0.02/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.02/0.12 % Command : run_vampire %s %d THM 0.11/0.34 % Computer : n024.cluster.edu 0.11/0.34 % Model : x86_64 x86_64 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.34 % Memory : 8042.1875MB 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.34 % CPULimit : 1920 0.11/0.34 % WCLimit : 240 0.11/0.34 % DateTime : Wed Jul 30 03:03:04 EDT 2025 0.11/0.34 % CPUTime : 0.11/0.35 This is a THF_ problem 0.11/0.36 Running higher-order theorem proving 0.11/0.37 Running /export/starexec/sandbox/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/sandbox/tmp/tmp.8iVLfgu9Bl/E---3.1_4133.p -m 16384 -t 240 0.22/0.39 % (4247)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_4133 for (2399ds/275Mi) 0.22/0.39 % (4244)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_4133 for (2399ds/27Mi) 0.22/0.39 % (4243)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_4133 for (2399ds/4Mi) 0.22/0.39 % (4245)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_4133 for (2399ds/2Mi) 0.22/0.39 % (4246)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_4133 for (2399ds/2Mi) 0.22/0.39 % (4248)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_4133 for (2399ds/18Mi) 0.22/0.39 % (4245)Instruction limit reached! 0.22/0.39 % (4245)------------------------------ 0.22/0.39 % (4245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.39 % (4245)Termination reason: Unknown 0.22/0.39 % (4245)Termination phase: shuffling 0.22/0.39 0.22/0.39 % (4245)Memory used [KB]: 1023 0.22/0.39 % (4246)Instruction limit reached! 0.22/0.39 % (4246)------------------------------ 0.22/0.39 % (4246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.39 % (4246)Termination reason: Unknown 0.22/0.39 % (4246)Termination phase: shuffling 0.22/0.39 0.22/0.39 % (4246)Memory used [KB]: 1023 0.22/0.39 % (4246)Time elapsed: 0.002 s 0.22/0.39 % (4246)Instructions burned: 2 (million) 0.22/0.39 % (4246)------------------------------ 0.22/0.39 % (4246)------------------------------ 0.22/0.39 % (4245)Time elapsed: 0.002 s 0.22/0.39 % (4245)Instructions burned: 2 (million) 0.22/0.39 % (4245)------------------------------ 0.22/0.39 % (4245)------------------------------ 0.22/0.39 % (4243)Instruction limit reached! 0.22/0.39 % (4243)------------------------------ 0.22/0.39 % (4243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.39 % (4243)Termination reason: Unknown 0.22/0.39 % (4243)Termination phase: shuffling 0.22/0.39 0.22/0.39 % (4243)Memory used [KB]: 1023 0.22/0.39 % (4243)Time elapsed: 0.003 s 0.22/0.39 % (4243)Instructions burned: 4 (million) 0.22/0.39 % (4243)------------------------------ 0.22/0.39 % (4243)------------------------------ 0.22/0.39 % (4242)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_4133 for (2399ds/183Mi) 0.22/0.39 % (4247)Refutation not found, incomplete strategy 0.22/0.39 % (4247)------------------------------ 0.22/0.39 % (4247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.39 % (4247)Termination reason: Refutation not found, incomplete strategy 0.22/0.39 0.22/0.39 0.22/0.39 % (4247)Memory used [KB]: 5628 0.22/0.39 % (4247)Time elapsed: 0.007 s 0.22/0.39 % (4247)Instructions burned: 13 (million) 0.22/0.39 % (4247)------------------------------ 0.22/0.39 % (4247)------------------------------ 0.22/0.40 % (4248)Instruction limit reached! 0.22/0.40 % (4248)------------------------------ 0.22/0.40 % (4248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.40 % (4248)Termination reason: Unknown 0.22/0.40 % (4248)Termination phase: Saturation 0.22/0.40 0.22/0.40 % (4248)Memory used [KB]: 5628 0.22/0.40 % (4248)Time elapsed: 0.010 s 0.22/0.40 % (4248)Instructions burned: 20 (million) 0.22/0.40 % (4248)------------------------------ 0.22/0.40 % (4248)------------------------------ 0.22/0.40 % (4244)Instruction limit reached! 0.22/0.40 % (4244)------------------------------ 0.22/0.40 % (4244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.40 % (4244)Termination reason: Unknown 0.22/0.40 % (4244)Termination phase: Saturation 0.22/0.40 0.22/0.40 % (4244)Memory used [KB]: 5756 0.22/0.40 % (4244)Time elapsed: 0.013 s 0.22/0.40 % (4244)Instructions burned: 27 (million) 0.22/0.40 % (4244)------------------------------ 0.22/0.40 % (4244)------------------------------ 0.22/0.41 % (4250)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_4133 for (2399ds/37Mi) 0.22/0.41 % (4249)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_4133 for (2399ds/3Mi) 0.22/0.41 % (4251)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_4133 for (2399ds/15Mi) 0.22/0.41 % (4249)Instruction limit reached! 0.22/0.41 % (4249)------------------------------ 0.22/0.41 % (4249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.41 % (4249)Termination reason: Unknown 0.22/0.41 % (4249)Termination phase: shuffling 0.22/0.41 0.22/0.41 % (4249)Memory used [KB]: 1023 0.22/0.41 % (4249)Time elapsed: 0.003 s 0.22/0.41 % (4249)Instructions burned: 4 (million) 0.22/0.41 % (4249)------------------------------ 0.22/0.41 % (4249)------------------------------ 0.22/0.41 % (4252)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_4133 for (2399ds/3Mi) 0.22/0.41 % (4252)Instruction limit reached! 0.22/0.41 % (4252)------------------------------ 0.22/0.41 % (4252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.41 % (4252)Termination reason: Unknown 0.22/0.41 % (4252)Termination phase: shuffling 0.22/0.41 0.22/0.41 % (4252)Memory used [KB]: 1023 0.22/0.41 % (4252)Time elapsed: 0.003 s 0.22/0.41 % (4252)Instructions burned: 4 (million) 0.22/0.41 % (4252)------------------------------ 0.22/0.41 % (4252)------------------------------ 0.22/0.41 % (4251)Instruction limit reached! 0.22/0.41 % (4251)------------------------------ 0.22/0.41 % (4251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.41 % (4251)Termination reason: Unknown 0.22/0.41 % (4251)Termination phase: Saturation 0.22/0.41 0.22/0.41 % (4251)Memory used [KB]: 1151 0.22/0.41 % (4251)Time elapsed: 0.009 s 0.22/0.41 % (4251)Instructions burned: 16 (million) 0.22/0.41 % (4251)------------------------------ 0.22/0.41 % (4251)------------------------------ 0.22/0.41 % (4253)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_4133 for (2399ds/1041Mi) 0.22/0.41 % (4254)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on E---3.1_4133 for (2399ds/7Mi) 0.22/0.42 % (4254)Instruction limit reached! 0.22/0.42 % (4254)------------------------------ 0.22/0.42 % (4254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.42 % (4254)Termination reason: Unknown 0.22/0.42 % (4254)Termination phase: Preprocessing 3 0.22/0.42 0.22/0.42 % (4254)Memory used [KB]: 1023 0.22/0.42 % (4254)Time elapsed: 0.005 s 0.22/0.42 % (4254)Instructions burned: 8 (million) 0.22/0.42 % (4254)------------------------------ 0.22/0.42 % (4254)------------------------------ 0.22/0.42 % (4250)Instruction limit reached! 0.22/0.42 % (4250)------------------------------ 0.22/0.42 % (4250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.42 % (4250)Termination reason: Unknown 0.22/0.42 % (4250)Termination phase: Saturation 0.22/0.42 0.22/0.42 % (4250)Memory used [KB]: 5756 0.22/0.42 % (4250)Time elapsed: 0.017 s 0.22/0.42 % (4250)Instructions burned: 38 (million) 0.22/0.42 % (4250)------------------------------ 0.22/0.42 % (4250)------------------------------ 0.22/0.42 % (4256)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on E---3.1_4133 for (2399ds/16Mi) 0.22/0.43 % (4257)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_4133 for (2399ds/3Mi) 0.22/0.43 % (4257)Instruction limit reached! 0.22/0.43 % (4257)------------------------------ 0.22/0.43 % (4257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.43 % (4257)Termination reason: Unknown 0.22/0.43 % (4257)Termination phase: shuffling 0.22/0.43 0.22/0.43 % (4257)Memory used [KB]: 1023 0.22/0.43 % (4257)Time elapsed: 0.003 s 0.22/0.43 % (4257)Instructions burned: 3 (million) 0.22/0.43 % (4257)------------------------------ 0.22/0.43 % (4257)------------------------------ 0.22/0.43 % (4258)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_4133 for (2399ds/3Mi) 0.22/0.43 % (4256)Instruction limit reached! 0.22/0.43 % (4256)------------------------------ 0.22/0.43 % (4256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.43 % (4256)Termination reason: Unknown 0.22/0.43 % (4256)Termination phase: Saturation 0.22/0.43 0.22/0.43 % (4256)Memory used [KB]: 5628 0.22/0.43 % (4256)Time elapsed: 0.009 s 0.22/0.43 % (4256)Instructions burned: 17 (million) 0.22/0.43 % (4256)------------------------------ 0.22/0.43 % (4256)------------------------------ 0.22/0.43 % (4258)Instruction limit reached! 0.22/0.43 % (4258)------------------------------ 0.22/0.43 % (4258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.43 % (4258)Termination reason: Unknown 0.22/0.43 % (4258)Termination phase: shuffling 0.22/0.43 0.22/0.43 % (4258)Memory used [KB]: 1023 0.22/0.43 % (4258)Time elapsed: 0.004 s 0.22/0.43 % (4258)Instructions burned: 5 (million) 0.22/0.43 % (4258)------------------------------ 0.22/0.43 % (4258)------------------------------ 0.22/0.43 % (4259)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_4133 for (2399ds/7Mi) 0.22/0.44 % (4259)Instruction limit reached! 0.22/0.44 % (4259)------------------------------ 0.22/0.44 % (4259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.44 % (4259)Termination reason: Unknown 0.22/0.44 % (4259)Termination phase: Preprocessing 3 0.22/0.44 0.22/0.44 % (4259)Memory used [KB]: 1023 0.22/0.44 % (4259)Time elapsed: 0.005 s 0.22/0.44 % (4259)Instructions burned: 7 (million) 0.22/0.44 % (4259)------------------------------ 0.22/0.44 % (4259)------------------------------ 0.22/0.44 % (4260)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_4133 for (2399ds/3Mi) 0.22/0.44 % (4260)Instruction limit reached! 0.22/0.44 % (4260)------------------------------ 0.22/0.44 % (4260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.44 % (4260)Termination reason: Unknown 0.22/0.44 % (4260)Termination phase: shuffling 0.22/0.44 0.22/0.44 % (4260)Memory used [KB]: 1023 0.22/0.44 % (4260)Time elapsed: 0.003 s 0.22/0.44 % (4260)Instructions burned: 3 (million) 0.22/0.44 % (4260)------------------------------ 0.22/0.44 % (4260)------------------------------ 0.22/0.44 % (4261)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on E---3.1_4133 for (2399ds/4Mi) 0.22/0.44 % (4261)Instruction limit reached! 0.22/0.44 % (4261)------------------------------ 0.22/0.44 % (4261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.44 % (4261)Termination reason: Unknown 0.22/0.44 % (4261)Termination phase: shuffling 0.22/0.44 0.22/0.44 % (4261)Memory used [KB]: 1023 0.22/0.44 % (4261)Time elapsed: 0.003 s 0.22/0.44 % (4261)Instructions burned: 4 (million) 0.22/0.44 % (4261)------------------------------ 0.22/0.44 % (4261)------------------------------ 0.22/0.45 % (4262)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_4133 for (2399ds/18Mi) 0.22/0.45 % (4263)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on E---3.1_4133 for (2399ds/710Mi) 0.22/0.45 % (4264)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on E---3.1_4133 for (2399ds/6Mi) 0.22/0.45 % (4265)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_4133 for (2399ds/902Mi) 0.22/0.45 % (4264)Instruction limit reached! 0.22/0.45 % (4264)------------------------------ 0.22/0.45 % (4264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.45 % (4264)Termination reason: Unknown 0.22/0.45 % (4264)Termination phase: Property scanning 0.22/0.45 0.22/0.45 % (4264)Memory used [KB]: 1023 0.22/0.45 % (4264)Time elapsed: 0.004 s 0.22/0.45 % (4264)Instructions burned: 7 (million) 0.22/0.45 % (4264)------------------------------ 0.22/0.45 % (4264)------------------------------ 0.22/0.46 % (4262)Instruction limit reached! 0.22/0.46 % (4262)------------------------------ 0.22/0.46 % (4262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.46 % (4262)Termination reason: Unknown 0.22/0.46 % (4262)Termination phase: Saturation 0.22/0.46 0.22/0.46 % (4262)Memory used [KB]: 5628 0.22/0.46 % (4262)Time elapsed: 0.011 s 0.22/0.46 % (4262)Instructions burned: 19 (million) 0.22/0.46 % (4262)------------------------------ 0.22/0.46 % (4262)------------------------------ 0.22/0.46 % (4266)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_4133 for (2399ds/21Mi) 0.22/0.46 % (4265)Refutation not found, incomplete strategy 0.22/0.46 % (4265)------------------------------ 0.22/0.46 % (4265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.46 % (4265)Termination reason: Refutation not found, incomplete strategy 0.22/0.46 0.22/0.46 0.22/0.46 % (4265)Memory used [KB]: 5628 0.22/0.46 % (4265)Time elapsed: 0.007 s 0.22/0.46 % (4265)Instructions burned: 10 (million) 0.22/0.46 % (4265)------------------------------ 0.22/0.46 % (4265)------------------------------ 0.22/0.47 % (4266)Instruction limit reached! 0.22/0.47 % (4266)------------------------------ 0.22/0.47 % (4266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.47 % (4266)Termination reason: Unknown 0.22/0.47 % (4266)Termination phase: Saturation 0.22/0.47 0.22/0.47 % (4242)Instruction limit reached! 0.22/0.47 % (4242)------------------------------ 0.22/0.47 % (4242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.47 % (4266)Memory used [KB]: 5628 0.22/0.47 % (4266)Time elapsed: 0.011 s 0.22/0.47 % (4266)Instructions burned: 23 (million) 0.22/0.47 % (4266)------------------------------ 0.22/0.47 % (4266)------------------------------ 0.22/0.47 % (4242)Termination reason: Unknown 0.22/0.47 % (4242)Termination phase: Saturation 0.22/0.47 0.22/0.47 % (4242)Memory used [KB]: 6396 0.22/0.47 % (4242)Time elapsed: 0.078 s 0.22/0.47 % (4242)Instructions burned: 184 (million) 0.22/0.47 % (4242)------------------------------ 0.22/0.47 % (4242)------------------------------ 0.22/0.47 % (4267)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on E---3.1_4133 for (2399ds/5Mi) 0.22/0.47 % (4267)Instruction limit reached! 0.22/0.47 % (4267)------------------------------ 0.22/0.47 % (4267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.47 % (4267)Termination reason: Unknown 0.22/0.47 % (4267)Termination phase: Unused predicate definition removal 0.22/0.47 0.22/0.47 % (4267)Memory used [KB]: 1023 0.22/0.47 % (4267)Time elapsed: 0.005 s 0.22/0.47 % (4267)Instructions burned: 7 (million) 0.22/0.47 % (4267)------------------------------ 0.22/0.47 % (4267)------------------------------ 0.22/0.47 % (4268)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_4133 for (2399ds/6Mi) 0.22/0.47 % (4269)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on E---3.1_4133 for (2399ds/377Mi) 0.22/0.48 % (4268)Instruction limit reached! 0.22/0.48 % (4268)------------------------------ 0.22/0.48 % (4268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.48 % (4268)Termination reason: Unknown 0.22/0.48 % (4268)Termination phase: Preprocessing 1 0.22/0.48 0.22/0.48 % (4268)Memory used [KB]: 1023 0.22/0.48 % (4268)Time elapsed: 0.005 s 0.22/0.48 % (4268)Instructions burned: 8 (million) 0.22/0.48 % (4268)------------------------------ 0.22/0.48 % (4268)------------------------------ 0.22/0.48 % (4270)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_4133 for (2399ds/779Mi) 0.22/0.48 % (4271)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_4133 for (2399ds/19Mi) 0.22/0.49 % (4273)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on E---3.1_4133 for (2399ds/17Mi) 0.22/0.49 % (4271)Instruction limit reached! 0.22/0.49 % (4271)------------------------------ 0.22/0.49 % (4271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.49 % (4271)Termination reason: Unknown 0.22/0.49 % (4271)Termination phase: Saturation 0.22/0.49 0.22/0.49 % (4271)Memory used [KB]: 5628 0.22/0.49 % (4271)Time elapsed: 0.010 s 0.22/0.49 % (4271)Instructions burned: 21 (million) 0.22/0.49 % (4271)------------------------------ 0.22/0.49 % (4271)------------------------------ 0.22/0.49 % (4272)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_4133 for (2399ds/879Mi) 0.22/0.50 % (4273)Instruction limit reached! 0.22/0.50 % (4273)------------------------------ 0.22/0.50 % (4273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.50 % (4273)Termination reason: Unknown 0.22/0.50 % (4273)Termination phase: Saturation 0.22/0.50 0.22/0.50 % (4273)Memory used [KB]: 5628 0.22/0.50 % (4273)Time elapsed: 0.009 s 0.22/0.50 % (4273)Instructions burned: 17 (million) 0.22/0.50 % (4273)------------------------------ 0.22/0.50 % (4273)------------------------------ 0.22/0.51 % (4274)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on E---3.1_4133 for (2398ds/3Mi) 0.22/0.51 % (4274)Instruction limit reached! 0.22/0.51 % (4274)------------------------------ 0.22/0.51 % (4274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.51 % (4274)Termination reason: Unknown 0.22/0.51 % (4274)Termination phase: shuffling 0.22/0.51 0.22/0.51 % (4274)Memory used [KB]: 1023 0.22/0.51 % (4274)Time elapsed: 0.003 s 0.22/0.51 % (4274)Instructions burned: 3 (million) 0.22/0.51 % (4274)------------------------------ 0.22/0.51 % (4274)------------------------------ 0.22/0.51 % (4275)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on E---3.1_4133 for (2398ds/30Mi) 0.22/0.53 % (4275)Instruction limit reached! 0.22/0.53 % (4275)------------------------------ 0.22/0.53 % (4275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.53 % (4275)Termination reason: Unknown 0.22/0.53 % (4275)Termination phase: Saturation 0.22/0.53 0.22/0.53 % (4275)Memory used [KB]: 5756 0.22/0.53 % (4275)Time elapsed: 0.014 s 0.22/0.53 % (4275)Instructions burned: 30 (million) 0.22/0.53 % (4275)------------------------------ 0.22/0.53 % (4275)------------------------------ 1.19/0.53 % (4276)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_4133 for (2398ds/127Mi) 1.19/0.54 % (4277)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_4133 for (2398ds/100Mi) 1.33/0.58 % (4253)First to succeed. 1.33/0.59 % (4276)Instruction limit reached! 1.33/0.59 % (4276)------------------------------ 1.33/0.59 % (4276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1.33/0.59 % (4276)Termination reason: Unknown 1.33/0.59 % (4276)Termination phase: Saturation 1.33/0.59 1.33/0.59 % (4276)Memory used [KB]: 6012 1.33/0.59 % (4276)Time elapsed: 0.061 s 1.33/0.59 % (4276)Instructions burned: 127 (million) 1.33/0.59 % (4276)------------------------------ 1.33/0.59 % (4276)------------------------------ 1.33/0.59 % (4277)Instruction limit reached! 1.33/0.59 % (4277)------------------------------ 1.33/0.59 % (4277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1.33/0.59 % (4277)Termination reason: Unknown 1.33/0.59 % (4277)Termination phase: Saturation 1.33/0.59 1.33/0.59 % (4277)Memory used [KB]: 5884 1.33/0.59 % (4277)Time elapsed: 0.047 s 1.33/0.59 % (4277)Instructions burned: 101 (million) 1.33/0.59 % (4277)------------------------------ 1.33/0.59 % (4277)------------------------------ 1.33/0.59 % (4253)Refutation found. Thanks to Tanya! 1.33/0.59 % SZS status Theorem for E---3.1_4133 1.33/0.59 % SZS output start Proof for E---3.1_4133 1.33/0.59 thf(type_def_5, type, mu: $tType). 1.33/0.59 thf(func_def_0, type, mu: $tType). 1.33/0.59 thf(func_def_1, type, qmltpeq: mu > mu > $i > $o). 1.33/0.59 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o). 1.33/0.59 thf(func_def_4, type, mnot: ($i > $o) > $i > $o). 1.33/0.59 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o). 1.33/0.59 thf(func_def_6, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o). 1.33/0.59 thf(func_def_7, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o). 1.33/0.59 thf(func_def_8, type, mtrue: $i > $o). 1.33/0.59 thf(func_def_9, type, mfalse: $i > $o). 1.33/0.59 thf(func_def_10, type, mand: ($i > $o) > ($i > $o) > $i > $o). 1.33/0.59 thf(func_def_11, type, mimplies: ($i > $o) > ($i > $o) > $i > $o). 1.33/0.59 thf(func_def_12, type, mimplied: ($i > $o) > ($i > $o) > $i > $o). 1.33/0.59 thf(func_def_13, type, mequiv: ($i > $o) > ($i > $o) > $i > $o). 1.33/0.59 thf(func_def_14, type, mxor: ($i > $o) > ($i > $o) > $i > $o). 1.33/0.59 thf(func_def_15, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o). 1.33/0.59 thf(func_def_16, type, exists_in_world: mu > $i > $o). 1.33/0.59 thf(func_def_17, type, mforall_ind: (mu > $i > $o) > $i > $o). 1.33/0.59 thf(func_def_18, type, mexists_ind: (mu > $i > $o) > $i > $o). 1.33/0.59 thf(func_def_19, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o). 1.33/0.59 thf(func_def_20, type, mreflexive: ($i > $i > $o) > $o). 1.33/0.59 thf(func_def_21, type, msymmetric: ($i > $i > $o) > $o). 1.33/0.59 thf(func_def_22, type, mserial: ($i > $i > $o) > $o). 1.33/0.59 thf(func_def_23, type, mtransitive: ($i > $i > $o) > $o). 1.33/0.59 thf(func_def_24, type, meuclidean: ($i > $i > $o) > $o). 1.33/0.59 thf(func_def_25, type, mpartially_functional: ($i > $i > $o) > $o). 1.33/0.59 thf(func_def_26, type, mfunctional: ($i > $i > $o) > $o). 1.33/0.59 thf(func_def_27, type, mweakly_dense: ($i > $i > $o) > $o). 1.33/0.59 thf(func_def_28, type, mweakly_connected: ($i > $i > $o) > $o). 1.33/0.59 thf(func_def_29, type, mweakly_directed: ($i > $i > $o) > $o). 1.33/0.59 thf(func_def_30, type, mvalid: ($i > $o) > $o). 1.33/0.59 thf(func_def_31, type, msatisfiable: ($i > $o) > $o). 1.33/0.59 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o). 1.33/0.59 thf(func_def_33, type, minvalid: ($i > $o) > $o). 1.33/0.59 thf(func_def_34, type, rel_s4: $i > $i > $o). 1.33/0.59 thf(func_def_35, type, mbox_s4: ($i > $o) > $i > $o). 1.33/0.59 thf(func_def_36, type, mdia_s4: ($i > $o) > $i > $o). 1.33/0.59 thf(func_def_37, type, member: mu > mu > $i > $o). 1.33/0.59 thf(func_def_38, type, intersect: mu > mu > $i > $o). 1.33/0.59 thf(func_def_58, type, ph1: !>[X0: $tType]:(X0)). 1.33/0.59 thf(func_def_59, type, sK2: $i > mu). 1.33/0.59 thf(func_def_62, type, sK5: mu). 1.33/0.59 thf(func_def_64, type, sK7: mu). 1.33/0.59 thf(f1314,plain,( 1.33/0.59 $false), 1.33/0.59 inference(trivial_inequality_removal,[status(thm)],[f1313])). 1.33/0.59 thf(f1313,plain,( 1.33/0.59 ($false = $true)), 1.33/0.59 inference(boolean_simplification,[status(thm)],[f1312])). 1.33/0.59 thf(f1312,plain,( 1.33/0.59 ((~ $true) = $true)), 1.33/0.59 inference(forward_demodulation,[status(thm)],[f1311,f359])). 1.33/0.59 thf(f359,plain,( 1.33/0.59 ((exists_in_world @ sK7 @ sK6) = $true)), 1.33/0.59 inference(binary_proxy_clausification,[status(thm)],[f342])). 1.33/0.59 thf(f342,plain,( 1.33/0.59 ($false = ((exists_in_world @ sK7 @ sK6) => (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (!! @ $i @ (^[Y2 : $i]: ((member @ Y1 @ sK7 @ Y2) | (~ (rel_s4 @ Y0 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((member @ Y1 @ sK5 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((intersect @ sK5 @ sK7 @ Y1) | (~ (rel_s4 @ Y0 @ Y1))))))) | (~ (rel_s4 @ sK6 @ Y0)))))))), 1.33/0.59 inference(beta_eta_normalization,[status(thm)],[f341])). 1.33/0.59 thf(f341,plain,( 1.33/0.59 ($false = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ Y0 @ Y3) | (~ (rel_s4 @ Y1 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ sK5 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((intersect @ sK5 @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2))))))) | (~ (rel_s4 @ sK6 @ Y1))))))) @ sK7))), 1.33/0.59 inference(sigma_clausification,[status(thm)],[f335])). 1.33/0.59 thf(f335,plain,( 1.33/0.59 ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ Y0 @ Y3) | (~ (rel_s4 @ Y1 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ sK5 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((intersect @ sK5 @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2))))))) | (~ (rel_s4 @ sK6 @ Y1)))))))))), 1.33/0.59 inference(boolean_simplification,[status(thm)],[f334])). 1.33/0.59 thf(f334,plain,( 1.33/0.59 ($false = ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ Y0 @ Y3) | (~ (rel_s4 @ Y1 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ sK5 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((intersect @ sK5 @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2))))))) | (~ (rel_s4 @ sK6 @ Y1)))))))) | $false))), 1.33/0.59 inference(backward_demodulation,[status(thm)],[f324,f332])). 1.33/0.59 thf(f332,plain,( 1.33/0.59 ($false = (~ (rel_s4 @ sK4 @ sK6)))), 1.33/0.59 inference(binary_proxy_clausification,[status(thm)],[f324])). 1.33/0.59 thf(f324,plain,( 1.33/0.59 ($false = ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ Y0 @ Y3) | (~ (rel_s4 @ Y1 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ sK5 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((intersect @ sK5 @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2))))))) | (~ (rel_s4 @ sK6 @ Y1)))))))) | (~ (rel_s4 @ sK4 @ sK6))))), 1.33/0.59 inference(beta_eta_normalization,[status(thm)],[f323])). 1.33/0.59 thf(f323,plain,( 1.33/0.59 ($false = ((^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: (((~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => ((~ (!! @ $i @ (^[Y4 : $i]: ((member @ Y3 @ Y1 @ Y4) | (~ (rel_s4 @ Y2 @ Y4)))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((member @ Y3 @ sK5 @ Y4) | (~ (rel_s4 @ Y2 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((intersect @ sK5 @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3))))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK4 @ Y0)))) @ sK6))), 1.33/0.59 inference(sigma_clausification,[status(thm)],[f274])). 1.33/0.59 thf(f274,plain,( 1.33/0.59 ($false = (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: (((~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => ((~ (!! @ $i @ (^[Y4 : $i]: ((member @ Y3 @ Y1 @ Y4) | (~ (rel_s4 @ Y2 @ Y4)))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((member @ Y3 @ sK5 @ Y4) | (~ (rel_s4 @ Y2 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((intersect @ sK5 @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3))))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK4 @ Y0))))))), 1.33/0.59 inference(binary_proxy_clausification,[status(thm)],[f260])). 1.33/0.59 thf(f260,plain,( 1.33/0.59 ($false = ((exists_in_world @ sK5 @ sK4) => (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: (((~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => ((~ (!! @ $i @ (^[Y4 : $i]: ((member @ Y3 @ Y1 @ Y4) | (~ (rel_s4 @ Y2 @ Y4)))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((member @ Y3 @ sK5 @ Y4) | (~ (rel_s4 @ Y2 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((intersect @ sK5 @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3))))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK4 @ Y0)))))))), 1.33/0.59 inference(beta_eta_normalization,[status(thm)],[f259])). 1.33/0.59 thf(f259,plain,( 1.33/0.59 ($false = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK4) => (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: (((~ (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y2 @ Y5) | (~ (rel_s4 @ Y3 @ Y5)))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y0 @ Y5) | (~ (rel_s4 @ Y3 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((intersect @ Y0 @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4))))))) | (~ (rel_s4 @ Y1 @ Y3)))))))) | (~ (rel_s4 @ sK4 @ Y1))))))) @ sK5))), 1.33/0.59 inference(sigma_clausification,[status(thm)],[f253])). 1.33/0.59 thf(f253,plain,( 1.33/0.59 ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK4) => (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: (((~ (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y2 @ Y5) | (~ (rel_s4 @ Y3 @ Y5)))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y0 @ Y5) | (~ (rel_s4 @ Y3 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((intersect @ Y0 @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4))))))) | (~ (rel_s4 @ Y1 @ Y3)))))))) | (~ (rel_s4 @ sK4 @ Y1)))))))))), 1.33/0.59 inference(boolean_simplification,[status(thm)],[f252])). 1.33/0.59 thf(f252,plain,( 1.33/0.59 (((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK4) => (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: (((~ (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y2 @ Y5) | (~ (rel_s4 @ Y3 @ Y5)))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y0 @ Y5) | (~ (rel_s4 @ Y3 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((intersect @ Y0 @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4))))))) | (~ (rel_s4 @ Y1 @ Y3)))))))) | (~ (rel_s4 @ sK4 @ Y1)))))))) | $false) = $false)), 1.33/0.59 inference(backward_demodulation,[status(thm)],[f245,f250])). 1.33/0.59 thf(f250,plain,( 1.33/0.59 ($false = (~ (rel_s4 @ sK3 @ sK4)))), 1.33/0.59 inference(binary_proxy_clausification,[status(thm)],[f245])). 1.33/0.59 thf(f245,plain,( 1.33/0.59 (((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK4) => (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: (((~ (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y2 @ Y5) | (~ (rel_s4 @ Y3 @ Y5)))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y0 @ Y5) | (~ (rel_s4 @ Y3 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((intersect @ Y0 @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4))))))) | (~ (rel_s4 @ Y1 @ Y3)))))))) | (~ (rel_s4 @ sK4 @ Y1)))))))) | (~ (rel_s4 @ sK3 @ sK4))) = $false)), 1.33/0.59 inference(beta_eta_normalization,[status(thm)],[f244])). 1.33/0.59 thf(f244,plain,( 1.33/0.59 (((^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: (((~ (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y4) => ((~ (!! @ $i @ (^[Y6 : $i]: ((member @ Y5 @ Y3 @ Y6) | (~ (rel_s4 @ Y4 @ Y6)))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((member @ Y5 @ Y1 @ Y6) | (~ (rel_s4 @ Y4 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((intersect @ Y1 @ Y3 @ Y5) | (~ (rel_s4 @ Y4 @ Y5))))))) | (~ (rel_s4 @ Y2 @ Y4)))))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK3 @ Y0)))) @ sK4) = $false)), 1.33/0.59 inference(sigma_clausification,[status(thm)],[f239])). 1.33/0.59 thf(f239,plain,( 1.33/0.59 ($false = (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: (((~ (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y4) => ((~ (!! @ $i @ (^[Y6 : $i]: ((member @ Y5 @ Y3 @ Y6) | (~ (rel_s4 @ Y4 @ Y6)))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((member @ Y5 @ Y1 @ Y6) | (~ (rel_s4 @ Y4 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((intersect @ Y1 @ Y3 @ Y5) | (~ (rel_s4 @ Y4 @ Y5))))))) | (~ (rel_s4 @ Y2 @ Y4)))))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK3 @ Y0))))))), 1.33/0.59 inference(beta_eta_normalization,[status(thm)],[f238])). 1.33/0.59 thf(f238,plain,( 1.33/0.59 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => (!! @ $i @ (^[Y5 : $i]: (((~ (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => ((~ (!! @ $i @ (^[Y7 : $i]: ((member @ Y6 @ Y4 @ Y7) | (~ (rel_s4 @ Y5 @ Y7)))))) | (~ (!! @ $i @ (^[Y7 : $i]: ((member @ Y6 @ Y2 @ Y7) | (~ (rel_s4 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((intersect @ Y2 @ Y4 @ Y6) | (~ (rel_s4 @ Y5 @ Y6))))))) | (~ (rel_s4 @ Y3 @ Y5)))))))) | (~ (rel_s4 @ Y1 @ Y3)))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) @ sK3))), 1.33/0.59 inference(sigma_clausification,[status(thm)],[f232])). 1.33/0.59 thf(f232,plain,( 1.33/0.59 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => (!! @ $i @ (^[Y5 : $i]: (((~ (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => ((~ (!! @ $i @ (^[Y7 : $i]: ((member @ Y6 @ Y4 @ Y7) | (~ (rel_s4 @ Y5 @ Y7)))))) | (~ (!! @ $i @ (^[Y7 : $i]: ((member @ Y6 @ Y2 @ Y7) | (~ (rel_s4 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((intersect @ Y2 @ Y4 @ Y6) | (~ (rel_s4 @ Y5 @ Y6))))))) | (~ (rel_s4 @ Y3 @ Y5)))))))) | (~ (rel_s4 @ Y1 @ Y3)))))))) | (~ (rel_s4 @ Y0 @ Y1))))))))), 1.33/0.59 inference(not_proxy_clausification,[status(thm)],[f174])). 1.33/0.59 thf(f174,plain,( 1.33/0.59 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => (!! @ $i @ (^[Y5 : $i]: (((~ (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => ((~ (!! @ $i @ (^[Y7 : $i]: ((member @ Y6 @ Y4 @ Y7) | (~ (rel_s4 @ Y5 @ Y7)))))) | (~ (!! @ $i @ (^[Y7 : $i]: ((member @ Y6 @ Y2 @ Y7) | (~ (rel_s4 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((intersect @ Y2 @ Y4 @ Y6) | (~ (rel_s4 @ Y5 @ Y6))))))) | (~ (rel_s4 @ Y3 @ Y5)))))))) | (~ (rel_s4 @ Y1 @ Y3)))))))) | (~ (rel_s4 @ Y0 @ Y1)))))))))), 1.33/0.59 inference(boolean_simplification,[status(thm)],[f173])). 1.33/0.59 thf(f173,plain,( 1.33/0.59 ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => (!! @ $i @ (^[Y5 : $i]: (((~ (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => (~ (~ ((~ (!! @ $i @ (^[Y7 : $i]: ((member @ Y6 @ Y4 @ Y7) | (~ (rel_s4 @ Y5 @ Y7)))))) | (~ (!! @ $i @ (^[Y7 : $i]: ((member @ Y6 @ Y2 @ Y7) | (~ (rel_s4 @ Y5 @ Y7))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((intersect @ Y2 @ Y4 @ Y6) | (~ (rel_s4 @ Y5 @ Y6))))))) | (~ (rel_s4 @ Y3 @ Y5)))))))) | (~ (rel_s4 @ Y1 @ Y3)))))))) | (~ (rel_s4 @ Y0 @ Y1)))))))) = $true)), 1.33/0.59 inference(beta_eta_normalization,[status(thm)],[f168])). 1.33/0.59 thf(f168,plain,( 1.33/0.59 ((~ ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : mu]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))))) @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))))) @ (intersect @ Y0 @ Y1)) @ ((^[Y2 : mu > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ ((^[Y3 : mu > $i > $o]: ((^[Y4 : $i]: (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) @ (^[Y3 : mu]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ (Y2 @ Y3)))))) @ (^[Y2 : mu]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: ((Y6 @ Y7) | (Y5 @ Y7))))))) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ Y3) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ Y4)))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5) | (~ (rel_s4 @ Y4 @ Y5)))))))) @ (member @ Y2 @ Y0)) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5) | (~ (rel_s4 @ Y4 @ Y5)))))))) @ (member @ Y2 @ Y1))))))))))))))) = $true)), 1.33/0.59 inference(definition_unfolding,[status(thm)],[f131,f127,f150,f156,f150,f156,f150,f159,f150,f164,f158,f150,f150])). 1.33/0.59 thf(f158,plain,( 1.33/0.59 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))), 1.33/0.59 inference(definition_unfolding,[status(thm)],[f145,f143,f154,f143,f143])). 1.33/0.59 thf(f154,plain,( 1.33/0.59 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))), 1.33/0.59 inference(cnf_transformation,[status(thm)],[f94])). 1.33/0.59 thf(f94,plain,( 1.33/0.59 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))), 1.33/0.59 inference(fool_elimination,[status(thm)],[f93])). 1.33/0.59 thf(f93,plain,( 1.33/0.59 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor)), 1.33/0.59 inference(rectify,[status(thm)],[f3])). 1.33/0.59 thf(f3,axiom,( 1.33/0.59 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))) = mor)), 1.33/0.59 file('/export/starexec/sandbox/tmp/tmp.8iVLfgu9Bl/E---3.1_4133.p',mor)). 1.33/0.59 thf(f143,plain,( 1.33/0.59 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))), 1.33/0.59 inference(cnf_transformation,[status(thm)],[f72])). 1.33/0.59 thf(f72,plain,( 1.33/0.59 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))), 1.33/0.59 inference(fool_elimination,[status(thm)],[f71])). 1.33/0.59 thf(f71,plain,( 1.33/0.59 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)), 1.33/0.59 inference(rectify,[status(thm)],[f2])). 1.33/0.59 thf(f2,axiom,( 1.33/0.59 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)), 1.33/0.59 file('/export/starexec/sandbox/tmp/tmp.8iVLfgu9Bl/E---3.1_4133.p',mnot)). 1.33/0.59 thf(f145,plain,( 1.33/0.59 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))), 1.33/0.59 inference(cnf_transformation,[status(thm)],[f107])). 1.33/0.59 thf(f107,plain,( 1.33/0.59 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))), 1.33/0.59 inference(fool_elimination,[status(thm)],[f106])). 1.33/0.59 thf(f106,plain,( 1.33/0.59 ((^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))) = mand)), 1.33/0.59 inference(rectify,[status(thm)],[f8])). 1.33/0.59 thf(f8,axiom,( 1.33/0.59 ((^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))) = mand)), 1.33/0.59 file('/export/starexec/sandbox/tmp/tmp.8iVLfgu9Bl/E---3.1_4133.p',mand)). 1.33/0.59 thf(f164,plain,( 1.33/0.59 (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ (Y0 @ Y1)))))))), 1.33/0.59 inference(definition_unfolding,[status(thm)],[f129,f143,f156,f143])). 1.33/0.59 thf(f129,plain,( 1.33/0.59 (mexists_ind = (^[Y0 : mu > $i > $o]: (mnot @ (mforall_ind @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))))))), 1.33/0.59 inference(cnf_transformation,[status(thm)],[f54])). 1.33/0.59 thf(f54,plain,( 1.33/0.59 (mexists_ind = (^[Y0 : mu > $i > $o]: (mnot @ (mforall_ind @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))))))), 1.33/0.59 inference(fool_elimination,[status(thm)],[f53])). 1.33/0.59 thf(f53,plain,( 1.33/0.59 (mexists_ind = (^[X0 : mu > $i > $o] : (mnot @ (mforall_ind @ (^[X1 : mu] : (mnot @ (X0 @ X1)))))))), 1.33/0.59 inference(rectify,[status(thm)],[f15])). 1.33/0.59 thf(f15,axiom,( 1.33/0.59 (mexists_ind = (^[X3 : mu > $i > $o] : (mnot @ (mforall_ind @ (^[X0 : mu] : (mnot @ (X3 @ X0)))))))), 1.33/0.59 file('/export/starexec/sandbox/tmp/tmp.8iVLfgu9Bl/E---3.1_4133.p',mexists_ind)). 1.33/0.59 thf(f159,plain,( 1.33/0.59 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))), 1.33/0.59 inference(definition_unfolding,[status(thm)],[f140,f154,f143])). 1.33/0.59 thf(f140,plain,( 1.33/0.59 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))), 1.33/0.59 inference(cnf_transformation,[status(thm)],[f88])). 1.33/0.59 thf(f88,plain,( 1.33/0.59 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))), 1.33/0.59 inference(fool_elimination,[status(thm)],[f87])). 1.33/0.59 thf(f87,plain,( 1.33/0.59 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))), 1.33/0.59 inference(rectify,[status(thm)],[f9])). 1.33/0.59 thf(f9,axiom,( 1.33/0.59 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))), 1.33/0.59 file('/export/starexec/sandbox/tmp/tmp.8iVLfgu9Bl/E---3.1_4133.p',mimplies)). 1.33/0.59 thf(f156,plain,( 1.33/0.59 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))), 1.33/0.59 inference(cnf_transformation,[status(thm)],[f86])). 1.33/0.59 thf(f86,plain,( 1.33/0.59 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))), 1.33/0.59 inference(fool_elimination,[status(thm)],[f85])). 1.33/0.59 thf(f85,plain,( 1.33/0.59 (mforall_ind = (^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : ((exists_in_world @ X2 @ X1) => (X0 @ X2 @ X1)))))), 1.33/0.59 inference(rectify,[status(thm)],[f14])). 1.33/0.59 thf(f14,axiom,( 1.33/0.59 (mforall_ind = (^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : ((exists_in_world @ X0 @ X2) => (X3 @ X0 @ X2)))))), 1.33/0.59 file('/export/starexec/sandbox/tmp/tmp.8iVLfgu9Bl/E---3.1_4133.p',mforall_ind)). 1.33/0.59 thf(f150,plain,( 1.33/0.59 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))))), 1.33/0.59 inference(cnf_transformation,[status(thm)],[f56])). 1.33/0.59 thf(f56,plain,( 1.33/0.59 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))))), 1.33/0.59 inference(fool_elimination,[status(thm)],[f55])). 1.33/0.59 thf(f55,plain,( 1.33/0.59 (mbox_s4 = (^[X0 : $i > $o, X1 : $i] : (! [X2 : $i] : (~(rel_s4 @ X1 @ X2) | (X0 @ X2)))))), 1.33/0.59 inference(rectify,[status(thm)],[f32])). 1.33/0.59 thf(f32,axiom,( 1.33/0.59 (mbox_s4 = (^[X3 : $i > $o, X2 : $i] : (! [X6 : $i] : (~(rel_s4 @ X2 @ X6) | (X3 @ X6)))))), 1.33/0.59 file('/export/starexec/sandbox/tmp/tmp.8iVLfgu9Bl/E---3.1_4133.p',mbox_s4)). 1.33/0.59 thf(f127,plain,( 1.33/0.59 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))), 1.33/0.59 inference(cnf_transformation,[status(thm)],[f76])). 1.33/0.59 thf(f76,plain,( 1.33/0.59 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))), 1.33/0.59 inference(fool_elimination,[status(thm)],[f75])). 1.33/0.59 thf(f75,plain,( 1.33/0.59 ((^[X0 : $i > $o] : (! [X1 : $i] : (X0 @ X1))) = mvalid)), 1.33/0.59 inference(rectify,[status(thm)],[f27])). 1.33/0.59 thf(f27,axiom,( 1.33/0.59 ((^[X3 : $i > $o] : (! [X2 : $i] : (X3 @ X2))) = mvalid)), 1.33/0.59 file('/export/starexec/sandbox/tmp/tmp.8iVLfgu9Bl/E---3.1_4133.p',mvalid)). 1.33/0.59 thf(f131,plain,( 1.33/0.59 ($true = (~ (mvalid @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @ (mexists_ind @ (^[Y2 : mu]: (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ (mbox_s4 @ (member @ Y2 @ Y1))))))))))))))))), 1.33/0.59 inference(cnf_transformation,[status(thm)],[f48])). 1.33/0.59 thf(f48,plain,( 1.33/0.59 ($true = (~ (mvalid @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @ (mexists_ind @ (^[Y2 : mu]: (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ (mbox_s4 @ (member @ Y2 @ Y1))))))))))))))))), 1.33/0.59 inference(fool_elimination,[status(thm)],[f47])). 1.33/0.59 thf(f47,plain,( 1.33/0.59 ~(mvalid @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : (mbox_s4 @ (mforall_ind @ (^[X1 : mu] : (mbox_s4 @ (mimplies @ (mbox_s4 @ (intersect @ X0 @ X1)) @ (mexists_ind @ (^[X2 : mu] : (mand @ (mbox_s4 @ (member @ X2 @ X0)) @ (mbox_s4 @ (member @ X2 @ X1))))))))))))))), 1.33/0.59 inference(rectify,[status(thm)],[f38])). 1.33/0.59 thf(f38,negated_conjecture,( 1.33/0.59 ~(mvalid @ (mbox_s4 @ (mforall_ind @ (^[X11 : mu] : (mbox_s4 @ (mforall_ind @ (^[X12 : mu] : (mbox_s4 @ (mimplies @ (mbox_s4 @ (intersect @ X11 @ X12)) @ (mexists_ind @ (^[X13 : mu] : (mand @ (mbox_s4 @ (member @ X13 @ X11)) @ (mbox_s4 @ (member @ X13 @ X12))))))))))))))), 1.33/0.59 inference(negated_conjecture,[status(cth)],[f37])). 1.33/0.59 thf(f37,conjecture,( 1.33/0.59 (mvalid @ (mbox_s4 @ (mforall_ind @ (^[X11 : mu] : (mbox_s4 @ (mforall_ind @ (^[X12 : mu] : (mbox_s4 @ (mimplies @ (mbox_s4 @ (intersect @ X11 @ X12)) @ (mexists_ind @ (^[X13 : mu] : (mand @ (mbox_s4 @ (member @ X13 @ X11)) @ (mbox_s4 @ (member @ X13 @ X12))))))))))))))), 1.33/0.59 file('/export/starexec/sandbox/tmp/tmp.8iVLfgu9Bl/E---3.1_4133.p',prove_th15)). 1.33/0.59 thf(f1311,plain,( 1.33/0.59 ((~ (exists_in_world @ sK7 @ sK6)) = $true)), 1.33/0.59 inference(boolean_simplification,[status(thm)],[f1310])). 1.33/0.59 thf(f1310,plain,( 1.33/0.59 (((exists_in_world @ sK7 @ sK6) => $false) = $true)), 1.33/0.59 inference(boolean_simplification,[status(thm)],[f1309])). 1.33/0.59 thf(f1309,plain,( 1.33/0.59 (((exists_in_world @ sK7 @ sK6) => (~ $true)) = $true)), 1.33/0.59 inference(boolean_simplification,[status(thm)],[f1308])). 1.33/0.59 thf(f1308,plain,( 1.33/0.59 (((exists_in_world @ sK7 @ sK6) => (~ ((~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((intersect @ sK5 @ sK7 @ Y1) | (~ (rel_s4 @ Y0 @ Y1))))) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (!! @ $i @ (^[Y2 : $i]: ((member @ Y1 @ sK7 @ Y2) | (~ (rel_s4 @ Y0 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((member @ Y1 @ sK5 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))))) | (~ (rel_s4 @ sK6 @ Y0)))))) | $true))) = $true)), 1.33/0.59 inference(boolean_simplification,[status(thm)],[f1296])). 1.33/0.59 thf(f1296,plain,( 1.33/0.59 (((exists_in_world @ sK7 @ sK6) => (~ ((~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((intersect @ sK5 @ sK7 @ Y1) | (~ (rel_s4 @ Y0 @ Y1))))) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (!! @ $i @ (^[Y2 : $i]: ((member @ Y1 @ sK7 @ Y2) | (~ (rel_s4 @ Y0 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((member @ Y1 @ sK5 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))))) | (~ (rel_s4 @ sK6 @ Y0)))))) | (~ $false)))) = $true)), 1.33/0.59 inference(superposition,[status(thm)],[f1283,f358])). 1.33/0.59 thf(f358,plain,( 1.33/0.59 ($false = (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (!! @ $i @ (^[Y2 : $i]: ((member @ Y1 @ sK7 @ Y2) | (~ (rel_s4 @ Y0 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((member @ Y1 @ sK5 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((intersect @ sK5 @ sK7 @ Y1) | (~ (rel_s4 @ Y0 @ Y1))))))) | (~ (rel_s4 @ sK6 @ Y0))))))), 1.33/0.59 inference(binary_proxy_clausification,[status(thm)],[f342])). 1.33/0.59 thf(f1283,plain,( 1.33/0.59 ( ! [X1 : mu] : ((((exists_in_world @ X1 @ sK6) => (~ ((~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((intersect @ sK5 @ X1 @ Y1) | (~ (rel_s4 @ Y0 @ Y1))))) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (!! @ $i @ (^[Y2 : $i]: ((member @ Y1 @ X1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((member @ Y1 @ sK5 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))))) | (~ (rel_s4 @ sK6 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (!! @ $i @ (^[Y2 : $i]: ((member @ Y1 @ X1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((member @ Y1 @ sK5 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((intersect @ sK5 @ X1 @ Y1) | (~ (rel_s4 @ Y0 @ Y1))))))) | (~ (rel_s4 @ sK6 @ Y0))))))))) = $true)) )), 1.33/0.59 inference(beta_eta_normalization,[status(thm)],[f1280])). 1.33/0.59 thf(f1280,plain,( 1.33/0.59 ( ! [X1 : mu] : ((((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (~ ((~ (!! @ $i @ (^[Y1 : $i]: (((!! @ $i @ (^[Y2 : $i]: ((intersect @ sK5 @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2))))) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ Y0 @ Y3) | (~ (rel_s4 @ Y1 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ sK5 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))))) | (~ (rel_s4 @ sK6 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ Y0 @ Y3) | (~ (rel_s4 @ Y1 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ sK5 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((intersect @ sK5 @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2))))))) | (~ (rel_s4 @ sK6 @ Y1)))))))))) @ X1) = $true)) )), 1.33/0.59 inference(pi_clausification,[status(thm)],[f542])). 1.33/0.59 thf(f542,plain,( 1.33/0.59 ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (~ ((~ (!! @ $i @ (^[Y1 : $i]: (((!! @ $i @ (^[Y2 : $i]: ((intersect @ sK5 @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2))))) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ Y0 @ Y3) | (~ (rel_s4 @ Y1 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ sK5 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))))) | (~ (rel_s4 @ sK6 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ Y0 @ Y3) | (~ (rel_s4 @ Y1 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ sK5 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((intersect @ sK5 @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2))))))) | (~ (rel_s4 @ sK6 @ Y1))))))))))) = $true)), 1.33/0.59 inference(boolean_simplification,[status(thm)],[f541])). 1.33/0.59 thf(f541,plain,( 1.33/0.59 (((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (~ ((~ (!! @ $i @ (^[Y1 : $i]: (((!! @ $i @ (^[Y2 : $i]: ((intersect @ sK5 @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2))))) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ Y0 @ Y3) | (~ (rel_s4 @ Y1 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ sK5 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))))) | (~ (rel_s4 @ sK6 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ Y0 @ Y3) | (~ (rel_s4 @ Y1 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ sK5 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((intersect @ sK5 @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2))))))) | (~ (rel_s4 @ sK6 @ Y1))))))))))) | $false) = $true)), 1.33/0.59 inference(boolean_simplification,[status(thm)],[f537])). 1.33/0.59 thf(f537,plain,( 1.33/0.59 ($true = ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (~ ((~ (!! @ $i @ (^[Y1 : $i]: (((!! @ $i @ (^[Y2 : $i]: ((intersect @ sK5 @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2))))) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ Y0 @ Y3) | (~ (rel_s4 @ Y1 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ sK5 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))))) | (~ (rel_s4 @ sK6 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ Y0 @ Y3) | (~ (rel_s4 @ Y1 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ sK5 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((intersect @ sK5 @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2))))))) | (~ (rel_s4 @ sK6 @ Y1))))))))))) | (~ $true)))), 1.33/0.59 inference(superposition,[status(thm)],[f518,f336])). 1.33/0.59 thf(f336,plain,( 1.33/0.59 ((rel_s4 @ sK4 @ sK6) = $true)), 1.33/0.59 inference(not_proxy_clausification,[status(thm)],[f332])). 1.33/0.59 thf(f518,plain,( 1.33/0.59 ( ! [X1 : $i] : ((((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ ((~ (!! @ $i @ (^[Y1 : $i]: (((!! @ $i @ (^[Y2 : $i]: ((intersect @ sK5 @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2))))) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ Y0 @ Y3) | (~ (rel_s4 @ Y1 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ sK5 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))))) | (~ (rel_s4 @ X1 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ Y0 @ Y3) | (~ (rel_s4 @ Y1 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((member @ Y2 @ sK5 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((intersect @ sK5 @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2))))))) | (~ (rel_s4 @ X1 @ Y1))))))))))) | (~ (rel_s4 @ sK4 @ X1))) = $true)) )), 1.33/0.59 inference(beta_eta_normalization,[status(thm)],[f516])). 1.33/0.59 thf(f516,plain,( 1.33/0.59 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ ((~ (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((intersect @ sK5 @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3))))) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => ((~ (!! @ $i @ (^[Y4 : $i]: ((member @ Y3 @ Y1 @ Y4) | (~ (rel_s4 @ Y2 @ Y4)))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((member @ Y3 @ sK5 @ Y4) | (~ (rel_s4 @ Y2 @ Y4))))))))))) | (~ (rel_s4 @ Y0 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: (((~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => ((~ (!! @ $i @ (^[Y4 : $i]: ((member @ Y3 @ Y1 @ Y4) | (~ (rel_s4 @ Y2 @ Y4)))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((member @ Y3 @ sK5 @ Y4) | (~ (rel_s4 @ Y2 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((intersect @ sK5 @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3))))))) | (~ (rel_s4 @ Y0 @ Y2))))))))))) | (~ (rel_s4 @ sK4 @ Y0)))) @ X1) = $true)) )), 1.33/0.59 inference(pi_clausification,[status(thm)],[f395])). 1.33/0.59 thf(f395,plain,( 1.33/0.59 ((!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ ((~ (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((intersect @ sK5 @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3))))) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => ((~ (!! @ $i @ (^[Y4 : $i]: ((member @ Y3 @ Y1 @ Y4) | (~ (rel_s4 @ Y2 @ Y4)))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((member @ Y3 @ sK5 @ Y4) | (~ (rel_s4 @ Y2 @ Y4))))))))))) | (~ (rel_s4 @ Y0 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: (((~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => ((~ (!! @ $i @ (^[Y4 : $i]: ((member @ Y3 @ Y1 @ Y4) | (~ (rel_s4 @ Y2 @ Y4)))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((member @ Y3 @ sK5 @ Y4) | (~ (rel_s4 @ Y2 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((intersect @ sK5 @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3))))))) | (~ (rel_s4 @ Y0 @ Y2))))))))))) | (~ (rel_s4 @ sK4 @ Y0))))) = $true)), 1.33/0.59 inference(boolean_simplification,[status(thm)],[f389])). 1.33/0.59 thf(f389,plain,( 1.33/0.59 ($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ ((~ (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((intersect @ sK5 @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3))))) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => ((~ (!! @ $i @ (^[Y4 : $i]: ((member @ Y3 @ Y1 @ Y4) | (~ (rel_s4 @ Y2 @ Y4)))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((member @ Y3 @ sK5 @ Y4) | (~ (rel_s4 @ Y2 @ Y4))))))))))) | (~ (rel_s4 @ Y0 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: (((~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => ((~ (!! @ $i @ (^[Y4 : $i]: ((member @ Y3 @ Y1 @ Y4) | (~ (rel_s4 @ Y2 @ Y4)))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((member @ Y3 @ sK5 @ Y4) | (~ (rel_s4 @ Y2 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((intersect @ sK5 @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3))))))) | (~ (rel_s4 @ Y0 @ Y2))))))))))) | (~ (rel_s4 @ sK4 @ Y0)))))))), 1.33/0.59 inference(superposition,[status(thm)],[f371,f275])). 1.33/0.59 thf(f275,plain,( 1.33/0.59 ((exists_in_world @ sK5 @ sK4) = $true)), 1.33/0.59 inference(binary_proxy_clausification,[status(thm)],[f260])). 1.33/0.59 thf(f371,plain,( 1.33/0.59 ( ! [X0 : $i,X1 : mu] : (($true = ((exists_in_world @ X1 @ X0) => (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ ((~ (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((intersect @ X1 @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3))))) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => ((~ (!! @ $i @ (^[Y4 : $i]: ((member @ Y3 @ Y1 @ Y4) | (~ (rel_s4 @ Y2 @ Y4)))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((member @ Y3 @ X1 @ Y4) | (~ (rel_s4 @ Y2 @ Y4))))))))))) | (~ (rel_s4 @ Y0 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: (((~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => ((~ (!! @ $i @ (^[Y4 : $i]: ((member @ Y3 @ Y1 @ Y4) | (~ (rel_s4 @ Y2 @ Y4)))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((member @ Y3 @ X1 @ Y4) | (~ (rel_s4 @ Y2 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((intersect @ X1 @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3))))))) | (~ (rel_s4 @ Y0 @ Y2))))))))))) | (~ (rel_s4 @ X0 @ Y0)))))))) )), 1.33/0.59 inference(beta_eta_normalization,[status(thm)],[f370])). 1.33/0.59 thf(f370,plain,( 1.33/0.59 ( ! [X0 : $i,X1 : mu] : (($true = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ X0) => (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ ((~ (!! @ $i @ (^[Y3 : $i]: (((!! @ $i @ (^[Y4 : $i]: ((intersect @ Y0 @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4))))) | (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y2 @ Y5) | (~ (rel_s4 @ Y3 @ Y5)))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y0 @ Y5) | (~ (rel_s4 @ Y3 @ Y5))))))))))) | (~ (rel_s4 @ Y1 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: (((~ (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y2 @ Y5) | (~ (rel_s4 @ Y3 @ Y5)))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y0 @ Y5) | (~ (rel_s4 @ Y3 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((intersect @ Y0 @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4))))))) | (~ (rel_s4 @ Y1 @ Y3))))))))))) | (~ (rel_s4 @ X0 @ Y1))))))) @ X1))) )), 1.33/0.59 inference(pi_clausification,[status(thm)],[f309])). 1.33/0.59 thf(f309,plain,( 1.33/0.59 ( ! [X0 : $i] : (((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X0) => (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ ((~ (!! @ $i @ (^[Y3 : $i]: (((!! @ $i @ (^[Y4 : $i]: ((intersect @ Y0 @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4))))) | (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y2 @ Y5) | (~ (rel_s4 @ Y3 @ Y5)))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y0 @ Y5) | (~ (rel_s4 @ Y3 @ Y5))))))))))) | (~ (rel_s4 @ Y1 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: (((~ (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y2 @ Y5) | (~ (rel_s4 @ Y3 @ Y5)))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y0 @ Y5) | (~ (rel_s4 @ Y3 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((intersect @ Y0 @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4))))))) | (~ (rel_s4 @ Y1 @ Y3))))))))))) | (~ (rel_s4 @ X0 @ Y1)))))))) = $true)) )), 1.33/0.59 inference(boolean_simplification,[status(thm)],[f308])). 1.33/0.59 thf(f308,plain,( 1.33/0.59 ( ! [X0 : $i] : ((((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X0) => (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ ((~ (!! @ $i @ (^[Y3 : $i]: (((!! @ $i @ (^[Y4 : $i]: ((intersect @ Y0 @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4))))) | (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y2 @ Y5) | (~ (rel_s4 @ Y3 @ Y5)))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y0 @ Y5) | (~ (rel_s4 @ Y3 @ Y5))))))))))) | (~ (rel_s4 @ Y1 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: (((~ (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y2 @ Y5) | (~ (rel_s4 @ Y3 @ Y5)))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y0 @ Y5) | (~ (rel_s4 @ Y3 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((intersect @ Y0 @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4))))))) | (~ (rel_s4 @ Y1 @ Y3))))))))))) | (~ (rel_s4 @ X0 @ Y1)))))))) | $false) = $true)) )), 1.33/0.59 inference(boolean_simplification,[status(thm)],[f306])). 1.33/0.59 thf(f306,plain,( 1.33/0.59 ( ! [X0 : $i] : ((((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X0) => (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ ((~ (!! @ $i @ (^[Y3 : $i]: (((!! @ $i @ (^[Y4 : $i]: ((intersect @ Y0 @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4))))) | (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y2 @ Y5) | (~ (rel_s4 @ Y3 @ Y5)))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y0 @ Y5) | (~ (rel_s4 @ Y3 @ Y5))))))))))) | (~ (rel_s4 @ Y1 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: (((~ (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y2 @ Y5) | (~ (rel_s4 @ Y3 @ Y5)))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y0 @ Y5) | (~ (rel_s4 @ Y3 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((intersect @ Y0 @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4))))))) | (~ (rel_s4 @ Y1 @ Y3))))))))))) | (~ (rel_s4 @ X0 @ Y1)))))))) | (~ $true)) = $true)) )), 1.33/0.59 inference(superposition,[status(thm)],[f297,f181])). 1.33/0.59 thf(f181,plain,( 1.33/0.59 ( ! [X1 : $i] : (((rel_s4 @ X1 @ X1) = $true)) )), 1.33/0.59 inference(beta_eta_normalization,[status(thm)],[f180])). 1.33/0.59 thf(f180,plain,( 1.33/0.59 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (rel_s4 @ Y0 @ Y0)) @ X1))) )), 1.33/0.59 inference(pi_clausification,[status(thm)],[f172])). 1.33/0.59 thf(f172,plain,( 1.33/0.59 ((!! @ $i @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))) = $true)), 1.33/0.59 inference(beta_eta_normalization,[status(thm)],[f171])). 1.33/0.59 thf(f171,plain,( 1.33/0.59 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ rel_s4) = $true)), 1.33/0.59 inference(definition_unfolding,[status(thm)],[f151,f122])). 1.33/0.59 thf(f122,plain,( 1.33/0.59 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))), 1.33/0.59 inference(cnf_transformation,[status(thm)],[f70])). 1.33/0.59 thf(f70,plain,( 1.33/0.59 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))), 1.33/0.59 inference(fool_elimination,[status(thm)],[f69])). 1.33/0.59 thf(f69,plain,( 1.33/0.59 (mreflexive = (^[X0 : $i > $i > $o] : (! [X1 : $i] : (X0 @ X1 @ X1))))), 1.33/0.59 inference(rectify,[status(thm)],[f17])). 1.33/0.59 thf(f17,axiom,( 1.33/0.59 (mreflexive = (^[X5 : $i > $i > $o] : (! [X8 : $i] : (X5 @ X8 @ X8))))), 1.33/0.59 file('/export/starexec/sandbox/tmp/tmp.8iVLfgu9Bl/E---3.1_4133.p',mreflexive)). 1.33/0.59 thf(f151,plain,( 1.33/0.59 ((mreflexive @ rel_s4) = $true)), 1.33/0.59 inference(cnf_transformation,[status(thm)],[f111])). 1.33/0.59 thf(f111,plain,( 1.33/0.59 ((mreflexive @ rel_s4) = $true)), 1.33/0.59 inference(fool_elimination,[status(thm)],[f110])). 1.33/0.59 thf(f110,plain,( 1.33/0.59 (mreflexive @ rel_s4)), 1.33/0.59 inference(rectify,[status(thm)],[f35])). 1.33/0.59 thf(f35,axiom,( 1.33/0.59 (mreflexive @ rel_s4)), 1.33/0.59 file('/export/starexec/sandbox/tmp/tmp.8iVLfgu9Bl/E---3.1_4133.p',a1)). 1.33/0.59 thf(f297,plain,( 1.33/0.59 ( ! [X2 : $i,X1 : $i] : ((((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ ((~ (!! @ $i @ (^[Y3 : $i]: (((!! @ $i @ (^[Y4 : $i]: ((intersect @ Y0 @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4))))) | (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y2 @ Y5) | (~ (rel_s4 @ Y3 @ Y5)))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y0 @ Y5) | (~ (rel_s4 @ Y3 @ Y5))))))))))) | (~ (rel_s4 @ Y1 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: (((~ (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y2 @ Y5) | (~ (rel_s4 @ Y3 @ Y5)))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((member @ Y4 @ Y0 @ Y5) | (~ (rel_s4 @ Y3 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((intersect @ Y0 @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4))))))) | (~ (rel_s4 @ Y1 @ Y3))))))))))) | (~ (rel_s4 @ X2 @ Y1)))))))) | (~ (rel_s4 @ X1 @ X2))) = $true)) )), 1.33/0.59 inference(beta_eta_normalization,[status(thm)],[f296])). 1.33/0.59 thf(f296,plain,( 1.33/0.59 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (~ ((~ (!! @ $i @ (^[Y4 : $i]: (((!! @ $i @ (^[Y5 : $i]: ((intersect @ Y1 @ Y3 @ Y5) | (~ (rel_s4 @ Y4 @ Y5))))) | (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y4) => ((~ (!! @ $i @ (^[Y6 : $i]: ((member @ Y5 @ Y3 @ Y6) | (~ (rel_s4 @ Y4 @ Y6)))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((member @ Y5 @ Y1 @ Y6) | (~ (rel_s4 @ Y4 @ Y6))))))))))) | (~ (rel_s4 @ Y2 @ Y4)))))) | (~ (!! @ $i @ (^[Y4 : $i]: (((~ (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y4) => ((~ (!! @ $i @ (^[Y6 : $i]: ((member @ Y5 @ Y3 @ Y6) | (~ (rel_s4 @ Y4 @ Y6)))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((member @ Y5 @ Y1 @ Y6) | (~ (rel_s4 @ Y4 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((intersect @ Y1 @ Y3 @ Y5) | (~ (rel_s4 @ Y4 @ Y5))))))) | (~ (rel_s4 @ Y2 @ Y4))))))))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ X1 @ Y0)))) @ X2))) )), 1.33/0.59 inference(pi_clausification,[status(thm)],[f287])). 1.33/0.59 thf(f287,plain,( 1.33/0.59 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (~ ((~ (!! @ $i @ (^[Y4 : $i]: (((!! @ $i @ (^[Y5 : $i]: ((intersect @ Y1 @ Y3 @ Y5) | (~ (rel_s4 @ Y4 @ Y5))))) | (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y4) => ((~ (!! @ $i @ (^[Y6 : $i]: ((member @ Y5 @ Y3 @ Y6) | (~ (rel_s4 @ Y4 @ Y6)))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((member @ Y5 @ Y1 @ Y6) | (~ (rel_s4 @ Y4 @ Y6))))))))))) | (~ (rel_s4 @ Y2 @ Y4)))))) | (~ (!! @ $i @ (^[Y4 : $i]: (((~ (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y4) => ((~ (!! @ $i @ (^[Y6 : $i]: ((member @ Y5 @ Y3 @ Y6) | (~ (rel_s4 @ Y4 @ Y6)))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((member @ Y5 @ Y1 @ Y6) | (~ (rel_s4 @ Y4 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((intersect @ Y1 @ Y3 @ Y5) | (~ (rel_s4 @ Y4 @ Y5))))))) | (~ (rel_s4 @ Y2 @ Y4))))))))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ X1 @ Y0))))) = $true)) )), 1.33/0.59 inference(beta_eta_normalization,[status(thm)],[f286])). 1.33/0.59 thf(f286,plain,( 1.33/0.59 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => (~ ((~ (!! @ $i @ (^[Y5 : $i]: (((!! @ $i @ (^[Y6 : $i]: ((intersect @ Y2 @ Y4 @ Y6) | (~ (rel_s4 @ Y5 @ Y6))))) | (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => ((~ (!! @ $i @ (^[Y7 : $i]: ((member @ Y6 @ Y4 @ Y7) | (~ (rel_s4 @ Y5 @ Y7)))))) | (~ (!! @ $i @ (^[Y7 : $i]: ((member @ Y6 @ Y2 @ Y7) | (~ (rel_s4 @ Y5 @ Y7))))))))))) | (~ (rel_s4 @ Y3 @ Y5)))))) | (~ (!! @ $i @ (^[Y5 : $i]: (((~ (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => ((~ (!! @ $i @ (^[Y7 : $i]: ((member @ Y6 @ Y4 @ Y7) | (~ (rel_s4 @ Y5 @ Y7)))))) | (~ (!! @ $i @ (^[Y7 : $i]: ((member @ Y6 @ Y2 @ Y7) | (~ (rel_s4 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((intersect @ Y2 @ Y4 @ Y6) | (~ (rel_s4 @ Y5 @ Y6))))))) | (~ (rel_s4 @ Y3 @ Y5))))))))))) | (~ (rel_s4 @ Y1 @ Y3)))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) @ X1) = $true)) )), 1.33/0.59 inference(pi_clausification,[status(thm)],[f178])). 1.33/0.59 thf(f178,plain,( 1.33/0.59 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => (~ ((~ (!! @ $i @ (^[Y5 : $i]: (((!! @ $i @ (^[Y6 : $i]: ((intersect @ Y2 @ Y4 @ Y6) | (~ (rel_s4 @ Y5 @ Y6))))) | (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => ((~ (!! @ $i @ (^[Y7 : $i]: ((member @ Y6 @ Y4 @ Y7) | (~ (rel_s4 @ Y5 @ Y7)))))) | (~ (!! @ $i @ (^[Y7 : $i]: ((member @ Y6 @ Y2 @ Y7) | (~ (rel_s4 @ Y5 @ Y7))))))))))) | (~ (rel_s4 @ Y3 @ Y5)))))) | (~ (!! @ $i @ (^[Y5 : $i]: (((~ (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => ((~ (!! @ $i @ (^[Y7 : $i]: ((member @ Y6 @ Y4 @ Y7) | (~ (rel_s4 @ Y5 @ Y7)))))) | (~ (!! @ $i @ (^[Y7 : $i]: ((member @ Y6 @ Y2 @ Y7) | (~ (rel_s4 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((intersect @ Y2 @ Y4 @ Y6) | (~ (rel_s4 @ Y5 @ Y6))))))) | (~ (rel_s4 @ Y3 @ Y5))))))))))) | (~ (rel_s4 @ Y1 @ Y3)))))))) | (~ (rel_s4 @ Y0 @ Y1))))))) = $true)), 1.33/0.59 inference(boolean_simplification,[status(thm)],[f177])). 1.33/0.59 thf(f177,plain,( 1.33/0.59 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => (~ ((~ (!! @ $i @ (^[Y5 : $i]: (((!! @ $i @ (^[Y6 : $i]: ((intersect @ Y2 @ Y4 @ Y6) | (~ (rel_s4 @ Y5 @ Y6))))) | (~ (~ (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => ((~ (!! @ $i @ (^[Y7 : $i]: ((member @ Y6 @ Y4 @ Y7) | (~ (rel_s4 @ Y5 @ Y7)))))) | (~ (!! @ $i @ (^[Y7 : $i]: ((member @ Y6 @ Y2 @ Y7) | (~ (rel_s4 @ Y5 @ Y7))))))))))))) | (~ (rel_s4 @ Y3 @ Y5)))))) | (~ (!! @ $i @ (^[Y5 : $i]: (((~ (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => ((~ (!! @ $i @ (^[Y7 : $i]: ((member @ Y6 @ Y4 @ Y7) | (~ (rel_s4 @ Y5 @ Y7)))))) | (~ (!! @ $i @ (^[Y7 : $i]: ((member @ Y6 @ Y2 @ Y7) | (~ (rel_s4 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((intersect @ Y2 @ Y4 @ Y6) | (~ (rel_s4 @ Y5 @ Y6))))))) | (~ (rel_s4 @ Y3 @ Y5))))))))))) | (~ (rel_s4 @ Y1 @ Y3)))))))) | (~ (rel_s4 @ Y0 @ Y1))))))) = $true)), 1.33/0.59 inference(boolean_simplification,[status(thm)],[f176])). 1.33/0.59 thf(f176,plain,( 1.33/0.59 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => (~ ((~ (!! @ $i @ (^[Y5 : $i]: (((!! @ $i @ (^[Y6 : $i]: ((intersect @ Y2 @ Y4 @ Y6) | (~ (rel_s4 @ Y5 @ Y6))))) | (~ (~ (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => (~ (~ ((~ (!! @ $i @ (^[Y7 : $i]: ((member @ Y6 @ Y4 @ Y7) | (~ (rel_s4 @ Y5 @ Y7)))))) | (~ (!! @ $i @ (^[Y7 : $i]: ((member @ Y6 @ Y2 @ Y7) | (~ (rel_s4 @ Y5 @ Y7))))))))))))))) | (~ (rel_s4 @ Y3 @ Y5)))))) | (~ (!! @ $i @ (^[Y5 : $i]: (((~ (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => (~ (~ ((~ (!! @ $i @ (^[Y7 : $i]: ((member @ Y6 @ Y4 @ Y7) | (~ (rel_s4 @ Y5 @ Y7)))))) | (~ (!! @ $i @ (^[Y7 : $i]: ((member @ Y6 @ Y2 @ Y7) | (~ (rel_s4 @ Y5 @ Y7))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((intersect @ Y2 @ Y4 @ Y6) | (~ (rel_s4 @ Y5 @ Y6))))))) | (~ (rel_s4 @ Y3 @ Y5))))))))))) | (~ (rel_s4 @ Y1 @ Y3)))))))) | (~ (rel_s4 @ Y0 @ Y1))))))) = $true)), 1.33/0.59 inference(beta_eta_normalization,[status(thm)],[f167])). 1.33/0.59 thf(f167,plain,( 1.33/0.59 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : mu]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))))) @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))))) @ (intersect @ Y0 @ Y1)) @ ((^[Y2 : mu > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ ((^[Y3 : mu > $i > $o]: ((^[Y4 : $i]: (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) @ (^[Y3 : mu]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ (Y2 @ Y3)))))) @ (^[Y2 : mu]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: ((Y6 @ Y7) | (Y5 @ Y7))))))) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ Y3) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ Y4)))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5) | (~ (rel_s4 @ Y4 @ Y5)))))))) @ (member @ Y2 @ Y0)) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5) | (~ (rel_s4 @ Y4 @ Y5)))))))) @ (member @ Y2 @ Y1))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : mu > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ ((^[Y3 : mu > $i > $o]: ((^[Y4 : $i]: (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) @ (^[Y3 : mu]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ (Y2 @ Y3)))))) @ (^[Y2 : mu]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: ((Y6 @ Y7) | (Y5 @ Y7))))))) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ Y3) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ Y4)))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5) | (~ (rel_s4 @ Y4 @ Y5)))))))) @ (member @ Y2 @ Y0)) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5) | (~ (rel_s4 @ Y4 @ Y5)))))))) @ (member @ Y2 @ Y1))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))))) @ (intersect @ Y0 @ Y1)))))))))))) = $true)), 1.33/0.59 inference(definition_unfolding,[status(thm)],[f118,f127,f150,f156,f150,f156,f158,f150,f159,f150,f164,f158,f150,f150,f150,f159,f164,f158,f150,f150,f150])). 1.33/0.59 thf(f118,plain,( 1.33/0.59 ((mvalid @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (mforall_ind @ (^[Y1 : mu]: (mand @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @ (mexists_ind @ (^[Y2 : mu]: (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ (mbox_s4 @ (member @ Y2 @ Y1))))))) @ (mbox_s4 @ (mimplies @ (mexists_ind @ (^[Y2 : mu]: (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ (mbox_s4 @ (member @ Y2 @ Y1))))) @ (mbox_s4 @ (intersect @ Y0 @ Y1)))))))))))) = $true)), 1.33/0.59 inference(cnf_transformation,[status(thm)],[f100])). 1.33/0.59 thf(f100,plain,( 1.33/0.59 ((mvalid @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (mforall_ind @ (^[Y1 : mu]: (mand @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @ (mexists_ind @ (^[Y2 : mu]: (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ (mbox_s4 @ (member @ Y2 @ Y1))))))) @ (mbox_s4 @ (mimplies @ (mexists_ind @ (^[Y2 : mu]: (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ (mbox_s4 @ (member @ Y2 @ Y1))))) @ (mbox_s4 @ (intersect @ Y0 @ Y1)))))))))))) = $true)), 1.33/0.59 inference(fool_elimination,[status(thm)],[f99])). 1.33/0.59 thf(f99,plain,( 1.33/0.59 (mvalid @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : (mbox_s4 @ (mforall_ind @ (^[X1 : mu] : (mand @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (intersect @ X0 @ X1)) @ (mexists_ind @ (^[X2 : mu] : (mand @ (mbox_s4 @ (member @ X2 @ X0)) @ (mbox_s4 @ (member @ X2 @ X1))))))) @ (mbox_s4 @ (mimplies @ (mexists_ind @ (^[X3 : mu] : (mand @ (mbox_s4 @ (member @ X3 @ X0)) @ (mbox_s4 @ (member @ X3 @ X1))))) @ (mbox_s4 @ (intersect @ X0 @ X1))))))))))))), 1.33/0.59 inference(rectify,[status(thm)],[f40])). 1.33/0.59 thf(f40,axiom,( 1.33/0.59 (mvalid @ (mbox_s4 @ (mforall_ind @ (^[X11 : mu] : (mbox_s4 @ (mforall_ind @ (^[X12 : mu] : (mand @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (intersect @ X11 @ X12)) @ (mexists_ind @ (^[X13 : mu] : (mand @ (mbox_s4 @ (member @ X13 @ X11)) @ (mbox_s4 @ (member @ X13 @ X12))))))) @ (mbox_s4 @ (mimplies @ (mexists_ind @ (^[X13 : mu] : (mand @ (mbox_s4 @ (member @ X13 @ X11)) @ (mbox_s4 @ (member @ X13 @ X12))))) @ (mbox_s4 @ (intersect @ X11 @ X12))))))))))))), 1.33/0.59 file('/export/starexec/sandbox/tmp/tmp.8iVLfgu9Bl/E---3.1_4133.p',intersect_defn)). 1.33/0.59 % SZS output end Proof for E---3.1_4133 1.33/0.59 % (4253)------------------------------ 1.33/0.59 % (4253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1.33/0.59 % (4253)Termination reason: Refutation 1.33/0.59 1.33/0.59 % (4253)Memory used [KB]: 7036 1.33/0.59 % (4253)Time elapsed: 0.177 s 1.33/0.59 % (4253)Instructions burned: 361 (million) 1.33/0.59 % (4253)------------------------------ 1.33/0.59 % (4253)------------------------------ 1.33/0.59 % (4241)Success in time 0.209 s 1.33/0.59 EOF