0.11/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.12	% Command    : run_vampire %s %d THM
0.11/0.33	% Computer   : n018.cluster.edu
0.11/0.33	% Model      : x86_64 x86_64
0.11/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.33	% Memory     : 8042.1875MB
0.11/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.11/0.33	% CPULimit   : 1920
0.11/0.33	% WCLimit    : 240
0.11/0.33	% DateTime   : Wed Jul 30 03:49:04 EDT 2025
0.11/0.33	% CPUTime    : 
0.11/0.34	This is a THF_ problem
0.11/0.34	Running higher-order theorem proving
0.11/0.36	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.lqBJqlBc6h/E---3.1_14946.p -m 16384 -t 240
0.19/0.38	% (15059)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_14946 for (2399ds/183Mi)
0.19/0.38	% (15064)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_14946 for (2399ds/275Mi)
0.19/0.38	% (15061)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_14946 for (2399ds/27Mi)
0.19/0.38	% (15060)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_14946 for (2399ds/4Mi)
0.19/0.38	% (15065)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_14946 for (2399ds/18Mi)
0.19/0.38	% (15063)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_14946 for (2399ds/2Mi)
0.19/0.38	% (15062)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_14946 for (2399ds/2Mi)
0.19/0.38	% (15062)Instruction limit reached!
0.19/0.38	% (15062)------------------------------
0.19/0.38	% (15062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.38	% (15062)Termination reason: Unknown
0.19/0.38	% (15063)Instruction limit reached!
0.19/0.38	% (15063)------------------------------
0.19/0.38	% (15063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.38	% (15063)Termination reason: Unknown
0.19/0.38	% (15063)Termination phase: shuffling
0.19/0.38	
0.19/0.38	% (15063)Memory used [KB]: 1023
0.19/0.38	% (15063)Time elapsed: 0.004 s
0.19/0.38	% (15063)Instructions burned: 4 (million)
0.19/0.38	% (15063)------------------------------
0.19/0.38	% (15063)------------------------------
0.19/0.38	% (15062)Termination phase: shuffling
0.19/0.38	
0.19/0.38	% (15062)Memory used [KB]: 1023
0.19/0.38	% (15062)Time elapsed: 0.004 s
0.19/0.38	% (15062)Instructions burned: 3 (million)
0.19/0.38	% (15062)------------------------------
0.19/0.38	% (15062)------------------------------
0.19/0.38	% (15060)Instruction limit reached!
0.19/0.38	% (15060)------------------------------
0.19/0.38	% (15060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.38	% (15060)Termination reason: Unknown
0.19/0.38	% (15060)Termination phase: Property scanning
0.19/0.38	
0.19/0.38	% (15060)Memory used [KB]: 1151
0.19/0.38	% (15060)Time elapsed: 0.005 s
0.19/0.38	% (15060)Instructions burned: 5 (million)
0.19/0.38	% (15060)------------------------------
0.19/0.38	% (15060)------------------------------
0.19/0.39	% (15064)Refutation not found, incomplete strategy
0.19/0.39	% (15064)------------------------------
0.19/0.39	% (15064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.39	% (15064)Termination reason: Refutation not found, incomplete strategy
0.19/0.39	
0.19/0.39	
0.19/0.39	% (15064)Memory used [KB]: 5628
0.19/0.39	% (15064)Time elapsed: 0.010 s
0.19/0.39	% (15064)Instructions burned: 17 (million)
0.19/0.39	% (15064)------------------------------
0.19/0.39	% (15064)------------------------------
0.19/0.39	% (15065)Instruction limit reached!
0.19/0.39	% (15065)------------------------------
0.19/0.39	% (15065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.39	% (15065)Termination reason: Unknown
0.19/0.39	% (15065)Termination phase: Saturation
0.19/0.39	
0.19/0.39	% (15065)Memory used [KB]: 5628
0.19/0.39	% (15065)Time elapsed: 0.011 s
0.19/0.39	% (15065)Instructions burned: 20 (million)
0.19/0.39	% (15065)------------------------------
0.19/0.39	% (15065)------------------------------
0.19/0.39	% (15061)Instruction limit reached!
0.19/0.39	% (15061)------------------------------
0.19/0.39	% (15061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.39	% (15061)Termination reason: Unknown
0.19/0.39	% (15061)Termination phase: Saturation
0.19/0.39	
0.19/0.39	% (15061)Memory used [KB]: 5756
0.19/0.39	% (15061)Time elapsed: 0.014 s
0.19/0.39	% (15061)Instructions burned: 28 (million)
0.19/0.39	% (15061)------------------------------
0.19/0.39	% (15061)------------------------------
0.19/0.40	% (15067)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_14946 for (2399ds/37Mi)
0.19/0.40	% (15068)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_14946 for (2399ds/15Mi)
0.19/0.40	% (15066)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_14946 for (2399ds/3Mi)
0.19/0.40	% (15066)Instruction limit reached!
0.19/0.40	% (15066)------------------------------
0.19/0.40	% (15066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.40	% (15066)Termination reason: Unknown
0.19/0.40	% (15066)Termination phase: shuffling
0.19/0.40	
0.19/0.40	% (15066)Memory used [KB]: 1023
0.19/0.40	% (15066)Time elapsed: 0.003 s
0.19/0.40	% (15066)Instructions burned: 3 (million)
0.19/0.40	% (15066)------------------------------
0.19/0.40	% (15066)------------------------------
0.19/0.41	% (15068)Instruction limit reached!
0.19/0.41	% (15068)------------------------------
0.19/0.41	% (15068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.41	% (15068)Termination reason: Unknown
0.19/0.41	% (15068)Termination phase: Saturation
0.19/0.41	
0.19/0.41	% (15068)Memory used [KB]: 1151
0.19/0.41	% (15068)Time elapsed: 0.009 s
0.19/0.41	% (15068)Instructions burned: 15 (million)
0.19/0.41	% (15068)------------------------------
0.19/0.41	% (15068)------------------------------
0.19/0.41	% (15070)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_14946 for (2399ds/1041Mi)
0.19/0.41	% (15069)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_14946 for (2399ds/3Mi)
0.19/0.41	% (15069)Instruction limit reached!
0.19/0.41	% (15069)------------------------------
0.19/0.41	% (15069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.41	% (15069)Termination reason: Unknown
0.19/0.41	% (15069)Termination phase: shuffling
0.19/0.41	
0.19/0.41	% (15069)Memory used [KB]: 1023
0.19/0.41	% (15069)Time elapsed: 0.003 s
0.19/0.41	% (15069)Instructions burned: 4 (million)
0.19/0.41	% (15069)------------------------------
0.19/0.41	% (15069)------------------------------
0.19/0.41	% (15071)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on E---3.1_14946 for (2399ds/7Mi)
0.19/0.41	% (15071)Instruction limit reached!
0.19/0.41	% (15071)------------------------------
0.19/0.41	% (15071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.41	% (15071)Termination reason: Unknown
0.19/0.41	% (15071)Termination phase: Property scanning
0.19/0.41	
0.19/0.41	% (15071)Memory used [KB]: 1151
0.19/0.41	% (15071)Time elapsed: 0.005 s
0.19/0.41	% (15071)Instructions burned: 7 (million)
0.19/0.41	% (15071)------------------------------
0.19/0.41	% (15071)------------------------------
0.19/0.42	% (15067)Instruction limit reached!
0.19/0.42	% (15067)------------------------------
0.19/0.42	% (15067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.42	% (15067)Termination reason: Unknown
0.19/0.42	% (15067)Termination phase: Saturation
0.19/0.42	
0.19/0.42	% (15067)Memory used [KB]: 5884
0.19/0.42	% (15067)Time elapsed: 0.020 s
0.19/0.42	% (15067)Instructions burned: 38 (million)
0.19/0.42	% (15067)------------------------------
0.19/0.42	% (15067)------------------------------
0.19/0.42	% (15072)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on E---3.1_14946 for (2399ds/16Mi)
0.19/0.42	% (15073)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_14946 for (2399ds/3Mi)
0.19/0.42	% (15073)Instruction limit reached!
0.19/0.42	% (15073)------------------------------
0.19/0.42	% (15073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.42	% (15073)Termination reason: Unknown
0.19/0.42	% (15073)Termination phase: shuffling
0.19/0.42	
0.19/0.42	% (15073)Memory used [KB]: 1151
0.19/0.42	% (15073)Time elapsed: 0.004 s
0.19/0.42	% (15073)Instructions burned: 4 (million)
0.19/0.42	% (15073)------------------------------
0.19/0.42	% (15073)------------------------------
0.19/0.43	% (15074)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_14946 for (2399ds/3Mi)
0.19/0.43	% (15072)Instruction limit reached!
0.19/0.43	% (15072)------------------------------
0.19/0.43	% (15072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.43	% (15072)Termination reason: Unknown
0.19/0.43	% (15072)Termination phase: Saturation
0.19/0.43	
0.19/0.43	% (15072)Memory used [KB]: 5628
0.19/0.43	% (15072)Time elapsed: 0.010 s
0.19/0.43	% (15072)Instructions burned: 17 (million)
0.19/0.43	% (15072)------------------------------
0.19/0.43	% (15072)------------------------------
0.19/0.43	% (15074)Instruction limit reached!
0.19/0.43	% (15074)------------------------------
0.19/0.43	% (15074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.43	% (15074)Termination reason: Unknown
0.19/0.43	% (15074)Termination phase: shuffling
0.19/0.43	
0.19/0.43	% (15074)Memory used [KB]: 1023
0.19/0.43	% (15074)Time elapsed: 0.004 s
0.19/0.43	% (15074)Instructions burned: 3 (million)
0.19/0.43	% (15074)------------------------------
0.19/0.43	% (15074)------------------------------
0.19/0.43	% (15075)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_14946 for (2399ds/7Mi)
0.19/0.43	% (15075)Instruction limit reached!
0.19/0.43	% (15075)------------------------------
0.19/0.43	% (15075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.43	% (15075)Termination reason: Unknown
0.19/0.43	% (15075)Termination phase: Property scanning
0.19/0.43	
0.19/0.43	% (15075)Memory used [KB]: 1151
0.19/0.43	% (15075)Time elapsed: 0.006 s
0.19/0.43	% (15075)Instructions burned: 8 (million)
0.19/0.43	% (15075)------------------------------
0.19/0.43	% (15075)------------------------------
0.19/0.44	% (15076)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_14946 for (2399ds/3Mi)
0.19/0.44	% (15076)Instruction limit reached!
0.19/0.44	% (15076)------------------------------
0.19/0.44	% (15076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.44	% (15076)Termination reason: Unknown
0.19/0.44	% (15076)Termination phase: shuffling
0.19/0.44	
0.19/0.44	% (15076)Memory used [KB]: 1023
0.19/0.44	% (15076)Time elapsed: 0.003 s
0.19/0.44	% (15076)Instructions burned: 3 (million)
0.19/0.44	% (15076)------------------------------
0.19/0.44	% (15076)------------------------------
0.19/0.44	% (15078)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_14946 for (2399ds/18Mi)
0.19/0.44	% (15077)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on E---3.1_14946 for (2399ds/4Mi)
0.19/0.44	% (15079)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on E---3.1_14946 for (2399ds/710Mi)
0.19/0.44	% (15077)Instruction limit reached!
0.19/0.44	% (15077)------------------------------
0.19/0.44	% (15077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.44	% (15077)Termination reason: Unknown
0.19/0.44	% (15077)Termination phase: shuffling
0.19/0.44	
0.19/0.44	% (15077)Memory used [KB]: 1023
0.19/0.44	% (15077)Time elapsed: 0.004 s
0.19/0.44	% (15077)Instructions burned: 4 (million)
0.19/0.44	% (15077)------------------------------
0.19/0.44	% (15077)------------------------------
0.19/0.45	% (15080)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on E---3.1_14946 for (2399ds/6Mi)
0.19/0.45	% (15078)Instruction limit reached!
0.19/0.45	% (15078)------------------------------
0.19/0.45	% (15078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.45	% (15078)Termination reason: Unknown
0.19/0.45	% (15078)Termination phase: Saturation
0.19/0.45	
0.19/0.45	% (15078)Memory used [KB]: 5756
0.19/0.45	% (15078)Time elapsed: 0.012 s
0.19/0.45	% (15078)Instructions burned: 19 (million)
0.19/0.45	% (15078)------------------------------
0.19/0.45	% (15078)------------------------------
0.19/0.45	% (15080)Instruction limit reached!
0.19/0.45	% (15080)------------------------------
0.19/0.45	% (15080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.45	% (15080)Termination reason: Unknown
0.19/0.45	% (15080)Termination phase: Property scanning
0.19/0.45	
0.19/0.45	% (15080)Memory used [KB]: 1151
0.19/0.45	% (15080)Time elapsed: 0.005 s
0.19/0.45	% (15080)Instructions burned: 6 (million)
0.19/0.45	% (15080)------------------------------
0.19/0.45	% (15080)------------------------------
0.19/0.45	% (15081)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_14946 for (2399ds/902Mi)
0.19/0.46	% (15082)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_14946 for (2399ds/21Mi)
0.19/0.46	% (15081)Refutation not found, incomplete strategy
0.19/0.46	% (15081)------------------------------
0.19/0.46	% (15081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.46	% (15081)Termination reason: Refutation not found, incomplete strategy
0.19/0.46	
0.19/0.46	
0.19/0.46	% (15081)Memory used [KB]: 5628
0.19/0.46	% (15081)Time elapsed: 0.009 s
0.19/0.46	% (15081)Instructions burned: 13 (million)
0.19/0.46	% (15081)------------------------------
0.19/0.46	% (15081)------------------------------
0.19/0.47	% (15083)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on E---3.1_14946 for (2399ds/5Mi)
0.19/0.47	% (15084)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_14946 for (2399ds/6Mi)
0.19/0.47	% (15082)Instruction limit reached!
0.19/0.47	% (15082)------------------------------
0.19/0.47	% (15082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.47	% (15082)Termination reason: Unknown
0.19/0.47	% (15082)Termination phase: Saturation
0.19/0.47	
0.19/0.47	% (15059)Instruction limit reached!
0.19/0.47	% (15059)------------------------------
0.19/0.47	% (15059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.47	% (15059)Termination reason: Unknown
0.19/0.47	% (15059)Termination phase: Saturation
0.19/0.47	
0.19/0.47	% (15059)Memory used [KB]: 7164
0.19/0.47	% (15059)Time elapsed: 0.093 s
0.19/0.47	% (15059)Instructions burned: 184 (million)
0.19/0.47	% (15059)------------------------------
0.19/0.47	% (15059)------------------------------
0.19/0.47	% (15082)Memory used [KB]: 5756
0.19/0.47	% (15082)Time elapsed: 0.012 s
0.19/0.47	% (15082)Instructions burned: 22 (million)
0.19/0.47	% (15082)------------------------------
0.19/0.47	% (15082)------------------------------
0.19/0.47	% (15083)Instruction limit reached!
0.19/0.47	% (15083)------------------------------
0.19/0.47	% (15083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.47	% (15083)Termination reason: Unknown
0.19/0.47	% (15083)Termination phase: shuffling
0.19/0.47	
0.19/0.47	% (15083)Memory used [KB]: 1151
0.19/0.47	% (15083)Time elapsed: 0.004 s
0.19/0.47	% (15083)Instructions burned: 5 (million)
0.19/0.47	% (15083)------------------------------
0.19/0.47	% (15083)------------------------------
0.19/0.47	% (15084)Instruction limit reached!
0.19/0.47	% (15084)------------------------------
0.19/0.47	% (15084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.47	% (15084)Termination reason: Unknown
0.19/0.47	% (15084)Termination phase: Property scanning
0.19/0.47	
0.19/0.47	% (15084)Memory used [KB]: 1151
0.19/0.47	% (15084)Time elapsed: 0.005 s
0.19/0.47	% (15084)Instructions burned: 6 (million)
0.19/0.47	% (15084)------------------------------
0.19/0.47	% (15084)------------------------------
0.19/0.48	% (15085)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on E---3.1_14946 for (2398ds/377Mi)
0.19/0.49	% (15088)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_14946 for (2398ds/879Mi)
0.19/0.49	% (15086)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_14946 for (2398ds/779Mi)
0.19/0.49	% (15087)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_14946 for (2398ds/19Mi)
0.19/0.49	% (15090)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on E---3.1_14946 for (2398ds/17Mi)
0.19/0.50	% (15090)Instruction limit reached!
0.19/0.50	% (15090)------------------------------
0.19/0.50	% (15090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.50	% (15090)Termination reason: Unknown
0.19/0.50	% (15090)Termination phase: Saturation
0.19/0.50	
0.19/0.50	% (15090)Memory used [KB]: 5628
0.19/0.50	% (15090)Time elapsed: 0.010 s
0.19/0.50	% (15090)Instructions burned: 17 (million)
0.19/0.50	% (15090)------------------------------
0.19/0.50	% (15090)------------------------------
0.19/0.50	% (15087)Instruction limit reached!
0.19/0.50	% (15087)------------------------------
0.19/0.50	% (15087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.50	% (15087)Termination reason: Unknown
0.19/0.50	% (15087)Termination phase: Saturation
0.19/0.50	
0.19/0.50	% (15087)Memory used [KB]: 5756
0.19/0.50	% (15087)Time elapsed: 0.011 s
0.19/0.50	% (15087)Instructions burned: 20 (million)
0.19/0.50	% (15087)------------------------------
0.19/0.50	% (15087)------------------------------
0.19/0.52	% (15092)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on E---3.1_14946 for (2398ds/3Mi)
0.19/0.52	% (15093)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on E---3.1_14946 for (2398ds/30Mi)
0.19/0.52	% (15092)Instruction limit reached!
0.19/0.52	% (15092)------------------------------
0.19/0.52	% (15092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.52	% (15092)Termination reason: Unknown
0.19/0.52	% (15092)Termination phase: shuffling
0.19/0.52	
0.19/0.52	% (15092)Memory used [KB]: 1151
0.19/0.52	% (15092)Time elapsed: 0.004 s
0.19/0.52	% (15092)Instructions burned: 4 (million)
0.19/0.52	% (15092)------------------------------
0.19/0.52	% (15092)------------------------------
0.19/0.53	% (15093)Instruction limit reached!
0.19/0.53	% (15093)------------------------------
0.19/0.53	% (15093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.53	% (15093)Termination reason: Unknown
0.19/0.53	% (15093)Termination phase: Saturation
0.19/0.53	
0.19/0.53	% (15093)Memory used [KB]: 5756
0.19/0.53	% (15093)Time elapsed: 0.016 s
0.19/0.53	% (15093)Instructions burned: 30 (million)
0.19/0.53	% (15093)------------------------------
0.19/0.53	% (15093)------------------------------
0.19/0.54	% (15094)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_14946 for (2398ds/127Mi)
0.19/0.55	% (15095)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_14946 for (2398ds/100Mi)
0.19/0.60	% (15095)Instruction limit reached!
0.19/0.60	% (15095)------------------------------
0.19/0.60	% (15095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.60	% (15095)Termination reason: Unknown
0.19/0.60	% (15095)Termination phase: Saturation
0.19/0.60	
0.19/0.60	% (15095)Memory used [KB]: 6140
0.19/0.60	% (15095)Time elapsed: 0.051 s
0.19/0.60	% (15095)Instructions burned: 101 (million)
0.19/0.60	% (15095)------------------------------
0.19/0.60	% (15095)------------------------------
0.19/0.60	% (15070)First to succeed.
0.19/0.60	% (15094)Instruction limit reached!
0.19/0.60	% (15094)------------------------------
0.19/0.60	% (15094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.60	% (15094)Termination reason: Unknown
0.19/0.60	% (15094)Termination phase: Saturation
0.19/0.60	
0.19/0.60	% (15094)Memory used [KB]: 6268
0.19/0.60	% (15094)Time elapsed: 0.066 s
0.19/0.60	% (15094)Instructions burned: 127 (million)
0.19/0.60	% (15094)------------------------------
0.19/0.60	% (15094)------------------------------
0.19/0.61	% (15070)Refutation found. Thanks to Tanya!
0.19/0.61	% SZS status Theorem for E---3.1_14946
0.19/0.61	% SZS output start Proof for E---3.1_14946
0.19/0.61	thf(type_def_5, type, mu: $tType).
0.19/0.61	thf(type_def_7, type, reg: $tType).
0.19/0.61	thf(func_def_0, type, mu: $tType).
0.19/0.61	thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
0.19/0.61	thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
0.19/0.61	thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
0.19/0.61	thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
0.19/0.61	thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
0.19/0.61	thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
0.19/0.61	thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
0.19/0.61	thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
0.19/0.61	thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
0.19/0.61	thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
0.19/0.61	thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
0.19/0.61	thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
0.19/0.61	thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
0.19/0.61	thf(func_def_15, type, mtrue: $i > $o).
0.19/0.61	thf(func_def_16, type, mfalse: $i > $o).
0.19/0.61	thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
0.19/0.61	thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
0.19/0.61	thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
0.19/0.61	thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
0.19/0.61	thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
0.19/0.61	thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
0.19/0.61	thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
0.19/0.61	thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
0.19/0.61	thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
0.19/0.61	thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
0.19/0.61	thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
0.19/0.61	thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
0.19/0.61	thf(func_def_29, type, mvalid: ($i > $o) > $o).
0.19/0.61	thf(func_def_30, type, minvalid: ($i > $o) > $o).
0.19/0.61	thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
0.19/0.61	thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
0.19/0.61	thf(func_def_33, type, reg: $tType).
0.19/0.61	thf(func_def_34, type, c: reg > reg > $o).
0.19/0.61	thf(func_def_35, type, dc: reg > reg > $o).
0.19/0.61	thf(func_def_36, type, p: reg > reg > $o).
0.19/0.61	thf(func_def_37, type, eq: reg > reg > $o).
0.19/0.61	thf(func_def_38, type, o: reg > reg > $o).
0.19/0.61	thf(func_def_39, type, po: reg > reg > $o).
0.19/0.61	thf(func_def_40, type, ec: reg > reg > $o).
0.19/0.61	thf(func_def_41, type, pp: reg > reg > $o).
0.19/0.61	thf(func_def_42, type, tpp: reg > reg > $o).
0.19/0.61	thf(func_def_43, type, ntpp: reg > reg > $o).
0.19/0.61	thf(func_def_44, type, catalunya: reg).
0.19/0.61	thf(func_def_45, type, france: reg).
0.19/0.61	thf(func_def_46, type, spain: reg).
0.19/0.61	thf(func_def_47, type, paris: reg).
0.19/0.61	thf(func_def_48, type, a: $i > $i > $o).
0.19/0.61	thf(func_def_49, type, fool: $i > $i > $o).
0.19/0.61	thf(func_def_66, type, ph1: !>[X0: $tType]:(X0)).
0.19/0.61	thf(func_def_67, type, sK2: $i > $i > $i).
0.19/0.61	thf(func_def_71, type, sK6: reg).
0.19/0.61	thf(func_def_72, type, sK7: reg).
0.19/0.61	thf(func_def_73, type, sK8: reg).
0.19/0.61	thf(func_def_74, type, sK9: reg).
0.19/0.61	thf(func_def_75, type, sK10: reg).
0.19/0.61	thf(func_def_76, type, sK11: reg).
0.19/0.61	thf(func_def_77, type, sK12: $i > $i > $i).
0.19/0.61	thf(func_def_78, type, sK13: reg).
0.19/0.61	thf(func_def_79, type, sK14: reg).
0.19/0.61	thf(func_def_80, type, sK15: reg).
0.19/0.61	thf(func_def_81, type, sK16: reg).
0.19/0.61	thf(func_def_82, type, sK17: reg).
0.19/0.61	thf(func_def_83, type, sK18: reg).
0.19/0.61	thf(func_def_84, type, sK19: reg).
0.19/0.61	thf(func_def_85, type, sK20: reg).
0.19/0.61	thf(func_def_86, type, sK21: reg).
0.19/0.61	thf(func_def_87, type, sK22: reg).
0.19/0.61	thf(func_def_88, type, sK23: reg).
0.19/0.61	thf(func_def_89, type, sK24: reg).
0.19/0.61	thf(func_def_90, type, sK25: reg).
0.19/0.61	thf(func_def_91, type, sK26: reg).
0.19/0.61	thf(func_def_92, type, sK27: reg).
0.19/0.61	thf(func_def_93, type, sK28: reg).
0.19/0.61	thf(func_def_94, type, sK29: reg).
0.19/0.61	thf(func_def_95, type, sK30: reg).
0.19/0.61	thf(func_def_96, type, sK31: reg).
0.19/0.61	thf(f2571,plain,(
0.19/0.61	  $false),
0.19/0.61	  inference(avatar_sat_refutation,[status(thm)],[f296,f351,f380,f1198,f1727,f2570])).
0.19/0.61	thf(f2570,plain,(
0.19/0.61	  ~spl0_5 | ~spl0_19),
0.19/0.61	  inference(avatar_contradiction_clause,[status(thm)],[f2569])).
0.19/0.61	thf(f2569,plain,(
0.19/0.61	  $false | (~spl0_5 | ~spl0_19)),
0.19/0.61	  inference(trivial_inequality_removal,[status(thm)],[f2568])).
0.19/0.61	thf(f2568,plain,(
0.19/0.61	  ($true = $false) | (~spl0_5 | ~spl0_19)),
0.19/0.61	  inference(boolean_simplification,[status(thm)],[f2567])).
0.19/0.61	thf(f2567,plain,(
0.19/0.61	  ($true = (~ $true)) | (~spl0_5 | ~spl0_19)),
0.19/0.61	  inference(backward_demodulation,[status(thm)],[f2455,f2563])).
0.19/0.61	thf(f2563,plain,(
0.19/0.61	  ($true = (c @ sK29 @ paris)) | ~spl0_19),
0.19/0.61	  inference(boolean_simplification,[status(thm)],[f2559])).
0.19/0.61	thf(f2559,plain,(
0.19/0.61	  ($true = ($true => (c @ sK29 @ paris))) | ~spl0_19),
0.19/0.61	  inference(superposition,[status(thm)],[f2377,f2436])).
0.19/0.61	thf(f2436,plain,(
0.19/0.61	  ($true = (c @ sK29 @ sK25)) | ~spl0_19),
0.19/0.61	  inference(binary_proxy_clausification,[status(thm)],[f2423])).
0.19/0.61	thf(f2423,plain,(
0.19/0.61	  (((c @ sK29 @ sK25) => (c @ sK29 @ france)) = $false) | ~spl0_19),
0.19/0.61	  inference(beta_eta_normalization,[status(thm)],[f2419])).
0.19/0.61	thf(f2419,plain,(
0.19/0.61	  (((^[Y0 : reg]: ((c @ Y0 @ sK25) => (c @ Y0 @ france))) @ sK29) = $false) | ~spl0_19),
0.19/0.61	  inference(sigma_clausification,[status(thm)],[f2113])).
0.19/0.61	thf(f2113,plain,(
0.19/0.61	  ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK25) => (c @ Y0 @ france)))) = $false) | ~spl0_19),
0.19/0.61	  inference(boolean_simplification,[status(thm)],[f2111])).
0.19/0.61	thf(f2111,plain,(
0.19/0.61	  (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK25) => (c @ Y0 @ france)))) & $true) = $false) | ~spl0_19),
0.19/0.61	  inference(superposition,[status(thm)],[f1734,f2099])).
0.19/0.61	thf(f2099,plain,(
0.19/0.61	  ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK25) => (c @ Y0 @ sK10)))) = $true)),
0.19/0.61	  inference(boolean_simplification,[status(thm)],[f2098])).
0.19/0.61	thf(f2098,plain,(
0.19/0.61	  (($true & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK25) => (c @ Y0 @ sK10))))) = $true)),
0.19/0.61	  inference(backward_demodulation,[status(thm)],[f2019,f2097])).
0.19/0.61	thf(f2097,plain,(
0.19/0.61	  ($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK25) => (c @ Y0 @ paris)))))),
0.19/0.61	  inference(binary_proxy_clausification,[status(thm)],[f2019])).
0.19/0.61	thf(f2019,plain,(
0.19/0.61	  ($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK25) => (c @ Y0 @ paris)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK25) => (c @ Y0 @ sK10))))))),
0.19/0.61	  inference(beta_eta_normalization,[status(thm)],[f2017])).
0.19/0.61	thf(f2017,plain,(
0.19/0.61	  ($true = ((^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK10)))))) @ sK25))),
0.19/0.61	  inference(sigma_clausification,[status(thm)],[f1239])).
0.19/0.61	thf(f1239,plain,(
0.19/0.61	  ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK10))))))) = $true)),
0.19/0.61	  inference(binary_proxy_clausification,[status(thm)],[f672])).
0.19/0.61	thf(f672,plain,(
0.19/0.61	  (((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK10))))))) & (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK10)))))))) = $true)),
0.19/0.61	  inference(binary_proxy_clausification,[status(thm)],[f660])).
0.19/0.61	thf(f660,plain,(
0.19/0.61	  ((((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK10))))))) & (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK10)))))))) => ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK10))))))) & (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK10))))))))) = $false)),
0.19/0.61	  inference(beta_eta_normalization,[status(thm)],[f659])).
0.19/0.61	thf(f659,plain,(
0.19/0.61	  (((^[Y0 : reg]: (((?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0))))))) & (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) => ((?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0))))))) & (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))))) @ sK10) = $false)),
0.19/0.61	  inference(sigma_clausification,[status(thm)],[f422])).
0.19/0.61	thf(f422,plain,(
0.19/0.61	  ((!! @ reg @ (^[Y0 : reg]: (((?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0))))))) & (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) => ((?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0))))))) & (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0))))))))))) = $false)),
0.19/0.61	  inference(binary_proxy_clausification,[status(thm)],[f346])).
0.19/0.61	thf(f346,plain,(
0.19/0.61	  (((~ (a @ sK3 @ sK4)) | (!! @ reg @ (^[Y0 : reg]: (((?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0))))))) & (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) => ((?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0))))))) & (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))))))) = $false)),
0.19/0.61	  inference(beta_eta_normalization,[status(thm)],[f345])).
0.19/0.61	thf(f345,plain,(
0.19/0.61	  (((^[Y0 : $i]: ((~ (a @ sK3 @ Y0)) | (!! @ reg @ (^[Y1 : reg]: (((?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ catalunya)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1))))))) & (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) => ((?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1))))))) & (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1))))))))))))) @ sK4) = $false)),
0.19/0.61	  inference(sigma_clausification,[status(thm)],[f342])).
0.19/0.61	thf(f342,plain,(
0.19/0.61	  ((!! @ $i @ (^[Y0 : $i]: ((~ (a @ sK3 @ Y0)) | (!! @ reg @ (^[Y1 : reg]: (((?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ catalunya)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1))))))) & (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) => ((?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1))))))) & (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))))))))) = $false)),
0.19/0.61	  inference(beta_eta_normalization,[status(thm)],[f341])).
0.19/0.61	thf(f341,plain,(
0.19/0.61	  (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (!! @ reg @ (^[Y2 : reg]: (((?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ catalunya)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2))))))) & (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ paris)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) => ((?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ spain)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2))))))) & (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ france)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2))))))))))))))) @ sK3) = $false)),
0.19/0.61	  inference(sigma_clausification,[status(thm)],[f336])).
0.19/0.61	thf(f336,plain,(
0.19/0.61	  ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (!! @ reg @ (^[Y2 : reg]: (((?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ catalunya)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2))))))) & (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ paris)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) => ((?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ spain)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2))))))) & (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ france)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))))))))))) = $false)),
0.19/0.61	  inference(not_proxy_clausification,[status(thm)],[f225])).
0.19/0.61	thf(f225,plain,(
0.19/0.61	  ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (!! @ reg @ (^[Y2 : reg]: (((?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ catalunya)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2))))))) & (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ paris)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) => ((?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ spain)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2))))))) & (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ france)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2))))))))))))))))))),
0.19/0.61	  inference(beta_eta_normalization,[status(thm)],[f215])).
0.19/0.61	thf(f215,plain,(
0.19/0.61	  ($true = (~ ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))) @ a @ (^[Y0 : $i]: (!! @ reg @ (^[Y1 : reg]: ((((^[Y2 : reg]: ((^[Y3 : reg]: (?? @ reg @ (^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3) & ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y2))))))) @ Y1 @ catalunya) & ((^[Y2 : reg]: ((^[Y3 : reg]: (?? @ reg @ (^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3) & ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y2))))))) @ Y1 @ paris)) => (((^[Y2 : reg]: ((^[Y3 : reg]: (?? @ reg @ (^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3) & ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y2))))))) @ Y1 @ spain) & ((^[Y2 : reg]: ((^[Y3 : reg]: (?? @ reg @ (^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3) & ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y2))))))) @ Y1 @ france))))))))))),
0.19/0.61	  inference(definition_unfolding,[status(thm)],[f171,f178,f187,f206,f206,f206,f206])).
0.19/0.61	thf(f206,plain,(
0.19/0.61	  (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y3) => (c @ Y5 @ Y4))))))) @ Y2 @ Y1) & ((^[Y3 : reg]: ((^[Y4 : reg]: (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y3) => (c @ Y5 @ Y4))))))) @ Y2 @ Y0))))))))),
0.19/0.61	  inference(definition_unfolding,[status(thm)],[f147,f163,f163])).
0.19/0.61	thf(f163,plain,(
0.19/0.61	  (p = (^[Y0 : reg]: ((^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ Y1))))))))),
0.19/0.61	  inference(cnf_transformation,[status(thm)],[f75])).
0.19/0.61	thf(f75,plain,(
0.19/0.61	  (p = (^[Y0 : reg]: ((^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ Y1))))))))),
0.19/0.61	  inference(fool_elimination,[status(thm)],[f74])).
0.19/0.61	thf(f74,plain,(
0.19/0.61	  ((^[X0 : reg, X1 : reg] : (! [X2 : reg] : ((c @ X2 @ X0) => (c @ X2 @ X1)))) = p)),
0.19/0.61	  inference(rectify,[status(thm)],[f33])).
0.19/0.61	thf(f33,axiom,(
0.19/0.61	  ((^[X0 : reg, X1 : reg] : (! [X11 : reg] : ((c @ X11 @ X0) => (c @ X11 @ X1)))) = p)),
0.19/0.61	  file('/export/starexec/sandbox/tmp/tmp.lqBJqlBc6h/E---3.1_14946.p',p)).
0.19/0.61	thf(f147,plain,(
0.19/0.61	  (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: ((p @ Y2 @ Y1) & (p @ Y2 @ Y0))))))))),
0.19/0.61	  inference(cnf_transformation,[status(thm)],[f64])).
0.19/0.61	thf(f64,plain,(
0.19/0.61	  (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: ((p @ Y2 @ Y1) & (p @ Y2 @ Y0))))))))),
0.19/0.61	  inference(fool_elimination,[status(thm)],[f63])).
0.19/0.61	thf(f63,plain,(
0.19/0.61	  ((^[X0 : reg, X1 : reg] : (? [X2 : reg] : ((p @ X2 @ X0) & (p @ X2 @ X1)))) = o)),
0.19/0.61	  inference(rectify,[status(thm)],[f35])).
0.19/0.61	thf(f35,axiom,(
0.19/0.61	  ((^[X0 : reg, X1 : reg] : (? [X11 : reg] : ((p @ X11 @ X0) & (p @ X11 @ X1)))) = o)),
0.19/0.61	  file('/export/starexec/sandbox/tmp/tmp.lqBJqlBc6h/E---3.1_14946.p',o)).
0.19/0.61	thf(f187,plain,(
0.19/0.61	  (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
0.19/0.61	  inference(cnf_transformation,[status(thm)],[f142])).
0.19/0.61	thf(f142,plain,(
0.19/0.61	  (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
0.19/0.61	  inference(fool_elimination,[status(thm)],[f141])).
0.19/0.61	thf(f141,plain,(
0.19/0.61	  (mbox = (^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3 : $i] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))))),
0.19/0.61	  inference(rectify,[status(thm)],[f16])).
0.19/0.61	thf(f16,axiom,(
0.19/0.61	  (mbox = (^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7 : $i] : ((X3 @ X7) | ~(X6 @ X2 @ X7)))))),
0.19/0.61	  file('/export/starexec/sandbox/tmp/tmp.lqBJqlBc6h/E---3.1_14946.p',mbox)).
0.19/0.61	thf(f178,plain,(
0.19/0.61	  (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
0.19/0.61	  inference(cnf_transformation,[status(thm)],[f81])).
0.19/0.61	thf(f81,plain,(
0.19/0.61	  (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
0.19/0.61	  inference(fool_elimination,[status(thm)],[f80])).
0.19/0.61	thf(f80,plain,(
0.19/0.61	  (mvalid = (^[X0 : $i > $o] : (! [X1 : $i] : (X0 @ X1))))),
0.19/0.61	  inference(rectify,[status(thm)],[f28])).
0.19/0.61	thf(f28,axiom,(
0.19/0.61	  (mvalid = (^[X3 : $i > $o] : (! [X2 : $i] : (X3 @ X2))))),
0.19/0.61	  file('/export/starexec/sandbox/tmp/tmp.lqBJqlBc6h/E---3.1_14946.p',mvalid)).
0.19/0.61	thf(f171,plain,(
0.19/0.61	  ($true = (~ (mvalid @ (mbox @ a @ (^[Y0 : $i]: (!! @ reg @ (^[Y1 : reg]: (((o @ Y1 @ catalunya) & (o @ Y1 @ paris)) => ((o @ Y1 @ spain) & (o @ Y1 @ france))))))))))),
0.19/0.61	  inference(cnf_transformation,[status(thm)],[f122])).
0.19/0.61	thf(f122,plain,(
0.19/0.61	  ($true = (~ (mvalid @ (mbox @ a @ (^[Y0 : $i]: (!! @ reg @ (^[Y1 : reg]: (((o @ Y1 @ catalunya) & (o @ Y1 @ paris)) => ((o @ Y1 @ spain) & (o @ Y1 @ france))))))))))),
0.19/0.61	  inference(fool_elimination,[status(thm)],[f121])).
0.19/0.61	thf(f121,plain,(
0.19/0.61	  ~(mvalid @ (mbox @ a @ (^[X0 : $i] : (! [X1 : reg] : (((o @ X1 @ paris) & (o @ X1 @ catalunya)) => ((o @ X1 @ france) & (o @ X1 @ spain)))))))),
0.19/0.61	  inference(rectify,[status(thm)],[f45])).
0.19/0.61	thf(f45,negated_conjecture,(
0.19/0.61	  ~(mvalid @ (mbox @ a @ (^[X0 : $i] : (! [X11 : reg] : (((o @ X11 @ paris) & (o @ X11 @ catalunya)) => ((o @ X11 @ france) & (o @ X11 @ spain)))))))),
0.19/0.61	  inference(negated_conjecture,[status(cth)],[f44])).
0.19/0.61	thf(f44,conjecture,(
0.19/0.61	  (mvalid @ (mbox @ a @ (^[X0 : $i] : (! [X11 : reg] : (((o @ X11 @ paris) & (o @ X11 @ catalunya)) => ((o @ X11 @ france) & (o @ X11 @ spain)))))))),
0.19/0.61	  file('/export/starexec/sandbox/tmp/tmp.lqBJqlBc6h/E---3.1_14946.p',con)).
0.19/0.61	thf(f1734,plain,(
0.19/0.61	  ( ! [X1 : reg] : (($false = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ france)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ sK10))))))) ) | ~spl0_19),
0.19/0.61	  inference(beta_eta_normalization,[status(thm)],[f1730])).
0.19/0.61	thf(f1730,plain,(
0.19/0.61	  ( ! [X1 : reg] : ((((^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK10)))))) @ X1) = $false)) ) | ~spl0_19),
0.19/0.61	  inference(pi_clausification,[status(thm)],[f1194])).
0.19/0.61	thf(f1194,plain,(
0.19/0.61	  ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK10))))))) = $false) | ~spl0_19),
0.19/0.61	  inference(avatar_component_clause,[status(thm)],[f1193])).
0.19/0.61	thf(f1193,definition,(
0.19/0.61	  spl0_19 <=> ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK10))))))) = $false)),
0.19/0.61	  introduced(definition,[new_symbols(naming,[spl0_19])],[avatar_definition])).
0.19/0.61	thf(f2377,plain,(
0.19/0.61	  ( ! [X1 : reg] : (($true = ((c @ X1 @ sK25) => (c @ X1 @ paris)))) )),
0.19/0.61	  inference(beta_eta_normalization,[status(thm)],[f2376])).
0.19/0.61	thf(f2376,plain,(
0.19/0.61	  ( ! [X1 : reg] : ((((^[Y0 : reg]: ((c @ Y0 @ sK25) => (c @ Y0 @ paris))) @ X1) = $true)) )),
0.19/0.61	  inference(pi_clausification,[status(thm)],[f2097])).
0.19/0.61	thf(f2455,plain,(
0.19/0.61	  ((~ (c @ sK29 @ paris)) = $true) | (~spl0_5 | ~spl0_19)),
0.19/0.61	  inference(boolean_simplification,[status(thm)],[f2448])).
0.19/0.61	thf(f2448,plain,(
0.19/0.61	  ($true = ((c @ sK29 @ paris) => $false)) | (~spl0_5 | ~spl0_19)),
0.19/0.61	  inference(superposition,[status(thm)],[f407,f2443])).
0.19/0.61	thf(f2443,plain,(
0.19/0.61	  ((c @ sK29 @ france) = $false) | ~spl0_19),
0.19/0.61	  inference(boolean_simplification,[status(thm)],[f2442])).
0.19/0.61	thf(f2442,plain,(
0.19/0.61	  (($true => (c @ sK29 @ france)) = $false) | ~spl0_19),
0.19/0.61	  inference(backward_demodulation,[status(thm)],[f2423,f2436])).
0.19/0.61	thf(f407,plain,(
0.19/0.61	  ( ! [X1 : reg] : (($true = ((c @ X1 @ paris) => (c @ X1 @ france)))) ) | ~spl0_5),
0.19/0.61	  inference(beta_eta_normalization,[status(thm)],[f405])).
0.19/0.61	thf(f405,plain,(
0.19/0.61	  ( ! [X1 : reg] : ((((^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))) @ X1) = $true)) ) | ~spl0_5),
0.19/0.61	  inference(pi_clausification,[status(thm)],[f404])).
0.19/0.61	thf(f404,plain,(
0.19/0.61	  ($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))))) | ~spl0_5),
0.19/0.61	  inference(boolean_simplification,[status(thm)],[f403])).
0.19/0.61	thf(f403,plain,(
0.19/0.61	  ($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france)))) & $true)) | ~spl0_5),
0.19/0.61	  inference(backward_demodulation,[status(thm)],[f394,f401])).
0.19/0.61	thf(f401,plain,(
0.19/0.61	  ($true = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris)))))) | ~spl0_5),
0.19/0.61	  inference(binary_proxy_clausification,[status(thm)],[f394])).
0.19/0.61	thf(f394,plain,(
0.19/0.61	  ($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris))))))) | ~spl0_5),
0.19/0.61	  inference(boolean_simplification,[status(thm)],[f393])).
0.19/0.61	thf(f393,plain,(
0.19/0.61	  (($true & ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris))))))) = $true) | ~spl0_5),
0.19/0.61	  inference(backward_demodulation,[status(thm)],[f379,f392])).
0.19/0.61	thf(f392,plain,(
0.19/0.61	  ($true = (~ (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ france)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ paris))))))) | ~spl0_5),
0.19/0.61	  inference(binary_proxy_clausification,[status(thm)],[f379])).
0.19/0.61	thf(f379,plain,(
0.19/0.61	  (((~ (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ france)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ paris)))))) & ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris))))))) = $true) | ~spl0_5),
0.19/0.61	  inference(avatar_component_clause,[status(thm)],[f378])).
0.19/0.61	thf(f378,definition,(
0.19/0.61	  spl0_5 <=> (((~ (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ france)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ paris)))))) & ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris))))))) = $true)),
0.19/0.61	  introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
0.19/0.61	thf(f1727,plain,(
0.19/0.61	  ~spl0_4 | ~spl0_20),
0.19/0.61	  inference(avatar_contradiction_clause,[status(thm)],[f1726])).
0.19/0.61	thf(f1726,plain,(
0.19/0.61	  $false | (~spl0_4 | ~spl0_20)),
0.19/0.61	  inference(trivial_inequality_removal,[status(thm)],[f1725])).
0.19/0.61	thf(f1725,plain,(
0.19/0.61	  ($true = $false) | (~spl0_4 | ~spl0_20)),
0.19/0.61	  inference(forward_demodulation,[status(thm)],[f1723,f1657])).
0.19/0.61	thf(f1657,plain,(
0.19/0.61	  ((c @ sK20 @ catalunya) = $false) | (~spl0_4 | ~spl0_20)),
0.19/0.61	  inference(trivial_inequality_removal,[status(thm)],[f1656])).
0.19/0.61	thf(f1656,plain,(
0.19/0.61	  ($true = $false) | ((c @ sK20 @ catalunya) = $false) | (~spl0_4 | ~spl0_20)),
0.19/0.61	  inference(boolean_simplification,[status(thm)],[f1650])).
0.19/0.61	thf(f1650,plain,(
0.19/0.61	  ((c @ sK20 @ catalunya) = $false) | (((c @ sK20 @ sK15) => $true) = $false) | (~spl0_4 | ~spl0_20)),
0.19/0.61	  inference(superposition,[status(thm)],[f1634,f369])).
0.19/0.61	thf(f369,plain,(
0.19/0.61	  ( ! [X1 : reg] : (((c @ X1 @ spain) = $true) | ((c @ X1 @ catalunya) = $false)) ) | ~spl0_4),
0.19/0.61	  inference(binary_proxy_clausification,[status(thm)],[f367])).
0.19/0.61	thf(f367,plain,(
0.19/0.61	  ( ! [X1 : reg] : ((((c @ X1 @ catalunya) => (c @ X1 @ spain)) = $true)) ) | ~spl0_4),
0.19/0.61	  inference(beta_eta_normalization,[status(thm)],[f365])).
0.19/0.61	thf(f365,plain,(
0.19/0.61	  ( ! [X1 : reg] : ((((^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain))) @ X1) = $true)) ) | ~spl0_4),
0.19/0.61	  inference(pi_clausification,[status(thm)],[f364])).
0.19/0.61	thf(f364,plain,(
0.19/0.61	  ($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain))))) | ~spl0_4),
0.19/0.61	  inference(boolean_simplification,[status(thm)],[f363])).
0.19/0.61	thf(f363,plain,(
0.19/0.61	  (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))) & $true) = $true) | ~spl0_4),
0.19/0.61	  inference(backward_demodulation,[status(thm)],[f360,f361])).
0.19/0.61	thf(f361,plain,(
0.19/0.61	  ($true = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya)))))) | ~spl0_4),
0.19/0.61	  inference(binary_proxy_clausification,[status(thm)],[f360])).
0.19/0.61	thf(f360,plain,(
0.19/0.61	  (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya)))))) = $true) | ~spl0_4),
0.19/0.61	  inference(boolean_simplification,[status(thm)],[f359])).
0.19/0.61	thf(f359,plain,(
0.19/0.61	  ($true = (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya)))))) & $true)) | ~spl0_4),
0.19/0.61	  inference(backward_demodulation,[status(thm)],[f295,f357])).
0.19/0.61	thf(f357,plain,(
0.19/0.61	  ($true = (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ catalunya)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ spain)))))) | ~spl0_4),
0.19/0.61	  inference(binary_proxy_clausification,[status(thm)],[f295])).
0.19/0.61	thf(f295,plain,(
0.19/0.61	  ($true = (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya)))))) & (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ catalunya)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ spain))))))) | ~spl0_4),
0.19/0.61	  inference(avatar_component_clause,[status(thm)],[f294])).
0.19/0.61	thf(f294,definition,(
0.19/0.61	  spl0_4 <=> ($true = (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya)))))) & (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ catalunya)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ spain)))))))),
0.19/0.61	  introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
0.19/0.61	thf(f1634,plain,(
0.19/0.61	  (((c @ sK20 @ sK15) => (c @ sK20 @ spain)) = $false) | ~spl0_20),
0.19/0.61	  inference(beta_eta_normalization,[status(thm)],[f1630])).
0.19/0.61	thf(f1630,plain,(
0.19/0.61	  (((^[Y0 : reg]: ((c @ Y0 @ sK15) => (c @ Y0 @ spain))) @ sK20) = $false) | ~spl0_20),
0.19/0.61	  inference(sigma_clausification,[status(thm)],[f1461])).
0.19/0.61	thf(f1461,plain,(
0.19/0.61	  ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK15) => (c @ Y0 @ spain)))) = $false) | ~spl0_20),
0.19/0.61	  inference(boolean_simplification,[status(thm)],[f1454])).
0.19/0.61	thf(f1454,plain,(
0.19/0.61	  (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK15) => (c @ Y0 @ spain)))) & $true) = $false) | ~spl0_20),
0.19/0.61	  inference(superposition,[status(thm)],[f1440,f1268])).
0.19/0.61	thf(f1268,plain,(
0.19/0.61	  ($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK15) => (c @ Y0 @ sK10)))))),
0.19/0.61	  inference(boolean_simplification,[status(thm)],[f1267])).
0.19/0.61	thf(f1267,plain,(
0.19/0.61	  ($true = ($true & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK15) => (c @ Y0 @ sK10))))))),
0.19/0.61	  inference(backward_demodulation,[status(thm)],[f1258,f1266])).
0.19/0.61	thf(f1266,plain,(
0.19/0.61	  ($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK15) => (c @ Y0 @ catalunya)))))),
0.19/0.61	  inference(binary_proxy_clausification,[status(thm)],[f1258])).
0.19/0.61	thf(f1258,plain,(
0.19/0.61	  ($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK15) => (c @ Y0 @ catalunya)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK15) => (c @ Y0 @ sK10))))))),
0.19/0.61	  inference(beta_eta_normalization,[status(thm)],[f1257])).
0.19/0.61	thf(f1257,plain,(
0.19/0.61	  (((^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK10)))))) @ sK15) = $true)),
0.19/0.61	  inference(sigma_clausification,[status(thm)],[f1243])).
0.19/0.61	thf(f1243,plain,(
0.19/0.61	  ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK10))))))) = $true)),
0.19/0.61	  inference(boolean_simplification,[status(thm)],[f1242])).
0.19/0.61	thf(f1242,plain,(
0.19/0.61	  ($true = ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK10))))))) & $true))),
0.19/0.61	  inference(backward_demodulation,[status(thm)],[f672,f1239])).
0.19/0.61	thf(f1440,plain,(
0.19/0.61	  ( ! [X1 : reg] : ((((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ spain)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ sK10))))) = $false)) ) | ~spl0_20),
0.19/0.61	  inference(beta_eta_normalization,[status(thm)],[f1439])).
0.19/0.61	thf(f1439,plain,(
0.19/0.61	  ( ! [X1 : reg] : (($false = ((^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK10)))))) @ X1))) ) | ~spl0_20),
0.19/0.61	  inference(pi_clausification,[status(thm)],[f1197])).
0.19/0.61	thf(f1197,plain,(
0.19/0.61	  ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK10))))))) = $false) | ~spl0_20),
0.19/0.61	  inference(avatar_component_clause,[status(thm)],[f1196])).
0.19/0.61	thf(f1196,definition,(
0.19/0.61	  spl0_20 <=> ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK10))))))) = $false)),
0.19/0.61	  introduced(definition,[new_symbols(naming,[spl0_20])],[avatar_definition])).
0.19/0.61	thf(f1723,plain,(
0.19/0.61	  ($true = (c @ sK20 @ catalunya)) | ~spl0_20),
0.19/0.61	  inference(boolean_simplification,[status(thm)],[f1717])).
0.19/0.61	thf(f1717,plain,(
0.19/0.61	  (($true => (c @ sK20 @ catalunya)) = $true) | ~spl0_20),
0.19/0.61	  inference(superposition,[status(thm)],[f1485,f1649])).
0.19/0.61	thf(f1649,plain,(
0.19/0.61	  ($true = (c @ sK20 @ sK15)) | ~spl0_20),
0.19/0.61	  inference(binary_proxy_clausification,[status(thm)],[f1634])).
0.19/0.61	thf(f1485,plain,(
0.19/0.61	  ( ! [X1 : reg] : (($true = ((c @ X1 @ sK15) => (c @ X1 @ catalunya)))) )),
0.19/0.61	  inference(beta_eta_normalization,[status(thm)],[f1482])).
0.19/0.61	thf(f1482,plain,(
0.19/0.61	  ( ! [X1 : reg] : ((((^[Y0 : reg]: ((c @ Y0 @ sK15) => (c @ Y0 @ catalunya))) @ X1) = $true)) )),
0.19/0.61	  inference(pi_clausification,[status(thm)],[f1266])).
0.19/0.61	thf(f1198,plain,(
0.19/0.61	  spl0_19 | spl0_20),
0.19/0.61	  inference(avatar_split_clause,[status(thm)],[f1191,f1196,f1193])).
0.19/0.61	thf(f1191,plain,(
0.19/0.61	  ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK10))))))) = $false) | ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK10))))))) = $false)),
0.19/0.61	  inference(binary_proxy_clausification,[status(thm)],[f671])).
0.19/0.61	thf(f671,plain,(
0.19/0.61	  (((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK10))))))) & (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK10)))))))) = $false)),
0.19/0.61	  inference(binary_proxy_clausification,[status(thm)],[f660])).
0.19/0.61	thf(f380,plain,(
0.19/0.61	  spl0_5 | spl0_3),
0.19/0.61	  inference(avatar_split_clause,[status(thm)],[f376,f291,f378])).
0.19/0.61	thf(f291,definition,(
0.19/0.61	  spl0_3 <=> ! [X2 : $i,X1 : $i] : ($true = (~ (a @ X1 @ X2)))),
0.19/0.61	  introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
0.19/0.61	thf(f376,plain,(
0.19/0.61	  ( ! [X2 : $i,X1 : $i] : ((((~ (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ france)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ paris)))))) & ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris))))))) = $true) | ($true = (~ (a @ X1 @ X2)))) )),
0.19/0.61	  inference(binary_proxy_clausification,[status(thm)],[f329])).
0.19/0.61	thf(f329,plain,(
0.19/0.61	  ( ! [X2 : $i,X1 : $i] : (($true = ((~ (a @ X1 @ X2)) | ((~ (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ france)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ paris)))))) & ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris)))))))))) )),
0.19/0.61	  inference(beta_eta_normalization,[status(thm)],[f328])).
0.19/0.61	thf(f328,plain,(
0.19/0.61	  ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | ((~ (?? @ reg @ (^[Y1 : reg]: (((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ france)) & ((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ paris)))))) & ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ paris) => (c @ Y1 @ france)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ france) => (c @ Y1 @ paris))))))))) @ X2))) )),
0.19/0.61	  inference(pi_clausification,[status(thm)],[f314])).
0.19/0.61	thf(f314,plain,(
0.19/0.61	  ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | ((~ (?? @ reg @ (^[Y1 : reg]: (((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ france)) & ((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ paris)))))) & ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ paris) => (c @ Y1 @ france)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ france) => (c @ Y1 @ paris)))))))))) = $true)) )),
0.19/0.61	  inference(beta_eta_normalization,[status(thm)],[f313])).
0.19/0.61	thf(f313,plain,(
0.19/0.61	  ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | ((~ (?? @ reg @ (^[Y2 : reg]: (((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ france)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ france)) & ((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ paris)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ paris)))))) & ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ paris) => (c @ Y2 @ france)))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ france) => (c @ Y2 @ paris))))))))))) @ X1))) )),
0.19/0.61	  inference(pi_clausification,[status(thm)],[f220])).
0.19/0.61	thf(f220,plain,(
0.19/0.61	  ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | ((~ (?? @ reg @ (^[Y2 : reg]: (((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ france)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ france)) & ((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ paris)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ paris)))))) & ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ paris) => (c @ Y2 @ france)))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ france) => (c @ Y2 @ paris)))))))))))))),
0.19/0.61	  inference(beta_eta_normalization,[status(thm)],[f217])).
0.19/0.61	thf(f217,plain,(
0.19/0.61	  ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))) @ a @ (^[Y0 : $i]: ((^[Y1 : reg]: ((^[Y2 : reg]: ((~ (?? @ reg @ (^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: ((~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6))))))) @ Y4 @ Y5)) & (c @ Y4 @ Y5))))) @ Y3 @ Y2) & ((^[Y4 : reg]: ((^[Y5 : reg]: ((~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6))))))) @ Y4 @ Y5)) & (c @ Y4 @ Y5))))) @ Y3 @ Y1))))) & ((^[Y3 : reg]: ((^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y3 @ Y4) & (~ ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3)))))) @ Y1 @ Y2))))) @ paris @ france)))))),
0.19/0.61	  inference(definition_unfolding,[status(thm)],[f185,f178,f187,f211])).
0.19/0.61	thf(f211,plain,(
0.19/0.61	  (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ (?? @ reg @ (^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: ((~ ((^[Y5 : reg]: ((^[Y6 : reg]: (?? @ reg @ (^[Y7 : reg]: (((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y6) & ((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y5))))))) @ Y3 @ Y4)) & (c @ Y3 @ Y4))))) @ Y2 @ Y1) & ((^[Y3 : reg]: ((^[Y4 : reg]: ((~ ((^[Y5 : reg]: ((^[Y6 : reg]: (?? @ reg @ (^[Y7 : reg]: (((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y6) & ((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y5))))))) @ Y3 @ Y4)) & (c @ Y3 @ Y4))))) @ Y2 @ Y0))))) & ((^[Y2 : reg]: ((^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y2 @ Y3) & (~ ((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y3 @ Y2)))))) @ Y0 @ Y1))))))),
0.19/0.61	  inference(definition_unfolding,[status(thm)],[f183,f208,f208,f209])).
0.19/0.61	thf(f209,plain,(
0.19/0.61	  (pp = (^[Y0 : reg]: ((^[Y1 : reg]: (((^[Y2 : reg]: ((^[Y3 : reg]: (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y2) => (c @ Y4 @ Y3))))))) @ Y0 @ Y1) & (~ ((^[Y2 : reg]: ((^[Y3 : reg]: (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y2) => (c @ Y4 @ Y3))))))) @ Y1 @ Y0)))))))),
0.19/0.61	  inference(definition_unfolding,[status(thm)],[f189,f163,f163])).
0.19/0.61	thf(f189,plain,(
0.19/0.61	  (pp = (^[Y0 : reg]: ((^[Y1 : reg]: ((p @ Y0 @ Y1) & (~ (p @ Y1 @ Y0)))))))),
0.19/0.61	  inference(cnf_transformation,[status(thm)],[f146])).
0.19/0.61	thf(f146,plain,(
0.19/0.61	  (pp = (^[Y0 : reg]: ((^[Y1 : reg]: ((p @ Y0 @ Y1) & (~ (p @ Y1 @ Y0)))))))),
0.19/0.61	  inference(fool_elimination,[status(thm)],[f145])).
0.19/0.61	thf(f145,plain,(
0.19/0.61	  ((^[X0 : reg, X1 : reg] : (~(p @ X1 @ X0) & (p @ X0 @ X1))) = pp)),
0.19/0.61	  inference(rectify,[status(thm)],[f38])).
0.19/0.61	thf(f38,axiom,(
0.19/0.61	  ((^[X0 : reg, X1 : reg] : (~(p @ X1 @ X0) & (p @ X0 @ X1))) = pp)),
0.19/0.61	  file('/export/starexec/sandbox/tmp/tmp.lqBJqlBc6h/E---3.1_14946.p',pp)).
0.19/0.61	thf(f208,plain,(
0.19/0.61	  (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ ((^[Y2 : reg]: ((^[Y3 : reg]: (?? @ reg @ (^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3) & ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y2))))))) @ Y0 @ Y1)) & (c @ Y0 @ Y1))))))),
0.19/0.61	  inference(definition_unfolding,[status(thm)],[f173,f206])).
0.19/0.61	thf(f173,plain,(
0.19/0.61	  (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ (o @ Y0 @ Y1)) & (c @ Y0 @ Y1))))))),
0.19/0.61	  inference(cnf_transformation,[status(thm)],[f85])).
0.19/0.61	thf(f85,plain,(
0.19/0.61	  (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ (o @ Y0 @ Y1)) & (c @ Y0 @ Y1))))))),
0.19/0.61	  inference(fool_elimination,[status(thm)],[f84])).
0.19/0.61	thf(f84,plain,(
0.19/0.61	  ((^[X0 : reg, X1 : reg] : ((c @ X0 @ X1) & ~(o @ X0 @ X1))) = ec)),
0.19/0.61	  inference(rectify,[status(thm)],[f37])).
0.19/0.61	thf(f37,axiom,(
0.19/0.61	  ((^[X0 : reg, X1 : reg] : ((c @ X0 @ X1) & ~(o @ X0 @ X1))) = ec)),
0.19/0.61	  file('/export/starexec/sandbox/tmp/tmp.lqBJqlBc6h/E---3.1_14946.p',ec)).
0.19/0.61	thf(f183,plain,(
0.19/0.61	  (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y1) & (ec @ Y2 @ Y0))))) & (pp @ Y0 @ Y1))))))),
0.19/0.61	  inference(cnf_transformation,[status(thm)],[f71])).
0.19/0.61	thf(f71,plain,(
0.19/0.61	  (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y1) & (ec @ Y2 @ Y0))))) & (pp @ Y0 @ Y1))))))),
0.19/0.61	  inference(fool_elimination,[status(thm)],[f70])).
0.19/0.61	thf(f70,plain,(
0.19/0.61	  ((^[X0 : reg, X1 : reg] : ((pp @ X0 @ X1) & ~? [X2 : reg] : ((ec @ X2 @ X0) & (ec @ X2 @ X1)))) = ntpp)),
0.19/0.61	  inference(rectify,[status(thm)],[f40])).
0.19/0.61	thf(f40,axiom,(
0.19/0.61	  ((^[X0 : reg, X1 : reg] : ((pp @ X0 @ X1) & ~? [X11 : reg] : ((ec @ X11 @ X0) & (ec @ X11 @ X1)))) = ntpp)),
0.19/0.61	  file('/export/starexec/sandbox/tmp/tmp.lqBJqlBc6h/E---3.1_14946.p',ntpp)).
0.19/0.61	thf(f185,plain,(
0.19/0.61	  ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france)))) = $true)),
0.19/0.61	  inference(cnf_transformation,[status(thm)],[f134])).
0.19/0.61	thf(f134,plain,(
0.19/0.61	  ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france)))) = $true)),
0.19/0.61	  inference(fool_elimination,[status(thm)],[f133])).
0.19/0.61	thf(f133,plain,(
0.19/0.61	  (mvalid @ (mbox @ a @ (^[X0 : $i] : (ntpp @ paris @ france))))),
0.19/0.61	  inference(rectify,[status(thm)],[f50])).
0.19/0.61	thf(f50,axiom,(
0.19/0.61	  (mvalid @ (mbox @ a @ (^[X0 : $i] : (ntpp @ paris @ france))))),
0.19/0.61	  file('/export/starexec/sandbox/tmp/tmp.lqBJqlBc6h/E---3.1_14946.p',ax3)).
0.19/0.61	thf(f351,plain,(
0.19/0.61	  ~spl0_3),
0.19/0.61	  inference(avatar_contradiction_clause,[status(thm)],[f350])).
0.19/0.61	thf(f350,plain,(
0.19/0.61	  $false | ~spl0_3),
0.19/0.61	  inference(trivial_inequality_removal,[status(thm)],[f349])).
0.19/0.61	thf(f349,plain,(
0.19/0.61	  ($true = $false) | ~spl0_3),
0.19/0.61	  inference(boolean_simplification,[status(thm)],[f348])).
0.19/0.61	thf(f348,plain,(
0.19/0.61	  (($true | (!! @ reg @ (^[Y0 : reg]: (((?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0))))))) & (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) => ((?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0))))))) & (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))))))) = $false) | ~spl0_3),
0.19/0.61	  inference(boolean_simplification,[status(thm)],[f347])).
0.19/0.61	thf(f347,plain,(
0.19/0.61	  (((~ $false) | (!! @ reg @ (^[Y0 : reg]: (((?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0))))))) & (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) => ((?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0))))))) & (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))))))) = $false) | ~spl0_3),
0.19/0.61	  inference(forward_demodulation,[status(thm)],[f346,f299])).
0.19/0.61	thf(f299,plain,(
0.19/0.61	  ( ! [X2 : $i,X1 : $i] : (((a @ X1 @ X2) = $false)) ) | ~spl0_3),
0.19/0.61	  inference(not_proxy_clausification,[status(thm)],[f292])).
0.19/0.61	thf(f292,plain,(
0.19/0.61	  ( ! [X2 : $i,X1 : $i] : (($true = (~ (a @ X1 @ X2)))) ) | ~spl0_3),
0.19/0.61	  inference(avatar_component_clause,[status(thm)],[f291])).
0.19/0.61	thf(f296,plain,(
0.19/0.61	  spl0_3 | spl0_4),
0.19/0.61	  inference(avatar_split_clause,[status(thm)],[f289,f294,f291])).
0.19/0.61	thf(f289,plain,(
0.19/0.61	  ( ! [X2 : $i,X1 : $i] : (($true = (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya)))))) & (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ catalunya)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ spain))))))) | ($true = (~ (a @ X1 @ X2)))) )),
0.19/0.61	  inference(binary_proxy_clausification,[status(thm)],[f285])).
0.19/0.61	thf(f285,plain,(
0.19/0.61	  ( ! [X2 : $i,X1 : $i] : (($true = ((~ (a @ X1 @ X2)) | (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya)))))) & (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ catalunya)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ spain))))))))) )),
0.19/0.61	  inference(beta_eta_normalization,[status(thm)],[f284])).
0.19/0.61	thf(f284,plain,(
0.19/0.61	  ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | (((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ catalunya) => (c @ Y1 @ spain)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ spain) => (c @ Y1 @ catalunya)))))) & (?? @ reg @ (^[Y1 : reg]: (((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ catalunya)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ catalunya)) & ((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ spain)))))))) @ X2))) )),
0.19/0.61	  inference(pi_clausification,[status(thm)],[f279])).
0.19/0.61	thf(f279,plain,(
0.19/0.61	  ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | (((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ catalunya) => (c @ Y1 @ spain)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ spain) => (c @ Y1 @ catalunya)))))) & (?? @ reg @ (^[Y1 : reg]: (((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ catalunya)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ catalunya)) & ((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ spain))))))))) = $true)) )),
0.19/0.61	  inference(beta_eta_normalization,[status(thm)],[f278])).
0.19/0.61	thf(f278,plain,(
0.19/0.61	  ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ catalunya) => (c @ Y2 @ spain)))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ spain) => (c @ Y2 @ catalunya)))))) & (?? @ reg @ (^[Y2 : reg]: (((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ catalunya)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ catalunya)) & ((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ spain)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ spain)))))))))) @ X1))) )),
0.19/0.61	  inference(pi_clausification,[status(thm)],[f221])).
0.19/0.61	thf(f221,plain,(
0.19/0.61	  ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ catalunya) => (c @ Y2 @ spain)))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ spain) => (c @ Y2 @ catalunya)))))) & (?? @ reg @ (^[Y2 : reg]: (((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ catalunya)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ catalunya)) & ((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ spain)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ spain))))))))))) = $true)),
0.19/0.61	  inference(beta_eta_normalization,[status(thm)],[f214])).
0.19/0.61	thf(f214,plain,(
0.19/0.61	  ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))) @ a @ (^[Y0 : $i]: ((^[Y1 : reg]: ((^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y3 @ Y4) & (~ ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3)))))) @ Y1 @ Y2) & (?? @ reg @ (^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: ((~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6))))))) @ Y4 @ Y5)) & (c @ Y4 @ Y5))))) @ Y3 @ Y1) & ((^[Y4 : reg]: ((^[Y5 : reg]: ((~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6))))))) @ Y4 @ Y5)) & (c @ Y4 @ Y5))))) @ Y3 @ Y2)))))))) @ catalunya @ spain)))))),
0.19/0.61	  inference(definition_unfolding,[status(thm)],[f157,f178,f187,f210])).
0.19/0.61	thf(f210,plain,(
0.19/0.61	  (tpp = (^[Y0 : reg]: ((^[Y1 : reg]: (((^[Y2 : reg]: ((^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y2 @ Y3) & (~ ((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y3 @ Y2)))))) @ Y0 @ Y1) & (?? @ reg @ (^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: ((~ ((^[Y5 : reg]: ((^[Y6 : reg]: (?? @ reg @ (^[Y7 : reg]: (((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y6) & ((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y5))))))) @ Y3 @ Y4)) & (c @ Y3 @ Y4))))) @ Y2 @ Y0) & ((^[Y3 : reg]: ((^[Y4 : reg]: ((~ ((^[Y5 : reg]: ((^[Y6 : reg]: (?? @ reg @ (^[Y7 : reg]: (((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y6) & ((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y5))))))) @ Y3 @ Y4)) & (c @ Y3 @ Y4))))) @ Y2 @ Y1)))))))))),
0.19/0.61	  inference(definition_unfolding,[status(thm)],[f190,f209,f208,f208])).
0.19/0.61	thf(f190,plain,(
0.19/0.61	  (tpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1)))))))))),
0.19/0.61	  inference(cnf_transformation,[status(thm)],[f114])).
0.19/0.61	thf(f114,plain,(
0.19/0.61	  (tpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1)))))))))),
0.19/0.61	  inference(fool_elimination,[status(thm)],[f113])).
0.19/0.61	thf(f113,plain,(
0.19/0.61	  ((^[X0 : reg, X1 : reg] : (? [X2 : reg] : ((ec @ X2 @ X1) & (ec @ X2 @ X0)) & (pp @ X0 @ X1))) = tpp)),
0.19/0.61	  inference(rectify,[status(thm)],[f39])).
0.19/0.61	thf(f39,axiom,(
0.19/0.61	  ((^[X0 : reg, X1 : reg] : (? [X11 : reg] : ((ec @ X11 @ X1) & (ec @ X11 @ X0)) & (pp @ X0 @ X1))) = tpp)),
0.19/0.61	  file('/export/starexec/sandbox/tmp/tmp.lqBJqlBc6h/E---3.1_14946.p',tpp)).
0.19/0.61	thf(f157,plain,(
0.19/0.61	  ($true = (mvalid @ (mbox @ a @ (^[Y0 : $i]: (tpp @ catalunya @ spain)))))),
0.19/0.61	  inference(cnf_transformation,[status(thm)],[f106])).
0.19/0.61	thf(f106,plain,(
0.19/0.61	  ($true = (mvalid @ (mbox @ a @ (^[Y0 : $i]: (tpp @ catalunya @ spain)))))),
0.19/0.61	  inference(fool_elimination,[status(thm)],[f105])).
0.19/0.61	thf(f105,plain,(
0.19/0.61	  (mvalid @ (mbox @ a @ (^[X0 : $i] : (tpp @ catalunya @ spain))))),
0.19/0.61	  inference(rectify,[status(thm)],[f46])).
0.19/0.61	thf(f46,axiom,(
0.19/0.61	  (mvalid @ (mbox @ a @ (^[X0 : $i] : (tpp @ catalunya @ spain))))),
0.19/0.61	  file('/export/starexec/sandbox/tmp/tmp.lqBJqlBc6h/E---3.1_14946.p',ax1)).
0.19/0.61	% SZS output end Proof for E---3.1_14946
0.19/0.61	% (15070)------------------------------
0.19/0.61	% (15070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.19/0.61	% (15070)Termination reason: Refutation
0.19/0.61	
0.19/0.61	% (15070)Memory used [KB]: 7164
0.19/0.61	% (15070)Time elapsed: 0.204 s
0.19/0.61	% (15070)Instructions burned: 370 (million)
0.19/0.61	% (15070)------------------------------
0.19/0.61	% (15070)------------------------------
0.19/0.61	% (15057)Success in time 0.244 s
0.19/0.61	EOF