)) = $false) | ((k @ X4 @ X7) = $false) | ((~ (l @ X6 @ (sK14 @ X3 @ X6))) = $false) | ((j @ X2 @ (sK15 @ X7 @ X2)) = $true)) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f280])). 1.41/0.68 thf(f280,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((j @ X2 @ (sK15 @ X7 @ X2)) & (l @ X7 @ (sK15 @ X7 @ X2)))) | ((~ (l @ X6 @ (sK14 @ X3 @ X6))) = $false) | ((i @ X4 @ X2) = $false) | ($true = (~ (k @ X1 @ X6))) | ((k @ X4 @ X7) = $false) | ((X3 @ (sK13 @ X3 @ X5)) = $false) | ((i @ X1 @ X5) = $false)) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f262])). 1.41/0.68 thf(f262,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((X3 @ (sK13 @ X3 @ X5)) | (~ (j @ X5 @ (sK13 @ X3 @ X5)))) = $false) | ($true = ((j @ X2 @ (sK15 @ X7 @ X2)) & (l @ X7 @ (sK15 @ X7 @ X2)))) | ((k @ X4 @ X7) = $false) | ((i @ X4 @ X2) = $false) | ((~ (l @ X6 @ (sK14 @ X3 @ X6))) = $false) | ((i @ X1 @ X5) = $false) | ($true = (~ (k @ X1 @ X6)))) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f261])). 1.41/0.68 thf(f306,plain,( 1.41/0.68 spl0_4 | spl0_1), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f286,f293,f304])). 1.41/0.68 thf(f286,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((i @ X4 @ X2) = $false) | ($true = (l @ X6 @ (sK14 @ X3 @ X6))) | ((i @ X1 @ X5) = $false) | ((k @ X1 @ X6) = $false) | ((k @ X4 @ X7) = $false) | ($true = (l @ X7 @ (sK15 @ X7 @ X2))) | ((X3 @ (sK13 @ X3 @ X5)) = $false)) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f285])). 1.41/0.68 thf(f285,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((i @ X4 @ X2) = $false) | ((X3 @ (sK13 @ X3 @ X5)) = $false) | ((~ (l @ X6 @ (sK14 @ X3 @ X6))) = $false) | ((k @ X1 @ X6) = $false) | ((i @ X1 @ X5) = $false) | ($true = (l @ X7 @ (sK15 @ X7 @ X2))) | ((k @ X4 @ X7) = $false)) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f281])). 1.41/0.68 thf(f281,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((k @ X4 @ X7) = $false) | ((i @ X4 @ X2) = $false) | ($true = (~ (k @ X1 @ X6))) | ((i @ X1 @ X5) = $false) | ($true = (l @ X7 @ (sK15 @ X7 @ X2))) | ((X3 @ (sK13 @ X3 @ X5)) = $false) | ((~ (l @ X6 @ (sK14 @ X3 @ X6))) = $false)) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f280])). 1.41/0.68 thf(f302,plain,( 1.41/0.68 spl0_2 | spl0_3), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f291,f300,f296])). 1.41/0.68 thf(f291,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((k @ X1 @ X6) = $false) | ((j @ X2 @ (sK15 @ X7 @ X2)) = $true) | ($true = (j @ X5 @ (sK13 @ X3 @ X5))) | ((i @ X1 @ X5) = $false) | ((k @ X4 @ X7) = $false) | ((i @ X4 @ X2) = $false) | ($true = (l @ X6 @ (sK14 @ X3 @ X6)))) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f289])). 1.41/0.68 thf(f289,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (j @ X5 @ (sK13 @ X3 @ X5))) | ((i @ X4 @ X2) = $false) | ($true = (l @ X6 @ (sK14 @ X3 @ X6))) | ((k @ X1 @ X6) = $false) | ((k @ X4 @ X7) = $false) | ((i @ X1 @ X5) = $false) | ($true = ((j @ X2 @ (sK15 @ X7 @ X2)) & (l @ X7 @ (sK15 @ X7 @ X2))))) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f288])). 1.41/0.68 thf(f288,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (~ (k @ X1 @ X6))) | ((k @ X4 @ X7) = $false) | ($true = ((j @ X2 @ (sK15 @ X7 @ X2)) & (l @ X7 @ (sK15 @ X7 @ X2)))) | ((i @ X4 @ X2) = $false) | ($true = (l @ X6 @ (sK14 @ X3 @ X6))) | ($true = (j @ X5 @ (sK13 @ X3 @ X5))) | ((i @ X1 @ X5) = $false)) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f287])). 1.41/0.68 thf(f287,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((i @ X1 @ X5) = $false) | ((k @ X4 @ X7) = $false) | ((~ (j @ X5 @ (sK13 @ X3 @ X5))) = $false) | ($true = (~ (k @ X1 @ X6))) | ($true = ((j @ X2 @ (sK15 @ X7 @ X2)) & (l @ X7 @ (sK15 @ X7 @ X2)))) | ((i @ X4 @ X2) = $false) | ($true = (l @ X6 @ (sK14 @ X3 @ X6)))) )), 1.41/0.68 inference(not_proxy_clausification,[status(thm)],[f279])). 1.41/0.68 thf(f279,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((i @ X1 @ X5) = $false) | ((i @ X4 @ X2) = $false) | ((k @ X4 @ X7) = $false) | ((~ (l @ X6 @ (sK14 @ X3 @ X6))) = $false) | ($true = (~ (k @ X1 @ X6))) | ((~ (j @ X5 @ (sK13 @ X3 @ X5))) = $false) | ($true = ((j @ X2 @ (sK15 @ X7 @ X2)) & (l @ X7 @ (sK15 @ X7 @ X2))))) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f262])). 1.41/0.68 thf(f298,plain,( 1.41/0.68 spl0_1 | spl0_2), 1.41/0.68 inference(avatar_split_clause,[status(thm)],[f290,f296,f293])). 1.41/0.68 thf(f290,plain,( 1.41/0.68 ( ! [X2 : $i,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (l @ X6 @ (sK14 @ X3 @ X6))) | ($true = (l @ X7 @ (sK15 @ X7 @ X2))) | ((i @ X4 @ X2) = $false) | ((k @ X4 @ X7) = $false) | ($true = (j @ X5 @ (sK13 @ X3 @ X5))) | ((i @ X1 @ X5) = $false) | ((k @ X1 @ X6) = $false)) )), 1.41/0.68 inference(binary_proxy_clausification,[status(thm)],[f289])). 1.41/0.68 % SZS output end Proof for E---3.1_2816099 1.41/0.68 % (2816186)------------------------------ 1.41/0.68 % (2816186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1.41/0.68 % (2816186)Termination reason: Refutation 1.41/0.68 1.41/0.68 % (2816186)Memory used [KB]: 6652 1.41/0.68 % (2816186)Time elapsed: 0.150 s 1.41/0.68 % (2816186)Instructions burned: 205 (million) 1.41/0.68 % (2816186)------------------------------ 1.41/0.68 % (2816186)------------------------------ 1.41/0.68 % (2816142)Success in time 0.261 s 1.41/0.68 EOF